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Sucker Draw Yard Sale Game. Instead of having my kids sell lemonade at our yard sales we have them host games for the kids instead. My son did the "Sucker Draw". The kids pick a sucker from the box, if it has a colored stick at the bottom they win a bigger prize. The prizes can be toys in good condition that you were going to sell anyways. This game is also fun at reunions, parties and carnivals. An alternative way to playing this game is making it into a ring-toss game. The kids have to ring a sucker before they win. | tomekkorbak/pile-curse-small | Pile-CC |
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Dolphins release 2008 starting linebacker Matt Roth
Linebacker Matt Roth’s bizarre season just came to an abrupt and unceremonious end.
The Dolphins released Roth on Tuesday, ending a season which began with a mysterious groin injury that sidelined him during training camp and the season’s first six weeks.
In the four games since his Nov. 1 return at the New York Jets, Roth has four tackles in limited action.
To replace Roth and nose tackle Jason Ferguson, who was placed on the injured-reserve list Monday, the Dolphins signed cornerback Evan Oglesby and defensive end Ikaika Alma-Francis, according to the team.
The team also announced the release of safety Nate Ness, who was promoted from the practice squad last week when the team placed running back Ronnie Brown on IR. The Dolphins still have one spot open on the 53-man roster.
Roth, 27, is in the fifth and final year of his rookie contract. Instead of earning an extension, Roth will be looking for a new team with six games remaining this season.
Despite the move, the team still owes Roth the balance of his $700,000 base salary.
The Dolphins roster now has just nine players drafted prior to the arrival of Bill Parcells and Jeff Ireland. Just 17 players on the roster overall were Dolphins prior to Parcells’ arrival.
Roth played only 14 snaps, but number of them caught the eye of Sparano.
“He was really impressive in some of those plays,” he said. “Not all of them, but some of them.”
Roth had just one tackle, but at 275 pounds offered a physical presence no other Dolphins’ outside linebacker can match.
Roth was listed behind Jason Taylor on the team’s depth chart at outside linebacker on the strong side.
When the team signed Taylor in May, he was expected to come in and provide a pass-rushing presence opposite Joey Porter, who lines up on the weak side near the left tackle. Roth, meanwhile, was to handle more run-stopping duties because of his size and strength.
But Roth showed up at training camp with a mysterious groin injury and failed the team’s conditioning run.
Roth did have off-season surgery to repair his groin, but had participated in the team’s off-season program, OTAs and mini-camp.
This time, Roth didn’t recover in time for the season, forcing the team to place him on the non-football injury list, which required him to sit out the season’s first six weeks. | tomekkorbak/pile-curse-small | Pile-CC |
992 F.2d 831
UNITED STATES of America, Appellee,v.George William RAMSEY, Appellant.
No. 92-2923.
United States Court of Appeals,Eighth Circuit.
Submitted Feb. 15, 1993.Decided May 7, 1993.
Burton H. Shostak of St. Louis, MO, argued, for appellant.
Mark W. Eggert, Asst. U.S. Atty., St. Louis, MO, argued, for appellee.
Before RICHARD S. ARNOLD, Chief Judge, FAGG, and BEAM, Circuit Judges.
FAGG, Circuit Judge.
1
George William Ramsey appeals his convictions for failing to comply with the lawful directions of a Federal Protective Officer, disorderly conduct which created a nuisance, and distributing handbills without a permit. See 41 C.F.R. §§ 101-20.304, .305, & .309 (1992). Ramsey also appeals his condition of probation that he comply with the federal income tax laws. We affirm.
2
On April 15, 1992, Ramsey entered an Internal Revenue Service (IRS) taxpayer assistance office in a federal building to protest the Government's use of tax money for military expenditures. Ramsey displayed a sign, distributed handbills, and explained his beliefs to taxpayer service representatives and individuals who had come to the office for taxpayer assistance. Ramsey did not request or receive a permit to distribute handbills in the building as required by posted regulations. IRS officials called Federal Protective Officers, and one of the officers ordered Ramsey to leave the office after learning Ramsey was distributing handbills without a permit. The officers arrested Ramsey when he refused. Ramsey resisted the officers by going limp, and the officers carried him from the office.
3
Before trial, Ramsey informed the district court he intended to represent himself. After questioning Ramsey at length and advising him to obtain counsel, the district court accepted Ramsey's waiver of counsel. After hearing the evidence, the district court convicted Ramsey. The district court fined Ramsey fifty dollars for each charge and placed him on three years probation on the condition that Ramsey perform community service, file his federal income tax returns, and pay his federal income taxes.
4
On appeal, Ramsey first contends his conviction for issuing handbills without a permit is invalid because the Government's arbitrary refusal to issue permits for the IRS office infringes on his First Amendment right of free speech. Ramsey also contends the regulations requiring compliance with the lawful directions of a Federal Protective Officer and prohibiting disorderly conduct are unconstitutionally vague and overbroad. Ramsey did not raise these constitutional issues before the district court. Because Ramsey was unaware of the posted regulations and did not apply for a permit before distributing his handbills, we are unwilling to consider Ramsey's attacks on the regulations for the first time on appeal. Smith v. Gould, Inc., 918 F.2d 1361, 1364 (8th Cir.1990). Although there are circumstances in which we may exercise our discretion to consider an issue not passed on below, this is not one of those cases. See Singleton v. Wulff, 428 U.S. 106, 120-21, 96 S.Ct. 2868, 2877-78, 49 L.Ed.2d 826 (1976).
5
Second, Ramsey contends his conviction for failing to comply with the lawful directions of a Federal Protective Officer is invalid because the evidence was insufficient to show the officer had legal authority to order Ramsey to leave the office. We disagree. In reviewing the sufficiency of the evidence, we view the evidence in the light most favorable to the Government. United States v. Ramsey, 871 F.2d 1365, 1367 (8th Cir.1989). Ramsey concedes he was distributing handbills without a permit required by 41 C.F.R. § 101-20.309. Thus, it was lawful for the officers to order Ramsey to leave the office.
6
Third, Ramsey contends the charge of disorderly conduct which created a nuisance is invalid because the complaint did not specify the conduct on which the charge was based. Again, we disagree. The complaint and accompanying attachments were sufficient to inform Ramsey of the charge he must defend against at trial. United States v. Olderbak, 961 F.2d 756, 759 (8th Cir.1992).
7
Fourth, Ramsey contends he did not knowingly and intelligently waive his Sixth Amendment right to counsel because the district court did not tell him the maximum penalties he faced or explain how the charges against him might be decided. Before accepting Ramsey's waiver of counsel, the district court questioned Ramsey to make sure he was aware of his right to counsel and the dangers and disadvantages of self-representation. United States v. Yagow, 953 F.2d 427, 431 (8th Cir.), cert. denied, --- U.S. ----, 113 S.Ct. 103, 121 L.Ed.2d 62 (1992). The district court substantially followed the model inquiry in the Bench Book for United States District Judges that we approved in Yagow. Ramsey stated he was forty-four years old, had a masters degree in theology, and understood the charges. Ramsey also stated he had been in federal court ten or twelve times, understood the rules of evidence, and had conferred with attorneys about the rules of criminal procedure. Ramsey acknowledged the district court could not advise him how to try his case. The district court told Ramsey he faced up to a fifty dollar fine and a thirty day prison sentence for each charge, which could be imposed consecutively. The district court repeatedly advised Ramsey to retain an attorney and offered to appoint an attorney, but Ramsey insisted on representing himself. In declining the district court's offer to appoint counsel, Ramsey told the district court he was financially able to pay two attorneys who were available to assist him.
8
The district court's failure to tell Ramsey the maximum fine was $5000 for each charge did not affect Ramsey's decision to waive counsel. The district court made known it would limit the fine to fifty dollars for each charge on which Ramsey was convicted, thus making the maximum fine information irrelevant. Also, the district court had no duty to tell Ramsey how the charges might be decided before hearing the evidence. We find no merit in Ramsey's contention that his waiver of counsel was not knowing and intelligent.
9
Finally, Ramsey contends the district court abused its discretion in imposing a probation requirement that he file his federal income tax returns and pay his federal income taxes. Ramsey contends this condition requires him to violate his pacifist religious beliefs. Ramsey told the district court he had not paid his income taxes for the past twenty years and did not intend to pay his current income taxes. Ramsey, however, has no First Amendment right to avoid federal income taxes on religious grounds. United States v. Lee, 455 U.S. 252, 260, 102 S.Ct. 1051, 1056, 71 L.Ed.2d 127 (1982); Wall v. United States, 756 F.2d 52, 53 (8th Cir.1985) (per curiam). Willful failure to file returns or pay taxes is a criminal offense, 26 U.S.C. § 7203 (Supp. II 1990), and it is a mandatory probation requirement that Ramsey not commit another federal crime, 18 U.S.C. § 3563(a)(1) (1988). The district court did not abuse its discretion by requiring Ramsey to comply with the federal income tax laws.
10
Accordingly, we affirm.
| tomekkorbak/pile-curse-small | FreeLaw |
I Like It Like That (album)
I Like It Like That is an album by Motown group the Miracles, compiled for the UK market and released on the UK Tamla-Motown label (TML11003) as one of its initial group of six albums in March 1965 (there was no equivalent album to this in the USA). Known as the Miracles' "forgotten album", few people, outside of Motown insiders, hard-core Miracles fans, and collectors, remember that it had even existed. This album featured a combination of several new-for-1964 songs along with previously-issued material from the group's album from the year before, The Miracles Doin' Mickey's Monkey. New for 1964 songs included "I Like It Like That" (the Top 30 title song), the Bobby Rogers-led flip side "You're So Fine and Sweet,"(this is the only original Miracles studio album that has that song), "That's What Love Is Made Of", another 1964 hit that the group performed on the American International Pictures release, the T.A.M.I. Show that year, and "Would I Love You", a song that became a popular regional hit tune for the group in Pennsylvania and The Midwest. The album also featured a Claudette Robinson-led cover version of the Orlons' #2 Pop smash, "The Wah-Watusi". (Claudette is also featured with the rest of the group on the album's cover), and the group's 1963 Top 40 Hit, "I Gotta Dance to Keep From Crying". Several of the group's other 1964 songs, including the chart hits "(You Can't Let the Boy Overpower) The Man in You", "Come On Do the Jerk", and its "B" side, "Baby Don't You Go", were not included. The new 1964 recordings "I Like It Like That", "Would I love You" and "That's What Love Is Made Of" were included on the only US Miracles 1964 album release "Miracles Greatest Hits From The Beginning" which was the first double album released by Motown Records.
As of 2018, The Miracles' "I Like It Like That" album has yet to see an official CD release.
Track listing
Side one
All lead vocals by Smokey Robinson except where noted
"I Like It Like That" (Smokey Robinson, Marv Tarplin)
"Dance What You Wanna (Sam Cooke, James Alexander, Clifton White)
"The Wah-Watusi" (Kal Mann, Dave Appell) (lead vocals: Claudette Robinson)
"Such Is Love, Such Is Life" (Robinson)
"The Groovy Thing" (Robinson)
"I Gotta Dance to Keep From Crying" (Brian Holland, Lamont Dozier, Eddie Holland)
Side two
"That's What Love Is Made Of" (Robinson, Bobby Rogers, Pete Moore)
"The Monkey Time" (Curtis Mayfield)
"You're So Fine and Sweet" (Robinson, Rogers, Moore, Ronnie White, Tarplin, Don Whited) (lead vocals: Bobby Rogers)
"Would I Love You" (Robinson)
"Dancin' Holiday" (Diane Rogers, Fred Smith, Zelda Samuels)
"Twist and Shout" (Bert Berns, Phil Medley)
Personnel
The Miracles
Smokey Robinson – lead and background vocals
Claudette Robinson – lead and background vocals
Marv Tarplin – guitar
Pete Moore – background vocals
Bobby Rogers – lead and background vocals
Ronnie White – background vocals
Additional
The Funk Brothers - instrumentation
External links
[ The Miracles - I Like It Like That (album info) All Music Guide]
I Like It Like That- by ''The Miracles (Title song-1964)
Tamla Album Discography
''The Miracles: Bio and Discography,including Tamla T249 info
Category:The Miracles albums
Category:1964 albums
Category:Tamla Records albums
Category:Albums produced by Lamont Dozier
Category:Albums produced by Brian Holland
Category:Albums produced by Smokey Robinson
Category:Albums recorded at Hitsville U.S.A. | tomekkorbak/pile-curse-small | Wikipedia (en) |
Testing for adverse impact when sample size is small.
Adverse impact evaluations often call for evidence that the disparity between groups in selection rates is statistically significant, and practitioners must choose which test statistic to apply in this situation. To identify the most effective testing procedure, the authors compared several alternate test statistics in terms of Type I error rates and power, focusing on situations with small samples. Significance testing was found to be of limited value because of low power for all tests. Among the alternate test statistics, the widely-used Z-test on the difference between two proportions performed reasonably well, except when sample size was extremely small. A test suggested by G. J. G. Upton (1982) provided slightly better control of Type I error under some conditions but generally produced results similar to the Z-test. Use of the Fisher Exact Test and Yates's continuity-corrected chi-square test are not recommended because of overly conservative Type I error rates and substantially lower power than the Z-test. | tomekkorbak/pile-curse-small | PubMed Abstracts |
Update: Vicente Padilla (4.67, 95 ERA+) scratched, flu-like symptoms. Nippert has pitched in four games this season, all in July, two starts and two relief: 10 innings, 13 hits, 4 walks, 8 strikeouts.
Also: Adam LaRoche will join the team in Boston on Friday. The Yankees beat the Orioles 6-4 this afternoon.Adam Kilgore, Globe:
On Friday, Clay Buchholz walked around the Red Sox clubhouse in Toronto and shook hands with some of his closest teammates. ... "Hopefully I'll see you soon," Buchholz told them. ...
Buchholz [had] assumed he would rejoin Boston in September or maybe next season.
Buchholz has thrown 104.2 innings total this season, and the Red Sox wanted him to take a scheduled, one-start sabbatical. He would rest for two days and then resume his usual throwing schedule.
The next day, Buchholz received a call from a Sox official telling him to throw. A day later, he was told to throw a complete bullpen session. "I sort of knew what was going on without them telling me."
I felt a little twinge on Friday on my way to Toronto, and I had a lot of work to do that day - threw a simulated game. I felt fine, but just afterwards it just tightened up on me. ... I've been getting treatment every day. ... It's just a minor setback.
Wake said he was "very confident" that he will be 100% by the time he is eligible to come off the DL on August 2 -- his 43rd birthday.
"I like the move for the Red Sox. ... He’s real streaky [offensively] and an outstanding defender. ... Most of his bad at-bats come against lefthanded pitching ... He’s a rhythm hitter. If he’s a little off, he can look real ugly. If he’s right, he can get real hot. There’s no in-between with him. ... He plays the game with a very easy pace. Sometimes people criticize that because it can look lackadaisical. ... He’s not just a pull guy. He can go all over the field. There’s ability there. You can’t put up 25 [home runs] and 75 [RBI] every year and not have something."
I will not be watching this game, but I will be receiving regular updates from someones iPhone at a kegger, then from tickers at the post-kegger bar. Last Wednesday summer kegger in the history of the world! of my school career.
he should not repeat what orsillo says, he should not recap what we just saw and he must stop with the "can't give in" and "good at-bat" and "being aggressive" over and over and over and praising players for showing up at the park -- and the incessant "you know".
get someone who can do the job.
red sox fans deserve better than this.
i love him as a player. he sucks in the booth.
and i am muting nesn now. i didn't do that even when remy was hawking his shit website every other batter.
This is a big difference between Buchholz and Halladay that won't change. Buchholz will not consistently go deep into games. Maybe in a few years he can learn to be consistent enough to go 6-7, which is fine these days. But Halladay would give you more. But for how long?
Seriously - you don't bat for Tek there?That water is crystal clear clean.
At least my LL team didn't lose. Although we BLEW a victory. Lightning stopped us after 4 1/2, 1/2 an inning after my 2nd baseman booted a ball into RF that let 2 runs score with 2 outs and tie the damn game. Next batter K's. Lightning stops the game before we can score so we have to finish it later. Without the error, it's official and we win.
No shame on the mound this trip (pitchers held the opponents to 4 or fewer runs in 4 out of 6 games giving up 6 in each of the other two)... the failure all lies with the offensive offense. We should have gone at least 3-3 on this trip.
Seriosly, I for one would never have dreamed we would offense issues coming into this year.At least not the kind of issues we are having right now.I mean everyone hits a slump once in a while, but how often does an entire freaking team slump at once?Let's hope the off day and some good jams from RS, along with a return to Fenway, will put things aright.
OK, RS must be writing the wrap-up. I hope you're bitching a little ;>I'm off to the showers. With my upcoming schedule I might not be live again until we're REALLY live!I'll continue to talk to myself after the games as usual though :)
I guess the question is is this 2004 (A slump followed by an awesome recovery) or 2006 (a slump that just kind of becomes permanent.)? My money's on more like 2004. I think this team's too good to tally fall apart. | tomekkorbak/pile-curse-small | Pile-CC |
Pages
Monday, November 7, 2011
Riverside Lunch.
Back during the Paleolithic Period, I worked as a secretary to an otolaryngologist in a hospital. Fancy term for an ear, nose, and throat guy. And none of this “administrative assistant” bullshit, I was a secretary. I took dictation, made coffee, ran useless errands, and generally made sure he was where he was supposed to be when he was supposed to be there.
It was a thankless job. He ran the place like a fiddle-playing Nero, and the department administrator had a Napoleon complex. Two tyrants does not a happy workplace make. The highlight of my day was when my workmate Cathy and I headed over to the Skull and Bones for lunch. Now Cathy was a lifer, a real Joan Holloway, and she’d secretaried in the same hospital since she was 19. Now she was in her 60’s, which meant she’d done time in every department that ever existed, and knew the dirt on everyone. She knew what days the cafeteria chicken salad was fresh, and what times to avoid the ER. Which doctor was sleeping with who, who was drunk most of the time, and who was the real deal, an angel put here on earth to save people. A bottomless pit of useful information. Sometimes her daughter, also named Cathy, would join us, the two of them smoking like chimneys, laughing deep, raspy laughs as they gossiped and joked. I adored them.
I also adored the Skull and Bones. A real lunch joint. All the coffee cups and diner plates were ringed in red, the waitresses were surly and wore uniforms, and you could buy and olive and cream cheese sandwich for $1.75. While service might be surly, it was dynamite fast. We’d sit down at 12:07 and have our meals in front of us by 12:12, leaving us more than 45 minutes to relax, eat, smoke, and dish before heading back to the trenches. When they tore down the Skull and Bones, replacing it with a McDonald’s, I was crushed.
Jennifer got a burger, and I (having just had a patty melt the night before) decided on the BLT. I’ve since learned Riverside is famous for their “flat burgers” and feel kinda stupid I didn’t order one. Guess I’ll just have to go back. Often. Because the food at Riverside is one helluva place for some fried greasy goodness. My BLT on wheat was PERFECT. Huge chunks of dark green romaine jabbed up next to huge slabs of crispy bacon overhanging the bread. Lots of mayo, lots of crunch, lots of grease, lots of yum. Ditto the basket of fries we shared on the waitress’s recommendation. Good thing too, because this was a HUGE portion. Took the remainder home (also on the waitress’s recommendation), and made delicious homefries the next day with some peppers and onions.
Speaking of the waitress, she was a doll. Gum-chewing, chatty-Cathy friendly. Loved her. Even when Jennifer and I hogged her table for almost 2 hours gabbing she didn’t mind, just kept refilling our iced teas. Asking whether we liked the food and whether we’d ever been in before. Real small-town greasy spoon diner talk. My kinda people.
And yes, Jennifer and I talked for almost 2 hours because she’s great! Her and her boyfriend just moved to Charlottesville, and her blog, Cville Field Notes, is a blow-by-blow, day-to-day experience of our fair ‘ville from a newbie’s perspective. Her breakdown of the Craig’s List listings alone are howlingly funny.
Her boyfriend has just launched Potter’s Craft Cider, soon to be found in every store near you. Great news for this food writer, who just happens to be obsessed with hard cider and always wonders why we don’t have more local brands.. . . I mean, we are an APPLE state after all. Not just grapes growin’ here you know.
We talked and talked, then talked some more. And as we left, making plans for cocktails and cider sometime soon, and I saw the humongous line of Harleys in the parking lot, I knew I’d be back. I hear their onion rings are outta this world…
*I am woefully late, once again, on this blog musing slash review of my time with Jennifer. To her I apologize. I blame old age memory loss, as I wrote this a while ago, and just discovered the draft on my desktop. Published to coincide with the debut of Potter’s Craft Hard Cider THIS WEEK. So there’s that :D
Love the post, edible! It's one of my favorite places in town too. But you seriously trying to tell me that you didn't know Riverside was famous for its burgers until after this summer? I'm not buying it. Why you being coy about this one? ;-) | tomekkorbak/pile-curse-small | Pile-CC |
Study: Hot Chili Peppers Aid Weight Loss
According to new research, the spicy ingredient increases calorie expenditure when consumed as part of a low-calorie diet. Researchers at the University of California have discovered some exciting news about the humble chili pepper. Not only does it work wonders in our food, it can work miracles on our waistlines too.
According to the study, including capsaicin (the active ingredient in chili peppers) as part of a low-calorie diet increases fat oxidation, therefore pushing the body to use stored fat as fuel, reports Britain's The Telegraph. The results were so conclusive, those who were given the chili component as part of their 28-day liquid
diet, burned almost twice as many calories as the placebo group. As Paris Hilton would say: That's hot!"
And there's good news for those who don't like the burn of the fiery little fruit. As part of their research, the team, led by Dr. David Heber, discovered a similar effect in certain plants, which contain a non-burning version of capsaicin called dihydrocapsiate (DCT) giving us all the benefits of the
pepper without the fiery aftertaste.
With health benefits including aiding digestion, fighting cancer and protecting your heart, (oh and did we mention fighting terrorism?) it looks like the chili pepper is climbing its way to super food stardom.
Tonic is a digital media company dedicated to promoting the good that happens around the world each day. We share the stories of people and organizations that are making a difference by inspiring good in themselves and others. | tomekkorbak/pile-curse-small | Pile-CC |
They’re Back
After an interminably long and dry summer the rain and clouds have returned to the Pacific Northwest just in time to welcome fall. Though we desperately needed the rain, the change was rather abrupt and will take some getting used to. Still, I love the clouds.
Yes, I was so happy to see such beautiful clouds (instead of smoke) last night, and the bright contour of evening light on the hills! Cumulo-nimbus clouds are gathering now, and I look forward to more rain!
Yes, we’ve had a few more of those this week, too 🙂 Woke just before 5 this morning to thunder and lightning and the rain hammering down. As with you, Romania desperately needs the rain, so I’d be happy to see a bit more of it, but it soon seems to take itself off somewhere else. Things to do, places to go, obviously 😉
We had the hammering rain last night too. It’s surprising to me how quickly everything changes, from long, golden, sunny days to cool, rainy, and gray ones. But I do love the changing of the seasons! 🙂 | tomekkorbak/pile-curse-small | Pile-CC |
Q:
Can you cast Dispel Magic on a Shadow Monk's Silence?
Let's say a Wizard is outside the range of a 3rd Level Shadow Monk's Silence, cast using ki points.
Can the Wizard dispel it?
My gut inclination is that the Wizard can indeed dispel the Shadow Monk's Silence despite it not being technically a spell, due to the Sage Advice Compendium containing this ruling:
Is it a spell? Or does it let you create the effects of a spell
that’s mentioned in its description?
[...]
If your answer to any of those questions is yes, the feature is magical.
Now, consider the Way of Shadow Monk's Shadow Arts feature (PHB, p. 80):
You can use your ki to duplicate the effects of certain spells. As an action, you can spend 2 ki points to cast darkness, darkvision, pass without trace, or silence, without providing material components. Additionally, you gain the minor illusion cantrip if you don't already know it.
Seems clear enough. However, the only reason I'm unsure is due to to the "best answer" selected to the question, "Does ki count as magic for the purpose of an antimagic field, or is it only fluff?"
That answer seems to conclude that ki magic is NOT in fact magical. (Note that the second answer, which is more highly rated, concluding that it IS in fact magical.)
I'm likely to face this specific, niche situation in an upcoming session I'm running, and I want a clear, community consensus on how to resolve this specific problem. Other examples and evidence are extremely welcome as well.
A:
Yes, you can dispel it
The Shadow Arts feature says:
Starting when you choose this tradition at 3rd level, you can use your
ki to duplicate the effects of certain spells. As an action, you can
spend 2 ki points to cast darkness, darkvision, pass without
trace, or silence, without providing material components.
The key term here is "cast" because it means you are dealing with an actual spell. The ability simply allows you to cast a spell. It even talks about components, something that is only relevant if you are dealing with actual spells (not "spell-like" abilities). And dispel magic works against spells.
Yes, that first line is a bit deceiving because you'd expect the thing coming after to be duplicating the effects of the spell only and not be one, but the language after it is pretty unambiguous that you cast an actual spell.
If you want to dive deeper into what things count as spells or not you can take a look at my answer on What counts as a spell?
The whole issue with ki being magical or not is also a red herring here. Dispel magic (despite its name) only works on actual spells and doesn't care if something is technically magical or not.
Therefore, dispel magic will indeed work on any of the shadow monk's Shadow Arts spells.
| tomekkorbak/pile-curse-small | StackExchange |
Biological characterization of Trichinella isolates from various host species and geographical regions.
Forty isolates of Trichinella collected from 5 continents were compared for 7 biological characters: newborn larvae produced per female worm cultured in vitro at the seventh, eighth, and ninth day postinfection, host muscle nurse cell development time, reproductive capacity index in rats and chickens, and resistance of muscle larvae to freezing. The isolates also were compared by analyses of an environmental character of the location from which they were isolated: the isotherms for January and July. By factorial analysis of correspondence of the biological and environmental data, the 40 isolates were grouped into 8 gene pools (T1-T8). The environmental temperature-related distribution was more evident for the sylvatic isolates (T2, T3, T5, T6, T7, T8), than for T1, which was isolated from domestic pigs, and for T4, a bird-adapted, nonencapsulating genetic type. The 8 biological groups correlated closely with the 8 gene pools previously identified on the basis of allozyme analysis. These results support the concept that the genus Trichinella is composed of at least 5 distinct gene pools or sibling species: Trichinella spiralis sensu stricto (T1), Trichinella nativa (T2), Trichinella sp. (T3), Trichinella pseudospiralis (T4), and Trichinella nelsoni (T7), and 3 other groups of uncertain taxonomic status (i.e., T5, T6, and T8). | tomekkorbak/pile-curse-small | PubMed Abstracts |
Mar 18th, 2019
Mar 18th, 2019
Gold Coast will likely be calling on their new-found depth much sooner than hoped after the side lost both their starting halves in a forgettable NRL opener on Sunday.
The Titans were beaten 21-0 by Canberra on a wet night in Robina, where Ashley Taylor (quadriceps) was a late scratching and Tyrone Roberts (Achilles) lasted less than 15 minutes.
On Monday the club revealed Roberts has sustained a minor strain and will be ruled out for two to three weeks.
Taylor is also unavailable for Saturday's trip to Cronulla following scans on his injury, though it is hoped he'll be fit for the round three clash with South Sydney.
Coach Garth Brennan admitted they had no answer to the injuries on the night in a "rudderless" display riddled with errors as AJ Brimson and Tyrone Peachey were hastily slotted into the vacancies.
But with Melbourne recruit Ryley Jacks on the books, and playing well in the Queensland Cup for Tweed Heads, Brennan does have options.
Mitch Rein was a strong performer at NRL level off the bench last year but has also been squeezed out of the Titans' best side this year along with regular on the wing Anthony Don.
"I thought he (Jacks) did a decent job there at Tweed and played well there last week too," Brennan said.
"On the bright side we do have a little bit of depth there in that position and I've faith in Ryley if he gets his call next week he'll do a good job."
The Titans made 14 errors to the Raiders' 13 but the visitors made better use of the opportunities as new No.6 Jack Wighton showed poise alongside Aidan Sezer and hooker Josh Hodgson.
Brennan was still happy with the side's defence through the middle of the park though, with two of three tries from kicks.
Their inability to hang onto the ball meant it mattered little, though.
"We probably do have to cut them some slack there (due to the pair of injuries, but we need to be better than that," Brennan said.
"But it's round one isn't it; we can dust ourselves and move on from that."
©AAP2019 | tomekkorbak/pile-curse-small | OpenWebText2 |
This invention relates to an apparatus for recovering sulfur from gases containing hydrogen sulfide by the process described in German Auslegeschrift No. 1,941,703, which apparatus is, however, suitable for processing gas mixtures containing any concentration of hydrogen sulfide met with in industrial processes.
When industrial gases containing more than 15 percent by volume of hydrogen sulfide are produced and are thus intended for further treatment, it has hitherto been generally customary to oxidize with atmospheric oxygen the appropriate quantity of hydrogen sulfide present in the feed gas in order to produce the quantity of sulfur dioxide required by the proportions for the recovery of sulfur. The appropriate quantity of air for combustion is precisely adjusted and continuously regulated automatically in accordance with the quantity and composition of the gas containing hydrogen sulfide. The reaction is carried out at high temperatures (approximately 1,000.degree. C.) in an open flame in a bricklined combustion chamber. The mixing of the combustion gas with the residual gas takes place simultaneously in this combustion chamber in the absence of any operational or external action on the mixing process.
The following text summarizes the effects which take place, or are to be expected, in accordance with experience, on the overall reaction and thus on the overall yield when a sulfur recovery plant is operated in the above-mentioned manner.
As a result of the oxidation of hydrogen sulfide with air, water of combustion is formed simultaneously and in a quantity equal to that of the sulfur dioxide required for the reaction. Since the reactions leading to the formation of sulfur are reversible, the effect of increasing the proportion of water in the reaction gas mixture is to cause a shift to the left in the equilibrium in the equation: 2H.sub.2 S+SO.sub.2 .revreaction.2H.sub.2 O+3S; this shift in the equilibrium is associated with a corresponding reduction in the yield of sulfur. At the same time, the substantially greater water content of the gas means a considerable increase in the dew point. In order to avoid corrosive effects caused by condensation, it is necessary to keep the operating temperatures in all sections of the plant carrying gas always at a temperature which has an adequate safety margin above the dew point temperature. The most advantageous operating temperature in the catalytic reaction of the sulfur is within a relatively low temperature range. As soon as this temperature range is exceeded, the formation of sulfur is necessarily reduced, regardless of the cause. In order to keep the yield constant, it would either be necessary to reduce the space velocity in the catalyst containers, or alternatively the throughput of the sulfur recovery plant, or to increase the quantity of catalyst.
Stemming from the raw materials, for example petroleum and coal, proportions of hydrocarbons, carbon oxysulfide and carbon disulfide, which in most cases also vary in quantity and composition, are present in the mixed gases containing hydrogen sulfide, which are obtained from desulfurization plants for further processing in sulfur recovery plants. The effect of the non-catalytic high temperature--combustion at about 1,000.degree. C. to 1,300.degree. C.--is to promote, in the combustion chamber, not only the dissociation into its elements of hydrogen sulfide, but also, in particular, that of the hydrocarbon. The formation of H.sub.2 O and CO.sub.2 in conjunction with the free atmospheric oxygen is only brought about to a limited extent. The moderated and greatly retarded formation of SO.sub.2 can also be explained by the high temperatures in the radiant zone of the free flame. The cracked products from the hydrocarbon combine principally with the diatomic sulfur which is present in abundant quantities in the form of vapor and is considerably superheated. Admittedly these compounds can, to a limited extent, be re-decomposed and converted into elementary sulfur in one of the down-stream catalytic reaction stages. However, this requires a very highly active catalyst and, in addition, an operating temperature which is far above the most favorable figures which have been determined for the reaction of H.sub.2 S with SO.sub.2. A diminution in this reaction is a fundamental factor for the overall yield and, looking further, determines the quantity of noxious material with which the environment will be polluted in a particular case.
As a result of the process, the oxidation temperature in the combustion chamber also rises if there is a greater quantity of hydrogen sulfide in the feed gas. If the combustion is carried out with air, it must in any case be expected that the formation of nitric oxide will be promoted at very high temperatures. For this reason, a detectable quantity of nitric oxide can, in some cases, be present in the reaction gas if the operating procedures which are customary according to the state of the art known at the present time are used. It is assumed that oxides of nitrogen are a possible cause of certain obstructions which are often found in the layers of catalyst after interruptions to operation. Gaseous nitric oxide, which dissolves in the liquid sulfur when the gaseous sulfur condenses in the phase of its formation, results in undesirable impurities in the end product.
Corrosive effects and blockages which are difficult to locate can be initiated in the liquid sulfur lines as the result of the formation of crystals containing nitrogen. The nitric oxide content in the exit gases which pass into the free atmosphere should be monitored precisely. The exit gas rate and the exit gas temperature are decisive factors for the quantity of sulfur which is passed in the form of gas and mist, first to the after-combustion furnace, and from there as SO.sub.2 to a chimney stack. To sum up, the atmospheric nitrogen which is necessarily associated with the use of atmospheric oxygen entails, for the processes hitherto customary, the considerable disadvantages that the conditions required for the development of undesirable side reactions are provided, that the reaction gas mixture is so greatly diluted with inert constituents that the conversion and also the yield undergo an appreciable reaction, and that the losses in the exit gases caused by entrained flying particles of elementary sulfur increase in step with the ratio between the quantity of nitrogen and the total quantity of exit gas.
The facts listed in the above description and also many further unsolved problems and unexplained difficulties originate from carrying out, on an industrial scale, the existing process for recovering sulfur from gases containing hydrogen sulfide. An exact proof on the basis of operating results is not yet possible for many valuable pieces of experience in this field of work. For example, no serviceable method of determination has yet been developed for carrying out systematic sampling and satisfactory determination of the composition of the reaction gas mixture at such high combustion temperatures at the exit of the combustion chamber. In most cases the results obtained by gas analysis are much better and more favorable than the operating figures actually found. Since the reaction of hydrogen sulfide with sulfur dioxide is favored as the temperature falls, the formation of sulfur continues in the sampling container after a sample has been taken. It has been proved by tests that at temperatures between 250.degree. C. and 350.degree. C., the reaction only proceeds to completion on solid surfaces and best on glass, aluminum or Al.sub.2 O.sub.3.
The scope of the facts available from operating experience or from tests carried out, and also of the data available from the specialized literature on the relationships and the actual course of the formation of sulfur, is relatively small.
If the process in German Auslegeschrift No. 1,941,703 is used, it is possible to eliminate completely the disadvantages and difficulties caused by the partial combustion of the hydrogen sulfide with air and, furthermore, to achieve in addition considerable advantages in the construction and in the operation of the plant by feeding in the quantity of sulfur dioxide required for carrying out the process, by means of burning sulfur with oxygen.
At present, a large number of processes and types of equipment are known for the manufacture of sulfur dioxide by burning elementary sulfur with air, oxygen or gases enriched with oxygen, especially for obtaining sulfuric acid. However, jet burners, or alternatively atomization burners or nozzle burners, of a variety of designs are used preferentially.
These types of burner, including their respective accessories for obtaining sulfur dioxide, are unsuitable in every form for a further processing step such as corresponds to the process defined in German Auslegeschrift No. 1,941,703, because the combustion of the liquid sulfur is carried out in every case in the same space in which, at the same time, the gas containing hydrogen sulfide is also added. If the hydrogen sulfide content is 15 percent by volume or less, the quantity of sulfur corresponding to the stoichiometric formation of sulfur dioxide is also reduced proportionately. The heat of combustion liberated is too low to vaporize the sulfur, which is finely atomized in the gas mixture, rapidly and sufficiently into the diatomic state. As a result, it is not possible to expect or to ensure proper and complete oxidation with the very dilute oxygen. | tomekkorbak/pile-curse-small | USPTO Backgrounds |
Black Hippy - U.O.E.N.O. (Remix)
Yesterday, Kendrick Lamar and his Black Hippy colleagues kicked off the good kid, m.A.A.d. city World Tour in Las Vegas, Nevada. Even while on the road, K.Dot and company are committed to keeping their hungry online fanbase satisfied. For their latest collective release, the crew have come together to remixU.O.E.N.O., the recent, non-featured single from ATL rapper Rocko. Over Childish Major‘s eerie synths, Lamar turns in a characteristically adroit opening verse, which is followed by strong contributions from Ab-Soul, Jay Rock and ScHoolBoy Q (the last-named putting his own twist on Rick Ross’ infamous “molly” line). Could this remix be better than the original? Usually I try to remain impartial, but who am I kidding—of course it is. If you’re feeling it, why not click here and cop tickets to one of Black Hippy’s upcoming performances before they sell out? | tomekkorbak/pile-curse-small | Pile-CC |
The issues began in January. My school had a lot of issues this year with truancy (I know. In sixth grade. Atrocious, right?) and one day, Slick decided to join in. He and three of his friends ditched. Which wouldn’t have been SO bad, except they also decided to throw rocks. Through windows. Of houses. And then they ended up with felony charges.
The kids involved were suspended for a week, post-ditching (because THAT’S a punishment), and when they came back, we were told to not treat them any differently than any other kids. Okay, fine. It’s not like I’d been planning on some sort of public self-flagellation, but I’d make every effort to treat Slick and his pals just like everyone else.
Apparently, Slick didn’t feel I was following through. Slick felt I was singling him out by doing things like calling on him during class for the answer to a question, or by asking him where his homework was when he didn’t have it out. I got a lot of pained sighs and rolled eyes, ignoring me when I asked him questions, refusing to follow directions.
And here’s the thing. That doesn’t fly in my class. Ain’t nobody going to treat me with that kind of disrespect.
But Slick was, and because of the edict to treat him like everyone else, I let it slide for a couple of days, despite that fact that I was absolutely treating him differently by being easier on him than I normally would have been. My back? Bent over to make sure this delicate tulip didn’t feel awkward.
I talked to Slick about it. I talked to his mom about it. I talked to my colleagues and my admin about it. After about two weeks of his jackassery, I set up a parent meeting, and the rest of my core came too, as he’d been giving them all kinds of crap as well. In the meeting, I made it clear that I wanted him to be successful but that I would not stand for him undermining me in front of his peers. Subtext: if he wanted to fight, we could fight, but I would win. His mom agreed that was not okay, and it got better. Mostly. One day he did attempt to turn in a paper by shaking it in my face, but after a brief chat, he reluctantly acknowledged that he’d made an inappropriate choice and would not do so again.
A few months passed, and Slick was absent for over a week, unexcused. I asked his class if anyone knew what was up. The Natural Athlete piped up with, “Maybe he’s ditching because he hates your class so much.” I silenced him with a look, and then asked him to join me in the hall. We discussed how it’s probably not the best idea to tell a teacher how bad their class sucks during class, to which the Natural Athlete assured me that he loved my class, it was his second favorite, just Slick didn’t like it. We moved on from there, but honestly, I was taken aback. Because the thing is, I thought things had changed. I thought Slick and I had worked through the previous animosity. Recently he’d been joking around with me some, turning in work, doing assignments without repeated requests. So the Natural Athlete’s comment was disappointing.
Slick came back, and still seemed fine. A couple of weeks later, he asked me if I needed any help with anything. He owed community service from the January incident and wanted to serve it with me. Again, taken aback, but I agreed. He started staying after school to help with whatever I needed.
A few hours into the community service, I couldn’t take it anymore. “Hey, Slick?”
He looked up from his filing. “Yeah?”
“Would you agree that for a while there, you and I weren’t getting along so well?”
He nodded emphatically. “Oh yeah. Absolutely. Really bad.”
“And now, would you say we’re getting along better?”
He nodded even more emphatically. “Yup. Waaaaaay better. Like totally different.”
I paused. “So….what changed? Why are we getting along better now?”
He paused too. “Well…I don’t know.”
“No?”
“Well…I think mostly the difference? The difference is that I kinda grew up and figured some things out.”
What a great response, I thought, but I didn’t want to push it. I nodded. “Got it.” We both went back to work.
As I mentioned before, Thursday was the last day with kids. Slick still needed three community service hours, so he came in on Friday to help me out. After three hours, I signed his card and told him how much I’d appreciated his help. He didn’t move. “So, um, what else do you need help with?”
I looked at him. “Slick, you’re done. You’ve been great, but you can totally go if you want to.”
He fidgeted with a pencil. “I could still help if you need more help. Because, like, I needed the hours, but mostly I just wanted to help.”
“Really? Are you sure?”
“I’m sure.” He stayed for two more hours and is coming back on Tuesday to help me move my room.
This is the kid who hated me more than anyone. This is the kid who made me dread seeing my second period some days, because he could be such an asshole. This is the kid who told the whole class that writing was boring and pointless.
I don’t know what happened, I don’t know how I did it except to treat him with respect and try to be aware when he seemed to be on the verge of shutting down, but somehow, this is a kid I reached. This is a kid who hugged me goodbye on the last day of school. This is a kid who laughs at my corny jokes. This is a kid who says Language Arts is his favorite class now, when he hates reading and writing. This is a kid I reached.
What did I learn from him? Treat everyone with respect. Sometimes you can’t control how people feel about you. Everyone deserves a second, and third, and eighth, and seventeenth chance. Anyone can change, but sometimes you have to change first.
3
comments:
Aww, Sweetie, you've been through a lot with that job. They just don't pay us a whole hell of a lot and we really put up with some mess. Bless you for having the patience and respect to deal with people who don't show you dignity.How uplifting it must have been to see that your hard work paid off.
What a great story. It shows how we think we understand what's going on with kids (with everyone, really), but our interpretations are just our interpretations. Good for you for sticking with this guy. It can't have been easy. | tomekkorbak/pile-curse-small | Pile-CC |
Indiana Governor Mike Pence said on Thursday that while he believes no one should be fired “for who they are or who they love”, he will defend so-called “religious freedom” because he believe it’s in keeping with the state’s constitution.
Pence was asked at a Town Hall in Kokomo, Indiana about LGBT rights, a subject that’s been a hot button issue in the Hoosier state since Pence signed the aggressively anti-LGBT Religious Freedom Restoration Act into law last year. The audience member, who presumably was a pastor given Pence’s response, said to Pence, “A simple yes or no answer. Do you believe that gay and transgender people should be able to be fired from their jobs just for that reason?”
After a long pause and some applause from the audience, Pence responded,
“I don’t think anyone should ever be discriminated against because of who they are or who they love. My position is, as I expressed in my State of the State address and did again today, is we are a state with a constitution. And as you know as a pastor, that constitution has very strong safeguards for the freedom of conscience and freedom of religion of Hoosiers. And my strong conviction is that should the general assembly put legislation on my desk which they considered this year…[iomust be consistent with the constitution. But I will not support legislation that diminishes religious freedom. I hope you hear my heart a little bit as much as my head on this.”
Did he finally give a yes or no answer? Hardly. Once again, the Governor tried to have it both ways. After more than a year of this issue dominating public discourse and his promise to give it thorough consideration, Governor Pence STILL can’t answer a very simple, straight-forward question.
…even if he refuses to answer, Hoosiers won’t stop asking the obvious question. If the Governor truly believes, as he said today, that “no one should ever be discriminated against,” then why does he flat-out refuse to support a simple solution to add “sexual orientation, gender identity” to our state’s civil rights law.
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The networked computing environment (e.g., cloud computing environment) is an enhancement to the predecessor grid environment, whereby multiple grids and other computation resources may be further enhanced by one or more additional abstraction layers (e.g., a cloud layer), thus making disparate devices appear to an end-consumer as a single pool of seamless resources. These resources may include such things as physical or logical computing engines, servers and devices, device memory, storage devices, among others.
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---
abstract: 'The number of $n$-edge embedded graphs (rooted maps) on the $g$-torus is known to grow as $t_gn^{5(g-1)/2}12^n$ when $g$ is fixed and $n$ tends to infinity. The constants $t_g$ can be computed thanks to the non-linear “$t_g$-recurrence”, strongly related to the KP hierarchy and the double scaling limit of the one-matrix model. The combinatorial meaning of this simple recurrence is still mysterious, and the purpose of this note is to point out an interpretation, via a connection with random (Brownian) maps on surfaces. Namely, we show that the $t_g$-recurrence is equivalent, via known combinatorial bijections, to the fact that $\mathbf{E}X_g^2=\frac{1}{3}$ for any $g\geq 0$, where $X_g,1-X_g$ are the masses of the nearest-neighbour cells surrounding two randomly chosen points in a Brownian map of genus $g$. This raises the question (that we leave open) of giving an independent probabilistic or combinatorial derivation of this second moment, which would then lead to a concrete (combinatorial or probabilistic) interpretation of the $t_g$-recurrence. We also compute a similar moment in the case of three marked points, for which a similar phenomenon occurs. In fact, we conjecture that for any $g\geq 0$ and any $k\geq 2$, the masses of the $k$ nearest-neighbour cells induced by $k$ uniform points in the genus $g$ Brownian map have the same law as a uniform $k$-division of the unit interval. We leave this question open even for $(g,k)=(0,2)$.'
author:
- 'Guillaume Chapuy[^1]'
bibliography:
- 'biblio.bib'
title: 'On tessellations of random maps and the $t_g$-recurrence'
---
Introduction and results
========================
In this note a *map* is a graph embedded without edge crossings on a closed oriented surface, in such a way that the connected components of the complement of the graph, called *faces*, are each homeomorphic to a disk. Loops and multiple edges are allowed, and maps are considered up to oriented homeomorphisms. A map is *rooted* if an edge is distinguished and oriented. The number $m_g(n)$ of rooted maps with $n$ edges on the surface of genus $g$ satisfies, for fixed $g\geq 0$ and $n\rightarrow \infty$: $$\begin{aligned}
\label{eq:mgn}
m_g(n) \sim t_g n^{\frac{5(g-1)}{2}} 12^n, \mbox{ for }t_g >0.\end{aligned}$$ In genus $0$, this result follows from the exact formula $m_0(n)=\frac{2\cdot 3^n}{(n+2)(n+1)}{2n \choose n}$ due to Tutte [@Tutte:census]. In higher genus, it was proved in [@BC0] using generating functions. A direct combinatorial interpretation of Tutte’s formula for maps of genus $0$ was given by Cori and Vauquelin [@CV] and much simplified by Schaeffer [@Schaeffer:phd; @ChassaingSchaeffer]. A combinatorial interpretation of was given in [@CMS] using the Marcus-Schaeffer bijection [@MS] and further developped in [@Chapuy:trisections].
None of the methods just mentioned enable to say much about the sequence of constants $(t_g)_{g\geq 0}$ that appear in , and indeed these references give explicit values only for very small values of $g$. There is however a remarkable recurrence formula to compute these numbers, that we call the *$t_g$-recurrence*. It is better expressed in terms of the numbers $\tau_g=2^{5g-2}\Gamma\left(\frac{5g-1}{2}\right)t_g$ and is given by: $$\begin{aligned}
\label{eq:tg}
\tau_{g+1} = \frac{(5g+1)(5g-1)}{3}\tau_{g}+\tfrac{1}{2}\sum_{g_1=1}^{g}\tau_{g1}\tau_{g+1-g1}, \ \ g \geq 0,\end{aligned}$$ which enables to compute these numbers easily starting from $\tau_0=-1$. This result was first stated in mathematical physics in relation with the *double scaling limit* of the one-matrix model, and obtained via a non-rigorous scaling of expressions involving orthogonal polynomials (we refer to [@LZ p201] for historical references). A more algebraic approach is based on the fact that the partition function of maps on surfaces, with infinitely many parameters marking vertex degrees, is a tau-function of the KP hierarchy. Going from the KP hierarchy to the recurrence (or to an equivalent Painlevé-I ODE for an associated generating function) relies on a trick of elimination of variables that can be performed in different ways and whose generality is, as far as we know, yet to be fully understood (for the case of triangulations see [@mcfly Appendix B.] or [@GJ; @tg] and for general maps see[@CC]).
The main observation of this note is to relate the recurrence to another side of the story, namely the study of random maps and their scaling limits. We refer to [@miermont:survey] for an introduction to this topic. To state our main observation we first need a few more definitions. A *quadrangulation* is a map in which each face contains exactly four corners, [*i.e.*]{} is bordered by exactly four edge-sides. It is *bipartite* if its vertices can be colored in black and white in such a way that there is no monochromatic edge. For each $n,g\geq0$, there is a classical bijection, due to Tutte, between rooted maps of genus $g$ with $n$ edges and rooted bipartite quadrangulations of genus $g$ with $n$ faces. For $n,g\geq 0$, we let ${\mathcal{Q}_n^{(g)}}$ be the set of rooted bipartite quadrangulations of genus $g$ with $n$ faces (with the convention that there is a single quadrangulation with $0$ face, which has genus $0$, no edge, and two vertices). We let ${{\mathbf{q}}_{n}^{(g)}}\in_u {\mathcal{Q}_n^{(g)}}$ be a bipartite quadrangulation of genus $g$ with $n$ faces chosen uniformly at random (the notation $\in_u$ to denote a uniform random element of a set will be used throughout this note). We equip the vertex set of ${{\mathbf{q}}_{n}^{(g)}}$ with the graph distance, noted $\mathbf{d}_n$, and with the uniform measure, noted $\mathbf{\mu}_n$. This makes ${{\mathbf{q}}_{n}^{(g)}}\equiv ({{\mathbf{q}}_{n}^{(g)}},\mathbf{d}_n,\mu_n)$ into a compact measured metric space. The set of (isometry classes of) such spaces is equipped with the Gromov-Hausdorff-Prokhorov (GHP) topology as in [@Miermont:tessellations Sec. 6]. A *Brownian map of genus $g$* is a random compact measured metric space $({\mathbf{q}}_\infty, d_\infty, \mu_\infty)$ that is such that: $$({{\mathbf{q}}_{n}^{(g)}},\tfrac{1}{n^{1/4}}\mathbf{d}_n,\mu_n)
\longrightarrow
({{\mathbf{q}}_\infty^{(g)}}, d_\infty, \mu_\infty),$$ in distribution along some subsequence for the GHP topology. The existence of Brownian maps of genus $g$ was proved in [@Miermont:tessellations], and their unicity for each $g \geq 1$ has been announced by Bettinelli and Miermont [@BettinelliMiermont] (in genus $0$ the unicity is an important result proved independently by Miermont [@Miermont:GH] and Le Gall [@LG:GH]). However the unicity of the limit is not needed for our discussion since we will prove the convergence of all the observables we are interested in. Also note that some authors prefer to introduce an additional scaling factor $(8/9)^{1/4}$ to the distance, but this is irrelevant to our discussion so we prefer avoid it.
\[thm:obs1\] For $g\geq 0$, let $({{\mathbf{q}}_\infty^{(g)}}, d_\infty, \mu_\infty)$ be a Brownian map of genus $g$. Let ${\mathbf{v}}_1,{\mathbf{v}}_2 \in {\mathbf{q}}^{(g)}_\infty$ be chosen independently according to the probability measure $\mu_\infty$, and let ${\mathbf{X}}_g, 1-{\mathbf{X}}_g$ be the masses of the corresponding cells in the nearest neighbour tessellation of ${{\mathbf{q}}_\infty^{(g)}}$ induced by ${\mathbf{v}}_1$ and ${\mathbf{v}}_2$, that is to say: $${\mathbf{X}}_g := \mu_\infty\Big(\big\{x\in {{\mathbf{q}}_\infty^{(g)}},\ d_\infty(x,{\mathbf{v}}_1)<\mathbf{d}_\infty(x,{\mathbf{v}}_2) \big\}\Big).$$ Then the sequence of numbers $\tau_g=2^{5g-2}\Gamma\left(\frac{5g-1}{2}\right)t_g$ satisfies: $$\tau_{g+1} = 2(5g+1)(5g-1)\tau_{g}\cdot \mathbf{E}[{\mathbf{X}}_{g}(1-{\mathbf{X}}_g)]
+\frac{1}{2}\sum_{g_1=1}^{g}\tau_{g1}\tau_{g+1-g1}, \ \ \ g\geq 0.$$
From we immediately deduce:
\[cor:main\] For any $g\geq 0$, the random variable ${\mathbf{X}}_g$ satisfies $$\mathbb{E}[{\mathbf{X}}_g(1-{\mathbf{X}}_g)]=\frac{1}{6},$$ or equivalently $\mathbf{E}{\mathbf{X}}_g^2=\frac{1}{3}.$
The reader may find surprising that $\mathbf{E}{\mathbf{X}}_g^2$ does not depend on $g\geq0$: indeed, although it is natural to expect that *local* statistics of Brownian maps do not depend on the genus, the nearest-neighbour tessellation depends *globally* of the metric space ${{\mathbf{q}}_\infty^{(g)}}$, that *is* genus dependent. In fact, this unexpected property is the main reason why this note is written. It suggests that there exists a simple probabilistic or combinatorial interpretation of this mysterious fact, based on a symmetry of the Brownian map, but we have not been able to find it. We emphasize that, via Theorem \[thm:obs1\], such an interpretation would provide a proof of the $t_g$-recurrence independent of orthogonal polynomials, matrix models or integrable hierarchies.
It is natural to ask if other moments of the variables ${\mathbf{X}}_g$ or related random variables are computable, and in which way they depend on the genus. Unfortunately we won’t go very far in this direction. Let ${\mathbf{v}}_1,{\mathbf{v}}_2,\dots,{\mathbf{v}}_k$ be $k\geq 2$ points in ${{\mathbf{q}}_\infty^{(g)}}$ chosen independently at random according to the Lebesgue measure $\mu_\infty$. Let $({\mathbf{Y}}_g^{(i:k)})_{1\leq i \leq k}$ be the masses of the $k$-nearest-neighbour cells induced by the ${\mathbf{v}}_i$’s, *i.e.* for $i\in[1..k]$ let $${\mathbf{Y}}_g^{(i:k)}:=\mu_\infty \big\{ x\in {{\mathbf{q}}_\infty^{(g)}}, \ \forall j\in [1..k]\setminus\{i\}, \ d_\infty(x,{\mathbf{v}}_i)<d_\infty(x,{\mathbf{v}}_j)\big\}.$$ We note that ${\mathbf{X}}_g={\mathbf{Y}}_g^{(1:2)}$, so we could have used a single notation, but we prefer to keep the lighter notation ${\mathbf{X}}_g$ for ${\mathbf{Y}}_g^{(1:2)}$ throughout this note. The following result is similar to, and as mysterious as Theorem \[cor:main\]:
\[thm:3points\] For $g\geq 0$, the masses ${\mathbf{Y}}_g^{(1:3)}, {\mathbf{Y}}_g^{(2:3)}, {\mathbf{Y}}_g^{(3:3)}$ of the Voronoï cells induced by three independent Lebesgue distributed points in the Brownian map of genus $g$ satisfy, for $g\geq 0$: $$\mathbf{E}[{\mathbf{Y}}_g^{(1:3)}{\mathbf{Y}}_g^{(2:3)}{\mathbf{Y}}_g^{(3:3)}]
=\frac{1}{60}.$$
As we will see, the fact that this moment is computable reflects the existence of a combinatorial device known as the “trisection lemma” [@Chapuy:trisections]. The fact that it does not depend on the genus, and that it coincides[^2] with the corresponding moment for a uniform three-division of the interval $[0,1]$, is as mysterious as for the previous result (or even more, since as we will see the computations leading to Theorem \[thm:3points\] are quite delicate and involve intermediate expressions that are complicated and magically become simpler at the last minute).
We won’t prove anything on higher moments or other values of $k$ since we lack the tools to study them. However, numerical simulations suggest that the first joint moments of the random variables $({\mathbf{Y}}_g^{(i:k)})_{1\leq i \leq k}$, for small values of $g$ and $k$, are close to what they are for a uniform partition of $[0,1]$ into $k$ intervals. Of course one has to be prudent with simulations, given that the metric observables in random discrete maps of size $n$ typically converge to their Brownian map analogue at speed $O(n^{-1/4})$, and that our numerical simulations are performed only for $n\approx 10^6$ to $10^7$. However Theorems \[thm:obs1\] and \[thm:3points\] support this conjecture, so we dare to state it explicitly:
\[conjecture\] For $k\geq 2, g\geq 0$, let ${{\mathbf{q}}_\infty^{(g)}}\equiv ({{\mathbf{q}}_\infty^{(g)}}, d_\infty, \mu_\infty)$ be a genus $g$ Brownian map and let ${\mathbf{v}}_1,\dots,{\mathbf{v}}_k$ be chosen according to $\mu_\infty^{\otimes k}$. Then the random vector $({\mathbf{Y}}_g^{(1:k)},{\mathbf{Y}}_g^{(2:k)},\dots, {\mathbf{Y}}_g^{(k:k)})$ has the same law as the subdivision of the unit interval induced by $k-1$ independent uniform variables. In particular, for any $g\geq 0$, ${\mathbf{X}}_g={\mathbf{Y}}_g^{(1:2)}$ is uniform on $[0,1]$.
To conclude this introduction, we emphasize that our main observation relates the moment $\mathbf{E}{\mathbf{X}}_g^2$ to the $g$-th step of the $t_g$-recurrence. In particular, the fact that $\mathbf{E}{\mathbf{X}}_0^2=1/3$ for the *genus $0$* Brownian map is only “equivalent” to the computation of the genus $1$ constant $t_1$, that can be performed by hand in several ways (and similarly, our proof of Theorem \[thm:3points\] for $g=0$ relies only on the value of the constants $t_1$ and $t_2$). However, proving Conjecture \[conjecture\] even for $(g,k)=(0,2)$ would be interesting in itself. Readers familiar with Miermont’s bijection [@Miermont:tessellations] may try to approach this problem by exact counting of well-labelled 2-face maps (we have failed trying to do so). One could also hope that in the future purely probabilistic methods (for example using the QLE viewpoint on the Brownian map [@MillerSheffield]) will enable to determine the full law of ${\mathbf{X}}_0$ or even the law of the vector $({\mathbf{Y}}_0^{(i:k)})_{1\leq i\leq k}$ for each $k$. In an opposite direction, we recall that the $t_g$-recurrence is only a “shadow” of the fact that the generating functions of maps satisfy a set of infinitely many partial differential equations called the KP hierarchy. It is natural to expect that other joint moments of the variables ${\mathbf{Y}}_g^{(i:k)}$, apart from the two cases we have been able to track, are related to these equations. This may lead to a way, based on integrable hierarchies, of approaching Conjecture \[conjecture\].
Proof of our main observation (Theorem \[thm:obs1\])
====================================================
Preliminaries
-------------
For $g\geq 0$ we let $Q_g(z)$ be the generating function of rooted bipartite quadrangulations of genus $g$ by the number of faces, and we let $Q_g^\bullet(z)$ be the g.f. of the same objects where an additional vertex is pointed. We let $m_g(n) = [z^n] Q_g(z)$ and we use the same notation with $~^\bullet$. In what follows the notation $a(n)\sim b(n)$ means (classically) that $a(n)/b(n)\rightarrow 1$ when $n$ tends to infinity, while the notation $F(z)\sim G(z) $ means that both $F$ and $G$ are algebraic functions of radius of convergence $\tfrac{1}{12}$, both have a unique dominant singularity at $z=\tfrac{1}{12}$, and we have $F(z)= G(z) (1+o(1))$ when $z\rightarrow \tfrac{1}{12}$ uniformly in a neighbourhood of $z=\tfrac{1}{12}$ slit along the line $[\tfrac{1}{12}, \infty)$.
From [@BC0] (see also [@CMS] for purely combinatorial proofs) we have for fixed $g\geq 0$: $$m_g(n) \sim t_g n^{\frac{5g-5}{2}} 12^n
\ \ , \ \
m^\bullet_g(n)
= (n+2-2g) m_g(n) \sim t_g n^{\frac{5g-3}{2}} 12^n$$ $$\begin{aligned}
\label{eq:singQg}
Q^\bullet_g(z) \sim \Gamma(\tfrac{5g-1}{2}) t_g (1-12z)^{\frac{1-5g}{2}}
=
2^{2-5g}\tau_{g}
(1-12z)^{\frac{1-5g}{2}}
.
$$
A *labelled map* of genus $g$ is a rooted map $M$ of genus $g$ equipped with a fonction $\ell: V(M)\rightarrow \mathbb{Z}$ such that for any edge $(u,v)$ of $M$ one has $\ell(u)-\ell(v)\in \{-1,0,1\}$. We consider these objects up to global translation of the labels (we will often fix a translation class by fixing the label of a particular vertex, often the root, to $0$). A *labelled one-face map (l.1.f.m.)* is a labelled map having only one face. We let $\mathcal{L}_n^{(g)}$ be the set of all (rooted) l.1.f.m. of genus $g$ with $n$ edges.
The Marcus-Schaeffer bijection ([@MS], see also [@CMS] for the version needed here) is an explicit bijection: $$\mathcal{Q}_n^{(g)\bullet} \longrightarrow \{\uparrow,\downarrow\} \times \mathcal{L}_n^{(g)},$$ where $\mathcal{Q}_n^{(g)\bullet}$ is the set of rooted bipartite quadrangulations of genus $g$ and $n$ faces equipped with a pointed vertex. It follows that $Q^\bullet_g(z)=2L_g(z)$ where $L_g(z)$ is the generating function of rooted l.1.f.m. of genus $g$ by the number of edges. Moreover, in genus $0$, rooted one-face maps are nothing but rooted plane trees, and a standard root-edge decomposition leads to the quadratic equation $
L_0(z)= 1+3zL_0(z)^2,
$ from which we get the explicit formula: $$\begin{aligned}
\label{eq:valKernel}
1-6zL_0(z) = \sqrt{1-12z}.\end{aligned}$$
The decomposition equation, Miermont’s bijection, and proof of Theorem \[thm:obs1\]
-----------------------------------------------------------------------------------
![Illustration of the decomposition leading to Equation \[eq:Tutte\][]{data-label="fig:Tutte"}](decomp2.pdf){width="\linewidth"}
We now come to the substance of this note, which is simply to try to write an equation for the generating function of l.1.f.m. by root-edge decomposition, and see what happens. We fix $g\geq 0$, and we consider a l.1.f.m. $M$ of genus $g+1$. If we remove the root edge of this map, two things can happen (see Figure \[fig:Tutte\]):
- we disconnect the map into two l.1.f.m. $M_1$ and $M_2$ whose genera sum up to $g+1$;
- we do not disconnect the map; in this case we are left with a map $M'$ of genus $g$ with two faces. Each face of $M'$ carries a distinguished corner, and the labels of these two corners differ by $-1$, $0$, or $1$.
Translating this operation into an equation for generating functions we obtain $$\begin{aligned}
\label{eq:Tutte}
L_{g+1}(z)
=
3z\sum_{g_1+g_2=g+1\atop g_1,g_2\geq 0}
L_{g_1}(z)
L_{g_2}(z)
+
z A_g(z)\end{aligned}$$ where:
- in the first term the factor $3z$ takes into account the choice of the increment of label along the root-edge in $\{-1,0,1\}$;
- $A_g(z)$ is the generating function by the number of edges, of unrooted labelled two-face maps, with faces numbered $F_1,F_2$, such that the face $F_i$ contains a marked corner $c_i$ for $i=1..2$, and that $|\ell(c_i)-\ell(c_2)|\leq 1$.
Objects counted by $A_g(z)$ can be related to quadrangulations thanks to Miermont’s bijection [@Miermont:tessellations]. This bijection is a generalization of the Marcus-Schaeffer bijection where the l.1.f.m is replaced by a labelled map having an arbitrary number, say $K$, of faces. We will apply it for $K=2$. In the following discussion, where we assume some familiarity with Miermont’s bijection, we will show how to arrive informally at Lemma \[lemma:convergenceCell\] below, and why this implies Theorem \[thm:obs1\]. Details of the proof of Lemma \[lemma:convergenceCell\] are postponed to the next sections.
Let us consider an object counted by $[z^n] A_g(z)$. Let us fix the translation class of the labels by saying that the minimum label in face $F_1$ is zero, and let us call $\delta$ the minimum label in face $F_2$. Let $i_1\geq 0$ and $i_2\geq \delta$ be the labels of the two marked corners $c_1$ and $c_2$, respectively, and recall that $i_1-i_2\in \{-1,0,1\}$. Applying Miermont’s bijection [@Miermont:tessellations] to this object, we construct a bipartite quadrangulation $Q$ of genus $g$ by adding a new vertex $s_1, s_2$ inside each face $F_1, F_2$, and applying a certain closure operation. At the end of the construction, we obtain a quadrangulation such that $d(s_1,s_2)+\delta$ is even. Moreover, the two corners $c_1$ and $c_2$ of the original two-face map are naturally associated to two edges $e_1$ and $e_2$ of the quadrangulation, and the construction is such that if $m_i$ is the endpoint of $e_i$ closer from $s_i$ in $Q$, for $i\in \{1,2\}$ one has: $$d(s_1,m_1)=i_1 \ \ ,\ \ d(s_2,m_2)=i_2-\delta \ \ , \ \
d(s_2,m_1)\geq i_1-\delta \ \ ,\ \ d(s_1,m_2)\geq i_2.$$ These constraints can simply be rewritten as: $$\begin{aligned}
\label{eq:crossed}
d(s_1,m_1) \leq d(s_1,m_2) -\epsilon\ \ , \ \
d(s_2,m_2) \leq d(s_2,m_1) -\epsilon,\end{aligned}$$ where $\epsilon = i_2-i_1$ is such that $|\epsilon|\leq 1$. Loosely speaking, the properties in say that, *up to an error at most 1*, $s_i$ is (weakly) closer to $m_i$ than to $m_{3-i}$ for $i=1..2$. Unfortunately these constraints do not entirely characterize these objects (see next section) but they do, in some sense, asymptotically. Thinking heuristically for a moment, we can expect that the analogue in the continuum limit of these discrete configurations is a Brownian map with four marked points $(m_1^\infty, m_2^\infty, s_1^\infty, s_2^\infty)$ such that if we subdivide the space in two nearest-neighbour cells induced by $m_1^\infty$ and $m_2^\infty$, the point $s_i^\infty$ belongs the nearest-neighbour cell induced by $m_i^\infty$ for each $i=1..2$. Up to technical details that we will carry out in the next section, this leads us quite naturally to the following conclusion:
\[lemma:convergenceCell\] The coefficient $[z^n]A_g(z)$ is such that, as $n$ goes to $\infty$: $$\begin{aligned}
\label{eq:convergenceCell}
\frac{[z^n]A_g(z)}{3/2 \cdot n^3m_{g}(n)} \longrightarrow \mathbb{E}[{\mathbf{X}}_g(1-{\mathbf{X}}_g)]\end{aligned}$$ with the notation of Theorem \[thm:obs1\].
\[rem:1\] The reader can understand heuristically the meaning of the denominator $3/2 \cdot n^3 m_{g}(n)$ as follows. The tuple $(Q,s_1,s_2,e_1,e_2)$ is a quadrangulation with two vertices and two marked edges. We can use $e_1$ as the root-edge of $Q$, and orient it by deciding that its source is at even distance from $s_1$. We can choose the “error” $\epsilon$ freely in $\{-1,0,1\}$ (since asymptotically we do not expect this error to play any role), and set $i_1:=d(s_1,m_1)$ and $\delta:=i_1+\epsilon - d(s_2,m_2)$. Since Miermont’s bijection requires that $d(s_1,s_2)+\delta$ is even, we are left with a rooted quadrangulation with one marked edge $e_2$, and two marked vertices $(s_1,s_2)$ subject to *two* parity constraints (that $s_1$ is at even distance from the root, and that $d(s_1,s_2)+\delta$ is even). Since a quadrangulation with $n$ faces has $2n$ edges and $n+2-2g$ vertices, and since it is natural to expect each parity constraint to contribute an asymptotic factor $\frac{1}{2}$, the total number of “base configurations” we obtain is $\sim 3\times (2n) n^2/4 \cdot m_g(n)$, hence the denominator in .
We can now conclude the proof of Theorem \[thm:obs1\]. First, we can rewrite the decomposition equation as: $$\begin{aligned}
\label{eq:TutteKernel}
(1-6zL_0(z)) L_{g+1}(z)
-
3z\sum_{g_1+g_2=g+1,\atop g_1,g_2>0}
L_{g_1}(z)
L_{g_2}(z)
=
z A_g(z),\end{aligned}$$ which expresses the generating function $L_{g+1}(z)$ in terms of the lower genus functions $L_i(z)$ for $i=1..g$, and of the “unknown” quantity $A_g(z)$. We recall that $Q^\bullet_g(z)=2L_g(z)$ and , from which we observe that each term in the L.H.S. of has a dominant singularity at $z=\tfrac{1}{12}$ with the same order of magnitude. More precisely, for the first term, using , we obtain $(1-6zL_0(z))L_{g+1}(z)\sim 2^{1-5(g+1)}\tau_{g+1}(1-12z)^{1-\frac{5}{2}(g+1)}$. For product terms we have $L_{g_1}(z) L_{g_2}(z)\sim
2^{2-5(g+1)}\tau_{g_1}\tau_{g_2}(1-12z)^{1-\frac{5}{2}(g_1+g_2)}$. It follows, using standard transfer theorems for algebraic functions [@Flajolet] that when $n$ goes to infinity: $$\begin{aligned}
[z^{n-1}] A_g(z) \sim 12^n n^{\frac{5g+1}{2}}
2^{1-5(g+1)}\Gamma\left(\tfrac{5g+3}{2}\right)^{-1}
\left(\tau_{g+1} - \tfrac{1}{2}\sum_{g_1+g_2=g+1\atop g_1,g_2>0} \tau_{g_1}\tau_{g_2} \right).\end{aligned}$$ But from Lemma \[lemma:convergenceCell\], we have another expansion of the “unknown” coefficient $[z^{n-1}] A_g(z)$, namely: $$[z^{n-1}] A_g(z) =\mathbb{E}{\mathbf{X}}_g(1-{\mathbf{X}}_g) \cdot 3/2\cdot n^3 m_{g}(n-1)
\sim\mathbb{E}{\mathbf{X}}_g(1-{\mathbf{X}}_g)\cdot 3\cdot 2^{1-5g}\Gamma(\tfrac{5g-1}{2})^{-1} \tau_g n^{\frac{5g+1}{2}} 12^{n-1}.$$ Theorem \[thm:obs1\] follows by comparing the last two expansions of the “unknown” quantity $[z^{n-1}]A_g(z)$ (we recall that $\Gamma(\frac{5g+3}{2})/\Gamma(\tfrac{5g-1}{2})=\frac{(5g+1)(5g-1)}{4}$).
Remaining proofs, I: general properties
---------------------------------------
Because we will need to pick both edges and vertices at random, we first need a lemma that compares both:
\[lemma:vertexvsedge\] Given a quadrangulation $Q$ of genus $g$ with $n$ faces, there exists a probability measure $\mu_n^E$ on edges of $Q$ and a mapping $\phi:E(Q)\rightarrow V(Q)$ that associates to each edge of $E$ a vertex at distance at most one of one of its endpoints, such that the distance in total variation between $\mu_n^{E}$ and the uniform measure on edges, and between $\phi \circ \mu_n^{E}$ and the uniform measure on vertices, are both $O(\tfrac{1}{n})$.
Let $L$ be the l.1.f.m associated to $Q$ via the Marcus-Schaeffer bijection and let $v_0\in V(L)$. The map $L$ has $n+1-2g$ vertices, so it is possible to choose a set $E'_L$ of $n-2g$ edges of $L$ and an orientation of edges of $E'_L$ such that each vertex of $V\setminus\{v_0\}$ has exactly one outgoing edge from $E'_L$ (to see this, take a spanning tree of $L$ and orient edges towards $v_0$). If $e \in E'_L$, we let $v(e)$ be its source, which is an element of $V\setminus\{v_0\}$. The edge $e$ of $E'_L$ is associated, via the Marcus-Schaeffer bijection, to a face $f(e)$ of the quadrangulation $Q$ that is incident to the vertex $v(e)$. We let $E'_Q$ be the subset of edges of $Q$ that border a face of the form $f(e)$ for some $e\in E_L$ and that are oriented from white to black when going clockwise around $f(e)$ (in some fixed bicoloration of $Q$). If $\tilde{e}\in E'_Q$, corresponding to the face $f(e)$, we define $\phi(\tilde{e}):=v(e)$. Since $\tilde{e}$ and $\psi(\tilde{e})$ both border the face $f(e)$, they are at distance at most one from each other. Moreover, if we choose $\tilde{e}$ uniformly at random from $E'_Q$, then by construction $\psi(\tilde{e})$ is uniform in $V\setminus \{v_0\}$. Since $E'_Q$ contains $2(n-2g)$ edges of $Q$ (among $2n$) and $V\setminus\{v_0\}$ contains $n-2g$ vertices of $Q$ (among $n+2-2g$), we are done.
In the following discussion we will implicitly restrict ourselves to a subsequence along which we have the GHP distributional convergence: $$({{\mathbf{q}}_{n}^{(g)}},\tfrac{1}{n^{1/4}}\mathbf{d}_n,\mu_n)
\longrightarrow
({{\mathbf{q}}_\infty^{(g)}}, d_\infty, \mu_\infty).$$ We will need the following direct consequence of [@Chapuy:trisections Thm. 4]. We state separately a discrete and a continuous statement, although they are intimately related:
\[lemma:zeroProba\]
\(i) Let $({{\mathbf{q}}_\infty^{(g)}},d_\infty, \mu_\infty)$ be a Brownian map of genus $g$ and let $({\mathbf{v}}_1^\infty, {\mathbf{v}}_2^\infty, {\mathbf{v}}_3^\infty)$ chosen at random according to $\mu_\infty^{\otimes 3}$. Then almost surely we have $d_\infty ({\mathbf{v}}_1^\infty,{\mathbf{v}}_3^\infty) \neq
d_\infty ({\mathbf{v}}_2^\infty,{\mathbf{v}}_3^\infty)$.
\(ii) Fix $K\geq 0$, and pick three uniform random vertices ${\mathbf{v}}_1^n$, ${\mathbf{v}}_2^n$, ${\mathbf{v}}_3^n$ in ${{\mathbf{q}}_{n}^{(g)}}$. Then the probability that $|d({\mathbf{v}}_1^n,{\mathbf{v}}_3^n)-d({\mathbf{v}}_2^n,{\mathbf{v}}_3^n)|\leq K$ goes to zero when $n$ goes to infinity.
It is proved in [@Chapuy:trisections] that if ${\mathbf{v}}_1\in_u V({{\mathbf{q}}_{n}^{(g)}})$, the random measure $$\eta_n^{(g)}:=\displaystyle \tfrac{1}{|V({{\mathbf{q}}_{n}^{(g)}})|}\sum_{v \in V({{\mathbf{q}}_{n}^{(g)}})} \delta_{d_n(v,{\mathbf{v}}_1)/n^{1/4}}$$ converges in distribution to a random measure $\eta_g$ that, almost surely, has no atoms (this last fact following from the fact that it is true for the ISE measure, see e.g. [@MBMJanson], and from the relation between $\eta_g$ and ISE given in [@Chapuy:trisections]). Now for $\alpha>0$, let ${p_{n,\alpha}}:=\mathbf{P}\big\{|d({\mathbf{v}}_1^n,{\mathbf{v}}_3^n)-d({\mathbf{v}}_2^n,{\mathbf{v}}_3^n)|\leq \alpha n^{1/4}\big\} = \mathbf{E}\langle ({\eta_n^{(g)}})^{\otimes 2} | h_\alpha\rangle$ where $h_\alpha(x,y):=\mathbf{1}_{|y-x|\leq \alpha}$ (here for a measure $\nu$ and a function $h$ we note $\langle\nu|h\rangle:=\int h(x)d\nu(x)$). Convergence in law implies that $\lim_n \mathbf{E}\langle(\eta_n^{(g)})^{\otimes 2} | f \rangle = \mathbf{E} \langle \eta_g^{\otimes 2}| f\rangle$ for any bounded and continuous function $f$, so choosing $f=f_\alpha$ continuous such that $h_\alpha \leq f_\alpha \leq h_{2\alpha}$ we get $\limsup_n p^n_\alpha \leq \mathbf{E}\langle ({\eta_g})^{\otimes 2} | h_{2\alpha}\rangle$, and since $\eta_g$ has no atoms we get: $$\begin{aligned}
\label{eq:limsup}
\lim_{\alpha\rightarrow 0} \limsup_n {p_{n,\alpha}}=0,\end{aligned}$$ from which (ii) follows (in fact, in a much stronger form that allows $K$ to be as large as $o(n^{1/4})$).
Now, by GHP convergence and [@Miermont:tessellations Prop. 6] one can define on the same probability space $({{\mathbf{q}}_{n}^{(g)}},\tilde{\mathbf{v}}_1^n,\tilde{\mathbf{v}}_2^n,\tilde{\mathbf{v}}_3^n)$ and $({{\mathbf{q}}_\infty^{(g)}},\tilde{\mathbf{v}}_1^\infty, \tilde{\mathbf{v}}_2^\infty, \tilde{\mathbf{v}}_3^\infty)$ such that $\tilde{\mathbf{v}}_i^{M}$ is $o(1)$-close to ${\mathbf{v}}_i^{M}$ in total variation distance for each $i\in\{1,2,3\}$ and $M\in\{n,\infty\}$, and such that almost surely $|d_n(\tilde{\mathbf{v}}_i^n,\tilde{\mathbf{v}}_j^n)/n^{1/4}-d_\infty(\tilde{\mathbf{v}}_i^\infty, \tilde{\mathbf{v}}_j^\infty)|=o(1)$ for each $i$, $j$. Letting $q_\alpha:=\mathbf{P}\{|d_\infty ({\mathbf{v}}_1^\infty,{\mathbf{v}}_3^\infty) -
d_\infty ({\mathbf{v}}_2^\infty,{\mathbf{v}}_3^\infty)|\leq \alpha\}$, it easily follows that $$q_{\alpha/2} \leq \limsup_n {p_{n,\alpha}}.$$ From this implies that $\limsup_{\alpha\rightarrow 0} q_\alpha =0$, which implies (i).
Remaining proofs, II: Lemma \[lemma:convergenceCell\] {#sec:technical}
-----------------------------------------------------
Before proving Lemma \[lemma:convergenceCell\], we need to describe more precisely the objects Miermont’s bijection leaves us with. We use the same notation as in the previous section for objects counted by $A_g(z)$ (marked faces $F_1, F_2$, minimum label in each face $0,\delta$, marked corners $c_1,c_2$). We will introduce the refinement $$A_g(z) = \sum_{\epsilon\in\{-1,0,1\}} A_g^\epsilon(z)$$ where $A_g^\epsilon(z)$ counts the same objects as $A_g(z)$ but with the restriction that $\ell(c_2)-\ell(c_1)=\epsilon$. Unpacking the definitions in [@Miermont:tessellations] we have:
\[lemma:MiermontConstraints\] For each $\epsilon\in\{-1,0,1\}$, the labelled two-face maps counted by $[z^{n}]A^{\epsilon}_g(z)$ are in bijection with tuples $(Q,s_1,s_2,e_1,e_2)$ such that:
- $Q$ is a bipartite quadrangulation of genus $g$ with $n$ faces (unrooted);
- $s_1,s_2$ are two vertices of $Q$ and $e_1,e_2$ are two marked edges of $Q$;
- for $j=1..2$ let $m_j$ be the endpoint of $e_j$ closer from $s_j$, and let $\delta := d(s_1,m_1)+\epsilon-d(s_2,m_2).$ Then the quantity $d(s_1,s_2)+\delta$ is even.
- Label each vertex $v$ of the quadrangulation $Q$ by $\ell(v):=\min(d(v,s_1),d(v,s_2)+\delta)$, and orient each edge towards its vertex of minimum label [^3]. From an edge $e$, define the *leftmost geodesic oriented path* as the oriented path starting from $e$ and continuing after each edge with the first oriented edge encountered in counterclockwise order around its endpoint, stopped when it reaches $s_1$ or $s_2$. Then for $i=1..2$, the leftmost geodesic oriented path starting at $e_i$ ends at $s_i$.
Note that, since $Q$ is bipartite, the property $(M2)$ is equivalent to the following:
- $d(m_1,m_2) \equiv \epsilon \mod 2.$
As for the complicated property $(M3)$, up to subdominating cases, it can be rephrased in simpler terms closely related to nearest neighbours tessellations. Indeed, we have:
\[lemma:GeoToVor\] Let $b_g^\epsilon(n)$ be the number of tuples $(Q,s_1,s_2,e_1,e_2)$ satisfying (M0), (M1), (M2) of the last lemma, and such that moreover we have:
- $d(s_1,e_1) < d(s_1,e_2) -4$ and $
d(s_2,e_2) < d(s_2,e_1) -4 .$
Then for each $\epsilon\in \{-1,0,1\}$ we have $[z^n]A_g^{\epsilon}(z) = b^\epsilon_g(n) + o(n^3m_g(n))$.
Note that $(M'3)$ implies that $d(s_1,m_1) < d(s_1,m_2) -2$ and $
d(s_2,m_2) < d(s_2,m_1) -2.$
Let $(Q,s_1,s_2,e_1,e_2)$ satisfying the hypotheses of Lemma \[lemma:GeoToVor\]. Then we claim that it also satisfies the hypotheses of Lemma \[lemma:MiermontConstraints\]. Indeed define $\ell(v)=\min(d(s_1,v),d(s_2,v)+\delta)$ as in Lemma \[lemma:MiermontConstraints\]. We observe that (M’3) implies that $$d(s_1,m_1) < d(s_1,m_1)+(d(s_2,m_1)-d(s_2,m_2)+\epsilon) = d(s_2,m_1)+\delta,$$ which shows that the minimum in the definition of $\ell(v)$ for $v=m_1$ is reached only by its *first* argument. Similarly, for $v=m_2$ we have by (M’3) that: $$d(s_2,m_2) < d(s_2,m_2)+(d(s_1,m_2)-d(s_1,m_1)-\epsilon)
=d(s_1,m_2)-\delta,$$ which shows that the minimum in the definition of $\ell(v)$ for $v=m_2$ is reached only by its *second* argument. Thus the discussion in [@Miermont:tessellations Sec 2.2] (more precisely the first inclusion sign $\subsetneq$ in the last displayed equation of that section) precisely says that (M3) is satisfied.
Conversely assume the hypotheses of Lemma \[lemma:MiermontConstraints\]. By general properties of Miermont’s labelling (namely, the fact that leftmost oriented geodesic paths as defined in the lemma are, in particular, geodesic paths), property $(M3)$ ensures that the minima defining $\ell(m_1)=\min(d(m_1,s_1),d(m_1,s_2)+\delta)$ and $\ell(m_2)=\min(d(m_2,s_1),d(m_2,s_2)+\delta)=\min(d(m_2,s_1),d(m_1,s_1)+\epsilon)$ are reached respectively by their first and second argument (and possibly reached twice). This implies: $$d(s_1,m_1)+\epsilon \leq d(s_1,m_2), \ d(s_2,m_2)\leq d(m_1,s_2)+\epsilon.$$ Thus, if hypothesis (M’3) is *not* satisfied, it must hold that either $|d(s_1,m_1)-d(s_1,m_2)|\leq 2$ or $|d(s_2,m_2)-d(s_2,m_1)|\leq 2$. It thus suffices to show that there are at most $o(n^3m_g(n))$ tuples $(Q,s_1,s_2,e_1,e_2)$ such that one of these two properties holds. For this it suffices to show that if $({\mathbf{q}},{\mathbf{e}}_1) \in_u {\mathcal{Q}_n^{(g)}}$ is a random rooted quadrangulation and $({\mathbf{s}}_1,{\mathbf{s}}_2,{\mathbf{e}}_2)$ are two vertices and an edge chosen independently uniformly at random in ${\mathbf{q}}$, the probability that $|d({\mathbf{s}}_1,{\mathbf{e}}_2)-d({\mathbf{s}}_1,{\mathbf{e}}_2)|\leq 2$ or $|d({\mathbf{s}}_2,{\mathbf{e}}_2)-d({\mathbf{s}}_2,{\mathbf{e}}_1)|\leq 2$ goes to zero as $n$ goes to infinity. This directly follows from Lemmas \[lemma:vertexvsedge\] and \[lemma:zeroProba\](ii).
In view of getting rid of the constraint $(M'2)$, we state the following lemma:
\[lemma:equalContrib\] For any $\epsilon\in \{-1,0,1\}$ we have as $n$ goes to infinity: $$[z^n] A^\epsilon_g (z) \sim \frac{1}{3} [z^n]A_g(z).$$
This can be proved by asymptotic analysis of generating functions using a simple adaptation of the method developed in [@CMS] for the enumeration of labelled one-face maps by *scheme decomposition*: one can enumerate objects counted by $A^\epsilon_g(z)$ with this approach and realize that changing the parameter $\epsilon$ only affects the principal singularity by a factor $1-O((1-12z)^{1/4})$, from which the result follows. We leave details to the reader.
We are now ready to conclude the proof.
First, we remark that from the last lemma: $$\begin{aligned}
\label{eq:linearSmart}
[z^n] \big(A_g^0(z) + A_g^1(z)\big) \sim \frac{2}{3} [z^n] A_g(z),\end{aligned}$$ while from Lemma \[lemma:GeoToVor\] and the remark preceeding it, $[z^n] A_g^0(z) + A_g^1(z)$ is equivalent to the number of tuples $(Q,s_1,s_2,e_1,e_2)$ satisfying properties $(M0),(M1)$, and $(M'3)$ (note that property $(M'2)$ disappears since we sum over both parities $\epsilon=0,1$). We will thus focus on such objects in the rest of the proof.
We note that a bipartite quadrangulation with a marked edge $e_1$ and a marked vertex $v_1$ can be canonically rooted by orienting $e_1$ towards its unique endpoint at even distance from $v_1$. This gives a one-to-two correspondence between elements of $\mathcal{Q}^{g}_n$ with a marked vertex and (unrooted) bipartite quadrangulations of genus $g$ with a marked vertex and a marked unoriented edge. We thus have: $$\begin{aligned}
\label{eq:proba}
\frac{[z^n]\big(A_g^0(z) + A_g^1(z)\big)}
{(2n) \cdot n^2 \cdot m_g(n)}
\sim \frac{1}{2}\cdot \mathbf{P}\Big\{d({\mathbf{s}}_1,{\mathbf{e}}_1) < d({\mathbf{s}}_1,{\mathbf{e}}_2) -4, \
d({\mathbf{s}}_2,{\mathbf{e}}_2) < d({\mathbf{s}}_2,{\mathbf{e}}_1) -4 \Big\},\end{aligned}$$ where the probability is taken over ${{\mathbf{q}}_{n}^{(g)}}\in_u \mathcal{Q}^g_n$ with two uniform marked vertices ${\mathbf{s}}_1,{\mathbf{s}}_2$, a uniform marked edge ${\mathbf{e}}_2$ and ${\mathbf{e}}_1$ is the root edge (in the denominator, the factor $n^2$ corresponds to the choice of the two vertices, while the factor $(2n)$ corresponds to the choice of the edge ${\mathbf{e}}_2$).
We recall that we implicitly restrict ourselves to a subsequence along which the GHP distributional convergence $$({{\mathbf{q}}_{n}^{(g)}},\tfrac{1}{n^{1/4}}\mathbf{d}_n,\mu_n)
\longrightarrow
({{\mathbf{q}}_\infty^{(g)}}, d_\infty, \mu_\infty)$$ holds. We will make use of this convergence using a coupling between ${{\mathbf{q}}_{n}^{(g)}}$ and ${{\mathbf{q}}_\infty^{(g)}}$. More precisely, according to [@Miermont:tessellations Proposition 6], we can build ${{\mathbf{q}}_{n}^{(g)}}$ and ${{\mathbf{q}}_\infty^{(g)}}$ on the same probability space, and define a measure $\nu$ on ${{\mathbf{q}}_{n}^{(g)}}\times {{\mathbf{q}}_\infty^{(g)}}$ such that for each $k\geq 1$, if $(\tilde{\mathbf{w}}^i_n, \tilde{\mathbf{w}}^i_\infty)_{1\leq i \leq k} \sim \nu^{\otimes k}$ we have almost surely $|d_n(\tilde{\mathbf{w}}^i_n,\tilde{\mathbf{w}}^j_n)n^{-1/4}-d_\infty(\tilde{\mathbf{w}}_\infty^i, \tilde{\mathbf{w}}_\infty^j)| \leq \epsilon_n$ for any $i,j$, and moreover the law of $\tilde{\mathbf{w}}^i_n$ (resp. $\tilde{\mathbf{w}}^i_\infty)$ differs from $\mu_n$ (resp. $\mu_\infty$) by at most $\epsilon_n$ in total variation distance, where $\epsilon_n$ is a nonnegative real sequence going to zero when $n$ goes to infinity. We will apply this with $k=4$. Using Lemma \[lemma:vertexvsedge\], we can moreover assume the vertices $\tilde{\mathbf{w}}_3^n$ and $\tilde{\mathbf{w}}_4^n$ are at distance at most $2$ of two random edges $\tilde{\mathbf{e}}_1^n$ and $\tilde{\mathbf{e}}_2^n$ respectively, and that the law of $\tilde{\mathbf{e}}_1^n$ and $\tilde{\mathbf{e}}_2^n$ is $\epsilon_n$-close in total variation to that of two uniform random edges (if necessary, we modify the sequence $\epsilon_n$ for this to be true, still asking that $\epsilon_n\rightarrow 0$).
If $v_1,v_2,v_3,v_4$ are points (or subsets) in some metric space of underlying distance $d$, and $K\in\mathbb{R}$ let us define the events: $$V_K(v_1,v_2,v_3,v_4) := \{ d(v_1,v_3)<d(v_1,v_4)-K, d(v_2,v_4)<d(v_2,v_3)-K\}$$ $$W_K(v_1,v_2,v_3):=\{|d(v_1,v_3)-d(v_2,v_3)|\leq K\}.$$ By the assumptions made on the coupling between ${{\mathbf{q}}_{n}^{(g)}}$ and ${{\mathbf{q}}_\infty^{(g)}}$ and from the triangle inequality we have, denoting $\Delta$ the symmetric difference: $$\begin{aligned}
V_{4}(\tilde{\mathbf{w}}_1^n, \tilde{\mathbf{w}}_2^n, \tilde{\mathbf{e}}_1^n,\tilde{\mathbf{e}}_2^n)
\Delta
V_0^\infty(\tilde{\mathbf{w}}_1^\infty, \tilde{\mathbf{w}}_2^\infty, \tilde{\mathbf{w}}_3^\infty,\tilde{\mathbf{w}}_4^\infty)
\subset W_{\delta_n}^\infty(\tilde{\mathbf{w}}_1^\infty, \tilde{\mathbf{w}}_2^\infty, \tilde{\mathbf{w}}_3^\infty)
\cup W_{\delta_n}^\infty(\tilde{\mathbf{w}}_1^\infty, \tilde{\mathbf{w}}_2^\infty, \tilde{\mathbf{w}}_4^\infty)\end{aligned}$$ with $\delta_n = O(\epsilon_n+n^{-1/4})$. We thus have: $$\begin{aligned}
\limsup_n \big|\mathbf{P}
V_{4}(\tilde{\mathbf{w}}_1^n, \tilde{\mathbf{w}}_2^n, \tilde{\mathbf{e}}_1^n,\tilde{\mathbf{e}}_2^n)
-\mathbf{P}
V_0(\tilde{\mathbf{w}}_1^\infty, \tilde{\mathbf{w}}_2^\infty, \tilde{\mathbf{w}}_3^\infty,\tilde{\mathbf{w}}_4^\infty)
\big|
&\leq
\limsup_n
2 \mathbf{P}W_{\delta_n}^\infty(\tilde{\mathbf{w}}_1^\infty, \tilde{\mathbf{w}}_2^\infty, \tilde{\mathbf{w}}_3^\infty) \\
&\leq \limsup_n \left(\epsilon_n+
2 \mathbf{P}W_{\delta_n}^\infty({\mathbf{w}}_1^\infty, {\mathbf{w}}_2^\infty, {\mathbf{w}}_3^\infty)\right)\end{aligned}$$ where $({\mathbf{w}}_i^\infty)_{1\leq i\leq 3} \sim \mu_\infty^{\otimes 3}$ are three random vertices in ${{\mathbf{q}}_\infty^{(g)}}$ chosen according to $\mu_\infty$, and where we just used the definition of total variation distance. From Lemma \[lemma:zeroProba\](i), the last $\limsup$ is equal to zero, which implies: $$\begin{aligned}
\limsup_n \big|\mathbf{P}
V_{4}({\mathbf{w}}_1^n, {\mathbf{w}}_2^n, {\mathbf{e}}_1^n,{\mathbf{e}}_2^n)
-\mathbf{P}
V_0({\mathbf{w}}_1^\infty, {\mathbf{w}}_2^\infty, {\mathbf{w}}_3^\infty,{\mathbf{w}}_4^\infty)
\big|
&=0\end{aligned}$$ where ${\mathbf{w}}_1^n, {\mathbf{w}}_2^n, {\mathbf{e}}_1^n,{\mathbf{e}}_2^n$ are two vertices and two edges of ${{\mathbf{q}}_{n}^{(g)}}$ chosen independently uniformly at random, and where $({\mathbf{w}}_i^\infty)_{1\leq i\leq 4} \sim \mu_\infty^{\otimes 4}$ are uniform in ${{\mathbf{q}}_\infty^{(g)}}$.
Now by rerooting invariance of random quadrangulations $\mathbf{P}
V_{4}({\mathbf{w}}_1^n, {\mathbf{w}}_2^n, {\mathbf{e}}_1^n,{\mathbf{e}}_2^n)$ is equal to the probability appearing in the R.H.S. of , while it follows directly from Lemma \[lemma:zeroProba\](i) and the Fubini theorem that the quantity $
\mathbf{P}
V_0({\mathbf{w}}_1^\infty, {\mathbf{w}}_2^\infty, {\mathbf{w}}_3^\infty,{\mathbf{w}}_4^\infty)$ is equal to $\mathbf{E}{\mathbf{X}}_g(1-{\mathbf{X}}_g)$. This concludes the proof.
To be fully complete we also state the:
The only thing to prove is that $\mathbf{E}\mathbf{X}_g = \tfrac{1}{2}$, which is a direct consequence of Lemma \[lemma:zeroProba\].
Three marked points (proof of Theorem \[thm:3points\])
======================================================
In this section we sketch the proof of Theorem \[thm:3points\]. We will insist on the combinatorial decompositions and the computation, since the details of the convergence results are very similar to what we did in the previous section.
We first need some definitions from [@CMS; @Chapuy:trisections]. If $L$ is a one-face map, its *skeleton* is the map obtained by removing all vertices of degree $1$ in $L$, and continuing to do so recursively until only vertices of degree at least $2$ remain. Vertices of a one-face map that are vertices of degree at least $3$ of its skeleton are called *nodes*. A node $v$ that has degree $k$ in the skeleton is called a $k$-node (note that its degree as a vertex in the one-face map can be larger than $k$). A one-face map is *dominant* if all vertices of its skeleton have degree at most $3$, *i.e.* if all its nodes are $3$-nodes. It is proved in [@CMS] that for fixed $g$, as $n$ goes to infinity, a proportion at least $1-O(n^{-1/4})$ of l.1.f.m. of genus $g$ with $n$ edges are dominant. By Euler’s formula, a dominant one-face map has $4g-2$ nodes.
Following [@Chapuy:trisections], we introduce the operation of *opening*. If $L$ is a one-face map and $v$ is a $3$-node of $L$, the *opening* of $v$ is the operation that consists in replacing $v$ by three new vertices, each linked to one edge of the skeleton, and distributing the three (possibly empty) subtrees attached to $v$ among these new vertices as on the following figure:
{width="0.4\linewidth"}
Following [@Chapuy:trisections][^4], we distinguish two types of $3$-nodes in a one-face map: *intertwined nodes*, that are such that their opening results in a one-face map of genus $g-1$ with three marked vertices; and *non-intertwined nodes*, that are such that their opening results in a map of genus $g-2$ with three faces, and one marked vertex inside each face (here the map can be disconnected, and its genus and number of faces are defined additively on connected components). The *trisection lemma* [@Chapuy:trisections Lemma 5], which is the key result underlying this section, asserts that any dominant map of genus $g\geq 1$ has exactly $2g$ intertwined nodes, hence $2g-2$ non-intertwined ones.
It follows that the number $K_{g+2}(n)$ of l.1.f.m. of genus $g+2$ with $n$ edges whose root edge is a skeleton-edge leaving a *non-intertwined* $3$-node satisfies: $$\begin{aligned}
\label{eq:doubleRooting}
K_{g+2}(n)\sim\frac{6(g+1)}{2n} [z^n] L_{g+2}(z).\end{aligned}$$ Indeed, the first-order contribution is given by dominant l.1.f.m., and in a dominant l.1.f.m. of genus $g+2$ we can choose $3(2(g+2)-2)=6(g+1)$ edges outgoing from a non-intertwined node as a new root edge, but we obtain each map $2n$ times in this way (since maps counted by $L_{g+2}(z)$ are already rooted at one of their $2n$ oriented edges).
We are now going to obtain another expression for the number $K_{g+2}(n)$ by performing a combinatorial decomposition. Comparing the two expressions will, in the end, lead us to Theorem \[thm:3points\].
Let $L$ be a dominant l.1.f.m of genus $g+2$ whose root edge is a skeleton-edge leaving a non-intertwined $3$-node $v$. We distinguish three cases, according to what happens when we perform the opening of the node $v$ (see Figure \[fig:Tutte3\]):
- we disconnect the map into three components;
- we disconnect the map into two components;
- we do not disconnect the map.
We let $C_{g+2}^{(i)}(z)$, $C_{g+2}^{(ii)}(z)$, $C_{g+2}^{(iii)}(z)$ be the generating function for these three cases, respectively.
![The three cases for a one-face map of genus $g+2$ rooted at skeleton edge leaving a non-intertwined $3$-node $v$.[]{data-label="fig:Tutte3"}](decomp3.pdf){width="\linewidth"}
Configurations corresponding to (i) can be reconstructed by starting with three rooted l.1.f.m. of positive genera summing up to $g+2$, and joining the three root vertices by new edges to a new vertex $v$. The generating function for the contribution of this case is thus: $$\begin{aligned}
\label{eq:case1}
C_{g+2}^{(i)}(z) = (3zL_0(z))^3
\sum_{g_1+g_2+g_3=g+2\atop g_1,g_2,g_3>0} L_{g_1}(z)L_{g_2}(z)L_{g_3}(z)\end{aligned}$$ where for each new edge a factor $3zL_0(z)$ takes into account the increment of this edge, and the attachment of a rooted tree (possibly empty) in the newly created corner (see Figure \[fig:Tutte3\]–Left).
Configurations corresponding to (ii) can be reconstructed by joining with a new edge the root vertex of a l.1.f.m. to the root vertex of another one which is rooted at a *non-isthmic* edge of its skeleton (see Figure \[fig:Tutte3\]–Center). Now, arguing as in the previous section, for each $h\geq 1$, the generating function $S_{h}(z)$ of l.1.f.m. of genus $h$ rooted at a non-isthmic edge of their skeleton satisfies: $$L_h(z) = S_h(z) + 3z\sum_{g_1+g_2=h\atop g_1,g_2\geq 0} L_{g_1}(z)L_{g_2}(z),$$ from which we get: $$S_h(z)=(1-6zL_0(z))L_h - 3z \sum_{g_1+g_2=h\atop g_1,g_2>0} L_{g_1}(z)L_{g_2}(z).$$ It follows that the contribution for case (ii) is given by: $$\begin{aligned}
\label{eq:case2}
C_{g+2}^{(ii)} =
3\cdot (3z L_0(z)) \sum_{h+h'=g+2\atop h,h'>0} L_{h'}(z) \left(
(1-6zL_0(z))L_h - 3z \sum_{g_1+g_2+g_3=h\atop g_1,g_2>0} L_{g_1}(z)L_{g_2}(z)\right),\end{aligned}$$ where as before the factor $3zL_0(z)$ takes into account the increment of the newly created edge, and the (possibly empty) rooted tree to attach in the newly created corner, and where the global factor of $3$ takes into account the choice of the root edge among the three skeleton-edges incident to the newly created vertex.
Summing up and we obtain the leading-order contribution for the sum of the first two cases: $$C_{g+2}^{(i)}(z) + C_{g+2}^{(ii)} (z) \sim C\cdot (1-12z)^{\frac{3}{2}-\frac{5}{2}(g+2)}$$ with $$\begin{aligned}
C&=& 2^{-5(g+2)} \sum_{\scriptscriptstyle g_1+g_2+g_3=g+2} \tau_{g_1}\tau_{g_2}\tau_{g_3}
+
\frac{3\cdot 4}{2} 2^{-5(g+2)}
\sum_{\scriptscriptstyle g_1+g_2=g+2} \tau_{g_1}\tau_{g_2}
-
3\cdot 2^{-5(g+2)}
\sum_{\scriptscriptstyle g_1+g_2+g_3=g+2} \tau_{g_1}\tau_{g_2} \tau_{g_3}\\
&=&
2^{-5(g+2)} \left(
6\cdot
\sum_{\scriptscriptstyle g_1+g_2=g+2} \tau_{g_1}\tau_{g_2}
-2\cdot
\sum_{\scriptscriptstyle g_1+g_2+g_3=g+2} \tau_{g_1}\tau_{g_2} \tau_{g_3}
\right)\end{aligned}$$ where we have used that $L_0(\frac{1}{12})=2$, and all sums are taken over positive indices ([*i.e.*]{} $g_1,g_2,g_3 >0$).
Now, the leading-order contribution for the sum of three cases (i), (ii), (iii), which from corresponds to the dominant singularity of the generating function $3(g+1) \int L_{g+2}(z) \frac{dz}{z}$ is given by (since all series are algebraic we can integrate expansions with no fear): $$3(g+1) \frac{1}{\frac{3}{2}-\frac{5}{2}(g+2)} 2^{1-5(g+2)} \tau_{g+2} (1-12z)^{\frac{3}{2}-\frac{5}{2}(g+2)}.$$ Taking the difference with the previous expression, we obtain that the leading order contribution corresponding to case (iii) is given by $$\begin{aligned}
\label{eq:case3}
C_{g+2}^{(iii)}(z) \sim C' 2^{-5(g+2)}(1-12)^{\frac{3}{2}-\frac{5}{2}(g+2)}\end{aligned}$$ where: $$C'= \frac{12(g+1)}{5g+7} \tau_{g+2}-\left(
6\cdot
\sum_{\scriptscriptstyle g_1+g_2=g+2} \tau_{g_1}\tau_{g_2}
-2\cdot
\sum_{\scriptscriptstyle g_1+g_2+g_3=g+2} \tau_{g_1}\tau_{g_2} \tau_{g_3}
\right)$$ This expression can be considerably simplified. To this end, define the formal power series $U(s)=\sum_{g\geq 1} \tau_g s^g$. Then the $t_g$-recurrence is equivalent to the equation: $$\begin{aligned}
\label{eq:tgdiff}
U(s)=\tfrac{s}{3} + \tfrac{1}{2}U(s)^2 + \frac{s}{3}
(5(\tfrac{sd}{ds})+1)
(5(\tfrac{sd}{ds})-1)
U(s).\end{aligned}$$ In view of the bi- and tri-linear sums appearing in the definition of $C'$, we would like to find an equation involving the series $6U(s)^2-2U(s)^3$. Luckily, we have:
\[lemma:eliminate\] The following differential equation holds: $$\begin{aligned}
\label{eq:tgdiff2}
\tfrac{4}{15}
(5\tfrac{sd}{ds}-3 )_{((5))} \big(s^2U\big)
=
-(5(\tfrac{sd}{ds})-3) \big(6U^2-2U^3\big)
+ 12 (\tfrac{sd}{ds}-1)\big(U-\tfrac{s}{3}\big)
- 28 s^2 \end{aligned}$$ where we use the notation $(5\tfrac{sd}{ds}-3 )_{((5))} =
(5\tfrac{sd}{ds}-3 )(5\tfrac{sd}{ds}-5 )(5\tfrac{sd}{ds}-7 )(5\tfrac{sd}{ds}-9 )(5\tfrac{sd}{ds}-11)$.
Extracting the coefficient of $s^{g+2}$ in , we directly obtain that the constant $C'$ can be rewritten in the much simpler form: $$C' = \frac{4}{15} (5g+5)(5g+3)(5g+1)(5g-1) \tau_{g}.$$
To sum up the present discussion, we have determined the first order asymptotic of the generating function $C_{g+2}^{(iii)}(z)$ of rooted maps counted by case (iii). Applying standard transfer theorems, the corresponding coefficient $c_{g+2}^{(iii)}(n):=[z^n]C_{g+2}^{(iii)}(z)$ satisfies: $$\begin{aligned}
\label{eq:cg3}
c_{g+2}^{(iii)}(n)\sim \frac{1}{15} 2^{6-5(g+2)} / \Gamma(\tfrac{5}{2}g-\tfrac{1}{2}) \tau_g \cdot n^{\frac{5}{2}(g+1)} 12^n,\end{aligned}$$ where we have used that $(5g+5)(5g+3)(5g+1)(5g-1) \Gamma(\tfrac{5}{2}g-\tfrac{1}{2})=2^4\cdot \Gamma(\tfrac{5(g+2)}{2}-\tfrac{3}{2})$
It is now time to apply Miermont’s bijection. If we disconnect the three endpoints belonging to the skeleton and the root vertex in a map from case (iii), we obtain a labelled map of genus $g$ with three faces, with one marked vertex inside each face, subject to the constraint that those three vertices have the same label (see Figure \[fig:Tutte3\]-Right). Miermont’s bijection transforms this object into a bipartite quadrangulation of genus $g$ with *six* marked vertices $(s_1,s_2,s_3,v_1,v_2,v_3)$, such that for $i=1..3$ the source $v_i$ is closer from the vertex $s_i$ than from the two other vertices $s_j$ (to see this, write precisely the inequalities analogue to as in the previous section). Arguing as in the previous section (see the sketch of proof below), up to subdominating cases, this property asymptotically characterizes those configurations, and we get:
\[combiToMoment3points\] The number $c_{g+2}^{(iii)}(n)$ of configurations in case (iii) satisfies: $$\frac{c_{g+2}^{(iii)}(n)}{n^5/4 \cdot 2^{-2} m_g(n)} \sim \mathbf{E}[{\mathbf{Y}}_g^{(1:3)}{\mathbf{Y}}_g^{(2:3)}{\mathbf{Y}}_g^{(3:3)}].$$
The reader can understand heuristically the denominator in the previous expression as follows. The factor $n^5/4$ comes from the fact that we have $\sim n^6$ ways to mark 6 vertices (among $n+2-2g$) but that the quadrangulation is unrooted so we divide by $4n$. The factor $2^{-2}$ corresponds to the fact that we have two parity constraints relating the distances of the six points together (these constraints enable us to choose the delays in such a way that the target vertices get the same label while respecting the parity constraints on delays required by Miermont’s bijection). We only sketch the proof of the lemma, since it is similar to what we did in the previous section.
First, $A(n):=2n \cdot c_{g+2}^{(iii)}(n)$ counts *rooted* labelled three-face maps of genus $g$ with $n$ edges, with faces numbered $F_1,F_2,F_3$, with three marked vertices $v_1,v_2,v_3$ such that $v_i$ is incident to the face $F_i$ only, and such that $\ell(v_1)=\ell(v_2)=\ell(v_3)$. For $(\epsilon_2,\epsilon_3)\in\{0,1\}^2$, we introduce a variant $A^{\epsilon_2,\epsilon_3}(n)$ of this number, counting the same objects but where the last property is replaced by $\ell(v_1)=\ell(v_2)-\epsilon_2=\ell(v_3)-\epsilon_3$. For such an object we let $\delta_i$ be the minimum label in face $F_i$ for $i=1,2,3$, and we fix a translation class of labels by assuming that $\delta_1=0$. We also note $\epsilon_1:=0$.
Let $L$ be a three-face map counted by $A^{\epsilon_2,\epsilon_3}(n)$ and $Q$ be its associated quadrangulation by Miermont’s bijection. Then $Q$ is a bipartite quadrangulation of genus $g$ with $n$ faces, carrying three source vertices $s_1,s_2,s_3$ and the three marked vertices $v_1,v_2,v_3$, and is such that $$\begin{aligned}
\label{eq:constraints3}
\ell(v_i) = d(v_i,s_i)+\delta_i \leq d(v_i,s_j)+\delta_j, i\neq j.\end{aligned}$$ Indeed this equation says that the minimum defining the label $\ell(v_i):=\min_{1\leq j\leq 3} d(v_i,s_j)+\delta_j$ in the Miermont labelling of the delayed quadrangulation $Q$ is reached by its $i$-th argument, which corresponds to the fact that vertex $v_i$ is incident to the face $F_i$ in $L$. Writing that $\ell(v_i)-\epsilon_i =\ell(v_j)-\epsilon_j$ and applying , we find that : $$\begin{aligned}
\label{eq:voro3}
d(v_i,s_i)-\epsilon_i \leq d(v_j,s_i)-\epsilon_j.\end{aligned}$$ Since $|\epsilon_i-\epsilon_j|\leq 2$ we can say, loosely speaking, that up to an error at most $2$, $s_i$ is closer from $v_i$ than from other $v_j$’s in $Q$. Note that another constraint from Miermont’s bijection is that, in $Q$, we have that $d(s_i,s_j)\equiv \delta_i+\delta_j\mod 2$ for all $i,j$, or equivalently, from , that $d(v_i,v_j)\equiv \epsilon_i-\epsilon_j \mod 2$.
Conversely, let $B^{\epsilon_2,\epsilon_3}(n)$ be the number of rooted bipartite quadrangulations of genus $g$ with $n$ faces and six marked vertices $s_1,s_2,s_3,v_1,v_2,v_3$ such that we have, for all $i\neq j$: $$\begin{aligned}
\label{eq:constraints3Strong}
d(v_i,s_i) < d(v_j,s_i)-2\end{aligned}$$ and such that $d(v_i,v_j)\equiv \epsilon_i-\epsilon_j\mod 2$. Given such an object, defining for each vertex $\ell(v)=\min_{1\leq i \leq 3}d(s_i,v)+\delta_i$, where $\delta_i:= d(v_i,s_i)-\epsilon_i+\epsilon_1-d(v_1,s_1)$, we see from that the minimum defining $\ell(v_i)$ is reached only by its $i$-th argument, and that $\ell(v_1)=\ell(v_2)-\epsilon_2=\ell(v_3)-\epsilon_3$. This ensures that the three-face map associated to such a quadrangulation by the (reverse) Miermont bijection is one of the objects counted by $A^{\epsilon_2,\epsilon_3}(n)$. In fact, the converse is true up to asymptotically negligible terms. Indeed, configurations counted by $A^{\epsilon_1,\epsilon_2}(n)-B^{\epsilon_2,\epsilon_3}(n)$ correspond to cases where for at least one $i\neq j$, holds but does not: such configurations are few by Lemma \[lemma:zeroProba\](ii). Details are similar to the proof of Lemma \[lemma:GeoToVor\] and we obtain that $$B^{\epsilon_2,\epsilon_3}(n) = 2 A^{\epsilon_1,\epsilon_2}(n) + o(n^6 m_g(n)),$$ where the factor of $2$ comes from the 2-to-1 nature of Miermont’s bijection.
Now, similarly as in Lemma \[lemma:equalContrib\], it is easy to see that for different $\epsilon_1,\epsilon_2$ the numbers $A^{\epsilon_1,\epsilon_2}(n)$ have the same first order contribution and: $$\sum_{(\epsilon_1,\epsilon_2)\in\{0,1\}^2} A^{\epsilon_1,\epsilon_2}(n) \sim 4 \cdot A^{0,0}(n).$$ Now $\sum_{(\epsilon_1,\epsilon_2)\in\{0,1\}^2} B^{\epsilon_2,\epsilon_3}(n) $ counts rooted bipartite quadrangulations with marked vertices $v_1,v_2,v_3,$ $s_1,s_2,s_3$ such that holds, and in which no parity constraints remain. Recalling that $c_{g+2}^{(iii)}(n)=\tfrac{1}{2n}A^{0,0}(n)$ we finally get $$c_{g+2}^{(iii)}(n) \sim \frac{1}{8\cdot 2n} n^6 m_g(n)
\cdot \mathbf{P}\big\{\forall\, 1\leq i\neq j \leq 3:\, d({\mathbf{v}}_i,{\mathbf{s}}_i) < d({\mathbf{v}}_j,{\mathbf{s}}_i)-2\big\}$$ where the probability is over ${{\mathbf{q}}_{n}^{(g)}}\in_u{\mathcal{Q}_n^{(g)}}$ and six uniform independent vertices $({\mathbf{v}}_1,{\mathbf{v}}_2,{\mathbf{v}}_3,{\mathbf{s}}_1,{\mathbf{s}}_2,{\mathbf{s}}_3)$ in ${{\mathbf{q}}_{n}^{(g)}}$. Finally, arguing exactly as in the proof of Lemma \[lemma:convergenceCell\], the last probability converges to $\mathbf{E}[{\mathbf{Y}}_g^{(1:3)}{\mathbf{Y}}_g^{(2:3)}{\mathbf{Y}}_g^{(3:3)}]$ and we are done.
From the last lemma and the expansion of $m_g(n)$ it follows that $$c_{g+2}^{(iii)}(n) \sim 2^{-2-5g}/\Gamma(\tfrac{5}{2}g-\tfrac{1}{2})\tau_g
\cdot \mathbf{E}[{\mathbf{Y}}_g^{(1:3)}{\mathbf{Y}}_g^{(2:3)}{\mathbf{Y}}_g^{(3:3)}]
\cdot n^{5+\frac{5}{2}(g-1)} 12^n.$$ Comparing with the previously obtained expansion of $c_{g+2}^{(iii)}(n)$ we find: $$\mathbf{E}[{\mathbf{Y}}_g^{(1:3)}{\mathbf{Y}}_g^{(2:3)}{\mathbf{Y}}_g^{(3:3)}] \sim \frac{1}{15 \cdot 2^2} =\frac{1}{60}$$ as claimed!
It only remains to prove Lemma \[lemma:eliminate\]:
We give a simple proof based on linear algebra, relatively brutal and (therefore) easily computerized. Let $E_0$ denote Equation , and consider its derivatives $E_i:=(\tfrac{d}{ds})^i E_0$ for $i\in[1..3]$. We thus obtain a polynomial system of four equations $\{E_i,i\in[0..3]\}$, involving the quantities $U_i=(\tfrac{d}{ds})^i U(s)$ for $i=0..5$. This system is *linear* and *triangular* in $U_2,U_3,U_4,U_5$ (note that it is *not* linear in $U_0$ and $U_1$). We can then solve for these four quantities and we obtain an expression of each $U_i$ for $i\in[2..5]$ as a (nonlinear) polynomial of $U_0=U(s)$ and $U_1=\tfrac{d}{ds}U(s)$ (with coefficients that are Laurent polynomials of $s$). Now expand the quantity $(5\tfrac{sd}{ds}-3 )_{((5))} \big(s^2U\big)$ as a linear combination of the $U_i$’s, and substitute the expressions just obtained of $U_i$ for $i=2..5$ in it. We obtain an equation of the form: $$(5\tfrac{sd}{ds}-3 )_{((5))} \big(s^2U\big) = \mbox{Polynomial}(s,s^{-1},U(s),\tfrac{d}{ds}U(s))$$ which, computations made, is .
### Acknowledgements {#acknowledgements .unnumbered}
I thank Jean-François Marckert and Grégory Miermont for interesting discussions related to the content of this note.
[^1]: Support from *Agence Nationale de la Recherche*, grant number ANR 12-JS02-001-01 “Cartaplus”, and from the City of Paris, grant “Émergences Paris 2013, Combinatoire à Paris”. Email: [guillaume.chapuy@liafa.univ-paris-diderot.fr]{}.
[^2]: if $U_1,U_2$ are two independent uniforms on $[0,1]$ and $I_1, I_2, I_3$ are the lengths of the three intervals they define, then $\mathbf{E} (I_1I_2I_3)=2\int_0^1dx\int_0^x dy \cdot y (y\!-\!x)(1\!-\!x\!-\!y) = \frac{1}{60}$. For a combinatorial calculation, notice that $\mathbf{E} (I_1I_2I_3)$ is the probability that five independent uniforms $U_1,U_2,V_1,V_2,V_3$ are ordered as $V_1<U_{1}\wedge U_2<V_2<U_1\vee U_{2}<V_3$, which is clearly equal to $\frac{2}{5!}=\tfrac{1}{60}$.
[^3]: As observed in [@Miermont:tessellations] under assumption (M2) the label varies by $\pm1$ along each edge so this is well defined.
[^4]: Strictly speaking, these notions are defined only for dominant maps in that reference. Here it will be convenient for the presentation of the decompositions to extend them to general $3$-nodes – but this is not a fundamental need, since in all quantities involved in our discussion will be led by dominant maps at the first order.
| tomekkorbak/pile-curse-small | ArXiv |
Q:
How to show information when I will come in a range of created location
Sorry if my question could be "silly" but I am new Android programmer.
I've wrote the app based on that example:
http://developer.android.com/training/location/receive-location-updates.html
Everything works fine. It show my current location and I receive location updates.
I've added a specific location.
When I come in a range of that location only show the text "ERROR".
What I did wrong?
public void firstLocation (View v) {
final Location loc = new Location ("");
loc.setLatitude(47.2175723);
loc.setLongitude(17.1427797);
loc.setAccuracy(10);
if (mLocationClient.getLastLocation() == loc) {
Toast.makeText(this, "SOME INFORMATION",
Toast.LENGTH_SHORT).show();
}
else
Toast.makeText(this, "ERROR",
Toast.LENGTH_SHORT).show();
}
A:
What you are looking for is called Proximity Alerts.
Proximity Alert gives you notification (triggers piece of code) when you come in or goes out from particular location range.
http://androidmyway.wordpress.com/2012/08/07/proximity-alert-in-android/#more-143
or
http://myandroidtuts.blogspot.in/2012/10/proximity-alerts.html
can help you to start.
| tomekkorbak/pile-curse-small | StackExchange |
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What's next for Netflix? The fourth season of Arrested Development. All 15 episodes of the cult hit will hit Netflix on May 26th. | tomekkorbak/pile-curse-small | Pile-CC |
---
abstract: 'We consider the generalized Segal–Bargmann transform, defined in terms of the heat operator, for a noncompact symmetric space of the complex type. For radial functions, we show that the Segal–Bargmann transform is a unitary map onto a certain $L^{2}$ space of meromorphic functions. For general functions, we give an inversion formula for the Segal–Bargmann transform, involving integration against an unwrapped version of the heat kernel for the dual compact symmetric space. Both results involve delicate cancellations of singularities.'
address:
- |
University of Notre Dame\
www.nd.edu/\~ bhall
- Robert Morris University
author:
- 'Brian C. Hall'
- 'Jeffrey J. Mitchell'
date: January 2005
title: 'The Segal–Bargmann transform for noncompact symmetric spaces of the complex type'
---
Introduction\[intro.sec\]
=========================
The Segal–Bargmann transform for $\mathbb{R}^{d}$ [@Se1; @Se2; @Se3; @Ba1] is a widely used tool in mathematical physics and harmonic analysis. The transform is unitary map $C_{t}$ from $L^{2}(\mathbb{R}^{d})$ onto $\mathcal{H}L^{2}(\mathbb{C}^{d},\nu_{t}),$ where $\nu_{t}$ is a certain Gaussian measure on $\mathbb{C}^{d}$ (depending on a positive parameter $t$) and where $\mathcal{H}L^{2}$ denotes the space of holomorphic functions that are square integrable with respect to the indicated measure. (See Section \[rn.sec\] for details.) From the point of view of harmonic analysis, one can think of the Segal–Bargmann transform as combining information about a function $f(x)$ on $\mathbb{R}^{d}$ with information about the Fourier transform $\hat{f}(\xi)$ into a single holomorphic function $(C_{t}%
f)(x+i\xi).$ From the point of view of quantum mechanics for a particle moving in $\mathbb{R}^{d},$ one can think of the Segal–Bargmann transform as a unitary map between the position Hilbert space $L^{2}(\mathbb{R}^{d})$ and the phase space Hilbert space $\mathcal{H}L^{2}(\mathbb{C}%
^{d},\nu_{t}).$ In this setting, the parameter $t$ can be interpreted as Planck’s constant. Conceptually, the advantage of applying the Segal–Bargmann transform is that it gives a description of the state of the particle that is closer to the underlying classical mechanics, because we now have a function on the classical phase space rather than on the classical configuration space. See Section 2, [@mexnotes], and [@Fo] for more information about the Segal–Bargmann transform for $\mathbb{R}^{d}$ and its uses.
In the paper [@H1], the first author introduced a generalization of the Segal–Bargmann transform in which the configuration space $\mathbb{R}^{d}$ is replaced by a connected compact Lie group $K$ and the phase space $\mathbb{C}^{d}$ is replaced by the complexification $K_{\mathbb{C}}$ of $K.$ (See also the expository papers [@bull; @range; @mexnotes].) The complex group $K_{\mathbb{C}}$ can also be identified in a natural way with the cotangent bundle $T^{\ast}(K),$ which is the usual phase space associated to the configuration space $K.$ A main result of [@H1] is a unitary map $C_{t}$ from $L^{2}(K)$ onto $\mathcal{H}L^{2}(K_{\mathbb{C}},\nu_{t})$, where $\nu_{t}$ is a certain heat kernel measure on the complex group $K_{\mathbb{C}%
}.$ The transform itself is given by applying the time-$t$ heat operator to a function $f$ in $L^{2}(K)$ and then analytically continuing the result from $K$ to $K_{\mathbb{C}}.$ The paper [@H2] then gave an inversion formula for $C_{t}$ in which to recover the function $f$ on $K$ one integrates the holomorphic function $C_{t}f$ over each fiber in $T^{\ast}(K)\cong
K_{\mathbb{C}}$ with respect to a suitable heat kernel measure. See also [@KTX] for a study of the Segal–Bargmann transform, defined in terms of the heat operator, on the Heisenberg group.
The motivation for the generalized Segal–Bargmann transform for $K$ was work of Gross in stochastic analysis, specifically the Gross ergodicity theorem [@Gr] for the loop group over $K.$ See [@bull; @GM; @HS; @ergodic] for connections between the generalized Segal–Bargmann transform and stochastic analysis. The generalized Segal–Bargmann transform has also been used in the theory of loop quantum gravity [@A; @Th; @TW1; @TW2; @Das1; @Das2]. It has a close connection to the canonical quantization of $(1+1)$-dimensional Yang–Mills theory [@Wr; @DH1; @ymcoherent]. It can be understood from the point of view of geometric quantization [@geoquant; @FMMN; @FMMN2]. Most recently, it has been used in studying nonabelian theta functions and the conformal blocks in WZW conformal field theory [@FMN1; @FMN2]. (See also [@Ty].) See the paper [@bull] for a survey of the generalized Segal–Bargmann transform and related notions.
In the paper [@St], Stenzel extended the results of [@H1; @H2] from the case of compact Lie groups to the case of general compact symmetric spaces. We give here a schematic description of Stenzel’s results; see Section \[compact.sec\] for details. If $X$ is a compact symmetric space, there is a natural complexification $X_{\mathbb{C}}$ of $X.$ There is a natural diffeomorphism between the cotangent bundle $T^{\ast}(X)$ and the complexification $X_{\mathbb{C}}.$ Under this diffeomorphism, each fiber in $T^{\ast}(X)$ maps to a set inside $X_{\mathbb{C}}$ that can be identified with the *dual noncompact symmetric space to* $X.$ (For example, if $X$ is the $d$-sphere $S^{d},$ then each fiber in $T^{\ast}(S^{d})$ gets identified with hyperbolic $d$-space.) Thus the complexified symmetric space $X_{\mathbb{C}}$ is something like a product of the compact symmetric space $X$ and the dual noncompact symmetric space. Since each fiber in $T^{\ast}(X)\cong X_{\mathbb{C}}$ is identified with this noncompact symmetric space, we can put on each fiber the *heat kernel measure* for that noncompact symmetric space (based at the origin in the fiber).
The Segal–Bargmann transform now consists of applying the time-$t$ heat operator to a function in $L^{2}(X)$ and analytically continuing the resulting function to $X_{\mathbb{C}}.$ The first main result is an inversion formula: to recover a function from its Segal–Bargmann transform, one simply integrates the Segal–Bargmann transform over each fiber in $T^{\ast}(X)\cong
X_{\mathbb{C}}$ with respect to the appropriate heat kernel measure. The second main result is an isometry formula: the $L^{2}$ norm of the original function can be computed by integrating the absolute-value squared of the Segal–Bargmann transform, first over each fiber using the heat kernel measure and then over the base with using the Riemannian volume measure. See Theorem \[compact.thm\] in Section \[compact.sec\] for details. See Section 3.4 of [@bull] for more information on the transform for general compact symmetric spaces and [@range; @KR1; @KR2; @HM1; @HM2] for more on the special case in which $X$ is a $d$-sphere.
Since we now have a Segal–Bargmann transform for the Euclidean symmetric space $\mathbb{R}^{d}$ and for compact symmetric spaces, it is natural to consider also the case of noncompact symmetric spaces. Indeed, since the duality relationship between compact and noncompact symmetric spaces is a symmetric one, it might seem at first glance as if one might be able to simply reverse the roles of the compact and the noncompact spaces to obtain a transform starting on a noncompact symmetric space. Unfortunately, further consideration reveals significant difficulties with this idea. First, if $X$ is a noncompact symmetric space, then the fibers in $T^{\ast}(X)$ are not compact and therefore cannot be identified with the compact dual to $X.$ (For example, if $X$ is hyperbolic $d$-space, then the fibers in $T^{\ast}(X)$ are diffeomorphic to $\mathbb{R}^{d}$ and not to $S^{d}.$) Second, if one applies the time-$t$ heat operator to a function on a noncompact symmetric space $X$ and then tries to analytically continue, one encounters singularities that do not occur in the compact case.
The present paper is a first step in overcoming these difficulties. (See the end of this section for other recent work in this direction.) We consider noncompact symmetric spaces of the complex type, namely, those that can be described as $G/K,$ where $G$ is a connected *complex* semisimple group and $K$ is a maximal compact subgroup of $G.$ (The simplest example is hyperbolic 3-space.) The complex case is nothing but the noncompact dual of the compact group case. For noncompact symmetric spaces of the complex type, we obtain two main results.
Our first main result is an isometry formula for the Segal–Bargmann transform on the space of radial functions. We state this briefly here; see Section \[isometry.sec\] for details. Consider a function $f$ in $L^{2}(G/K)$ ($G$ complex) that is radial in the symmetric space sense, that is, invariant under the left action of $K$ on $G/K.$ Let $F=e^{t\Delta/2}f$ and consider the map$$X\rightarrow F(e^{X}),\quad X\in\mathfrak{p}, \label{fex1}%$$ where the Lie algebra $\mathfrak{g}$ of $G$ is decomposed in the usual way as $\mathfrak{g}=\mathfrak{k}+\mathfrak{p}.$ We show that the map (\[fex1\]) has a *meromorphic* (but usually not holomorphic) extension from $\mathfrak{p}$ to $\mathfrak{p}_{\mathbb{C}}:=\mathfrak{p}+i\mathfrak{p}$. The main result of Section \[isometry.sec\] is that there exist a constant $c$ and a holomorphic function $\delta$ on $\mathfrak{p}_{\mathbb{C}}$ such that for all radial $f$ in $L^{2}(G/K)$ we have$$\int_{G/K}\left\vert f(x)\right\vert ^{2}dx=e^{ct}\int_{\mathfrak{p}%
_{\mathbb{C}}}\left\vert F(e^{X+iY})\right\vert ^{2}\left\vert \delta
(X+iY)\right\vert ^{2}\frac{e^{-\left\vert Y\right\vert ^{2}/t}}{(\pi
t)^{d/2}}dX~dY,\quad F=e^{t\Delta/2}f. \label{isometry.intro}%$$
There is a cancellation of singularities occurring here: although in most cases the function $F(e^{X+iY})$ is singular at certain points, the singularities occur only at points where $\delta(X+iY)$ is zero. Thus, the singularities in $F(e^{X+iY})$ are canceled by the zeros in the density of the measure occurring on the right-hand side of (\[isometry.intro\]). Furthermore, by considering radial functions, we are introducing a distinguished basepoint (the identity coset). Thus, in the radial case, we are able to use the complexified tangent space at the basepoint (namely, $\mathfrak{p}_{\mathbb{C}}$) as our complexification of $G/K,$ and we simply do not attempt to identify $\mathfrak{p}_{\mathbb{C}}$ with $T^{\ast}(G/K).$ Of course, because we are treating the identity coset differently from other points, this approach is not $G$-invariant and is not the correct approach for the general (nonradial) case.
Our second main result is an inversion formula for the Segal–Bargmann transform of general (not necessarily radial) functions. We state this briefly here; see Section \[inversion.sec\] for details. We continue to assume that $G$ is a connected *complex* semisimple group and $K$ a maximal compact subgroup. For each point $x$ in $G/K$, we have the geometric exponential map $\exp_{x}$ taking the tangent space $T_{x}(G/K)$ into $G/K.$ Let $f$ be in $L^{2}(G/K)$ and let $F=e^{t\Delta/2}f.$ Then, for each $x\in G/K,$ the function$$X\rightarrow F(\exp_{x}X),\quad X\in T_{x}(G/K), \label{fex2}%$$ admits an analytic continuation to some ball around zero. For each $x\in G/K,$ define$$G(x,R)=e^{ct/2}\int_{\substack{Y\in T_{x}(G/K)\\\left\vert Y\right\vert \leq
R}}F(\exp_{x}iY)\delta(iY)\frac{e^{-\left\vert Y\right\vert ^{2}/2t}}{(2\pi
t)^{d/2}}~dY$$ for all sufficiently small $R.$ (Here the constant $c$ and the function $\delta$ are the same as in the isometry formula (\[isometry.intro\]).)
Our main result is that for each $x$ in $G/K,$ $G(x,R)$ admits a real-analytic continuation in $R$ to $(0,\infty)$ and, if $f$ is sufficiently regular,$$f(x)=\lim_{R\rightarrow\infty}G(x,R).$$ We may write this informally as$$f(x)=\text{ \textquotedblleft}\lim_{R\rightarrow\infty}%
\text{\textquotedblright\ }e^{ct/2}\int_{\left\vert Y\right\vert \leq R}%
F(\exp_{x}iY)\delta(iY)\frac{e^{-\left\vert Y\right\vert ^{2}/2t}}{(2\pi
t)^{d/2}}~dY, \label{inversion.intro}%$$ where the expression $\lim_{R\rightarrow\infty}{}%
$ means that we interpret the right-hand side of (\[inversion.intro\]) literally for small $R$ and then extend to large $R$ by means of analytic continuation.
As in the isometry formula for radial functions, there is a cancellation of singularities here that allows $G(x,R)$ to extend analytically to $(0,\infty),$ even though $F(\exp_{x}iY)$ itself may have singularities for large $Y.$ Because of the rotationally invariant nature of the integral in (\[inversion.intro\]), the integral only sees the part of the function $F(\exp_{x}iY)$ that is rotationally invariant. Taking the rotationally invariant part eliminates some of the singularities in $F(\exp_{x}iY).$ The remaining singularities are canceled by the zeros in the function $\delta(iY).$
The measure against which we are integrating $F(\exp_{x}iY)$ in (\[inversion.intro\]), namely, $$d\sigma_{t}(Y)=e^{ct/2}\delta(iY)\frac{e^{-\left\vert Y\right\vert ^{2}/2t}%
}{(2\pi t)^{d/2}}~dY,$$ is closely related to the heat kernel measure on the *compact* symmetric space dual to $G/K.$ Specifically, it is an unwrapped version of that heat kernel measure, in a precise sense described in Section \[inversion.sec\].
The papers [@H2] and [@St] use the inversion formula for the Segal–Bargmann transform (for compact groups and compact symmetric spaces, respectively) to deduce the isometry formula. Since we now have an inversion formula for the Segal–Bargmann transform for noncompact symmetric spaces of the complex type, it is reasonable to hope to obtain an isometry formula as well, following the line of reasoning in [@H2] and [@St]. The hoped-for isometry formula in the complex case would involve integrating $\left\vert F\right\vert ^{2}$ over a tube of radius $R$ (with respect to the appropriate measure) and then analytically continuing with respect to $R.$ Since, however, there are many technicalities to attend to in carrying out this idea, we defer this project to a future paper. (See [@range] for an additional discussion of this matter.)
Meanwhile, it would be desirable to extend the results of this paper to other symmetric spaces of the noncompact type. Unfortunately, the singularities that occur in general are worse than in the complex case and are not as easily canceled out. We discuss the prospects for other symmetric spaces in Section \[conclude.sec\].
We conclude this introduction by comparing our work here to other types of Segal–Bargmann transform for noncompact symmetric spaces. First, Ólafsson and Ørsted [@OO] have introduced another sort of Segal–Bargmann transform for noncompact symmetric spaces, based on the restriction principle. This has been developed in [@DOZ1; @DOZ2] and used to study Laplace transforms and various classes of orthogonal polynomials connected to noncompact symmetric spaces. This transform does not involve the heat operator and is thus not directly comparable to the Segal–Bargmann transform in this paper.
Meanwhile, Krötz, Ólafsson, and Stanton [@KS1; @KS2; @KOS] have considered the Segal–Bargmann transform for a general symmetric space $G/K$ of the noncompact type (not necessarily of the complex type), defined in the same way as here, in terms of the heat equation. In [@KS2], Krötz and Stanton identify the maximal domain inside $G_{\mathbb{C}}/K_{\mathbb{C}}$ to which a function of the form $e^{t\Delta/2}f$ can be analytically continued. Then in [@KOS], Krötz, Ólafsson, and Stanton give an isometry result identifying the image of $L^{2}(G/K)$ under the Segal–Bargmann transform in terms of certain orbital integrals. There is also a cancellation of singularities in their approach, in that the pseudodifferential operator $D$ in Theorem 3.3 of [@KOS] is used to extend the orbital integrals into the range where the function involved becomes singular. It remains to be worked out how the results of [@KOS] relate, in the complex case, to the isometry result suggested by the results we obtain in this paper.
Review of the $\mathbb{R}^{d}$ case\[rn.sec\]
=============================================
We give here a very brief review of results concerning the Segal–Bargmann transform for $\mathbb{R}^{d}.$ We do this partly to put into perspective the results for noncompact symmetric spaces and partly because we will use the $\mathbb{R}^{d}$ results in our analysis of the symmetric space case. See also Section \[compact.sec\] for a description of Stenzel’s results for the case of compact symmetric spaces.
In the $\mathbb{R}^{d}$ case, we consider the invariant form of the the Segal–Bargmann transform, which uses slightly different normalization conventions from Segal [@Se3] or Bargmann [@Ba1]. (See [@mexnotes] or [@newform] for a comparison of normalizations.) The transform is the map $C_{t}$ from $L^{2}%
(\mathbb{R}^{d})$ into the space $\mathcal{H}(\mathbb{C}^{d})$ of holomorphic functions on $\mathbb{C}^{d}$ given by$$(C_{t}f)(z)=\int_{\mathbb{R}^{d}}(2\pi t)^{-d/2}e^{-(z-x)^{2}/2t}f(x)~dx,\quad
z\in\mathbb{C}^{d}.$$ Here $(z-x)^{2}=(z_{1}-x_{1})^{2}+\cdots+(z_{d}-x_{d})^{2}$ and $t$ is an arbitrary positive parameter. It is not hard to show that the integral is convergent for all $z\in\mathbb{C}^{d}$ and the result is a holomorphic function of $z.$
Recognizing that the function $(2\pi t)^{-d/2}e^{-(z-x)^{2}/2t}$ is (for $z$ in $\mathbb{R}^{d}$) the heat kernel for $\mathbb{R}^{d},$ we may also describe $C_{t}f$ as$$C_{t}f=\text{analytic continuation of }e^{t\Delta/2}f.$$ Here the analytic continuation is from $\mathbb{R}^{d}$ to $\mathbb{C}^{d}$ with $t$ fixed. We take the Laplacian $\Delta=\Sigma\partial^{2}/\partial
x_{k}^{2}$ to be a negative operator, so that $e^{t\Delta/2}$ is the *forward* heat operator.
\[Segal–Bargmann\]\[rn.thm\]Let $f$ be in $L^{2}(\mathbb{R}^{d})$ and let $F=C_{t}f.$ Then we have the following results.
1\. The **inversion formula**. If $f$ is sufficiently regular we have$$f(x)=\int_{\mathbb{R}^{d}}F(x+iy)\frac{e^{-y^{2}/2t}}{(2\pi t)^{d/2}}~dy
\label{rn.inv}%$$ with absolute convergence of the integral for all $x.$
2\. The **isometry formula**. For all $f$ in $L^{2}(\mathbb{R}^{d})$ we have$$\int_{\mathbb{R}^{d}}\left\vert f(x)\right\vert ^{2}dx=\int_{\mathbb{R}^{d}%
}\int_{\mathbb{R}^{d}}\left\vert F(x+iy)\right\vert ^{2}\frac{e^{-y^{2}/t}%
}{(\pi t)^{d/2}}~dy~dx. \label{rn.isom}%$$
3\. The **surjectivity theorem**. For any holomorphic function $F$ on $\mathbb{C}^{d}$ such that the integral on the right-hand side of (\[rn.isom\]) is finite, there exists a unique $f$ in $L^{2}$ with $F=C_{t}f.$
The reason for the sufficiently regular assumption in the inversion formula is to guarantee the convergence of the integral on the right-hand side of (\[rn.inv\]). It suffices to assume that $f$ has $n$ derivatives in $L^{2}(\mathbb{R}^{d}),$ with $n>d/2.$ (See Section 2.1 of [@range].)
The isometry and surjectivity formulas are obtained by adapting results of Segal [@Se3] or Bargmann [@Ba1] to our normalization of the transform. The inversion formula is elementary (e.g., [@range]) but does not seem to be as well known as it should be. The inversion formula is implicit in Theorem 3 of [@Se0] and is essentially the same as the inversion formula for the $S$-transform in [@Ku Theorem 4.3]. In quantum mechanical language, the inversion formula says that the position wave function $f(x)$ can be obtained from the phase space wave function $F(x+iy)$ by integrating out the momentum variables (with respect to a suitable measure).
It should be noted that because $F(x+iy)$ is holomorphic, there can be many different inversion formulas, that is, many different integrals involving $F(x+iy)$ all of which yield the value $f(x).$ For example, we may think of the heat operator as a unitary map from $L^{2}(\mathbb{R}^{d})$ to the Hilbert space of holomorphic functions for which the right-hand side of (\[rn.isom\]) is finite. Then we may obtain one inversion formula by noting that the adjoint of a unitary map is its inverse. The resulting inverse = adjoint formula is sometimes described as the inversion formula for the Segal–Bargmann transform. Nevertheless, the inversion formula in (\[rn.inv\]) is *not* the one obtained by this method.
In light of what we are going to prove in Section \[isometry.sec\], it is worth pointing out that we could replace holomorphic with meromorphic in the statement of Theorem \[rn.thm\]. That is, we could describe $F$ as the meromorphic extension of $e^{t\Delta/2}f$ from $\mathbb{R}^{d}$ to $\mathbb{C}^{d}$ (if $F$ is holomorphic then it is certainly meromorphic), and we could replace the surjectivity theorem by saying that if $F$ is any meromorphic function for which the integral on the right-hand side of (\[rn.isom\]) is finite arises as the meromorphic extension of $e^{t\Delta/2}f$ for some $f$ in $L^{2}(\mathbb{R}^{d}).$ After all, since the density in (\[rn.isom\]) is strictly positive everywhere, such an $F$ would have to be locally square-integrable with respect to Lebesgue measure, and it is not hard to show that a meromorphic function with this property must actually be holomorphic. (This can be seen from the Weierstrass Preparation Theorem [@GH p. 8].) That is, under the assumption that the right-hand side of (\[rn.isom\]) is finite, meromorphic and holomorphic are equivalent.
Isometry for radial functions\[isometry.sec\]
=============================================
In this section we describe an isometric version of the Segal–Bargmann transform for radial functions on a noncompact symmetric space $X$ of the complex type (e.g., hyperbolic 3-space). We give two different forms of this result. The first involves integration over the complexified tangent space to the symmetric space at the basepoint. The second involves integration over the complexified tangent space to the maximal flat at the base point. Both results characterize the image under the Segal–Bargmann transform of the radial subspace of $L^{2}(X)$ as a certain holomorphic $L^{2}$ space of *meromorphic* functions. In Section \[conclude.sec\], we discuss the prospects for extending these results to nonradial function and to other symmetric spaces of the noncompact type.
If $f$ is a function on a noncompact symmetric space $X=G/K$, then we wish to define the Segal–Bargmann transform of $f$ to be some sort of analytic continuation of the function $F:=e^{t\Delta/2}f.$ The challenge in the noncompact case is to figure out precisely what sort of analytic continuation is the right one. One could try to analytically continue to $G_{\mathbb{C}%
}/K_{\mathbb{C}},$ but examples show that $F$ does not in general admit an analytic continuation to $G_{\mathbb{C}}/K_{\mathbb{C}}.$ Alternatively, one could consider the maximal domain $\Omega$ to which functions of the form $F=e^{t\Delta/2}f$ actually have an analytic continuation. This domain was identified by Krötz and Stanton [@KS2 Thm. 6.1] as the Akhiezer–Gindikin crown domain in $G_{\mathbb{C}}/K_{\mathbb{C}}.$ Unfortunately, it seems that there can be no measure $\mu$ on $\Omega$ such that the map sending $f$ to the analytic continuation of $F$ is an isometry of $L^{2}(G/K)$ into $L^{2}(\Omega,\mu).$ (See the discussion in [@KOS Remark 3.1].) Thus, to get an isometry result of the sort that we have in the $\mathbb{R}^{d}$ case and the compact case, we must venture beyond the domain $\Omega$ into the region where $F$ has singularities and find a way to deal with those singularities.
In this section, we assume that the symmetric space is of the complex type and that $f$ (and thus also $F$) is radial. We then write $F$ in exponential coordinates at the basepoint, which makes $F$ a function on the tangent space at the basepoint. We show that $F$ admits a *meromorphic* extension to the complexified tangent space at the basepoint. This meromorphic extension of $F$ is then square-integrable with respect to a suitable measure; the zeros in the density of the measure cancel the singularities in $F.$ We obtain in this way an isometry of the radial part of $L^{2}(X)$ onto a certain $L^{2}$ space of meromorphic functions.
In the next section, we consider the more complicated case of nonradial functions. We obtain there an inversion formula involving a more subtle type of cancellation of singularities.
The set-up is as follows. We let $G$ be a connected *complex* semisimple group and $K$ a maximal compact subgroup of $G.$ Since $G$ is complex, $K$ will be a compact real form of $G$. We decompose $\mathfrak{g}$ as $\mathfrak{g}=\mathfrak{k}+\mathfrak{p},$ where $\mathfrak{p}%
=i\mathfrak{k}.$ We then choose an inner product on $\mathfrak{p}$ that is invariant under the adjoint action of $K.$ We consider the manifold $G/K$ and we think of the tangent space at the identity coset to $G/K$ as the space $\mathfrak{p}.$ There is then a unique $G$-invariant Riemannian structure on $G/K$ whose value at the identity is the given inner product on $\mathfrak{p}%
.$ Then $G/K$ is a Riemannian symmetric space of the complex type.
We emphasize that the word complex here does *not* mean that $G/K$ is a complex manifold but rather that $G$ is a complex Lie group. The complex structure on $G$ will play no direct role in any definitions or proofs; for example, we will never consider holomorphic functions on $G.$ Nevertheless, the complex case is quite special among all symmetric spaces of the noncompact type (i.e., compared to spaces of the form $G/K$ with $G$ *real* semisimple and $K$ maximal compact). What is special about the complex case is not the complex structure *per se*, but rather the structure of the root system for $G/K$ in this case: it is a reduced root system in which all roots have multiplicity 2. Still, it is easier to say complex than to say reduced root system with all roots having multiplicity 2! The simplest example of a noncompact symmetric space of the complex type is hyperbolic 3-space, and this is the only hyperbolic space that is of the complex type.
We will make use of special intertwining formulas for the Laplacian that hold only in the complex case. (See the proof of Theorem \[isometry.thm1\] for a discussion of why the intertwining formulas hold only in this case.) Nevertheless, there is hope for obtaining similar but less explicit results for other symmetric spaces of the noncompact type. See Section \[conclude.sec\] for a discussion.
We consider the geometric exponential mapping for $G/K$ at the identity coset. This coincides with the group-theoretical exponential mapping in the sense that if we identify the tangent space at the identity coset with $\mathfrak{p},$ then the geometric exponential of $X\in\mathfrak{p}$ is just the coset containing the exponential of $X$ in the Lie-group sense. In this section, we will use the notation $e^{X}$ to denote the the geometric exponential at the identity coset of a vector $X$ in $\mathfrak{p}.$ We let $\delta$ be the square root of the Jacobian of the exponential mapping at the identity coset. This is the positive function satisfying$$\int_{G/K}f(x)~dx=\int_{\mathfrak{p}}f(e^{X})\delta(X)^{2}dX,
\label{volume.relation}%$$ where $dx$ is the Riemannian volume measure on $G/K$ and where $dX$ is the Lebesgue measure on $\mathfrak{p}$ (normalized by the inner product). Explicitly, $\delta$ is the unique Ad-$K$-invariant function on $\mathfrak{p}$ whose restriction to a maximal commutative subspace $\mathfrak{a}$ is given by$$\delta(H)=\prod_{\alpha\in R^{+}}\frac{\sinh\alpha(H)}{\alpha(H)}.
\label{delta.form}%$$ Here $R$ is the set of (restricted) roots for $G/K$ (relative to $\mathfrak{a}$) and $R^{+}$ is the set of positive roots relative to some fixed Weyl chamber in $\mathfrak{a}.$ The expression (\[delta.form\]) may be obtained by specializing results [@He1 Thm. IV.4.1] for general symmetric spaces of the noncompact type to the complex case, in which *all roots have multiplicity two*. (Compare Equation (14) in Section V.5 of [@He3].)
We consider functions on $G/K$ that are radial in the symmetric space sense, meaning invariant under the left action of $K.$ (These functions are not necessarily functions of the distance from the identity coset, except in the rank-one case.) We give two isometry results, one involving integration over $\mathfrak{p}%
_{\mathbb{C}}:=\mathfrak{p}+i\mathfrak{p}$ and one involving integration over $\mathfrak{a}_{\mathbb{C}}:=\mathfrak{a}+i\mathfrak{a}.$
\[isometry.thm1\]Let $f$ be a radial function in $L^{2}(G/K)$ ($G$ complex) and let $F=e^{t\Delta_{G/K}/2}f.$ Then the function$$X\rightarrow F(e^{X}),\quad X\in\mathfrak{p}, \label{meromorphic1}%$$ has a meromorphic extension from $\mathfrak{p}$ to $\mathfrak{p}_{\mathbb{C}}$ and this meromorphic extension satisfies$$\int_{G/K}\left\vert f(x)\right\vert ^{2}dx=e^{ct}\int_{\mathfrak{p}%
_{\mathbb{C}}}\left\vert F(e^{X+iY})\right\vert ^{2}\left\vert \delta
(X+iY)\right\vert ^{2}\frac{e^{-\left\vert Y\right\vert ^{2}/t}}{(\pi
t)^{d/2}}~dY~dX. \label{isometry1}%$$ Here $c$ is the norm-squared of half the sum (with multiplicities) of the positive roots for $G/K,$ and $d=\dim(G/K).$
Conversely, suppose $\Phi$ is a meromorphic function on $\mathfrak{p}%
_{\mathbb{C}}$ that is invariant under the adjoint action of $K$ and that satisfies$$e^{ct}\int_{\mathfrak{p}_{\mathbb{C}}}\left\vert \Phi(X+iY)\right\vert
^{2}\left\vert \delta(X+iY)\right\vert ^{2}\frac{e^{-\left\vert Y\right\vert
^{2}/t}}{(\pi t)^{d/2}}~dY~dX<\infty. \label{finiteness1}%$$ Then there exists a unique radial function $f$ in $L^{2}(G/K)$ such that $$\Phi(X)=(e^{t\Delta_{G/K}/2}f)(e^{X})$$ for all $X\in\mathfrak{p}.$
On the right-hand side of (\[isometry1\]), the expression $F(e^{X+iY})$ means the meromorphic extension of the function $X\rightarrow F(e^{X}),$ evaluated at the point $X+iY.$ The proof will show that $F(e^{X+iY}%
)\delta(X+iY)$ is holomorphic (not just meromorphic) on $\mathfrak{p}%
_{\mathbb{C}}.$ This means that although $F(e^{X+iY})$ will in most cases have singularities, these singularities can be canceled out by multiplying by $\delta(X+iY).$ This cancellation of singularities is the reason that the integral on the right-hand side of (\[isometry1\]) is even *locally* finite. Note that in contrast to the $\mathbb{R}^{d}$ case (where the density of the relevant measure is nowhere zero), there exist here meromorphic functions $F$ that are not holomorphic and yet are square-integrable with respect to the measure in (\[isometry1\]). Theorem \[isometry.thm1\] holds also for the Euclidean symmetric space $\mathbb{R}^{d},$ where in that case $e^{X+iY}=X+iY,$ $c=0,$ and $\delta\equiv1,$ so that we have (\[rn.isom\]) in the case where $f$ happens to be radial.
Observe that if $f$ is radial, then $F=e^{t\Delta/2}f$ is also radial. Thus $F$ is determined by its values on a maximal flat $A:=\exp\mathfrak{a},$ where $\mathfrak{a}$ is any fixed maximal commutative subspace of $\mathfrak{p}.$ Thus it is reasonable to hope that we could replace the right-hand side of (\[isometry1\]) with an expression involving integration only over $\mathfrak{a}_{\mathbb{C}}.$ Our next result is of this sort. We fix a Weyl chamber in $\mathfrak{a}$ and let $R^{+}$ be the positive roots relative to this chamber. We let $\eta$ be the function on $\mathfrak{a}$ given by$$\eta(H)=\delta(H)\prod_{\alpha\in R^{+}}\alpha(H)=\prod_{\alpha\in R^{+}}%
\sinh\alpha(H).$$ This function has an analytic continuation to $\mathfrak{a}_{\mathbb{C}},$ also denoted $\eta.$
\[isometry.thm2\]Let $f$ be a radial function in $L^{2}(G/K)$ ($G$ complex) and let $F=e^{t\Delta_{G/K}/2}f.$ Then the function$$H\rightarrow F(e^{H}),\quad H\in\mathfrak{a},$$ has a meromorphic extension to $\mathfrak{a}_{\mathbb{C}}$ and this meromorphic extension satisfies$$\int_{G/K}\left\vert f(x)\right\vert ^{2}dx=Be^{ct}\int_{\mathfrak{a}%
_{\mathbb{C}}}\left\vert F(e^{H+iY})\right\vert ^{2}\left\vert \eta
(H+iY)\right\vert ^{2}\frac{e^{-\left\vert Y\right\vert ^{2}/t}}{(\pi
t)^{r/2}}~dY~dH, \label{isometry2}%$$ where $r=\dim\mathfrak{a}$ is the rank of $G/K$ and $c$ is as in Theorem \[isometry.thm1\]. Here $B$ is a constant independent of $f$ and $t.$
Conversely, suppose $\Phi$ is a meromorphic function on $\mathfrak{a}%
_{\mathbb{C}}$ that is invariant under the action of the Weyl group and that satisfies$$Be^{ct}\int_{\mathfrak{a}_{\mathbb{C}}}\left\vert \Phi(H+iY)\right\vert
^{2}\left\vert \eta(H+iY)\right\vert ^{2}\frac{e^{-\left\vert Y\right\vert
^{2}/t}}{(\pi t)^{r/2}}\ dY~dH<\infty. \label{finiteness2}%$$ Then there exists a unique radial function $f$ in $L^{2}(G/K)$ such that$$\Phi(H)=(e^{t\Delta_{G/K}/2}f)(e^{H})$$ for all $H\in\mathfrak{a}.$
In the dual compact case, an analogous result was established by Florentino, Mourão, and Nunes [@FMN2 Thm. 2.2] and is described in Theorem \[compact.radial\] in Section \[compact.sec\].
Note that the function $F(e^{X+iY})$ is invariant under the adjoint action of $K_{\mathbb{C}}$ on $\mathfrak{p}_{\mathbb{C}}.$ Since almost every point in $\mathfrak{p}_{\mathbb{C}}$ can be mapped into $\mathfrak{a}_{\mathbb{C}}$ by the adjoint action of $K_{\mathbb{C}}$, it should be possible to show directly that the right-hand side of (\[isometry2\]) is equal to the right-hand side of (\[isometry1\]). Something similar to this is done in the compact group case in [@FMN2 Thm. 2.3]. However, we will follow a different approach here using intertwining formulas.
(Of Theorem \[isometry.thm1\].) For radial functions in the complex case we have a very special intertwining formula relating the non-Euclidean Laplacian $\Delta_{G/K}$ for $G/K$ and the Euclidean Laplacian $\Delta_{\mathfrak{p}}$ for $\mathfrak{p}$. Let us temporarily identify $\mathfrak{p}$ and $G/K$ by means of the exponential mapping, so that it makes sense to apply both $\Delta_{G/K}$ and $\Delta_{\mathfrak{p}}$ to the same function. Then the intertwining formula states that (for radial functions in the complex case)$$\Delta_{G/K}f=\frac{1}{\delta}[\Delta_{\mathfrak{p}}-c](\delta f), \label{id1}%$$ where $c$ is the norm-squared of half the sum (with multiplicities) of the positive roots for $G/K.$ (See Proposition V.5.1 in [@He3] and the calculations in the complex case on p. 484.)
One way to prove the identity (\[id1\]) is to first verify it for spherical functions, which are known explicitly in the complex case, and then build up general radial functions from the spherical functions. A more geometric approach is to work with the bilinear form associated to the Laplacian, namely, $$D(f,g):=\int_{G/K}f(x)\Delta g(x)~dx=-\int_{G/K}\nabla f(x)\cdot
\bigtriangledown g(x)~dx, \label{gr}%$$ where $f$ and $g$ are, say, smooth real-valued functions of compact support. If $f$ and $g$ are radial, then at each point $\bigtriangledown f$ and $\bigtriangledown g$ will be tangent to the maximal flat, since the tangent space to a generic $K$-orbit is the orthogonal complement of the tangent space to the flat. From this, it is not hard to see that the *Euclidean* gradients of $f$ and $g,$ viewed as functions on $\mathfrak{p}$ by means of the exponential mapping, coincide with the non-Euclidean gradients.
Thinking of $\bigtriangledown f$ and $\bigtriangledown g$ as Euclidean gradients, let us multiply and divide in (\[gr\]) by the Jacobian of the exponential mapping, thus turning the integral into one over $\mathfrak{p}$ with respect to Lebesgue measure. If we then do a Euclidean integration by parts on $\mathfrak{p},$ we will get one term involving the Laplacian for $\mathfrak{p}$ and one term involving derivatives of the Jacobian $\delta^{2}$ of the exponential mapping. With a bit of manipulation, this leads to an expression of the same form as (\[id1\]), except with the constant $c$ replaced by the *function* $\Omega:=\Delta_{\mathfrak{p}}%
(\delta)/\delta.$ (See Proposition V.5.1 in [@He3] or Theorem II.3.15 in [@He2].)
Now, up to this point, the argument is valid for an arbitrary symmetric space of the noncompact type. What is special about the complex case is that in this case [@He3 p. 484], we have that $\Delta_{\mathfrak{p}}(\delta)=c\delta,$ so that $\Omega$ is a constant. It turns out that having $\Delta
_{\mathfrak{p}}(\delta)$ be a constant multiple of $\delta$ is equivalent to having $\Delta_{G/K}(\delta^{-1})$ be a constant multiple (with the opposite sign) of $\delta^{-1}.$ It is shown in detail in [@HSt Sect. 2] that this last condition holds precisely when we have a reduced root system with all roots of multiplicity 2, that is, precisely in the complex case.
Meanwhile, formally exponentiating (\[id1\]) would give$$e^{t\Delta_{G/K}/2}f=\frac{1}{\delta}e^{-ct/2}e^{t\Delta_{\mathfrak{p}}%
/2}(\delta f). \label{id2}%$$ Indeed, (\[id2\]) holds for all radial functions $f$ in $L^{2}(G/K),$ in which case $\delta f$ is an Ad-$K$-invariant function in $L^{2}(\mathfrak{p}%
)$. It is not hard to prove that (\[id2\]) follows from (\[id1\]), once we have established that in the Hilbert space of $L^{2}$ radial functions (on either $G/K$ or $\mathfrak{p}$), the Laplacian is essentially self-adjoint on $C^{\infty}$ radial functions of compact support. To prove the essential self-adjointness, we start with the well-known essential self-adjointness of the Laplacian on $C_{c}^{\infty},$ as an operator on the full $L^{2}$ space. We then note that the projection onto the radial subspace (again, on either $G/K$ or $\mathfrak{p}$) commutes with Laplacian and preserves the space of $C^{\infty}$ of compact support. From this, essential self-adjointness on $C^{\infty}$ radial functions of compact support follows by elementary functional analysis.
Let us rewrite (\[id2\]) as$$e^{t\Delta_{\mathfrak{p}}/2}(\delta f)=e^{ct/2}\delta e^{t\Delta_{G/K}/2}f
\label{id2.5}%$$ and then apply the *Euclidean* Segal–Bargmann transform for $\mathfrak{p}$ to the function $\delta f$ in $L^{2}(\mathfrak{p}).$ The properties of this transform tell us that $e^{t\Delta_{\mathfrak{p}}/2}(\delta
f)$ has an entire analytic continuation to $\mathfrak{p}_{\mathbb{C}}$ and that$$\int_{\mathfrak{p}}\left\vert \delta(X)f(X)\right\vert ^{2}dX=\int
_{\mathfrak{p}_{\mathbb{C}}}\left\vert e^{t\Delta_{\mathfrak{p}}/2}(\delta
f)(X+iY)\right\vert ^{2}\frac{e^{-\left\vert Y\right\vert ^{2}/2}}{(\pi
t)^{d/2}}dX~dY. \label{id3}%$$ Equation (\[id2.5\]) then tells us that $\delta e^{t\Delta_{G/K}/2}f$ also has an analytic continuation to $\mathfrak{p}_{\mathbb{C}}$ and that$$\int_{\mathfrak{p}}\left\vert \delta(X)f(X)\right\vert ^{2}dX=e^{ct}%
\int_{\mathfrak{p}_{\mathbb{C}}}\left\vert \delta(X+iY)(e^{t\Delta_{G/K}%
/2}f)(X+iY)\right\vert ^{2}\frac{e^{-\left\vert Y\right\vert ^{2}/2}}{(\pi
t)^{d/2}}dX~dY. \label{isom.int}%$$ Since the function $\delta e^{t\Delta_{G/K}}f$ has a *holomorphic* extension to $\mathfrak{p}_{\mathbb{C}},$ the function $e^{t\Delta_{G/K}}f$ has a *meromorphic* extension to $\mathfrak{p}_{\mathbb{C}}.$
Let us now undo the identification of $\mathfrak{p}$ with $G/K$ in (\[isom.int\]). The functions $f$ and $e^{t\Delta_{G/K}/2}f$ are radial functions on $G/K.$ To turn these functions into functions on $\mathfrak{p}$ we compose with the exponential mapping. So we now write $f(e^{X})$ on the left-hand side of (\[isom.int\]) and $(e^{t\Delta_{G/K}/2}f)(e^{X+iY})$ on the right-hand side. We then apply (\[volume.relation\]) to the left-hand side of (\[isom.int\]) to obtain$$\int_{G/K}\left\vert f(x)\right\vert ^{2}dx=e^{ct}\int_{\mathfrak{p}%
_{\mathbb{C}}}\left\vert \delta(X+iY)(e^{t\Delta_{G/K}/2}f)(e^{X+iY}%
)\right\vert ^{2}\frac{e^{-\left\vert Y\right\vert ^{2}/2}}{(\pi t)^{d/2}%
}dX~dY.$$ This establishes the first part of the theorem.
For the second part of the theorem, suppose that $\Phi$ is meromorphic on $\mathfrak{p}_{\mathbb{C}},$ radial (that is, invariant under the adjoint action of $K$ on $\mathfrak{p}_{\mathbb{C}}$), and satisfies$$e^{ct}\int_{\mathfrak{p}_{\mathbb{C}}}\left\vert \Phi(X+iY)\right\vert
^{2}\left\vert \delta(X+iY)\right\vert ^{2}\frac{e^{-\left\vert Y\right\vert
^{2}/t}}{(\pi t)^{d/2}}~dY~dX<\infty.$$ Then the function $\Phi\delta$ is meromorphic on $\mathfrak{p}_{\mathbb{C}}$ and square-integrable with respect to a measure with a strictly positive density. This, as pointed out in Section \[rn.sec\], implies that $\Phi\delta$ is actually holomorphic on $\mathfrak{p}_{\mathbb{C}}.$ Then by the surjectivity of the Segal–Bargmann transform for $\mathfrak{p},$ there exists a unique function $g$ in $L^{2}(\mathfrak{p})$ with $e^{t\Delta
_{\mathfrak{p}}/2}g=\Phi\delta.$ Since the Segal–Bargmann transform commutes with the action of $K$, $g$ must also be invariant under the adjoint action of $K.$ If we let $f$ be the unique function on $G/K$ such that $$f(e^{X})=\frac{e^{ct/2}g(X)}{\delta(X)},$$ then $f$ is radial and in $L^{2}(G/K).$ By (\[id2\]) we have that $\delta\cdot e^{t\Delta_{G/K}/2}f=\frac{1}{\delta}e^{t\Delta_{\mathfrak{p}}%
/2}(g)=\Phi$ on $\mathfrak{p}.$ This establishes the existence of the function $f$ in the second part of the theorem. The uniqueness of this $f$ follows from the injectivity of the operator $e^{t\Delta_{G/K}/2}$ on $L^{2}(G/K).$
(Of Theorem \[isometry.thm2\].) The argument is similar to that in the preceding proof, except that in this case we use an intertwining formula that relates the non-Euclidean Laplacian on $G/K$ to the Euclidean Laplacian on $\mathfrak{a}.$ This formula says that (for radial functions $f$ in the complex case) we have$$\left. (\Delta_{G/K}f)\right\vert _{\mathfrak{a}}=\frac{1}{\eta}%
[\Delta_{\mathfrak{a}}-c](\eta f_{\mathfrak{a}}), \label{id4}%$$ where $c$ is the same constant as in (\[id1\]) and where $f_{\mathfrak{a}}$ is the restriction of $f$ to $\mathfrak{a}$. (See [@He2 Prop. II.3.10].) An important difference between this formula and (\[id1\]) above is that the function $\eta f_{\mathfrak{a}}$ is Weyl-*anti*-invariant, whereas the function $\delta f$ in (\[id1\]) is Ad-$K$-*invariant*. Exponentiating (\[id4\]) gives that$$e^{t\Delta_{G/K}/2}f=\frac{1}{\eta}e^{-ct/2}e^{t\Delta_{\mathfrak{a}}/2}(\eta
f_{\mathfrak{a}}) \label{heatop0}%$$ and so$$e^{t\Delta_{\mathfrak{a}}/2}(\eta f_{\mathfrak{a}})=e^{ct/2}\eta
e^{t\Delta_{G/K}/2}f. \label{heatop1}%$$
From properties of the Segal–Bargmann transform for $\mathfrak{a}$ we then see that $e^{t\Delta_{\mathfrak{a}}/2}(\eta f_{\mathfrak{a}})$ has a holomorphic extension to $\mathfrak{a}_{\mathbb{C}}$ and that$$\int_{\mathfrak{a}}\left\vert \eta(H)f(H)\right\vert ^{2}dH=\int
_{\mathfrak{a}_{\mathbb{C}}}\left\vert e^{t\Delta_{\mathfrak{a}}/2}(\eta
f_{\mathfrak{a}})(X+iY)\right\vert ^{2}\frac{e^{-\left\vert Y\right\vert
^{2}/2}}{(\pi t)^{r/2}}dX~dY, \label{isometry3}%$$ where $r=\dim\mathfrak{a}.$ Using (\[heatop1\]) then gives$$\int_{\mathfrak{a}}\left\vert \eta(H)f(H)\right\vert ^{2}dH=e^{ct}%
\int_{\mathfrak{a}_{\mathbb{C}}}\left\vert (e^{t\Delta_{G/K}/2}f)(X+iY)\eta
(X+iY)\right\vert ^{2}\frac{e^{-\left\vert Y\right\vert ^{2}/2}}{(\pi
t)^{r/2}}dX~dY.$$ We now recognize the left-hand side as being—up to an overall constant—the $L^{2}$ norm of $f$ over $G/K,$ written using (\[volume.relation\]) and then generalized polar coordinates for $\mathfrak{p}$ [@He2 Thm. I.5.17]. We thus obtain the first part of the theorem. The unspecified constant $B$ in Theorem \[isometry.thm2\] comes from the constant $c$ in Theorem I.5.17 of [@He2].
For the second part of the theorem, assume that $\Phi$ is meromorphic, Weyl-invariant, and satisfies (\[finiteness2\]). Then, as in the proof of Theorem \[isometry.thm1\], $\Phi\eta$ is holomorphic. In addition, $\Phi
\eta$ is Weyl-*anti*-invariant. There then exists a Weyl-anti-invariant function $g$ in $L^{2}(\mathfrak{a})$ with $e^{t\Delta_{\mathfrak{a}}/2}%
g=\Phi\eta.$ We now let $f$ be the function on $A:=\exp\mathfrak{a}$ satisfying$$f(e^{X})=\frac{e^{ct/2}g(X)}{\eta(X)}.$$ Then $f$ is Weyl-invariant on $A$ and has a unique radial extension to $G/K.$ In light of the comments in the preceding paragraph, this extension of $f$ is square-integrable over $G/K.$ Then (\[heatop0\]) tells us that $e^{t\Delta_{G/K}/2}f=\Phi.$
Inversion formula\[inversion.sec\]
==================================
In this section, we continue to consider symmetric spaces $G/K$ of the complex type. However, we now consider functions $f$ on $G/K$ that are not necessarily radial. We let $F=e^{t\Delta_{G/K}/2}f$ and we want to define the Segal–Bargmann transform as some sort of analytic continuation of $F.$ In the radial case, we wrote $F$ in exponential coordinates at the basepoint and then meromorphically extended $F$ from $\mathfrak{p}$ to $\mathfrak{p}_{\mathbb{C}%
}.$ In the nonradial case, this approach is not appropriate, because we no longer have a distinguished basepoint. Instead we will analytically continue $F$ to a neighborhood of $G/K$ inside $G_{\mathbb{C}}/K_{\mathbb{C}}.$
For each $x$ in $G/K,$ we have the geometric exponential map $\exp_{x}%
:T_{x}(G/K)\rightarrow G/K.$ It is not hard to show that this can be analytically continued to a holomorphic map, also denoted $\exp_{x}$, mapping the complexified tangent space $T_{x}(G/K)_{\mathbb{C}}$ into $G_{\mathbb{C}%
}/K_{\mathbb{C}}.$ We now consider tubes $T^{R}(G/K)$ in the tangent bundle of $G/K,$$$T^{R}(G/K)=\left\{ (x,Y)\in T(G/K)\left\vert ~\left\vert Y\right\vert
<R\right. \right\} .$$ Then we let $U_{R}$ be the set in $G_{\mathbb{C}}/K_{\mathbb{C}}$ given by$$U_{R}=\left\{ \exp_{x}(iY)\left\vert (x,Y)\in T^{R}(G/K)\right. \right\} .$$ Here, $\exp_{x}(iY)$ refers to the analytic continuation of the exponential map at $x.$ (In the $\mathbb{R}^{d}$ case, $\exp_{x}(iy)$ would be nothing but $x+iy.$)
It can be shown that for all sufficiently small $R,$ $U_{R}$ is an open set in $G_{\mathbb{C}}/K_{\mathbb{C}}$ and the map $(x,Y)\rightarrow\exp_{x}(iY)$ is a diffeomorphism of $T^{R}(G/K)$ onto $U_{R}.$ The complex structure on $T^{R}(G/K)$ obtained by identification with $U_{R}$ is the adapted complex structure of [@GStenz1; @GStenz2; @LS; @Sz1]. Furthermore, Krötz and Stanton have shown that for any $f$ in $L^{2}(G/K),$ the function $F=e^{t\Delta_{G/K}/2}f$ has an analytic continuation to $U_{R}$, for all sufficiently small $R$ [@KS2 Thm. 6.1]. (These results actually hold for arbitrary symmetric spaces of the noncompact type, not necessarily of the complex type.) We think of the analytic continuation of $F$ to $U_{R}$ as the Segal–Bargmann transform of $f.$
Our goal in this section is to give an inversion formula that recovers $f$ from the analytic continuation of $F.$ In analogy to the $\mathbb{R}^{d}$ case and the case of compact symmetric spaces, this should be done by integrating $F$ over the fibers in $U_{R}\cong T^{R}(G/K).$ Something similar to this is done by Leichtnam, Golse, and Stenzel in [@LGS], in a very general setting. However, in [@LGS Thm. 0.3] there is a term involving integration over the boundary of the tube of radius $R.$ This boundary term involves $e^{s\Delta/2}f,$ for all $s<t,$ and an integration with respect to $s.$ This term is undesirable for us because we wish to think of $t$ as fixed. In the case of compact symmetric spaces, Stenzel [@St] showed that the boundary term in [@LGS] could be removed by letting the radius $R$ tend to infinity, thus leading to the inversion formula described in Section \[compact.sec\].
Now, our results here will not be based on the work of [@LGS]. Nevertheless, [@LGS] and [@St] suggest that it is not possible to get an inversion formula of the sort we want by working with one fixed finite $R$; rather, we need to let $R$ tend to infinity. Unfortunately, (1) the map $(x,Y)\rightarrow\exp_{x}(iY)$ ceases to be a diffeomorphism of $T^{R}(G/K)$ with $U_{R}$ for large $R,$ and (2) the function $F=e^{t\Delta_{G/K}/2}f$ does not in general have a holomorphic (or even meromorphic) extension to $U_{R}$ for large $R.$ For noncompact symmetric spaces of the complex type, we will nevertheless find a way to let $R$ tend to infinity, by means of a cancellation of singularities. This leads to an inversion formula that is analogous to what we have in the compact and Euclidean cases. These results also lead to a natural conjecture of what the isometry formula should be in this setting, something we hope to address in a future paper.
Inversion for radial functions at identity coset
------------------------------------------------
Suppose that $f$ is a radial function in $L^{2}(G/K).$ Then we may use the intertwining formula (\[id2.5\]) and the inversion formula (\[rn.inv\]) in Theorem \[rn.thm\] to obtain the following. As in the previous section, we let $\delta$ denote the square root of the Jacobian of the exponential mapping for $G/K$ and we let $c$ denote the norm-squared of half the sum (with multiplicities) of the positive roots for $G/K.$
\[radinv.thm\]Let $f$ be a sufficiently regular radial function in $L^{2}(G/K)$ ($G$ complex) and let $F=e^{t\Delta_{G/K}/2}f.$ Then$$f(x_{0})=e^{ct/2}\int_{\mathfrak{p}}F(e^{iY})\delta(iY)\frac{e^{-\left\vert
Y\right\vert ^{2}/2t}}{(2\pi t)^{d/2}}~dY, \label{invert1}%$$ with absolute convergence of the integral. Here $x_{0}=e^{0}$ is the identity coset in $G/K.$
Specifically, sufficiently regular may be taken to mean that $f$ has $n$ derivatives in $L^{2}(X)$ (with respect to the Riemannian volume measure) for some some $n>d/2.$ Note that the proof of Theorem \[isometry.thm1\] shows that the function $X\rightarrow F(e^{X})\delta(X)$ has an entire analytic continuation to $\mathfrak{p}_{\mathbb{C}}.$ Thus the expression $F(e^{iY})\delta(iY)$ is well defined and nonsingular on all of $\mathfrak{p}%
.$
At first glance, it may seem as if this inversion formula is not very useful, since it applies only to radial functions and then gives only the value of $f$ at the identity coset. Nevertheless, we will see in the next subsection that this result leads to a much more general inversion formula that applies to not-necessarily-radial functions at arbitrary points.
Let us think about how this result compares to the inversion formula that holds for the compact symmetric space $U/K$ that is dual to $G/K$ (where, since $G/K$ is of the complex type, $U/K$ is isometric to a compact Lie group). In (\[invert1\]), the meromorphically continued function $F(e^{iY})$ is being integrated against the signed measure given by$$d\sigma_{t}(Y):=e^{ct/2}\delta(iY)\frac{e^{-\left\vert Y\right\vert ^{2}/2t}%
}{(2\pi t)^{d/2}}~dY,\quad Y\in\mathfrak{p}. \label{pseudo.measure}%$$ By analogy with the compact case (Theorem \[compact.thm\] in the special form of Theorem \[group.thm\]), we would expect that the (signed) measure $\sigma_{t}$ should be the heat kernel measure at the identity coset for the *compact* symmetric space $U/K$ dual to $G/K,$ written in exponential coordinates. Clearly, this cannot be precisely true, first, because one does not have global exponential coordinates on the compact symmetric space and, second, because the density of the measure in (\[pseudo.measure\]) assumes negative values, whereas the heat kernel measure is a positive measure.
Nevertheless, the signed measure in (\[pseudo.measure\]) turns out to be very closely related to the heat kernel measure for $U/K.$ Specifically, the *push-forward* of the measure (\[pseudo.measure\]) under the exponential mapping for $U/K$ is precisely the heat kernel measure (at the identity coset) for $U/K.$ Thus (\[pseudo.measure\]) itself may be thought of as an unwrapped version of the heat kernel for $U/K,$ where we think of the exponential map as wrapping the tangent space (in a many-to-one way) around $U/K.$ What is going on is that the heat kernel at a point $x$ in $U/K$ may be expressed as a sum of contributions from all of the geodesics connecting the identity coset to $x.$ The quantity in (\[pseudo.measure\]) is what we obtain by breaking apart those contributions, thus obtaining a something on the space of geodesics, that is, on the tangent space at the identity coset. Although some geodesics make a negative contribution to the heat kernel, the heat kernel itself (obtained by summing over all geodesics) is positive at every point.
\[pushforward.thm\]We may identify $\mathfrak{p}$ with the tangent space at the identity coset to $U/K$ in such a way that the following holds: The push-forward of the signed measure $\sigma_{t}$ in (\[pseudo.measure\]) under the exponential mapping for $U/K$ coincides with the heat kernel measure for $U/K$ at the identity coset.
Let us now recall the construction [@He1 Sect. V.2] of $U/K$ and explain how $\mathfrak{p}$ is identified with the tangent space to $U/K$ at the identity coset. Let $G_{\mathbb{C}}$ be the unique simply connected Lie group whose Lie algebra is $\mathfrak{g}_{\mathbb{C}}.$ Let $\tilde{G}$ be the connected Lie subgroup of $G_{\mathbb{C}}$ whose Lie algebra is $\mathfrak{g}%
.$ For notational simplicity, let us assume that the inclusion of $\mathfrak{g}$ into $\mathfrak{g}_{\mathbb{C}}$ induces an isomorphism of $G$ with $\tilde{G}.$ (Every symmetric space of the noncompact type can be realized as $G/K$ with $G$ having this property.) Let $U$ be the connected Lie subgroup of $G_{\mathbb{C}}$ whose Lie algebra is $\mathfrak{\ u}%
=\mathfrak{k}+i\mathfrak{p}$. Then the connected Lie subgroup of $U$ with Lie algebra $\mathfrak{k}$ is simply the group $K.$
We consider the quotient manifold $U/K$ and we identify the tangent space at the identity coset in $U/K$ with $\mathfrak{p}_{\ast}:=i\mathfrak{p}.$ If we use the multiplication by $i$ map to identify $\mathfrak{p}$ with $\mathfrak{p}_{\ast},$ then we may transport the inner product on $\mathfrak{p}$ to $\mathfrak{p}_{\ast}.$ There is then a unique $U$-invariant Riemannian metric on $U/K$ coinciding with this inner product at the identity coset. With this Riemannian metric, $U/K$ becomes a simply connected symmetric space of the compact type, and is called the dual of the symmetric space $G/K$ of the noncompact type. The duality construction is valid starting with any symmetric space of the noncompact type, producing a symmetric space of the compact type (and a very similar procedure goes from compact type to noncompact type). If one begins with a noncompact symmetric space of the complex type, the dual compact symmetric space will be isometric to a compact Lie group with a bi-invariant measure.
(Of Theorem \[radinv.thm\].) Let us again identify $G/K$ with $\mathfrak{p}$ by means of the exponential mapping at the identity coset. Suppose $f$ is a radial function square-integrable with respect to the Riemannian volume measure for $G/K.$ Then $\delta f$ is a radial function square-integrable with respect to the Lebesgue measure for $\mathfrak{p}.$ According to (\[id2.5\]) in the previous section, we have$$e^{t\Delta_{\mathfrak{p}}/2}(\delta f)=e^{ct/2}\delta e^{t\Delta_{G/K}/2}f
\label{identity}%$$ If $\delta f$ is sufficiently regular, then we may apply the inversion formula for the Euclidean Segal–Bargmann transform ((\[rn.inv\]) in Theorem \[rn.thm\]) to the function $\delta f.$ Noting that $\delta(0)=1,$ applying the inversion at the origin gives$$f(0)=(\delta f)(0)=e^{ct/2}\int_{\mathfrak{p}}F(iY)\delta(iY)\frac
{e^{-\left\vert Y\right\vert ^{2}/2t}}{(2\pi t)^{d/2}}~dY,$$ with absolute convergence of the integral, where $F$ is the meromorphic extension of $e^{t\Delta_{G/K}/2}f.$ To undo the identification of $G/K$ with $\mathfrak{p},$ we simply replace $f(0)$ with $f(e^{0})$ and $F(Y)$ with $F(e^{iY}).$ This establishes Theorem \[radinv.thm\], provided that $\delta
f$ is sufficiently regular.
To address the regularity condition, we recall the intertwining formula (\[id1\]). From this formula it is not hard to show that if $f$ is radial and in the domain of $(cI-\Delta_{G/K})^{n/2}$ for some $n,$ then $\delta f$ is in the domain of $(cI-\Delta_{\mathfrak{p}})^{n/2}.$ However, the domain of $(cI-\Delta_{G/K})^{n/2}$ is precisely the Sobolev space of functions on $G/K$ having $n$ derivatives in $L^{2}.$ Thus if $f$ is in this Sobolev space with $n>d/2,$ $\delta f$ will be in the corresponding Sobolev space on $\mathfrak{p}$ and $\delta f$ will indeed be sufficiently regular in the sense of [@range Sect. 2.1].
(Of Theorem \[pushforward.thm\].) We make use of the formula for the heat kernel function (at the identity) on a compact Lie group, as originally obtained by Èskin [@E] and rediscovered by Urakawa [@U]. We continue to use symmetric space notation for $U/K$, rather than switching to group notation. Nevertheless, the following formula is valid *only* in the case that $U/K$ is isometric to a compact Lie group (which is precisely when $G/K$ is of the complex type). We think of $\mathfrak{p}_{\ast
}:=i\mathfrak{p}$ as the tangent space to $U/K$ at the identity coset and we write $e^{Y}$ for the exponential (in the geometric sense) of $Y\in
\mathfrak{p}_{\ast}.$ For any maximal commutative subspace $\mathfrak{a}$ of $\mathfrak{p},$ the space $\mathfrak{a}_{\ast}:=i\mathfrak{a}$ is a maximal commutative subspace of $\mathfrak{p}_{\ast}$ (and every maximal commutative subspace of $\mathfrak{p}_{\ast}$ arises in this way). Given a fixed such subspace $\mathfrak{a}_{\ast},$ the set $A_{\ast}=\exp(\mathfrak{a}_{\ast})$ is a maximal flat in $U/K$ and $A_{\ast}$ is isometric to a flat Euclidean torus. Let $\Gamma\subset\mathfrak{a}_{\ast}$ denote the kernel of the exponential mapping for $\mathfrak{a}_{\ast},$ so that $\Gamma$ is a lattice in $\mathfrak{a}_{\ast}.$
We now let $\rho_{t}$ denote the fundamental solution at the identity coset to the heat equation $\partial u/\partial t=\frac{1}{2}\Delta u$ on $U/K$. The heat kernel formula asserts that for any maximal commutative subspace $\mathfrak{a}_{\ast}$ of $\mathfrak{p}_{\ast}$ we have$$\rho_{t}(e^{H})=\frac{e^{ct/2}}{(2\pi t)^{d/2}}\sum_{\gamma\in\Gamma}%
j^{-1/2}(H+\gamma)e^{-\left\vert H+\gamma\right\vert ^{2}/2t},\quad
H\in\mathfrak{a}_{\ast}. \label{ur.form}%$$ The function $\rho_{t}$ is the heat kernel *function*, that is, the density of the heat kernel *measure* (at the identity coset) with respect to the (un-normalized) Riemannian volume measure on $U/K.$
In this formula, $d=\dim(U/K)$ and $c$ is the norm squared of half the sum (with multiplicities) of the positive roots for $U/K.$ Since (it is easily seen) the roots and multiplicities for $U/K$ are the same as for $G/K,$ this definition of $c$ agrees with the one made earlier in this section. Meanwhile, the function $j$ is the Jacobian of the exponential mapping for $U/K$, $j^{1/2}$ is the unique *smooth* square root of $j$ that is positive near the origin, and $j^{-1/2}$ is the reciprocal of $j^{1/2}.$ Explicitly, for $H$ in $\mathfrak{a}_{\ast}$ we have$$j^{1/2}(H)=\prod_{\alpha\in R^{+}}\frac{\sin\alpha(H)}{\alpha(H)}%
,\label{j.half}%$$ where $R^{+}$ is a set of positive roots for $U/K.$ Note that $j^{1/2}$ takes on both positive and negative values; the non-negative square root of $j$ is not a smooth function. Properly, the formula (\[ur.form\]) is valid only for $H$ such that $j(H)$ is nonzero, in which case $j(H+\gamma)$ will be nonzero for all $\gamma\in\Gamma.$ However, since $\rho_{t}$ is continuous, we may then extend the right-hand side by continuity to all $H\in\mathfrak{a}_{\ast
}.$
Since the roots for $U/K$ are the same as for $G/K$ (under the obvious identification of $\mathfrak{p}_{\ast}$ with $\mathfrak{p}$), comparing the formula (\[delta.form\]) with (\[j.half\]) gives that $$j^{1/2}(Y)=\delta(iY) \label{j.delta}%$$ for all $Y$ in $\mathfrak{p}\cong\mathfrak{p}_{\ast}.$
The formula (\[ur.form\]) is not quite what is given in [@E] or [@U], but can be deduced from those papers. Our formula differs from the one in Urakawa by some factors of 2 having to do with group notation versus symmetric space notation, some additional factors of 2 having to do with different normalizations of the heat equation, and an overall constant coming from different normalizations of the measure on $U/K.$
Now, a generic point in $U/K$ (in a sense to be specified later) is contained in a *unique* maximal flat $A_{\ast}.$ If $x$ is contained in a unique maximal flat $A_{\ast}$ and if $e^{Y}=x$ for some $Y$ in $\mathfrak{p}_{\ast},$ then we must have $Y\in\mathfrak{a}_{\ast}.$ (If $Y$ were not in $\mathfrak{a}_{\ast},$ then $Y$ would be contained in some maximal commutative subspace $\mathfrak{b}_{\ast
}\neq\mathfrak{a}_{\ast}$ and then $x$ would be in the maximal flat $B_{\ast
}\neq A_{\ast}.$) Fix such a point $x$ and pick one $H$ in $\mathfrak{a}%
_{\ast}$ with $e^{H}=x.$ Then the elements of the form $Y=H+\gamma,$ with $\gamma$ in $\Gamma,$ represent *all* the points in $\mathfrak{p}%
_{\ast}$ with $e^{Y}=x.$ This means that for a generic point $x=e^{H},$ the sum in (\[ur.form\]) may be thought of as a sum over all the geodesics connecting the identity coset to $x.$ If we also make use of (\[j.delta\]), we may rewrite (\[ur.form\]) as$$\rho_{t}(x)=\frac{e^{ct/2}}{(2\pi t)^{d/2}}\sum_{\left\{ Y\in\mathfrak{p}%
_{\ast}|e^{Y}=x\right\} }\delta^{-1}(iY)e^{-\left\vert Y\right\vert ^{2}/2t},
\label{ur.form2}%$$ whenever $x$ in $U/K$ is contained in a unique maximal flat.
We are now in a position to understand why Theorem \[pushforward.thm\] holds. If we push forward the signed measure in $\sigma_{t}$ in (\[pseudo.measure\]), we will get a factor of $1/j(Y)$ ($=1/\delta^{2}(iY)$) from the change of variables formula, which will change the $\delta$ in (\[pseudo.measure\]) to $\delta^{-1}.$ The density of the pushed-forward measure at a generic point $x$ in $U/K$ will then be a sum over $\left\{
Y|e^{Y}=x\right\} $ of the density in (\[pseudo.measure\]) multiplied by $1/\delta(iY),$ which is precisely what we have in (\[ur.form2\]). This is what Theorem \[pushforward.thm\] asserts.
To make the argument in the preceding paragraphs into a real proof, we need to attend to a few technicalities, including an appropriate notion of generic. We call an element $Y$ of $\mathfrak{p}_{\ast}$ *singular* if there exist a maximal commutative subspace $\mathfrak{a}$ containing $Y,$ a root $\alpha$ for $\mathfrak{a}$, and an integer $n$ such that $\alpha(Y)=n\pi$; we call $Y$ *regular* otherwise. We call an element $x$ of $U/K$ singular if $x$ can be expressed as $x=e^{Y}$ for some singular element $Y\in\mathfrak{p}_{\ast}$; we call $x$ regular otherwise. It can be shown that $e^{Y}$ is regular whenever $Y$ is regular (this is not immediately evident from the definitions). In both $\mathfrak{p}_{\ast}$ and $U/K,$ the singular elements form a closed set of measure zero. Thus in pushing forward the signed measure $\sigma_{t},$ we may simply ignore the singular points and regard the exponential mapping as taking the open set of regular elements in $\mathfrak{p}_{\ast}$ onto the open set of regular elements in $U/K.$ (See Sections VII.2 and VII.5 of [@He1].)
If $x$ is regular and $x=e^{Y},$ then (by definition) $Y$ is regular and it follows that $j(Y)$ is nonzero. Furthermore, if $x$ is regular then (it can be shown) $x$ is contained in a unique maximal flat. Thus (\[ur.form2\]) is valid for all regular elements. Furthermore, it is easily seen that the function $j(Y)=\delta(iY)$ has constant sign on each connected component of the set of regular elements in $\mathfrak{p}_{\ast}.$ Finally, we note that the exponential mapping is a local diffeomorphism near each regular element of $\mathfrak{p}_{\ast},$ since the Jacobian of the exponential mapping is nonzero at regular points. From all of this, it is not hard to use a partition of unity to show that the argument given above is correct.
Inversion for general functions
-------------------------------
At each point $x$ in $G/K,$ we have the geometric exponential mapping, $\exp_{x},$ mapping the tangent space $T_{x}(G/K)$ into $G/K.$ We have also the square root of the Jacobian of the exponential mapping for $\exp_{x},$ denoted $\delta_{x}.$ Now, the action of $G$ gives a linear isometric identification of $T_{x}(G/K)$ with $T_{x_{0}}(G/K)\cong\mathfrak{p}.$ This identification is unique up to the adjoint action of $K$ on $\mathfrak{p}.$ Under any such identification, the function $\delta_{x}$ will coincide with the function $\delta=\delta_{x_{0}}$ considered in the previous section. Thus, in a slight abuse of notation, we let $\delta$ stand for the square root of the Jacobian of $\exp_{x}$ at any point $x.$ For example, in the case of 3-dimensional hyperbolic space (with the usual normalization of the metric), we have $\delta(X)=\sinh\left\vert X\right\vert /\left\vert X\right\vert $ (for all $x$). For any $x,$ the function $\delta$ has an entire analytic continuation to the complexified tangent space at $x.$
\[inv.thm2\]Let $f$ be in $L^{2}(G/K)$ ($G$ complex) and let $F=e^{t\Delta_{G/K}/2}f.$ Then define$$L(x,R)=e^{ct/2}\int_{\left\vert Y\right\vert \leq R}F(\exp_{x}(iY))\delta
(iY)\frac{e^{-\left\vert Y\right\vert ^{2}/2t}}{(2\pi t)^{d/2}}~dY,
\label{l.def}%$$ for all sufficiently small $R.$
Then for each $x,$ $L(x,R)$ admits a real-analytic continuation in $R$ to $(0,\infty).$ Furthermore, if $f$ is sufficiently regular, then$$f(x)=\lim_{R\rightarrow\infty}L(x,R) \label{fake.inv0}%$$ for all $x$ in $G/K.$ Thus we may write, informally,$$f(x)=\text{ \textquotedblleft}\lim_{R\rightarrow\infty}%
\text{\textquotedblright\ }e^{ct/2}\int_{\left\vert Y\right\vert \leq R}%
F(\exp_{x}iY)\delta(iY)\frac{e^{-\left\vert Y\right\vert ^{2}/2t}}{(2\pi
t)^{d/2}}~dY, \label{fake.inv}%$$ with the understanding that the right-hand side is to be interpreted literally for small $R$ and by analytic continuation in $R$ for large $R.$
As in the radial case, sufficiently regular may be interpreted to mean that $f$ has $n$ derivatives in $L^{2}(G/K),$ for some $n$ with $n>d/2.$
The formula (\[fake.inv\]) should be thought of as the noncompact dual to the compact group formula (\[group.inv\]) in Theorem \[group.thm\]. Specifically (as in (\[j.delta\])), $\delta(iY)$ is nothing but the square root of the Jacobian of the exponential mapping for the dual compact symmetric space $U/K,$ so that this factor in (\[fake.inv\]) is dual to the factor of $j(Y)^{1/2}$ in (\[group.inv\]). The positive constant $c$ has the same value in (\[fake.inv\]) as in (\[group.inv\]) (because the roots and multiplicities for $G/K$ and $U/K$ are the same); the change from $e^{-ct/2}$ in (\[group.inv\]) to $e^{ct/2}$ in (\[fake.inv\]) is part of the duality. (For example, the exponential factors are related to the scalar curvature, which is negative in $G/K$ and positive in $U/K.$)
Let us think about why $L(x,R)$ admits an analytic continuation in $R,$ despite the singularities that develop in $F(\exp_{x}(iY))$ when $Y$ is not small. The key observation is that the signed measure in the definition of $L(x,R)$ (denoted $\sigma_{t}$ in (\[pseudo.measure\])) is radial. Thus the integral in (\[l.def\]) only sees the part of $F(\exp_{x}(iY))$ that is radial as a function of $Y.$ Taking the radial part of $F(\exp_{x}(iY))$ eliminates many of the singularities. The singularities that remain in the radial part of $F(\exp_{x}(iY))$ are then of a universal nature, coming essentially from the singularities in the analytically continued spherical functions for $G/K.$ These remaining singularities are canceled by the zeros in the function $\delta(iY).$ See Section 5 of the expository paper [@range] for further discussion of the cancellation of singularities.
For any $x$ in $G/K,$ we let $K_{x}$ denote the subgroup of $G$ that stabilizes $x.$ (This group is conjugate in $G$ to $K.$) For any continuous function $\phi$ on $G/K,$ we let $\phi^{(x)}$ denote the radial part of $\phi$ relative to $x$, given by$$\phi^{(x)}(y)=\int_{K_{x}}\phi(k\cdot y)~dk,$$ where $dk$ is the normalized Haar measure on $K_{x}.$
We wish to reduce the inversion formula in Theorem \[inv.thm2\] to the radial case in Theorem \[radinv.thm\]. Of course, there is nothing special about the identity coset in Theorem \[radinv.thm\]; the same result applies to functions that are radial with respect to any point $x$ in $G/K.$ Now, note that$$f^{(x)}(x)=f(x)$$ and that (since the heat operator commutes with the action of $K_{x}$)$$e^{t\Delta_{G/K}/2}(f^{(x)})=(e^{t\Delta_{G/K}/2}f)^{(x)}=F^{(x)}.$$ Furthermore, if $f$ is sufficiently regular, then so is $f^{(x)}.$
Thus, by Theorem \[radinv.thm\] (extended to functions that are radial around $x$) we have$$\begin{aligned}
f(x) & =f^{(x)}(x)\nonumber\\
& =\int_{T_{x}(G/K)}e^{t\Delta_{G/K}/2}(f^{(x)})(\exp_{x}(iY))\delta
(iY)\frac{e^{-\left\vert Y\right\vert ^{2}/2t}}{(2\pi t)^{d/2}}~dY\nonumber\\
& =\int_{T_{x}(G/K)}F^{(x)}(\exp_{x}(iY))\delta(iY)\frac{e^{-\left\vert
Y\right\vert ^{2}/2t}}{(2\pi t)^{d/2}}~dY. \label{fx.inv}%\end{aligned}$$ Note that the function $X\rightarrow F^{(x)}(\exp_{x}(X))\delta(X)$ has an entire analytic continuation to $T_{x}(G/K)_{\mathbb{C}}$ and therefore $F^{(x)}(\exp_{x}(iY))\delta(iY)$ is nonsingular for all $Y.$
Now, the action of $K_{x}$ commutes with $\exp_{x}$ and with analytic continuation from $T_{x}(G/K)$ to $T_{x}(G/K)_{\mathbb{C}}.$ Thus$$F^{(x)}(\exp_{x}(iY))=\int_{K_{x}}F(\exp_{x}(i\mathrm{Ad}_{k}(Y)))~dk.$$ From this and the fact that $\delta(iY)$ and $\left\vert Y\right\vert ^{2}$ are radial functions of $Y,$ we obtain the following: We may replace $F(\exp_{x}(iY))$ in (\[l.def\]) with $F^{(x)}(\exp_{x}(iY))$ without affecting the value of the integral. This establishes the existence of the analytic continuation in $R$ of $L(x,R)$: The analytic continuation is given by$$L(x,R)=e^{ct/2}\int_{\left\vert Y\right\vert \leq R}F^{(x)}(\exp
_{x}(iY))\delta(iY)\frac{e^{-\left\vert Y\right\vert ^{2}/2t}}{(2\pi t)^{d/2}%
}~dY$$ for all $R.$ (This expression is easily seen to be analytic in $R.$) Letting $R$ tend to infinity gives the inversion formula (\[fake.inv0\]), by (\[fx.inv\]).
Review of the compact case\[compact.sec\]
=========================================
In order to put our results for noncompact symmetric spaces of the complex type into perspective, we review here the main results from the compact case. We describe first the results of Stenzel [@St] for general compact symmetric spaces. Then we describe how those results simplify in the case of a compact Lie group, recovering results of [@H1; @H2]. Finally, we describe a recent result of Florentino, Mourão, and Nunes [@FMN2] for radial functions in the compact group case. Our isometry formula for radial functions in the complex case (especially Theorem \[isometry.thm2\]) should be compared to the result of [@FMN2], as described in our Section \[groupradial.sec\]. Our inversion formula for general functions (Theorem \[inv.thm2\]) should be compared to the inversion formula in the compact group case, as described in (\[group.inv\]) of Theorem \[group.thm\].
For additional information on the Segal–Bargmann transform for compact groups and compact symmetric spaces, see the expository papers [@bull; @range]. See also [@HM1; @HM2] for more on the special case of spheres.
We make use here of standard results about compact symmetric spaces (see, for example, [@He1]) as well as results from Section 2 of [@St] (or Section 8 of [@LGS]).
The general compact case\[compactgen.sec\]
------------------------------------------
We consider a compact symmetric space $X$, assumed for simplicity to be simply connected. Suppose that $U$ is a compact, simply connected Lie group (necessarily semisimple) and that $\sigma$ is an involution of $U.$ Let $K$ be the subgroup of $U$ consisting of the elements fixed by $\sigma.$ Then $K$ is automatically a closed, connected subgroup of $U$. Consider the quotient manifold $X:=U/K$, together with any Riemannian metric on $U/K$ that is invariant under the action of $U.$ Then $X$ is a simply connected compact symmetric space, and every simply connected compact symmetric space arises in this way. We will assume (without loss of generality) that $U$ acts in a locally effective way on $X,$ that is, that the set of $u\in U$ for which $u$ acts trivially on $X$ is discrete. Under this assumption, the $U$ and $\sigma$ are unique up to isomorphism for a given $X,$ and $U$ is isomorphic to the universal cover of the identity component of the isometry group of $X.$
We consider the complexification of the group $U$, denoted $U_{\mathbb{C}}.$ Since we assume $U$ is simply connected, $U_{\mathbb{C}}$ is just the unique simply connected group whose Lie algebra is $\mathfrak{u}_{\mathbb{C}%
}:=\mathfrak{u}+i\mathfrak{u}$ (where $\mathfrak{u}$ is the Lie algebra of $U$), and $U$ sits inside $U_{\mathbb{C}}$ as a maximal compact subgroup. We also let $K_{\mathbb{C}}$ denote the connected Lie subgroup of $U_{\mathbb{C}%
}$ whose Lie algebra is $\mathfrak{k}_{\mathbb{C}}:=\mathfrak{k}%
+i\mathfrak{k}$ (where $\mathfrak{k}$ is the Lie algebra of $K$). Then $K_{\mathbb{C}}$ is always a closed subgroup of $U_{\mathbb{C}}.$ We may introduce the complexification of $U/K,$ namely, the complex manifold $$X_{\mathbb{C}}:=U_{\mathbb{C}}/K_{\mathbb{C}}.$$ It can be shown that $K_{\mathbb{C}}\cap U=K$; as a result, the inclusion of $U$ into $U_{\mathbb{C}}$ induces an inclusion of $U/K$ into $U_{\mathbb{C}%
}/K_{\mathbb{C}}$.
We write $g\cdot x$ for the action of an element $g$ in $U_{\mathbb{C}}$ on a point $x$ in $U_{\mathbb{C}}/K_{\mathbb{C}}$ and we let $x_{0}$ denote the identity coset in $U/K\subset U_{\mathbb{C}}/K_{\mathbb{C}}.$
The **Segal–Bargmann transform** for $U/K$ is the map $$C_{t}:L^{2}(U/K)\rightarrow\mathcal{H}(U_{\mathbb{C}}/K_{\mathbb{C}})$$ given by$$C_{t}f=\text{ analytic continuation of }e^{t\Delta/2}f.$$ Here $e^{t\Delta/2}$ is the time-$t$ forward heat operator and the analytic continuation is from $U/K$ to $U_{\mathbb{C}}/K_{\mathbb{C}}$ with $t$ fixed.
It follows from [@H1 Sect. 4] (applied to $K$-invariant functions on $U$) that for any $f$ in $L^{2}(U/K)$ (with respect to the Riemannian volume measure), $e^{t\Delta/2}f$ has a unique analytic continuation from $U/K$ to $U_{\mathbb{C}}/K_{\mathbb{C}}.$
At each point $x$ in $U/K,$ we have the geometric exponential map$$\exp_{x}:T_{x}(U/K)\rightarrow U/K.$$ (If $\gamma$ is the unique geodesic with $\gamma(0)=x$ and $\dot{\gamma
}(0)=Y,$ then $\exp_{x}(Y)=\gamma(1).$) For each $x,$ the map $\exp_{x}$ can be analytically continued to a holomorphic map of the complexified tangent space $T_{x}(U/K)_{\mathbb{C}}$ into $U_{\mathbb{C}}/K_{\mathbb{C}}.$
\[Identification of $T(X)$ with $X_{\mathbb{C}}$\]\[complex.prop\]The map $\Phi:T(U/K)\rightarrow U_{\mathbb{C}}/K_{\mathbb{C}}$ given by$$\Phi(x,Y)=\exp_{x}(iY),\quad x\in U/K,~Y\in\mathfrak{p}_{x}%$$ is a diffeomorphism. On right-hand side of the above formula, $\exp_{x}(iY)$ refers to the analytic continuation of geometric exponential map.
From the point of view of quantization, we should really identify $U_{\mathbb{C}}/K_{\mathbb{C}}$ with the *co*tangent bundle $T^{\ast
}(U/K).$ However, since $U/K$ is a Riemannian manifold we naturally and permanently identify $T^{\ast}(U/K)$ with the tangent bundle $T(U/K).$ In the $\mathbb{R}^{d}$ case, $\exp_{x}(iy)$ would be nothing but $x+iy.$
The Lie algebra $\mathfrak{u}$ of $U$ decomposes as $\mathfrak{u}%
=\mathfrak{k}+\mathfrak{p},$ where $\mathfrak{p}$ is the $-1$ eigenspace for the action of the involution $\sigma$ on $\mathfrak{u}.$ For any $x$ in $U/K$ we define$$\begin{aligned}
K_{x} & =\mathrm{Ad}_{u}(K)\\
\mathfrak{k}_{x} & =\mathrm{Ad}_{u}(\mathfrak{k}),\\
\mathfrak{p}_{x} & =\mathrm{Ad}_{u}(\mathfrak{p}),\end{aligned}$$ where $u$ is any element of $U$ such that $u\cdot x_{0}=x.$ We identify $\mathfrak{p}=\mathfrak{p}_{x_{0}}$ with the tangent space to $U/K$ at $x_{0}%
$; more generally, we identify $\mathfrak{p}_{x}$ with the tangent space at $x$ to $U/K$. With this identification, we have$$\exp_{x}(Y)=e^{Y}\cdot x,\quad x\in U/K,~Y\in\mathfrak{p}_{x},$$ where $e^{Y}\in U$ is the exponential of $Y$ in the Lie group sense.
Now, for each $x\in U/K,$ define a subspace $\mathfrak{g}_{x}$ of $\mathfrak{u}_{\mathbb{C}}$ by$$\mathfrak{g}_{x}=\mathfrak{k}_{x}+i\mathfrak{p}_{x}.$$ Then $\mathfrak{g}_{x}$ is a Lie subalgebra of $\mathfrak{u}_{\mathbb{C}}.$ We let $G_{x}$ denote the connected Lie subgroup of $U_{\mathbb{C}}$ whose Lie algebra is $\mathfrak{g}_{x}.$ Note that $e^{iY}$ belongs to $G_{x}$ for any $Y$ in $\mathfrak{p}_{x}.$ Thus, the image under $\Phi$ of $T_{x}(U/K)$ is contained in the $G_{x}$-orbit of $x.$ In fact, $\Phi(T_{x}(U/K))$ is precisely the $G_{x}$-orbit of $x,$ and the stabilizer in $G_{x}$ of $x$ is precisely $K_{x}.$ We record this result in the following.
\[Identification of the Fibers\]For any $x\in U/K,$ the image inside $U_{\mathbb{C}}/K_{\mathbb{C}}$ of $T_{x}(U/K)\cong\mathfrak{p}_{x}$ under $\Phi$ is precisely the orbit of $x$ under $G_{x}.$ Thus the image of $T_{x}(U/K)$ may be identified naturally with $G_{x}/K_{x}.$
Now, each $G_{x}$ is conjugate under the action of $U$ to $G:=G_{x_{0}}.$ Thus each quotient space $G_{x}/K_{x}$ may be identified with $G/K.$ This identification depends on the choice of an element $u$ of $U$ mapping $x_{0}$ to $x$ and is therefore unique only up to the action of $K$ on $G/K.$ The space $G/K$, with an appropriately chosen $G$-invariant Riemannian metric, is the *dual noncompact symmetric space* to $U/K$. Thus we see that the map $\Phi$ leads naturally to an identification (unique up to the action of $K$) of each fiber in $T(U/K)$ with the noncompact symmetric space $G/K.$
Another way to think about the appearance of the geometry of $G/K$ in the problem is from the following result of Leichtnam, Golse, and Stenzel. If we analytically continue the metric tensor from $U/K$ to $U_{\mathbb{C}%
}/K_{\mathbb{C}}$ and then restrict to the image of $T_{x}(U/K)$ under $\Phi.$ The result is the *negative of* a Riemannian metric and the image of $T_{x}(U/K)$, with the resulting Riemannian metric, is isometric to $G/K.$ (See [@LGS Prop. 1.17 and Thm 8.5].)
On each fiber $T_{x}(U/K)\cong G/K$ we may then introduce the *heat kernel measure* (at the identity coset). This measure is given by the Riemannian volume measure for $G/K$ multiplied by the *heat kernel function*, denoted $\nu_{t}.$ Under the identification of $T_{x}(U/K)$ with $G/K,$ the Riemannian volume measure on $G/K$ corresponds to Lebesgue measure on $T_{x}(U/K)$ multiplied by an explicitly computable Jacobian function $j.$ Thus the heat kernel measure on $T_{x}(U/K)$ is the measure $\nu
_{t}(Y)j(Y)~dY,$ where $dY$ denotes Lebesgue measure.
We are now ready to state the main results of Stenzel’s paper [@St].
\[Stenzel\]\[compact.thm\]Let $f$ be in $L^{2}(U/K)$ and let $F=e^{t\Delta
/2}f.$ Then we have the following results.
1\. The **inversion formula**. If $f$ is sufficiently regular we have$$f(x)=\int_{T_{x}(U/K)}F(\exp_{x}(iY))\nu_{t}(Y)j(Y)~dY, \label{compact.inv}%$$ with absolute convergence of the integral for all $x.$
2\. The **isometry formula**. For all $f$ in $L^{2}(U/K)$ we have$$\int_{U/K}\left\vert f(x)\right\vert ^{2}dx=\int_{U/K}\int_{T_{x}%
(U/K)}\left\vert F(\exp_{x}(iY))\right\vert ^{2}\nu_{2t}(2Y)j(2Y)~2^{d}dY~dx,
\label{compact.isom}%$$ where $d=\dim(U/K).$
3\. The **surjectivity theorem**. For any holomorphic function $F$ on $U_{\mathbb{C}}/K_{\mathbb{C}}\cong T(U/K)$ such that the integral on the right-hand side of (\[compact.isom\]) is finite, there exists a unique $f$ in $L^{2}(U/K)$ with $F=C_{t}f.$
Note that in (\[compact.inv\]) we have $\nu_{t}(Y)j(Y),$ whereas in (\[compact.isom\]) we have $\nu_{2t}(2Y)j(2Y).$ The smoothness assumption on $f$ in the inversion formula is necessary to guarantee the convergence in the inversion formula (\[compact.inv\]). (The optimal smoothness conditions are not known in general; Stenzel actually assumes that $f$ is $C^{\infty}.$) As in the $\mathbb{R}^{n}$ case, the inversion formula in (\[compact.inv\]) is *not* the one obtained by viewing the heat operator as a unitary map (as in the isometry formula) and then taking the adjoint.
The special case of Theorem \[compact.thm\] in which $U/K$ is a compact Lie group was established in [@H1] and [@H2]. (The compact group case is the one in which $U$ is $H\times H$ and $K$ is the diagonal copy of $H$ inside $H\times H,$ where $H$ is a simply connected compact Lie group.) See also [@HM1; @KR2] for an elementary proof of the isometry formula in the case of $X=S^{d}.$
The proof of the inversion formula hinges on the duality between the compact symmetric space $U/K$ and noncompact symmetric space $G/K.$ Specifically, for a holomorphic function $F$ on $U_{\mathbb{C}}/K_{\mathbb{C}}\cong T(U/K)$ we have that applying the Laplacian for $G_{x}/K_{x}$ in each fiber and then restricting to the base gives the negative of the result of first restricting $F$ to the base and then applying the Laplacian for $U/K.$ So, roughly, the Laplacian in the fiber is the negative of the Laplacian on the base, on holomorphic functions. (Compare the result in $\mathbb{C}$ that $d^{2}/dy^{2}$ is the negative of $d^{2}/dx^{2}$ when applied to a holomorphic function.) The argument is then that applying the *forward* heat equation in the fibers (by integrating against the heat kernel) has the effect of computing the *backward* heat equation in the base. The proof of the isometry formula may then be reduced to the inversion formula; in the process of this reduction, the change from $\nu_{t}(Y)j(Y)$ to $\nu_{2t}(2Y)j(2Y)$ occurs naturally.
The compact group case\[compactgrp.sec\]
----------------------------------------
Although the Jacobian function $j$ is explicitly computable for any symmetric space, the heat kernel $\nu_{t}$ is not. Nevertheless, if $X$ is isometric to a simply connected compact Lie group with a bi-invariant metric, then the dual noncompact symmetric space is of the complex type and in this case there is an explicit formula for $\nu_{t}$ due to Gangolli [@Ga Prop. 3.2]. Expressed in terms of the heat kernel *measure*, this formula becomes$$\nu_{t}(Y)j(Y)~dY=e^{-ct/2}j(Y)^{1/2}\frac{e^{-\left\vert Y\right\vert
^{2}/2t}}{(2\pi t)^{d/2}}~dY,$$ where $dY$ is Lebesgue measure on the fiber, $d=\dim(U/K)=\dim(G/K),$ and $c$ is the norm-squared of half the sum of the positive roots for $X$ (thinking of $X$ as a symmetric space and counting the roots with their multiplicities). In the expression for the heat kernel *function*, we would have $j(Y)^{-1/2}$ instead of $j(Y)^{1/2}.$ Thus we obtain the following.
\[group.thm\]In the compact group case, the **inversion formula** take the form$$f(x)=e^{-ct/2}\int_{T_{x}(U/K)}F(\exp_{x}(iY))j(Y)^{1/2}\frac{e^{-\left\vert
Y\right\vert ^{2}/2t}}{(2\pi t)^{d/2}}~dY \label{group.inv}%$$ and the **isometry formula** takes the form$$\int_{U/K}\left\vert f(x)\right\vert ^{2}dx=e^{-ct}\int_{U/K}\int_{T_{x}%
(U/K)}\left\vert F(\exp_{x}(iY))\right\vert ^{2}j(2Y)^{1/2}\frac
{e^{-\left\vert Y\right\vert ^{2}/t}}{(\pi t)^{d/2}}~dY~dx. \label{group.isom}%$$
As in the general case, (\[group.inv\]) holds for sufficiently regular $f$ in $L^{2}(U/K)$ and (\[group.isom\]) holds for all $f$ in $L^{2}(U/K).$
If we specialize further to the case in which $X$ is the unit sphere $S^{3}$ inside $\mathbb{R}^{4}$ (so that $X$ is isometric to the compact group $\mathrm{SU}(2)$) and put in the explicit expression for $j(Y)$, the inversion formula becomes$$f(x)=e^{-t/2}\int_{T_{x}(S^{3})}F(\exp_{x}(iY))\frac{\sinh\left\vert
Y\right\vert }{\left\vert Y\right\vert }\frac{e^{-\left\vert Y\right\vert
^{2}/2t}}{(2\pi t)^{3/2}}~dY, \label{s3.inv}%$$ and this isometry formula becomes$$\int_{S^{3}}\left\vert f(x)\right\vert ^{2}~dx=e^{-t}\int_{S^{3}}\int
_{T_{x}(S^{3})}\left\vert F(\exp_{x}(iY))\right\vert ^{2}\frac{\sinh\left\vert
2Y\right\vert }{\left\vert 2Y\right\vert }\frac{e^{-\left\vert Y\right\vert
^{2}/t}}{(\pi t)^{3/2}}~dY. \label{s3.isom}%$$
Radial functions in the compact group case\[groupradial.sec\]
-------------------------------------------------------------
In the compact group case, Florentino, Mourão, and Nunes have obtained a special form of the isometry theorem for radial functions. In this case, the radial functions (in the symmetric space sense) are simply the class functions on the compact group. Our Theorem \[isometry.thm2\] is just the noncompact dual to Theorem 2.2 of [@FMN2]. There does not appear to be an analog of our Theorem \[isometry.thm1\] in the compact group case, because there the exponential mapping is not a global diffeomorphism.
We continue to use symmetric space notation rather than switching to compact group notation. Let $\mathfrak{a}$ be a maximal commutative subspace of $\mathfrak{p}$ and let $A=\exp_{x_{0}}(\mathfrak{a}).$ Then $A$ is a maximal flat in $X$ and is isometric to a flat Euclidean torus. Every point $x$ in $U/K$ can be mapped by the left action of $K$ into $A.$ Thus a radial function is determined by its values on $A.$
Because $\mathfrak{a}$ is commutative, we can simultaneously identify the tangent space at every point in $A$ with $\mathfrak{a}.$ We now define the complexification $A_{\mathbb{C}}$ of $A$ to be the image under $\Phi$ of $T(A)\subset T(X),$ where $\Phi$ is the map in Proposition \[complex.prop\]. That is to say, we define$$A_{\mathbb{C}}=\left\{ \left. \exp_{a}(iY)\in X_{\mathbb{C}}\right\vert a\in
A,~Y\in\mathfrak{a}\right\} .$$ The restriction of $\Phi$ to $T(A)$ is a diffeomorphism of $T(A)$ with $A_{\mathbb{C}}.$ (If we identify $X$ with a compact Lie group $H,$ then $A$ is a maximal torus $T$ inside $H$ and $A_{\mathbb{C}}$ is the complexification of $T$ inside $H_{\mathbb{C}}.$)
It is convenient to multiply the Riemannian volume measures on $X$ and $A$ by normalizing factors, so that the total volume of each manifold is equal to 1. If we used instead the un-normalized Riemannian volume measures, there would be an additional normalization constant in Theorem \[compact.radial\], as in Theorem \[isometry.thm2\]. We now let $\eta$ be the Weyl denominator function on $A.$ This is the smooth, real-valued function, unique up to an overall sign, with the property that$$\int_{X}f(x)~dx=\frac{1}{\left\vert W\right\vert }\int_{A}f(a)\eta(a)^{2}~da,$$ for all continuous radial functions $f$ on $X.$ Here $\left\vert W\right\vert
$ is the order of the Weyl group for $X,$ and $dx$ and $da$ are the normalized volume measures on $X$ and $A,$ respectively. The function $\eta$ has an entire analytic continuation from $A$ to $A_{\mathbb{C}},$ also denoted $\eta.$
We are now ready to state Theorem 2.2 of [@FMN2], using slightly different notation.
\[Florentino, Mourão, and Nunes\]\[compact.radial\]Suppose $X$ is isometric to a compact Lie group with a bi-invariant metric. If $f$ is any radial function in $L^{2}(X),$ let $F$ denote the analytic continuation to $X_{\mathbb{C}}$ of $e^{t\Delta/2}f.$ Then$$\int_{X}\left\vert f(x)\right\vert ^{2}~dx=\frac{e^{-ct}}{\left\vert
W\right\vert }\int_{A}\int_{\mathfrak{a}}\left\vert F(\exp_{a}(iY)\right\vert
^{2}\left\vert \eta(\exp_{a}(iY)\right\vert ^{2}\frac{e^{-\left\vert
Y\right\vert ^{2}/t}}{(\pi t)^{r/2}}~dY~da, \label{compact.radialisom}%$$ Here $r$ is the dimension of $\mathfrak{a},$ the constant $c$ is the same as in (\[group.inv\]) and (\[group.isom\]), $|W|$ is the order of the Weyl group, and $dx$ and $da$ are the normalized Riemannian volume measures on $X$ and $A,$ respectively.
Furthermore, if $F$ is any Weyl-invariant holomorphic function on $A_{\mathbb{C}}$ for which the integral on the right-hand side of (\[compact.radialisom\]) is finite, then there exists a unique radial function $f$ in $L^{2}(X)$ such that $F=e^{t\Delta/2}f$ on $A.$
Consider, for example, the case in which $X$ is the unit sphere $S^{3}$ in $\mathbb{R}^{4}$, in which case $X_{\mathbb{C}}$ is the complexified sphere $$S_{\mathbb{C}}^{3}:=\left\{ \left. z\in\mathbb{C}^{4}\right\vert z_{1}%
^{2}+z_{2}^{2}+z_{3}^{2}+z_{4}^{2}=1\right\} .$$ Fix the basepoint $x_{0}:=(0,0,0,1).$ In that case, a radial function on $S^{3}$ is one that is invariant under the rotations that fix $x_{0}.$ If we take $\mathfrak{a}$ to be the one-dimensional subspace of $T_{x_{0}}(S^{3})$ spanned by the vector $e_{2}=(0,1,0,0)$, then $A$ is the set$$A=\left\{ \left. (\cos\theta,\sin\theta,0,0)\right\vert \theta\in
\mathbb{R}\right\} \label{a.form}%$$ and $A_{\mathbb{C}}$ is the set of points in $S_{\mathbb{C}}^{3}$ of the same form as in (\[a.form\]), except with $\theta$ in $\mathbb{C}.$ In the $S^{3}$ case, $\left\vert W\right\vert =2,$ $c=1,$ the Weyl denominator is $2\sin\theta,$ and the normalized measure on $A$ is $d\theta/2\pi.$ Thus (\[compact.radialisom\]) becomes$$\begin{aligned}
& \int_{S^{3}}\left\vert f(x)\right\vert ^{2}~dx\nonumber\\
& =\frac{e^{-t}}{2}\int_{0}^{2\pi}\int_{-\infty}^{\infty}\left\vert F\left[
(\cos(\theta+iy),\sin(\theta+iy),0,0)\right] \right\vert ^{2}~\left\vert
2\sin(\theta+iy)\right\vert ^{2}\frac{e^{-y^{2}/t}}{(\pi t)^{1/2}}%
~dy~\frac{d\theta}{2\pi}.\end{aligned}$$
Concluding remarks\[conclude.sec\]
==================================
In this paper we have established an isometry formula (in two different versions) for the Segal–Bargmann transform of radial functions and an inversion formula for the Segal–Bargmann transform of general functions, both in the case of a noncompact symmetric space of the complex type. Both the isometry formula and the inversion formula require a cancellation of singularities, but otherwise they closely parallel the results from the compact group case. Specifically, Theorem \[isometry.thm2\] in the complex case is very similar to Theorem \[compact.radial\] in the compact group case and Theorem \[inv.thm2\] in the complex case is very similar to the inversion formula in Theorem \[group.thm\] in the compact group case. Besides the cancellation of singularities, the main difference between the formulas in the two cases is the interchange of hyperbolic sine with ordinary sine. It is natural, then, to look ahead and consider the prospects for obtaining results in the noncompact setting paralleling *all* of the results we have for compact symmetric spaces. This would entail extending the isometry result to nonradial functions and then extending both the isometry and the inversion results to other noncompact symmetric spaces, beyond those of the complex type. In [@H2] in the compact group case and in [@St] in the general compact symmetric space case, the inversion formula is proved first and the isometry formula obtained from it. As a result, we fully expect that the inversion formula we prove here will lead to an isometry formula for not-necessarily-radial functions in the complex case. A precise statement of the result we have in mind is given in [@range] in the case of hyperbolic 3-space.
Meanwhile, we have recently received a preprint by Krötz, Ólafsson, and Stanton [@KOS] that establishes an isometry formula for general functions (not necessarily radial) on general symmetric spaces of the noncompact type (not necessarily of the complex type). However, this isometry formula does not, at least on the surface, seem parallel to the compact case. In particular, in the complex case, this isometry formula does *not* reduce to the one we have in mind, at least not without some substantial manipulation of the formula in [@KOS Thm. 3.3]. Nevertheless, the result of [@KOS] is a big step toward understanding the situation for general symmetric spaces of the noncompact type. There may well be a connection, in the complex case, between the results of [@KOS] and the isometry formula we have in mind, but this remains to be worked out. If the isometry formula can be understood better for general noncompact symmetric spaces, this understanding may pave the way for progress on the inversion formula as well.
Note that in the case of compact symmetric spaces, the results take on a particularly simple and explicit form in the compact group case. (Compare Theorem \[compact.thm\] to Theorem \[group.thm\].) Our results in this paper are for the noncompact symmetric spaces of the complex type; this case is just the dual of the compact group case. Thus, one cannot expect the same level of explicitness for noncompact symmetric spaces that are not of the complex type. Instead, we may hope for results that involve some suitably unwrapped version of the heat kernel measure on the dual compact symmetric space, where in general there will not be an explicit formula for this unwrapped heat kernel.
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| tomekkorbak/pile-curse-small | ArXiv |
Coulda-woulda-shoulda packed that.
I can’t count the number of times I’ve found myself saying something like, “If only I had packed the (blank) we wouldn’t be in this mess.”
I’ve said it time and time again, having the right gear on hand can make a huge difference. It might not make a difference every time or every tenth time, but it only has to save your butt the one time to make it worth having.
So, whether you’re going on a road-trip or an adventure into the back country, here are my top ten essentials nobody should ever leave home without.
10: A Jack
A good jack can make a big difference. I recommend a 6-ton bottle jack over conventional scissor jacks, they are smaller, safer and more stable.
Not the crappy one that comes with your car. The scissor jack found in the trunk of most automobiles these days is junk. Just good enough to swap a tire, but nothing else.
What you want is a cheap bottle jack, rated to lift, at a minimum, the curb weight of your car. I’ve got a 6-ton bottle jack in the back of my Jeep for this reason.
Most scissor jacks that come with people’s cars these days are designed to lift a fraction of the vehicles curb weight because they are only intended to lift one corner in an emergency.
A bottle jack is also less likely to catastrophically fail than a scissor jack and doesn’t take up anymore space in your trunk.
Just because bottle jacks are better than scissor jacks, doesn’t mean they don’t have problems on their own.
Bottle jacks have small bases and small lift points making them far from the most stable way to lift a vehicle.
For added safety, I recommend throwing a couple jack stands in your kit if you find yourself using the jack for more than emergency maintenance.
What ever jack you decide on, make sure you know how to use it before you need to. Consult your manual for where your vehicle’s lift points are located and always remember to set the parking break and chock the wheels.
Remember, you can always keep the scissor jack in your trunk as a back-up.
9: WD-40
Everyone’s favorite lubricant that isn’t a lubricant. WD-40 is great at breaking down rust and loosening stuck bolts, nuts and anything else.
WD-40 is a must, but before we get started on why you should have it, lets establish what everyone’s favorite lubricant isn’t. It is not a lubricant.
That’s not to say it doesn’t function as a perfectly good lubricant, and that’s how a lot of people use it, but its true purpose is a rust remover and water-displacer.
The base of WD-40 is a light-weight oil, which functions as a lubricant. The problem is, WD-40 also contains petroleum distillates, which are likely to cause more damage than good on most things that go squeak.
What WD-40 does, and why I’m sure plenty of people still think it’s a lubricant, is work as a penetrating fluid. It’s great at getting stuck bolts loose in a pinch.
So when you’re trying to get a stuck bolt or nut loose, reach for the WD-40, but if you’ve got a squeaky door, find a good silicon or Teflon lubricant.
8: Tow Strap
I never kept a tow strap in the back of my car, until I started driving my dads old truck.
He’d always taught me to be prepared for the worse and hope for the best. So, when I borrowed his truck last winter, he made sure it had everything I might need.
When I bought my Jeep this past spring one of the first things to go in the trunk was a tow strap.
Thankfully, I’ve only ever had to use it once and it was to help someone else get their truck out of a mud pit. Ultimately, my vehicle wasn’t able to get them out, but my tow strap and someone else’s Jeep was.
Before you go out and pick up a tow strap, it’s important to know where your tow points are.
You don’t ever want to wrap a tow strap around tires or an axle. It will cause more damage than waiting for a tow truck to arrive.
Most vehicles these days have a tow point hidden somewhere on the front behind a plastic cover..
Getting to it typically requires removing a plastic insert and screwing in a long hook.
Most trucks and many SUVs have tow hooks readily available, but not always where you need them. Many SUVs for example have tow points on the front but not in the back.
7: Essential fluids
Sometimes a quart of oil is all you need.
Cars need more than gas in the tank to run. Oil, anti-freeze, power-steering fluid, etc.… There’s a lot that goes into keeping an engine running.
So, what should you keep in your vehicle? That really depends on a couple of factors. How old your vehicle is would be a big one. Newer vehicles aren’t as likely to have problems, but as they get older and start to develop them, that’s when you should take note of what fluids it might need.
If you’ve got an older vehicle that has a habit of overheating, a bottle of 50-50 mix anti-freeze rated for your vehicle might not be a bad idea. Just make sure you consult your manual before you go out and buy a bottle.
At a minimum, I keep a quart of motor-oil in my trunk, just in case. Synthetic or conventional oil doesn’t really matter. Long road trips can do a number on your engine, especially if you haven’t had the oil changed in a few thousand miles. Having something to add to your engine when it’s running low on oil is better than nothing.
I remember coming home after my first year in college and having to pull over every 50 miles to let Niecie’s car cool down. Her little red Pontiac Sunfire couldn’t make it 50 miles without overheating. A quart of oil and topping off the coolant reservoir was all it took to get her rolling again. For whatever reason, the oil seemed to make the biggest difference.
6: Full Tool Kit
The right tools for the job don’t have to take up a lot of space in your trunk. I can’t count the number of times I’ve been glad to have a socket wrench handy to tighten or loosen up a bolt.
I won’t leave home without a full tool kit equipped with torx bits, sockets, hex keys, vice grips and adjustable wrenches. You name it, I have it in my tool kit or soon will.
I’ve had my share of trouble where having the right tools saved the day.
On one occasion, having a fully stocked tool kit allowed me to remove my spare tire and tire carrier so we could fit a bike rack on my Jeep.
It wasn’t mission critical, but it meant getting my mom’s new bike back from the store and making her day. It was a real win-win for everyone.
If you’re not sure what should go into your kit, Craftsman has an automotive tool set available on Amazon.com with just about everything you could possibly need. For about $110 for the kit, it’s not a bad value either.
5: Duct Tape
You will seldom find a faster fix than a wad of duct tape. Whether its sealing a leaky radiator hose or keeping a loose body panel in place, duct tape is one thing I’ll never be without.
Everyone knows duct tape is magic, what else do I need to say. If you’ve got the room, throw some electrical tape in your pack too! That stuff solves all kinds of problems that duct tape can’t.
Seriously, if you don’t have a roll of duct tape, or better yet Gorilla Tape in your car, go get some and toss it in your trunk. You won’t be sorry.
4: Tire Repair kit
Tires are important, really, really important. Tires are important because, without them, your car isn’t going anywhere.
That’s why being able to repair your tires are a must. Sure, everyone’s got a spare tire hiding in their trunk or hanging off or under the back end of their vehicle, but the problem with spare tires is sometimes it’s not safe or convenient to change a tire.
Sometimes your only option is to make a quick repair and get moving again.
Eventually, everyone gets a flat tire and, thankfully, there are lots of ways to go about fixing one.
Fix-a-Flat
Fix-a-Flat is a quick, easy way to get moving again after a flat. It may seem too good to be true, but it’s not.
For small leaks, a can of compressed tire sealant, like Fix-a-Flat, is hard to beat.
These cans connect to the tire stem and pump compressed air and a sealing gel into the tire. This gel works to fill in puncture and increase the tire pressure high enough to allow you to drive on it safely again.
Cheap and easy to use, I keep a big can of the stuff in my trunk. No one wants to change a tire on the side of the interstate.
It’s a temporary solution that works well enough to get you moving again after a flat. Just make sure you get the right sized can for your size vehicle. As a general rule, the bigger the tire, the bigger the can you’ll need.
Tire puncture repair kit
Sometimes the only thing that’s going to get you rolling again is a good old-fashioned tire repair kit, like this one from Slime.
Sometimes, a can of Fix-a-Flat isn’t going to cut it. Maybe the puncture is just a little bit too big for the gel to do its magic. Whatever the case may be, you need to get moving again.
This is where a cheap tire repair kit can come in handy. These typically consist of a reamer, plugger and a few lengths of repair ropes.
A simple puncture repair kit can mean the difference between getting moving again and being stranded.
The kit works by filling the puncture with a tightly packed wad of tar soaked cord. The end result is a tire that holds air, and will continue to hold air indefinitely in some cases.
The best part is these kits are cheap, simple to use and can work even if the tire has gone completely flat. Just make sure you have a portable air pump on hand to so your tire doesn’t come off the wheel.
3: Jumper Cables or Jump Box
Processed with Snapseed.Sooner or later, you’re going to leave your lights on or forget to turn the map lights off, and before long your car’s battery will be flat and you’ll going nowhere fast.
There might be plenty of people around who could help you, but unless you have jumper cables they might not be able to.
So don’t risk it. A good set of cables can be had for less than $15.
A jump kit is perfect for when you’re on an adventure that takes you far from the nearest good samaritan.
A great alternative to jumper cables, though you should still have them, is a portable jump pack.
These jump packs can provide enough juice to start your car. These jump kits are basically big car batteries with a handle and built in jumper cables.
I keep one of these in my Jeep in case of emergencies. No one wants to be 100 miles from civilization just to have the battery go flat.
A good jump pack can be had for less than $50 and only needs to be charged about once a month.
If you’re headed out on solo adventures, I’d highly recommend picking one of these up before you go.
2: First Aid Kit
Why vehicles don’t come with one under your seat or in the spare tire compartment, I will never know. A first aid kit is one of the first items to make it into any car I drive.
I seriously don’t understand why vehicle manufacturers don’t just throw in a first aid kit with the spare tire. They’re just as important and can save a life.
A first aid kit is a must, and don’t skimp out on a cheap bare bones one. Start with a good one and add to it.
First aid kits often come with individually wrapped packs of pain killers like ibuprofen or acetaminophen. These are great, but they won’t last very long. Fill a lunch or snack bag with ibuprofen or acetaminophen and throw it in there. It costs basically nothing to do and you just extended the life of the first aid kit by months, if not years.
If you have a medical condition or allergy it might be a good idea to keep a few days’ worth, or even a week’s worth, of medication in your first aid kit just in case.
No one wants to be 500 miles into a road trip to discover they forgot their meds.
It might not be a bad idea to learn basic first aid either. A first aid kit is only as good as the person using it.
1: Food and water
If there is anything worth keeping in your trunk for an emergency it’s food and water.
Food and water are the two most important things you can keep in your vehicle.
You never know when you’re going to be stuck on the side of the road or find yourself in the ditch during a blizzard. You might just be miles from civilization and a little hungry or thirsty.
I like to keep a few high calorie snacks, like Cliff Bars or Salted Nut Roles, in my trunk. These foods have lots of calories and plenty of sugar, which makes them ideal survival food.
The other reason I like Cliff Bars is they keep well. They don’t melt in extreme temperatures and stay good for long periods of time. You can set it and forget it, until you really need it.
Water is the more important of the two. Human beings can go without food for weeks, but can only make it days without water.
It doesn’t matter how you carry the water.
I like to fill a 2-gallon freezer bag with four or five 500ml water bottles. The sealed containers keep the water fresh tasting and, because they are individually wrapped, I can pass them out quickly to anybody who needs them.
Did you like the list?
Did I miss something? Tell me what your top ten essentials are. Maybe you’ll have me smacking my forehead and replacing a bullet point.
Disclaimer: “Adventure Bent is a participant in the Amazon Services LLC Associates Program, an affiliate advertising program designed to provide a means for us to earn fees by linking to Amazon.com and affiliated sites.” | tomekkorbak/pile-curse-small | OpenWebText2 |
El ex candidato presidencial Cuauht�moc C�rdenas Sol�rzano descart� que su hijo L�zaro C�rdenas Batel represente la opci�n para lograr cohesi�n entre perredistas. �Ni los milagros de cualquier santo� conciliar�n las divisiones en el partido, declar�
Video Dif�cil cohesionar al PRD: C�rdenas. El fundador del PRD ve `estancado´ a este instituto político y afirma que `ni los milagros de cualquier santo´ podrían conciliar los intereses al interior del partido
CR�TICA. El ingeniero dio a conocer su libro �Sobre mis pasos�, en el que relata su vida pol�tica y endereza cr�ticas a PRD.. (Foto: Esperanza Orea/EL UNIVERSAL )
Martes 18 de enero de 2011
Jorge Ramos P�rez | El Universal | tomekkorbak/pile-curse-small | OpenWebText2 |
In an embarrassing turn of events, an Indian army soldier who was supposed to give a presentation during a military gathering ended up playing a pornographic video on his official laptop.The Border Security Force (BSF) officer was supposed to give a presentation on training at Ferozepur city during ‘Sainik Sammelan’ at the headquarters of the 77Battalion on Saturday, according to Press Trust of India Instead, a porn clip started playing which went on for about 90 seconds, embarrassing the force which ordered a probe into the incident. “A probe has been ordered and details will emerge once it is completed,” BSF DIG RS Kataria said. “Any such action which affects BSF’s discipline and efficiency would not be tolerated.”The development comes less than two months after India’s BSF dismissed a soldier who shot a viral video to ‘expose’ the poor quality of food being served to the military men deputed at the border. Tej Bahadur Yadav accused senior officers of selling off various ingredients in the market, leaving substandard food for the soldiers.In March, another Indian soldier who accused officers of maltreatment was found dead in his barracks in Maharashtra. Roy Mathew had gone missing from his artillery centre on February 25 after a video in which he criticised the British-era ‘sahayak’ or orderly system in the Indian Army, went viral on the internet.In January, Pakistan Army returned an Indian soldier, Chandu Babulal Chohan, after he had deserted his post at Line of Control due to grievances of maltreatment against his commanders. | tomekkorbak/pile-curse-small | OpenWebText2 |
Posted
by
Soulskill
on Friday February 14, 2014 @12:35PM
from the follow-the-leader dept.
GuerillaRadio writes "Following the decision for Debian to switch to the systemd init system, Ubuntu founder and SABDFL Mark Shuttleworth has posted a blog entry indicating that Ubuntu will now follow in this decision. 'Nevertheless, the decision is for systemd, and given that Ubuntu is quite centrally a member of the Debian family, that's a decision we support. I will ask members of the Ubuntu community to help to implement this decision efficiently, bringing systemd into both Debian and Ubuntu safely and expeditiously.'"
I think it's good Shuttleworth was able to suck up his pride and go along with this decision to prevent fragmentation. I do however call the original decision slightly into question, but that's only because I've gotten sort of used to upstart. Hopefully anything good that was implemented in upstart but was not in systemd will make its way over.
Having switched from System V to upstart to systemd I can safely say that yes, systemd is better for a full server or desktop OS. It has better reporting tools, it has more fine grained control, and it's fast. The trade off is complexity and size. There are many computer systems that the cost of switching to systemd will not bear fruit for a very long time (ex. embedded), but for servers and desktops that time has arrived.
I don't think very much embedded stuff will ever use systemd. Most use System V or Busybox init or spin their own simpler version. If someone is using a general purpose install like Ubuntu for embedded work, they're doing it wrong right from the start.
This is a fallacy. A shell script running on a non-bloated shell (e.g. Busybox ash) consumes less than 50k of dirty pages per instance. It would take at least 20-30 such scripts running to even come close to rivaling systemd's memory usage, and that's not even counting other resources systemd is consuming.
It's actually a drain on embedded systems to do so much through shell scripting, having all those processes running scripts in an interpreted language.
This is a fallacy. A shell script running on a non-bloated shell (e.g. Busybox ash) consumes less than 50k of dirty pages per instance. It would take at least 20-30 such scripts running to even come close to rivaling systemd's memory usage, and that's not even counting other resources systemd is consuming.
Memory isn't the only resource. (And if you're using Linux, you're already using a ton of memory.) Systemd brings standardized, concurrent, event-driven startup, so it takes less time to start up, both CPU time and wall clock time. For example, systemd's declarative unit files have much less boilerplate and take less effort to parse than SysV-style init scripts.
At this point, systemd has also been concentrating on correctness and functionality. They aren't even optimizing for speed and memory consumption, yet. It would be interesting if Busybox added a systemd-style init.
Startup speed is simply not an issue anymore. Your typical server is supposed to be up most of the time, your typical desktop or mobile device is sleeping or suspended when it's not running, and your embedded device only has very few services that it needs to start, to the point where even SysV init is overkill and you're better off with rc.conf or something similar.
That's incorrect.
The big excitement in servers is Elastic Compute. There, you do want servers that can boot up and shut down as quickly as possible, to handle varying demands. It seems that even Linux is considered to take too long, so some Linux kernel maintainers are making their own cloud OS that boots up even faster. [lwn.net]
Desktops and mobiles do reboot sometimes. Fast booting was a major selling point for Unix during the age of The UNIX-HATERS Handbook. [washington.edu] A bigger benefit for modern PCs is how systemd uses soc
At a point when even the cheapest SoC has more processing power, memory, and storage space than your current desktop the cost of learning and using a custom system like Busybox will outweigh the benefit for many. For devices that need instant-on capabilities I don't think it's realistic to expect anything other than a custom init, but for the rest I expect programmers to programmers; that is, lazy.
I am using Angstrom, which uses systemd, for embedded stuff. Haven't had any problems with systemd, but haven't tried to do anything complex either. It gets stuff started at startup time, that's all I have needed.
Mostly, unless I've needed to hack something I've ignored the init system more or less completely. SYSV seemed to work OK (never noticed any obvious problems) and on Arch it used to be really rather fast to boot as well.
I genuinely do not know what is bad about wrong with SYSV and what is better about systemd.
There seems to be a lot of hot air in general and people arguing from a point of ignorance. You seem to have looked into it. What's the beef?
I am with you, I never saw a reason to get rid of SYSV. The reason Linux started pushing is based on the same Logic Sun had to go away from it. A master daemon which monitors all services and their current states, restart when necessary, etc... The Sun implementation took a bit of getting used to, but in reality the daemon used XML files which contained mostly SH scripts. It was still hackable, which is why SYSV stuck around for so long. When something does not work, write a new SH script and stick it in init.
The Linux implementation is not as straight forward as Sun's implementation which to me says a lot. RH6 went to systemd and I hated it. Cryptic, not hackable, and simply a pain in the ass to customize unless you run everything in legacy mode which is still SYSV. The alleged better logging did not exist, and was much harder to access than "set -x" in an init script.
The overlord daemon is an advantage, previously we all used monitoring scripts to do things for us. The system now has it built in. I never saw an issue with writing restart options into BigBrother, Nagios, etc.. so don't save much with this small feature. In the grand scheme of things, I lose a lot of flexibility with this system. So most of my custom tools, code, and scripts will run in legacy mode.
RH6 went to systemd? I don't see systemd on any of my RHEL6 or CentOS6 machines.
I am running a RHEL7 beta box, and it does have systemd. And it's not really that cryptic or unhackable. In fact getting a new daemon installed and running is far simpler than with sysv. You don't have to write an init script. Just create a simple ini file, and away it goes. Because there's no init script to screw up, things are easier to debug. If you can run the daemon from the command line and it's happy, then you know
One of the biggest selling points of Linux for me was that its log and config files were text files.
When I first started working with OS/2, one of my principal frustrations was that each and every IBM program product had its own proprietary config and log file format that could only be accessed using a product-specific utility. In Linux, the standard text utilities were all that were needed, and there are text utilities for almost every conceiveable way to search or update those files.
While there are certain things I like about systemctl and the newer Linux logging manager, their departure from this inherent simplicity disturbs me. It's aking to the trend to provide "improved" systems like Gnome3 or Windows 8 where your gains are offset by your losses.
Even a relatively open binary system like OLE/COM turned out to be more trouble than it was worth for me. I'd rather not throw out the good with the bad.
Indeed, journalctl is probably what I dislike the most about the current systemd stack. For one thing it is slow with full text search in large log files -- it is reasonably fast if you use the built-in column-specific search, but just running fgrep on it is not really feasible. In contrast, fgrep is ridiculously fast on modern systems as long as your log files stay below a few gigabytes in size. Also, the output of journalctl changes (mostly for the better) when you use it with pipes, which can be quite surprising.
The other major problem with systemd is how difficult it is to debug boot failures. It is quite annoying when an fstab which was correct with upstart results in silent boot failure with systemd.
Well good then that the ini files for SystemD is text and that you can export the textlogs from the logger.
Exporting isn't the same as processing in place. And the other day, in fact, I ran into an issue where messages that I expect to be able to "tail" out of the older log simply couldn't be found.
The systemd authors have already admitted that there are certain functions that the older script-based ini's could provide that their strictly-declarative system at present cannot. Having text formatted files is useful but not being excessively restricted in what the text can do is also important.
Starting with version 6, however, CentOS has turned to a new and better init system – Upstart. Upstart is faster than System V init because it starts services simultaneously rather than one by one in a certain order. Upstart is also more flexible and robust, because it is event-based.
System V has a scrict sense of a run level. For example, if you want a full desktop, run level 5 is often used, for a headless server, run level 3. What if you have a box that is headless most of the time, but you want to be able to run a full desktop sometimes? With System V you would change from run level 3 to run level 5 which would, depending on implimentation, stop and start services that are needed by both. Systemd instead has the concept of targets. Your full desktop target would have the headless server target as a dependency, and starting the full desktop would only run what isn't already running. You typically also have individual sevices that have dependencies. For example, you'd want your dhcp server to wait to start until the network has come online. In System V you have to define network as a number and make sure everything that depends on it has a bigger number and everything it depends on to have a smaller number. systemd's dependency model is also smart enough to start processes in parallel.
All of that is just the most exposed part of systemd (to me at least). It also supplants other processes such as xinetd and udev. Instead of having three different ways to start processes based on system events (startup, port connection, hardware event) you have a single system to manage all three. It can get complicated (wasn't udev already complicated?) but the consistency is worth it.
To keep all the consitency systemd provides a series of functions and magic variables. By magic variables I mean you set a list dependencies, which IMHO is less magic than the chkconfig comment lines in a typical System V init script. Both the magic variables and functions mean your typical service initaliation script is 10 lines instead of 100. While they may not be as obvious what's going on (a System V script is self-contained and can be ran on it's own) it is once you've become familiar with them.
Yes, and you have to understand that that only works because your DE of choice has bent over backwards to make sure all it's dependencies are running and functional when you try to start it. That is to say, startx has to duplicate functionality of init because init is too stupid or too unreliable to be able to do it for your DE.
This issue can be generalized to any significantly complex application. That means you already have a half dozen "init systems" working on your systems. They're all independent (even though they maybe should know about each other), and you can't manage them universally (even though you might want to fire things off with system level events, like restarting a service if it crashes), and you certainly can't be sure you're not stepping on each others' toes.
Essentially: a large enough number of people noticed that the same features for starting and managing processes were getting implemented over, and over, and over. They realized that these functions belong in the init role -- because only init has the authority and knowledge required to not screw it up -- but that sysv-init didn't have the capability to do any of that.
All this began to happen perhaps 10 years ago, when other operating systems (e.g., Windows, which has had service dependencies and crash recovery since Windows 2000) showed what a more feature-complete init system was capable of.
At this point these "why do we even need a new init system?" questions are like someone watching I-40 getting repaved in the 1970s and asking "why do we even need Interstates?"
In System V you have to define network as a number and make sure everything that depends on it has a bigger number and everything it depends on to have a smaller number. systemd's dependency model is also smart enough to start processes in parallel.
If only systemd were really "smart enough", it would be great. Unfortunately, if you have a sevice that needs another service 100% functional before it can run, systemd has no way to describe that in the dependency files nor to test it.
All systemd uses to define a "running" service is that a process doesn't throw an immediate error upon startup. And, that's all it can ever have, unless the service is specially coded to be systemd-aware or does something like create a file in/var/run after it has fully initialized, and the dependency can be written using file existence. This really isn't any different in SysV, but at least there I could trivially edit the startup script of the dependent service and add some sort of test.
Because there is no way to test every combination of services, there is no way to reliably create systemd dependency files that will always work. Because of that, we get things like rc.local running before other services have started completely.
Unfortunately, if you have a sevice that needs another service 100% functional before it can run, systemd has no way to describe that in the dependency files nor to test it.
All systemd uses to define a "running" service is that a process doesn't throw an immediate error upon startup. And, that's all it can ever have, unless the service is specially coded to be systemd-aware or does something like create a file in/var/run after it has fully initialized, and the dependency can be written using file existence.
That isn't true. Putting aside the systemd-specific sd_notify() API for reporting just how completely the service has been initialized, and the socket activation model which allows other services to connect while startup is still in progress, systemd also supports traditional "forking" daemons which complete their initialization before the main process exits. You can also use the ExecStartPre and ExecStartPost fields to inject arbitrary commands into the startup process separate from the daemon itself.
The best case short of actual systemd integration is that the service already does the right thing with the fork-and-exit model, so that it's ready to be used before any other services are started which depend on it. But even if that isn't the case there are ways to deal with it under systemd, up to and including custom shell scripts for the really complex cases.
This might be ok for servers but lets say you have a laptop with Ubuntu. You are on a network and it goes to sleep at work. You grab it and head to the airport for a trip and the laptop wakes up elsewhere. All of your SYSV scripts to do things like pass settings to daemons relating to network and Samba get messed up.
With an event driven system you tell it to do things based on conditions or events such as your laptop going to sleep and waking up on a different network as an example. You can use SystemD to re-initialize itself not just on startup but when things happen with this new ability. A hacking attempt on a server, an unplanned reboot, or anything else
The bad about SystemD compared to upstart and Apple's or Sun's event driven systems:- no text files- binary reporting- quite complicated compared to other event driven systems like the older upstart
System admins hate systemD as it does not follow the Unix philosophy of text files and now awk, sed, grep, or perl to batch jobs:-(
Some also is resistance to change as many unix old timers hated anything new by Sun and did not want to relearn writing new scripts all over again. But, this tries to solve a problem like the laptop example but at the cost of complexity and non integration.
The bad about SystemD compared to upstart and Apple's or Sun's event driven systems:... - no text files
What do you mean by that? The database used by journald may be binary (with the ability to export to text), but systemd unit files are simple text files with an INI-style layout. There are some other systemd configuration files with different formats for historical reasons, but to my knowledge all of them are still text.
> System admins hate systemD as it does not follow the Unix philosophy of text files and now awk, sed, grep, or perl to batch jobs:-(
Firstly, it's systemd. I'm not sure where you're getting the capital from.
Secondly, generalise much? I'm a long-time Linux system admin and I can't wait until systemd filters down to server distros like CentOS and Ubuntu LTS. It will make my job a whole lot easier.
Don't be so quick to count embedded guys out yet. While there isn't much in systemd itself, but as I understand it it will integrate well with kdbus. And kdbus (I think) plans to support QNX style "yield CPU to destination" type message passing. Which is a very nice feature for realtime systems.
The tradeoff is complexity and size. I've got to say, I still don't buy it, this entire concept of requiring more resources to do the same job and yet somehow being more scalable to a degree that makes the trade-off worthwhile. If you have to upgrade your system to see the benefits (embedded systems are no slouches these days, look at any ARM tablet specs) then those benefits are seriously questionable.
Current systems, even phones, have dual and quad core processors. That means the existing hardware can run four threads on the CPU simultaneously, or about 16 active processes. System V runs one process at a time, meaning it's only using 6% of the hardware's capability.
Systemd, on the other hand, runs several processes at once, getting things done faster by making use of post-1995 hardware.
You say you don't see point of changes that take advantage of modern hardware. You only really benefit from 64 bit if y
I say you're wrong because we don't need systemd to do that. No, we don't, because it's been possible to multiplex the SysV style init for ages. My debian server does it, with a slow SSD, and the results are beautiful. I'm all about taking advantage of modern hardware, but you're seriously talking about rewriting init because you don't want to use one of the pre-existing options for multiplexing the start up process. That's silly.
In truth, like System V, it's a set it and forget it sort of thing for most users (or more realistic, never realize it's even there sort of thing). For me, I have about 40 servers, physical and virtual, and about 150 thin clients to manage using various shades of Fedora, CentOS and RHEL. The thin clients boot over pxe to and then connect via xdmcp to a Fedora 19 box for their desktop environment. As Fedora 19 isn't exactly the best, and users do strange things, one will end up getting rebooted every week or
In truth, like System V, it's a set it and forget it sort of thing for most users (or more realistic, never realize it's even there sort of thing). For me, I have about 40 servers, physical and virtual, and about 150 thin clients to manage using various shades of Fedora, CentOS and RHEL. The thin clients boot over pxe to and then connect via xdmcp to a Fedora 19 box for their desktop environment. As Fedora 19 isn't exactly the best, and users do strange things, one will end up getting rebooted every week or so. The thin clients end up getting rebooted all the time (people think they should turn off their computer at night, so they do). Being able to use journalctl to see exactly what process took how much time was instrumental in getting a fast bootup time, which makes users happier. Happy users = happy admin. Happy admin = the building doesn't get burned down in a quest to get back the stapler. Every time I have to mess with anything other than systemd (on the CentOS and RHEL servers) I die a little inside. It's like using ipchains instead of iptables. Yes it worked, but the world moved on (and yes, I know, iptables is archaic at this point in time).
Good call Mark, glad to see Ubuntu embrace what is comming. Now, for the interesting part, it is time for sys admins to rally and push for the interfaces/workflows that we need. systemd obviously has certain strengths, now lets bring the experience and know how of good sys admins to make working with systemd mutually beneficial for all.
People talk about parallel start up , well you can do that with init anyway. Its it smarter with dependencies or is it just change for the sake of it? I'm really not thrilled with the prospect of yet another config language, there are quite enough already.
Lets face it, sysV init is complicated. Well, the theory behind the old linear start from init script 00 and move to init script 99 isn't, but the modern implementations and the scripts themselves are complicated. I mean you're doing dependency checking and a whole bunch of other things in bash scripts. Compare that to a systemd service file, which is overall nice and readable. So, part of it is factoring out the logic from the variables. The other big thing is bash and the tools used by init scripts are like using a sledgehammer to tap in a finishing nail.
I'm not going to say that systemd is perfect. I like the "unix" way which is to use small units that do one thing well instead of anything. That's part of the reason I see bash init scripts as too much for the job. Unfortunately, the systemd authors look like they want to throw in everything but the kitchen sink. Well, everything that they can't just port to kernel space that is. But that's the thing, Linux is a Monolithic kernel. Like it or not, the "Linux" way is to have one uber optimized thing with modules to handle everything.
In the end, I just really like the ease of use of service files. Oh, and the stupidly fast boot time on my laptop is really nice. People who say boot times don't matter aren't living in the real world.
Lets face it, sysV init is complicated. Well, the theory behind the old linear start from init script 00 and move to init script 99 isn't, but the modern implementations and the scripts themselves are complicated. I mean you're doing dependency checking and a whole bunch of other things in bash scripts. Compare that to a systemd service file, which is overall nice and readable. So, part of it is factoring out the logic from the variables. The other big thing is bash and the tools used by init scripts are like using a sledgehammer to tap in a finishing nail.
I'm not going to say that systemd is perfect. I like the "unix" way which is to use small units that do one thing well instead of anything. That's part of the reason I see bash init scripts as too much for the job. Unfortunately, the systemd authors look like they want to throw in everything but the kitchen sink. Well, everything that they can't just port to kernel space that is. But that's the thing, Linux is a Monolithic kernel. Like it or not, the "Linux" way is to have one uber optimized thing with modules to handle everything.
Well, the BIG problem is maintenance. SysV scripts have both a S and K variant on when to run when switching levels, and you can bet very few people have it properly set up if you do switch levels. Enough so that switching levels is fraught with danger - you can probably start at level 1 (single user), and switch to 3, 4, or 5. Maybe you can get back to 1 because the extra demons get killed. Maybe.
In the end, it's bit of a maintenance hassle, and while completely understandable, it's a nightmare.
In fact, I'm guessing most utilities don't even bother handling the case - you just reboot and forget about it.
After all, computers are good at doing stuff automatically - so stuff like maintaining which services should run at which runlevels should be automated - the init can figure out what it needs to start, what it needs to kill and the order based on dependencies. All the user needs to do is select what needs to run at what runlevel, and the tool does the rest.
Then there are the various hacks to SysV - PID files (if so many tools need to know the daemon PID, why not have init actually do that work than requiring every script to do it manually?), the fact that state tracking isn't really in the system, and if you need services to relaunch on failure within limits, there ought to be a way to do it without requiring a trip to/etc/inittab to specify that fact.
Well, the BIG problem is maintenance. SysV scripts have both a S and K variant on when to run when switching levels, and you can bet very few people have it properly set up if you do switch levels. Enough so that switching levels is fraught with danger - you can probably start at level 1 (single user), and switch to 3, 4, or 5. Maybe you can get back to 1 because the extra demons get killed. Maybe.
I know what you mean. I've used Linux systems that were set up that way, and it's messy and a bit of a nuisance to make sure the system is really going to do what I think it's going to do.
Personally I'm a long-time Gentoo user and my system runs OpenRC. Have you ever used it? It eliminates the sources of confusion you illustrate there. It's neat and it's simple and it works and I can forget that it's there. That's what I like about it. There's nothing I want it to do that it doesn't already implement.
Right now Gentoo is one of the few distros that supports a non-systemd installation, mainly because the idea that as little as possible should ever be forced on the user is one of their core principles. Gentoo has very few mandated default anythings and they encourage users to file a bug if they discover an unnecessary one. I am interested in systemd and I acknowledge it probably isn't taking off so well for no reason, but this is why I'm not in any hurry to adopt it.
BTW OpenRC does have a form of state tracking. It simply uses start-stop-daemon for this, so that each initscript doesn't need to worry about it.
Yup. I suspect Gentoo will be one of the last distros to make systemd a default, and I think that is because openrc really is the best traditional sysvinit implementation out there. I've used systemd on some of my Gentoo VMs and when you get into edge cases it can be clunky (I couldn't get it to wait until after getting an IP to try to mount NFS, for example).
The fundamental design is very good, but it will be a while before it completely surpasses openrc. It isn't unlike ext4 vs btrfs - the latter is al
Yes, you can do parallel startup with System V. You also can make a systemd init process that doesn't do anything in parallel.
Yes, systemd is smarter with dependencies in the sense that it has dependencies and not a numered list. Yes, you can have a System V script that manages it's own dependencies, but because you can do an infinite number of things with System V scripts many people have tried. I've ran across dozens of System V scripts that are hundreds of lines long even without couting the standard "./etc/init.d/functions" size, which, on my system, is almost 600 lines long. Systemd simplies this by having a much larger library of functions and uses the presumption that you'll never call a script without using systemd to manage it. No longer does every script have to define a start, stop, restart, condrestart, status function; it's handled by systemd. No longer do you have to do checks for your PID file; it's handled by systemd. No longer do you have to make sure your script will always run after another script even if that script's chkconfig number changed; it's handled by systemd.
In the end, yes, it's another config language you'll have to learn, but it's worth it.
And if I'm not mistaken your script can be set to start when/var/run/mysql.socket becomes ready instead of being started directly after/etc/init.d/mysql started and the mysql process decides to do a major table check so that the server is not accessible for 5 minutes which makes your daemon exit with an error since the database was not available at start.
In the end, yes, it's another config language you'll have to learn, but it's worth it.
Why is it worth it?
I've heard lots of "systemd is better" claims, but not one real-world example of how it took 27 hours to debug a startup issue when using SysV, but only 13 seconds using systemd. And, I really don't care about boot times, because my physical servers take 10 times as long running through BIOS checks as they do going from grub load to system ready. Even VMs don't matter much, as they don't get rebooted very often, so saving 5 seconds on a 30-second boot time isn't really a big deal.
On the other hand, I've heard lots of stories from people who have to install a custom service (i.e., not from a "apt-get" or "yum install") on a systemd system and complain about how it took hours to get the dependencies right.
It is nice for example is you can set your laptop up for different networks and when conditions change such as it sleeps and wakes up on a different network it can respond differently. You do not have to write a complex script for every possible combination you can think of.
Just put in the parameters and tell it what to do with events.
It can be used too after booting up for servers so if a hacking attempt is detected it can dynamically change its firewall settings as
The config language, if you mean the syntax of what used to be the service files, is actually nice. Most keywords are well chosen and you can do partial or complete overrides of them by adding a file in the appropriate place in/etc.
The dependency system is good too, and being able to launch daemons without the traditional double fork is brilliant. The only surprise I have hit so far is that network.target does not actually wait till the network is up -- network-online.target does that.
"I know nothing about this software but I'm gonna bitch, complain and sling shit at it anyway. How dare they move my cheese!"
- Typical Slashtard
Knowledge of the new software is a separate (easier to cheaply ridicule, stay classy) question. The issue with systemd: it reeks of a solution looking for a problem.
If the existing init systems were causing widespread grief I'd be much more receptive to it. So would just about anyone currently questioning systemd's rapid adoption. Right now the reason for installing it is "everyone else is adopting it as the new standard and it will be increasingly difficult to go against that standard." That's not the best of selling points. It's not like "wow all these problems and limitations I had been experiencing will finally go away!" like you get with truly sensible and evolutionary changes.
If you think that shouldn't matter to anyone, you could explain why you think so. In the meantime, please make an effort to understand the viewpoint of those who disagree with you. Then you stand a real chance of actually addressing the issue, or at least of not embarassing yourself with smug hand-waving and knee-jerk dismissals based on your annoyance that everyone doesn't already agree with you.
The issue I belive is that the Linux kernel has been expanding its capabilities and the init system has not kept pace. Part of that reason is that to take advantage of Linux specific issues means breaking compatibility with other *nix systems.
Take cgroups for example. It is a Linux specific feature, and a great one at that. It can limit CPU, memory, and I/O processes not just just for one process, but for all of the processes that fork off of it. Along the way it solves the "escape by double forking" issue. For systems doing virtualization or running multiple servers it is exactly the kind of thing an admin would want for his services.
Or how about service dependancies? The sysem of A depends on B,F,K works great for all of our package managing systems, and has been for years. The is the reason upstart was adopted, the runlevel system is a very inelegant solution.
I'm not saying systemd is perfect. I really like status messages, but using a binary log file I think is a mistake. But it does provide new features that a lot of developers and admins will be able to take advantage of.
Outside it that, I fully understand that attitude of people who don't like change for the sake of change...I'm one of them. Having to learn a new configure language is a pain when I'd rather be doing something else. But if there's a valid reason, that makes things more acceptable.
Knowledge of the new software is a separate (easier to cheaply ridicule, stay classy) question. The issue with systemd: it reeks of a solution looking for a problem.
Based on having used it or because your cheese got moved? All these distros wouldn't be adopting it if what you say is true, especially Debian. Get back to me when you have a real argument not cliches.
So you prefer to repeat yourself rather than address the real root cause of the remaining resistance to systemd? You definitely missed an opportunity there.
I said I question systemd's adoption. I didn't say I was against it, nor did I say that other people shouldn't use it. Even that offends you, and you resort to a form of "everyone else is doing it!" (the antithesis of thinking) to justify yourself. This is why you are smug.
I reasonably put a valid question to you and you weren't prepared for th
I'm sorry but the systemd thing is really, really a mole hill when it comes to Ubuntu embracing things. From my perspective it doesn't matter what init scheme you use as long as it does it efficiently and allows you to augment things when you need to. Shit most Linux users don't even know what their distro's choice is for init scripting! Cripes you'd think that folks would have thought that the Vatican was now allowing electronic balloting and using Green Friendly e-smoke for electing the Pope or something with all this nonsensical whoopla.
Users rightfully do not care about what init system they use, as long as it works.But making it work requires time and effort from some people. And we don't live in a world of infinite resources.
By announcing they're switching Ubuntu from Upstart to systemd, Ubuntu aligned themselves with the majority of the developer comunity and Ubuntu reduced the ammount of effort they and others developers have to put in to make it work efficiently as you said.Ubuntu will not have to write and debug Upstart configuration files for services, they can just the share the same systemd files as Debian.GUbuntu and KUbuntu developers will have less trouble to make Gnome Shell and KWin, which are moving towards somewhat depending on systemd, work on a Ubuntu derived distribution.
Users rightfully do not care about what init system they use, as long as it works.
But making it work requires time and effort from some people. And we don't live in a world of infinite resources.
By announcing they're switching Ubuntu from Upstart to systemd, Ubuntu aligned themselves with the majority of the developer comunity and Ubuntu reduced the ammount of effort they and others developers have to put in to make it work efficiently as you said.
Ubuntu will not have to write and debug Upstart configuration files for services, they can just the share the same systemd files as Debian.
GUbuntu and KUbuntu developers will have less trouble to make Gnome Shell and KWin, which are moving towards somewhat depending on systemd, work on a Ubuntu derived distribution.
And that means they can actually spend time fixing other stuff.
This is more like the kind of answer I was expecting to my earlier posts in this discussion. It makes a lot of sense. Thank you for that.
It's nice to seen an adult person give a reason that makes sense instead of getting all pissy that everyone doesn't already see it his or her way.
I don't know what Slashdot you're reading but the one I'm reading is packed with supportive comments about the decision. I think there's just relief that Shuttleworth hasn't decided to NIH something for once.
(Not that I'm particularly upset that they tried to do something different with Unity. GNOME 3 needed a good alternative, the problem was that Unity seems to be just as flawed, not with the principle of doing something. It'd be nice to see them stick with X.org rather than go Wayland, but they've als
The philosophy of modularity. Tools are many and small and simple, do one thing and do it well. But then, the Linux kernel also violates this principle.
There's also this seeming drive to make more tools dependent on systemd. Does udev really need to depend on systemd?
Wayland may be an example of an approach more in line with the UNIX philosophy. X has a lot of baggage that has become useless over the years. Lot of basic graphics functionality has moved into specialized graphics hardware.
Wayland is actually one of the "new Linux" things that I'm interested in. I'm not getting rid of X anytime soon, but when Wayland has the tools, hardware support, etc. I need, I'll likely switch to it without any fuss. (For the curious, I use i3 as a window manager, and there's just no equivalent compositor for Wayland yet. None of my applications are GTK+3 or QT5, either, so I'd be using the X compatibility layer for essentially everything too.)
But systemd I really am not fond of. It's not an issue of being different (though that is some part of it), so much as the way it dictates so much of how you use things. It seems to touch every single part of your system on an ongoing basis, rather than just booting the system and staying out of the way. I sincerely doubt there would be as much distaste for it if it was just the init system part, rather than stuffing everything else in too.
There's this new thing called "init.d" which makes things really simple - you can start a system up and step through things, and though the boot takes 5 seconds instead of 1 second, that isn't really a problem.
Once I read the original post about systemd, [0pointer.de] and all the other let's-invent-a-problem-to-fix nonsense surrounding init.d, I literally hung up my hat and stopped being a syseng. I was a unix guy starting in 93, so it was probably time anyway, but it was the straw that broke my back, as it were.As mentioned, the central responsibility of an init system is to bring up userspace. And a good init system does that fast. I especially "loved" this line:
As mentioned, the central responsibility of an init system is to bring up userspace. And a good init system does that fast.
No. A good init system does it reliably, with no drama and no politics. A good init system allows one to easily determine the state of a system, and doesn't assume things like GUIs and such. A good unix init system does all this with commands which can be piped and parsed easily with grep and awk - two things the original post about systemd actually complains about. The idea that a unix person would complain about grep and awk was so mind-boggling to me that...well, I just hung up the hat. You did all this nonsense, just to save a few seconds? Because what, the only thing linux is used for, is laptops? Meh.
oh boo, slashdot dropped the pre tag? Dorks. "As mentioned, the central responsibility of an init system is to bring up userspace. And a good init system does that fast." = that was a quote from that original post about systemd
No they did all that nonsense to have features like monitoring and recovery that init.d didn't have. If a daemon has problems and needs to restart itself how does it do that? Heck if you really mean init.d and not xinit.d how does a system support triggers for hundreds or thousands of daemons most of which run very infrequently?
If a daemon has problems and needs to restart itself how does it do that?
...Monit [mmonit.com]? runit [smarden.org]? Two completely different approaches to service monitoring, one not even in an init system. And there are more (s6, daemontools, etc.).
hundreds or thousands of daemons
...What the heck are you running that puts thousands of daemons on a single server? If you're doing something this large, you might want to consider virtualization. Thousands of daemons is a gigantic attack surface to have on a single system, and a mess if something were to go wrong with one of them that takes down everything.
Correction: The original post about systemd was not complaining about using grep and awk on the scripts. The complaint was that the scripts where calling these commands way too often during the normal boot up procedure.
On my system the scripts in/etc/init.d call grep at least 77 times. awk is called 92 times, cut 23 and sed 74. Every time those commands (and others) are called, a process is spawned, the libraries searched, some start-up stuff like i18n and so on set up and more.
A few mails down the line, I saw someone (Ian Jackson, I think), call for a vote to depose Bdale as the TC chairman, and another vote with more options. The mail thread went on and on...Can anyone summarize what happened then? Is Shuttleworth premature in this decision?
systemd is as good as init daemons management system - the problem is how the transition is going to be performed? Hopefully it won't be like the gnome-classic => Unity mess. Init and systemd will both have to be available, giving time to administrators to migrate what could not be automatically transferred and specific applications.
Fedora made the transition some time ago, and from a user's point of view it was completely transparent.
RHEL7 beta has transitioned to systemd, and again it's pretty transparent. The old service command is still there and thunks through to systemd. The only time you really notice the difference is if you want to install a custom daemon. You can either use an init script, or you can create a simple systemd service file. There are a few systemctl commands to learn. But really, it's as close to a painless
Only if you blindly ignore all the advantages. Neither init or systemd will solve the world's hunger problem. The distros have decided for all the advantages to go with systemd. But they must be stupid not to see your point of view, right?
The distros are going with it presumably because they think they need it to turn Linux into a desktop or notebook OS. However, they seem to be ignoring the issues it presents for servers. Let's take my *THREE HOUR* debugging session on systemd yesterday. I had a netboot system up and running. Client boots from Server and mounts root filesystem from Server. I changed from Server A to Server B. Due to an NFSv4 vs. NFSv3 issue, Client could no longer mount the root filesystem read/write. Simple, right? It would've been with SysV init because the errors during the mount would've been spewed to the console and I would've seen them. What *actually* happened is that a bunch of services failed to start. Instead of spewing the error message, systemd "helpfully" told me to run "systemctl status" on the service to see the error message. Except that I never got to a login prompt due to the errors. And I couldn't mount the filesystem read/write so it lost the logs.
Two+ hours later, I managed to disable enough stuff to get to a login prompt where I was finally able to figure out what was going on (never did get systemctl to show me the logs, probably because they couldn't be written to disk and it doesn't seem to hold them in RAM).
Please explain to me what the advantage of systemd is again? Because I'm *REALLY* not seeing it. It took something that was trivial to figure out and made it astronomically difficult. I no longer have any idea what order my services start in or whether that order is repeatable. Yes, SysV init scripts were really long. But once you learned them, you realized that you only had to modify 5 or 6 lines of them to get a new service going. I have yet to figure out how to even create a service with systemd or how I figure out what I'm depending on.
In short, for a server, I have yet to see a single advantage of systemd over SysV init. Maybe I'm missing something and someone will enlighten me, but I'm extremely skeptical.
Am I just resistant to learning new things? Maybe, but learning stuff takes time and my time is money for my employer. So if I'm not getting a return on my investment of time (in new capabilities or reduced debugging time or *something*), why would I invest the time to become an expert on systemd?
> I have yet to figure out how to even create a service with systemd or how I figure out what I'm depending on.
man systemd.profile
> Let's take my *THREE HOUR* debugging session on systemd yesterday. [...] It would've been [simple] with SysV init because the errors during the mount would've been spewed to the console and I would've seen them.
Yes if you think systemd is bad, either rip it out on your machine or roll your own distro. Or move to FreeBSD. It's available now, and it runs great. So no need to whine. Just move to an operating system that fits your personal parameters. More likely you'll stick with your current distro and whine and moan about something that you don't well understand.
On the desktop side of things, I've been watching Linux struggle for years to do simple things like deal with removable media and USB devices. For a while there was hal, then udev, and now systemd. And finally things are actually working, and working rather well. Mostly thanks to udev, but systemd now builds on that. I know many people don't mind manually mounting devices and loading modules to make usb devices work (I don't mind, really). But it's nice to have things automatically work.
And really systemd on the service isn't that bad an idea either. Fine-grained logging is very useful and conventional syslog is still available and will always be there. Process supervision is something that's been needed for a long while now.
The big problem with systemd is that it is trying very hard to make itself a non-replaceable component. Gnome effectively depends on it now, for example, and with udev being merged into it you basically can't avoid systemd without forking udev (which some Gentoo guys are trying to do). It also exposes public DBus APIs and a wrapper lib that's intended to be used by daemons to e.g. report lifecycle events, which obviously makes them systemd-specific. And the developer of systemd is actively campaigning for p | tomekkorbak/pile-curse-small | Pile-CC |
Resurrector
Resurrector (born Grant McDonald Chambers, May 10, 1971 in New Haven, CT) is an electronic music producer best known as founder of Colorado/San Francisco Dub Hop band Heavyweight Dub Champion and the ethnically diverse Liberation Movement. He is the co-producer of both Heavyweight Dub Champion studio albums and is main creator of the band's philosophical ideology defined by the Last Champion Manifesto, a booklet included with the 2002 album, Survival Guide For The End of Time. Chambers now lives in San Francisco, CA and performs and produces for Heavyweight Dub Champion and Liberation Movement, among others.
Early Years
Chambers grew up mostly near Baltimore, MD, but lived in multiple countries where his father, a college professor, had visiting fellowships. As a teen, he promoted punk concerts and frequented the D.C. punk scene. His father, Dr. Robert H. Chambers III was president of McDaniel College from 1984–2000. In 1988, as a high school junior, he promoted a punk concert in the basement of the McDaniel College President's house. The event space was known as The Dungeon and the inaugural event was featured on the front page of the Carroll County Times. He went on to promote concerts with DC hardcore punk groups Government Issue and M.F.D. among others.
Chambers attended University at McDaniel College in Maryland, Harlaxton College in Grantham, England and received a degree in Religious Studies from University of Colorado at Boulder.
In 1995, while living in Boulder, Colorado, he founded hip hop reggae group Roots Revolt. Many of the key players in Roots Revolt would later show up on Heavyweight Dub Champion recordings, including HDC co-founder Patch Rubin.
Heavyweight Dub Champion
Heavyweight Dub Champion was founded in Gold Hill, CO in 1997 and played its first show on October 31, 1997. In 2005, the band relocated to San Francisco. With Heavyweight Dub Champion, Chambers has produced two albums as Resurrector, 2002's Survival Guide For The End of Time and 2009's Rise of the Champion Nation, featuring multiple tracks with KRS-One. HDC has performed throughout the US, Canada and Europe. As described by Marquee Magazine, "The live performance is referred to as the ‘Liberation Process’ because it's intended that the music can put the audience in something like a vibratory trance and can remove layers of deception through the music." According to a review in the La Weekly, "Their genius is the great virtue of ’70s dub: never overdoing it." Another review says HDC, "sounds something like hip-hop colliding with dub inside the eye of an electronica hurricane."
Survival Guide For The End Of Time
In 2002, HDC released their debut album, Survival Guide For The End of Time- "an ill-bent mix of industrial apocalyptic hip-hop dubtronica" that "aims to topple the foundations of modern-day Babylon" as well as offering "prescriptions for survival and victory in a tension-filled time." The album was recorded and mixed in Colorado and Los Angeles and "can safely be called a concept album". As described by Resurrector, Survival Guide "relates to the coming of the Last Champion, an interdimensional spiritual warrior, who is bringing people together throughout the world to try to elevate consciousness in a way that will focus people on the healing of themselves and the healing of the world, and help put people in a more offensive position."
Survival Guide has an ambitious package including the band's credo, Last Champion Manifesto, a 70-page booklet "detailing their mission of 'Unconditional Liberation of the Human Race,'” a poster by Jher 451 and sticker of their "protector" logo. As described by Denver's Westword Magazine, "Structurally, the record moves from the announcement of the battle to the rallying calls of the Last Champion's chosen army – followers who unite to liberate individuals and the Earth – to the eventual announcement of the Last Champion as a victor in the championship against predators who have put a stranglehold on humanity's innate desire to creatively seek truth, beauty, pleasure and power."
Last Champion Manifesto
"Penned just hours after the arrival of the new millennium", the Last Champion Manifesto and included in Survival Guide is a 70-page document "steeped in allegory and at times reading like ancient scripture", according to The Source Weekly. The LA Weekly calls it a "bible/babble manifesto" and the Denver Westword refers to it as a "scripturally spirited rant." The Westword reports that, at an early age, Chambers received visions from the "Last Champion" during periods of "severe headaches and lengthy vomiting sessions." The Last Champion Manifesto serves as the ideological foundation of both the album Survival Guide for the End of Time and the band Heavyweight Dub Champion as a whole- "We're a concept band. Everything we do is related to the manifesto. Every album will be that way," says Chambers.
There are seven chapters broken into mini-chapters named after the songs on Survival Guide and 2008's Rise of the Champion Nation. Each album serves as a sort of soundtrack to elements presented in the booklet. Songs relate to actions such as the Arrival, which was remixed by San Francisco's award-winning favorite Bassnectar, "Liberation Process", "Exorcism" and so on. Most of the themes relate to becoming a Warrior and the development of the "Last Champion's Chosen Army" known as "Champion Nation", which is also the name of the record label founded by Chambers.
Rise Of The Champion Nation
Heavyweight Dub Champion's follow up album (a "limited edition" was released at shows in Fall of 2008) includes guest appearances and endorsements from KRS-One, who states in the title track, "Heavyweight Dub Champion restores all hope", Killah Priest and Brooklyn Dub pioneer Dr. Israel, in addition to the familiar cast of A.P.O.S.T.L.E. and others. The project was mixed by Bill Laswell's veteran engineer Oz Fritz and is mastered by industry favorite Brian Gardner. Rise is described by one reviewer as "a rock-opera (or hip-hop opera) of sorts – a concept album of the highest sorts – and almost cinematic in its mostly dark themes and structure."
The album is conceptual following "the Warrior" from the Arrival, through Warrior Divination One, Two and Three, to emerge as King Of The Mountain and the eventual journey ends with Promised Land. Throughout the album the character of Emcee Vill is again beckoned to by "N.A.F. Agents" while on his quest to infiltrate Champion Nation and assassinate the Last Champion. Pop Matters describes the album as using "socially conscience and spiritual weapons of words to tell a story whose central plot leads to a philosophical and spiritual revival and a genuine awakening of the human spirit... (with) an apocalyptic and epic cinematic soundtrack."
Reviewed by Derek Beres in the Huffington Post, he calls the album "A conversion, the ending of an era, a new dawn". He goes on, "Their hope might feel bitter to the taste, but only because they are correctly reflecting reality. By the glean of their astute and painstaking cultural observations, we are invited to join into their dance. It may require we pound our fists and wave our heads—their trance is fitful, not wistful... this band does achieve greatness." Music Connection Magazine describes the album as "A consortium of prophets heralding our doomed planet."
Liberation Movement
Reality Sandwich calls Liberation Movement "a new collaborative music project that pushes the boundaries of human experience". Liberation Movement was developed out of experiences Chambers had working with the Shipibo Tribe in Peru. It was formed in 2010 in San Francisco. Chambers explains in an interview, "The project was seeded at the Temple of the Way of Light in the Peruvian Amazon, at which point I was recruited to work with and create recordings of shamans in traditional ceremonies in Peru. From that foundation, I wanted to start gathering artists and musicians that represent "archetypal gateways" ; veterans in different musical fields whose goal is to connect with the deepest life journey." He says he chose the name because "speaking the name is a revolutionary potential in and of itself.
Resurrector explains his work in Liberation Movement:
Work with the Shipibo Tribe of the Peruvian Amazon
In 2010, Chambers "went to Peru to learn about how music and vibration are connected to shamanism". This led to him recording more than 25 indigenous singers from the Shipibo Tribe at the Temple Of The Way Of Light near Iquitos, Peru and produce and release the album Onáyabaon Bewá – Messages from Mother Earth by Shamans of the Temple of the Way of Light.
In 2014, in collaboration with Peruvian-based NGO Alianza Arkana and the Rubin Foundation, he led Liberation Movement to Peru with bandmates Sasha Rose, Noah King and filmmakers Mitch Schultz (Writer/Director of DMT: The Spirit Molecule), Donald Schultz and Jason Gamble Harter to document a concert and surrounding journeys to villages along the Amazon River. Mitch Schultz stated, "Cross-cultural interfaces are paramount for accessing indigenous knowledge through a modern lens, or in this case the musical experience of Liberation Movement."
"Jiwexon Axebo" Concert
On May 2, 2014, Liberation Movement collaborated on a concert with Peruvian-based NGO Alianza Arkana called "Jiwexon Axebo" in the Shipibo Tribe's language and "Cultural Revival" in English. They "performed to 600 indigenous Peruvians"in the town square of Yarinacocha in Pucallpa, Peru and had two indigenous shamans perform with them. Also performing at the concert was a local Cumbia orchestra called Sensacìon Shipibo. The event was described as "a progressive leap forward, bringing together cultures in a productive and creative light and working together for a common purpose- the preservation of the rainforest, its people and traditions."
Olivia Arévalo Lomas
Often heralded as the leader and "spiritual mother" of the indigenous Shipibo-konibo community, Maestra Olivia Arévalo Lomas who both performed and recorded with Liberation Movement was tragically murdered in April 2018 at her home. She is featured on the Resurrector produced album Onáyabaon Bewá – Messages from Mother Earth.
Live Performance
Liberation Movement has received many accolades for its live performances and they have performed at festivals throughout the Americas including Lightning in a Bottle, Symbiosis Gathering, Sonic Bloom, Joshua Tree Music Festival, Envision in Costa Rica, Atmosphere Gathering in Canada and many others. A review by Everest.com of their performance at the Oregon Eclipse Festival in 2017 stated that Liberation Movement, "shone brightest among the Earth Stage's magnificent programming... Resurrector himself, Grant Chambers, provided a veritable séance in deep dubby beat-science... This was a spiritualized journey that burrowed many thousands of leagues beneath the Earth's surface, penetrating the consciousness of all who had assembled." Liberation Movement live performances often feature a wide variety of collaborators and guests from varied genres including Peruvian shamans, champion Tuvan throat singer Soriah, Butoh dance troupe Bad Unkl Sista, SORNE and many others.
Ideology
Resurrector focuses on ideological perspectives in many of his interviews on behalf of his projects. He often speaks about music being Sonic Shamanistic Alchemy and the members of Heavyweight Dub Champion are often referred to as Sonic Shamanistic Alchemists. He defines the process as, "basically taking a range of vibrational materials, from tribal instruments to electronic instruments, and manipulating them through devices like tape delays and old analog stomp boxes to try to find the personality of each piece... looking for particular voices, particular vibrations that would contribute to the spectrum of sound we're trying to bring forth, a spectrum of liberational revolutionary energy. Whatever we do with a sound, we have a specific mission: to change the chemistry of the planet leading to unconditional liberation of the human race."
A defining quotation written by Resurrector that is often used to represent his projects is "the liberation process is in full effect". He describes the process in an interview with Reality Sandwich about Liberation Movement:
Discography
with Roots Revolt
His Foundation is in the Holy Mountains (1996). Live Blend
with Heavyweight Dub Champion
"Whirlwinds of Revolt" – Voodoo, Sacraments, Oddities and Other Holy Anthems. (1998). Reggae on the Rocks Compilation. What Are Records?
Survival Guide for the End of Time. (2002). Champion Nation Recordings
"Arrival" – Bassnectar Remix (2006 & 2008). Bassnectar. Om Records & Organic Records
"Snared" – Freq Nasty vs. Heavyweight Dub Champion. (2008). Give Back Compilation
Rise of the Champion Nation – Limited Edition. (2008). Champion Nation Recordings
"Rise" – Liquid Stranger and Heavyweight Dub Champion".(2011).Interchill
"Babylon Beast" – Liquid Stranger and Heavyweight Dub Champion. (2011). Interchill
"Babylon Beast(feat. Killah Priest)" – In Defense: A Benefit for the Civil Liberties Defense Center, Vol. 1. Compilation. (2010). Autonomous Music
Labyrinth in Dub – EP Kraddy & Heavyweight Dub Champion. (2013). Minotaur
"Praise The Father" – The Bloom Series Vol. 3: Ways of the Sacred Pt.2. 2013. Muti Music
As Producer
"Onáyabaon Bewá – Messages from Mother Earth". (2011). Shamans of the Temple of the Way of Light.
References
General
Green, Joshua (1996). Perfectly Revolting. Denver's Westword
Mayo, James (2003). Survival of the Chillest. Westword Magazine
Burk, Greg (2006). I Got Riddim- Dr. Israel and Heavyweight Dub Champion. LA Weekly
Bookey, Mike (2006). A Heavyweight Manifesto: Heavyweight Dub Champion and the art of soul maintenance . The Source Weekly
Oshlo, Lisa (2007). Heavyweight Dub Champion move from Colorado to take music to the masses. The Marquee
Source Staff (2009). Beyond Sonic Intentions: Heavyweight Dub Champion finally unleashes its second brain bending album. The Source Weekly
Rivett, Deborah (2014). Musical Liberation: Collaborative Cultural Convergence in the Amazon. Alianza Arkana
Keyframe Entertainment (2017). Liberating The Masses: An Interview with Resurrector of Liberation Movement. Reality Sandwich
Getz, B. (2017). The Standout Musical Performances of Global Eclipse Gathering. Everfest
Everfest Magazine / Getz, B. (2018). Festival All-Stars: Liberation Movement. Everfest
Heavyweight Dub Champion Sources
Resurrector (2002). Last Champion Manifesto. Champion Nation Recordings publisher
Heavyweight Dub Champion (2002). Survival Guide for the End of Time. Liner Notes. Champion Nation Recordings
Heavyweight Dub Champion (2008). Rise of the Champion Nation – Limited Edition. Liner Notes. Champion Nation Recordings
Notes
External links
Heavyweight Dub Champion Youtube
Liberation Movement Facebook Page
Liberation Movement YouTube
Category:Dub musicians
Category:American electronic musicians
Category:Musicians from the San Francisco Bay Area
Category:American experimental musicians
Category:American reggae musicians
Category:1971 births
Category:Living people | tomekkorbak/pile-curse-small | Wikipedia (en) |
As the Kenyan government declared that its forces were close to achieving success after three days of carnage which has left 61 dead and 240 injured, a lethal and grim threat was emerging from the fires of the Westland shopping complex – that of international jihad.
“A multinational collection from all over the world” has descended to bring mayhem to Nairobi, were the words of Kenya’s Interior Minister Joseph Ole Lenku. The head of the military, General Julius Karangi, spoke of “foreigners from so many nations” who had taken part in the elaborate attack. “We have an idea who they are, their nationalities. We are fighting global terrorism here,” he stressed. Overnight, Kenya's Foreign Minister Amina Mohamed spoke of a British woman who had "done this many times before," as well as three Americans.
The terrorist “spectacular” with which al-Shabaab sought to demonstrate that it was not confined to Somalia was carried out by fighters from the US, Britain, Canada, Sweden, Syria, Finland, Russia, Dagestan and Kenya as well as Somalia, according to the organisation’s own tweets.
Download the new Independent Premium app Sharing the full story, not just the headlines
The victims, too, came from different backgrounds: 10 countries. Four of them were UK citizens, among them Ross Langdon, who held dual Australian nationality, and his partner Elif Yavuz, who was due to give birth in a few weeks’ time.
Those among the terrified hostages at the mall who failed to prove they were Muslims were selected for execution. Al-Shabaab said two Britons were among those doing the killing. They were Liban Adam, 23, and Ahmed Nasir Shirdoon, 24, both from London. Security agencies have refused to confirm their identities but acknowledge that it would be no surprise if UK citizens were involved.
Three years ago the then head of MI5, Sir Jonathan Evans, warned that Muslim extremists from the UK were increasingly switching from Pakistan to Somalia to receive training. “It is only a matter of time before we see terrorism on our streets inspired by those who are today fighting alongside al-Shabaab,” predicted Sir Jonathan. At the time, about a 100 UK passport-holders were estimated to be in Somalia. That number is believed to have grown threefold, along with others from Europe and America seeking to join the jihad. The upward trend has continued despite the recent rush to Syria.
The terrorist threat is one of the reasons for a heavy Western security presence in Kenya, including the British, whose military carry out training there. The SAS were put on standby but UK involvement in the operation, according to Whitehall sources, consisted of liaison work by MI6. Kenyan officials have acknowledged that Israeli and American security personnel have taken part in planning the operation to retake the complex and provided logistical support.
There were conflicting accounts on casualty figures. The Kenyan government maintained none of its forces has been killed; Western diplomatic sources report, however, that three commandos and 10 civilians they were trying to escort to safety were killed by the Islamists on Sunday evening.
One high-profile British terror suspect, Samantha Lewthwaite, whose husband Jermaine Lindsay was one of the 7/7 suicide bombers in London, has taken part in the assault, it has been claimed.
One British newspaper revealed that the “White Widow” was actually leading it and had been witnessed in a veil, “shouting instructions in Arabic”. It did not say why she should be using that language to a group who spoke Somali and, many of them, seemingly, English. Kenyan officials pointed out that the fighters were all men, although some of them had gone into Westgate pretending to be women, dressed in niqabs.
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Later, however, Kenya's Foreign Minister, Amina Mohamed, contradicted this by telling US television that a British woman experienced in terrorist activities was involved in the siege, fuelling the speculation surrounding Lewthwaite.
In an interview with PBS she said: "From the information that we have, two or three Americans (were involved) and I think, so far, I have heard of one Brit... a woman ... and I think she has done this many times before."
Lewthwaite, 29, who grew up in Aylesbury, is not known to the law-enforcement agencies as a combatant. She is, however, seen as a facilitator and is wanted in connection with a plot to blow up a shopping centre and hotels in Mombasa two years ago. She is believed still to be engaged in clandestine activity.
UK security sources said they could not rule out that she had been involved, although it was likely to be behind the scenes. A tweet, purportedly from al-Shabaab, announced she had taken part, but its provenance could not be verified.An associate of Lewthwaite, Habib Ghani, a UK citizen from Hounslow in west London, is reported to have been shot dead along with Omar Hammami, an American from Alabama with a Syrian mother, in an al-Shabaab internal feud earlier this month.
Ghani, of Pakistani and Kenyan extraction, went on the run after Kenyan police arrested another Briton, Jermaine Grant, in Mombasa over alleged possession of explosives.
The largest group of foreign fighters is said to have come from various parts of the US including the states of Kansas, Maine, and Illinois, and the city of Minneapolis. According to evidence before the US Congress, a number of mosques in the cities of Minneapolis and St Paul were running recruitment programmes and sending volunteers to fight in Somalia.
The FBI is said to have launched an investigation into the American connection in the attack, but questions will be asked as to why Western intelligence agencies failed to track the gathering of international jihadists in Nairobi.
Further reading:
British boy freed after telling jihadist: 'You're a bad man'
Hero ex-Marine re-entered mall 12 times to save 100 people
The victims came from around the world. So did their killers
Was wife of 7/7 bomber among attackers?
'All hostages freed' as Kenyan soldiers take control of mall
Kenyans are more united in tragedy’s aftermath
The victims: The architect and his pregnant wife
Video: Amateur footage from Kenya shopping mall attack
Ian Birrell: How to fight al-Shabaab | tomekkorbak/pile-curse-small | OpenWebText2 |
The large payment brands fiddle while Rome burns, seemingly unaware of the approaching bitcoin onslaught that is free of processing fees and political boundaries.
One of those barbarians at the gate, formerly known as WalletBit, has broadened its functionality and cut its pricing to expand directly into merchant processing. The company, based in Denmark, has rebranded itself Bitcoin Internet Payment System, or BIPS.
Best of all is that BIPS’ merchant tools and digital wallet services will be free unless, of course, conversion to national currencies is required, in which case it will charge 2.5% to convert out of bitcoin. Denmark and Canada have special reduced cash-out rates with same-day interbank transfers for Canadian accounts, says BIPS Director of Marketing Adam Harding. The strategy is to make it easy for merchants to get started and then aggregate their bitcoin balances with the company, which will make money over time providing foreign exchange conversion and premium services to the client.
This approach directly challenges the leading bitcoin merchant processor, BitPay, which just received yet another follow-on round of funding, and U.S.-only Coinbase, which appears to have a good future on the merchant side of the business.
Bitcoin's appeal to merchants is not only the lack of chargebacks and interchange fees but also the broadening of the customer base to include consumers from about 60 countries not served by PayPal. Also, traditional credit card products are typically not available in many countries either for political reasons, higher fraud rates, or lack of retail credit infrastructure.
The business model for bitcoin merchant processing was bound to mature and evolve, because an intermediary processor is not inherently required in this alternative payment system. In the world of Visa and MasterCard, it makes sense to have someone process transactions because authorization and settlement services are needed. But with bitcoin, the pure merchant processors are an interim step at best since third-party authorizations and chargebacks are not part of the architecture due to the distributed nature of transaction confirmation on the bitcoin block chain.
What's important to merchants is the coin management with various mobile apps and shopping cart plug-ins as well as the optional foreign exchange conversion. This is where the industry is headed and BIPS realizes that.
Merchant plug-ins are becoming commoditized and foreign exchange options are driven by strong partnerships with domestic and international financial institutions. This leaves the wallet technology as the wedge for innovative differences, such as management reporting capabilities and online secure access. All of the current so-called merchant processors offer online wallets that are under the control of the operator, meaning that bitcoin private keys are stored and protected by the operating company.
Smartly deploying two-factor authentication for wallet account access with a one-time passcode technique, BIPS (the former WalletBit) uses Secure Card and Google Authenticator, BitPay uses Google Authenticator, and Coinbase uses Authy.
I believe that online wallets, or eWallets, that do not store the client’s private key, such as BlockChain's My Wallet and StrongCoin, have an advantage in the long term because this setup removes the need to trust and audit the company's procedures. Although performing the cryptographic operations in the browser has its own challenges, the risks are reduced substantially compared to a localized breach since the threats to non-private-key-holding wallets are limited to a man-in-the-middle attack or a court order demanding “rogue” javascript delivery (the browser equivalent of a wiretap).
As bitcoin wallet functionality becomes more mature and robust, merchants will simply elect to partner with the best standalone client wallets and the best eWallets. If and when those accumulated bitcoin balances need to be exchanged for national currencies, then the wallet providers with the most attractive conversion options and limits will be the leaders.
BIPS has an advantage here because it supports 42 different currencies for converting out of bitcoin at 2.5%, whereas BitPay supports 11 different currencies at 2% fee, and Coinbase offers cash-out only in U.S. dollars at 1% with strict limits. Additionally, the cost of conversion has to be looked at in conjunction with the merchant processing fees. On that score BIPS and Coinbase are free while BitPay charges 0.99%. So, for merchants choosing to store bitcoin with the processor rather than convert it to government currency, BIPS and Coinbase are zero charge. (For a merchant that takes in 10% or less of its monthly sales in bitcoin, storing it with the processor can be an inexpensive way to acquire the currency and have a market position.)
Looking towards the future, barriers to entry are very low for the bitcoin merchant processing business. The differentiators for success will be online wallet security configurations, foreign exchange conversion options, and merchant software tools – in that order. With the market spread regionally now, it's still a jump ball.
Jon Matonis is an e-money researcher and crypto economist focused on expanding the circulation of nonpolitical digital currencies. His career has included senior posts at Sumitomo Bank, Visa, VeriSign, and Hushmail. Currently, he serves on the board of the Bitcoin Foundation. Follow him on Twitter: @jonmatonis | tomekkorbak/pile-curse-small | OpenWebText2 |
117 F.Supp.2d 500 (2000)
Teresa T. DIAZ, and Timothy J. Hall, Plaintiffs,
v.
VIRGINIA HOUSING DEVELOPMENT AUTHORITY, and National City Mortgage Co., Defendants.
No. Civ.A. 00-637-A.
United States District Court, E.D. Virginia, Alexandria Division.
October 12, 2000.
*501 Barry Michael Parsons, Crowell & Moring, Washington, DC, for plaintiff.
Carl P. Bowmer, Christian & Barton, L.L.P., Richmond, VA, for Virginia Housing Development Authority.
Paul Warren Mengel, Vorys, Sater, Seymour & Pease, L.L.P., Alexandria, VA, for National City Mortgage Co.
MEMORANDUM OPINION
ELLIS, District Judge.
Plaintiffs Teresa T. Diaz and Timothy J. Hall brought this action under the federal Equal Credit Opportunity Act ("ECOA" or "Act"), 15 U.S.C. §§ 1691 et seq., and its Virginia counterpart ("VA ECOA"),[1] Va. Code § 59.1-21.21:1, when they were denied a home loan because of their status as an unmarried couple. Specifically, plaintiffs claim that defendants National City Mortgage ("NCM") and Virginia Housing Development Authority ("VHDA") violated ECOA by denying plaintiffs credit based on their unmarried status and by failing to provide plaintiffs with proper written notice of the credit denial. The claims asserting the unlawfulness of the credit denial against VHDA were dismissed on a threshold motion. See Diaz v. Virginia Housing Auth., 101 F.Supp.2d 415 (E.D.Va.2000) ("Diaz I"). Thereafter, the parties stipulated to a dismissal of plaintiffs' claims for unlawful failure to provide notice of adverse action against VHDA. At *502 issue now on summary judgment[2] are the remaining claims concerning the statutory adequacy of NCM's notice of denial of credit and the unlawfulness of its credit denial.
I.
The essential facts are not disputed. Plaintiffs Teresa Diaz and Timothy Hall are an unmarried couple who together sought to purchase a home in 1998. To that end, they applied for financing from NCM, a company that offers mortgage loans sponsored by both the Federal Housing Authority ("FHA") and VHDA. A loan originating officer at NCM recommended that plaintiffs apply for the VHDA "FHA Plus" loan program for low and moderate income Virginia residents in need of down payment assistance. Plaintiffs accordingly completed and submitted a VHDA loan application and attended a VHDA-sponsored home ownership education program required to qualify for the FHA Plus loan program. Plaintiffs then found a suitable home and entered into an agreement for the purchase of that home, with a closing date scheduled for late April 1998.
Approximately two days before the scheduled closing, the NCM loan officer called plaintiffs and informed them that they did not qualify for the loan because VHDA regulations require recipients of FHA Plus loans to be married. Plaintiffs were told, however, that they qualified for an alternative FHA loan that required a greater down payment than the FHA Plus loan. On or about April 28, 1998, plaintiffs accepted and executed the requisite documents for the alternative loan. Plaintiffs were never provided with written notice of the denial of their FHA Plus application.[3]
In April of this year, plaintiffs filed suit against VHDA and NCM for unlawful denial of credit and for unlawful failure to provide notice of adverse action to each of them in violation of ECOA and VA ECOA, seeking compensatory and punitive damages, declaratory relief, and injunctive relief. See 15 U.S.C. § 1691e; Va.Code § 59.1-21.23. Specifically, the eight-count complaint included claims by each plaintiff against both NCM and VHDA for: (i) unlawful denial of credit in violation of federal ECOA (Counts I and II); (ii) unlawful failure to provide notice of adverse action in violation of federal ECOA (Counts III and IV); (iii) unlawful denial of credit in violation of VA ECOA (Counts V and VI); and (iv) unlawful failure to provide notice of adverse action in violation of VA ECOA (Counts VII and VIII).
VHDA previously moved to dismiss plaintiffs' unlawful denial of credit claims pursuant to Rule 12, Fed.R.Civ.P, which motion was granted. See Diaz I. For the same reasons, plaintiffs' unlawful denial of credit claims against NCM must fail. In addition, plaintiffs' unlawful denial of notice claims against VHDA have been dismissed by stipulation. See Diaz v. Virginia Hous. Dev. Auth., No. 00-637-A (Oct. 4, 2000) (order granting plaintiffs' stipulated motion to dismiss with prejudice Counts III, IV, VII, and VIII against VHDA). Thus, all that remains in this matter are plaintiffs' claims against NCM for unlawful failure to provide written notice of adverse action under federal ECOA and VA ECOA. NCM has moved for summary *503 judgment on these remaining countsCounts III, IV VII, and VII solely against NCM.
II.
Summary judgment under Rule 56 of the Federal Rules of Civil Procedure is appropriate where "the pleadings, depositions, answers to interrogatories, and admissions on file, together with affidavits, if any, show that there is no genuine issue as to any material fact" and that the movant is entitled to judgment as a matter of law. Celotex Corp. v. Catrett, 477 U.S. 317, 322, 106 S.Ct. 2548, 91 L.Ed.2d 265 (1986). In deciding whether there is a genuine issue of material fact, the evidence must be viewed in a light most favorable to the nonmoving party, and all inferences must be drawn in that party's favor. See Anderson v. Liberty Lobby Inc., 477 U.S. 242, 255, 106 S.Ct. 2505, 91 L.Ed.2d 202 (1986); Matsushita Elec. Indus. Co. v. Zenith Radio Corp., 475 U.S. 574, 587-88, 106 S.Ct. 1348, 89 L.Ed.2d 538; Nguyen v. CNA Corp., 44 F.3d 234, 236-37 (4th Cir. 1995); Ross v. Communications Satellite Corp., 759 F.2d 355, 364 (4th Cir.1985). Summary judgment is appropriate when a party "fails to make a showing sufficient to establish the existence of an element essential to that party's case, and on which that party will bear the burden of proof at trial." Rule 56, Fed.R.Civ.P.; Celotex, 477 U.S. at 322, 106 S.Ct. 2548. These principles govern whether the current factual record is suitable for summary judgment.
III.
The parties' contentions as to notice are straightforward: Plaintiffs contend that NCM violated ECOA's notice requirement when it failed to provide plaintiffs with written notice that they were denied the VHDA "FHA Plus" loan on the basis of their unmarried status, and NCM counters by arguing that ECOA does not require written notice where, as here, an alternative loan is offered and accepted.[4] As there is no controlling circuit authority, analysis must begin with a consideration of the pertinent statutory provisions and end with the application of those provisions, as properly construed, to the facts presented.
Notice is an integral part of the ECOA scheme to prevent discrimination "with respect to any aspect of a credit transaction." 15 U.S.C. § 1691(a); accord Va.Code § 59.1-21.21:1(a). To that end, ECOA and the implementing regulations mandate that a creditor "notify the applicant of its action on the application," within thirty days after receiving a completed credit application,[5] and provide that "[e]ach applicant against whom adverse action is taken" is entitled to written notification of both the action and "the specific reasons for the adverse action taken."[6]*504 This notice requirement serves as "a necessary adjunct to the anti-discrimination purpose of the legislation, for only if creditors know that they must explain their decisions will they effectively be discouraged from discriminatory practices." Jochum v. Pico Credit Corp., 730 F.2d 1041, 1043 (5th Cir.1984) (quotation omitted).
Significantly, ECOA's written-notice requirement is triggered only in the event a creditor takes "adverse action" with respect to an application for credit. This follows from the fact that ECOA's plain language requires written notice for "adverse actions," but is otherwise silent as to other types of actionnamely, "approval[s] of [and] counteroffer[s] to" applications for credit. 12 C.F.R. § 202.9(a)(1)(i). In these circumstances, it is well-settled under the doctrine of expressio unius est exclusio alterius that "[w]hen a statute limits a thing to be done in a particular mode, it includes the negative of any other mode." National R.R. Passenger Corp. v. National Ass'n of R.R. Passengers, 414 U.S. 453, 458, 94 S.Ct. 690, 38 L.Ed.2d 646 (1974) (quotation omitted); see also Bates v. United States, 522 U.S. 23, 30, 118 S.Ct. 285, 139 L.Ed.2d 215 (1997) ("[W]here Congress includes particular language in one section of a statute but omits it in another section of the same Act, it is generally presumed that Congress acts intentionally and purposely in the disparate inclusion or exclusion.") (quotation omitted). Therefore, whether ECOA required NCM to provide plaintiffs with written notice of NCM's action turns on whether NCM took "adverse action" on plaintiffs' application.
ECOA broadly defines "adverse action" to mean "a denial or revocation of credit, a change in the terms of an existing credit arrangement, or a refusal to grant credit in substantially the amount or on substantially the terms requested."[7] 15 U.S.C. § 1691(d)(6); accord Va.Code § 59.1-21.20(e). But this broad definition is not the end of the matter, for the implementing regulations of the Board of Governors of the Federal Reserve System (the "Board") refine and narrow the definition of "adverse action" by excluding from the set of such actions denials of credit that are coupled with counteroffers that are accepted. In the words of the regulation, an "adverse action" occurs when there is "[a] refusal to grant credit in substantially the amount or on substantially the terms requested in an application unless the creditor makes a counteroffer (to grant credit in a different amount or on other terms) and the applicant uses or expressly accepts the credit offered." 12 C.F.R. § 202.2(c) (emphasis added). Moreover, these regulations recognize as distinct (i) "approval[s] of," (ii) "counteroffer[s] to," and (iii) "adverse action[s] on" loan applications. Id. § 202.9(a)(1)(i). It is clear, therefore, that the regulations exclude from the definition of "adverse action" any credit denials that are coupled with "counteroffers" or a "grant [of] credit in a different amount or on other terms"and, by logical extension, such denials coupled with counteroffers are also excluded from ECOA's written-notice requirements, where the applicant accepts the counteroffer. Accordingly, plaintiffs' argument that ECOA required written notice in this case because "counteroffers are, for all practical purposes, denials of credit under ECOA," and because "[d]enials of credit, in turn, are included within ECOA's definition of `adverse action'" is unpersuasive.
*505 The Board's regulations, applied here, compel the conclusion that ECOA's written-notice requirement was never triggered because no "adverse action" occurred. Thus, there is no dispute that although NCM denied plaintiffs' application for the "VHA Plus" loan program, NCM, contemporaneously with oral notice of the denial, also offered plaintiffs a "straight" VHA loan that plaintiffs ultimately accepted. The "straight" VHA loan clearly was a counteroffer "to grant credit in a different amount or on other terms." And, having made this counteroffer in conjunction with its denial of plaintiffs' "VHA Plus" loan application, NCM was not required to notify plaintiffs in writing of the denial, because there was no "adverse action" under the regulations. See Dorsey v. Citizens & South. Fin. Corp., 678 F.2d 137, 139 (11th Cir.1982) (per curiam) ("[T]he action of a creditor in rejecting a credit application ... when that rejection is coupled with a counteroffer that the applicant accepts .... is not adverse action and does not trigger the notification provision of section 701(d)(2)."), withdrawn, 687 F.2d 140, reinstated 706 F.2d 1203 (11th Cir.1983).
Seeking to avoid this result, plaintiffs present three arguments, none of which is persuasive. First, Plaintiffs argue that the Board's issuance of a sample adverse action notice formdenominated "Form C-4" to be used where a creditor denies an application for credit and instead extends a counteroffer, indicates the Board's intent to require written adverse action notices for denials of credit coupled with counter-offers. See 12 C.F.R. Pt. 202, App. C, Form C-4. Plaintiffs, however, misunderstand the purpose of Form C-4. Nowhere does the Board state that the form must be used for all denials coupled with counteroffers, or that all such actions are "adverse actions." Rather, the regulations and, indeed, common sensemake clear that the use of Form C-4 as an adverse action notice would be appropriate if, and only if, the action taken by the creditor i.e., the denial of credit and the counteroffer qualifies as an "adverse action," as defined in the regulations. In fact, the Board has explained that "Forms C-1 through C-4 are intended for use in notifying an applicant that adverse action has been taken on an application or account under § 202.9(a)(1) and (2)(i) of this regulation." Equal Credit Opportunity Business Credit, 12 C.F.R. Pt. 202. The dispositive inquiry, therefore, is whether a particular denial of creditcounteroffer combination constitutes an "adverse action" on an application. In this regard, it is important to recall that the regulations limit the circumstances in which a denial of credit coupled with counteroffer qualifies as an "adverse action." These circumstances do not include situations where a creditor "makes a counteroffer (to grant credit in a different amount or on other terms) and the applicant uses or expressly accepts the credit offered." Id. § 202.2(c) (emphasis added). Thus, plaintiffs' reliance on Form C-4 is unpersuasive.[8]
Plaintiffs, in their second argument, point to two ECOA provisions and *506 three regulations allowing a creditor to communicate orally with an applicant as necessarily implying that written notice is required in other circumstances involving denials of credit.[9] This argument, too, must fail. These ECOA provisions and regulations constitute mere exceptions to the general rule that adverse actions require written notice and, therefore, do not address ECOA's notice requirements when the action taken by a creditor is not "adverse."[10] Moreover, plaintiffs' repeated characterization of these ECOA provisions and regulations as standing for the proposition that "denials of credit" generally require written notice does not change this conclusion, for plaintiffs' focus on "denials of credit" misses the mark. The relevant inquiry is not whether the action taken by a creditor was a denial of credit; rather, the necessary determination for purposes of ECOA's written-notice requirement is whether the action taken is an "adverse action." This distinction matters, for a denial of credit is not always an "adverse action" under ECOA and the regulations; accordingly, not every denial of credit requires written notification. In this regard, the regulations carve out an exception to the definition of "adverse action" for a denial of credit coupled with a counteroffer that the applicant accepts. The existence of other exceptions to the adverse-action notice requirement is, therefore, consistent with the exception for a denial of credit coupled with a counteroffer accepted by the applicant.[11]
Plaintiffs' third argument is a challenge to the Board's authority to interpret "adverse action" for ECOA's purposes as excluding a denial of credit coupled with a counteroffer that is ultimately accepted by the applicant.[12] For, in the end, it is *507 clear that this interpretation applies to this case, and that NCR's duty to inform plaintiffs of its action in writing ultimately depends on whether this regulation is a legitimate exercise of the Board's regulatory authority under ECOA. In this regard, settled law teaches that "considerable weight should be accorded to [the Board's] construction of a statutory scheme it is entrusted to administer,"[13] and that "courts must give [the Board's] decision controlling weight unless it is `arbitrary, capricious, or manifestly contrary to the statute.'"[14]
ECOA contemplatesindeed, requires the active involvement of the Board in the interpretation of its provisions and in the administration of its consumer protections. To that end, ECOA grants the Board broad authority to "provide for such adjustments and exceptions for any class of transactions, as in the judgment of the Board are necessary or proper to effectuate the purposes" of the Act. 15 U.S.C. § 1691b(a)(1); cf. Ford Credit Co. v. Milhollin, 444 U.S. 555, 559-60, 100 S.Ct. 790, 63 L.Ed.2d 22 (1980) (noting, in a Truth in Lending Act case, that "Congress ... delegated expansive authority to the Federal Reserve Board to elaborate and expand the legal framework governing commerce in credit"). Accordingly, deference and respect must be paid to ECOA's mandate and the lawmaking authority and expertise of the Board, "so long as [the Board's] lawmaking is not irrational" and is consistent with the congressional purpose. Milhollin, 444 U.S. at 568, 100 S.Ct. 790; see Dorsey, 678 F.2d at 139; Besaw v. General Fin. Corp., 693 F.2d 1032, 1034 (11th Cir.1982). In this case, as in Dorsey, there is "no persuasive reason to find that the relevant portion of Regulation B is anything but a rational exercise of the Board's rulemaking authority," and "Section 202.2 obviously represents a well considered and reasonable interpretation of the notification requirements" of ECOA. Dorsey, 678 F.2d at 139. It is reasonable for the Board to determine, for example, that an applicant eliminates any adversity stemming from the original loan application denial by accepting a creditor's counteroffer for a different loan. This is so because an applicant's acceptance of a counteroffer may reasonably be taken to represent the applicant's agreement with the creditor's independent assessment of the applicant's credit profile. As one commentator put it, it would be "pointless to designate the lender's action as adverse ... when the lender and the applicant ha[ve] agreed on a new arrangement."[15] More importantly, the Board's determination in this regard is consistent with ECOA's goal of preventing discrimination in consumer credit transactions, for an applicant, by simply rejecting a creditor's counteroffer, can express her disagreement with the creditor's assessment and thereby require the creditor to provide a full explanation for an initial denial of credit. A creditor, facing the very real possibility that a rejected applicant would exercise this right to a written notice, has every incentive to ensure not only that its initial denial of credit is nondiscriminatory, but also that its counteroffer is an accurate assessment of the applicant's credit profile.
Thus, the Board's Regulation B, which exempts from the definition of "adverse action" under ECOA a creditor's denial of a credit application that is coupled with a counteroffer that the applicant accepts, is a reasonable and valid exercise of the *508 Board's authority and applies to this case. In this regard, plaintiffs have failed to show that the Board exceeded its authority under ECOA in promulgating the regulation, thereby "thwart[ing] the statutory mandate it was designed to implement." Jochum, 730 F.2d at 1047. Accordingly, NCM was not required to provide written notice of its denial of plaintiffs' "FHA Plus" loan application. It follows, therefore, that NCM's motion for summary judgment on plaintiffs' claims for unlawful failure to provide notice of adverse action under ECOA and VA ECOA must be granted.
IV.
For the foregoing reasons, defendant NCM's motion for summary judgment on plaintiffs' claims for unlawful failure to provide notice of adverse action under ECOA and VA ECOA (Counts III, IV, VII, and VIII) is GRANTED. In addition, NCM's motion for summary judgment on plaintiffs' unlawful denial of credit claims (Counts I, II, V, and VI) is GRANTED.
An appropriate Order shall issue.
NOTES
[1] As VA ECOA's language mirrors that of the federal ECOA, the term "ECOA" is used herein to refer to both statutes.
[2] Although NCM initially moved for a judgment on the pleadings, the motion was converted to one for summary judgment on NCM's oral motion.
[3] The documentary record is unclear as to whether the Uniform Residential Loan Application ("Application") that plaintiffs filled out on February 21, 1998, was an application for both an "FHA Plus" loan and a "straight" FHA loan or simply an application for the former. This lack of clarity on the matter is further compounded by the existence of a second Application, dated April 30, 1998, that plaintiffs claim they never saw, dated, or executed (although the April Application bears plaintiffs' signatures). At the hearing, NCM conceded that the February Application was limited to the "FHA Plus" loan, and that only after this application was denied were plaintiffs considered for the "straight" FHA loan. The analysis thus proceeds on this basis.
[4] Initially, plaintiffs also argued that NCM failed to give plaintiffs any noticewhether written or otherwiseof its action on their "FHA Plus" loan application within thirty days after receiving a completed application, as required by ECOA. Plaintiffs abandoned this contention when discovery disclosed that their loan application was not completed until April 16, 1998, when they completed a mandatory educational program, and that less than two weeks later, on or about April 23, 1993, an NCM loan officer called plaintiffs to inform them that the FHA Plus application had been denied, but that they qualified instead for the "straight" FHA loan. In short, the parties dispute not the timeliness of notice, but only that it was provided orally rather than in writing.
[5] 15 U.S.C. § 1691(d)(1); accord Va.Code § 59.1-21.21:1(d)(1); see 12 C.F.R. § 202.9(a)(1).
[6] 15 U.S.C. §§ 1691(d)(2)-(3) (emphasis added); accord Va.Code § 59.1-21.21:1 (d)(2)-(3); see 12 C.F.R. § 202.9(a)(2). A creditor may fulfill this requirement under ECOA by:
(A) providing statements of reasons in writing as a matter of course to applicants against whom adverse action is taken; or (B) giving written notification of adverse action which discloses (i) the applicant's right to a statement of reasons within thirty days after receipt by the creditor of a request made within sixty days after such notification, and (ii) the identity of the person or office from which such statement may be obtained. Such statement may be given orally if the written notification advises the applicant of his right to have the statement of reasons confirmed in writing on written request.
15 U.S.C. § 1691(d)(2); see 12 C.F.R. § 202.9(2).
[7] Under this broad definition, NCM's action on plaintiffs' application for the FHA Plus loan was arguably "adverse," for it is undisputed both that NCM denied plaintiffs' "FHA Plus" loan and that the "straight" FHA loan plaintiffs ultimately accepted is not a grant of credit "in substantially the amount or on substantially the terms requested."
[8] Also unpersuasive is plaintiffs' reference to a staff interpretation that provides:
Counteroffer combined with adverse action notice. A creditor that gives the applicant a combined counteroffer and adverse action notice that complies with § 202.9(a)(2) need not send a second adverse action notice if the applicant does not accept the counteroffer. A sample of a combined notice is contained in form C-4 of Appendix C to the regulation.
12 C.F.R. Pt. 202, Supp. 1, Section 202.9 Notifications, Paragraph 9(a)(1), point number 6. The interpretation's reference to a "second adverse action notice" may, at first blush, suggest that there must be a preliminary "combined counteroffer and adverse action notice" to obviate the need for the second notice "if the applicant does not accept the counteroffer." Yet, a close reading of this interpretation reveals that it is limited to describing the duties of a creditor when the applicant rejects a counterofferexempting a creditor from providing an adverse action notice if it already had done soand does not otherwise require the initial provision of an adverse action notice before a rejection.
[9] The two ECOA provisions state that a creditor acting on fewer than one hundred and fifty applications during a calendar year preceding a denial of credit may provide oral notice of the denial, and that a creditor may orally communicate the "identity of the person or office" from which the applicant can obtain a written statement if certain conditions are met. See 15 U.S.C. §§ 1691(5), (d)(2)(B). The first regulation provides that, for business credit applications for businesses with gross revenues of one million dollars or less, "[t]he statement of the action taken maybe given orally or in writing, when adverse action is taken." 12 C.F.R. § 202.9(a)(3)(A). The second allows oral notification of a denial of credit where the applicant is a business with gross revenues of over one million dollars. See id. § 202.9(a)(3)(ii)(A). Finally, plaintiffs point to a regulation allowing, "[a]t its option, a creditor [to] inform the applicant orally of the need for additional information," but providing that, "if the application remains incomplete the creditor shall send a notice in accordance with paragraph (c)(1) of this section." Id. § 202.9(c)(3).
[10] Indeed, Regulation 202.9(c)(3), which allows a creditor to inform an applicant orally of the need for more information, does not even relate to any of the three actions a creditor may take on an applicationnamely, approval, denial, or counteroffer. See 12 C.F.R. § 202.9(c)(3).
[11] Indeed, plaintiffs' argument proves too much, as neither ECOA nor any regulation expressly provides for oral notice of credit approvals, and such oral notice would also not be allowed under the rationale of plaintiffs' argument. Yet, plaintiffs themselves acknowledge that "notice of credit approval can be implicit by the granting of the requested credit." Plaintiffs' Memorandum in Opposition to National City Mortgage Company's Motion for Judgment on the Pleadings, at 5. An explicit exception for this universally acknowledged practice is not required because only an "adverse action" requires the provision of written notice under ECOA and the regulations.
[12] VA ECOA charges the Virginia State Corporation Commission with "adopt[ing] regulations to effectuate the purposes of this chapter provided that such regulations conform to and are no broader in scope than regulations, and amendments thereto, adopted by the Board of Governors of the Federal Reserve System under the Consumer Credit Protection Act, Title VII." Va.Code § 59.1-21.24. The Commission, in turn, has "incorporated by reference and adopted for use in the Commonwealth of Virginia," Regulation B of the Board. 10 Va.Adm.Code 5-180-10. Thus, the discussion here concerning whether the Board's definition of "adverse action" exceeds the Board's statutory authority applies with equal force to whether the Commission's adoption of the Board's "adverse action" regulation is a valid exercise of its power under VA ECOA.
[13] Chevron, U.S.A., Inc. v. Natural Resources Defense Council, 467 U.S. 837, 844, 104 S.Ct. 2778, 81 L.Ed.2d 694 (1984).
[14] ABF Freight Sys., Inc. v. NLRB, 510 U.S. 317, 325, 114 S.Ct. 835, 127 L.Ed.2d 152 (1994) (quoting Chevron, 467 U.S. at 844, 104 S.Ct. 2778).
[15] Elwin Griffith, The Quest for Fair Credit Reporting and Equal Credit Opportunity in Consumer Transactions, 25 U.Mem.L.Rev. 37, 115 (1994).
| tomekkorbak/pile-curse-small | FreeLaw |
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Salina de la Renta of MLW was on Univision's sports show this week promoting Saturday's episode of MLW Fusion.
Burt Watson's MMA Live comes to the Hard Rock Event Center at the Seminole Hard Rock in Hollywood, FL on 6/15 at 7 p.m. The main event of his first show has Jose Caceres (14-8-1) vs. Fred Moncaoio (6-3) at welterweight. Caceres is the only fighter ever to have beaten UFC welterweight champion Kamaru Usman, and he is the brother of UFC star Alex "Bruce Leroy" Caceres.
Combate Americas announced a 6/7 show in Tucson, AZ at Casino del Sol on Univision headlined by Jose Alday (12-4-1) vs. Irwin Rivera (7-4).
Tickets for an ROH TV taping on 7/20 in New York at the Hammerstein Ballroom and for 7/21 in Lowell, MA at the Memorial Arena go on sale tomorrow.
C.M. Punk and A.J. Mendez will be appearing at the Children's Mental Health Gala on Saturday in Chicago.
Shane Douglas will wrestle for UnderGround Wrestling Lupus Mania 2 fund raiser on Saturday at 4 p.m. at Santangelo's Party Center in Massillon,OH.
After 3 shows of buildup, Austin Aries and Eddie Edwards face off for the final time at Warrior Wrestling 5 on Sunday, May 12th in Chicago in a steel cage match.
Daily Pro Wrestling History: Curt Hennig wins AWA World title
F4W Empire Convention Info:
Ed in San Antonio presents PODER~! at the FSW arena on Friday 5/24 - Showtime is at noon - Main event: Bryan Alvarez vs. Logan Stunt
Empire dinner on Friday 5/24 at 8:30 p.m. at Texas de Brazil - Price is $82 - All you can eat meat and salad, sodas, tea, and coffee, plus dessert included
Empire suite party on Friday 5/24 for those who were not able to get the Q&A package - Price is $25
Purchase tickets here.
CONTACT INFORMATION | tomekkorbak/pile-curse-small | OpenWebText2 |
The President Who Deserves the Credit for Reviving Presidential Debates May Have Lost Because of Them
Yanek Mieczkowski
is the author of Eisenhower’s Sputnik Moment: The Race for
Space and World Prestige (2013), Gerald Ford and the
Challenges of the 1970s (2005), and The Routledge Historical
Atlas of Presidential Elections (2001). He is currently a
visiting professor at the University of North Florida.
As Americans settle
down to watch the presidential candidates debate, they should
remember how this tradition made a comeback. Exactly forty years
ago, presidential debates reappeared as an American political
institution. In the summer of 1976, President Gerald Ford, after
fending off Ronald Reagan’s formidable challenge for the Republican
nomination, found himself trailing Democratic nominee Jimmy Carter by
thirty-three points in the polls. Boldly gambling to close that gap,
Ford challenged Carter to debate on national television. The ensuing
face-offs renewed the high-stakes political gamesmanship that John
Kennedy and Richard Nixon established in 1960 and marked the first
time an incumbent president took to the debate stage. Ever since,
debates have been a staple of presidential races.
The 1976 debates
also created one of the most inexplicable moments in campaign
history. In the second debate that fall, devoted to foreign policy,
Ford answered a question from panelist Max Frankel by declaring,
“There is no Soviet domination of Eastern Europe, and there never
will be under a Ford administration.”
The stunning remark
flew in the face of history and defied borders that any observer
could see on a map. Apparently, Ford refused to recognize Cold War
realities that had existed since the end of World War II, when Soviet
forces occupied much of Eastern Europe.
The statement also
contradicted Ford’s own past. In the war’s Pacific theater, he
had fought for the U.S. Navy, witnessing the conflict firsthand and
observing the wrenching changes it wrought. Intellectually, he had
no reason to make the mistake. He was one of the nation’s
best-educated presidents, a University of Michigan and Yale Law
School alumnus. As a quarter-century veteran of Congress, a vice
president, and president, he was steeped in diplomacy, and in 1975,
he ventured behind the Iron Curtain, visiting Poland, Romania, and
Yugoslavia to show solidarity with those Soviet satellites.
That trip provided
one explanation for the gaffe. In a 2003 interview with me, Ford
explained that he sensed the vibrant spirit of Eastern Europeans
there, even as they strained under the Soviet yoke. “My real
feeling,” he said, “was that the Polish people would never
accept, over the long haul, Soviet domination.”
Other explanations
account for Ford’s misstatement. He was answering a question about
the Helsinki Accords, which he considered the crowning diplomatic
achievement of his presidency. In 1975, Ford attended the Conference
on Security and Cooperation in Europe, where 35 nations signed an
agreement pledging to increase the movement of people and information
across borders. In his interview with me, Ford called the Helsinki
accords the “spark…that brought about the demise of the Soviet
Union.”
At the time,
though, critics charged that the accords ratified the Iron Curtain,
and Ford faced withering criticism that he had conceded too much to
the Soviets. Parrying such attacks for more than a year, Ford grew
defensive about the accords, and Frankel’s question only provoked
him. The reporter rattled off a laundry list of Soviet gains and
noted that “we virtually signed, in Helsinki, an agreement that the
Russians have dominance in Eastern Europe.” Ford was eager to
rebut the charge, but that eagerness led him to overstate his case.
The Ford White
House expected Helsinki questions at the debate. Aides crafted
responses that the president could deploy, one of them denying “that
my policies accept Soviet domination over Eastern Europe….” As
Ford rehearsed for the debate, he took careful notes. He jotted down
the words “Sonnenfeldt Doctrine,” referring to Assistant
Secretary of State Helmut Sonnenfeldt’s argument that the U.S.S.R.
had an “organic union” with its satellites, which conservatives
and Americans of Eastern European descent stoutly rejected. After
noting this doctrine, Ford wrote, “There is none,” underlining
those words twice for emphasis.
Ford’s gaffe
might have boiled down to a trick that his memory played on him,
compounded by the slippery slope of semantics. Always a
conscientious student, he likely pored over his handwritten notes as
he prepared for the debate, and he might have remembered that key
phrase—“There is none”—but embellished it incorrectly by
adding the words about Soviet domination of Eastern Europe. If he
had articulated the sentence his aides had prepared, saying that the
“Ford administration does not accept” or “does not concede”
Soviet domination of Eastern Europe—as he did in clarifying his
remarks to Frankel—his initial response would have passed muster,
and debate history would have been kinder to him.
As it was, Ford’s
answer generated a media firestorm that sucked oxygen from his
campaign. On election day, he lost by two percentage points. He had
staged a remarkable comeback; his strategy of using televised debates
to overtake Carter almost worked. But his words became one of those
defining debate mistakes—like Nixon’s sweaty, haggard appearance
in 1960 or Al Gore’s patronizing sighs in 2000—that contributed
to defeat.
Despite the
misstep, though, Ford’s legacy from the 1976 debates has endured.
After Watergate’s traumas and the secrecy shrouding the Nixon
administration, Ford touted his White House’s “open, accessible”
nature. Bringing debates back became one way to open a window on
political campaigns, allowing Americans to view their candidates in
an unscripted setting. That process has become a vital part of U.S.
politics, and these contests provide moments that define campaigns
and sometimes decide elections. Forty years later, let the debates
begin again. | tomekkorbak/pile-curse-small | Pile-CC |
Planning is an important manager function. It provides the guidance of a desired end state and the means of how to accomplish the organization's objectives. In other words, planning is the process of thinking before doing. To problem solve and take advantage of the opportunities created by rapid change, managers must develop formal long- and short-range plans so that organizations can move forward toward their objectives.
Organizing
The second function is getting prepared and organized. Management must organize all its resources prior to putting them into practice. The course of action that decides what has been planned must first be organized and well thought out. Through this process, management now determines how to proceed with established and maintained relationships, and also allocate necessary resources.
They also see to the harmonization of staff, and try to find out the best way to handle the important tasks and expenditure of information within the company. Management determines the division of work according to its need. It also has to decide for suitable departments to hand over authority and responsibilities.
Importance of the organization process and organization structure.
– Promote specialization.
– Defines jobs.
– Classifies authority and power.
– Facilitators' coordination.
– Act as a source of support security satisfaction.
– Facilitators' adaptation.
– Facilitators' growth.
– Stimulators creativity.
Leading
Directing is the third function of management. Working under this function helps the manager to control and supervise the staff. This helps assist the staff in... | tomekkorbak/pile-curse-small | Pile-CC |
A 22-year-old inmate who had help from his girlfriend when he escaped from a jail last week in northwest Indiana was arrested Tuesday in San Antonio, Texas.
Richard N. Campos, 22, was last seen April 30 working as a trustee assigned to laundry detail at the Lake County Jail complex in Crown Point, according to a statement from the sheriff’s office.
Authorities believe the escape was planned in advance and that Campos had assistance from his girlfriend, 20-year-old Elysia Marie Jeronimo of Hammond.
Campos, a member of the Latin Kings, was arrested April 25 for operating a vehicle while intoxicated, and also on active warrants from Whiting and Hammond, according to the sheriff’s office.
On Tuesday, Campos and Jeronimo were taken into custody in Texas, the sheriff’s office said. After they tried to flee, the couple was apprehended by San Antonio law enforcement.
The Lake County sheriff’s office will file for extradition for both Campos and Jeronimo. The escape remains under investigation, but police said human error may have occurred.
Detectives in Indiana worked “non-stop for over 72 hours to successfully locate these individuals,” the sheriff’s office said. | tomekkorbak/pile-curse-small | OpenWebText2 |
Ugly Thai babe with her small boobs titty fucks and tries her best | tomekkorbak/pile-curse-small | OpenWebText2 |
Archive for the ‘chapter 7’ Category
It should go without saying that, particularly in the legal arena, those who take part in proceedings before courts and tribunals need to feel that they have been treated equally.
This is, of course, easier said than done, as David Lammy’s report on the Criminal Justice System, published in 2017 showed. (See this blog 29 Sept 2017). But for many years first the Judicial Studies Board and now the Judicial College have offered guidance to judges (and by extension to others involved in the justice system) about the best ways to try to ensure that people are treated fairly.
Much of this focusses on the language that judges and others involved in the justice system use generally (for example in relation to litigants in person) and in relation to those from specific sectors of society, who may be defined by their religion, their ethnicity, their sexual orientation, mental or physical disabilities, their gender.
In February 2018, the Judicial College published an on-line updated revision to its ‘Equal Treatment Bench Book’. Bench books were originally devised as a handy guide to key issues which could sit on the judge’s desk, available for him to refer to it that seemed necessary.
I am not sure whether this particular Bench Book can be used in this way. For one thing, it is very long – well over 400 pages. And the issues raised are such that I would have thought judges would need to have considered them before a case or other proceedings have started. (It would not be desirable for a judge to stop in the middle of a sentence in order to look up how a particular person should be addressed.)
But I don’t agree, as some comments in the press have suggested, that the Equal Treatment Bench Book is an example of political correctness gone mad. It seems to me to be an honourable attempt to raise questions and address issues that arise in practice but that many judges may not have thought about before. (Indeed, I think there are some parts of the book that would be of interest to a wider readership.)
I set out the link to the text here, and invite readers to take a look at the Book and come to their own view on its value.
Hot on the heels of the announcement of on-line divorce applications (see this blog Feb 2 2018), information has just been published as a blog from HMCTS on developments relating to the digitalisation of procedures relating to public law childrens’ cases.
Emma Petty, Service Manager for the Public Law project, writes:
We want to make the public law process more efficient, ensuring the court, parties and their representatives have access to the right information at the right time to help decide the best outcomes for children involved in public law cases. Based on our early thinking, the aims of the project could be to:
provide an online application process which speeds up the gatekeeping process and shares information with partner agencies at the point of submission
improve the process for dealing with urgent applications
enable users to see the progress of their case and to take action to progress their case online
provide clear signposting to support available outside HMCTS, to assist parties acting in person and without a lawyer
enable users to upload and access documents and evidence digitally both outside and inside the courtroom
ensure suitable facilities and support are provided at hearing centres
enable hearings, where appropriate, to be conducted online
provide fast digital access to outcomes of hearings
ensure those who need it get the support they need to access our digital services.
Over coming months, the Public Law Project team will be working with practitioners and others involved in these types of case in developing practices and procedures to deliver these goals. This is an important development within the scope of the Transformation of the Justice System policy.
On January 30 2018 the Government announced that a fully online divorce application process is being tested across England and Wales for the first time. (It had been trialled in a small number of areas from 2017.)
The initial pilot allowed people seeking a divorce to use an online system which offered prompts and guidance to assist them in completing their application. But they still had to print off the form and send it to the court.
HM Courts & Tribunals Service (HMCTS) has now extended the service so that the application is now fully digital – submitting the form, sending the relevant documents, and payment. In the first week HMCTS received 130 online applications.
According to HMCTS the online system has drastically cut the number of applications being returned because of errors – showing a 90% improvement from paper forms. This is particularly important given the increasing numbers seeking a divorce without using a lawyer to help them.
Users of the new service seem to like it. It has already gained positive feedback with people welcoming the simplified, streamlined and easy to understand system which delivers their application instantly – without the worry of it being lost in the post.
The next stages will include making the system available for use by legal representatives. A date has not yet been publicly announced for this further development.
Experience in other contexts suggests that once up and running, use of on-line application procedures will increase very rapidly. Indeed, people will wonder why this development had not occurred years ago. This sort of development is at the heart of the Transformation of our Justice System reform programme.
2018 will witness the start of a new approach to dealing with the financial matters that can arise when married couples are divorced. The current President of the Family Division, Sir James Munby has set out his ambition that disputes about financial matters should be treated quite separately from the process of getting the divorce itself.
To this end, a series of pilots is being launched in February 2018 in which, in three trial areas of the country, financial matters will be dealt with by specially trained judges in a reduced number of family court hearing centres. The courts undertaking this work will be known generally as Financial Remedies Courts.
The new system will initially be operated on a trial basis in three areas of the country: London, the Black Country and South East Wales.
The President clearly hopes that expansion of the scheme to other parts of the country will take place rapidly.
In a recent Circular, Sir James wrote:
My core ambition for financial remedy work is to improve significantly both the application of procedural justice and the delivery of substantive justice.
Procedural justice will be bettered by the appointment of a cadre of specialist judges to the Financial Remedies Court (FRC) and by a process of early allocation of a case to the right judge at the right level at the right place, so as to ensure maximum efficiency. It will be bettered by the application and enforcement of standard directions and interim orders and by ensuring that FDRs (where the majority of cases settle already) are conducted with consistency, with sufficient time being allowed not only for the hearing but also for judicial preparation.
The delivery of substantive justice will be improved by an improved programme of judicial training; by the reporting of judgments in small and medium cases by the judges of the FRC to promote transparency and consistency; and by ensuring that sufficient time is allowed for the preparation and conduct of final hearings.
An increase in transparency will result in increased predictability of outcome, which in turn should lead to a higher rate of settlement or, for those cases that do not settle, a reduced rate of appeals.
Although initially hearings will be paper-based, it is intended that – in common with other changes being made in the justice system – there should be rapid moves to making the process an entirely digitised one.
These changes are being accompanied by another reform which has seen the introduction of many more standarised orders, which will be used by judges and avoid the need for parties or their legal advisers to draw up orders that then have to be approved by the judges. Sir James hopes this will particularly assist litigants in person.
This was the title of an extremely important and interesting lecture, given by Sir James Munby, President of the Family Court, to the Howard League for Penal Reform at the end of October 2017
What, it might be asked, was our leading family judge doing talking to those whose interest is in the criminal justice system?
Sir James used his lecture as an opportunity to argue for a new approach to the treatment of young people who come into contact with the criminal justice and penal systems. He sets out with admirable clarity what he sees as the main problems with current arrangements, including: the very complex set of institutions with which the young offender may come into contact; the huge variety of government departments – both central and local – charged with developing and delivering policy in relation to young offender; and the inconsistency of approach of different agencies towards how young offenders and their families should be dealt with.
Sir James argues that, in this context, family justice and criminal justice should be brought together. Specifically, he argues that the role of the Family Drug and Alcohol Court should be expanded to enable it to take on cases which are currently dealt with in the Youth Court.
He recognizes that such a development would represent a big policy change and could not come into being in the short-term. He therefore also proposes interim measures that might go someway towards meeting the objective he has outlined.
So far as I am aware,the Government is not currently contemplating such a major change, but I think Sir James offers ideas that should be carefully considered.
Despite the loss of the Prisons and Courts Bill 2017 at the General Election, held in June 2017, work on the Transforming our Justice System programme continues apace. (For those aspects of the reforms which need legislation, a replacement bill is expected shortly.)
Keeping up to date with the progress that has been made is hard, as most of the changes do not hit the headlines in the media. (About the only issue which has been subject to any public discussion has been criticism from the Bar about a pilot trialling the use of courts for longer periods during the day. The criticism focussed almost entirely on the inconvenience this would cause to barristers – no mention of the possibility that the public might prefer court hearings outside the traditional 10-4 Monday-Friday time frame.)
Specific developments can be noted by keeping an eye on Press Releases from the Ministry of Justice. A recent example is the announcement of the opening of the first two Courts and Tribunals Service Centres in Birmingham and Stoke on Trent
A more rolling source of news can be found in the extremely interesting blog relating to the transformation programme – now called Transformation: Courts and Tribunals 2022. This provides news about the new services that are being developed for modernising the courts and tribunals system, both giving accounts of what is currently on going and also what is planned.
In 2008, the then Labour Government announced its support for the concept of post-legislative scrutiny of legislation. It stated that “the basis for a new process for post-legislative scrutiny should be for the Commons committees themselves, on the basis of a Memorandum on appropriate Acts submitted by the relevant Government department, and published as a Command paper, to decide whether to conduct further post-legislative scrutiny of the Act in question.”
The Ministry of Justice has just (October 30 2017) published a post-legislative memorandum on the Legal Aid, Sentencing and Punishment of Offenders Act 2012 (LASPO), which it has sent to the Justice Select Committee. While much of the document seeks to explore the extent to which Government objectives in introducing the legislation have or have not been met, it also draws together a number of important other reports which have commented more critically on the effect of LASPO. These include, for example, the reports of the Low Commission, and the Bach Commission’s report on a Right to Justice (both noted in this blog). It also refers to other reports, e.g. from the National Audit Office, and the Equality and Human Rights Commission, and reports from a number of other Parliamentary Committees. It also notes how the Government has responded to a number of legal challenges that were made to LASPO. The response of the Justice Committee is not yet known.
Whether or not the Committee pursues its own post-legislative scrutiny, it is important to note that, in the memorandum, the Government confirms that in the course of the coming months it will undertake two more analytical reviews of aspects of LASPO, relating to,
the changes to the Legal Aid scheme, and
the changes to rules on the funding of litigation.
This will provide an opportunity for critics of LASPO to make their arguments and might lead to further thought being given to the ideas set out in the Low and Bach Commissions’ reports.
It will also provide the opportunity to reflect on the changes resulting from Lord Justice Jackson’s review of Costs and his 2017 Supplementary Report (also noted in this blog). | tomekkorbak/pile-curse-small | Pile-CC |
Q:
Converting multiple File geodatabase (.gdb) into multiple Personal geodatabase (.mdb)
Individually I will Export the gdb to XML Workspace then import that into the personnel geodatabase and all Domains go over fine. But...
Let's Say I have several file geodatabase in a folder and Each of the file geodatabase has 1 feature dataset name "URS" and rest are feature classes. "URS" Feature dataset has several feature class as well.
The task for me is to convert Multiple file geodatabase into multiple Personnel geodatabase without including "URS" Feature datasets. If the Geodatabase don't have "URS" Feature dataset or any other feature classes then the python program will create an empty personnel geodatabase.
I am using pyscripter and below mentioned concept is not workin for a single geodatabase. How can I convert multiple File geodatabase (.gdb) into multiple Personal geodatabase (.mdb)?
# Import system modules
import arcpy
# Set environment settings
arcpy.env.workspace = "I:\python\Multiplegdb"
print arcpy.env.workspace
# Set local variables
inFeatures = r'I:\python\Multiplegdb\ABC.gdb'
print inFeatures
outLocation = r'I:\python\Multiplegdb\ABC_Output.mdb'
print outLocation
# Execute TableToGeodatabase
arcpy.FeatureClassToGeodatabase_conversion(inFeatures, outLocation)
A:
Here is one approach that performs the following actions:
Create a new .mdb with old FGDB name, but in new workspace
Find all FC's in FGDB--take into account empty FDS's
Copy all FC's to .mdb
import arcpy, os
arcpy.env.workspace = r'C:\temp\inws'
inws = arcpy.env.workspace
outws = r'C:\temp\outws'
fgdb = arcpy.ListWorkspaces(workspace_type = "fileGDB")
counter = 1
for f in fgdb:
# Define the output .mdb name
name = os.path.basename(f).split(".")[0]
# Create a new personal gdb (.mdb)
arcpy.CreatePersonalGDB_management(outws, name)
outgdb = os.path.join(outws, name + ".mdb")
# Get the FC's in FDS and copy to .mdb
arcpy.env.workspace = os.path.join(inws, f, "")
fcs1 = arcpy.ListFeatureClasses()
for fc in fcs1:
arcpy.CopyFeatures_management(fc, os.path.join(outgdb, fc))
# Get stand-alone FC's and copy to .mdb
arcpy.env.workspace = os.path.join(inws, f, "URS")
fcs2 = arcpy.ListFeatureClasses()
# Make sure there are FC's in the FDS
if fcs2 != None:
for fc in fcs2:
arcpy.CopyFeatures_management(fc, os.path.join(outgdb, fc))
print "%s of %s workspaces converted" % (counter, len(fgdb))
counter = counter + 1
print "Processing complete."
| tomekkorbak/pile-curse-small | StackExchange |
How viruses and toxins disassemble to enter host cells.
Many viruses and toxins disassemble to enter host cells and cause disease. These conformational changes must be orchestrated temporally and spatially during entry to avoid premature disassembly leading to nonproductive pathways. Although viruses and toxins are evolutionarily distinct toxic agents, emerging findings in their respective fields have revealed that the cellular locations supporting disassembly, the host factors co-opted during disassembly, the nature of the conformational changes, and the physiological function served by disassembly are strikingly conserved. Here, we examine some of the shared disassembly principles observed in model viruses and toxins. Where appropriate, we also underscore their differences. Our major intention is to draw together the fields of viral and toxin cell entry by using lessons gleaned from each field to inform and benefit one another. | tomekkorbak/pile-curse-small | PubMed Abstracts |
Trump and Chinese President Xi Jinping tout growing friendship at opulent state dinner President Trump revels in his relationship with Chinese President Xi.
-- President Trump's first visit to China has cast a new spotlight on what he has framed as a growing kinship with the country's President Xi Jinping.
Despite their language barrier, the two have been regularly seen through the president's state visit laughing together in exchanges and repeatedly emphasizing a growing friendship and mutual respect.
Trump beamed with pride as he showed off a video today at an opulent Chinese state dinner of his granddaughter Arabella Kushner’s singing a poem in Chinese.
Arabella, 6, became somewhat of a celebrity in China after she first sang for Xi in his visit to Trump's Mar-a-Lago club this past April. In the newly recorded video shared by Trump, she greets Xi and his wife, Peng Linyuan, as "Grandpa Xi and Grandma Peng."
"Our children so often remind us of our shared humanity and true dignity," Trump said during a toast at the dinner before airing the video of Ivanka Trump and Jared Kushner's daughter.
The chemistry between Trump and Xi is not exactly surprising, but still serves as a highlight in what has become a major shift from the fiery rhetoric of Trump prior to his taking office to his actions after he assumed the presidency.
For years prior to his presidency, Trump paralleled his reputation as a skilled dealmaker with repeated inflammatory attacks regarding China's ability to "rape" the United States on economic issues and trade deals.
Such hostility seemed all but forgotten as Trump said alongside Xi at a signing ceremony today that he blamed the United States rather than China for the trade deficit between the two countries.
"After all, who can blame a country for being able to take advantage of another country to the benefit of its citizens?” Trump said to applause in the room.
Despite the president's vocal commitments to try to aggressively tackle the trade deficit and other imbalances, that assertiveness has been largely absent in Trump's public statements while in China. He also contrasted with previous presidents in avoiding mention on issues such as China's crackdown on protests and an independent press.
Xi said in his state dinner toast, “China and the United States, once involved in animosity, have grown into a community with our interests converging.”
It's a message echoed by Trump, who similarly painted a rosy forecast of future U.S.-China relations through his remaining time in office.
"To the people of your country and to a friendship that will only grow stronger and stronger in the many years to come," Trump said, closing off his toast at the state dinner today. | tomekkorbak/pile-curse-small | OpenWebText2 |
Q:
IE Fixes - Conditional Comment Script will not execute
I'm trying to build a website. I have it displaying correctly in every browser except IE versions 8 and lower. IE renders blue boxes around my img's that are also anchors. I can get rid of this by setting the border property to none but i'd like to do it with javascript. I can get my Javascript to execute in a conditional comment.
try
{
var ancs = document.getElementsByTagName("a");
for(var i=0; i<ancs.length; i++)
{
if(ancs[i].childNodes[0].nodeName == "IMG")
{
//Set border property to none
}
}
}
catch(err)
{
alert(err);
}
A:
I am sorry for not answering to the javascript part. But you should do it with CSS like this:
a img { border:0; }
| tomekkorbak/pile-curse-small | StackExchange |
Des Moines Speech: Delivered in Des Moines, Iowa, on September 11, 1941, this speech was met with outrage in many quarters
The following resources are offered as a resource to understand Charles Lindbergh's involvement within the America First Committee prior to the start of World War II. This site does not support the content of some of the information below, however, the goal of this page is to offer a perspective of available information to make your own judgment. Please feel free to submit additional information for this page.
Audio Clips: WAV Audio Clip
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MP3 Audio Clip- 9-11-41 Des Moines, IA speech by Charles Lindbergh Des Moines Speech: It is now two years since this latest European war began. From that day in September, 1939, until the present moment, there has been an over-increasing effort to force the United States into the conflict.
That effort has been carried on by foreign interests, and by a small minority of our own people; but it has been so successful that, today, our country stands on the verge of war.
At this time, as the war is about to enter its third winter, it seems appropriate to review the circumstances that have led us to our present position. Why are we on the verge of war? Was it necessary for us to become so deeply involved? Who is responsible for changing our national policy from one of neutrality and independence to one of entanglement in European affairs?
Personally, I believe there is no better argument against our intervention than a study of the causes and developments of the present war. I have often said that if the true facts and issues were placed before the American people, there would be no danger of our involvement.
Here, I would like to point out to you a fundamental difference between the groups who advocate foreign war, and those who believe in an independent destiny for America.
If you will look back over the record, you will find that those of us who oppose intervention have constantly tried to clarify facts and issues; while the interventionists have tried to hide facts and confuse issues.
We ask you to read what we said last month, last year, and even before the war began. Our record is open and clear, and we are proud of it.
We have not led you on by subterfuge and propaganda. We have not resorted to steps short of anything, in order to take the American people where they did not want to go.
What we said before the elections, we say [illegible] and again, and again today. And we will not tell you tomorrow that it was just campaign oratory. Have you ever heard an interventionist, or a British agent, or a member of the administration in Washington ask you to go back and study a record of what they have said since the war started? Are their self-styled defenders of democracy willing to put the issue of war to a vote of our people? Do you find these crusaders for foreign freedom of speech, or the removal of censorship here in our own country?
The subterfuge and propaganda that exists in our country is obvious on every side. Tonight, I shall try to pierce through a portion of it, to the naked facts which lie beneath.
When this war started in Europe, it was clear that the American people were solidly opposed to entering it. Why shouldn't we be? We had the best defensive position in the world; we had a tradition of independence from Europe; and the one time we did take part in a European war left European problems unsolved, and debts to America unpaid.
National polls showed that when England and France declared war on Germany, in 1939, less than 10 percent of our population favored a similar course for America. But there were various groups of people, here and abroad, whose interests and beliefs necessitated the involvement of the United States in the war. I shall point out some of these groups tonight, and outline their methods of procedure. In doing this, I must speak with the utmost frankness, for in order to counteract their efforts, we must know exactly who they are.
The three most important groups who have been pressing this country toward war are the British, the Jewish and the Roosevelt administration.
Behind these groups, but of lesser importance, are a number of capitalists, Anglophiles, and intellectuals who believe that the future of mankind depends upon the domination of the British empire. Add to these the Communistic groups who were opposed to intervention until a few weeks ago, and I believe I have named the major war agitators in this country.
I am speaking here only of war agitators, not of those sincere but misguided men and women who, confused by misinformation and frightened by propaganda, follow the lead of the war agitators.
As I have said, these war agitators comprise only a small minority of our people; but they control a tremendous influence. Against the determination of the American people to stay out of war, they have marshaled the power of their propaganda, their money, their patronage.
Let us consider these groups, one at a time.
First, the British: It is obvious and perfectly understandable that Great Britain wants the United States in the war on her side. England is now in a desperate position. Her population is not large enough and her armies are not strong enough to invade the continent of Europe and win the war she declared against Germany.
Her geographical position is such that she cannot win the war by the use of aviation alone, regardless of how many planes we send her. Even if America entered the war, it is improbable that the Allied armies could invade Europe and overwhelm the Axis powers. But one thing is certain. If England can draw this country into the war, she can shift to our shoulders a large portion of the responsibility for waging it and for paying its cost.
As you all know, we were left with the debts of the last European war; and unless we are more cautious in the future than we have been in the past, we will be left with the debts of the present case. If it were not for her hope that she can make us responsible for the war financially, as well as militarily, I believe England would have negotiated a peace in Europe many months ago, and be better off for doing so.
England has devoted, and will continue to devote every effort to get us into the war. We know that she spent huge sums of money in this country during the last war in order to involve us. Englishmen have written books about the cleverness of its use.
We know that England is spending great sums of money for propaganda in America during the present war. If we were Englishmen, we would do the same. But our interest is first in America; and as Americans, it is essential for us to realize the effort that British interests are making to draw us into their war.
The second major group I mentioned is the Jewish.
It is not difficult to understand why Jewish people desire the overthrow of Nazi Germany. The persecution they suffered in Germany would be sufficient to make bitter enemies of any race.
No person with a sense of the dignity of mankind can condone the persecution of the Jewish race in Germany. But no person of honesty and vision can look on their pro-war policy here today without seeing the dangers involved in such a policy both for us and for them. Instead of agitating for war, the Jewish groups in this country should be opposing it in every possible way for they will be among the first to feel its consequences.
Tolerance is a virtue that depends upon peace and strength. History shows that it cannot survive war and devastations. A few far-sighted Jewish people realize this and stand opposed to intervention. But the majority still do not.
Their greatest danger to this country lies in their large ownership and influence in our motion pictures, our press, our radio and our government.
I am not attacking either the Jewish or the British people. Both races, I admire. But I am saying that the leaders of both the British and the Jewish races, for reasons which are as understandable from their viewpoint as they are inadvisable from ours, for reasons which are not American, wish to involve us in the war.
We cannot blame them for looking out for what they believe to be their own interests, but we also must look out for ours. We cannot allow the natural passions and prejudices of other peoples to lead our country to destruction.
The Roosevelt administration is the third powerful group which has been carrying this country toward war. Its members have used the war emergency to obtain a third presidential term for the first time in American history. They have used the war to add unlimited billions to a debt which was already the highest we have ever known. And they have just used the war to justify the restriction of congressional power, and the assumption of dictatorial procedures on the part of the president and his appointees.
The power of the Roosevelt administration depends upon the maintenance of a wartime emergency. The prestige of the Roosevelt administration depends upon the success of Great Britain to whom the president attached his political future at a time when most people thought that England and France would easily win the war. The danger of the Roosevelt administration lies in its subterfuge. While its members have promised us peace, they have led us to war heedless of the platform upon which they were elected.
In selecting these three groups as the major agitators for war, I have included only those whose support is essential to the war party. If any one of these groups--the British, the Jewish, or the administration--stops agitating for war, I believe there will be little danger of our involvement.
I do not believe that any two of them are powerful enough to carry this country to war without the support of the third. And to these three, as I have said, all other war groups are of secondary importance.
When hostilities commenced in Europe, in 1939, it was realized by these groups that the American people had no intention of entering the war. They knew it would be worse than useless to ask us for a declaration of war at that time. But they believed that this country could be entered into the war in very much the same way we were entered into the last one.
They planned: first, to prepare the United States for foreign war under the guise of American defense; second, to involve us in the war, step by step, without our realization; third, to create a series of incidents which would force us into the actual conflict. These plans were of course, to be covered and assisted by the full power of their propaganda.
Our theaters soon became filled with plays portraying the glory of war. Newsreels lost all semblance of objectivity. Newspapers and magazines began to lose advertising if they carried anti-war articles. A smear campaign was instituted against individuals who opposed intervention. The terms "fifth columnist," "traitor," "Nazi," "anti-Semitic" were thrown ceaselessly at any one who dared to suggest that it was not to the best interests of the United States to enter the war. Men lost their jobs if they were frankly anti-war. Many others dared no longer speak.
Before long, lecture halls that were open to the advocates of war were closed to speakers who opposed it. A fear campaign was inaugurated. We were told that aviation, which has held the British fleet off the continent of Europe, made America more vulnerable than ever before to invasion. Propaganda was in full swing.
There was no difficulty in obtaining billions of dollars for arms under the guise of defending America. Our people stood united on a program of defense. Congress passed appropriation after appropriation for guns and planes and battleships, with the approval of the overwhelming majority of our citizens. That a large portion of these appropriations was to be used to build arms for Europe, we did not learn until later. That was another step.
To use a specific example; in 1939, we were told that we should increase our air corps to a total of 5,000 planes. Congress passed the necessary legislation. A few months later, the administration told us that the United States should have at least 50,000 planes for our national safety. But almost as fast as fighting planes were turned out from our factories, they were sent abroad, although our own air corps was in the utmost need of new equipment; so that today, two years after the start of war, the American army has a few hundred thoroughly modern bombers and fighters--less in fact, than Germany is able to produce in a single month.
Ever since its inception, our arms program has been laid out for the purpose of carrying on the war in Europe, far more than for the purpose of building an adequate defense for America.
Now at the same time we were being prepared for a foreign war, it was necessary, as I have said, to involve us in the war. This was accomplished under that now famous phrase "steps short of war."
England and France would win if the United States would only repeal its arms embargo and sell munitions for cash, we were told. And then [illegible] began, a refrain that marked every step we took toward war for many months--"the best way to defend America and keep out of war." we were told, was "by aiding the Allies."
First, we agreed to sell arms to Europe; next, we agreed to loan arms to Europe; then we agreed to patrol the ocean for Europe; then we occupied a European island in the war zone. Now, we have reached the verge of war.
The war groups have succeeded in the first two of their three major steps into war. The greatest armament program in our history is under way.
We have become involved in the war from practically every standpoint except actual shooting. Only the creation of sufficient "incidents" yet remains; and you see the first of these already taking place, according to plan [ill.]-- a plan that was never laid before the American people for their approval.
Men and women of Iowa; only one thing holds this country from war today. That is the rising opposition of the American people. Our system of democracy and representative government is on test today as it has never been before. We are on the verge of a war in which the only victor would be chaos and prostration.
We are on the verge of a war for which we are still unprepared, and for which no one has offered a feasible plan for victory--a war which cannot be won without sending our soldiers across the ocean to force a landing on a hostile coast against armies stronger than our own.
We are on the verge of war, but it is not yet too late to stay out. It is not too late to show that no amount of money, or propaganda, or patronage can force a free and independent people into war against its will. It is not yet too late to retrieve and to maintain the independent American destiny that our forefathers established in this new world.
The entire future rests upon our shoulders. It depends upon our action, our courage, and our intelligence. If you oppose our intervention in the war, now is the time to make your voice heard.
Help us to organize these meetings; and write to your representatives in Washington. I tell you that the last stronghold of democracy and representative government in this country is in our house of representatives and our senate.
There, we can still make our will known. And if we, the American people, do that, independence and freedom will continue to live among us, and there will be no foreign war.
| tomekkorbak/pile-curse-small | OpenWebText2 |
Q: Let me read you something from your own act: "I hope Mickey dies. I do. I hope he goddamn dies. I hope he gets ahold of some tainted cheese..."
A: "...and dies lonely and forgotten behind the baseboard of a soiled bathroom in a poor neighborhood with his hand in Goofy's pants."
Q: What did Mickey Mouse ever do to you?
A: That's not how these things generate themselves. What Mickey Mouse did to me was to represent something -- in this case, meaningless shit on the news, the way they fill our minds with all this stuff to distract us from the real tragedy. He's a symbolic figure.
Q: This spring marks your 20th year on HBO, your 40th year in show business, and your 60th year on the planet. What makes your birthday different from Mickey Mouse's?
A: I hope they don't ever use my birthday as a news item. That would be one distinction. I would also hope to tell people I'm 60 because it's a nice human fact for a guy like me to make it all the way to 60.
Q: Do you exercise?
A: I use a treadmill because I've had three heart attacks. My father died at 57. His first symptom of heart trouble was a trip to St. Raymond's Cemetery.
Q: Do you have any of the appliances or equipment that you make fun of in your comedy routines: camcorders, pasta makers...?
A: I have no pasta maker. I probably have a device at home that would take pictures of moving images and would pass for a camcorder, but I don't know where it is.
Q: What rating will your upcoming HBO special get?
A: Under the new rating system? I don't know all the terminology of that system yet.
Q: Somewhere around an NC-17?
A: Or NC-35, even.
Q: Has censorship gotten stronger or weaker during your years in the business?
A: I think the trend to control speech -- and therefore thought -- continues. Because of the freer flow of information now, there's more on the side of free thought.
A: ...This is rhetoric. Rhetoric paints with a broad brush. I try to find targets I feel something about and express it my way, so it's usually overdone.
Q: But aren't boomers the main audience for HBO?
A: Baby boomers helped me a great deal in my career. They launched me. They were there for me to sing my song to. And I'm not saying I'm better than anyone, but I think they turned that anti-authority baby boom mentality into their own enemy. Now I identify very closely with their children.
Q: What went wrong?
A: The two big mistakes were the belief in a sky god -- that there's a man in the sky with 10 things he doesn't want you to do and you'll burn for a long time if you do them -- and private property, which I think is at the core of our failure as a species. That's the source of my indignations, my dissatisfactions, however it comes out on the stage. I feel betrayed by the people I'm part of, these creatures, these magnificent creatures.
Q: Is there anyone or anything you like?
A: I love individuals. I think people are terrific as I meet and get to know them. I like imagination. I like the freedom that this society manages to parcel out to us in the midst of the rest of what they do to you. I also like thinking about the fact that the atoms in me are the same atoms that are in all the rest of the universe, and that every one of those atoms came from the middle of a star. In other words, it's only me out there.
We use up words like "spiritual" so fast in this culture. Twenty years ago "spiritual" had a distinct meaning. But now there's a lot of jack-off thinkers who just love to talk about the spiritual. And there is a lot of bogus -- is "bogosity" a word? It should be -- a lot of bogosity in these spiritual seekers. So you have to find another way to express it. I just call it "how I fit."
Q: Speaking of how you fit, where do you fit on the political spectrum?
A: If the center line is really there, and I were anywhere, I would come down on the left of center.
Q: Right there with Bill Clinton.
A: I like Bill, by the way. If there were only one cherry pie in the world, and Bill Clinton owned it, I might get a piece of it. If Bush or Reagan owned it, you'd have to kill them to get a piece of pie. That's my feeling about Bill. And Bill's a good bullshitter. America likes a good bullshitter. That's one of the reasons he was re-elected. Honesty has no place in politics. It would throw everything off.
Q: You don't vote now. When was the last time you voted?
A: Maybe 1980.
Q: Carter?
A: That probably would have been it. And that would have been one of the few lines I voted on. I'm on the left because I think there's a little more attention to human needs than to property rights. But I don't think much of political activism. It's so shortsighted. Most people are interested in their own personal comfort. I've said that about environmentalists -- I think they care about bike paths and places to park their Volvos, not the planet as an abstraction.
Q: But you have no particular love for the planet. You've wished disasters upon it.
A: When you look at it from that one picture, the one from space, it's really a rather attractive thing. I have nothing against the planet per se. I root for the big comet or asteroid as a way of cleansing the planet. The comet or asteroid 65 million years ago is probably what gave us our opening to replace the reptiles. The greatest entertainment I have in my life is chronicling internally, not necessarily for the public, the slow dissolution of order.
Q: You must love the blowing up of buildings for entertainment in Las Vegas.
A: Yes, I do. I saw the Dunes blow up in person.
Q: How is Vegas different from a concert hall for a performance?
A: In Las Vegas, people are there for other reasons, and you are a sideline, an attraction, an "also." So you don't get all hard-core fans. Secondly, when you have tables and drinks and a seating arrangement, people are on their guard a little more. They will not reveal as much about themselves in those settings as they will in the darkness of a theater facing front. Laughter reveals a lot about you. It's voting in a way. So I'd say I skim off about 10 percent of the venom or 10 percent of the attack stuff on things people hold dear.
Q: Does Mickey Mouse get skimmed off?
A: No, just religion and overt attacks on people's political affiliations. I don't use the word "Republican," for example, though I say a lot about conservatives. There's something about the word "conservative" that gives people a little more freedom to join you if they want.
Q: It's self-censorship.
A: Well, editing. It's accommodating the reality of the world.
Q: Do you really care if they "balance the stupid fucking budget"?
A: I don't care much about the outcome. I'd like for people to feel better and have better lives, but I don't think that's in the cards through political action. I think bloodshed is still the way you get dramatic change. That'll never happen because they've got all the guns now. At least they've got the nice guns, the big ones, the ones with night vision.
Q: You sound like one of the Freemen.
A: I've said to myself -- I don't think I've said it to anyone else -- that but for the racism and religious orientation of these militiamen, I very much like the spirit involved there. Those are two points that would stop me. Boy, do they hate "Jews and niggers" -- that's the way they say it, right? And they very much think Jesus has got a pretty good thing coming up soon. The end times, the tribulation...what's the other word?
Q: Apocalypse?
A: The apocalypse, that's even better, but there's another one. The rapture! That sounds like fun.
Q: Are you lonely?
A: There is a core of loneliness. It's partly existential. Secondly, I was raised a loner. My parents were not there. My father was asked to leave because he couldn't metabolize ethanol. Actually, my mother ran away with us when I was 2 months old and my brother was 5. Real dramatic stuff: down the fire escape, through backyards.
So, I sort of raised myself. I was alone a lot and I invented myself -- I lived through the radio and through my imagination.
One of the interesting things about "outsidership" is that underneath it there's a longing to belong. I just wish the thing I refused to belong to -- the species, Western capital culture -- was a little more respectable.
My one true relaxation is my flotation tank, in which I can either meditate or just drift off.
Q: Do you work in there?
A: No, that would defeat the whole idea.
Q: What was the bigger deal out of Dayton, the Bosnian peace accord or you meeting your wife, Brenda?
A: Ah, Brenda over Bosnia every time. These folks are wonderful, these peace people. The whole process of patching up these places that have thousand-year-old wounds....
Q: How have you and Brenda stuck together for more than 30 years?
A: There's a lot of luck involved. Brenda and I got lucky the very first time and didn't have to go through several spouses to do it. It's a kind of complementary way of filling each other out and making each individual more complete. The key for us has always been to put the twosome ahead of either individual whenever that was an issue. That helps. And then, I don't know, star-crossed something -- it's just magic. | tomekkorbak/pile-curse-small | Pile-CC |
470 S.E.2d 296 (1996)
220 Ga. App. 772
SCHERNEKAU et al.
v.
McNABB.
No. A95A2753.
Court of Appeals of Georgia.
March 15, 1996.
Certiorari Denied May 17, 1996.
*297 Williams & Henry, Benjamin S. Williams, Joseph A. Fried, Atlanta, W. Anthony Moss, Marietta, for appellants.
Downey & Cleveland, Joseph C. Parker, W. Curtis Anderson, Marietta, for appellee.
RUFFIN, Judge.
This underlying personal injury action arose when Christopher Schernekau was shot in the head with an air rifle while on a camping trip. His parents brought suit on his and their behalf against Judy DiBauda, the adult who supervised the trip, Jon McKeachie, the 15-year-old who fired the weapon, and Mary Alice McNabb, mother of the 11-year-old who brought the air rifle on the trip. The trial court granted summary judgment in favor of McNabb. Concluding that the trial court erred, we reverse.
On August 3, 1993, DiBauda, an unlicensed day care provider, organized a campout on Lake Allatoona for 12 children of varying ages, including five children ages six and under, and six children between nine and eleven. McNabb knew about and specifically consented to her 11-year-old son's bringing *298 his air rifle on the campout. McNabb and DiBauda disagree as to whether McNabb obtained DiBauda's permission to take the air rifle on the trip. McNabb testified that she sought and obtained DiBauda's permission for her son to take the rifle, while DiBauda testified McNabb never even mentioned the gun. DiBauda testified that she would not have consented because of the danger the gun posed and because its presence would have violated campground rules.
The evidence shows the air rifle gun was not an ordinary BB gun but a high-powered, pneumatic pump air rifle that, fully pumped, has the same velocity as a .22 caliber bullet and is capable of firing BB's or .177 caliber lead pellets.
DiBauda testified that en route to the camp, she informed McNabb's son that if she discovered that he had a BB gun she would be obligated to take it away because the park prohibited guns. When they arrived at the campsite, DiBauda confiscated the rifle from McNabb's son and placed it in her van. However, without DiBauda's knowledge, McNabb's son retrieved his gun from the van. DiBauda subsequently left the campsite with some of the younger children, leaving the older children under the care of 15-year-old Jon McKeachie. During DiBauda's absence, McKeachie took the rifle and began shooting it around the campsite. He testified that he fired it over the lake, in the trees, and into the tent belonging to Christopher and Jonathan Schernekau. The testimony conflicted as to whether Christopher Schernekau and McKeachie wrestled over the gun after McKeachie shot the tent or whether McKeachie, with no apparent reason, shot Christopher Schernekau in the head at point blank range.
The trial court granted McNabb's motion for summary judgment finding that there were "genuine issues of fact as to [McNabb's] negligence vel non" but that "any negligence on her part was not the proximate cause of [Schernekau's] injuries." The court determined that "McKeachie's act of shooting Schernekau was an independent intervening criminal act." The court held that McKeachie's act of shooting Schernekau was unforeseeable as a matter of law because there was "no evidence that McKeachie had a propensity to commit violent or criminal acts or that McNabb had any reason to believe that McKeachie would intentionally shoot at someone with the BB gun."
The Schernekaus contend that the trial court erred by finding as a matter of law that McNabb's negligence was not the proximate cause of Christopher Schernekau's injuries, and by concluding that McKeachie's actions were an unforeseeable intervening criminal act.
Proximate cause is properly reserved for the jury and can only be appropriately addressed on summary judgment in "plain and indisputable cases." Atlanta Ob. & Gyn. Group v. Coleman, 260 Ga. 569, 570, 398 S.E.2d 16 (1990). "The decision may be made by the trial judge or appellate court only if reasonable persons could not differ as to both the relevant facts and the evaluative application of legal standards (such as the legal concept of `foreseeability') to the facts." Id. "With reference to foreseeability of injury, the correct rule is that in order for a party to be held liable for negligence, it is not necessary that he should have been able to anticipate the particular consequences which ensued. It is sufficient if, in ordinary prudence, he might have foreseen that some injury would result from his act or omission, and that consequences of a generally injurious nature might result." (Citations and punctuation omitted.) Wallace v. Sears, Roebuck & Co., 196 Ga.App. 221, 222, 396 S.E.2d 41 (1990).
The Schernekaus contend that McNabb should have appreciated the inherent danger of introducing the rifle in such a setting. They argue that she knew or should have known that children are drawn to objects like air rifles, that they, particularly in group settings, are prone to horseplay and consequential injury, and that they lack the proper judgment to handle guns. We agree.
The evidence shows that McNabb was aware of the dangerous capabilities of the air rifle, knew that her son planned to take the rifle on a campout in the presence of many other children who were to be supervised by only one adult, and helped her son roll up the *299 rifle in his bedroll. Therefore, based on the evidence in the record, a jury could conclude that McNabb, in the exercise of ordinary prudence, might have foreseen that some injurious consequences could ensue from permitting her son to bring a dangerous weapon on a campout with many young children and limited adult supervision.
McNabb contends that regardless of any negligence on her part, the actions of McKeachie constituted unforeseeable, intervening, independent criminal acts which broke the chain of causation. McNabb claims that in order for her "to have any foreseeability, she must have had some prior knowledge that John McKeachie was likely to harm someone." Relying on Doe v. Howell, 212 Ga.App. 305, 441 S.E.2d 767 (1994) and Skelton v. Gambrell, 80 Ga.App. 880, 57 S.E.2d 694 (1950), McNabb claims that the injury was unforeseeable as a matter of law.
However, both of these cases are distinguishable and fail to sustain McNabb's argument. In Doe, this court affirmed summary judgment in favor of a second grade teacher on a negligent supervision claim which was based on a sexual assault by one student on another student in the classroom coat closet. We found no evidence that the teacher knew or should have known that one student's presence created an unreasonable risk of a sexual attack to her other students.
Here, it is not McKeachie's presence that is at issue, but rather, the air rifle's presence on the campground, with young children and very limited adult supervision. McNabb admitted she knew that the air rifle was dangerous and yet she gave her young son permission to take it on the campout. A jury issue is created as to whether McNabb knew or should have known that by her action she was creating an unreasonable risk of injury.
In Skelton, the defendants were grocery store owners who provided a pistol to their 14-year-old son who thereafter discharged the pistol and killed a customer. This Court determined that the pleadings were deficient because they did not set forth a sufficient showing that the parents had reason to know of the dangerousness of their actions. Skelton, supra at 884, 57 S.E.2d 694. However, the case was decided under a different standard of review not applicable in this case, and the merits of the underlying claim were never addressed.
McNabb's reliance on Dent v. Smith, 172 Ga.App. 90, 322 S.E.2d 100 (1984), is also misplaced because there was no evidence of possible parental negligence in furnishing or permitting a child access to an instrumentality with which the child could injure a third party.
Moreover, it appears that the trial court applied an incorrect definition of foreseeability. "`It is not necessary that an original wrongdoer shall anticipate or foresee the details of a possible injury that may result from his negligence. It is sufficient if he should anticipate from the nature and character of the negligent act committed by him that injury might result as a natural and reasonable consequence of his negligence.'" Coleman v. Atlanta Ob. & Gyn. Group, 194 Ga.App. 508, 510(1), 390 S.E.2d 856 (1990). Therefore, the trial court's application of the foreseeability doctrine was more stringent than the law requiresall that was necessary was that it was reasonably foreseeable that someone might get hurt as a consequence of McNabb's sending the air rifle on the campout. See Wallace, supra at 222, 396 S.E.2d 41. Moreover, even if McKeachie's actions were criminal in nature, McNabb could not avoid liability if the acts were reasonably foreseeable. See Confetti Atlanta v. Gray, 202 Ga.App. 241, 414 S.E.2d 265 (1991).
Accordingly, we find that the trial court erred in concluding that McKeachie's actions necessarily broke the causal chain thus eliminating any act or omission by her as the proximate cause of Schernekau's injuries. Therefore, the grant of summary judgment was erroneous.
Judgment reversed.
BEASLEY, C.J., and POPE, P.J., concur.
| tomekkorbak/pile-curse-small | FreeLaw |
Let’s first address the proverbial elephant in the room: Rodgers and Hammerstein’s Carousel is back—and it still glosses over domestic abuse.
When it opened almost exactly 73 years ago at the Majestic Theatre, critics hailed it a masterpiece. Lewis Nichols of The New York Times wrote, “Richard Rodgers and Oscar Hammerstein II who can do no wrong, have continued doing no wrong in adapting Liliom into a musical play.”
Subsequent New York productions have achieved equal amounts of praise and in 1999, Time Magazine proclaimed Carousel “the best Musical of the 20th Century.”
In 1945 however, #metoo and #blacklivesmatter didn’t exist. Sensibilities and sensitivities weren’t nearly as precarious as they are now. Thankfully, we’ve evolved since then.
Yet under Tony winner Jack O’Brien’s masterful direction, there is beauty, insight, and wisdom to be gleaned from this stunning new revival.
Based on Molnar’s Hungarian play Liliom, Carousel introduces us to Billy Bigelow (Joshua Henry), a carnival barker who falls for Julie Jordan (Jessie Mueller) a millworker who swears off marriage–until she meets Bigelow. Amidst a tenuous union and a job loss for both parties, we learn that Billy hit his wife. “He’s unhappy that he ain’t workin’,” Julie tells her friend and co-worker Carrie Pipperidge (Lindsay Mendez) “That’s really why he hit me on Monday,” she continues.
Billy hatches a plan with his pal, Jigger Craigin (Amar Ramasar): The two will stage a robbery and make a quick buck. After all, Billy is expecting a child and as the curtain falls on Act 1, he swears that in order to financially provide for his newborn, he will “go out and make it, or steal it, or take it or die.”
As Julie continues to make excuses for Billy’s domestic abuse, she foreshadows a gloomy ending in her and Nettie’s duet, “What’s the use of Wond’rin?” “Common sense may tell you, that the ending will be sad,” she sings. Carrie however, has been swept away by Enoch Snow (Alexander Gemignani), a fine, fishmongering gentleman who treats Carrie with respect and kindness.
Indeed, the ending will be sad–but it will also be hopeful.
Even with earnest intent, Billy cannot control his emotions in any other way besides anger. “All you ever do to get out of a difficulty-hit someone you love. Failure!”, says one of his heavenly friends.
At that moment, we fully understand Billy Bigelow. He is undeniably flawed and still, undeniably human. Like King Mongkut in Rodgers and Hammerstein’s other classic, The King and I, “they are men who think with their hearts, men who stumble and fall, but men who try. Men you’ll forgive and forgive and help and protect as long as you live.”
This is not to suggest that physical abuse is ever justified. It is not. Yet we must delineate the difference between understanding and acceptance. Billy, like so many who carry internal anger, are products of those who have gone before him. In turn, it is passed down to the next generation. And the vicious cycle– much like the carousel itself– spins and spins. The fact that Mr. Henry is African-American adds even deeper layers to this performance. Henry’s voice is as strong as his broad, muscled shoulders and he exudes more alluring masculinity than a Nascar rally.
Rodgers & Hammerstein probably never meant to tacitly condone spousal abuse, but if we don’t confront this problematic storyline, we do a great disservice to ourselves. But we’re also at fault if we’re blinded to the compassion and forgiveness that this show so generously offers. Our lives, as mentioned in Holy Scripture, are “a mist that appears for a little time and then vanishes.” Carousel reminds us all too painfully of this brevity–as well as the burden that lugging resentment casts on our souls.
There is a bounty of fine moments in this production, but the best one may come from Nettie Fowler (Renee Fleming), whose interpretation of “You’ll Never Walk Alone” is other-worldly and a spiritual hymn unto its own.
Ms. Mueller continues to define her status as a true Broadway star. From a lounge singer in On a Clear Day You Can See Forever to Carole King in Beautiful, another victim of abuse turned empowered protagonist in Waitress and everything in between, there is obviously little she can’t do. Once again, her gorgeous vocals and wonderful acting add credibility to this near perfect reboot.
Justin Peck‘s athletic and energetic choreography is thrilling and his ensemble executes it with immaculate precision. Santo Loquasto‘s dark, but not depressing sets, combined with Brian McDevitt‘s enthralling lighting design make this a sumptuous treat for the eyes. Arguably, Rodgers and Hammerstein’s soaring music is the finest score ever written for Broadway.
All of these elements combine to create the best Broadway musical revival I have ever seen.
Carousel is now playing at the Imperial Theatre (West 45th between Broadway and 8th). For tickets and information, visit Carousel on Broadway. | tomekkorbak/pile-curse-small | OpenWebText2 |
Main Menu
DIY Kid’s Trinket Box
I don’t know about you, but I definitely have a bunch of little stuff sitting around with no home. Rocks, shells, etc. I also know for sure it stemmed from when I was a kid! And Lord knows I had a lot more *stuff* sitting around my room with no home location haha! I was selected for the Blueprint Plaid Kids Craft campaign, and I think this is a perfect kids project! It gets them to get their little knick knacks off the floor, table, etc. , and it also brings out their creative side, and gives them something special of their very own. My favorite…it helps declutter your house! And as I’m going through a *nesting* stage myself–I like this part the best haha!
Here’s all the goodies I received for the campaign. I got the box from the dollar store (the Dollar Tree in particular). I’ve always loved Apple Barrel Paint because their affordable prices, so this is a super inexpensive project for the kids!
I started by painting just the top of the box with the non glow-in-the-dark blue paint.
Then, I used a fun painting technique to get a splatter effect on the top of the box. I added a little pool of the yellow glow-in-the-dark paint to a paper cup (ignore the purple paint, I reuse the cups sometimes!), dipped a straw in it, and then blew out onto the top of the box. **This is super fun for the kids, but you have to make sure they are old enough to understand that you don’t suck the paint up into the straw.** It can also be pretty messy, so it’s something to do either outside, or on lots and lots of newspaper 🙂
Check out how cool that looks! Kids would definitely be impressed with this technique.
Once the splatters dried completely, I took one of my stencils and dabbed a half moon with the green glow-in-the-dark paint, on the side of the top. When it dried, it became a bit see-through because of the dark blue underneath, so I simply outlined it with a paint marker I had to make it *pop*.
Once the top completely dried, I applied a coat of the Mod Podge Glitter. I have to say, I love this stuff! It looks awesome! I wish I could capture just how glittery it came out with the one coat, but the picture doesn’t do it justice.
Finally, after the top was all done, I painted the base with the purple, and applied the Gloaway over it.
I wish I could have gotten a picture of it glowing in the dark, but my camera couldn’t capture it! It looks super cool though and the kids would LOVE it! | tomekkorbak/pile-curse-small | Pile-CC |
Brian MacPhie
Brian MacPhie (born May 11, 1972 in San Jose) is a former professional tennis player from the United States.
MacPhie enjoyed most of his tennis success while playing doubles. During his career, he won seven doubles titles. He achieved a career-high doubles ranking of world No. 22 in 2002.
MacPhie is now coaching tennis to juniors and adults in Austin, Texas at the Hills of Lakeway Elevation Athletic Club.
Career finals
Doubles: 20 (7 titles)
External links
Category:American male tennis players
Category:Sportspeople from San Jose, California
Category:USC Trojans men's tennis players
Category:Tennis people from California
Category:Living people
Category:1972 births | tomekkorbak/pile-curse-small | Wikipedia (en) |
Q:
PyAutoGUI Key Press slow performance in Linux Ubuntu
I'm facing an issue running PyAutoGUI on Linux Ubuntu 19.06 x64, when I need to use the keyDown/KeyPress function.
After running the code, it freezes the computer for about 4 or 5 seconds, and the CPU usage goes to 100%
Something really simple like this:
import pyautogui
pyautogui.keyDown('altleft')
pyautogui.click(910, 477)
pyautogui.click(840, 477)
pyautogui.click(844, 412)
pyautogui.keyUp('altleft')
I can see the mouse moving on my screen, but the whole computer freezes after that. I tested in different computers, physicals and VM's, all the same behaviour.
I also did test in my Windows computer, and with that one I had no problems.
Any ideas about this?
I'm not very familiar with Python nor Linux. I believe I might be missing to install or configure something.
A:
Figure it out that the problem is actually on the graphical server.
The answer is in this post:
https://bugs.launchpad.net/ubuntu/+source/meta-gnome3/+bug/1777708
When I changed to Wayland I did not have the problem.
If anyone has similar issue, to change the graphical server, see the steps in the link below:
enter link description here
| tomekkorbak/pile-curse-small | StackExchange |
Q:
Uso della virgola con la congiunzione "però"
Ho la tendenza a scrivere la congiunzione "però" fra virgole in frasi come, per esempio, questa:
Mi domando, però, quale sia l'origine di quest'espressione.
Tuttavia, non sono sicura che quest'uso della virgola sia corretto. Ho l'impressione che sia un'influenza della mia lingua (il catalano). Potreste dirmi qualcosa al riguardo?
A:
Direi che non abbia niente che non vada, anche se l'italiano tollera anche una relativa scarsità di virgole: io probabilmente scriverei «Mi domando però quale sia l'origine di quest'espressione».
A favore dell'uso tra virgole, cito dal solito Serianni un passo di Pirandello: «Non esce mai di casa, però, la sua figliuola!», Così è (se vi pare), V 27. (A scanso di equivoci: la battuta compare in una conversazione in cui qualcuno ipotizza che la figlia della signora Frola faccia certe cose, e qualcun altro, rivolgendosi direttamente alla signora, osserva che così non può essere perché la ragazza non esce mai di casa.)
Qui si può trovare il testo della pièce pirandelliana.
Per l'uso senza virgole, ecco un esempio da Natalia Ginzburg: «La casa di via Pastrengo era molto grande [...]; era però molto buia», Lessico famigliare, 31.
A:
Le virgole intorno a "però" si possono sia mettere, sia non mettere. A mio avviso, vi è solo una lieve differenza tra le due possibilità.
Se le virgole ci sono, come ha già osservato bobie, c'è una maggiore enfasi sul "però", e dunque sul fatto che la frase è contrapposta ad un'altra affermazione precedente.
Se le virgole non ci sono, viene a mancare questa enfasi, dunque quello che viene esaltato è il significato della frase, piuttosto che la sua opposizione alla precedente.
A riguardo della frase in esame, nel primo caso io intendo che la persona che parla esprime un certo dubbio sul fatto che esista una spiegazione ragionevole all'origine dell'espressione di cui si discute (e, quindi, potrebbe anche mettere in discussione la liceità stessa dell'espressione, in un'interpretazione un po' esagerata). Nel secondo caso esprime piuttosto la curiosità di sapere l'origine dell'espressione.
Chiaramente si tratta comunque di una differenza piuttosto lieve.
A:
Dopo la congiunzione 'però' la virgola non ci vuole
"non vorrai negare però che sia un gran lavoratore", "aspettami a casa, se però non sarò arrivato per le sei, esci pure"
Il tuo esempio nella forma normale sarebbe: " la frase l'ho capita...., però mi domando quale...", inverrtendo l'ordine la punteggiatura non cambia: ", mi domando però quale...".
Le virgole sono possibili quando si aggiunge una precisazione o correzione a quanto già detto: "...è quasi la stessa cosa, con questa sola differenza, però, che ...", non sono però obbligatorie: "... sono molto debole, non tanto però da non poter camminare".
Infine, qualunque parola può essere messa tra virgole per varie ragioni, non ultima quella stilistica, in quanto suggeriscono una pausa e aggiungono enfasi.
Ricapitolando: la tua frase sempra proprio una precisazione, quindi le virgole ci possono stare, anche se non sono obbligatorie come in catalano. In ogni caso le puoi sempre mettere con la motivazione che vuoi dare un po' d'enfasi
A proposito della frase citata da DaG, si può ricordare che forse è un uso particolare: in genere all’inizio o alla fine di una frase 'però,' viene seguito da una virgola e viene pronunciato con tono interiettivo, come un'esclamazione per esprimere (finta) sorpresa o altro sentimento, per constatare una realtà apparentemente insospettata o contraria all’apparenza: "però, quella ragazza non è poi così male!"
Questa non è una interpretazione obbligata (ho detto: 'forse'), giustificata,però, dalla presenza di una virgola e dal punto esclamativo:"lui non esce molto, però, sua figlia quanto (non) esce (poverina)!
*nota: positivo o negativo, a chiunque si riferisce, non cambia il valore interiettivo, come già detto, è una interpretazione possibile che è servita solo a introdurre un nuovo concetto.
| tomekkorbak/pile-curse-small | StackExchange |
I just spent part of tonight beating my 7-year-old daughter at Chutes and Ladders. OK, it was only one game, but it was hard fought and I pulled it out at the end. It might sound like I enjoyed it, but c’mon, it’s Chutes and Ladders: no adult ever really enjoys that game.
But I did care who won and who lost.
In fact, whenever my wife and I play board games, sports, card games or hopscotch with our kids, we don’t let them win. We never have. Yes, I know, we are terrible parents, right?
Listen, we don’t pull out every trick in the book or use grand master strategy to destroy them. I don’t get up and do a happy dance or throw it back in their face when they lose. However, sometimes they do win and it is fun for everyone. The thing is games aren’t always just about fun, sometimes they can teach us about life.
What kind of horribly competitive parents would do this? We are the kind of parents who love our kids and who actually want them to learn something about winning AND losing as they grow up. Somewhere along the line, our culture came to the conclusion that our kids must win at everything. Every participant gets a trophy and we don’t use red marks on school papers. Well, sorry, kids — that doesn’t fly in our house and we will never “let” you beat us.
In his incredibly insightful book Oh the Places You’ll Go, Dr. Seuss has a few lines that have rooted themselves in my parental thought process. The good doctor says:
“Wherever you fly, you’ll be the best of the best.
Wherever you go, you will top all the rest.
Except when you don’t
Because, sometimes, you won’t.”
As parents, we forget this. We shield our kids from the disappointments and losing in life. Sometimes it’s because we love them so much we never want them to experience defeat. Sometimes it’s because our own identity is tied up in them winning and it’s our own ego that gets in the way. No matter what it is, it’s not helping our children.
I remember playing Little League baseball and seeing a few of my teammates getting trophies at the end of the season. I wanted one so bad that it drove me to be better. I practiced harder so that one day, I might get that trophy. If everyone got one would it have cheapened it? Absolutely. I want my kids to know the hunger that drives you to be the best and the exhilaration of accomplishing that. I also want them to know what it feels like to be humbled because someone is better than you. Because there is always someone better. It’s just a matter of time before you meet them.
It’s not that we don’t want them to win. It’s that losing “well” is just as important as winning “well.” My kids hate to lose. Honestly, there are times when they’ve cried after losing a game. These moments of emotional distress turn into teachable moments to talk to them about how you can’t and won’t always come out on top, and that’s OK. Losing sucks, there’s no way around it. However, losing can show us how we can improve and how to maturely let someone else have the limelight. I love teaching my kids strategy about the game as we are playing it. When they get beat because of it, they see firsthand how to get better. If I let them win, I would deprive them of all these things. I also want our kids to know that they don’t always have to win to make us proud and they don’t have to win to get our love. They have that no matter what.
We are proud of them when they are in the front holding the 1st place ribbon, and we are proud of them when they play the best they can and still lose. In fact, I will hate when they are old enough to be on a team where everyone gets a trophy. Not only is it something else to clutter our house with, but it also hinders the drive to get better.
I hope all three of my kids find where their talents are and beat the snot out of the competition. I will be there to cheer them on when they win. I will also be there to hold them when they lose. I hope they will do each with grace and maturity.
Now if you’ll excuse me, I need to get back to beating my son at Star Wars Chess.
A version of this first appeared on Lunchbox Dad. | tomekkorbak/pile-curse-small | OpenWebText2 |
---
abstract: 'A conjecture of Hirose, Watanabe, and Yoshida offers a characterization of when a standard graded strongly $F$-regular ring is Gorenstein, in terms of an $F$-pure threshold. We prove this conjecture under the additional hypothesis that the anti-canonical cover of the ring is Noetherian. Moreover, under this hypothesis on the anti-canonical cover, we give a similar criterion for when a normal $F$-pure (resp. log canonical) singularity is quasi-Gorenstein, in terms of an $F$-pure (resp. log canonical) threshold.'
address:
- 'Department of Mathematics, University of Utah, 155 South 1400 East, Salt Lake City, UT 84112, USA'
- 'Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan'
- 'Dipartimento di Matematica, Università di Genova, Via Dodecaneso 35, I-16146 Genova, Italy'
author:
- 'Anurag K. Singh'
- Shunsuke Takagi
- Matteo Varbaro
title: |
A Gorenstein criterion for strongly $F$-regular and\
log terminal singularities
---
Introduction
============
Let $R$ be an $F$-pure domain of positive characteristic, and ${\mathfrak{a}}$ a nonzero proper ideal. The $F$-pure threshold $\mathrm{fpt}({\mathfrak{a}})$ was defined by Watanabe and the second author of this paper [@TW]; it may be viewed as a positive characteristic analogue of the log canonical threshold, and is an important measure of the singularities of the pair $(\Spec R, V({\mathfrak{a}}))$. For example, a local ring $(R,{\mathfrak{m}})$ is regular if and only if $\mathrm{fpt}({\mathfrak{m}})>\dim R-1$.
We say that $R$ is strongly $F$-regular if $\mathrm{fpt}({\mathfrak{a}})>0$ for each nonzero proper ideal ${\mathfrak{a}}$ of $R$. It is well-known that each strongly $F$-regular ring is Cohen-Macaulay and normal; it is then natural to ask: when is a strongly $F$-regular ring Gorenstein? Toward answering this in the graded context, Hirose, Watanabe, and Yoshida proposed the following:
[[@HWY Conjecture 1.1 (2)]]{} \[conj:HWY\] Let $R$ be a standard graded strongly $F$-regular ring, with $R_0$ an $F$-finite field of characteristic $p>0$. Let ${\mathfrak{m}}$ be the unique homogeneous maximal ideal of $R$. Then $\mathrm{fpt}({\mathfrak{m}})=-a(R)$ if and only if $R$ is Gorenstein.
We prove that the conjecture holds for many classes of (not necessarily strongly $F$-regular) $F$-pure normal standard graded rings:
Let $R$ be an $F$-pure, normal, standard graded ring, with $R_0$ an $F$-finite field of characteristic $p>0$. Let ${\mathfrak{m}}$ denote the homogeneous maximal ideal of $R$. Set $X=\Spec R$, and suppose that the anti-canonical cover $\bigoplus_{n \ge 0} {\mathcal{O}}_X(-nK_X)$ of $X$ is a Noetherian ring. Then $\mathrm{fpt}({\mathfrak{m}})=-a(R)$ if and only if $R$ is quasi-Gorenstein.
Note that a ring is Gorenstein if and only if it is Cohen-Macaulay and quasi-Gorenstein. Under the hypotheses of Theorem A, the anti-canonical cover $\bigoplus_{n \ge 0} {\mathcal{O}}_X(-nK_X)$ is known to be Noetherian in each of the following cases:
1. $R$ is ${\mathbb{Q}}$-Gorenstein,
2. $R$ is a semigroup ring,
3. $R$ is a determinantal ring,
4. $R$ is a strongly $F$-regular ring of dimension at most three,
5. $R$ is a four-dimensional strongly $F$-regular ring, of characteristic $p>5$.
We give two proofs of Theorem A: the first has the advantage that it can be adapted to obtain results in the local setting, e.g., Theorem \[thm:anti-canonical\]. The second proof, while limited to the graded context, provides a technique for computing the numerical invariants at hand; see Proposition \[prop:determinantal\] for the case of determinantal rings. We describe the two techniques, after recalling some definitions:
Recall that a ring $R$ of prime characteristic $p$ is called $F$-finite if the Frobenius map $F\colon R \to F_*R$ is a finite map. Let $R$ be a local or standard graded $F$-finite domain of characteristic $p>0$, and suppose that $R$ is $F$-pure, i.e., the $e$-th iterated Frobenius map $F^e \colon R \to F^e_*R$ with $x\mapsto F^e_*x^{p^e}$ splits as an $R$-linear map for each $e\ge 1$. Given a nonzero ideal ${\mathfrak{a}}\subsetneq R$, and an integer $e\ge 1$, set $\nu_e({\mathfrak{a}})$ to be the largest integer $r \ge 0$ such that there exists a nonzero element $c$ in ${\mathfrak{a}}^r$ for which the composite map $$R \xrightarrow{F^e} F^e_*R \xrightarrow{\times F^e_*c} F^e_*R,\quad\text{ where }\quad x \mapsto F^e_*x^{p^e} \mapsto F^e_*(cx^{p^e}),$$ splits as an $R$-module homomorphism. Then, $\mathrm{fpt}({\mathfrak{a}})$ is defined to be $\lim_{e\to\infty}\nu_e({\mathfrak{a}})/p^e$.
The first proof of Theorem A uses an invariant $c({\mathfrak{a}})$ that was originally introduced in [@ST]: Given a nonzero ideal ${\mathfrak{a}}\subsetneq R$, this invariant is defined in terms of the Grothendieck trace of the iterated Frobenius map $\mathrm{Tr}^e \colon F^e_*\omega_R \to \omega_R$, where $\omega_R$ is the canonical module of $R$. For an $F$-pure normal graded ring $(R, {\mathfrak{m}})$, one has $$\mathrm{fpt}({\mathfrak{m}}) \le c({\mathfrak{m}}) \le -a(R),$$ with equality holding when $R$ is a quasi-Gorenstein standard graded ring; see Propositions \[prop:a\_i\] and \[prop:fit=-a\]. Thus, it suffices to show that if $\mathrm{fpt}({\mathfrak{m}})=c({\mathfrak{m}})$, then $R$ is quasi-Gorenstein. Generalizing the argument of [@TW Theorem 2.7], we are indeed able to prove this when the anti-canonical cover of $R$ is Noetherian. We also use the invariant $c({\mathfrak{m}})$ in answering another question of Hirose, Watanabe, and Yoshida, [@HWY Question 6.7]; see Corollary \[cor:toric charp\].
Our second proof uses the so-called Fedder-type criterion: Writing the standard graded ring $R$ as $S/I$, for $S$ a polynomial ring and $I$ a homogeneous ideal, we characterize $\nu_e({\mathfrak{m}})$ in terms of the ideal $I^{[p^e]}:_SI$, and use this to show that $-\nu_e({\mathfrak{m}})$ equals the degree of a minimal generator of the $(1-p^e)$-th symbolic power of $\omega_R$, see Theorem \[theorem:omega\]. Using this, we give explicit computations of $\mathrm{fpt}({\mathfrak{m}})$ in many situations, e.g., for determinant rings and for ${\mathbb{Q}}$-Gorenstein rings, see Propositions \[prop:determinantal\] and \[prop:fptQGor\]. We also prove that if $(R,{\mathfrak{m}})$ is a ${\mathbb{Q}}$-Gorenstein normal domain, with index coprime to $p$, then the pair $(R,{\mathfrak{m}}^{\mathrm{fpt}({\mathfrak{m}})})$ is sharply $F$-pure; see Proposition \[prop:critical value\].
Thus far we have discussed singularities in positive characteristic; we also prove an analogous result in characteristic zero. de Fernex-Hacon [@dFH] extended the definition of log terminal and log canonical singularities to the non-${\mathbb{Q}}$-Gorenstein setting, which can be regarded as the characteristic zero counterparts of strongly $F$-regular and $F$-pure rings. Using their definition, we formulate a characteristic zero analogue of Theorem A as follows:
Let $R$ be a standard graded normal ring, with $R_0$ an algebraically closed field of characteristic zero. Set ${\mathfrak{m}}$ to be the homogeneous maximal ideal of $R$. Assume that $X:=\Spec R$ has log canonical singularities in the sense of de Fernex-Hacon; set $$\mathrm{lct}({\mathfrak{m}})=\sup\{t \ge 0 \mid (X, {\mathfrak{m}}^t) \textup{ is log canonical in the sense of de~Fernex-Hacon}\}.$$
1. Then $\mathrm{lct}({\mathfrak{m}}) \le -a(R)$.
2. Suppose, in addition, that the anti-canonical cover $\bigoplus_{n \ge 0}{\mathcal{O}}_X(-nK_X)$ is Noetherian. Then $\mathrm{lct}({\mathfrak{m}})=-a(R)$ if and only if $R$ is quasi-Gorenstein.
We remark that in the situation of Theorem B, the anti-canonical cover is Noetherian whenever $X$ has log terminal singularities in the sense of de Fernex-Hacon, or if $R$ is ${\mathbb{Q}}$-Gorenstein. Thus, Theorem B gives an affirmative answer to a conjecture of De Stefani-Núñez-Betancourt [@dSNB Conjecture 6.9].
In order to prove Theorem B, we introduce a new invariant $\mathrm{d}({\mathfrak{a}})$ for an ideal ${\mathfrak{a}}$ of a normal variety $X$ with Du Bois singularities, in terms of a variant of multiplier modules, see Definition \[def:db threshold\]. We are then able to employ the same strategy as in the first proof of Theorem A, using $\mathrm{d}({\mathfrak{a}})$ in place of $c({\mathfrak{a}})$.
Throughout this paper, all rings are assumed to be Noetherian (except possibly for anti-canonical covers), commutative, with unity. By a *standard graded ring*, we mean an ${\mathbb{N}}$-graded ring $R=\bigoplus_{n \ge 0}R_n$, with $R_0$ a field, such that $R$ is generated as an $R_0$-algebra by finitely many elements of $R_1$.
Preliminaries on $F$-singularities
==================================
In this section, we briefly review the theory of $F$-singularities. In order to state the definitions, we first introduce the following notation:
Let $R$ be a ring of prime characteristic $p>0$. We denote by $R^{\circ}$ the set of elements of $R$ that are not in any minimal prime ideal. Given an $R$-module $M$ and $e \in {\mathbb{N}}$, the $R$-module $F^e_*M$ is defined by the following two conditions: (i) $F^e_*M=M$ as an abelian group, and (ii) the $R$-module structure of $F^e_*M$ is given by $r \cdot x:=r^{p^e}x$ for $r \in R$ and $x \in F^e_*M$. We write elements of $F^e_*M$ in the form $F^e_*x$ with $x \in M$. The $e$-th iterated *Frobenius map* is the $R$-linear map $F^e \colon R \to F^e_*R$ sending $x$ to $F^e_*x^{p^e}$. We say that $R$ is *$F$-finite* if the Frobenius map is finite, that is, $F^1_*R$ is a finitely generated $R$-module. When $(R,{\mathfrak{m}})$ is local, the $e$-th iterated Frobenius map $F^e \colon R \to F^e_*R$ induces a map $F^e_{H^i_{{\mathfrak{m}}}(R)} \colon H^i_{{\mathfrak{m}}}(R) \to H^i_{{\mathfrak{m}}}(R)$ for each $i$.
We recall the definition of classical $F$-singularities:
\[def:classical F-sing\] Let $R$ be an $F$-finite reduced ring of prime characteristic $p>0$.
1. We say that $R$ is *$F$-pure* if the Frobenius map $R \to F_*R$ splits as an $R$-linear map.
2. We say that $R$ is *strongly $F$-regular* if for every $c \in R^{\circ}$, there exists a power $q=p^e$ of $p$ such that the $R$-linear map $R \to F^e_*R$ sending $1$ to $F^e_*c$ splits.
3. When $(R, {\mathfrak{m}})$ is local, we say that $R$ is *$F$-injective* if $F_{H^i_{{\mathfrak{m}}}(R)} \colon H^i_{{\mathfrak{m}}}(R) \to H^i_{{\mathfrak{m}}}(R)$ is injective for each $i$. In general, we say that $R$ is $F$-injective if the localization $R_{{\mathfrak{m}}}$ is $F$-injective for each maximal ideal ${\mathfrak{m}}$ of $R$.
4. When $(R, {\mathfrak{m}})$ is local, we say that $R$ is *$F$-rational* if $R$ is Cohen-Macaulay and if for every $c \in R^{\circ}$, there exists $e \in {\mathbb{N}}$ such that $cF^e_{H^d_{{\mathfrak{m}}}(R)} \colon H^d_{{\mathfrak{m}}}(R) \to H^d_{{\mathfrak{m}}}(R)$ sending $z$ to $cF^e_{H^d_{{\mathfrak{m}}}(R)}(z)$ is injective. In general, we say that $R$ is $F$-rational if the localization $R_{{\mathfrak{m}}}$ is $F$-rational for each maximal ideal ${\mathfrak{m}}$ of $R$.
Next we generalize these to the pair setting, see [@HW; @Sch; @TW]:
Let ${\mathfrak{a}}$ be an ideal of an $F$-finite reduced ring $R$ of prime characteristic $p$ such that ${\mathfrak{a}}\cap R^{\circ} \ne \emptyset$.
1. Suppose that $R$ is local. For a real number $t \ge 0$, the pair $(R, {\mathfrak{a}}^t)$ is *sharply $F$-pure* if there exist $q=p^e$ and $c \in {\mathfrak{a}}^{\lceil t(q-1) \rceil}$ such that the $R$-linear map $R \to F^e_*R$ sending $1$ to $F^e_*c$ splits. The pair $(R, {\mathfrak{a}}^t)$ is *weakly $F$-pure* if there exist infinitely many $e \in {\mathbb{N}}$ and associated elements $c_e \in {\mathfrak{a}}^{\lfloor t(p^e-1) \rfloor}$ such that each $R$-linear map $R \to F^e_*R$ sending $1$ to $F^e_* c_e$ splits.
When $R$ is not local, $(R, {\mathfrak{a}}^t)$ is said to be sharply $F$-pure (resp. weakly $F$-pure) if the localization $(R_{{\mathfrak{m}}}, {\mathfrak{a}}_{\mathfrak{m}}^t)$ at ${\mathfrak{m}}$ is sharply $F$-pure (resp. weakly $F$-pure) for every maximal ideal ${\mathfrak{m}}$ of $R$.
2. Suppose that $R$ is $F$-pure. Then the *$F$-pure threshold* $\mathrm{fpt}({\mathfrak{a}})$ of ${\mathfrak{a}}$ is defined as $$\mathrm{fpt}({\mathfrak{a}})=\sup\{t \in {\mathbb{R}}_{\ge 0} \mid (R, {\mathfrak{a}}^t) \textup{ is weakly $F$-pure}\}.$$
3. Suppose that $R$ is a normal local domain and $\Delta$ is an effective ${\mathbb{Q}}$-divisor on $X:=\Spec R$. For a real number $t \ge 0$, the pair $((R, \Delta); {\mathfrak{a}}^t)$ is *sharply $F$-pure* if there exists $q=p^e$ and $c \in {\mathfrak{a}}^{\lceil t(q-1) \rceil}$ such that the $R$-linear map $$R \to F^e_*{\mathcal{O}}_X(\lceil (q-1) \Delta \rceil)\quad\text{ with }1 \mapsto F^e_*c$$ splits. The pair $((R, \Delta);{\mathfrak{a}}^t)$ is *weakly $F$-pure* if there exist infinitely many $e \in {\mathbb{N}}$ and associated elements $c_e \in {\mathfrak{a}}^{\lfloor t(p^e-1) \rfloor}$ such that each $R$-linear map $$R \to F^e_*{\mathcal{O}}_X(\lfloor (p^e-1) \Delta \rfloor)\quad\text{ with } 1 \mapsto F^e_* c_e$$ splits. If, in addition, ${\mathfrak{a}}={\mathcal{O}}_X$, then we simply say that $(X,\Delta)$ is *$F$-pure*.
If $(R, \Delta)$ is $F$-pure, then the *$F$-pure threshold* $\mathrm{fpt}(\Delta; {\mathfrak{a}})$ of ${\mathfrak{a}}$ with respect to the pair $(R, \Delta)$ is defined by $$\mathrm{fpt}(\Delta; {\mathfrak{a}})=\sup\{t \in {\mathbb{R}}_{\ge 0} \mid ((R, \Delta); {\mathfrak{a}}^t) \textup{ is weakly $F$-pure}\}.$$
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1. Sharp $F$-purity implies weak $F$-purity. When ${\mathfrak{a}}=R$, the sharp $F$-purity and the weak $F$-purity of $(R, {\mathfrak{a}}^t)$ are equivalent to the $F$-purity of $R$. Suppose that $R$ is $F$-pure. It is easy to check that if $(R, {\mathfrak{a}}^t)$ is weakly $F$-pure with $t>0$, then $(R, {\mathfrak{a}}^{t-\epsilon})$ is sharply $F$-pure for every $t \ge \epsilon>0$ (cf. [@Sch Lemma 5.2]). Thus, $$\mathrm{fpt}({\mathfrak{a}})=\sup\{t \in {\mathbb{R}}_{\ge 0} \mid (R, {\mathfrak{a}}^t) \textup{ is sharply $F$-pure}\}.$$
2. Our definition of the $F$-purity of $(R, \Delta)$ coincides with the one in [@HW Definition 2.1].
The following is a standard application of Matlis duality, which we will use in Section \[sec:char p I\].
\[lem:sharp F-purity\] Let $(R, {\mathfrak{m}})$ be a $d$-dimensional $F$-finite normal local ring of characteristic $p>0$, $\Delta$ be an effective ${\mathbb{Q}}$-divisor on $X=\Spec R$ and ${\mathfrak{a}}$ be a nonzero ideal of $R$. For any real number $t \ge 0$, the pair $((R, \Delta); {\mathfrak{a}}^t)$ is weakly $F$-pure if and only if there exist infinitely many $e \in {\mathbb{N}}$ and associated elements $c_e \in {\mathfrak{a}}^{\lfloor t(p^e-1) \rfloor}$ such that $$c_eF^e_{X, \Delta} \colon H^d_{{\mathfrak{m}}}(\omega_X) \xrightarrow{F^e_{X, \Delta}} H^d_{{\mathfrak{m}}}({\mathcal{O}}_X(\lfloor p^eK_X+(p^e-1)\Delta \rfloor)) \xrightarrow{\times c_e} H^d_{{\mathfrak{m}}}({\mathcal{O}}_X(\lfloor p^eK_X+(p^e-1)\Delta \rfloor))$$ is injective, where $F^e_{X, \Delta}$ is the map induced by the $R$-linear map $R \to F^e_*{\mathcal{O}}_X(\lfloor (p^e-1) \Delta \rfloor)$ sending $1$ to $F^e_*1$.
The following is a reformulation of the so-called “Fedder-type criterion," that we will use in Section \[sec:char p II\].
\[prop:Fedder criteria\] Let $S=k[x_1, \dots, x_n]$ be a polynomial ring over an $F$-finite field $k$ of characteristic $p>0$ and $I$ be a homogeneous ideal of $S$. Suppose that $R:=S/I$ is $F$-pure. Given an $e \in {\mathbb{N}}$ and a homogeneous ideal ${\mathfrak{a}}\subset S$ containing $I$ such that ${\mathfrak{a}}R \cap R^{\circ} \ne \emptyset$, we define the integer $\nu_e({\mathfrak{a}})$ by $$\nu_e({\mathfrak{a}}):=\max \{r \ge 0 \mid {\mathfrak{a}}^r(I^{[p^e]}:I) \not\subset (x_1^{p^e}, \dots, x_n^{p^e})\}.$$
1. For a real number $t\ge 0$, the pair $(R, ({\mathfrak{a}}R)^t)$ is sharply (resp. weakly) $F$-pure if and only if $\nu_e({\mathfrak{a}})\ge \lceil (p^e-1)t \rceil$ for some $e$ (resp. $\nu_e({\mathfrak{a}})\ge \lfloor (p^e-1)t \rfloor$ for infinitely many $e$).
2. $\mathrm{fpt}({\mathfrak{a}}R)=\lim_{e \to \infty}\nu_e({\mathfrak{a}})/p^e$.
It follows from [@Ta Lemma 3.9] (where the criterion for $F$-purity is stated in the local setting, but the same argument works in the graded setting).
In order to generalize the definition of $F$-rational and $F$-injective rings to the pair setting, we use the notion of ${\mathfrak{a}}^t$-tight closure and ${\mathfrak{a}}^t$-sharp Frobenius closure.
Let ${\mathfrak{a}}$ be an ideal of a reduced ring $R$ of prime characteristic $p>0$ such that ${\mathfrak{a}}\cap R^{\circ} \ne \emptyset$, and $t\ge 0$ be a real number.
1. ([@HY Definition 6.1]) For an ideal $I \subseteq R$, the ${\mathfrak{a}}^t$-*tight closure* $I^{*{\mathfrak{a}}^t}$ of $I$ is defined to be the ideal of $R$ consisting of all elements $x \in R$ for which there exists $c \in R^{\circ}$ such that $c {\mathfrak{a}}^{\lceil t(q-1) \rceil}x^q \subseteq I^{[q]}$ for all large $q=p^e$.
2. ([@Sch Definition 3.10]) For an ideal $I \subset R$, the ${\mathfrak{a}}^t$-*sharp Frobenius closure* $I^{F \sharp {\mathfrak{a}}^t}$ of $I$ is defined to be the ideal of $R$ consisting of all elements $x \in R$ such that ${\mathfrak{a}}^{\lceil t(q-1) \rceil}x^q \subseteq I^{[q]}$ for all large $q=p^e$.
3. Suppose that $(R, {\mathfrak{m}})$ is local. The ${\mathfrak{a}}^t$-*sharp Frobenius closure* $0^{F \sharp {\mathfrak{a}}^t}_{H^i_{{\mathfrak{m}}}(R)}$ of the zero submodule in $H^i_{{\mathfrak{m}}}(R)$ is defined to be the submodule of $H^i_{{\mathfrak{m}}}(R)$ consisting of all elements $z \in H^i_{{\mathfrak{m}}}(R)$ such that ${\mathfrak{a}}^{\lceil t(q-1) \rceil}F^e_{H^i_{{\mathfrak{m}}}(R)}(z)=0$ in $H^i_{{\mathfrak{m}}}(R)$ for all large $q=p^e$.
The following technical remark is useful for the study of the invariant $c({\mathfrak{a}})$, which will be introduced in Section \[sec:char p I\].
\[remark:hara-takagi\] Let $(R, {\mathfrak{m}})$ be an $F$-finite reduced local ring of characteristic $p>0$. Let $\mathrm{Tr}^e \colon F^e_*\omega_R \to \omega_R$ be the $e$-th iteration of the *trace map* on $R$, that is, the $\omega_R$-dual of the $e$-th iterated Frobenius map $F^e \colon R \to F^e_*R$. It then follows from an argument similar to the proof of [@HT Lemma 2.1] that $0^{F \sharp {\mathfrak{a}}^t}_{H^d_{{\mathfrak{m}}}(R)}=0$ if and only if $$\sum_{e \ge e_0}\mathrm{Tr}^e(F^e_*({\mathfrak{a}}^{\lceil t(p^e-1) \rceil}\omega_R))=\omega_R$$ for every integer $e_0 \ge 0$.
Let $R$ be an $F$-finite Cohen-Macaulay reduced ring of prime characteristic $p>0$, ${\mathfrak{a}}$ be an ideal of $R$ such that ${\mathfrak{a}}\cap R^{\circ} \ne \emptyset$, and $t \ge 0$ be a real number.
1. ([@ST Definition 6.1]) When $R$ is local, $(R, {\mathfrak{a}}^t)$ is said to be *$F$-rational* if $J^{*{\mathfrak{a}}^t}=J$ for every ideal $J$ generated by a full system of parameters for $R$.
2. When $R$ is local, $(R, {\mathfrak{a}}^t)$ is said to be *sharply $F$-injective* if $J^{F\sharp {\mathfrak{a}}^t}=J$ for every ideal $J$ generated by a full system of parameters for $R$.
When $R$ is not local, the pair $(R, {\mathfrak{a}}^t)$ is said to be $F$-rational (resp. sharply $F$-injective) if the localization $(R_{{\mathfrak{m}}}, {\mathfrak{a}}_{{\mathfrak{m}}}^t)$ at ${\mathfrak{m}}$ is $F$-rational (resp. sharply $F$-injective) for every maximal ideal ${\mathfrak{m}}$ of $R$. When ${\mathfrak{a}}=R$, this definition coincides with the one in Definition \[def:classical F-sing\].
We review basic properties of sharply $F$-injective pairs and $F$-rational pairs.
\[lemma:basic pair\] Let $R$ be an $F$-finite reduced ring of prime characteristic $p>0$, ${\mathfrak{a}}$ be an ideal of $R$ such that ${\mathfrak{a}}\cap R^{\circ} \ne \emptyset$, and $t \ge 0$ be a real number. Set $d:=\dim R$.
1. Suppose that $(R, {\mathfrak{m}})$ is Cohen-Macaulay. Then the following are equivalent:
1. $(R, {\mathfrak{a}}^t)$ is sharply $F$-injective (resp. $F$-rational).
2. $J^{F\sharp {\mathfrak{a}}^t}=J$ (resp. $J^{*{\mathfrak{a}}^t}=J$) for an ideal $J$ generated by a full system of parameters.
3. $0^{F \sharp {\mathfrak{a}}^t}_{H^d_{{\mathfrak{m}}}(R)}=0$ (resp. $0^{*{\mathfrak{a}}^t}_{H^d_{{\mathfrak{m}}}(R)}=0$).
2. Suppose that $R$ is $F$-rational.
1. There exists a rational number $t_0>0$ such that $(R, {\mathfrak{a}}^{t_0})$ is sharply $F$-injective.
2. If $(R, {\mathfrak{a}}^t)$ is sharply $F$-injective with $t>0$, then $(R, {\mathfrak{a}}^{t-\epsilon})$ is $F$-rational for every $t \ge \epsilon>0$.
3. Suppose that $(R, {\mathfrak{m}})$ is local. If $(R, {\mathfrak{a}}^t)$ is sharply $F$-pure, then $0^{F \sharp {\mathfrak{a}}^t}_{H^i_{{\mathfrak{m}}}(R)}=0$ for every $i$. When $R$ is quasi-Gorenstein, $(R, {\mathfrak{a}}^t)$ is sharply $F$-pure if and only if $0^{F \sharp {\mathfrak{a}}^t}_{H^d_{{\mathfrak{m}}}(R)}=0$.
4. Let $(R, {\mathfrak{m}}) \into (S, {\mathfrak{n}})$ be a flat local homomorphism of $F$-finite reduced local rings of characteristic $p>0$. Suppose that $S/{\mathfrak{m}}S$ is a field which is a separable algebraic extension of $R/{\mathfrak{m}}$. Then $0^{F \sharp {\mathfrak{a}}^t}_{H^d_{{\mathfrak{m}}}(R)}=0$ if and only if $0^{F \sharp ({\mathfrak{a}}S)^t}_{H^d_{{\mathfrak{n}}}(S)}=0$.
We may assume throughout that $(R, {\mathfrak{m}})$ is local. Let $J$ be an ideal generated by a full system of parameters for $R$.
\(1) The $F$-rational case follows from [@ST Lemma 6.3] and the sharp $F$-injective case follows from an analogous argument.
\(2) First we will show (a). Fix a nonzero element $f \in {\mathfrak{a}}$. Since $R$ is $F$-rational, there exists $e_0 \in {\mathbb{N}}$ such that $fF^{e_0}_{H^d_{{\mathfrak{m}}}(R)} \colon H^d_{{\mathfrak{m}}}(R) \to H^d_{{\mathfrak{m}}}(R)$ is injective. Then for each $n \in {\mathbb{N}}$, the map $$f^{1+p^{e_0}+\cdots+p^{(n-1)e_0}}F^{ne_0}_{H^d_{{\mathfrak{m}}}(R)} \colon H^d_{{\mathfrak{m}}}(R) \to H^d_{{\mathfrak{m}}}(R)$$ is also injective. Set $t_0=1/(p^{e_0}-1)$ and let $z \in 0^{F \sharp {\mathfrak{a}}^{t_0}}_{H^d_{{\mathfrak{m}}}(R)}$. Since $$f^{1+p^{e_0}+\cdots+p^{(n-1)e_0}}F^{ne_0}_{H^d_{{\mathfrak{m}}}(R)}(z) \in {\mathfrak{a}}^{t_0(p^{ne_0}-1)}F^{ne_0}_{H^d_{{\mathfrak{m}}}(R)}(z)=0$$ for sufficiently large $n$, one has $z=0$ by the injectivity of $f^{1+p^{e_0}+\cdots+p^{(n-1)e_0}}F^{ne_0}_{H^d_{{\mathfrak{m}}}(R)}$. It follows that $0^{F \sharp {\mathfrak{a}}^{t_0}}_{H^d_{{\mathfrak{m}}}(R)}=0$.
Next we will show (b). Let $x \in J^{* {\mathfrak{a}}^{t-\epsilon}}$. Since $1$ is a parameter ${\mathfrak{a}}^{t-\epsilon}$-test element by [@ST Lemma 6.8] (see [@ST Definition 6.6] for the definition of parameter ${\mathfrak{a}}^{t-\epsilon}$-test elements), ${\mathfrak{a}}^{\lceil t(q-1) \rceil}x^q \subseteq {\mathfrak{a}}^{\lceil (t-\epsilon)q \rceil}x^q \subseteq J^{[q]}$ for all sufficiently large $q=p^e$. Then the sharp $F$-injectivity of $(R, {\mathfrak{a}}^t)$ implies that $x \in J$, that is, $J^{* {\mathfrak{a}}^{t-\epsilon}}=J$.
\(3) Let $z \in 0^{F \sharp {\mathfrak{a}}^t}_{H^i_{{\mathfrak{m}}}(R)}$. Since $(R, {\mathfrak{a}}^t)$ is sharply $F$-pure, there exist a sufficiently large $q=p^e$ and $c \in {\mathfrak{a}}^{\lceil t(p^e-1) \rceil}$ such that the $R$-linear map $R \to F^e_*R$ sending $1$ to $F^e_*c$ splits, and in particular, $cF^e_{H^i_{{\mathfrak{m}}}(R)} \colon H^i_{{\mathfrak{m}}}(R) \to H^i_{{\mathfrak{m}}}(R)$ is injective. Then $z$ has to be zero, because $cF^e_{H^i_{{\mathfrak{m}}}(R)}(z) \in {\mathfrak{a}}^{\lceil t(p^e-1) \rceil} F^e_{H^i_{{\mathfrak{m}}}(R)}(z)=0$. That is, $0^{F \sharp {\mathfrak{a}}^t}_{H^i_{{\mathfrak{m}}}(R)}=0$.
For the latter assertion, suppose that $R$ is quasi-Gorenstein. Then by [@Sch Theorem 4.1], $(R, {\mathfrak{a}}^t)$ is sharply $F$-pure if and only if for infinitely many $q=p^e$, there exists $c \in {\mathfrak{a}}^{\lceil t(q-1) \rceil}$ such that $cF^e_{H^d_{{\mathfrak{m}}}(R)} \colon H^d_{{\mathfrak{m}}}(R) \to H^d_{{\mathfrak{m}}}(R)$ is injective. Looking at the socle of $H^d_{{\mathfrak{m}}}(R)$, we see that this condition is equivalent to saying that $0^{F \sharp {\mathfrak{a}}^{t}}_{H^d_{{\mathfrak{m}}}(R)}=0$.
\(4) Since $H^{d}_{{\mathfrak{n}}}(S)$ does not change by passing to the completion of $S$, we may assume that $S$ is complete. Let $\mathrm{Tr}_R^e \colon F^e_*\omega_R \to \omega_R$ (resp. $\mathrm{Tr}_S^e \colon F^e_*\omega_S \to \omega_S$) denote the $e$-th iteration of the trace map on $R$ (resp. $S$). It then follows from the proof of [@SrT Lemma 1.5 (2)] that $\mathrm{Tr}_R^e \otimes_R S \colon F^e_*\omega_R \otimes_R S \to \omega_R \otimes_R S$ is isomorphic to $\mathrm{Tr}_S^e$ for each $e \in {\mathbb{N}}$. By Remark \[remark:hara-takagi\], $0^{F \sharp {\mathfrak{a}}^t}_{H^d_{{\mathfrak{m}}}(R)}=0$ if and only if $$\bigoplus_{e \ge e_0}\mathrm{Tr}_R^e \colon \bigoplus_{e \ge e_0} F^e_*({\mathfrak{a}}^{\lceil t (p^e-1) \rceil}\omega_R) \to \omega_R$$ is surjective for every integer $e_0 \ge 0$. Tensoring with $S$, we see that this condition is equivalent to the surjectivity of $$\bigoplus_{e \ge 0} \mathrm{Tr}_S^e \colon \bigoplus_{e \ge e_0} F^e_*({\mathfrak{a}}^{\lceil t(p^e-1) \rceil}\omega_S) \to \omega_S$$ for every $e_0 \ge 0$, which holds by Remark \[remark:hara-takagi\] again if and only if $0^{F \sharp ({\mathfrak{a}}S)^t}_{H^d_{{\mathfrak{n}}}(S)}=0$.
Positive characteristic case I {#sec:char p I}
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We introduce a new invariant of singularities in positive characteristic, and study its basic properties. Using this, we give a partial answer to Conjecture \[conj:HWY\].
\[def:thresholds\] Let $(R, {\mathfrak{m}})$ be a $d$-dimensional $F$-finite $F$-injective local ring of characteristic $p>0$, ${\mathfrak{a}}$ be an ideal of $R$ such that ${\mathfrak{a}}\cap R^{\circ} \ne \emptyset$. For each integer $i$, the threshold $c_i({\mathfrak{a}})$ is defined by $$c_i({\mathfrak{a}})=\sup\{t \in {\mathbb{R}}_{\ge 0} \bigm| 0^{F\sharp {\mathfrak{a}}^t}_{H^i_{{\mathfrak{m}}}(R)}=0\}.$$ Note that $c_i({\mathfrak{a}})=\infty$ when $H^i_{{\mathfrak{m}}}(R)=0$. Also, we simply denote $c_d({\mathfrak{a}})$ by $c({\mathfrak{a}})$.
\[rem:graded case\] Let $R$ be an ${\mathbb{N}}$-graded ring with $R_0$ an $F$-finite field of characteristic $p>0$, and ${\mathfrak{m}}$ the homogeneous maximal ideal of $R$. Then we can define $c_i({\mathfrak{m}})$ similarly, that is, $$c_i({\mathfrak{m}})=\sup\{t \in {\mathbb{R}}_{\ge 0} \bigm| 0^{F\sharp {\mathfrak{m}}^t}_{H^i_{{\mathfrak{m}}}(R)}=0\}.$$ Since $H^i_{{\mathfrak{m}}}(R) \cong H^i_{{\mathfrak{m}}R_{{\mathfrak{m}}}}(R_{{\mathfrak{m}}})$, we have the equality $c_i({\mathfrak{m}})=c_i({\mathfrak{m}}R_{{\mathfrak{m}}})$.
\[lem:basic\] Let the notation be the same as in Definition \[def:thresholds\].
1. If $R$ is Cohen-Macaulay, then $$c({\mathfrak{a}})=\sup\{t \in {\mathbb{R}}_{\ge 0} \mid \textup{$(R, {\mathfrak{a}}^t)$ is sharply $F$-injective}\}.$$
2. If $R$ is $F$-rational, then $$c({\mathfrak{a}})=\sup\{t \in {\mathbb{R}}_{\ge 0} \mid \textup{$(R, {\mathfrak{a}}^t)$ is $F$-rational}\}.$$
3. Suppose that $R$ is $F$-pure. Then $c_i({\mathfrak{a}}) \ge \mathrm{fpt}({\mathfrak{a}})$ for each $i$. In addition, if $R$ is quasi-Gorenstein, then $c({\mathfrak{a}})=\mathrm{fpt}({\mathfrak{a}})$.
4. $c({\mathfrak{a}})$ is less than or equal to the height $\mathrm{ht}\; {\mathfrak{a}}$ of ${\mathfrak{a}}$.
5. Suppose that $R$ is Cohen-Macaulay and the residue field $R/{\mathfrak{m}}$ is infinite. If $J \subset R$ is a minimal reduction of ${\mathfrak{m}}$, then ${\mathfrak{m}}^{d+1-\lceil c({\mathfrak{m}}) \rceil} \subseteq J$.
6. Suppose that $R$ is Cohen-Macaulay. If $c({\mathfrak{m}})>d-1$, then $R$ is regular and in particular $c({\mathfrak{m}})=d$.
\(1) (resp. (2), (3)) follows from Lemma \[lemma:basic pair\] (1) (resp. (2), (3)).
\(4) Since the trace map commutes with localization, by Remark \[remark:hara-takagi\], $c({\mathfrak{a}}) \le c({\mathfrak{a}}R_{{\mathfrak{p}}})$ for every prime ideal ${\mathfrak{p}}$ containing ${\mathfrak{a}}$. Localizing at a minimal prime of ${\mathfrak{a}}$, we may assume that $\mathrm{ht}\; {\mathfrak{a}}=d$. We can also assume by Lemma \[lemma:basic pair\] (4) that the residue field $R/{\mathfrak{m}}$ is infinite. Let $J$ be a minimal reduction of ${\mathfrak{a}}$, and we will show that $0^{F\sharp {\mathfrak{a}}^t}_{H^d_{{\mathfrak{m}}}(R)} \supseteq (0:J)_{H^d_{{\mathfrak{m}}}(R)} \ne 0$ for every $t>d$. Let $z \in (0:J)_{H^d_{{\mathfrak{m}}}(R)}$. Note that if $t>d$, then $J^{[q]} \supseteq {\mathfrak{a}}^{\lceil t(q-1) \rceil}$ for all large $q=p^e$ (because ${\mathfrak{a}}^{\lceil t(q-1) \rceil}=J^{\lceil t'_q(q-1) \rceil}{\mathfrak{a}}^n$ for some fixed $n\in\mathbb{N}$, where $t'_q=t-n/(q-1)$). Then $${\mathfrak{a}}^{\lceil t(q-1) \rceil} F^e_{H^d_{{\mathfrak{m}}}(R)}(z) \subseteq J^{[q]}F^e_{H^d_{{\mathfrak{m}}}(R)}(z)=F^e_{H^d_{{\mathfrak{m}}}(R)}(Jz)=0$$ for such $q=p^e$, which implies that $z \in 0^{F\sharp {\mathfrak{a}}^t}_{H^d_{{\mathfrak{m}}}(R)}$.
\(5) It follows from Remark \[remark:hara-takagi\] that $\sum_{e \ge e_0}\mathrm{Tr}^e(F^e_*({\mathfrak{m}}^{\lceil (c({\mathfrak{m}})-\epsilon)(p^e-1) \rceil}\omega_R))=\omega_R$ for all $e_0 \in {\mathbb{Z}}_{\ge 0}$ and for all $c({\mathfrak{m}}) \ge \epsilon >0$ (when $c({\mathfrak{m}})=0$, we put $\epsilon=0$). Multiplying by ${\mathfrak{m}}^{d+1-\lceil c({\mathfrak{m}}) \rceil}$ on both sides, one has $$\begin{aligned}
{\mathfrak{m}}^{d+1-\lceil c({\mathfrak{m}}) \rceil}\omega_R & ={\mathfrak{m}}^{d+1-\lceil c({\mathfrak{m}}) \rceil} \sum_{e \ge e_0}\mathrm{Tr}^e\left(F^e_*({\mathfrak{m}}^{\lceil (c({\mathfrak{m}})-\epsilon)(p^e-1) \rceil}\omega_R)\right)\\
& \subseteq \sum_{e \ge e_0}\mathrm{Tr}^e\left(F^e_*({\mathfrak{m}}^{\lceil (c({\mathfrak{m}})-\epsilon)(p^e-1) \rceil+(d+1-\lceil c({\mathfrak{m}}) \rceil)p^e}\omega_R)\right)\\
& \subseteq \sum_{e \ge e_0}\mathrm{Tr}^e\left(F^e_*({\mathfrak{m}}^{d p^e}\omega_R)\right)\\
& \subseteq \sum_{e \ge e_0}\mathrm{Tr}^e\left(F^e_*(J^{[p^e]}\omega_R)\right)\\
& \subseteq J \omega_R\end{aligned}$$ for sufficiently large $e_0$ and for sufficiently small $\epsilon>0$. Since $R/J$ is the Matlis dual of $\omega_R/J \omega_R$, this means that ${\mathfrak{m}}^{d+1-\lceil c({\mathfrak{m}}) \rceil} \subseteq J$.
\(6) Let $J$ be a minimal reduction of ${\mathfrak{m}}$; we may assume by Lemma \[lemma:basic pair\] (4) that the residue field $R/{\mathfrak{m}}$ is infinite. It then follows from (5) that ${\mathfrak{m}}=J$, which means that ${\mathfrak{m}}$ is generated by at most $d$ elements, that is, $R$ is regular. If $R$ is regular, then $c({\mathfrak{m}})=\mathrm{fpt}({\mathfrak{m}})=d$ by (3) and [@TW Theorem 2.7 (1)].
Let $S$ be the $n$-dimensional polynomial ring $k[x_1, \dots, x_n]$ over an $F$-finite field $k$. Let $R=S^{(r)}$ be the $r$-th Veronese subring of $S$ and ${\mathfrak{m}}_R$ be the homogeneous maximal ideal of $R$. Then $\mathrm{fpt}({\mathfrak{m}}_R)=n/r$ and $c({\mathfrak{m}}_R)=\lceil n/r \rceil$.
When $R$ is an ${\mathbb{N}}$-graded ring, the $i$-th $a$-invariant $a_i(R)$ is defined by $$a_i(R)=\max\{n \in {\mathbb{Z}}\mid [H^i_{{\mathfrak{m}}}(R)]_n \ne 0\}$$ for each $i$. The following proposition can be viewed as an extension of [@dSNB Theorem 4.3].
\[prop:a\_i\] Let $R$ be an $F$-injective ${\mathbb{N}}$-graded ring, with $R_0$ an $F$-finite field of characteristic $p>0$. Let ${\mathfrak{m}}$ be the homogeneous maximal ideal of $R$. Then $c_i({\mathfrak{m}}) \le -a_i(R)$ for each $i$. In particular, if $R$ is $F$-pure, then by Lemma \[lem:basic\] (3), one has the inequality $\mathrm{fpt}({\mathfrak{m}}) \le -a_i(R)$ for every integer $i$.
We may assume that $H^i_{{\mathfrak{m}}}(R) \ne 0$. We will then show that $c_i({\mathfrak{m}}) \le -a_i(R)+\epsilon$, that is, $0^{F\sharp {\mathfrak{m}}^{-a_i(R)+\epsilon}}_{H^i_{{\mathfrak{m}}}(R)} \ne 0$, for every $\epsilon>0$. Note that $a_i(R) \le 0$, because $R$ is $F$-injective. Let $z \in [H^i_{{\mathfrak{m}}}(R)]_{a_i(R)}$ be a nonzero element. Since $\lceil (-a_i(R)+\epsilon)(q-1) \rceil +a_i(R)q >0$ for all sufficiently large $q=p^e$, one has $${\mathfrak{m}}^{\lceil (-a_i(R)+\epsilon)(q-1) \rceil}F^e_{H^i_{{\mathfrak{m}}}(R)}(z) \subseteq [H^i_{{\mathfrak{m}}}(R)]_{>0}=0$$ for such $q$, which means that $z \in 0^{F\sharp {\mathfrak{m}}^{-a_i(R)+\epsilon}}_{H^i_{{\mathfrak{m}}}(R)}$.
We record two cases in which the above result can be strengthened to an equality:
\[prop:fit=-a\] Let $R$ be an $F$-injective standard graded ring with $R_0$ an $F$-finite field of characteristic $p>0$. Let ${\mathfrak{m}}$ denote the homogeneous maximal ideal of $R$. Suppose that one of the following conditions is satisfied:
1. $R$ is Cohen-Macaulay,
2. $R$ is normal and quasi-Gorenstein.
Then $c({\mathfrak{m}})=-a(R)$.
Let $d$ be the dimension of $R$. First, we assume that the condition (1) holds and we will prove that $c({\mathfrak{m}}) \ge -a(R)-\epsilon$ for every $\epsilon>0$. We may assume by Lemma \[lemma:basic pair\] (4) that $R_0$ is an infinite field. Let $J$ be a minimal reduction of ${\mathfrak{m}}$. As $R$ is a Cohen-Macaulay standard graded ring, $J$ is generated by a homogeneous regular sequence of degree one. Then ${\mathfrak{m}}^{d+a(R)+1}$ is contained in $J$ but ${\mathfrak{m}}^{d+a(R)}$ is not.
It is enough to show that $J^{F\sharp {\mathfrak{m}}^{-a(R)-\epsilon}}=J$ by Lemma \[lemma:basic pair\] (1) and Lemma \[lem:basic\] (1). Let $x \in J^{F\sharp {\mathfrak{m}}^{-a(R)-\epsilon}}$, and we may assume that the degree of $x$ is less than or equal to $d+a(R)$. By definition, ${\mathfrak{m}}^{\lceil (-a(R)-\epsilon)(q-1) \rceil}x^q \subseteq J^{[q]}$ for all sufficiently large $q=p^e$. Thus, $$x^q \in (J^{[q]}:J^{\lceil (-a(R)-\epsilon)(q-1) \rceil}) \subseteq J^{[q]}+J^{dq-\lceil (-a(R)-\epsilon)(q-1) \rceil -d+1}.$$ The degree of $x^q$ is less than or equal to $(d+a(R))q$, but $dq-\lceil (-a(R)-\epsilon)(q-1) \rceil -d+1$ is greater than $(d+a(R))q$ for sufficiently large $q$, so $x^q$ has to lie in $J^{[q]}$ for such $q$. It then follows from the $F$-injectivity of $R$ that $x \in J$, that is, $J^{F\sharp {\mathfrak{m}}^{-a(R)-\epsilon}}=J$.
Next, we assume that the condition (2) holds and we will show that $c({\mathfrak{m}}) \ge -a(R)$. It is enough to show by Lemma \[lem:basic\] (3) that $\mathrm{fpt}({\mathfrak{m}}) \ge -a(R)$. Let $X=\Proj R$. Since $R$ is a quasi-Gorenstein normal standard graded ring, there exists a very ample divisor $H$ on $X$ such that $R=\bigoplus_{n \ge 0}H^0(X, {\mathcal{O}}_X(nH))$ and $K_X \sim a(R)H$. Note that $X$ is globally $F$-split and $a(R) \le 0$, because $R$ is $F$-pure. It then follows from an argument similar to the proof of [@SS Theorem 4.3] that there exists an effective Cartier divisor $D$ on $X$ such that $D \sim (1-p)a(R)H$ and that the composite map $${\mathcal{O}}_X \to F_*{\mathcal{O}}_X \to F_*{\mathcal{O}}_X(D) \quad x \mapsto F_*x^p \mapsto F_*(sx^p)$$ splits as an ${\mathcal{O}}_X$-module homomorphism, where $s$ is a defining section for $D$. This map induces the $R$-linear map $R \to F_*R$ with $1\mapsto F_*s$, which also splits. Since $s$ belongs to ${\mathfrak{m}}^{(1-p)a(R)}$ by the definition of $D$, the pair $(R, {\mathfrak{m}}^{-a(R)})$ is sharply $F$-pure. Thus, $\mathrm{fpt}({\mathfrak{m}}) \ge -a(R)$.
Motivated by Conjecture \[conj:HWY\], we propose the following conjecture.
\[conj:fpt=fit\] Let $(R, {\mathfrak{m}})$ be an $F$-finite $F$-pure normal local ring of characteristic $p>0$. Then $R$ is quasi-Gorenstein if and only if $\mathrm{fpt}({\mathfrak{m}})=c({\mathfrak{m}})$.
Conjecture \[conj:fpt=fit\] can fail if $R$ is not normal. Indeed, [@dSNB Example 5.3] and Proposition \[prop:fit=-a\] give a counterexample.
Conjecture \[conj:fpt=fit\] implies an extension of Conjecture \[conj:HWY\].
\[prop:imply\] Let $R$ be an $F$-pure normal standard graded ring, with $R_0$ an $F$-finite field of characteristic $p>0$. Let ${\mathfrak{m}}$ denote the homogeneous maximal ideal of $R$. Suppose that Conjecture \[conj:fpt=fit\] holds for the localization $R_{{\mathfrak{m}}}$ of $R$ at ${\mathfrak{m}}$. Then $R$ is quasi-Gorenstein if and only if $\mathrm{fpt}({\mathfrak{m}})=-a(R)$.
The “only if" part immediately follows from Lemma \[lem:basic\] (3) and Proposition \[prop:fit=-a\]. We will show the “if" part. Suppose that $\mathrm{fpt}({\mathfrak{m}})=-a(R)$. Then by Remark \[rem:graded case\], Lemma \[lem:basic\] (3) and Proposition \[prop:fit=-a\], $$-a(R)=\mathrm{fpt}({\mathfrak{m}}) \le \mathrm{fpt}({\mathfrak{m}}R_{{\mathfrak{m}}}) \le c({\mathfrak{m}}R_{{\mathfrak{m}}})=c({\mathfrak{m}})=-a(R),$$ which implies that $\mathrm{fpt}({\mathfrak{m}}R_{{\mathfrak{m}}}) = c({\mathfrak{m}}R_{{\mathfrak{m}}})$. It then follows from Conjecture \[conj:fpt=fit\] that $R_{{\mathfrak{m}}}$ is quasi-Gorenstein, which is equivalent to saying that $R$ is quasi-Gorenstein.
\[thm:non-Gorenstein\] Let $(R, {\mathfrak{m}})$ be an $F$-finite normal local ring of characteristic $p>0$ and $\Delta$ be an effective ${\mathbb{Q}}$-divisor on $X:=\Spec R$ such that $(X, \Delta)$ is $F$-pure and $K_X+\Delta$ is ${\mathbb{Q}}$-Cartier of index $r$. If $R$ is not quasi-Gorenstein, then $$\mathrm{fpt}(\Delta; {\mathfrak{m}})+\frac{1}{r} \le c({\mathfrak{m}}).$$
Let $d$ be the dimension of $R$. For every $\mathrm{fpt}(\Delta; {\mathfrak{m}})>\epsilon>0$ (when $\mathrm{fpt}(\Delta; {\mathfrak{m}})=0$, put $\epsilon=0$), by the definition of $\mathrm{fpt}(\Delta; {\mathfrak{m}})$ and Lemma \[lem:sharp F-purity\], there exist $q_0=p^{e_0}$ and $c$ in ${\mathfrak{m}}^{\lfloor (\mathrm{fpt}(\Delta; {\mathfrak{m}})-\epsilon)(q_0-1) \rfloor}$ such that $$cF^{e_0}_{X, \Delta} \colon H^d_{{\mathfrak{m}}}(\omega_X) \to H^d_{{\mathfrak{m}}}({\mathcal{O}}_X(\lfloor q_0K_X+(q_0-1)\Delta \rfloor))$$ is injective. We consider the following commutative diagram: $$\xymatrix{
\omega_X \times H^d_{{\mathfrak{m}}}(R) \ar[r] \ar[d] & H^d_{{\mathfrak{m}}}(\omega_X) \ar[d]^{cF^{e_0}_{X, \Delta}} \\
{\mathcal{O}}_X(\lfloor q_0K_X+ (q_0-1)\Delta \rfloor) \times H^d_{{\mathfrak{m}}}(R) \ar[r] & H^d_{{\mathfrak{m}}}({\mathcal{O}}_X(\lfloor q_0K_X+ (q_0-1)\Delta \rfloor)),
}$$ where the left vertical map sends $(x, z)$ to $(cx^{q_0}, F^{e_0}_{H^d_{{\mathfrak{m}}}(R)}(z))$.
For each $1/r>\epsilon'>0$, we will show that $0_{H^d_{{\mathfrak{m}}}(R)}^{F\sharp {\mathfrak{m}}^{\mathrm{fpt}(\Delta; {\mathfrak{m}})+1/r-\epsilon-\epsilon'}}=0$, which implies the assertion. Let $\xi \in 0_{H^d_{{\mathfrak{m}}}(R)}^{F\sharp {\mathfrak{m}}^{\mathrm{fpt}(\Delta; {\mathfrak{m}})+1/r-\epsilon-\epsilon'}}$, that is, there exists $q_1 \in {\mathbb{N}}$ such that $${\mathfrak{m}}^{\lceil (\mathrm{fpt}(\Delta; {\mathfrak{m}})+1/r-\epsilon-\epsilon')(q-1) \rceil}F^e_{H^d_{{\mathfrak{m}}}(R)}(\xi)=0$$ for all $q=p^e \ge q_1$. By the definition of weak $F$-purity, we may assume that $q_0$ is sufficiently large so that $q_0 \ge q_1$ and $\epsilon'(q_0-1) \ge 2$. Since $R$ is not quasi-Gorenstein, $r \ge 2$ or $\Delta$ is strictly effective. In either case, the fractional ideal $\omega_X^{r}={\mathcal{O}}_X(K_X)^{r}$ is contained in the fractional ideal ${\mathfrak{m}}{\mathcal{O}}_X(r(K_X+\Delta))$. Therefore, for all $x \in \omega_X$, one has $$\begin{aligned}
cx^{q_0} & \in {\mathfrak{m}}^{\lfloor (\mathrm{fpt}(\Delta; {\mathfrak{m}})-\epsilon)(q_0-1) \rfloor} \omega_X^{q_0}\\
& \subseteq {\mathfrak{m}}^{\lfloor (\mathrm{fpt}(\Delta; {\mathfrak{m}})-\epsilon)(q_0-1) \rfloor+\lfloor (q_0-1)/r \rfloor} {\mathcal{O}}_X(\lfloor q_0K_X+(q_0-1)\Delta \rfloor)\\
& \subseteq {\mathfrak{m}}^{\lceil (\mathrm{fpt}(\Delta; {\mathfrak{m}})+1/r-\epsilon-\epsilon')(q_0-1) \rceil} {\mathcal{O}}_X(\lfloor q_0K_X+(q_0-1)\Delta \rfloor) \end{aligned}$$ by the choice of $q_0$. Since $q_0 \ge q_1$, $$\begin{aligned}
cx^{q_0} F^{e_0}_{H^d_{{\mathfrak{m}}}(R)}(\xi) &\in {\mathfrak{m}}^{\lceil (\mathrm{fpt}(\Delta; {\mathfrak{m}})+1/r-\epsilon-\epsilon')(q_0-1) \rceil} {\mathcal{O}}_X(\lfloor q_0K_X+(q_0-1)\Delta \rfloor) F^{e_0}_{H^d_{{\mathfrak{m}}}(R)}(\xi)\\
&=0 \; \, \textup{in} \; \, H^d_{{\mathfrak{m}}}({\mathcal{O}}_X(\lfloor q_0K_X+ (q_0-1)\Delta \rfloor)),\end{aligned}$$ and it then follows from the commutativity of the above diagram that $cF^{e_0}_{X, \Delta}(x\xi)=0$. The injectivity of the map $cF^{e_0}_{X, \Delta}$ implies that $x \xi=0$ for all $x \in \omega_X$. This forces $\xi$ to be zero, because $\omega_X \times H^d_{{\mathfrak{m}}}(R) \to H^d_{{\mathfrak{m}}}(\omega_X)$ is the duality pairing. Thus, $0_{H^d_{{\mathfrak{m}}}(R)}^{F\sharp {\mathfrak{m}}^{\mathrm{fpt}(\Delta; {\mathfrak{m}})+1/r-\epsilon-\epsilon'}}=0$.
We give an example of a standard graded Cohen-Macaulay ring $R$ that is $F$-pure, with $a(R)=-1$ and $\mathrm{fpt}({\mathfrak{m}})=0$; this is based on [@Song]. The ring $R$ is ${\mathbb{Q}}$-Gorenstein, with index $2$.
Let $k$ be a field of characteristic $p\equiv 1\mod 4$, and set $$S=k[w,x,y,z]/(w^4+x^4+y^4+z^4)\,.$$ By the characteristic assumption, the ring $S$ is $F$-pure. Set $R$ to be the $k$-subalgebra generated by the monomials $$w^4,\ w^3x,\ w^2x^2,\ wx^3,\ x^4,\quad y^4,\ y^3z,\ y^2z^2,\ yz^3,\ z^4.$$ Then $R$ is a direct summand of $S$ as an $R$-module: one way to see this is to use the ${\mathbb{Z}}/4\times{\mathbb{Z}}/4$-grading on $S$ under which $\deg w=(1,0)=\deg x$, and $\deg y=(0,1)=\deg z$, in which case $R$ is the subring of $S$ generated by elements of degree $(0,0)$. It follows that $R$ is $F$-pure, normal, as well as Cohen-Macaulay.
The ring $R$ has a standard grading under which each of the monomials displayed is assigned degree one. Computing the socle modulo the system of parameters $x^4$, $y^4$, $z^4$, it follows that $a(R)=-1$. By Proposition \[prop:fit=-a\], we have $c({\mathfrak{m}})=1$.
The fractional ideal $$\omega_R = \frac{1}{w^2x^2}(w^3x, w^2x^2, wx^3)(y^3z, y^2z^2, yz^3)$$ is, up to isomorphism, the graded canonical module of $R$; its second symbolic power is $$\omega_R^{(2)} = \frac{y^2z^2}{w^2x^2}R,$$ so the ring $R$ is ${\mathbb{Q}}$-Gorenstein. Using Theorem \[theorem:omega\], one checks that that $\nu_e({\mathfrak{m}})=0$ for each $e\ge 1$. It follows that $\mathrm{fpt}({\mathfrak{m}})=0$.
\[cor:Delta\] Let $(R, {\mathfrak{m}})$ be an $F$-finite $F$-pure normal local ring of characteristic $p>0$.
1. Suppose that there exists an effective ${\mathbb{Q}}$-divisor $\Delta$ on $X=\Spec R$ such that $K_X+\Delta$ is ${\mathbb{Q}}$-Cartier, $(X, \Delta)$ is $F$-pure and $\mathrm{fpt}(\Delta; {\mathfrak{m}})=\mathrm{fpt}({\mathfrak{m}})$. Then Conjecture \[conj:fpt=fit\] holds for this $R$.
2. If $c({\mathfrak{m}})=0$, then $R$ is quasi-Gorenstein.
\(1) immediately follows from Theorem \[thm:non-Gorenstein\]. We will show (2). Since $R$ is $F$-pure, then by [@SS Theorem 4.3 (ii)], there exists an effective ${\mathbb{Q}}$-divisor $\Delta$ on $X$ such that $(R, \Delta)$ is sharply $F$-pure with $K_X+\Delta$ ${\mathbb{Q}}$-Cartier. Then $$0 \le \mathrm{fpt}(\Delta;{\mathfrak{m}}) \le \mathrm{fpt}({\mathfrak{m}}) \le c({\mathfrak{m}})=0,$$ and the assertion follows from (1).
When is the assumption of Corollary \[cor:Delta\] (1) satisfied? If the pair $(R, {\mathfrak{m}}^{\mathrm{fpt}({\mathfrak{m}})})$ is sharply $F$-pure, then by a similar argument to the proof of [@SS Theorem 4.3 (ii)], there exists an effective ${\mathbb{Q}}$-divisor $\Delta$ on $X$ such that $((R, \Delta);{\mathfrak{m}}^{\mathrm{fpt}({\mathfrak{m}})})$ is sharply $F$-pure with $K_X+\Delta$ ${\mathbb{Q}}$-Cartier. Then $\mathrm{fpt}(\Delta; {\mathfrak{m}})=\mathrm{fpt}({\mathfrak{m}})$, that is, the assumption of Corollary \[cor:Delta\] (1) is satisfied.
Let $(R, {\mathfrak{m}})$ be an $F$-finite $F$-pure normal local ring of characteristic $p>0$. When is the pair $(R, {\mathfrak{m}}^{\mathrm{fpt}({\mathfrak{m}})})$ sharply or weakly $F$-pure?
We will show in Proposition \[prop:critical value\] that if $(R, {\mathfrak{m}})$ is an $F$-pure ${\mathbb{Q}}$-Gorenstein normal standard graded ring over an $F$-finite field of characteristic $p>0$ with Gorenstein index not divisible by $p$, then $(R, {\mathfrak{m}}^{\mathrm{fpt}({\mathfrak{m}})})$ is sharply $F$-pure.
We now prove the main result of this section:
\[thm:anti-canonical\] Let $(R, {\mathfrak{m}})$ be an $F$-finite $F$-pure normal local ring of characteristic $p>0$. Suppose that the anti-canonical cover $\bigoplus_{n \ge 0}{\mathcal{O}}_X(-nK_X)$ of $X:=\Spec R$ is Noetherian. Then $\mathrm{fpt}({\mathfrak{m}})=c({\mathfrak{m}})$ if and only if $R$ is quasi-Gorenstein.
Since $\bigoplus_{n \ge 0}{\mathcal{O}}_X(-nK_X)$ is Noetherian, one can find an integer $r \ge 1$ satisfying the following: for every $q=p^e$, if we write $q-1=rn_e+j_e$ with $n_e \ge 0$ and $r-1 \ge j_e \ge 0$, then $${\mathcal{O}}_X((1-q)K_X)={\mathcal{O}}_X(-rK_X)^{n_e} {\mathcal{O}}_X(-j_eK_X).$$ Suppose that $R$ is not quasi-Gorenstein, and we will show that $\mathrm{fpt}({\mathfrak{m}})+\frac{1}{r} \le c({\mathfrak{m}})$. Let $\phi_1, \dots, \phi_l$ be a system of generators for ${\mathcal{O}}_X(-rK_X)$.
For every $\mathrm{fpt}({\mathfrak{m}}) >\epsilon>0$, there exist a sufficiently large $q=p^e$ and $c \in {\mathfrak{m}}^{\lfloor (\mathrm{fpt}({\mathfrak{m}})-\epsilon)(q-1) \rfloor}$ such that the $R$-linear map $R \to F^e_*R$ sending $1$ to $F^e_*c$ splits (when $\mathrm{fpt}({\mathfrak{m}})=0$, put $\epsilon=0$ and $c=1$). That is, there exists an $R$-linear map $\phi \colon F^e_*R \to R$ sending $F^e_*c$ to $1$. It follows from Grothendieck duality that there exists an isomorphism $$\Phi \colon \mathrm{Hom}_R(F^e_*R, R) \cong F^e_*{\mathcal{O}}_X((1-q)K_X)=F^e_*\left({\mathcal{O}}_X(-rK_X)^{n_e} {\mathcal{O}}_X(-j_eK_X)\right).$$ We write $\Phi(\phi)=\sum_{\underline{m}} F^e_*(\phi_1^{m_1} \cdots \phi_l^{m_l} \psi_{\underline{m}})$ with $\psi_{\underline{m}} \in {\mathcal{O}}_X(-j_eK_X)$, where $\underline{m}$ runs through all elements of $\{(m_1, \dots, m_l) \in {\mathbb{Z}}_{\ge 0}^l \mid m_1+\cdots+m_l=n_e\}$. Then $$\begin{aligned}
1=\phi(F^e_*c)
&=\Phi^{-1}\left(\sum_{\underline{m}} F^e_*(\phi_1^{m_1} \cdots \phi_l^{m_l} \psi_{\underline{m}})\right)(F^e_*c)\\
&=\sum_{\underline{m}}\Phi^{-1}\left(F^e_*(\phi_1^{m_1} \cdots \phi_l^{m_l} \psi_{\underline{m}})\right)(F^e_*c). \end{aligned}$$ Therefore, there exists $\underline{m}=(m_1, \dots, m_l) \in {\mathbb{Z}}_{\ge 0}^l$ with $\sum_{i=1}^l m_i=n_e$ such that $\Phi^{-1}(F^e_*(\phi_1^{m_1} \cdots \phi_l^{m_l} \psi_{\underline{m}}))(F^e_*c)$ is a unit. Replacing $c$ by a unit multiple, we may assume that $\Phi(\phi)=F^e_*(\phi_1^{m_1} \cdots \phi_l^{m_l} \psi_{\underline{m}})$.
Since each $\phi_i$ determines an effective divisor $D_i$ which is linearly equivalent to $-rK_X$, the section $F^e_*(\phi_1^{m_1} \cdots \phi_l^{m_l} \psi_{\underline{m}})$ lies in $F^e_*{\mathcal{O}}_X((1-q)K_X-m_1D_1-\cdots-m_lD_l)$ and we have the following commutative diagram: $$\xymatrix{
F^e_*{\mathcal{O}}_X((1-q)K_X-m_1D_1-\cdots-m_lD_l) \ar[r] & F^e_*{\mathcal{O}}_X((1-q)K_X)\\
\mathrm{Hom}_R(F^e_*{\mathcal{O}}_X(m_1D_1+\cdots+m_lD_l), R) \ar[r] \ar[u] & \mathrm{Hom}_R(F^e_*R, R) \ar[u]_{\Phi},
}$$ where the vertical maps are isomorphisms. Therefore, $\phi$ induces an $R$-linear map $$F^e_*{\mathcal{O}}_X(m_1D_1+\cdots+m_lD_l) \to R$$ sending $F^e_*c$ to $1$. Then its Matlis dual $$cF^e \colon H^d_{{\mathfrak{m}}}(\omega_R) \to H^d_{{\mathfrak{m}}}({\mathcal{O}}_X(qK_X+m_1D_1+\cdots+m_lD_l))$$ is injective. On the other hand, since $R$ is not quasi-Gorenstein and $rK_X+D_i\sim 0$, the fractional ideal $\omega_X^r={\mathcal{O}}_X(K_X)^r$ is contained in ${\mathfrak{m}}{\mathcal{O}}_X(rK_X+D_i)$ for each $i=1, \dots, l$. Hence, $\omega_X^q$ is contained in ${\mathfrak{m}}^{\lfloor (q-1)/r \rfloor} {\mathcal{O}}_X(qK_X+m_1D_1+\cdots+m_lD_l)$. It then follows from an analogous argument to the proof of Theorem \[thm:non-Gorenstein\] that $\mathrm{fpt}({\mathfrak{m}})+\frac{1}{r} \le c({\mathfrak{m}})$.
\[rem:finite generation\] In the setting of Theorem \[thm:anti-canonical\], it is well-known that $\bigoplus_{n \ge 0}{\mathcal{O}}_X(-nK_X)$ is Noetherian if $R$ is ${\mathbb{Q}}$-Gorenstein, $R$ is a normal semigroup ring or $R$ is a determinantal ring. We briefly explain the reason why $\bigoplus_{n \ge 0}{\mathcal{O}}_X(-nK_X)$ is Noetherian in the latter case.
Let $R$ be the determinantal ring $k[T]/I$, where $T$ is an $m\times n$ matrix of indeterminates with $m\le n$, and $I$ is the ideal generated by the size $t$ minors of $T$ where $1\le t\le m$. Then the anti-canonical class of $R$ is the class of the $(n-m)$-th symbolic power of the prime ideal ${\mathfrak{p}}$ generated by the size $t-1$ minors of the first $t-1$ rows of $T$ by [@BV Theorem 8.8]. Moreover, the symbolic powers of ${\mathfrak{p}}$ coincide with its ordinary powers by [@BV Corollary 7.10], so the anti-canonical cover is the Rees algebra of ${\mathfrak{p}}^{n-m}$. In particular, it is Noetherian.
Another case where $\bigoplus_{n \ge 0}{\mathcal{O}}_X(-nK_X)$ is Noetherian is the following:
\[cor:dim 3\] Let $X$ be a three-dimensional strongly $F$-regular variety over an algebraically closed field of characteristic $p>5$ and $x$ be a closed point of $X$. Then $\mathrm{fpt}({\mathfrak{m}}_x)=c({\mathfrak{m}}_x)$ if and only if $X$ is Gorenstein at $x$.
We may assume that $X$ is affine. By [@SS Theorem 4.3] and [@HW Theorem 3.3], there exists an effective ${\mathbb{Q}}$-divisor $\Delta$ on $X$ such that $K_X+\Delta$ is ${\mathbb{Q}}$-Cartier and $(X, \Delta)$ is strongly $F$-regular and in particular is klt. Since the minimal model program holds for three-dimensional klt pairs in characteristic $p>5$, the anti-canonical cover $\bigoplus_{n \ge 0}{\mathcal{O}}_X(-nK_X)$ is Noetherian (see for example [@CEMS Theorem 2.28]). Thus, the assertion follows from Theorem \[thm:anti-canonical\].
A combination of Proposition \[prop:imply\], Theorem \[thm:anti-canonical\], Remark \[rem:finite generation\] and Corollary \[cor:dim 3\] gives an extension of [@HWY Theorem 1.2 (2)]:
\[cor:conclusion I\] Let $R$ be an $F$-pure normal standard graded ring, with $R_0$ an $F$-finite field of characteristic $p>0$. Let ${\mathfrak{m}}$ be the homogeneous maximal ideal of $R$. Suppose that the anti-canonical cover $\bigoplus_{n \ge 0} {\mathcal{O}}_X(-nK_X)$ of $X:=\Spec R$ is Noetherian. This assumption is satisfied, for example, in each of the following cases:
1. $R$ is ${\mathbb{Q}}$-Gorenstein,
2. $R$ is a semigroup ring,
3. $R$ is a determinantal ring,
4. $R$ is a strongly $F$-regular ring of dimension at most three,
5. $R$ is a four-dimensional strongly $F$-regular ring and $p>5$.
Then $\mathrm{fpt}({\mathfrak{m}})=-a(R)$ if and only if $R$ is quasi-Gorenstein.
If $\bigoplus_{n \ge 0} {\mathcal{O}}_X(-nK_X)$ is Noetherian, then the assertion follows from Proposition \[prop:imply\] and Theorem \[thm:anti-canonical\]. By Remark \[rem:finite generation\], $\bigoplus_{n \ge 0} {\mathcal{O}}_X(-nK_X)$ is Noetherian in the case of (1), (2) and (3). We will explain why $\bigoplus_{n \ge 0} {\mathcal{O}}_X(-nK_X)$ is Noetherian in the case of (4) and (5).
Since two-dimensional strongly $F$-regular rings are ${\mathbb{Q}}$-Gorenstein, we may assume that $\dim X \ge 3$. Also, since strong $F$-regularity is preserved under flat base change by [@Ab Theorem 3.6], we may assume that $R_0$ is an algebraically closed field. Let $D$ be a very ample divisor on $Y:=\Proj R$ so that $R=\bigoplus_{m \ge 0}H^0(Y, {\mathcal{O}}_Y(mD))$. It follows from [@SS Theorem 1.1] that $Y$ is a normal projective variety of Fano type of dimension at most three. It is known that the minimal model program holds for klt surfaces and also for three-dimensional klt pairs in characteristic $p>5$ (see [@HX; @Bi; @BW]). Thus, applying essentially the same argument as the proof of [@BCHM Corollary 1.1.9], we can see that $$\bigoplus_{n \ge 0}{\mathcal{O}}_X(-nK_X) \cong \bigoplus_{m \in {\mathbb{Z}}} \bigoplus_{n \ge 0}H^0(Y, {\mathcal{O}}_Y(mD-nK_Y))$$ is Noetherian.
We also give an answer to [@HWY Question 6.7]. Before stating the result, we fix some notation. Let $M={\mathbb{Z}}^d$, $N=\Hom_{{\mathbb{Z}}}(M, {\mathbb{Z}})$, and denote the duality pairing between $M_{{\mathbb{R}}}:=M\otimes_{{\mathbb{Z}}} {\mathbb{R}}$ and $N_{{\mathbb{R}}}:=N\otimes_{{\mathbb{Z}}} {\mathbb{R}}$ by $\langle - , - \rangle\colon M_{{\mathbb{R}}} \times N_{{\mathbb{R}}} \to {\mathbb{R}}$. Let $\sigma \subset N_{{\mathbb{R}}}$ be a strongly convex rational polyhedral cone and denote its dual cone by $\sigma^{\vee}$. Let $R=k[\sigma^{\vee} \cap M]$ be the affine semigroup ring over a field $k$ defined by $\sigma$ and ${\mathfrak{m}}$ be the unique monomial maximal ideal of $R$. The Newton Polyhedron $P({\mathfrak{m}}) \subseteq M_{{\mathbb{R}}}$ of ${\mathfrak{m}}$ is defined as the convex hull of the set of exponents $m \in M$ of monomials $x^m \in {\mathfrak{m}}$. We define the function $\lambda_{{\mathfrak{m}}}$ by $$\lambda_{{\mathfrak{m}}}\colon\sigma^{\vee} \to {\mathbb{R}}\quad u \mapsto \sup\{\lambda \in {\mathbb{R}}_{ \ge 0} \mid u \in \lambda P({\mathfrak{m}})\},$$ where we set $\lambda P({\mathfrak{m}})=\sigma^{\vee}$ if $\lambda=0$, and denote $$a_{\sigma}(R):=-\min\{\lambda_{{\mathfrak{m}}}(u) \mid u \in \mathrm{Int}(\sigma^{\vee}) \cap M\}.$$ Note that $a_{\sigma}(R)$ coincides with the $a$-invariant $a(R)$ if $R$ is standard graded.
\[cor:toric charp\] We use the above notation. Let $R=k[\sigma^{\vee} \cap M]$ be a (not necessarily standard graded) affine semigroup ring over an $F$-finite field $k$ of characteristic $p>0$ defined by $\sigma$.
1. Then $c({\mathfrak{m}})=-a_{\sigma}(R)$.
2. $\mathrm{fpt}({\mathfrak{m}})=-a_{\sigma}(R)$ if and only if $R$ is Gorenstein.
Since (2) follows from (1) and Theorem \[thm:anti-canonical\], we will show only (1). Let $v_1, \dots, v_s$ be the primitive generators for $\sigma$, that is, the first lattice points on the edges of $\sigma$. Note that the graded canonical module $\omega_R$ consists of the monomials $x^m$ such that $\langle m, v_i \rangle \ge 1$ for all $i=1, \dots, s$. Hence, its $k$-dual $H^d_{{\mathfrak{m}}}(R)$ is written as $$H^d_{{\mathfrak{m}}}(R)=\bigoplus_{m \in S} k x^m,$$ where $S=\{m \in M \mid \langle m, v_i \rangle \le -1 \textup{ for all $i=1, \dots, s$}\}$. It follows from the fact that $1$ is an ${\mathfrak{m}}^t$-test element by [@HY Theorem 6.4] (see [@HY Definition 6.3] for the definition of ${\mathfrak{m}}^t$-test elements) that the pair $(R, {\mathfrak{m}}^t)$ is $F$-rational if and only if for each $m \in S$, one has ${\mathfrak{m}}^{\lceil tp^e \rceil}x^{p^e m} \ne 0$ in $H^d_{{\mathfrak{m}}}(R)$, or equivalently, $$\left(p^e m+\lceil tp^e \rceil P({\mathfrak{m}})\right) \cap S \ne \emptyset,$$ for infinitely many $e$. We can rephrase this condition as saying that $-m \in \mathrm{Int}(tP({\mathfrak{m}}))$, using an argument similar to the proof of [@Bl Theorem 3]. By Lemma \[lem:basic\] (2), $$\begin{aligned}
c({\mathfrak{m}})&=\sup\{t \in {\mathbb{R}}_{\ge 0} \mid (R, {\mathfrak{m}}^t) \textup{ is $F$-rational}\}\\
&=\sup\{t \in {\mathbb{R}}_{\ge 0} \mid -m \in \mathrm{Int}(tP({\mathfrak{m}})) \textup{ for all $m \in S$}\}\\
&=\min_{u \in -S}\lambda_{{\mathfrak{m}}}(u).\end{aligned}$$ Since $-S=\mathrm{Int}(\sigma^{\vee}) \cap M$, one has the equality $c({\mathfrak{m}})=-a_{\sigma}(R)$.
Positive characteristic case II {#sec:char p II}
===============================
In this section we give a different interpretation of the function $\nu_e({\mathfrak{m}})$, where ${\mathfrak{m}}$ is the homogeneous maximal ideal of an $F$-pure normal standard graded domain $R$ over an $F$-finite field (Theorem \[theorem:omega\]). Combining it with the Fedder-type criteria (Proposition \[prop:Fedder criteria\]), we give explicit computations of $\mathrm{fpt}({\mathfrak{m}})$ in many situations (e.g. Propositions \[prop:determinantal\] and \[prop:fptQGor\]), eventually yielding Corollary \[cor:conclusion I\] as a consequence (see Corollary \[cor:final\]).
\[theorem:omega\] Let $S$ be an $n$-dimensional standard graded polynomial ring over an $F$-finite field of characteristic $p>0$. Let $I$ be a homogeneous ideal such that $R:=S/I$ is an $F$-pure normal domain. Let $\omega_R$ denote the graded canonical module of $R$. Then, for each $q=p^e$, one has a graded isomorphism $$\frac{I^{[q]}:_S I}{I^{[q]}} \cong \left(\omega_R(n)\right)^{(1-q)}.$$ In particular, if ${\mathfrak{m}}$ is the homogeneous maximal ideal of $R$, then $-\nu_e({\mathfrak{m}})$ equals the degree of a minimal generator of $\omega_R^{(1-q)}$ (See Proposition \[prop:Fedder criteria\] for the definition of $\nu_e({\mathfrak{m}})$).
After taking a flat base change, we may assume that $S=k[x_1,\dots,x_n]$, where $k$ is a perfect field. It then follows that $S$ is a free $S^q$-module with basis $x_1^{i_1}\cdots x_n^{i_n}$ where $0\le i_j\le q-1$ for each $j$. Consider the homomorphism $\phi\in\Hom_{S^q}(S,S^q)$ that maps the basis element $(x_1\cdots x_n)^{q-1}$ to $1$, and every other basis element to $0$. It is readily seen that $\phi$ generates $\Hom_{S^q}(S,S^q)$ as an $S$-module.
Let $J$ be the ideal of $S^q$ consisting of $q$-th powers of elements of $I$; note that $JS=I^{[q]}$. Then $$\Hom_{S^q}(S/I,S^q/J)\ \cong\ \frac{I^{[q]}:_S I}{I^{[q]}}\phi,$$ see [@Fedder page 465]. Next, note that one has graded isomorphisms $$\begin{aligned}
\Hom_{S^q}(S/I,S^q/J) &\ \cong\ \Hom_{R^q}(R,R^q)\\
&\ \cong\ \Hom_{R^q}(R,\Hom_{R^q}(\omega_{R^q},\omega_{R^q}))\\
&\ \cong\ \Hom_{R^q}(R\otimes_{R^q}\omega_{R^q},\omega_{R^q})\\
&\ \cong\ \Hom_{R^q}(\omega_R^{(q)},\omega_{R^q})\\
&\ \cong\ \Hom_{R^q}(\omega_R^{(q)}\otimes_R R,\omega_{R^q})\\
&\ \cong\ \Hom_R(\omega_R^{(q)},\Hom_{R^q}(R,\omega_{R^q}))\\
&\ \cong\ \Hom_R(\omega_R^{(q)},\omega_R)\\
&\ \cong\ \omega_R^{(1-q)}.\end{aligned}$$ Since the homomorphism $\phi$ has degree $n-nq$, the desired isomorphism follows.
Suppose $\omega_R^{(1-q)}$ is generated in degrees $-d_1<\dots <-d_r$, then $(I^{[q]}:_SI)/I^{[q]}$ is generated in degrees $n(q-1)-d_1<\dots <n(q-1)-d_r$. Hence the least degree of a homogeneous element of $I^{[q]}:_SI$ that is not in ${\mathfrak{m}}^{[q]}$ belongs to the set $$\{n(q-1)-d_1,\ldots ,n(q-1)-d_r\},$$ and $I^{[q]}:_SI\subseteq {\mathfrak{m}}^{n(q-1)-d_1}$. Since the definition of $\nu_e({\mathfrak{m}})$ translates as $$\nu_e({\mathfrak{m}}) = \max\{r\in {\mathbb{N}}\mid (I^{[q]}:_S I) \not\subseteq {\mathfrak{m}}^{[q]}+{\mathfrak{m}}^{n(q-1)+1-r}\},$$ it follows that $\nu_e({\mathfrak{m}})\in \{d_1,\ldots ,d_r\}$.
As an immediate consequence we get:
If $R$ is an $F$-pure quasi-Gorenstein standard graded normal domain, over an $F$-finite field, with homogeneous maximal ideal ${\mathfrak{m}}$, then $$\mathrm{fpt}({\mathfrak{m}})=-a(R).$$ In particular, by Proposition \[prop:a\_i\], in this case $a(R)\ge a_i(R)$ for all $i=0,\ldots, \dim R$.
\[prop:determinantal\] Let $R$ be the determinantal ring $k[T]/I$, where $k$ is an $F$-finite field, the matrix of indeterminates $T$ has size $m\times n$ with $m\le n$, and $I$ is the ideal generated by the size $t$ minors of $T$ where $1\le t\le m$. Let ${\mathfrak{m}}$ be the homogeneous maximal ideal of $R$. Then $$\mathrm{fpt}({\mathfrak{m}}) = m(t-1).$$
In the notation of the proposition, the ring $R$ has $a$-invariant $-n(t-1)$. It follows that $\mathrm{fpt}({\mathfrak{m}})=-a(R)$ precisely when $m=n$ or $t=1$, i.e., if and only if $R$ is Gorenstein.
In the case $t=2$, the $F$-pure threshold has been calculated previously, see [@CM Corollary 1] or [@HWY Example 6.2]. Since $I$ is a homogeneous ideal of $k[T]$, which is $F$-pure, one can also ask for $\mathrm{fpt}(I)$. This threshold has been computed in [@MSV] (see [@HV] for various generalizations): $$\mathrm{fpt}(I)=\min\left\{\frac{(m-l)(n-l)}{t-l} \bigm| l=0,\ldots ,t-1\right\}.$$
The graded canonical module of $R$ is computed in [@BH:ainv Corollary 1.6], namely, it equals ${\mathfrak{q}}^{n-m}(m-mt)$, where ${\mathfrak{q}}$ is the prime ideal generated by the size $t-1$ minors of the first $t-1$ columns of the matrix $T$. The divisor class group of $R$ is described by [@BV Corollary 7.10], from which it follows that $\omega_R^{(1-q)}$ is generated by elements of degree $-m(q-1)(t-1)$. Theorem \[theorem:omega\] now gives $$\nu_e({\mathfrak{m}})=m(q-1)(t-1),$$ from which the result follows.
\[prop:fptQGor\] Let $R$ be an $F$-pure ${\mathbb{Q}}$-Gorenstein standard graded normal domain, over an $F$-finite field, with homogeneous maximal ideal ${\mathfrak{m}}$. If $c$ is the order of $\omega_R$ in the divisor class group and $\omega^{(c)}$ is generated in degree $D$, then: $$\mathrm{fpt}({\mathfrak{m}})=D/c.$$ In particular, $\mathrm{fpt}({\mathfrak{m}})=-a(R)$ if and only if $R$ is quasi-Gorenstein.
For $q=p^e$ let us write $1-q=a(q)c+b(q)$, with $0\le b(q)<c$. By the assumptions we have: $$\omega_R^{(1-q)}=\left(\omega^{(c)}\right)^{a(q)}\omega_R^{(b(q))}.$$ In particular, $\omega_R^{(1-q)}$ is generated in degrees $d$ satisfying: $$a(q)D+A\le d\le a(q)D+B,$$ where the minimal generators of $\omega_R^{(b(q))}$ have degrees between $A$ and $B$. Therefore $$-a(q)D-B\le \nu_e({\mathfrak{m}})\le -a(q)D-A,$$ and $\mathrm{fpt}({\mathfrak{m}})=\lim_{q\to\infty}\nu_e({\mathfrak{m}})/q=D/c$.
For the last part of the statement, simply notice that, if $\omega_R^{(c)}$ is principal but $\omega_R$ is not, then the generator of $\omega_R^{(c)}$ must have degree less than $-a(R)c$, since $\omega_R^{(c)}\subseteq \omega_R^c$.
In the above notation, if $c=p$ notice that $a(q)=-q/p$ and $b(q)=1$. Furthermore $A$ can be chosen to be the negative of the $a$-invariant of $R$, so: $$\nu_e({\mathfrak{m}})\le (q/p)D+a(R)=(q-1)D/p+D/p+a(R)=(q-1)\mathrm{fpt}({\mathfrak{m}})+\mathrm{fpt}({\mathfrak{m}})+a(R).$$
Given a finitely generated graded $R$-module $M$, we denote by $\delta(M)$ the least integer $d$ such that $M_d\neq 0$. In the case in which $R$ is a normal domain, the canonical module $\omega_R$ is isomorphic (as a graded module) to a divisorial ideal of $R$.
\[lem1\] If $R$ is a normal standard graded domain, and ${\mathfrak{a}}$ a graded divisorial ideal, then:
1. $\delta({\mathfrak{a}}^{(-1)})\ge -\delta({\mathfrak{a}})$.
2. $\delta({\mathfrak{a}}^{(-1)}) = -\delta({\mathfrak{a}})$ if and only if ${\mathfrak{a}}$ is principal.
Let ${\mathfrak{a}}=(a_1,\ldots ,a_r)$, where the $a_i$ are homogeneous elements of the quotient field of $R$ of degree $d_i\in{\mathbb{Z}}$, where $\delta({\mathfrak{a}})=d_1\le d_2\le \dots\le d_r$. If $b\in {\mathfrak{a}}^{(-1)}$ is a homogeneous nonzero element of degree $l$, then $l+d_1\ge 0$ since $a_1b$ is a homogeneous nonzero element of $R$. This shows (1).
Concerning point (2), if $b$ is a homogeneous nonzero element of ${\mathfrak{a}}^{(-1)}$ of degree $-d_1$, then $ba_1=u$ is a unit of $R$. Because $ba_i=f_i\in R$ for all $i=1,\ldots ,r$, we have $a_i=u^{-1}f_ia_1$ for all $i=1,\ldots ,r$, so that $a_1$ generates ${\mathfrak{a}}$ as an $R$-module.
\[prop:bound\] Let $R$ be an $F$-pure standard graded normal domain, over an $F$-finite field, with homogeneous maximal ideal ${\mathfrak{m}}$. Then: $$\nu_e({\mathfrak{m}})\le a(R)(1-q) \ \ \ \forall \ q=p^e.$$ In particular $\mathrm{fpt}({\mathfrak{m}})\le -a(R)$. Further, if $R$ is not quasi-Gorenstein, then: $$\nu_e({\mathfrak{m}})<a(R)(1-q) \ \ \ \forall \ q=p^e.$$
For the first part of the statement, notice that $\delta\left(\omega_R^{(q-1)}\right)\le \delta\left(\omega_R^{q-1}\right)=\delta(\omega_R)(q-1)=-a(R)(q-1)$, so $\delta\left(\omega_R^{(1-q)}\right)\ge a(R)(q-1)$ by Lemma \[lem1\], and $\nu_e({\mathfrak{m}})\le a(R)(1-q)$ by Theorem \[theorem:omega\].
For the second part, assume that $\nu_e({\mathfrak{m}})=a(R)(1-q)$ for some $q=p^e$. Since $\delta\left(\omega_R^{(q-1)}\right)\le a(R)(1-q)$, by putting together Theorem \[theorem:omega\] and Lemma \[lem1\], $\omega_R^{(q-1)}$ must be principal and generated in degree $-a(R)(q-1)$. Notice that $\omega_R^{(q-1)}\supseteq \omega_R^{q-1}$ and $\delta\left(\omega_R^{q-1}\right)=a(R)(1-q)$. Therefore the only possibility is that $\omega_R^{(q-1)} = \omega_R^{q-1}$, so that $\omega_R$ must be principal itself.
Let $R$ be an $F$-pure standard graded normal domain, over an $F$-finite field, with homogeneous maximal ideal ${\mathfrak{m}}$. If the anti-canonical cover $\bigoplus_{k\ge 0}\omega_R^{(-k)}$ of $R$ is Noetherian, then $\mathrm{fpt}({\mathfrak{m}})=-a(R)$ if and only if $R$ is quasi-Gorenstein.
If the anti-canonical cover of $R$ is Noetherian, then there exists a positive integer $c$ such that, if we write $1-q=-a(q)c-b(q)$ with $a(q)$ positive and $0\le b(q)<c$: $$\omega_R^{(1-q)}=\left(\omega^{(-c)}\right)^{a(q)}\omega_R^{(-b(q))}.$$ Let us say that $\omega^{(-c)}$ is generated in degrees $-d_1< \dots < -d_r$. Furthermore, let $-e_1< \dots < -e_s$ be the degrees of the minimal generators of $R,\omega^{(-1)},\ldots ,\omega^{(-c+1)}$. We have that $$\nu_e({\mathfrak{m}})\in\{a(q)d_i+e_j \mid i=1,\ldots ,r \ \mbox{and} \ j=1,\ldots ,s\} \ \ \ \forall \ q=p^e.$$ By choosing $i\in\{1,\ldots ,r\}$ such that $\nu_e({\mathfrak{m}})=a(q)d_i+e_j$ (for some $j$) for infinitely many $q$, then $$\mathrm{fpt}({\mathfrak{m}})=\lim_{q\to\infty}\nu_e({\mathfrak{m}})/q=d_i/c.$$
For the second part of the statement, simply note that if $R$ is not quasi-Gorenstein, with the above notation we have $-d_i\ge -d_1>a(R)c$ by (the same argument of) Proposition \[prop:bound\].
The above argument shows also that $\mathrm{fpt}({\mathfrak{m}})$ is a rational number whenever the assumptions of the corollary are satisfied; this was already known by [@CEMS].
Let $R$ be an $F$-pure standard graded normal domain, over an $F$-finite field, with homogeneous maximal ideal ${\mathfrak{m}}$. If there exists a positive integer $c$ such that $\delta\left(\omega^{(c)}\right)<-a(R)c$, then $\mathrm{fpt}({\mathfrak{m}})<-a(R)$.
Let $\delta\left(\omega^{(c)}\right)=D$. With the same notation of the proof above $q-1=a(q)c+b(q)$, so: $$\delta(\omega_R^{(q-1)})\le a(q)D+\delta\left(\omega_R^{(b(q))}\right).$$ Then, using Theorem \[theorem:omega\] together with Lemma \[lem1\], for such $q$: $$\nu_e({\mathfrak{m}})\le a(q)D.$$ Thus, $\mathrm{fpt}({\mathfrak{m}})=\lim_{q\to\infty}\nu_e({\mathfrak{m}})/q\le D/c<-a(R)$.
The following provides strong evidence for the conjecture of Hirose-Watanabe-Yoshida \[conj:HWY\] and, more generally, for the standard graded case of Conjecture \[conj:fpt=fit\].
\[cor:final\] Let $R$ be an $F$-pure standard graded normal domain, over an $F$-finite field, with homogeneous maximal ideal ${\mathfrak{m}}$. Suppose that one of the following is satisfied:
1. The anti-canonical cover $\bigoplus_{k\ge 0}\omega_R^{(-k)}$ of $R$ is noetherian.
2. For some positive integer $c$, there is a nonzero element of $\omega_R^{(c)}$ of degree $<-a(R)c$.
Then $\mathrm{fpt}({\mathfrak{m}})=-a(R)$ if and only if $R$ is quasi-Gorenstein.
The following gives an extension of [@HWY Proposition 3.4].
\[prop:critical value\] Let $R$ be an $F$-pure standard graded normal domain, over an $F$-finite field, with homogeneous maximal ideal ${\mathfrak{m}}$. Suppose that the $c$-th Veronese subring of the anti-canonical cover of $R$ is standard graded and $c$ is not a multiple of $p$. Then $\nu_e({\mathfrak{m}})=(p^e-1)\mathrm{fpt}({\mathfrak{m}})$ for infinitely many positive integers $e$. In particular, $(R, {\mathfrak{m}}^{\mathrm{fpt}({\mathfrak{m}})})$ is sharply $F$-pure.
Since $p$ does not divide $c$, there is an infinite subset $A\subseteq \{p^e \mid e\in{\mathbb{N}}\}$ such that $q-1=a(q)c$ for all $q\in A$, with $a(q)\in{\mathbb{N}}$. For such $q$ $$\omega_R^{(1-q)}=\left(\omega^{(-c)}\right)^{a(q)}.$$ So if $\omega^{(-c)}$ is generated in degrees $-d_1< \dots < -d_r$, then $$\nu_e({\mathfrak{m}})\in\{a(q)d_i \mid i=1,\ldots ,r\} \ \ \ \forall \ q\in A.$$ So there exists $i$ such that $\mathrm{fpt}({\mathfrak{m}})=d_i/c$, and for all but finitely many $q\in A$ $$\nu_e({\mathfrak{m}})=(q-1)\mathrm{fpt}({\mathfrak{m}}).$$
Characteristic zero case
========================
Throughout this section, let $X$ be a normal variety over an algebraically closed field of characteristic zero and ${\mathfrak{a}}$ be a nonzero coherent ideal sheaf on $X$.
We prove a characteristic zero analogue of Conjecture \[conj:HWY\]. First, we define a variant of multiplier submodules:
Let $\pi \colon Y \to X$ be a *log resolution* of $(X, {\mathfrak{a}})$, that is, $\pi$ is a proper birational morphism from a smooth variety $Y$ such that ${\mathfrak{a}}{\mathcal{O}}_Y={\mathcal{O}}_Y(-F)$ is invertible and $\mathrm{Exc}(\pi) \cup \mathrm{Supp}(F)$ is a simple normal crossing divisor. Let $E$ be the reduced divisor supported on $\mathrm{Exc}(\pi)$. For a real number $t \ge 0$, the *multiplier submodule* $\mathcal{J}(\omega_X, {\mathfrak{a}}^t)$ is defined by $$\mathcal{J}(\omega_X, {\mathfrak{a}}^t):=\pi_*\omega_Y(\lceil -tF \rceil) \subseteq \omega_X.$$ This submodule of $\omega_X$ is independent of the choice of $\pi$, see, for example, the proof of [@ST Proposition 3.4]. When ${\mathfrak{a}}={\mathcal{O}}_X$ or $t=0$, we simply denote $\mathcal{J}(\omega_X, {\mathfrak{a}}^t)$ by $\mathcal{J}(\omega_X)$.
As a variant of $\mathcal{J}(\omega_X, {\mathfrak{a}}^t)$, we define the submodule $\mathcal{I}(\omega_X, {\mathfrak{a}}^t)$ of $\omega_X$ by $$\mathcal{I}(\omega_X, {\mathfrak{a}}^t):=\left\{\begin{array}{ll}\pi_*\omega_Y(\lceil \epsilon E-(t-\epsilon)F \rceil) & \textup{if $t>0$}\\
\pi_*\omega_Y(E) & \textup{if $t=0$}
\end{array}
\right.$$ for sufficiently small $\epsilon>0$. It is easy to see that $\mathcal{I}(\omega_X, {\mathfrak{a}}^t)$ is independent of the choice of $\epsilon$ if $\epsilon>0$ is sufficiently small. When ${\mathfrak{a}}={\mathcal{O}}_X$ or $t=0$, we simply denote $\mathcal{I}(\omega_X, {\mathfrak{a}}^t)$ by $\mathcal{I}(\omega_X)$.
$\mathcal{I}(\omega_X, {\mathfrak{a}}^t)$ is independent of the choice of the resolution.
Although it immediately follows from [@FST Lemma 13.3 and Corollary 13.7], we give a more direct proof here.
We consider the case where $t>0$; the case $t=0$ follows from a similar argument. Let $f \colon Y \to X$ be a log resolution of $(X, {\mathfrak{a}})$ such that ${\mathfrak{a}}{\mathcal{O}}_X={\mathcal{O}}_X(-F)$ is invertible, and let $E_Y$ be the reduced divisor supported on $\mathrm{Exc}(f)$. Let $g \colon Z \to Y$ be a log resolution of $(Y, E_Y+F)$, and let $E_Z$ be the reduced divisor supported on $\mathrm{Exc}(g)$. Then it is enough to show that $$\omega_Y(\lceil \epsilon E_Y-(t-\epsilon) F\rceil)=g_*\omega_Z(\lceil \epsilon'(g^{-1}_*E_Y+E_Z)-(t-\epsilon')g^*F \rceil)$$ for sufficiently small real numbers $\epsilon, \epsilon'>0$, since two log resolutions of $(X, {\mathfrak{a}})$ can be dominated by a third log resolution. Let $\bigcup_i E_i$ be the irreducible decomposition of $\Supp (E_Y+F)$. For sufficiently small $\epsilon>0$, we can write $$\lceil K_Y+ \epsilon E_Y-(t-\epsilon) F\rceil=K_Y- tF+\sum_{i}a_i E_i,$$ where $1 \ge a_i>0$ for all $i$. Since $\sum_i E_i$ is a simple normal crossing divisor on $Y$, the pair $(Y, \sum_i a_i E_i)$ is log canonical. By the definition of log canonical pairs, we have $$\begin{aligned}
G:=& \lceil K_Z+\epsilon' (g^{-1}_*E_Y+E_Z)-(t-\epsilon')g^*F \rceil- g^*\lceil K_Y+ \epsilon E_Y-(t-\epsilon) F\rceil\\
= & \left\lceil K_{Z/Y}+\epsilon' \left(g^{-1}_*E_Y+E_Z+g^*F\right)-g^*\sum_i a_i E_i \right\rceil \ge 0.\end{aligned}$$ Note that $G$ is a $g$-exceptional divisor for sufficiently small $\epsilon'>0$. Therefore, $$\begin{aligned}
g_*\omega_Z(\lceil \epsilon'(g^{-1}_*E_Y+E_Z)-(t-\epsilon')g^*F \rceil)
=& g_*\left(g^*\left(\omega_Y(\lceil \epsilon E_Y-(t-\epsilon) F\rceil\right)) \otimes {\mathcal{O}}_Z(G) \right)\\
=& \omega_Y(\lceil \epsilon E_Y-(t-\epsilon) F\rceil) \otimes g_*{\mathcal{O}}_Z(G)\\
=& \omega_Y(\lceil \epsilon E_Y-(t-\epsilon) F\rceil).\qedhere\end{aligned}$$
\[rem:rational, db\]
1. $X$ has only rational singularities if and only if $X$ is Cohen-Macaulay and $\mathcal{J}(\omega_X)=\omega_X$, see [@KM Theorem 5.10].
2. If $X$ has only Du Bois singularities, then $\mathcal{I}(\omega_X)=\omega_X$, see [@KSS]. In case $X$ is Cohen-Macaulay, the converse holds as well. The reader is referred to [@Sch1] for the definition and a simple characterization of Du Bois singularities.
Using $\mathcal{I}(\omega_X, {\mathfrak{a}}^t)$, we define a new invariant of singularities in characteristic zero:
\[def:db threshold\] Suppose that $X$ has only Du Bois singularities. Then the threshold $\mathrm{d}({\mathfrak{a}})$ is defined by $$\mathrm{d}({\mathfrak{a}}):=\sup\{t \ge 0 \mid \mathcal{I}(\omega_X, {\mathfrak{a}}^t)=\omega_{X}\}.$$ If $x$ is a closed point of $X$, then the threshold $\mathrm{d}_x({\mathfrak{a}})$ is defined by $$\mathrm{d}_x({\mathfrak{a}}):=\sup\{t \ge 0 \mid \mathcal{I}(\omega_X, {\mathfrak{a}}^t)_x=\omega_{X,x}\}.$$
\[rem:graded char0\] Let $R$ be an ${\mathbb{N}}$-graded ring with $R_0$ an algebraically closed field $k$ of characteristic zero, and let ${\mathfrak{m}}$ be the homogeneous maximal ideal of $R$. Let $X=\Spec R$ and $x \in X$ be the closed point corresponding to ${\mathfrak{m}}$. By considering a $k^*$-equivariant log resolution of $(X, {\mathfrak{m}})$, we see that $\mathcal{I}(\omega_X, {\mathfrak{m}}^t)$ is a graded submodule of the graded canonical module $\omega_R$. This implies that $\mathrm{d}({\mathfrak{m}})=\mathrm{d}_x({\mathfrak{m}})$.
In [@dFH] de Fernex-Hacon extended the notion of log canonical thresholds to the non-${\mathbb{Q}}$-Gorenstein setting; we recall their definition:
Suppose that $t \ge 0$ is a real number.
1. The pair $(X, {\mathfrak{a}}^t)$ is said to be *klt* (resp. *log canonical*) in the sense of de Fernex-Hacon if there exists an effective ${\mathbb{Q}}$-divisor $\Delta$ on $X$ such that $K_X+\Delta$ is ${\mathbb{Q}}$-Cartier and $((X, \Delta); {\mathfrak{a}}^t)$ is klt (resp. log canonical) in the classical sense. That is, if $\pi \colon Y \to X$ is a log resolution of $(X, \Delta, {\mathfrak{a}})$ such that ${\mathfrak{a}}{\mathcal{O}}_Y={\mathcal{O}}_Y(-F)$ is invertible and if we write $$K_Y-\pi^*(K_X+\Delta)-tF=\sum_{i}a_i E_i,$$ where the $E_i$ are prime divisors on $Y$ and the $a_i$ are real numbers, then $a_i >-1$ (resp. $a_i \ge -1$) for all $i$. The *log canonical threshold* $\mathrm{lct}({\mathfrak{a}})$ of ${\mathfrak{a}}$ is defined by $$\hspace*{3em} \mathrm{lct}({\mathfrak{a}}):=\sup\{t \ge 0 \mid (X, {\mathfrak{a}}^t) \textup{ is log canonical in the sense of de~Fernex-Hacon} \}.$$
2. Let $x$ be a closed point of $X$. Then $(X, {\mathfrak{a}}^t)$ is *klt* (resp. *log canonical*) at $x$ in the sense of de Fernex-Hacon if there exists a open neighborhood $U$ of $x$ such that $(U, ({\mathfrak{a}}|_U)^t)$ is klt (resp. log canonical) in the sense of de Fernex-Hacon. If, in addition, ${\mathfrak{a}}={\mathcal{O}}_X$, then we say that $(X, x)$ is a *log terminal* (resp. *log canonical*) singularity in the sense of de Fernex-Hacon. The *log canonical threshold* $\mathrm{lct}_x({\mathfrak{a}})$ of ${\mathfrak{a}}$ at $x$ is defined by $$\hspace*{3.5em} \mathrm{lct}_x({\mathfrak{a}}):=\sup\{t \ge 0 \mid (X, {\mathfrak{a}}^t) \textup{ is log canonical at $x$ in the sense of de~Fernex-Hacon} \}.$$ If $\Delta$ is an effective ${\mathbb{Q}}$-divisor on $X$ such that $K_X+\Delta$ is ${\mathbb{Q}}$-Cartier and $(X, \Delta)$ is log canonical at $x$ (in the classical sense), then the *log canonical threshold* $\mathrm{lct}_x(\Delta;{\mathfrak{a}})$ is defined by $$\hspace*{3.5em} \mathrm{lct}_x(\Delta; {\mathfrak{a}}):=\sup\{t \ge 0 \mid ((X, \Delta);{\mathfrak{a}}^t) \textup{ is log canonical at $x$ (in the classical sense)} \}.$$
We prove some basic properties of $\mathrm{d}_x({\mathfrak{a}})$.
\[lem:dbt basic\] Let $(X, x)$ be a $d$-dimensional normal singularity.
1. If $(X, x)$ is a rational singularity, then $$\mathrm{d}_x({\mathfrak{a}})=\sup\{t \ge 0 \mid \mathcal{J}(\omega_X, {\mathfrak{a}}^t)_x=\omega_{X,x}\}.$$
2. Suppose that $(X, x)$ is a log canonical singularity in the sense of de Fernex-Hacon. Then $\mathrm{lct}_x({\mathfrak{a}}) \le \mathrm{d}_x({\mathfrak{a}})$. In addition, if $X$ is quasi-Gorenstein at $x$, then $\mathrm{lct}_x({\mathfrak{a}}) = \mathrm{d}_x({\mathfrak{a}})$.
3. Suppose that $(X,x)$ is a Cohen-Macaulay Du Bois singularity. Then $\mathrm{d}_x({\mathfrak{m}}_x) \le d$. If $J \subseteq {\mathcal{O}}_{X, x}$ is a minimal reduction of the maximal ideal ${\mathfrak{m}}_x$, then ${\mathfrak{m}}_x^{d+1-\lceil \mathrm{d}_x({\mathfrak{m}}_x) \rceil} \subseteq J$.
4. Suppose that $X$ is Cohen-Macaulay at $x$. If $\mathrm{d}_x({\mathfrak{m}}_x)>d-1$, then $X$ is nonsingular at $x$ and in particular $\mathrm{d}_x({\mathfrak{m}}_x)=d$.
\(1) Shrinking $X$ if necessary, we may assume that $X$ has only rational singularities. First we will check that $\mathrm{d}_x({\mathfrak{a}})>0$. Let $\pi \colon Y \to X$ be a log resolution of $(X, {\mathfrak{a}})$ such that ${\mathfrak{a}}{\mathcal{O}}_Y={\mathcal{O}}_Y(-F)$ is invertible and let $E$ be the reduced divisor supported on $\mathrm{Exc}(\pi)$. For sufficiently small $t>\epsilon>0$, $$K_Y+E \ge \lceil K_Y+\epsilon E-(t-\epsilon)F \rceil \ge K_Y.$$ Taking the pushforward $\pi_*$, we obtain inclusions $\omega_X \supset \mathcal{I}(\omega_X, {\mathfrak{a}}^t) \supset \mathcal{J}(\omega_X)=\omega_X$ by Remark \[rem:rational, db\] (1). That is, $\mathrm{d}_x({\mathfrak{a}}) \ge t>0$.
Now we will show the assertion. Since $\mathcal{J}(\omega_X, {\mathfrak{a}}^t) \subseteq \mathcal{I}(\omega_X, {\mathfrak{a}}^t)$, the inequality $$\mathrm{d}_x({\mathfrak{a}}) \ge \sup\{t \ge 0 \mid \mathcal{J}(\omega_X, {\mathfrak{a}}^t)_x=\omega_{X,x}\}$$ is obvious. We will prove the reverse inequality. It is enough to show that if $\mathcal{I}(\omega_X, {\mathfrak{a}}^t)_x=\omega_{X,x}$ with $t>0$, then $\mathcal{J}(\omega_X, {\mathfrak{a}}^{t-\epsilon})_x=\omega_{X,x}$ for all $t \ge \epsilon>0$. Fix a real number $t \ge \epsilon>0$. Shrinking $X$ again if necessary, we may assume that $X$ is affine and that $\mathcal{I}(\omega_X, {\mathfrak{a}}^t)=\omega_{X}$. This means that for sufficiently small $(1/2)\epsilon \ge \epsilon'>0$, $$\mathrm{ord}_{E_i}(K_Y+\mathrm{div}_Y(f)+\epsilon' E-(t-\epsilon')F)>-1$$ for every prime divisor $E_i$ on $Y$ and for every $f \in \omega_X$. If $E_i$ is an irreducible component of $\Supp F$, then $$\mathrm{ord}_{E_i}(K_Y+\mathrm{div}_Y(f)-(t-\epsilon)F) \ge \mathrm{ord}_{E_i}(K_Y+\mathrm{div}_Y(f)+\epsilon'E-(t-\epsilon')F)>-1.$$ On the other hand, since $X$ has only rational singularities, $K_Y+\mathrm{div}_Y(f) \ge 0$ by Remark \[rem:rational, db\] (1). Therefore, if $E_i$ is not a component of $\Supp F$, then $$\mathrm{ord}_{E_i}(K_Y+\mathrm{div}_Y(f)-(t-\epsilon)F)= \mathrm{ord}_{E_i}(K_Y+\mathrm{div}_Y(f)) \ge 0.$$ Summing up above, we conclude that $\lceil K_Y+\mathrm{div}_Y(f)-(t-\epsilon)F \rceil \ge 0$ for every $f \in \omega_X$, that is, $\mathcal{J}(\omega_X, {\mathfrak{a}}^{t-\epsilon})=\omega_X$.
\(2) For the former assertion, it is enough to show that if $(X, {\mathfrak{a}}^t)$ is log canonical at $x$ in the sense of de Fernex-Hacon, then $\mathcal{I}(\omega_X, {\mathfrak{a}}^t)_x=\omega_{X, x}$. Shrinking $X$ if necessary, we may assume that $X$ is affine and there exists an effective ${\mathbb{Q}}$-divisor $\Delta$ on $X$ such that $((X, \Delta);{\mathfrak{a}}^t)$ is log canonical with $K_X+\Delta$ ${\mathbb{Q}}$-Cartier of index $r$. Let $\pi \colon Y \to X$ be a log resolution of $(X, \Delta, {\mathfrak{a}})$ such that ${\mathfrak{a}}{\mathcal{O}}_Y={\mathcal{O}}_Y(-F)$ is invertible and let $E$ be the reduced divisor supported on $\mathrm{Exc}(\pi)$. By the definition of log canonical pairs, $$\lceil K_Y-\pi^*(K_X+\Delta)+\epsilon_1 E-(t-\epsilon_2)F \rceil \ge 0$$ for every $\epsilon_1>0$ and $t \ge \epsilon_2>0$ (when $t=0$, put $\epsilon_2=0$). Let $f \in \omega_X$. Since the fractional ideal $\omega_X^r$ is contained in ${\mathcal{O}}_X(r(K_X+\Delta))$, one has $\mathrm{div}_Y(f)+\pi^*(K_X+\Delta) \ge 0$. It follows from these two inequalities that $$\lceil K_Y+\epsilon_1 E-(t-\epsilon_2)F\rceil+\mathrm{div}_Y(f) \ge 0,$$ which implies that $f \in \mathcal{I}(\omega_X, {\mathfrak{a}}^t)$.
Now we will show the latter assertion. Shrinking $X$ again if necessary, we may assume that $\omega_X \cong {\mathcal{O}}_X$. Then $\mathcal{I}(\omega_X, {\mathfrak{a}}^t)$ can be identified with the maximal non-lc ideal $\mathcal{J}'(X, {\mathfrak{a}}^t)$ under this isomorphism (see [@FST Definition 7.4] for the definition of $\mathcal{J}'(X, {\mathfrak{a}}^t)$). Since $\mathcal{J}'(X, {\mathfrak{a}}^t)={\mathcal{O}}_X$ if and only if $(X, {\mathfrak{a}}^t)$ is log canonical by the definition of $\mathcal{J}'(X, {\mathfrak{a}}^t)$, one has the equality that $\mathrm{lct}_x({\mathfrak{a}}) = \mathrm{d}_x({\mathfrak{a}})$.
\(3) The proof is essentially the same as that of [@Sh Theorem 5.2.5]. Let $f \colon Y \to \Spec {\mathcal{O}}_{X, x}$ be the blow-up at ${\mathfrak{m}}_x$ with exceptional divisor $F_x$. Take a log resolution $\pi \colon \widetilde{X} \to \Spec {\mathcal{O}}_{X, x}$ of ${\mathfrak{m}}_x$. Then there exists a morphism $g \colon \widetilde{X} \to Y$ such that $\pi=f \circ g$. Let $E=\sum_{i=1}^s E_i$ be the reduced divisor supported on $\mathrm{Exc}(\pi)$. We may assume that $E_1, \dots, E_r$ are all the components of $E$ dominating an irreducible component of $F_x$, and put $E':=\sum_{i=r+1}^s E_i$. If $t>d$, then $$\begin{aligned}
\mathcal{I}(\omega_{X}, {\mathfrak{m}}_x^{t})_x &= \pi_*{\mathcal{O}}_{\widetilde{X}}(\lceil K_{\widetilde{X}}+\epsilon E-(t-\epsilon) g^*F_x \rceil)\\
& \subseteq \pi_*{\mathcal{O}}_{\widetilde{X}}( K_{\widetilde{X}}+E'-d g^*F_x )\\
& = f_*\left(g_*{\mathcal{O}}_{\widetilde{X}}(K_{\widetilde{X}}+E')\otimes {\mathcal{O}}_Y(-dF_x)\right)\\
& \subseteq f_*\omega_Y(-dF_x)\\
&=f_*{\mathfrak{m}}_x^d \omega_Y\end{aligned}$$ for sufficiently small $\epsilon>0$. It follows from [@HuTr Theorem 3.7] and [@HS Lemma 5.1.6] that $$\mathcal{I}(\omega_{X}, {\mathfrak{m}}_x^{t})_x :_{{\mathcal{O}}_{X, x}} \omega_{X,x} \subseteq f_*{\mathfrak{m}}_x^d \omega_Y:_{{\mathcal{O}}_{X, x}}\omega_{X, x}=\mathrm{core}({\mathfrak{m}}),$$ where $\mathrm{core}({\mathfrak{m}})$ is the intersection of all reductions of ${\mathfrak{m}}$. In particular, $\mathcal{I}(\omega_{X}, {\mathfrak{m}}_x^{t})_x \subsetneq \omega_{X, x}$, that is, $\mathrm{d}_x({\mathfrak{m}}_x)<t$. Thus, $\mathrm{d}_x({\mathfrak{m}}_x) \le d$.
Since $\mathcal{I}(\omega_{X}, {\mathfrak{m}}_x^{\mathrm{d}_x({\mathfrak{m}}_x)-\epsilon})_x=\omega_{X, x}$ for every $\epsilon>0$ (we put $\epsilon=0$ when $\mathrm{d}_x({\mathfrak{m}}_x)=0$), by the same argument as above, $${\mathfrak{m}}_x^{d+1-\lceil \mathrm{d}_x({\mathfrak{m}}_x) \rceil} \omega_{X, x} = {\mathfrak{m}}_x^{d+1-\lceil \mathrm{d}_x({\mathfrak{m}}_x) \rceil} \mathcal{I}(\omega_{X}, {\mathfrak{m}}_x^{\mathrm{d}_x({\mathfrak{m}}_x)-\epsilon})_x
\subseteq f_*{\mathfrak{m}}_x^d \omega_Y$$ for sufficiently small $\epsilon>0$. It then follows from [@HuTr Theorem 3.7] and [@HS Lemma 5.1.6] again that $${\mathfrak{m}}_x^{d+1-\lceil \mathrm{d}_x({\mathfrak{m}}_x) \rceil} \subseteq f_*{\mathfrak{m}}_x^d \omega_Y:_{{\mathcal{O}}_{X, x}}\omega_{X, x}=\mathrm{core}({\mathfrak{m}}) \subseteq J.$$
\(4) Let $J$ be a minimal reduction of ${\mathfrak{m}}_x$. It then follows from (3) that ${\mathfrak{m}}_x=J$, which means that ${\mathfrak{m}}_x$ is generated by at most $d$ elements, that is, $X$ is nonsingular at $x$. If $X$ is nonsingular at $x$, then by (2), we see that $\mathrm{d}_x({\mathfrak{m}}_x)=\mathrm{lct}_x({\mathfrak{m}}_x)=d$.
We can compute the log canonical threshold of the maximal ideal of an affine determinantal variety using $F$-pure thresholds:
Let $D:=\Spec k[T]/I$ be the affine determinantal variety over an algebraically closed field $k$ of characteristic zero, where $T$ is an $m \times n$ matrix of indeterminates with $m \le n$, and $I$ is the ideal generated by the size $t$ minors of $T$ where $1\le t\le m$. Let ${\mathfrak{m}}$ be the homogeneous maximal ideal of $k[T]/I$, corresponding to the origin $0$ in $D$. Then $$\mathrm{lct}({\mathfrak{m}}) = m(t-1).$$
For each prime integer $p$, let $R_p:={\mathbb{F}}_p[T]/I_{p}$ be the modulo $p$ reduction of $k[T]/I$, and ${\mathfrak{m}}_p$ the homogeneous maximal ideal of $R_p$. It then follows from [@CEMS Theorem 6.4] and Proposition \[prop:determinantal\] that $$\mathrm{lct}({\mathfrak{m}})=\lim_{p \to \infty} \mathrm{fpt}({\mathfrak{m}}_p)=m(t-1).\qedhere$$
\[prop:non-Gorenstein2\] Let $x$ be a closed point of $X$ and $\Delta$ be an effective ${\mathbb{Q}}$-divisor on $X$ such that $(X, \Delta)$ is log canonical at $x$ with $K_X+\Delta$ being ${\mathbb{Q}}$-Cartier of index $r$. If $X$ is not quasi-Gorenstein at $x$, then $$\mathrm{lct}_x(\Delta; {\mathfrak{m}}_x)+\frac{1}{r} \le \mathrm{d}_x({\mathfrak{m}}_x).$$ In particular, if $\mathrm{d}_x({\mathfrak{m}}_x)=0$, then $X$ is quasi-Gorenstein at $x$.
Shrinking $X$ if necessary, we may assume that $X$ is affine, ${\mathcal{O}}_X(r(K_X+\Delta)) \cong {\mathcal{O}}_X$ and $((X, \Delta); {\mathfrak{m}}_x^{\mathrm{lct}_x(\Delta;{\mathfrak{m}}_x)})$ is log canonical. Let $\pi \colon Y \to X$ be a log resolution of $(X, \Delta, {\mathfrak{m}}_x)$ such that ${\mathfrak{m}}_x {\mathcal{O}}_X={\mathcal{O}}_X(-F_x)$ is invertible, and let $E$ be the reduced divisor supported on $\mathrm{Exc}(\pi)$. Putting $t=\mathrm{lct}_x(\Delta; {\mathfrak{m}}_x)$, one has the inequality $$\lceil K_Y-\pi^*(K_X+\Delta)-(t-\epsilon)F_x+\epsilon E \rceil \ge 0$$ for every $\epsilon>0$. On the other hand, since $X$ is not quasi-Gorenstein at $x$, the fractional ideal $\omega_{X}^r$ is contained in ${\mathfrak{m}}_x {\mathcal{O}}_X(r(K_X+\Delta))$. Hence, for each $f \in \omega_X$, one has the inequality $$r\mathrm{div}_Y(f) +r\pi^*(K_X+\Delta)-F_x \ge 0.$$ It follows from these two inequalities that $$\begin{aligned}
0 \le & \lceil K_Y-\pi^*(K_X+\Delta)-(t-\epsilon)F_x+\epsilon E \rceil\\
= & \left\lceil K_Y+ \epsilon E-\left(t+\frac{1}{r}-\epsilon \right)F_x - \pi^*(K_X+\Delta)+\frac{1}{r}F_x \right\rceil\\
\le & K_Y+\left\lceil \epsilon E-\left(t+\frac{1}{r}-\epsilon \right)F_x \right\rceil+\mathrm{div}_Y(f)\end{aligned}$$ for all $\epsilon>0$ and all $f \in \omega_X$. This means that $\mathcal{I}(\omega_X, {\mathfrak{m}}_x^{\mathrm{lct}_x(\Delta; {\mathfrak{m}}_x)+1/r})=\omega_X$, that is, $\mathrm{d}_x({\mathfrak{m}}_x) \ge \mathrm{lct}_x(\Delta; {\mathfrak{m}}_x)+1/r$.
The following theorem is the main result of this section; this is a characteristic zero analogue of Theorem \[thm:anti-canonical\].
\[thm:lc\] Suppose that $(X, x)$ is a log canonical singularity in the sense of de Fernex-Hacon. Assume in addition that the anti-canonical cover $\bigoplus_{n \ge 0}{\mathcal{O}}_X(-nK_X)_x$ is Noetherian. Then $\mathrm{lct}_x({\mathfrak{m}}_x)=\mathrm{d}_x({\mathfrak{m}}_x)$ if and only if $(X, x)$ is quasi-Gorenstein.
Since the “if" part immediately follows from Lemma \[lem:dbt basic\] (2), we will show the “only if" part. Shrinking $X$ if necessary, we may assume that $X$ is log canonical in the sense of de Fernex-Hacon and that $\bigoplus_{n \ge 0}{\mathcal{O}}_X(-nK_X)$ is Noetherian. Then one can find an integer $r \ge 1$ such that ${\mathcal{O}}_X(-rmK_X)={\mathcal{O}}_X(-rK_X)^m$ for every integer $m \ge 1$. Fix a real number $\epsilon$ with $\min\{\mathrm{lct}({\mathfrak{m}}_x), 1/r\}>\epsilon>0$; when $\mathrm{lct}({\mathfrak{m}}_x)=0$, put $\epsilon=0$. Since $(X, {\mathfrak{m}}_x^{\mathrm{lct}({\mathfrak{m}}_x)-\epsilon})$ is log canonical in the sense of de Fernex-Hacon, there exists an integer $m_0 \ge 1$ such that the $m$-th limiting log discrepancy $a_{m, F}(X, {\mathfrak{m}}_x^{\mathrm{lct}({\mathfrak{m}}_x)-\epsilon})$ is nonnegative for every prime divisor $F$ over $X$ and for every positive multiple $m$ of $m_0$ by [@dFH Definition 7.1] (see *loc. cit.* for the definition of the $m$-th limiting log discrepancy of a pair). By the choice of $r$, one has $$a_{r, F}(X, {\mathfrak{m}}_x^{\mathrm{lct}({\mathfrak{m}}_x)-\epsilon})=a_{rm_0, F}(X, {\mathfrak{m}}_x^{\mathrm{lct}({\mathfrak{m}}_x)-\epsilon}) \ge 0.$$ It follows from an argument similar to the proof of [@dFH Proposition 7.2] that there exists an effective ${\mathbb{Q}}$-divisor $\Delta$ on $X$ such that $K_X+\Delta$ is ${\mathbb{Q}}$-Cartier of index $r$ and $((X, \Delta); {\mathfrak{m}}_x^{\mathrm{lct}({\mathfrak{m}}_x)-\epsilon})$ is log canonical. If $X$ is not quasi-Gorenstein at $x$, then by Proposition \[prop:non-Gorenstein2\], $$\mathrm{lct}_x({\mathfrak{m}}_x) <\mathrm{lct}_x({\mathfrak{m}}_x)-\epsilon +\frac{1}{r} \le \mathrm{lct}_x(\Delta; {\mathfrak{m}}_x) +\frac{1}{r} \le \mathrm{d}_x({\mathfrak{m}}_x).$$ This contradicts the assumption that $\mathrm{lct}_x({\mathfrak{m}}_x)=\mathrm{d}_x({\mathfrak{m}}_x)$.
\[cor:log terminal\] Suppose that $(X, x)$ is a log terminal singularity in the sense of de Fernex-Hacon. Then $\mathrm{lct}_x({\mathfrak{m}}_x)=\mathrm{d}_x({\mathfrak{m}}_x)$ if and only if $(X, x)$ is Gorenstein.
Since $(X, x)$ is log terminal, using the minimal model program for klt pairs, one can show that the anti-canonical cover $\bigoplus_{n \ge 0}{\mathcal{O}}_X(-nK_X)_x$ is Noetherian (see [@Ko Theorem 92]). Thus, the assertion follows from Theorem \[thm:lc\].
\[prop:dbt=-a\] Let $R$ be a normal standard graded ring, with $R_0$ an algebraically closed field of characteristic zero, and let ${\mathfrak{m}}$ denote the homogeneous maximal ideal of $R$. Suppose that $\Spec R$ has only Du Bois singularities. Then $\mathrm{d}({\mathfrak{m}}) \le -a(R)$.
Put $X=\Spec R$. Since $X$ has only Du Bois singularities, $a(R) \le 0$ by [@Ma Theorem 4.4]. Suppose that $\mathcal{I}(\omega_X, {\mathfrak{m}}^t)=\omega_X$ with $t>0$. Let $\phi \colon Y \to X$ be the blow-up of $X$ at ${\mathfrak{m}}$ and $E=\Proj R$ be its exceptional divisor. Take a log resolution $\psi \colon \widetilde{X} \to Y$ of $(Y, E)$ and let $\widetilde{E}$ be the strict transform of $E$ on $\widetilde{X}$. We fix a canonical divisor $K_{\widetilde{X}}$ on $\widetilde{X}$ such that $\psi_*K_{\widetilde{X}}=K_Y$. Since $\mathcal{I}(\omega_X, {\mathfrak{m}}^t)=\omega_X$, $$\mathrm{ord}_{\widetilde{E}}(\lceil K_{\widetilde{X}}+\mathrm{div}_{\widetilde{X}}(f)+\epsilon \widetilde{E}-(t-\epsilon) \psi^*E \rceil) \ge 0$$ for all $f \in \omega_X$ and all sufficiently small $\epsilon>0$. Taking the direct image by $\psi$, we see that $\mathrm{ord}_{E}(\lceil K_{Y}+\mathrm{div}_{Y}(f)+\epsilon E-(t-\epsilon) E \rceil) \ge 0$, that is, $\phi_*\omega_{Y}(\lceil \epsilon-t \rceil E)=\omega_X$ for sufficiently small $\epsilon>0$. On the other hand, it is easy to see by the definition of $\phi$ (see, for example, [@HS Proposition 6.2.1]) that $$\phi_*\omega_{Y}(\lceil \epsilon-t \rceil E)=[\omega_X]_{\ge \lfloor t- \epsilon \rfloor+1}.$$ Thus, $t \le -a(R)$, that is, $\mathrm{d}({\mathfrak{m}}) \le -a(R)$.
As a consequence, we can prove a characteristic zero analogue of Conjecture \[conj:HWY\], which gives an affirmative answer to [@dSNB Conjecture 6.9].
\[cor:char 0 main thm\] Let $R$ be a normal standard graded ring, with $R_0$ an algebraically closed field of characteristic zero. Let ${\mathfrak{m}}$ denote the homogeneous maximal ideal of $R$. Assume that $X:=\Spec R$ has log canonical singularities in the sense of de Fernex-Hacon.
1. Then $\mathrm{lct}({\mathfrak{m}}) \le -a(R)$.
2. Suppose in addition that the anti-canonical cover $\bigoplus_{n \ge 0}{\mathcal{O}}_X(-nK_X)$ is Noetherian (this assumption is satisfied, for example, if $X$ has log terminal singularities in the sense of de Fernex-Hacon or if $R$ is ${\mathbb{Q}}$-Gorenstein). Then $\mathrm{lct}({\mathfrak{m}})=-a(R)$ if and only if $R$ is quasi-Gorenstein.
Since (1) follows from Remark \[rem:graded char0\], Lemma \[lem:dbt basic\] (2) and Proposition \[prop:dbt=-a\], we will show (2). Let $x \in X$ be the closed point corresponding to ${\mathfrak{m}}$. If $\mathrm{lct}({\mathfrak{m}})=-a(R)$, then $\mathrm{lct}_x({\mathfrak{m}})$ has to be equal to $\mathrm{d}_x({\mathfrak{m}})$ by Remark \[rem:graded char0\], Lemma \[lem:dbt basic\] (2) and Proposition \[prop:dbt=-a\] again. It follows from Theorem \[thm:lc\] that $X$ is quasi-Gorenstein at $x$, which is equivalent to saying that $R$ is quasi-Gorenstein.
Next we will show the “if" part of (2). Suppose that $R$ is quasi-Gorenstein. Let $\phi \colon Y \to X$ be the blow-up of $X=\Spec R$ at ${\mathfrak{m}}$ and $E=\Proj R$ be its exceptional divisor. Note that $Y$ is normal and quasi-Gorenstein. It is easy to see that $K_{Y/X}=-(1+a(R))E$, see, for example, the proof of [@SS Proposition 5.4]. Take a log resolution $\psi \colon \widetilde{X} \to Y$ of $(Y, E)$, and then $$K_{\widetilde{X}/X}+a(R)\psi^*E=K_{\widetilde{X}/Y}+\psi^*(K_{Y/X}+a(R)E)=K_{\widetilde{X}/Y}-\psi^*E.$$ Since $X$ has only log canonical singularities, $E$ has also only log canonical singularities. It follows from inversion of adjunction for log canonical pairs [@Ka] that $(Y, E)$ is log canonical, which implies that all the coefficients of the divisor $K_{\widetilde{X}/Y}-\psi^*E$ are greater than or equal to $-1$. Thus, $(X, {\mathfrak{m}}^{-a(R)})$ is log canonical, that is, $\mathrm{lct}({\mathfrak{m}}) \ge -a(R)$.
Let $(R, {\mathfrak{m}})$ be the same as in Corollary \[cor:char 0 main thm\]. If $X=\Spec R$ is ${\mathbb{Q}}$-Gorenstein, then we can show that $\mathrm{lct}({\mathfrak{m}}) \le -a_i(R)$ for all $i$ (see the paragraph preceding Proposition \[prop:a\_i\] for the definition of $a_i(R)$). The proof is as follows.
We may assume that $i \ge 2$. Let $\varphi\colon Y \to X$ be the blow-up of $X$ at ${\mathfrak{m}}$ and $Z=\Proj R$ be its exceptional divisor. Since $R$ is a normal standard graded ring, there exists a very ample divisor $H$ on $Z$ such that $R=\bigoplus_{n \ge 0} H^0(Z, {\mathcal{O}}_Z(n H))$ and $rK_Z \sim aH$ for some $a \in {\mathbb{Z}}$, where $r$ is the Gorenstein index of $R$. We see by the same argument as the proof of [@SS Proposition 5.4] that $K_{Y/X}=-(1+a/r)Z$, which implies that $\mathrm{lct}({\mathfrak{m}})$ has to be less than or equal to $-a/r$. Therefore, in order to prove the inequality $\mathrm{lct}({\mathfrak{m}}) \le -a_i(R)$, it suffices to show that $-a/r \le -a_i(R)$. This condition is equivalent to saying that if $\ell$ is an integer greater than $a/r$, then $H^{i-1}(Z, {\mathcal{O}}_Z(\ell H))=0$, because $$a_i(R)=\max\{\ell \in {\mathbb{Z}}\mid H^{i-1}(Z, {\mathcal{O}}_Z(\ell H)) \ne 0\}.$$ However, since $\ell H-K_Z \sim_{{\mathbb{Q}}} (\ell-a/r)H$ is ample, this is immediate from [@Fu Theorem 1.7].
When the ring is toric, we have a similar characterization in the non-standard graded case:
Let the notation be the same as in Corollary \[cor:toric charp\]. Let $R=k[\sigma^{\vee} \cap M]$ be an affine semigroup ring over a field $k$ of characteristic zero, defined by a strongly convex rational polyhedral cone $\sigma$. Let ${\mathfrak{m}}$ be the unique monomial maximal ideal of $R$.
1. Then $\mathrm{d}({\mathfrak{m}})=-a_{\sigma}(R)$.
2. $\mathrm{lct}({\mathfrak{m}})=-a_{\sigma}(R)$ if and only if $R$ is Gorenstein.
It follows from the existence of a toric log resolution of ${\mathfrak{m}}$ that $\mathcal{J}'({\mathfrak{m}}^t)$ and $\mathcal{I}(\omega_X, {\mathfrak{m}}^t)$ are torus-invariant, and so $\mathrm{lct}({\mathfrak{m}})$ and $\mathrm{d}({\mathfrak{m}})$ are preserved under base field extension. Thus, we may assume that $k$ is algebraically closed.
Since (2) follows from (1), Remark \[rem:graded char0\], and Corollary \[cor:log terminal\], it remains to justify (1). For this, use the same strategy as the proof of Corollary \[cor:toric charp\], in which case the assertion follows from [@Bl Theorem 2] and Lemma \[lem:dbt basic\] (1).
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Claiborne & Barron Head 2011 Bronko Nagurski Trophy Finalists
FWAA - Five finalists for the 2011 Bronko Nagurski Trophy were announced on Thursday by the Football Writers Association of America and the Charlotte Touchdown Club. Alabama safety Mark Barron, LSU cornerback Morris Claiborne, Boston College linebacker Luke Kuechly, Illinois end Whitney Mercilus and Penn State tackle Devon Still are vying for one of the FWAA's highest honors, its National Defensive Player of the Year award. The winner will be announced on Dec. 12 and presented the Bronko Nagurski Trophy at a gala banquet at the Westin Hotel in Charlotte, N.C., where Georgia head coach Mark Richt will be the keynote speaker. In addition, the FWAA and Charlotte Touchdown Club will award the fifth Bronko Nagurski Legends Award, sponsored by Florida East Coast Railway, to Jack Youngblood, a standout end at Florida and a member of the 1970 FWAA All-America team. The FWAA's National Defensive Player of the Year Award is named after Bronko Nagurski, who dominated college football at the University of Minnesota as a bruising fullback and defensive tackle from 1927-29. He could have been an All-American at any position, playing 60 minutes as the best player wherever he lined up.
A look at the five 2011 Bronko Nagurski Trophy finalists, as selected by the FWAA All-America Committee:
Mark Barron, Free Safety, Alabama, 6-2, 218, Sr.
An anchor of a Crimson Tide defense that ranks No. 1 nationally in the four major statistical categories - rush defense, pass defense, total defense and scoring defense. Barron, a 2010 FWAA All-America, has made 57 tackles this season (33 unassisted) for the once-beaten team. Barron has two interceptions and has made four tackles for seven yards in losses. He has five passes broken up and one quarterback hurry. He had an interception and a fumble recovery in a victory at Penn State.
Morris Claiborne, Cornerback, LSU, 6-0, 185, Jr.
One of the stalwarts on a Tiger unit that ranks among the top six teams in college football in rush, pass, scoring and total defense. He has four interceptions with 128 yards in returns and one touchdown. He has made 38 tackles (22 unassisted) and collected one stop for a loss. Claiborne has broken up five passes and has registered one quarterback hurry. In a 19-6 victory over Mississippi State, he intercepted two passes.
Luke Kuechly, Linebacker, Boston College, 6-3, 237, Jr.
He has 168 tackles - 30 more than anyone else in the nation. He has 89 unassisted and 79 assisted tackles. His unassisted total leads the nation. He also has two interceptions, 10 tackles for loss, a pass breakup and two quarterback hurries. He has double-digit tackles in every game this season. He has played in 36 career games and has had double-digit tackles in 33, including 32 in a row. Kuechly was also a Nagurski finalist in 2010.
Whitney Mercilus, End, Illinois, 6-4, 265, Jr.
Illinois started the season 6-0 and Mercilus is one of the big reasons. He ranks fourth in the country in tackles for loss (17.5). Those tackles total 93 yards in losses, of which 12.5 are sacks (82 yards in losses). He has forced seven fumbles to lead the nation. He has six quarterback hurries and one pass breakup for college football's No. 9 team in total defense (288.3 yards per game). Overall, he has made 47 total tackles (24 assisted).
Devon Still, Tackle, Penn State, 6-5, 310, Sr.
Penn State's defense ranks third in points allowed (12.9 per game), trailing only Alabama and LSU. And the Nittany Lions' defense is eighth nationally in yards allowed per game (287.2). Still has been the defensive leader and ranks sixth in the country in tackles for loss (16.5) for 75 yards, of which four are sacks for 34 yards in losses. He has one pass breakup and one forced fumble. He has 53 total tackles (25 assisted).
The Charlotte Touchdown Club is a non-profit organization founded in 1990 for the purpose of promoting high school, collegiate, and professional football in the Charlotte, N.C., region. The club's activities and services focus community attention on the outstanding citizenship, scholarship, sportsmanship, and leadership of area athletes and
The official website of the Charlotte Touchdown Club is www.touchdownclub.com
The Football Writers Association of America, a non-profit organization founded in 1941, consists of more than 1,200 men and women who cover college football for a living. The membership includes journalists, broadcasters and publicists, as well as key executives in all the areas that involve the game. The FWAA works to govern areas that include game day operations, major awards and its annual All-America team.
The Bronko Nagurski Trophy is a member of the National College Football Awards Association (NCFAA). The NCFAA was founded in 1997 as a coalition of the major collegiate football awards to protect, preserve and enhance the integrity, influence and prestige of the game's predominant awards. The NCFAA encourages professionalism and the highest standards for the administration of its member awards and the selection of their candidates and recipients.
For more information, visit the association's official Web site, ncfaa.org * All-time Bronko Nagurski Trophy winners (from touchdownclub.com)
Please Note: More information on the Bronko Nagurski Trophy, including the list of all-time winners and finalists as well as the award's logo and high-resolution photos of the finalists, can be found in the awards section of collegepressbox.com, the official media website of the NCFAA. http://www.collegepressbox.com/media/awards/nagurski/index.html
Frank Coyle is a long time member of the FWAA and voter in College player awards - Heisman, Outland, Nagurski, Thorpe etc for the past 18 years. He writes College Football Mondays weekly during the season. He is a longtime scouting consultant for the Senior Bowl, the nation’s premier postseason All-star game.
Frank Coyle is a nationally known football scout who publishes Draft Insiders' Digest. In its 26th season, DraftInsiders.com is a website and publication dedicated to the coverage of NFL and NCAA Football. | tomekkorbak/pile-curse-small | Pile-CC |
I think this is a great juxtaposition to the cute, comedic 'Love Stage'. It's a bit unfortunate (as far as garnering readers) that it's a novel (the person above seems confused--it's a novel series with a couple of very short manga one-shots), because many people might skip it or not be able to get into it as much, but really it's worth it. I loved Rei's character as a non-stereotypical uke guy who didn't take his position in bed as a threat to his masculinity, who hit up Shougo for sex if he wanted it and didn't spend his time being all flaily and blushy--and while I still respect him for that, you see a different side to him in the novels that isn't pretty at all and left me feeling so heartbroken for Shougo, to the extent that now I feel like I want to cheer him on in his efforts :3
It's also got WAY more sex (well, Love Stage has no sex so far XD; so ANY sex is more sex) than Love Stage and is *fans self* super hot! Definitely a good recc <3333 | tomekkorbak/pile-curse-small | Pile-CC |
The mysterious third client of President Trump’s embattled personal lawyer Michael Cohen was revealed Monday as Fox News host Sean Hannity.
Cohen was ordered to appear in court by Judge Kimba Wood and cough up Hannity’s name as part of the investigation into $130,000 in hush money Cohen paid to porn star Stormy Daniels, who allegedly had an affair with Trump in 2006.
Cohen fought against having to reveal the confidential list — all of three clients — as part of a bid to block the feds from reviewing documents that could be protected under attorney-client privilege.
His lawyer Steve Ryan argued — in vain — that the unnamed third client is a “publicly prominent individual” who didn’t want to be associated with the ongoing investigation into Cohen’s business dealings.
“Mr. Cohen has asserted that he has more attorneys of his own than he has clients,” said prosecutor Thomas McKay.
McKay reiterated that feds are probing Cohen’s personal and financial dealings going back to 2011 — not his legal work.
“Michael Cohen might have a legal degree,” McKay said. But the government’s probe “is largely formed on his financial dealings and personal dealings.”
On Twitter, Hannity denied he was ever Cohen’s client.
“Michael Cohen has never represented me in any matter. I never retained him, received an invoice, or paid legal fees,” the pundit wrote. “I have occasionally had brief discussions with him about legal questions about which I wanted his input and perspective.”
“I assumed those conversations were confidential, but to be absolutely clear they never involved any matter between me and a third-party,” he added in another tweet.
On his daily afternoon radio show, Hannity said that he’s known “Michael a very long time.”
“Michael would very generously give me his time,” Hannity explained. “How did this blow up to be such a big deal?”
Last week, the FBI raided Cohen’s law office and home related to the payment he made to Daniels.
Cohen’s lawyers argued for a “special master” to determine which of the documents seized might be protected by attorney-client privilege.
“Yes, I believe obviously the issues of greatest importance relate to the president of the United States,” said Ryan.
Meanwhile, Trump attorney Joanna Hendon said the president is “objecting to anyone but himself making the initial determination of [attorney-client] privilege.”
“How much time can your client devote to this matter?” Wood asked dryly, prompting chuckles from the gallery.
Last week, it was also revealed that Cohen represented Republican National Committee fundraiser Elliott Broidy — who resigned from his post after admitting that the lawyer had arranged a $1.6 million payment to a former Playboy model whom he had impregnated. | tomekkorbak/pile-curse-small | OpenWebText2 |
Academic calendar and deadlines
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Your academic advisor will be your guide to UAF, connecting you with your program and helping you find the tools you need to succeed. The Academic Advising Center provides advising for General Studies (undecided), exploring possible majors learning outcomes of each major.
Policies
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The University of Alaska Fairbanks is an affirmative action/equal opportunity employer and educational institution and is a part of the University of Alaska system. UAF does not discriminate on the basis of race, color, creed, national origin, religion, age, sex, sexual orientation, gender identity, veteran status, physical or mental disability, marital status, changes in marital status, pregnancy or parenthood, genetic code or retaliation. This policy affects employment policies, as well as the delivery of educational services. Contact information, applicable laws, and complaint procedures are included on UAF's statement of non-discrimination. Photos by UAF photographers unless otherwise noted. | tomekkorbak/pile-curse-small | Pile-CC |
10 Gorgeous Buildings Made Out of Books
(Emily Temple) Here at Flavorpill, we’re pretty big book nerds. We’re such big book nerds that what we’d really like, more than anything, is to live in a house made of books — we think it’d totally work as long as we weren’t reading one from the ceiling when it started to rain. Plus, we’ve been known to appreciate books as much — or almost as much — for their aesthetic qualities as for their intellectual ones, so it only makes sense to use them as the grandest form of decor.
Therefore, we bring you our wish list of buildings made out of books that we’d really like to live (or play) in. Click through to check them out, and let us know which one you think would be best to house you, your cozy armchair and a cup of tea. | tomekkorbak/pile-curse-small | Pile-CC |
Coastal Carolina University has become aware of further activity in an unauthorized solicitation involving the sale of ads for a baseball poster or program that was first reported last week.
Please be advised that this is a promotion by a private for-profit company with no ties to CCU. Anyone who has questions about CCU athletic promotions may contact Matt Hogue, associate vice president for marketing, at 843-349-2809 or Mark Payne, senior associate athletic director for external relations, at 843-349-2771. | tomekkorbak/pile-curse-small | Pile-CC |
Q:
Enumerable LINQ extensions are hidden on strings... why and how?
Possible Duplicate:
Why doesn’t VS 2008 display extension methods in Intellisense for String class
Hi all.
Yesterday I noticed that Enumerable LINQ exstensions are hidden on strings (I mean hidden from the intellisense).
We all know string is an IEnumerable<char>, so automatically it should get Enumerable extensions, and actually compiles and works if you use them, but why .NET developers decided to hide them from intellisense?
And lastly, how we can hide extension methods from a specific type ?
P.S.
sorry for my poor english...
EDIT:
I forgot to say I'm targeting .net 3.5 on VS 2008
EDIT2:
Here 2 images of what happen:
Intellisense on string:
Intellisense on string http://img690.imageshack.us/img690/10/stringintelli.png
Intellisense on IEnumerable:
A:
When I have a string s and type s. I do get all the extensions methods (like FirstOrDefault etc).
I checked with VS2010 Express.
You should of course have the static class System.Linq.Enumerable in scope.
As for the How part, I guess that something like this attribute was used on String. But clearing the "Hide advanced" option for C# brought no change, so it is not exactly this attribute but something similar.
As for the Why part, no idea. But interesting that it was changed for Fx4
| tomekkorbak/pile-curse-small | StackExchange |
Nebraska Supreme Court Online Library
www.nebraska.gov/apps-courts-epub/
01/05/2018 08:13 AM CST
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Nebraska Supreme Court A dvance Sheets
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NADEEM v. STATE
Cite as 298 Neb. 329
Mohammed Nadeem, appellant, v.
State of Nebraska, appellee.
___ N.W.2d ___
Filed December 8, 2017. No. S-16-113.
1. Motions to Dismiss: Pleadings: Appeal and Error. An appellate court
reviews a district court’s order granting a motion to dismiss de novo,
accepting all allegations in the complaint as true and drawing all reason-
able inferences in favor of the nonmoving party.
2. Motions to Dismiss: Pleadings. For purposes of a motion to dismiss, a
court may consider some materials that are part of the public record or
do not contradict the complaint, as well as materials that are necessarily
embraced by the pleadings.
3. Pleadings: Complaints. Documents embraced by the pleadings are
materials alleged in a complaint and whose authenticity no party ques-
tions, but which are not physically attached to the pleadings.
4. ____: ____. Documents embraced by the complaint are not considered
matters outside the pleadings.
5. Res Judicata: Judgments. Res judicata bars relitigation of any right,
fact, or matter directly addressed or necessarily included in a former
adjudication if (1) the former judgment was rendered by a court of com-
petent jurisdiction, (2) the former judgment was a final judgment, (3)
the former judgment was on the merits, and (4) the same parties or their
privies were involved in both actions.
6. Convictions: Claims: Pleadings. Under Neb. Rev. Stat. § 29-4603
(Reissue 2016), a party alleging a wrongful conviction claim must plead
(1) conviction and sentence for a felony for which the party has served
at least part of the sentence; (2) pardon, vacation of the conviction, or
reversal and remand without a resulting retrial and conviction; (3) actual
innocence of the crime; and (4) that the plaintiff did not commit or sub-
orn perjury, fabricate evidence, or otherwise make a false statement to
cause or bring about such conviction or the conviction of another, except
for coerced confessions or guilty pleas.
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NADEEM v. STATE
Cite as 298 Neb. 329
7. Sentences: Words and Phrases. Legal innocence is defined as the
absence of one or more procedural or legal bases to support the sentence
given to a defendant.
8. ____: ____. Actual innocence refers to the absence of facts that are pre-
requisites for the sentence given to a defendant.
9. Actions: Complaints. In determining whether a complaint states a
cause of action, a court is free to ignore legal conclusions, unsupported
conclusions, unwarranted inferences, and sweeping legal conclusions
cast in the form of factual allegations.
Petition for further review from the Court of Appeals, Pirtle,
Bishop, and A rterburn, Judges, on appeal thereto from the
District Court for Lancaster County, Robert R. Otte, Judge.
Judgment of Court of Appeals reversed, and cause remanded
with directions.
Jeffry D. Patterson for appellant.
Douglas J. Peterson, Attorney General, and Ryan S. Post
for appellee.
Heavican, C.J., Miller-Lerman, Cassel, Stacy, K elch, and
Funke, JJ.
K elch, J.
INTRODUCTION
Mohammed Nadeem filed a claim against the State for
damages under the Nebraska Claims for Wrongful Conviction
and Imprisonment Act.1 The district court granted the State’s
motion to dismiss under Neb. Ct. R. Pldg. § 6-1112(b)(6) for
failure to state a claim. Nadeem appealed to the Nebraska
Court of Appeals, which reversed the district court’s dis
missal.2 We granted the State’s petition for further review.
Because Nadeem has not sufficiently pled a claim of actual
innocence, we reverse, and remand to the Court of Appeals
with directions to affirm the order of the district court.
1
Neb. Rev. Stat. §§ 29-4601 to 29-4608 (Reissue 2016).
2
Nadeem v. State, 24 Neb. App. 825, 899 N.W.2d 635 (2017).
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NADEEM v. STATE
Cite as 298 Neb. 329
FACTS
Background
Nadeem was convicted in 2010 of attempted first degree
sexual assault and attempted third degree sexual assault of
H.K., a minor. These offenses were based on an encounter that
Nadeem had with a 14-year-old girl in 2009 when he was 22
years old. The evidence presented at Nadeem’s criminal trial is
summarized in his original direct appeal,3 but the facts accord-
ing to Nadeem’s complaint are summarized below.
In 2009, Nadeem met a 14-year-old girl in a public library
and engaged in conversation with her. Nadeem asked the girl
questions such as how old she was, where she went to school,
and whether she had a boyfriend. The girl told Nadeem that
she was not allowed to give out her telephone number. Nadeem
asked the girl if he could give her his telephone number, and
she said, “‘I guess.’” Nadeem wrote down his telephone num-
ber for her and told her that he hoped she would call.
When the girl told her mother about her interaction with
Nadeem, the mother became very upset. She complained to the
head librarian, who suggested that she call the police.
The girl’s mother did call the police, and the next day, inves-
tigators invited the girl and her mother into their headquarters
for recorded interviews. The investigators then had the girl
make a recorded “‘controlled call’” to Nadeem, instructing the
girl on what to say and how to respond to Nadeem. According
to Nadeem, the purpose of the call was to induce him into a
conversation with the girl that involved sexual content. The
officers instructed the girl to tell Nadeem to meet her at the
library and to bring a condom. Nadeem went to the library as
requested, but did not bring a condom. Police met Nadeem
there and arrested him.
Nadeem’s convictions for attempted first degree sexual
assault and attempted third degree sexual assault of a minor
3
State v. Nadeem, 19 Neb. App. 565, 809 N.W.2d 825 (2012), reversed 284
Neb. 513, 822 N.W.2d 372.
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NADEEM v. STATE
Cite as 298 Neb. 329
were ultimately vacated by the Court of Appeals.4 Although
the Court of Appeals rejected Nadeem’s argument that there
was insufficient evidence to sustain his convictions, it reversed
Nadeem’s convictions and remanded the cause for a new trial
based on ineffective assistance of counsel and based on the
denial of a jury instruction for the defense of entrapment.5
The State sought further review with this court in 2013,
which we denied. During that time, Nadeem completed his
prison sentence.
Wrongful Conviction Claim
In 2015, Nadeem filed a claim against the State for com-
pensation under the Nebraska Claims for Wrongful Conviction
and Imprisonment Act, which claims are filed under the State
Tort Claims Act.6 In part of Nadeem’s complaint, he alleged
that he had been entrapped. The State then filed a motion to
dismiss Nadeem’s claim, arguing that the affirmative defense
of entrapment is legally insufficient to show actual innocence
(as opposed to legal innocence), which is a required element
of a wrongful conviction claim.7 The district court granted the
motion, and Nadeem appealed.
The Court of Appeals determined that the district court
erred in granting the State’s motion to dismiss. The major-
ity did not consider whether the defense of entrapment was
legally sufficient to show actual innocence. Instead, it noted
that Nebraska has a notice pleading system and stated, “[T]he
only issue we must decide is whether Nadeem sufficiently
alleges that he was [actually] innocent of attempted first
degree sexual assault.”8 Because his conviction was for an
4
State v. Nadeem, No. A-10-981, 2013 WL 674158 (Neb. App. Feb. 26,
2013) (selected for posting to court website).
5
Id.
6
See § 29-4607.
7
See Nadeem v. State, supra note 2.
8
Id. at 831, 899 N.W.2d at 639.
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Cite as 298 Neb. 329
attempted crime, the question was whether he “intention-
ally engaged in conduct which constituted a substantial step
toward” the completed crime.9 The Court of Appeals con-
cluded that because, “[i]n his complaint, Nadeem alleged that
he did not have the requisite intent to commit the alleged
crime and did not take a substantial step toward committing
that crime,” he had made sufficient factual allegations to
defeat the State’s motion to dismiss.10
The State’s petition for further review contends, among
other things, that the Court of Appeals failed to consider its
prior opinion in the criminal case, which Nadeem referenced
in his complaint. Relevant to this contention, the Court of
Appeals said:
We acknowledge that in this court’s previous
opinion,[11] we specifically found that the evidence pre-
sented at Nadeem’s criminal trial was sufficient to sus-
tain his convictions for attempted first degree sexual
assault and for attempted third degree sexual assault.
However, in the current appeal, we are analyzing only
whether the allegations in Nadeem’s complaint are suf-
ficient to state a cause of action under the [Nebraska
Claims for Wrongful Conviction and Imprisonment] Act.
As such, we are confined to review only the specific
allegations in Nadeem’s complaint. We cannot look to
evidence outside of the pleadings which may or may
not be presented at a subsequent phase of these proceed-
ings. We also cannot assess the nature and quality of the
evidence presented in past proceedings to predict the
outcome of this action.12
9
Id. at 832, 899 N.W.2d at 639.
10
Id. at 833, 899 N.W.2d at 640.
11
State v. Nadeem, supra note 4.
12
Nadeem v. State, supra note 2, 24 Neb. App. at 832-33, 899 N.W.2d at
640.
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NADEEM v. STATE
Cite as 298 Neb. 329
ASSIGNMENTS OF ERROR
The State assigns that the Court of Appeals erred (1) in con-
cluding that it was confined to review only the specific alle-
gations in the complaint and (2) by not affirming the district
court’s dismissal of the complaint.
STANDARD OF REVIEW
[1] We review a district court’s order granting a motion to
dismiss de novo, accepting all allegations in the complaint
as true and drawing all reasonable inferences in favor of the
nonmoving party.13
ANALYSIS
Whether Court of A ppeals Erred in
Not Considering Its Prior Opinion
The State first argues that the Court of Appeals erred in con-
cluding that it was limited to looking at the face of Nadeem’s
complaint and could not look to its prior opinion, which the
court viewed as “evidence outside of the pleadings.”14 The
State argues that the prior opinion is not outside the pleadings
because it was “necessarily embraced by the complaint.”15
In support of its argument, the State cites DMK Biodiesel
v. McCoy.16
[2-4] In DMK Biodiesel, we held that for purposes of a
motion to dismiss, a court may consider some materials that
are part of the public record or do not contradict the com-
plaint, as well as materials that are necessarily embraced by
the pleadings. We explained that documents embraced by
the pleadings are materials alleged in a complaint and whose
authenticity no party questions, but which are not physically
13
Davis v. State, 297 Neb. 955, 902 N.W.2d 165 (2017).
14
Nadeem v. State, supra note 2, 24 Neb. App. at 833, 899 N.W.2d at 640.
15
Memorandum brief for appellee in support of petition for further review
at 4.
16
DMK Biodiesel v. McCoy, 285 Neb. 974, 830 N.W.2d 490 (2013).
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Cite as 298 Neb. 329
attached to the pleadings.17 These documents are “not consid-
ered matters outside the pleadings.”18
We agree with the State that the Court of Appeals’ prior
opinion is “embraced by the complaint.” In Nadeem’s com-
plaint, he cites to the Court of Appeals’ 2013 opinion and
refers to numerous statements made by the court in that opin-
ion. Further, no party questions the authenticity of the opin-
ion. Thus, to the extent that the Court of Appeals suggested
that it could not consider the opinion in determining whether
Nadeem’s complaint sufficiently alleged facts to state a cause
of action, it was in error. However, as will be explained below,
only limited portions of the opinion by the Court of Appeals
are relevant to the matter before us.
Whether Court of A ppeals Erred in R eversing
District Court’s Dismissal
We next address the State’s argument that the Court of
Appeals erred in not affirming the district court’s dismissal
because the “facts [from the Court Appeals’ prior opinion]
show Nadeem cannot . . . establish his actual innocence.”19
[5] Although the Court of Appeals could have considered
its prior opinion, wherein it found that there was sufficient
evidence to sustain Nadeem’s conviction, the prior opinion
does not necessarily preclude Nadeem from alleging actual
innocence under § 29-4603(3),20 since his vacated conviction
does not have any res judicata effect on his current claim. Res
judicata bars relitigation of any right, fact, or matter directly
addressed or necessarily included in a former adjudication if
(1) the former judgment was rendered by a court of competent
17
See id.
18
Id. at 980, 830 N.W.2d at 496.
19
Memorandum brief for appellee in support of petition for further review
at 5.
20
See Neb. Rev. Stat. § 29-4603(3) (Reissue 2016) (that “he or she was
innocent of the crime or crimes”).
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jurisdiction, (2) the former judgment was a final judgment,
(3) the former judgment was on the merits, and (4) the same
parties or their privies were involved in both actions.21 Here,
although a final judgment was entered by the jury, the judg-
ment has since been vacated and has thus been deprived of its
conclusive character.22
The relevant issue at this stage of the litigation is whether
Nadeem’s complaint sufficiently placed the State on notice
of his wrongful conviction claim by setting forth “a short
and plain statement of the claim” showing that he is entitled
to relief.23
[6] Under § 29-4603, a party alleging a wrongful convic-
tion claim must plead (1) conviction and sentence for a felony
for which the party has served at least part of the sentence;
(2) pardon, vacation of the conviction, or reversal and remand
without a resulting retrial and conviction; (3) actual inno-
cence of the crime; and (4) that the plaintiff “did not com-
mit or suborn perjury, fabricate evidence, or otherwise make
a false statement to cause or bring about such conviction or
the conviction of another,” except for coerced confessions or
guilty pleas.
The State does not dispute that Nadeem sufficiently alleged
that he was convicted of and sentenced for a felony and
served at least part of the sentence, that the conviction was
vacated and the cause remanded without a resulting retrial
and conviction, and that he did not commit or suborn perjury
or fabricate evidence. However, the State does argue that
Nadeem has not sufficiently alleged facts to support a finding
of actual innocence.
21
State on behalf of Hopkins v. Batt, 253 Neb. 852, 573 N.W.2d 425 (1998).
22
See 50 C.J.S. Judgments § 958 at 282 (2009) (“[a]s a general rule, when a
judgment has been reversed on appeal, or vacated or set aside by the court
which rendered it, it is deprived of its conclusive character . . .”).
23
See Neb. Ct. R. Pldg. § 6-1108(a).
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Cite as 298 Neb. 329
[7,8] First, in Hess v. State,24 we delineated two distinct
definitions of innocence—legal and actual. Legal innocence
is defined as “‘[t]he absence of one or more procedural or
legal bases to support the sentence given to a defendant,’”25
whereas actual innocence refers to “‘[t]he absence of facts that
are prerequisites for the sentence given to a defendant.’”26 In
other words, actual innocence means that a defendant did not
commit the crime for which he or she is charged.27 Or, as the
U.S. Supreme Court has explained, “A prototypical example
of ‘actual innocence’ in a colloquial sense is the case where
the State has convicted the wrong person of the crime.”28
Accordingly, a defendant must plead more than lack of intent
to establish actual innocence.
[9] In determining whether a complaint states a cause of
action, we are free to ignore legal conclusions, unsupported
conclusions, unwarranted inferences, and sweeping legal con-
clusions cast in the form of factual allegations.29 Several of
the allegations in Nadeem’s complaint contain quotations
from the Court of Appeals’ opinion, wherein the Court of
Appeals evaluated the evidence from Nadeem’s criminal trial.
These are not factual allegations, but conclusions drawn by
the Court of Appeals from evidence presented at Nadeem’s
criminal trial, and thus, we do not consider them when evalu-
ating his complaint.
In addition, several of the allegations in Nadeem’s complaint
contain conclusory phrases, such as “hysterical speculation
24
Hess v. State, 287 Neb. 559, 843 N.W.2d 648 (2014).
25
Id. at 563, 843 N.W.2d at 653 (quoting Black’s Law Dictionary 859 (9th
ed. 2009)).
26
Id.
27
Hess v. State, supra note 24.
28
Sawyer v. Whitley, 505 U.S. 333, 340, 112 S. Ct. 2514, 120 L. Ed. 2d 269
(1992).
29
Kellogg v. Nebraska Dept. of Corr. Servs., 269 Neb. 40, 690 N.W.2d 574
(2005).
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and overreaction,” “entirely innocent,” “complete absence of
any evidence,” and “could not possibly be ‘ready and will-
ing.’” In evaluating Nadeem’s complaint, we do not consider
the information imparted by these unsupported conclusions.
Nadeem’s complaint does set forth that “[o]n August 6,
2009, . . . Nadeem engaged [H.K.] in an innocent conversation
while she was sitting in an open, public area of [a] Library.”
But after reviewing Nadeem’s entire complaint and the Court
of Appeals’ opinion, we discern that Nadeem’s reference to
the August 6 encounter clearly describes only the initial con-
tact Nadeem had with H.K. His complaint does not set forth
how his later telephone conversation with H.K. or his going
to meet H.K. at the library for a second time would reflect his
actual innocence.
Excluding from Nadeem’s complaint conclusions drawn by
the Court of Appeals and his own conclusory allegations, his
complaint does not allege an absence of facts which reflects
his actual innocence as we required in Hess.30 Even after draw-
ing all reasonable inferences of law and fact from Nadeem’s
pleadings in his favor, we find Nadeem has not sufficiently
pled a claim of actual innocence.
CONCLUSION
For the reasons set forth above, we reverse the decision of
the Court of Appeals that reversed the district court’s order
dismissing Nadeem’s complaint and remand the cause to the
Court of Appeals with directions to affirm the order of the
district court.
R eversed and remanded with directions.
Wright, J., not participating.
30
Hess v. State, supra note 24.
| tomekkorbak/pile-curse-small | FreeLaw |
The following is an excerpt from an incredibly detailed, 173 page paper titled “Embryology in the Qur’an: Much Ado about Nothing” authored by Captaindisguise who specialises in countering Islamic apologetics, Martin Taverville who also specialises in countering Islamic apologetics who has also authored other papers. 3 Saudi Arabians also contributed to the paper named “GodlessSaudi”, “AntiGoebbels” and “AtheistGhost”. It is a response paper to a pro-Quranic embryology paper by a man named Hamza Tzortis. Because of this paper, Hamza retracted his paper and urged muslims to stop promoting the “scientific miracles in the Quran” myth. All credit goes to them. The full study can be read here.
.
Sura 86:6-7 – Origin of semen between Backbone and Ribs
.
Sura 86 verses 6 to 7 from the Qur’an are very popular among the critics of Islam. Especially for those oriented with a scientific mindset, these verses would count as a factual error in the “holy text” of Quran. The verses state the following:
.
Transliteration: Khuliqa min ma’in dhafiqin yakhruju min bayni al-sulbi wa al-taraib
Translation: “He was created from a fluid (ma’in), ejected, Emerging from between the backbone and the ribs.”
.
At first sight, the verse seems to suggest that the substance from which humans are created originates from the backbone. This was also a commonly held view during ancient times as it can be observed in the teaching of Hippocrates who described the origin of semen in the brain which subsequently descends through “the spine to the sex organs”;[1]
Due to the fact that this has been a very common criticism of the veracity of the Qur’an, Hamza Tzortzis does address this contention in his paper. The following is his response,[2]
While there is a nugget of truth in Hamza’s rebuttal, he seems to have missed the larger picture of the criticism, all the while engaging in his usual academically dishonest tactics. The two keywords that need examination are “sulb” (translated as backbone) and “tara’ib” (translated as ribs). Beginning with “sulb”, Hamza’s defense of this word seems to be that it can also mean “the loins” and that “it is well known that the sperm and semen come from an area referred to as the loins.” There was no surprise in realizing that this too is an absurd assertion.
.
Misrepresenting the Meaning of “sulb”
.
Perhaps Hamza ought to have performed a lexical analysis on the word in question. Here are the relevant meanings given for “sulb” in Lane’s lexicon;[3]
The most accurate definition of this term is that of the backbone. However, does Hamza’s defense using the meaning of “loins” solve the problem for the Qur’an? Certainly not! What Hamza fails to realize or willfully ignores is that “the loins” as “a euphemism for genitalia or sex organs” is the product of the English language and Hamza provides no evidence to suggest that the same euphemism was maintained among the ancient Arabs. In contrast, the primary definition of loins is also provided in the lexicon as “the lumbar portion”. This can also be verified using the Oxford English Dictionary;[4]
The secondary, euphemistic meaning of loins, related to the private parts, is also explained in OED as well as the Online Etymology dictionary as follows.[5] (Note: the year of origin of this euphemism);
This euphemistic definition is explained as a secondary “biblical and poetic” metaphor for one’s private parts and one that originated only in the early 16th century. Thus, it is unreasonable for Hamza to assign a definition, which specifically arose in 16th century English, to an Arabic word used in the 7th century. Interestingly, Lane’s lexicon also provides an account for another metaphorical idea associated with “sulb” among the Arabs;
The lexicon explains the metaphorical idea expressed in the sayings of the Arabs; the origin of which was due to the belief that “the sperma of the man is held to proceed from the “sulb”(i.e. backbone) of the man” and then proceeds to site the contested verse, 86:7 as an example.
The take home point for Hamza or any other apologist is that there is no evidence to suggest that the 16th century English euphemistic meaning of the word “loins” applies to the Arabic “sulb”. An analogy of Hamza’s claim is that of a person looking up the definition of the Arabic term “sa’eed (سعيد)” in a dictionary and finding its meaning as “happy, gay” etc. However, the person then incompetently concludes that the Arabic word “sa’eed (سعيد)” means “homosexual” due to the double meaning of the word “gay” in English. Hamza’s defense is equally ludicrous.
Thus, the realistic and rational definition of “sulb” in the context of the verse 86:7 is certainly that of the “backbone”.
.
Distorting the meaning of “taraib”
.
The next keyword in sura 86:7 that needs examination is “tara’ib” which has been translated as “ribs”. Hamza’s defense for this word is yet again incompetent and deceitful. Hamza states the following,
Hamza’s plan of action is to suggest that “tara’ib” can also mean “the pelvic arch” from which “the ovum comes”. Hamza gives the following source for the meaning of “tara’ib” as “the pelvic arch”,[6]
Taj Al Arus is a 19th century lexicon of Classical Arabic similar to Lisan al-Arab. However rather than providing a direct and proper reference from Taj al-Arus, Hamza points to a footnote of an English translation of the Qur’an authored by a 20th century translator named Muhammad Asad. From the reference given the reader is supposed to understand that Muhammad Asad found the definition of “pelvic arch” in Taj al-Arus.
Now to ask the important question, is Hamza being dishonest again? The answer may not surprise you as it is a “big fat Yes”. The following is the footnote from Muhammad Asad’s translation,[7]
Muhammad Asad, who is certainly a more honest man than Hamza, openly admits that his translation of “pelvic arch” is his own rendering. Asad proceeds to mention the meanings of “tara’ib” as “ribs” and “arch of bones” (very likely referring to rib arches). The reference from Taj al-Arus is given regarding his statement that “tara’ib” refers “to female anatomy” and not to the invented definition of the “pelvic arch” as Hamza would have his readers believe.
Secondly, the assertion that Taj al-Arus defines “tara’ib” as the “pelvic arch” is weakened by Lane’s lexicon which heavily utilizes Taj al-Arus (abbreviated as TA) in its content. The following is the entry for “tara’ib” in Lane’s lexicon;[8]
Lane’s lexicon does not mention the meaning of “the pelvic arch”. Besides what is the purpose of language if two distinct terms in a related field are referred to by the same word. For an analogy, imagine a word such as HamDay which is defined by certain enthusiasts as both Monday and Friday”. What purpose is there for such a word other than to cause confusion? A sentence such as, “My birthday is this Hamday” would always require further clarification and thus would be nonsensical to assume such a word would even exist. Likewise, a word defined as two distinct anatomical parts is nonsensical. Therefore, apart from the fact that Hamza has no evidence for his claim regarding pelvic arches, it would also be unreasonable to think that “taraib” would have such a meaning. With this data in mind, the most sensible understanding of “taraib” would be of “ribs” or “breastbone” etc.
Having displayed a lack of lexical analysis skills with “sulb” and a lack of academic integrity with “taraib”, Hamza delivers yet another mind-bogglingly bad argument in order to vindicate his holy book. Here Hamza begins to assert that even if “sulb” and “taraib” were translated as “backbone” and “ribs” respectively, the Qur’an would not be in error. Hamza states the following,
Hamza also presents the following cartoon-ish “smirk-provoking” diagram, for which no reference was given,
Before analyzing Hamza’s claim, a factual error in his paragraph needs to be addressed. He stated that “semen is made up of sperm”. This is not an accurate representation of the relationship between semen and sperm. Semen should be considered as a vehicle that carries a distinct substance called sperm. Every credible biologist understands and explains semen and sperm as two distinct substances. That being corrected, what is Hamza’s argument here?
His argument attempts to show that semen is mostly produced in the seminal vesicle which, according to Hamza, is between the backbone and the ribs. While the cartoon-ish-image seems exaggerated, Hamza has finally delivered a statement that is not “technically” inaccurate. If one were to generously allow the meaning of “sulb” to extend the tip of the coccygeal bone, then Hamza’s statement would be “technically” accurate since the seminal vesicle is, more or less, in the adjacent area. That being said, Hamza has bought “accuracy” for this verse at the price of maximum ambiguity.
.
Maximum Ambiguity
.
This difficulty is a rather a discreet and nuanced one that would require considering the broader applications of Hamza’s reasoning. Ignoring whether the “fluid” (ma’in) mentioned in sura 86:6-7 is sperm (in a fluid as of version 2.1b) or semen, Hamza would still have to answer the consequences of the logical extension of his explanation for the alleged error in the verse.
What was Hamza’s alternative explanation for the alleged error in the verse if his pelvic arch and loin defenses were rejected? He stated that the semen is produced in the seminal vesicle which, according to Hamza, is between the “ribs” and the “backbone”. Of course, for this to be true, it is necessary to define the backbone as extending to coccyx (or tail bone) where the seminal vesicle is found in the nearby area. Yet if one is allowed to extend the definition of backbone to reach its very bottom, one could also define it to reach the very top i.e. the vertebrae extending into the skull. Similarly, the ribs can be defined as extending from the very top pair to the very bottom pair.
What is the consequence of this? It ultimately allows one to interpret the following words in Sura 86:6-7, “between the backbone and the ribs” as referring to the area encompassing the entire viscera of the human body. Below is a graphical representation of this point.[9]
Given the importance placed on semantics in Islamic apologetics, an apologist could also make the claim that the area “between backbone and ribs” can include the brain as well as the testicles the same way one can think of one’s head as situated between the two shoulders. However, what are the consequences of such reasoning? Would Islamic apologists be able to accurately claim that their verse (86:6-7) is factually correct? The answer is “technically” yes. However, the apologists would be buying the security of their “technical” accuracy at a price far more damaging to the veracity of their holy book. This is because of the principle of ‘maximum ambiguity”.
What is maximum ambiguity? Bertrand Russell, the celebrated philosopher and historian, once said, “I propose to prove that all language is vague, and that therefore my language is vague.”[10] Ambiguity of a sentence or a paragraph or an essay or a book maybe described mathematically as the amount of “vagueness” expressed in the language. The principle of maximum ambiguity states that if the language used in a statement allows for every practically possible interpretation to be accurate, then the language used is maximally ambiguous. This is to say that the language has attained the greatest possible level of ambiguity i.e. it would be impossible for anyone to make it more ambiguous and unspecific. The following is a concrete example involving mathematics. Imagine a student named Hamzter taking a math test in his class. He glances over the first question which is as follows,
The correct answer to this question is that out of 7 billion people, six billion, nine hundred and ninety-three million will burn in hell according to Prophet Muhammad (peace and blessings upon him and the 0.1% elite heaven-dwellers).
However is this, the only correct answer that could have been given to this question? What if Hamzter answered by saying, “it is a very big number”? This would be “technically” correct as well. What if Hamzter answered it is “a number between 0 and 7 billion”? This would also be “technically” correct.
What if Hamzter answered every question on the test with the following words, “some number”? Would Hamzter have given a correct answer to all the questions? Yes. Is there any reasonable teacher who would give this student an A+ on this test? Absolutely not! Along with accuracy, it is also important to have “precision”. Hence the teacher would grade the test with a 0 due to the absence of precision which is just as important as accuracy.
How does this relate to sura 86:6-7? If one were to logically extend Hamza’s reasoning in his defense of the verse’s veracity, the words “between the backbone and ribs” would necessarily encompass the entire human viscera including the brain and the testicles. If Hamza’s reasoning is considered valid then the Qur’an’s verse is a maximally ambiguous statement due to the fact that the Qur’an would be effectively saying that “the part of the body that produces semen is located in the body.” This statement would encompass every logically possible answer to the question of semen or sperm production. Consequently, that quranic verse would also be graded with a zero for the absolute lack of precision.
.
[1] Bernard, R. W. 1994. The Mysteries of Human Reproduction. Health Research Books. Page 32
[2]. Tzortzis, Hamza 2012. Embryology in the Quran: A Scientific-Linguistic Analysis of Chapter 23. Version 2.1. page 63
[3]. “صلب (sulb)” Edward William Lane. An Arabic-English Lexicon. Librairie Du Liban. 1968. Vol.4, page 1712 http://www.studyquran.org/LaneLexicon/Volume4/00000436.pdf
[4]. “loin, n.” The Oxford English Dictionary. 2nd edition, 1989; online version June 2012. http://www.oed.com/view/Entry/109878; accessed 02 July 2012
[5]. “Loin”. Online Etymology Dictionary. http://www.etymonline.com/index.php?term=loin&allowed_in_frame=0
[6]. Tzortzis, Hamza 2012. Embryology in the Quran: A Scientific-Linguistic Analysis of Chapter 23. Version 2.1. page 79
[7]. Muhammad Asad. The Message of the Qur’an. E-book. Pages 860-861
[8]. “taraib” Edward William Lane. An Arabic-English Lexicon. Librairie Du Liban 1968 Vol 1 page 301 http://www.studyquran.org/LaneLexicon/Volume1/00000338.pdf
[9]. Image acquired from http://www.anatronica.com. accessed 02 July 2012
[10]. Bertrand Russell 1923. Vagueness.http://cscs.umich.edu/~crshalizi/Russell/vagueness | tomekkorbak/pile-curse-small | OpenWebText2 |
After witnessing the Varus killing fields, They were furious and wanted revenge against Arminius and the Cherusci.
Maybe Germs had calculated this?
Or maybe it was an accident?
With the Bructeri out of reach Germanicus set out in pursuit of Arminius, who skillfully led him deeper into the pathless forests.
I feel like I’ve seen this movie before?
At last the Germans halted in a plain and Germanicus sent his cavalry forward against them.
But then of course More Germans appeared like magic from the woods, like Boccacio from behind the curtains in Maria’s bedroom, where they had been hiding for an ambush, and the Roman cavalry was nearly driven into a swamp
Lucky for them, Germanicus thew his legions into the fray and they managed to escape.
And then Germs looked as his watch and said “oh shit lookit the time, I have a thing” and the Romans went back to the Rhine.
He took his legions back on the boats but the other poor fuckers had to march with the Cherusci at their backs.
Caecina had to use a causeway through the marshes built about 2 BC by L. Domitius Ahenobarbus, one of the most distinguished commanders in Germany during the time of Tiberius’ retirement at Rhodes
He was told to WALK QUICKLY.
But he had a slow-moving baggage train, and Arminius was able to easily overtake him and occupy the woods on either side of the causeway.
And this wasn’t Caecina’s only problem.
The causeway itself was in a state of considerable dilapidation and needed repairs before it could be crossed in safety.
In this awkward predicament Caecina made camp and divided his forces, sending some to work on the causeway while others repelled the attacks of the enemy.
By night, the Germans had managed to undo most of the repair work the Romans had done on the causeway.
And the ghost of Varus appeared to Caecina in a dream, beckoning him to destruction in the marshes.
Tacitus: It was a restless night for different reasons, the barbarians in their festivity filling the valleys under the hills and the echoing glens with merry song or savage shouts, while in the Roman camp were flickering fires, broken exclamations, and the men lay scattered along the intrenchments or wandered from tent to tent, wakeful rather than watchful. A ghastly dream appalled the general. He seemed to see Quintilius Varus, covered with blood, rising out of the swamps, and to hear him, as it were, calling to him, but he did not, as he imagined, obey the call; he even repelled his hand, as he stretched it over him.
The next day, the Romans tried to move out but some of the legions got stuck in the mud.
When there was maximum chaos, Arminius charged.
He was hoping for a repeat of his victory over Varus.
But this time his Germans were too eager to grab the loot and by nightfall the surviving Romans had managed to get to dry ground.
But they had lost their tools and tents and first aid kits in the mud,
And the little food they had was covered in blood and slime.
That night a horse broke loose and ran through the camp created a panic among the troops.
Thinking that the Germans had breached the defences, they made a mad rush for the gates.
Caecina tried to stop them, but they wouldn’t listen to orders, they were in full panic mode.
The only thing to stop them from running away was when Caecina threw himself across the opening.
The troops didn’t really want to trample their commander to death – yet – and at last listened to everyone explain it was just a runaway horse.
When calm was restored, Caecina gave the order for a mass sortie that would bring the army to the Rhine.
Whether he could have succeeded if the Germans had adhered to the admirable tactics that Arminius had employed so far must remain doubtful, but fortunately for the Romans a dispute arose between Arminius, who wanted to let the Romans leave their camp and then finish the massacre begun on the previous day, and his uncle, Inglorious Bastard, who argues they should just storm the camp and so save the booty from getting needlessly muddy.
I don’t know about you, Ray, but there’s nothing I hate more than muddy booty.
Unfortunately for the Germans, but fortunately for the Romans, the greed of the Germans was too strong and they attacked the camp.
At first it seemed as if it might succeed, but the legions held firm and began to fight back.
In fact the Romans seem to get excited about it.
Nothing like fighting for your booty.
Or WITH your body.
At last they had the Germans on decent level ground.
The German’s confidence rapidly deserted them and the day ended in a resounding Roman victory.
Arminius himself escaped unscathed, but Inguiomerus was seriously wounded.
Serves him fucking right.
Meanwhile
Back at the Rhine base, rumours were spreading that the Germans had surrounded Caecina and were heading towards the river.
There was a mass panic and many of the people wanted to destroy the bridge over the river.
Only Agrippina, Germanicus’ wife, stopped them.
The stripped down naked and started dancing on the bridge.
Oh wait, maybe I just dreamed that.
Whatever she did, the bridge stayed up, which was lucky for the survivors of Caecina’s legions, as they straggled back, they were greeted by Agrippina on the bridge.
Maybe naked.
She saved lives – but Tibbo wasn’t happy about her efforts.
He already didn’t trust her.
He thought she had an unwomanly interest in the legions and this was just further proof of impatient ambition.
He thought she was trying to build up her popularity with the legions so she could use it against him.
Remember that she is daughter of Julia the Elder, his ex-wife, and Agrippa.
AND she’s the mother of Caligula.
He also felt like by her actions she had undermined HIS authority.
By making it look like she was more powerful than his commanders.
Tacitus says this paranoia was fostered by Sejanus, who was playing his own game.
Tacitus: A woman of heroic spirit, she assumed during those days the duties of a general, and distributed clothes or medicine among the soldiers, as they were destitute or wounded. According to Caius Plinius, the historian of the German wars, (we know him as Pliny The Elder) she stood at the extremity of the bridge, and bestowed praise and thanks on the returning legions. This made a deep impression on the mind of Tiberius. “Such zeal,” he thought, “could not be guileless; it was not against a foreign foe that she was thus courting the soldiers. Generals had nothing left them when a woman went among the companies, attended the standards, ventured on bribery, as though it showed but slight ambition to parade her son in a common soldier’s uniform, and wish him to be called Caesar Caligula. Agrippina had now more power with the armies than officers, than generals. A woman had quelled a mutiny which the sovereign’s name could not check.” All this was inflamed and aggravated by Sejanus, who, with his thorough comprehension of the character of Tiberius, sowed for a distant future hatreds which the emperor might treasure up and might exhibit when fully matured.
Do you know what happened to Pliny the Elder?
Just before he died, Vespasian appointed Pliny fleet commander of the Roman navy.
On August 24, 79, he was stationed at Misenum, at the time of the great eruption of Mount Vesuvius, which destroyed and buried Pompeii and Herculaneum.
He was preparing to cross the Bay of Naples to observe the phenomenon directly when a message arrived from his friend Rectina asking to rescue her and Pomponianus – OMG rectal vagina and pompos anus.
He raced towards them in a fast sailed cutter.
Pliny’s helmsman advised turning back, to which Pliny replied, “Fortune favors the brave; steer to where Pomponianus is.”
He got there, rescued Pomponianus, but they couldn’t find Rectina.
They loaded everyone they could onto the cutter, but the winds were too strong to allow them to leave.
Pliny reassured his party by feasting, bathing, and sleeping while waiting for the wind to abate but finally they had to leave the buildings for fear of collapse and try their luck in the pumice fall.
Pliny sat down and could not get up even with assistance and was left behind.
They found him three days later, covered by the pumice. (very light and porous volcanic rock formed when a gas-rich froth of glassy lava solidifies rapidly)
Just like Pliny, Germs had some problems getting back to the Rhine too.
To lighten to load on his ships, he made two legions get off and walk.
They did okay for a while, until sudden massive storms hit and they got flooded.
Eventually their commander, Vitellius, managed to get most of them to higher ground and the waters receded the next day.
Some historians blame Germs – storms like this were not uncommon at this season, and for not having more ships.
But none of this seems to have hampered his popularity.
Gaul, Spain and Italy all offered to provide him with new weapons, horses and money.
And he dipped into his own pockets to provide them for his men.
And his concern for their welfare seems to have blunted any criticism they may have had of him for his mismanagement.
Tacitus: And that he might also soften the remembrance of the disaster by kindness, he went round to the wounded, applauded the feats of soldier after soldier, examined their wounds, raised the hopes of one, the ambition of another, and the spirits of all by his encouragement and interest, thus strengthening their ardour for himself and for battle.
Officially the campaign was declared a success.
Caecina and two others were awarded Triumphal ornaments.
They got the dress and privileges traditionally granted to a triumphator, without the elaborate triumphal procession through Rome at the head of his troops.
They could wear triumphal dress in public: the corona triumphalis (a gold coronet fashioned in the shape of a laurel wreath with dangling gold ribbons); an ivory baton; the tunica palmata (a tunic embroidered with palm-leaves); and the toga picta (“painted toga”), a toga which was dyed entirely purple with embroidered gold border, a robe believed originally to have been the official dress of the Roman kings.
The only other Romans entitled to wear these garments were the emperor himself, the two Consuls in office and other magistrates when presiding over games.
In addition, a bronze statue of the beneficiary of triumphal honours was erected in the Forum of Augustus.
The beneficiary also had the right to display a further statue of himself in triumphal attire in the vestibule of his own house, which could also be displayed by his descendants.
Tacitus: The title of “father of his country,” which the people had so often thrust on him, Tiberius refused, nor would he allow obedience to be sworn to his enactments, though the Senate voted it, for he said repeatedly that all human things were uncertain, and that the more he had obtained, the more precarious was his position. But he did not thereby create a belief in his patriotism, for he had revived the law of treason, the name of which indeed was known in ancient times, though other matters came under its jurisdiction, such as the betrayal of an army, or seditious stirring up of the people, or, in short, any corrupt act by which a man had impaired “the majesty of the people of Rome.” Deeds only were liable to accusation; words went unpunished.
And Tacitus goes on to explain how accusations of treason became a tactic people used against each other.
But how Tiberius wasn’t ruthless about them – at first:
Tacitus: It will not be uninteresting if I relate in the cases of Falanius and Rubrius, Roman knights of moderate fortune, the first experiments at such accusations, in order to explain the origin of a most terrible scourge, how by Tiberius’s cunning it crept in among us, how subsequently it was checked, finally, how it burst into flame and consumed everything. Against Falanius it was alleged by his accuser that he had admitted among the votaries of Augustus (like a monk or nun), who in every great house were associated into a kind of brotherhood, one Cassius, a buffoon of infamous life, and that he had also in selling his gardens included in the sale a statue of Augustus. Against Rubrius the charge was that he had violated by perjury the divinity of Augustus. When this was known to Tiberius, he wrote to the consuls “that his father had not had a place in heaven decreed to him, that the honour might be turned to the destruction of the citizens. Cassius, the actor, with men of the same profession, used to take part in the games which had been consecrated by his mother to the memory of Augustus. Nor was it contrary to the religion of the State for the emperor’s image, like those of other deities, to be added to a sale of gardens and houses. As to the oath, the thing ought to be considered as if the man had deceived Jupiter. Wrongs done to the gods were the gods’ concern.”
Then there was the incident of Marcellus, proconsul of Bithynia, was accused of treason by his quaestor, Caepio Crispinus – he had placed his own statue above those of the Caesars, and had set the bust of Tiberius on another statue from which he had struck off the head of Augustus. At this the emperor’s wrath blazed forth, and, breaking through his habitual silence, he exclaimed that in such a case he would himself too give his vote openly on oath, that the rest might be under the same obligation. There lingered even then a few signs of expiring freedom. And so Cneius Piso asked, “In what order will you vote, Caesar? If first, I shall know what to follow; if last, I fear that I may differ from you unwillingly.” Tiberius was deeply moved, and repenting of the outburst, all the more because of its thoughtlessness, he quietly allowed the accused to be acquitted of the charges of treason. As for the question of extortion, it was referred to a special commission.
Sounds fairly moderate. | tomekkorbak/pile-curse-small | OpenWebText2 |
---
abstract: 'Generative Adversarial Networks (GANs) were intuitively and attractively explained under the perspective of game theory, wherein two involving parties are a discriminator and a generator. In this game, the task of the discriminator is to discriminate the real and generated (i.e., fake) data, whilst the task of the generator is to generate the fake data that maximally confuses the discriminator. In this paper, we propose a new viewpoint for GANs, which is termed as the *minimizing general loss* viewpoint. This viewpoint shows a connection between the general loss of a classification problem regarding a convex loss function and a $f$-divergence between the true and fake data distributions. Mathematically, we proposed a setting for the classification problem of the true and fake data, wherein we can prove that the general loss of this classification problem is exactly the negative $f$-divergence for a certain convex function $f$. This allows us to interpret the problem of learning the generator for dismissing the $f$-divergence between the true and fake data distributions as that of maximizing the general loss which is equivalent to the min-max problem in GAN if the Logistic loss is used in the classification problem. However, this viewpoint strengthens GANs in two ways. First, it allows us to employ any convex loss function for the discriminator. Second, it suggests that rather than limiting ourselves in NN-based discriminators, we can alternatively utilize other powerful families. Bearing this viewpoint, we then propose using the kernel-based family for discriminators. This family has two appealing features: i) a powerful capacity in classifying non-linear nature data and ii) being convex in the feature space. Using the convexity of this family, we can further develop Fenchel duality to equivalently transform the max-min problem to the max-max dual problem.'
author:
- |
rung Letrung.l@deakin.edu.au\
Centre for Pattern Recognition and Data Analytics, Australia\
u Dinh Nguyen tu.nguyen@deakin.edu.au\
Centre for Pattern Recognition and Data Analytics, Australia\
inh Phung dinh.phung@deakin.edu.au\
Centre for Pattern Recognition and Data Analytics, Australia
title: 'KGAN: How to Break The Minimax Game in GAN'
---
Generative Adversarial Networks, Generative Model, Fenchel Duality, Mini-max Problem.
Introduction\[sec:Introduction\]
================================
Related Background
==================
In this section, we present the related background used in our work. We depart with the introduction of *Fenchel conjugate*, a well-known notation in convex analysis, followed by the introduction of Fourier random feature [@rahimi_recht_nips07_random_feature] which can be used to approximate a shift-invariance and positive semi-definite kernel.
Fenchel Conjugate \[subsec:Fenchel-Conjugate\]
----------------------------------------------
Fourier Random Feature Representation
-------------------------------------
Generative Adversarial Network
------------------------------
Minimal General Loss Networks
=============================
Kernelized Generative Adversarial Networks
==========================================
Theory Related to KGAN \[sec:Theory\]
=====================================
Conclusion\[sec:Conclusion\]
============================
[24]{} \[1\][\#1]{} \[1\][`#1`]{} urlstyle \[1\][doi: \#1]{}
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| tomekkorbak/pile-curse-small | ArXiv |
Fourth Court of Appeals
San Antonio, Texas
JUDGMENT
No. 04-14-00135-CR
Zidney Kirk ZUNIGA,
Appellant
v.
The STATE of Texas,
Appellee
From the 112th Judicial District Court, Sutton County, Texas
Trial Court No. 2180
Honorable Pedro Gomez, Judge Presiding
BEFORE JUSTICE MARION, JUSTICE BARNARD, AND JUSTICE CHAPA
In accordance with this court’s opinion of this date, the trial court’s judgment is
AFFIRMED.
SIGNED October 8, 2014.
_____________________________
Luz Elena D. Chapa, Justice
| tomekkorbak/pile-curse-small | FreeLaw |
William Attewell
William Attewell (; commonly known as Dick Attewell) (12 June 1861 – 11 June 1927) was a cricketer who played for Nottinghamshire County Cricket Club and England. Attewell was a medium pace bowler who was renowned for his extraordinary accuracy and economy. On the many sticky or crumbling pitches encountered in his prime Attewell could get on a great deal of spin so as to always beat the bat, whilst his accuracy would make slogging – the only way to make runs under such conditions – very difficult. He was responsible for the development of "off theory" – bowling wide of the off stump to a packed off-side field to frustrate batsmen on the rapidly improving pitches of the 1890s. At times Attewell was a useful batsman for his county, and he scored 102 against Kent in 1897.
It is true that against the extremely fleet-footed Australian batsmen of his time, Attewell was fairly ineffective. Moreover, with bowlers such as Lohmann and J.T. Hearne available who could do all Attewell could, he had trouble maintaining his place at Test level despite all he did for Nottinghamshire and the Marylebone Cricket Club.
Attewell first played for Nottinghamshire in 1881 as a result of a strike by senior players such as Alfred Shaw and Fred Morley. He bowled very well but did not establish himself until 1884 after Morley had died, when he took 100 wickets for less than thirteen runs each. From then on, Attewell was always in the front rank of English bowlers, and after Shaw dropped out of the Nottinghamshire eleven in early 1887 he became the undisputed leader of the county's attack. His first Ashes tour was modest, partly owing to the dry weather, but he continued improving in England – taking 9 for 23 against Sussex at Trent Bridge in 1886 – and toured Australia again in 1887/1888. He proved deadly in a wet La Niña season in minor games, but had no opportunity of showing his deadliness on a sticky wicket at the highest level because Lohmann and Briggs were so effective. However, Attewell's skill and economy, along with the brilliant batting of Shrewsbury, allowed Nottinghamshire to maintain their position as one of the top counties in first-class county cricket right up to the end of 1892.
Even when Attewell became the MCC's chief bowler and increased his aggregate of wickets to around 150 from 1889 to 1892, he did not cement his Test spot, and improving pitches and a severe shortage of support bowling caused Attewell's average to blow out to 21 in 1893 – and his record of 111 wickets at 17.54 in 1894 was disappointing given how much the pitches helped a bowler of his type. Although for the following three years Attewell did remarkably well on all pitches considering Nottinghamshire had no other bowlers even approaching county standard, the great strength of English bowling meant he was not considered for a Test match after 1891. In 1898, Attewell's tireless bowling at last seemed to lose some of its sting, and he failed to reach 100 wickets for the first time in a decade. The extremely dry summer of 1899 showed Attewell's capacity to bowl and bowl all day really was no more: he took only 29 wickets at the extremely high (even on such pitches) cost of 34.62 – in county matches he took just 19 wickets for 38.73 each.
Attewell retired at the end of 1899 (apart from an abortive appearance for MCC in August 1900) and became a first-class umpire. He continued in this role on a regular basis until 1909, and even umpired at Lord's in an emergency in 1911.
He was the first person in test history to be dismissed for a King pair.
See also
Pairs in Test and first-class cricket
References
External links
All first-class bowling averages
Cricinfo page on William Attewell
CricketArchive page on William Attewell
Category:1861 births
Category:1927 deaths
Category:People from Keyworth
Category:English cricketers
Category:England Test cricketers
Category:Nottinghamshire cricketers
Category:Marylebone Cricket Club cricketers
Category:North v South cricketers
Category:Players cricketers
Category:Midland Counties cricketers
Category:Wisden Cricketers of the Year
Category:English cricket umpires
Category:C. I. Thornton's XI cricketers | tomekkorbak/pile-curse-small | Wikipedia (en) |
June 24, 2012
CR Sunday Interview: Ed Brubaker
******I've known Ed Brubaker for almost two decades now, and have had the pleasure of tracking his career from his member as a key player in Seattle's post-alternative scene of the mid- to late-1990s to his place today now as one of North America's top mainstream and independent comic book writers, with film and television work soon to follow. This week sees the publication of both the first trade paperback collection ofand its latest serial comic book issue is the latest of Brubaker's collaborations with the talented artist Sean Phillips , and mixes horror with a more typical Brubaker preoccupation:. I very much like the Brubaker/Phillips comics and Brubaker's work more generally, up to and including his superhero comics(just concluding) and(just getting started). I think this latest project in particular is extremely well-conceived and smartly presented in a market that sometimes just tosses work out there. I hope you'll givea try.In the following conversation, Brubaker and I talk about new projects and old ones and engage some of the creator's rights issues on everyone's mind right now. I am deeply grateful that Brubaker chose to speak with on some of those issues in a forthright manner. These are contentious items for which one imagines there's all sorts of potential downside. It's also extremely difficult to talk about a set of issues so rife with landmines of misunderstandingwhich folks have been talking about at much greater length over a three-month period. I think he handled it with aplomb. I learned a lot from what Brubaker had to say. -- Tom Spurgeon******FataleThe trade comes out on the 27th. We're doing a special midnight release thing at Meltdown on the 26th I think it's a combination of my experience and Image's experiences. Image has been really successful withand-- probably several other series,-- where with an ongoing series they'll put a collection of the first arc out the same day as the first issue of the next arc. That to me always seemed like, "I don't want to make retailers angry by not giving them enough time to sell the previous arc's single issues." But I talked to [Image Publisher] Eric Stephenson about it, and he was like, "Look, all of these issues are going out of of print immediately; we're back in second, third and fourth printings. This trade will be the thing that people want when issue #6 comes out. They'll help sell each other." That's what they've seen with their books, so I'm trusting that they know what they're doing. They seem to know what they're doing so far.As far as my experience, me and Sean have sort ofbeen doing our thing for six or seven years now. You have to do a bit of press when you announce the book. At that point I try to tell as little about the book as humanly possible. You want to excite people about the idea. That's why we do those sort of "movie trailers on paper" rather than showing a bunch of pages from the book. I want to tease people on the idea and what it might be.So that's been our way of announcing projects since. Then a month before the book actually comes out, you want to tell people more about it and release more artwork before the final order cutoff for all the retailers. Then when the book is out, you sort of pray that people will write about it and review it, that word of mouth will get around or that your friends will twitter about it. [laughs] Wil Wheaton and Warren Ellis , these guys that have a reach I don't have.I always like to read interviews with authors when their books are coming out. I kind of model that on the way standard book publishing has gone. Image will help me. I work in tandem with them. They'll help set up stuff.I don't know, actually. [laughs] I kind of always do this stuff instinctively. I want to make sure they're good no matter what they are. This one is weird because it's the first of three. But it's meant to be a self-contained thing that builds what comes next.It's a struggle, too, to fit as much in. Originally it was going to be four-issue arcs. We do 24-25 pages an issue, so I thought we could do three four-issue arcs and this could be a 12-issue project. I got halfway through issue #2 and I felt completely pressed for space to tell the story. There are so many characters in it, and it goes in so many different directions. I realized that, "Wait, there's nobody telling me that this thing has to be 12 issues other than me. I'm going to add one issue to the first arc." I'm considering adding even more to the second arc, because I like the epic-ness of it. I don't want to have to skimp on anything.It's like any long-term relationship. Sean and I have been working together 12 or 13 years pretty steadily.We've had breaks, but mostly I've done 10 or 12 comics a year with Sean for a decade now. It's weird. Every now and then I look at my bookshelf and I see all these books we've done together and I flip through them and I'm like, "Wow, that was amazing." Whenever anyone asks me if Sean's available for anything, I'm like, "Shut up!" I jealously hoard Sean, but I also probably take him for granted half the time. [laughs]weI think he's an incredibly strong storyteller. I think sometimes people lump him into a certain category that I don't think he's actually in. Artists that do this stiff, photo-y kind of stuff. Sean's stuff... what distinguishes him from a lot of those photo reference-y guys is that there's a looser artistic sensibility to what he does.You can empathize with characters that Sean draws. For a lot of artists are in that same school of drawing, you can't empathize with the characters. There are a lot of artists I really like that I look at their stuff and I feel nothing for their characters. You know?And Sean's design sense is amazing. His covers... every now and then we'll go back and forth on a cover sketch. He'll send me the little color roughs and we'll go back and forth and we'll get to the one where we're like "Oh yeah. That." We were going back and forth on the last cover he did for a while. It wasn't clicking for some reason. I wasn't giving him the right sort of feedback on it. We do these covers before the issues are written usually, and I have only a vague idea of what's going to be in the issue. He drew this one and I'm like, "That's really good, but what if we cropped it closer?" And he just sort of did that. "Oh yeah, that's it." And the next day he sends the inked and painted version of it and it's like the best cover he's ever done. [laughter]That's all Sean. At first when we started talking about the idea he started sending me various cover design ideas. They all had that white border around the edge and logo in white. He really wanted it to look like an old magazine from the '30s or '50s. He was finding these old photos of pin-up girls and putting that design around these old black and white photos, showing me the basic idea. We're always trying to make sure our book looks different than everything else on the market.I always say I want to work with Sean for the rest of my creative life. It's just such a simpatico relationship in my mind. I'd love to get to a point where our books were selling well enough that I only ever had to work with Sean. It'd be a lot easier to only have to write one comic a month. [laughter]FataleOh, yeah. I've written maybe one thing that would be considered any kind of horror at all.[laughs] It is. It's different.and crime stuff there's such an inevitability to your stories once people see how the groundwork is set. I wanted to do something that wouldn't do that. There's inevitability to certain things in the story, but you don't necessarily know what the fuck was going to happen next. I wanted to challenge myself to sort of not know. Can I do this for sure? Am I going to fail dramatically? Some of my favorite books that other people have done I think the writers and artists would consider well-intentioned failure. So I figured it was smarter to do something I'm unsure of and fail as opposed to coasting on what I know I can do.It's so hard to say you're happy with it while you're still working on it. We're only about a third of the way through the story at this point, so it's hard for me to judge. I think the way we've done it so far has worked. Certainly writers I respect have told me so far they like it, and that makes me happy. But I don't know how good I am at it yet. I do notice that I have to, when I'm working on my outlines go, "Oh yeah. Horror stuff, too." [laughter]I write so much through character. The second arc is already one of the strangest things I've ever written, and I think that's partly because I got a lot of establishing stuff done in the first arc. Establish the world and the rules of the story a little bit. Now with the second arc I get to play around with my own obsessions like growing up in the '70s. '70s Hollywood is really an interesting time for Hollywood, and America generally. Moving towards punk rock. Reagan 's coming. The Manson Family had happened. Son Of Sam . That's a horrific time for America just in terms of our culture. I think a lot more of my real-world research comes out in that aspect, even though I'm fictionalizing everything.And the nice thing is, much like, good horror comes from following characters through a story. They really do fit.Yeah. And I kind of love the idea of immortality being a tragic horror -- that you live forever. I think that part lends itself to adding something more to the story. At the end of the first arc when the guy goes to see his father and you realize that his father is in the insane asylum because of this woman somehow. It's nice to give hints of things to come that you may or may not learn. But I'm really into the fact that it's multi-generational and that these things are all linked.Sure. One of my favorite things about the process of doing this book the way we are, monthly, is that the end of the prologue part of issue one when the guy is sitting there and he's had his leg chopped off and he's reading the book. Everyone assumed that the next part of the story, that took place in the '50s, was the book he was reading. I knew that everyone was going to, and I knew when they got to issue #3, the opening when you learn what the book he's reading is, that people would be like, "So wait, this is all what really happens?"FataleFataleWell, that's our thing. It's not cheap to pay these guys to color and draw the comics. And I love serialized comics when they're done right. I've felt for a long time that as the price started to go up that you needed to give people extras to make them not just excited that they're getting a good comic, but that they're getting a package that's worth owning. That's been ouron our singles sincestarted, really, because we're living in the world of the "waiting for the trade" people. Now we're even living in the world of the "waiting for the deluxe hardback edition" people. There's literally a contingent of people that say they're going to wait five years from now.Captain AmericaYeah. By the time this interview comes out, I will have written my last issue.A little less than eight years. I think I started in August or September of 2004 writing my first issue, which came out in November of that year.Partly, it's the beginning a shift from work-for-hire to books I own, instead. I hit a point with the work-for-hire stuff where I was starting to feel burned out on it. Like my tank is nearing empty on superhero comics, basically. It's been a great job, and I think I found ways to bring my voice to it, but I have a lot of other things I want to do as a writer, too, so I'm going to try that for a while instead.Winter SoldierYeah, I am. That's going to be my only Marvel book soon. I'll doas long as it lasts... or, I'll do it for as long as I can. [Spurgeon laughs] Because I don't know if it'll last, but I'm really proud of that book and the second and third storylines on it are some of my favorite stuff I've done for Marvel, ever.It's a mix of stuff. There's a nostalgic aspect to it. I can vividly remember buying my first issue ofwhen I was like four years old at the PX in Gitmo . I remember the exact issue. I still own it to this day -- not the exact copy but that issue -- I've never spent more than 20 cents. Every time I've bought it I've been able to get it at cover price. #156 . Two Caps rushing at each other. The Cap from the '50s fighting modern Cap.It was like the third Englehart issue, I think. So there's a certain nostalgia to it. I grew up on military bases readingcomics and always kind of liked Captain America regardless of the spottiness of the runs that would happen. A Captain America fan in the '70s, you had the Englehart run which was great at the time and then there were a lot of other comics and then you had the [John] Byrne and [Roger] Stern run which was great and then there was a bunch of other comics [Spurgeon laughs] and there was a [J.M.] DeMatteis run with Mike Zeck , which was pretty great for a while. That was probably the end of buying the book as a kid for me, the end of that run.There's a certain amount of pride in wanting to follow in those guys' footsteps. And let's face it, when you're doing a book like that and you're successful, you pretty much get to do what you want. I never had anybody ever order me to do anything on. I never had to do anything I didn't want to do with that book. When you're on a character for that long, you sort of have proprietorship of it. You know that Marvel owns the character, but you lie to yourself to a certain amount that you're the one in charge. And if you lie effectively enough and do good enough stuff, you are the one in charge. [Spurgeon laughs]That's the nature of comics. They have to come out every month. Sometimes, if you just do a good job, no one will fuck with you. [laughs] The deadline that is your enemy can also be your friend. As long as your books have to ship every month and you're doing something cool... the worst thing that ever happened to me was being told I couldn't use some character because they were inor something.So there's a certain amount of that. Honestly, it was to the point I'd take on other projects here and there, like, and I'd get three or four issues in and I'd be like, "What am I doing? Why am I doing this? This is so not in my wheelhouse."It's just kind of funny: writingbecame second nature to me. And I think about 90 percent of the stuff I did I would hold up to any other comics that were coming out.I think I got to tell a long story. In the early days, I got to create a big soap opera about Steve Rogers and Bucky and Sharon Carter and keep this thrilling adventure ride going. And each arc bled into the next. Then we did the "Death of Cap" thing and I go to really do an 18-part story that still didn't end with Cap coming back to life yet. [laughs] I got to do some stuff that was really challenging. I got work with some great artists. Steve Epting , he probably drew 35 issues of my run in the early days. I think we developed a really great collaboration. And I always liked that kind of epic storytelling."The Death of Captain America" turned out to be the best thing that happened to the book in ways because everything we were able to do after that, because the main character wasn't in the book, was so much more interesting than when he was in the book. It was a total curveball and you didn't know what was going to come next. There was a lot of fun to be had in it, and at the same time it was driven by these characters that were characters I had an attachment to from childhood.Captain AmericaCaptain AmericaYou think about it a lot more than you should. [laughter]That is the tone I wanted to bring to it, that kind ofmeets Tom Clancy aspect. That really for me came from those Englehart issues and the Steranko issues. Captain America in those comics was always doing the right thing and it was always costing him. He carries the weight of a country on his shoulders.That's not on purpose for this one. That was a situation with scheduling. Marvel is trying to do this thing now that with some of their better-selling books they want to get out more copies per year than 12. They want to get out 15 or 18 issues.'s been doing more than one a month for a while now; someone I know doesor one of those books, and that comes out 18 times a year.I couldn't keep up with that schedule, honestly. I knew I was getting to the end of my run. I wanted to wrap up my run earlier. And [Marvel Senior Vice President Of Publishing] Tom [Brevoort] was like, "Well, you're going to leave a bunch of plot lines dangling... do you want to go out like that? It'll seem like you threw up your hands and said 'I can't keep up with this schedule.'" I was like, "No, I don't want to go out that way." So we brought in Cullen Bunn to write an arc with me. I gave him a list of a bunch of stuff. "Here's all the dangling plot threads and here's where we need them all to be by the time I get to my last issue." And then we figured out a storyline together.It's strange. I did all these issues as an uninterrupted run. Then there's four issues co-written by someone. Then there's a last issue. [laughs] It's a little odd.He's the John Wells of my. [laughter] It's not a hostile thing, certainly. I was involved in choosing him and stuff. It was just down to I was doing two monthly books at Marvel both of which needed multiple issues per month because of the way the scheduling had gotten. And I was writing a screenplay at the same time that was due. I was like, "My screenplay is due in three weeks. And I have all of these comics to write. There's no way this will happen without me dying." I didn't want to die. [laughter]I definitely think... they've got Jason Aaron , and Jonathan Hickman and Matt Fraction and Rick Remender . Obviously Brian Bendis , who writes so many comics I can't understand how he possibly keeps up. Kieron Gillen ... all of these guys are talented guys. I'm leaving some out -- Jeff Parker . There's a lot of really good writers doing multiple books a month up there.And it's such an interesting time in mainstream comics to me because of how in flux it feels. DC had a massive shake-up. Marvel's ramped up production on everything. It seems a little crazy sometimes. [laughs] I wonder from the outside if it looks as much like as it feels like it on the inside.When I was at DC... sales weren't necessarily great, but they were fairly stable. There was a certain amount of stability. Both DC and Marvel had stability, it felt like. But two years ago there started to be what seemed like freefall for a lot of books. My personal theory -- This happened to coincide [laughs] with the books suddenly costing $3.99 as opposed to $2.99. I think that was when you started to see some books really fall. On the other side, there's the argument that the best-selling books for the past ten years have been the $3.99 books.It's hard to say who's right or who's wrong on some of this stuff. But sales on these books were going down below what DC and Marvel would have found acceptable even a few years ago. So that stability just feels like it's missing all of a sudden.I mean, imagine how lucky I was to write the same book for eight years. That doesn't happen a lot anymore. Brian Bendis has been writingfor like nine years now. He's written more issues ofthan any other person. It's rarer and rarer to have these long runs on books.I can only talk for myself and my friends. Matt Fraction is one of my best friends. Brian Bendis is one of my best friends. They've both done really long runs onand. Brian's donefor 12 years or something. It can happen.I think it comes down to finding that chemistry with a character or an artist. Brian had Mark Bagley on like 120 issues of. It becomes rarer and rarer to find that kind of artist. I think that's when you find that groove, when you get a regular team. If not for Epting on, I don't know that I would have been successful on that book. The ideas I brought to it, they jibed with what he wanted to draw. So finding that artist you really click with... that's why I've been going back to the same artists over and over again. Michael Lark and Sean and Steve Epting... I can't wait to work with Steve Epting again on something.DaredevilAnd then it's gone for a few years until there's a new number one. Yeah, I miss the way it used to be. [laughter] Obviously I do because I'm obsessed with comics and nostalgia. My favorite era of mainstream comics was when every character had just one comic, or the odd character that was really popular had two. They had the same writers for years and years and years. They had the same artists for years and years and years. The occasional fill-in. These people got to tell a story. There were no events and crossovers.It's hard to speak for other people. I do kind of want to [Spurgeon laughs] but I don't. But I think there's a certain amount of anxiety that I didn't feel as much two or three years ago. Maybe I didn't feel it as much because I was in this rarefied air of doing some of the better-selling books at Marvel. I'm pretty well-established in the field, so maybe things felt stable to me when they didn't to people who were getting their books axed.But I don't talk to too many people about this because I've been moving in my own direction, knowing that I was winding down the superhero work-for-hire part of my career.It was less of a decision and more just following my instincts, trying to make sure I'm only writing things I really want to write. I used to have a lot of ideas for superhero stories, and they scratched a real old-fashioned pulp writer itch for a long time. But the past few years, I've wanted more and more to just focus on my own projects, and most of my ideas have been for new things, or things outside comics. I remember just sitting there with my Cap notebook, trying to figure out what to do after the next arc was finished, and suddenly I just was like, "I think I'm done here" and it was this huge relief. I talked to Dan Buckley at Marvel, and told him what I was thinking, and he was really supportive of me, really great about it. I mean, I know I'm still going to be doing the Winter Soldier for a while, potentially a long while, but this feels like a major change, anyway.They definitely played a part, because the movie gig and some TV work really helped me worry less about the risks. But I've been going down to L.A. for about ten years, writing and pitching, having things almost happen. But about two years ago, I wrote a pilot for FOX , and that was kind of a turning point. Then things started happening, and eventually the movie deal for Coward went through, with me attached to write it. So all that, along with how well me and Sean are doing with, all of that played a part. But, you know, I have no desire whatsoever to leave comics. Like you said, I'm a comics guy. They're one of the constants in my life, so I'll always do comics.I've got no problems with the limitations of mainstream comics, really. Limitations can help you. And it's not even really about the control, because I've always been good at lying to myself that I own Cap and Bucky. It's just literally following my creativity where it wants to go. I'm happier when I'm writing, even when I'm agonizing over every word of it, so I have to follow that path. I wish this were a more dramatic story for you, but Marvel have treated me really well over the past 8 years. I'm just ready for a change.Well, Joe Simon would say he co-created Captain America.Simon might actually take full credit, depending on his mood when you asked. It's just funny that everyone refers to him as Kirby-only, when it's Simon and Kirby.Sure.They do matter to me. I also worked at DC for a long time on characters that were probably co-created by Bill Finger without him getting anything for them. You know when you work on these company-owned characters that there's a history there, a lot of it ugly and unfair to the creators. So you go in eyes wide open to that past. And that's the problem, poor treatment of creators, that's supposed to be the, not the present.And now withyou're seeing people weighing in on Alan Moore, saying he's a hypocrite. "He's mad about this, but he used to work onor." But if you actually read interviews with Alan Moore , he'll talk about the fact that the more work he did on that stuff, the harder a time he had with doing it. So obviously, his views evolved through his personal experience, as views tend to do.But apparently there's some kind of moral absolutism where he's now not allowed to have an opinion. But I mean, murderers can still think murder is bad. Not really an apt comparison, I know. [laughter] But I remember I said something on Twitter -- something sort of snarky about. Someone said, "Well, you're hardly in a position to judge, since you're living on Jack Kirby's stolen properties." [Spurgeon laughs] So apparently I don't get an opinion, either.Yeah. To me, there's a difference between working on something like, and creating characters for a company that you know are going to be owned by that company going forward. I don't recall a time when Jack Kirby was standing there saying, "They promised me I'd own; nobody should be doing this."What I remember, from when I was becoming aware of this stuff in the '80s, is that Jack wanted his art back and he wanted a percent of the money generated from his creations. I don't recall Jack Kirby ever suggesting that someone shouldn't do. And I can't recall Marvel Comics ever holding up theas a victory for creator's rights like DC did withSo I think there's a clear distinction between the Jack Kirby thing and the Alan Moore thing. And I want to be very clear, I'm not trying to diminish Jack Kirby's contributions to Marvel Comics, which are immense, or say that he shouldn't have gotten more for his creations and co-creations, because I think he should have. But I don't think the situation is the same as what's going on withAt the same time, I've always felt good about the fact that the credits forsay, "created by Simon and Kirby" and that Marvel had settled with Simon and Kirby -- not Kirby himself, but Kirby's heirs -- over. So they are getting something from themovie, because of that. But the other stuff is all tied up in that huge lawsuit, so Marvel can't even publicly discuss any of these issues.Yeah, completely. Partly because even four or five years ago, Alan Moore was revered in comics, regardless of any fights he had with publishers or fallings out he'd had. He's been nominated for more awards than anyone in the history of the medium, I think. And then he gives a few cranky interviews about the mainstream comics market from the point of view of someone who clearly wasn't aware of what was going on in it, and people were suddenly like, "Fuck that guy."I was surprised by the bloodthirstiness, and I was surprised how much I cared about the issue, too. But the PR that came out... Some of the stuff JMS was saying in preemptive defense of the project... A lot of it made me kind of vomit in my mouth. The way that fans attacked Alan Moore -- "screw him, he signed a shitty contract!" -- and the debates back and forth about how he's done the same things withso he can't complain... which just... that makes no sense. An author always has the right to complain about the treatment of their work. You don't forfeit that when you write an issue of. To see that reaction from the fan base was disheartening. You expect them to be on the side of the creator.But the thing that really bugged me was whenwas announced it was, coincidentally, that same summer the entire industry rallied around Jack Kirby against Marvel. It was the era of the "Creator's Rights Revolution" and DC really usedat the time. Part of the PR was that it was creator-owned, that these guys would get this property back. DC used it to position themselves against Marvel as the more creator-friendly company.I was at the San Diego Comic-Con the year that Alan Moore was there. I saw him talk aboutand what a revolutionary thing it was that they'd gotten this deal for it. Part of it felt like a promise to the industry that things were changing. That this was different. And so while the book never went out of print and they never got their ownership, I always felt that on some level Paul Levitz seemed to respect the spirit of the deal: that they had created this thing and while DC officially owned it, Alan Moore and Dave Gibbons had moral ownership of it, at least.So to see this happen over the objection of the guy who wrote it, and then to see the responses, "Well, Alan Moore didn't really create those characters anyway; they're just the Charlton characters." Or "He did the same thing with. Would the people who created those characters be happy with the way Alan Moore treated them?" I don't think he was positioningas an official, in-continuity sequel to those author's books, for one, but I think two of them are on the record as saying they don't give a shit what anyone does with their characters. And clearly DC doesn't think thecharacters are just the Charlton heroes, because they copyrighted and trademarked them as totally different characters.began asbut he's clearly a different character. Where a character begins doesn't take away from what they end up becoming. Creation is a process. Lots of our favorite things began as some writer doing their take on some idea or character. And you don't know until they tell you -- "yeah, this character is like Punisher crossed with Tigra but with my views on animal rights" -- just like withit wasn't until Moore and Gibbons revealed the process, that it had begun as a pitch for the MLJ and then the Charlton heroes, that anyone made the connection.canshouldYeah. You're naïve if you want people to do the right thing. "Get over it, man. The Tyrell Corporation makes replicants. That's life."notYeah, it looks especially bad thatwas this special thing they left alone, they let it be a novel, which is what it was.Really, though, the saddest part for me is the "fuck Alan Moore; he signed a shitty contract" thing. That's really, really sad. When JMS at the Chicago Comicon -- or wherever that was -- said, "Did Alan Moore get a shitty contract? Yes. Jack Kirby got a shitty contract, too." That really, to me, when I was reading that I was like "Holy shit." Siegel 's and Shuster 's and Kirby's shitty deals are now being used to defend a project as opposed to...Yeah. Usually, that would be the opposite. Are we living in opposite-land now? "So and so got a shitty contract, too, so just get over it." Like I said, the poor treatment of creators by "the Big Two" was supposed to be part of the past. They'd changed their policies to be more creator-friendly, so things like this weren't supposed to happen anymore. And yet here it is, the only time during my entire career where we've seen the writer of a book standing there saying "I don't want this thing to happen." And people are just giving him the finger.Omega The UnknownYou're right. He was angry about that. He said Jonathan Lethem had made an enemy for life. Jonathan Lethem called him up and talked to him about it because he didn't know Steve Gerber wanted to do more. They ended up talking amicably, from what I gathered. There wasn't a big controversy over it. But yeah, you're right. Gerber is kind of the outlier of all this stuff.The thing is, I'm glad JMS said what he did, because while it appalled me at the time, there's an inherent truth to what he said. And it actually sparked a lot of people thinking about these issues more than they were doing. I think they had written it off. "Dave Gibbons is okay with it, and Alan Moore is a cranky old man, so fuck him." Then JMS said that thing, and people started re-examining the whole thing. [laughs]Yeah. They seemed like settled issues and now suddenly the entire industry is talking about them again.But that all feels naïve, too. I mean, once you get established in comics, you know to create your own material and not give up ownership to a publisher. I don't know any established pro that isn't currently planning or doing a project they have complete ownership of. That's one of the reasons Sean and I startedat Icon way back when, because we were at a point where we didn't need to give away anything to get it published. So it's not like comics needed this reminder, or like the next Alan Moore was waiting in line to give his next big thing to DC. You know giving away half the ownership and all the control isn't a great deal.Something that I was thinking about was what DC could have done when the market changed and they realizedwas never going to go out of print? Because they could have altered the deal if they wanted, to be more fair to Dave and Alan. I mean, the book was in profit when the single issues were coming out, so it's not like DC took some huge risk on. Alan Moore was their best writer and it was one of their bestselling things. The trade paperback was immediately a perennial best seller. They could have said, "Okay, we've made ten times our initial investment back, so we're going to give you guys 50 percent of profits from now on." They could have said they'd keep it in print and give them control over what happens to it. And who knows,might have still happened. Because Dave Gibbons signed off on it... He made that one public statement.Well, I don't know how Dave Gibbons feels, but in my own experience, with, you kind of get used to the fact that you don't own your work when you realize you've made a bad deal. [laughs] If I'd owned, my whole life would be different now. Other opportunities would have opened for me long ago.But that's all hindsight. It's really easy to look at things and say, "Wow, I should have done this; I should have done that." Whereas in '99 when Scott Dunbier asked me to create a monthly comic for WildStorm , nobody else was asking for me to create something like. So it's easy to look back and go, "I wish I had made a different deal."Still, Dave did give them an okay, and I think if Dave Gibbons were objecting the same way Alan Moore is, it most likely wouldn't exist. At least, I don't think so. Although, I don't know, maybe they wouldn't care? It's hard to imagine, but the whole situation is.Before WatchmenIt really is. I feel like this is the weirdest, most surreal thing that's happened since I've been in comics professionally.And I want to be very clear here, too, that I have no ill will toward anybody who's working on this project. I have friends working on this and I don't begrudge any of them doing it. It's a tough industry to make a living in, and it's a pretty scary time to be a professional in this industry. And they don't have to view it the same way I do. They don't have to make a distinction between this and any other company-owned job. And I assume they knew going in that not everyone would view it the same way they do.But what I can't get beyond is the way DC is sort of rewriting history here, and pretending like they didn't saywas this great new deal. It was supposed to be the thing that was different than, different than, and in the end, it wasn't at all.************* the cover to the new trade* a photo of Brubaker by Tom Spurgeon* a panel from pretty early on in the new book, I think* a couple of arresting single panels from Sean Phillips* the cover in question* one of the overt blendings of supernatural and crime/noir: these terrifying thugs* two scenes where the sense of scope and time is called upon and used* from Brubaker's* from Brubaker's* the first issue ofBrubaker bought -- he still has a copy* issues from the runs Brubaker liked on the title as a young man* a somber moment -- among many -- in Brubaker'srun* from one of the issues recently written in partnership with Cullen Bunn* Steve Epting art* a panel that harkens back to the character's origin/first appearances* three panels fromby Alan Moore and Dave Gibbons* the original* from, not owned by Ed Brubaker and Sean Phillips* the latest issue; you should try it out -- things get weird (below)****************** | tomekkorbak/pile-curse-small | OpenWebText2 |
For a decade, Football Outsiders has been using advanced analytics to measure and predict team performance. And since the Football Outsiders database now goes back to 1989, I thought it would be worthwhile to test the predictive power of Football Outsiders’ ratings.
If you’re not familiar, FO uses DVOA as its base measure of team strength. The goal here is to use DVOA ratings in Year N to predict win totals in Year N+1. Now, what expectations should we have for DVOA? The fact that the team with the best DVOA in history — Washington in 1991 — won only 9 games the following season is not a knock on DVOA. That was an outstanding Super Bowl team that declined significantly the following year. Ditto the 16-0 Patriots looking less impressive without Tom Brady in 2008. But at a minimum, DVOA must do better at predicting future wins than say, just wins. And it should also do better than Pythagenpat ratings, which only incorporate points scored and points allowed. So does it?
Let’s start with the basics. The best-fit formula to project wins in Year N+1 using *only* wins in Year N is:
5.343 + 0.332 * Year N Wins (Correlation Coefficient: 0.32)
And, as shown last week, by using Pythagenpat wins, we get a correlation coefficient of 0.36. So what happens if we instead use Year N DVOA as our input? We get the following best-fit formula:
8.01 + 6.378 * DVOA (Correlation Coefficient: 0.39)
As a result, DVOA does beat both regular wins and the Pythagenpat ratings. Now, what if we use both DVOA ratings and number of wins to predict future wins? As it turns out, the wins variable was nowhere near significant (p = 0.61), which means once we know the DVOA ratings, knowing the number of wins adds no predictive power. In other words, the evidence doesn’t prove that a team with a lot of wins but an average DVOA rating is better than a team with an average number of wins and an average DVOA rating.
But can we improve on DVOA? What if instead of using Team DVOA as our input, we use Offensive DVOA, Defensive DVOA, and Special Teams DVOA? Team DVOA obviously incorporates all three of these elements, but perhaps analyzing team strength on a more granular level will tell us more about the appropriate weights. Keeping in mind that for defenses, a negative DVOA grade means an above-average defense, here is the best-fit formula to predict future wins with those three inputs:
8.01 + 6.779 * OFFDVOA – 5.642 * DEFDVOA + 6.518 * STDVOA
All four variables are statistically significant, although as you might suspect the special teams one is the least statistically significant (at only p = 0.024; the other three have infinitely low p-values). As it turns out, this gives us the same correlation coefficient of 0.39, but I prefer looking at teams using this formula. Also, there’s something else to keep in mind when looking at the weights on the coefficients. In generally, range of DVOA grades is wider for offenses (removing outliers, about -35% to 35%) than it is for defenses (about -30% to 25%) or special teams (-8% to 10%). So even though the weight on the special teams variable is larger than the weight on the defense variable, this doesn’t mean special teams is more important than defense.
Continuing the momentary diversion, the standard deviation of DVOA grades from 1989 to 2012 , was 14.5% for offense, 10.4% for defense, and 3.9% for special teams. From those numbers, one could put forth the argument that offense is roughly 50% of the game, defense is about 36% of the game, and special teams is around 14%.
What if we instead break down DVOA into five parts: Pass DVOA, Rush DVOA, Pass Defense DVOA, Rush Defense DVOA, and Special Teams DVOA? The correlation coefficient does not change, but all variables wind up being statistically significant. The best-fit formula is:
7.64 + 3.069 * PASS OFF + 4.297 * RUSH OFF – 2.231 * PASS DEF – 3.990 * RUSH DEF + 6.368 * ST DVOA
The intercept drops to 7.64 because, on average, passing offenses have above-average ratings compared to the baseline FO is using. This is not the case with offenses as a whole, as team offensive DVOA had an average of zero throughout the period. That difference is due to the fact that false starts and delays of game are counted against the offense, but neither the pass offense nor the rush offense. The standard deviations for pass offense, rush offense, pass defense, and rush defense, are 22.0%, 11.1%, 15.1%, and 9.4%. Add in the 3.9% for special teams, and here’s another potential conclusion: pass offense is 33% of the game, rush offense is 17%, pas defense is 22%, rush defense is 14%, and special teams remains at 14%. Those numbers sound and feel appropriate to me.
So what does this mean for 2013? We can use the formula and the 2013 DVOA grades to project the number of wins for each team in 2014. Note that all the numbers for the five team grade columns should really be represented with a % sign, but including non-numeric data prevents the user from having the ability to sort the table.
Rk Team Pass O Rush O Pass D Rush D ST Proj 2014 Wins 1 SEA 27.7 6.2 -34.3 -15.1 4.8 10.5 2 DEN 60.7 4.3 10.2 -14.4 -1.1 10 3 PHI 29.9 23.7 16.6 -11.3 -2.8 9.5 4 CAR 11.5 9.4 -15.4 -16.3 1 9.5 5 SF 31.8 2.2 -2.1 -8.1 3.7 9.4 6 KC 5.5 12.3 -6.9 -6.4 7.8 9.3 7 NE 28.1 7 3.9 4.3 6.7 9 8 NO 35.9 -5.3 -9.2 -1.5 -2.5 8.7 9 CIN 13.7 -5.7 -14.5 -9.9 1.3 8.7 10 ARI 10.9 -9.7 -11.3 -24.9 -4 8.6 11 SD 51.3 3 23.9 8.6 0.8 8.6 12 CHI 28.6 1.4 7.5 9.8 2.1 8.2 13 DAL 15.8 7.9 20.8 4.3 3.5 8.1 14 IND 8.2 3.1 1.5 -0.1 -0.1 8 15 STL 0.1 -14.9 4.8 -17.1 6.3 8 16 DET 9.8 -11.8 9.9 -16.9 -0.5 7.9 17 GB 12.2 10.9 21.3 6.4 -0.4 7.8 18 NYJ -15.8 -7.9 7.4 -23.2 2.1 7.8 19 MIN -8.3 5.7 22 -6.2 3.9 7.7 20 TB -1.5 -11.6 -0.1 -15.4 -1.5 7.7 21 PIT 23.5 -14.9 8 -0.9 0.6 7.7 22 TEN 5.5 2.7 6.3 1.3 -3.2 7.6 23 BUF -14 -3.9 -22.8 -3.2 -5.6 7.4 24 BAL -8.4 -27.2 -4.8 -13.6 6.4 7.3 25 MIA 3.8 -4.1 0.1 4.8 -2.3 7.3 26 ATL 14.6 -6.9 24.6 1.3 -0.1 7.2 27 CLE -9.1 -7.1 14.1 0.6 1 6.8 28 NYG -18.9 -20.3 -6.9 -17.2 -5 6.8 29 WAS -14 4.5 12.7 -5.4 -12 6.6 30 HOU -19.4 -9.4 15.9 -11.4 -5.1 6.5 31 OAK -20.4 0.8 22.1 -3.6 -7.1 6.3 32 JAC -24.2 -27.2 20.1 1.1 2.6 5.5
It’s important not to infer too much from tables like these. The only inputs are 2013 DVOA grades, and the formula doesn’t know that Robert Griffin III should be a lot better this year or about Houston’s draft picks, Oakland’s cap room, or Green Bay getting twice as much Aaron Rodgers in 2014. But what’s interesting to me is the teams that stand out as different from their Pythagenpat ratings. Here are some thoughts:
The Eagles are projected for nearly one full win more using the DVOA projection (9.5) than Pythagenpat (8.6). That makes some sense, I think, because Philadelphia had excellent offensive pass and rush DVOA grades, and the below-average special teams grade doesn’t mean much. Philadelphia did rank 4th in points, but I think their DVOA grades are farther from the mean than their points scored number indicates.
The Jets are a less intuitive example. I think part of the reason for optimism here is that New York forced 18 fumbles but recovered only two of them! That’s an absurd result, and one that would make the Jets look much better in DVOA grades than points differential. Also, while pass defense is more important than run defense generally, perhaps it’s not as predictive: the regression has a significant weight on rush defense, where New York excels. That’s why Football Outsiders has the Jets as nearly an 8-win team, compared to the 7-win team from Pythagenpat.
The Buccaneers are another team that is projected for nearly one more full win (7.7 vs. 6.8) in 2014. Tampa Bay was 30th in points scored and 32nd in NY/A, but 22nd in Football Outsiders’ pass DVOA. I’m not sure the reason for the discrepancy — perhaps a higher weight on completion percentage? — but it does mean FO is more optimistic on the Bucs passing game, and by extension, the team. But perhaps the biggest reason is because of strength of schedule. Tampa’s schedule was the hardest in the league at 3.6 points tougher than average according to the Simple Rating System, and Football Outsiders also graded the Bucs as having the hardest schedule in the league.
Those three teams stand out as the biggest beneficiaries when using Football Outsiders’ analysis as opposed to just straight points differential. There’s no team significantly harmed by the analysis, although the Bengals, Colts, and Jaguars come closest. The Bengals lose about two-thirds of a win, and I suspect it’s because of the Andy Dalton effect. Cincinnati ranked 6th in points scored but just 12th in pass offense DVOA and 20th in rush offense DVOA. In other words, the Football Outsiders analysis is not nearly as high on the Bengals offense, which would reduce their expected wins total in 2014. The Bengals also had the 8th easiest schedule in 2013 by DVOA.
Anyway, I think these are a pretty useful starting point for your 2014 team projections rather than say, last year’s standings. Even Football Outsiders won’t use these for more than a starting point — their preseason projections will have the customary tweaks for things like teams getting new quarterbacks, injuries (or the lack thereof) in 2013, rookies, offensive line continuity, etc. Everyone will handle those questions differently, but I do think the table above presents a nice base for everyone’s team projections. | tomekkorbak/pile-curse-small | OpenWebText2 |
Tamenglong district
Tamenglong district (Pron:/tæmɛŋˈlɒŋ/) is one of the 16 districts of Manipur state in northeastern India.
History
In 1919, the British Government established four sub-divisions office in Manipur Hills known as North East Sub-Division, North West Sub-Division, South East Sub-Division and South West Sub-Division. The Head Quarters of North West Sub-Division was set up at Khunjao, Tamenglong Village (Nriangluang) and Mr. William Shaw was appointed as the Sub-Divisional Officer. In 1923, the head quarters of Northwest sub-division was shifted to the present site known as Tamenglong headquarters some 3 km away from Khunjao. Later the Manipur North West sub-division was renamed as Tamenglong Sub-Division. Tamenglong became a full-fledged district in 1969 and the first Deputy Commissioner was posted.
Geography
This district is bounded by Nagaland state on the north, by Senapati district on the north and east, by Churchandpur district on the south and by Imphal West district and Assam state on the west. Tamenglong town is the headquarters of this district. The district occupies an area of 4391 km.
Economy
In 2006 the Ministry of Panchayati Raj named Tamenglong one of the country's 250 most backward districts (out of a total of 640). It is one of the three districts in Manipur currently receiving funds from the Backward Regions Grant Fund Programme (BRGF).
Administrative divisions
The district is divided into 3 sub-divisions:
Tamenglong
Tamei
Tousem
Recently, Noney District was carved out from Tamenglong district; comprising sub-divisions of Longmei (Noney), Nungba, Khoupum, and Haochong.
Khoupum, a small town falling under the Nungba sub division is one of the most populated area within the district and the home town of Hon'ble MLA and former Deputy Chief Minister Shri. Gaikhangam Gangmei.
Demographics
According to the 2011 census Tamenglong district has a population of 140,651, roughly equal to the nation of Saint Lucia. This gives it a ranking of 607th in India (out of a total of 640). The district has a population density of . Its population growth rate over the decade 2001-2011 was 25.69%. Tamenglong has a sex ratio of 953 females for every 1000 males, and a literacy rate of 70.4%.
Languages
Majority of the people speaks Rongmei.
Sino-Tibetan languages spoken in Tamenglong district include:
Zeliangrong Language/dialect-
Zeme language
Liangmai language
Rongmei language
References
External links
Official website of Tamenglong district
Category:Districts of Manipur
Category:Minority Concentrated Districts in India
Category:Districts of India | tomekkorbak/pile-curse-small | Wikipedia (en) |
Incidence of myocardial infarction with shifts to and from daylight savings time.
Modulators of normal bodily functions such as the duration and quality of sleep might transiently influence cardiovascular risk. The transition to daylight savings time (DST) has been associated with a short-term increased incidence ratio (IR) of acute myocardial infarction (AMI). The present retrospective study examined the IR of AMIs that presented to our hospitals the week after DST and after the autumn switch to standard time, October 2006 to April 2012, with specific reference to the AMI type. Our study population (n = 935 patients; 59% men, 41% women) was obtained from the electronic medical records of the Royal Oak and Troy campuses of the Beaumont Hospitals in Michigan. Overall, the frequency of AMI was similar in the spring and autumn, 463 (49.5%) and 472 (50.5%), respectively. The IR for the first week after the spring shift was 1.17 (95% confidence interval 1.00 to 1.36). After the transition from DST in the autumn, the IR for the same period was lower, but not significantly different, 0.99 (95% confidence interval 0.85 to 1.16). Nevertheless, the greatest increase in AMI occurred on the first day (Sunday) after the spring shift to DST (1.71, 95% confidence interval 1.09 to 2.02; p <0.05). Also, a significantly greater incidence was found of non-ST-segment myocardial infarction after the transition to DST in the study group compared with that in the control group (p = 0.022). In conclusion, these data suggest that shifts to and from DST might transiently affect the incidence and type of acute cardiac events, albeit modestly. | tomekkorbak/pile-curse-small | PubMed Abstracts |
(CNN) Just three months after his second birthday, Eli Thompson, an Alabama baby born without a nose, passed away.
Jeremy Finch, Eli's biological father, posted on Facebook about his son's June 3 death.
"We lost our little buddy last night," Finch wrote. "I'll never be able to make sense of why this happened, and this will hurt deeply for a long time. But I'm so blessed to have had this beautiful boy in my life!"
CNN reported Eli's story when he was born in 2015 with an extremely rare condition called arhinia. It left him without a nose, nasal passage or sinus cavity.
Only about 40 people in the world have been born with the condition, according to a study in the American Journal of Case Reports
Eli's mother, Brandi McGlathery, told CNN she first realized there was something different right after he was born.
"And I stood there for a second, and I said something is wrong with him," said McGlathery. "And my doctor said no, he's perfectly fine. And I said no, he doesn't have a nose."
Join the conversation See the latest news and share your comments with CNN Health on Facebook and Twitter.
In his first days after birth, Eli had a tracheotomy put in to help him breathe and eat. His birth gained significant news coverage, and he was known by many as the "miracle baby" because he survived.
"He was in the public eye a lot. We appreciate the love and support that we've gotten from around the world," said Finch. "It's meant a lot for the family. We just ask for everyone's prayers at this time." | tomekkorbak/pile-curse-small | OpenWebText2 |
Soft-templating synthesis of mesoporous graphitic carbon nitride with enhanced photocatalytic H2 evolution under visible light.
g-C(3)N(4) with worm-like pore and narrow pore size distribution was synthesized by using Pluronic P123 as soft-template. The worm-like porous g-C(3)N(4) not only possesses high BET surface area but also redshifts its absorbance edge up to 800 nm, and shows photocatalytic activity even when the irradiation light λ > 700 nm. | tomekkorbak/pile-curse-small | PubMed Abstracts |
Introduction {#s1}
============
Enterococci are official fecal indicator bacteria (FIB) in many countries for determining the bathing water quality and monitoring with the intention to protect swimmers from exposure to enteric pathogens ([@B1], [@B2]). An ideal FIB has a similar decay rate to enteric pathogens ([@B3]). However, the wide taxonomic range of microbes in the water relevant to the health of swimmers might have a different response toward environmental stress and growth factors such as pH values, solar radiation, salinity, predation, temperature and nutrients ([@B4]). Further, studies provide evidence that enterococci and enteric pathogens may persist longer in aquatic sediment and vegetation than in water ([@B4], [@B5]). In certain aquatic conditions, enterococci may grow in beach environments ([@B5], [@B6]) and enterococci originating from natural sources may pose unnecessary false positive alarms of a health risk. In contrast, the higher persistence of pathogens over FIB may jeopardize the health of beach users due to false negative alarms ([@B4]). Therefore, understanding the ecological interactions of different fecal indicators and pathogens with various biotic and abiotic factors found at bathing sites is important.
In a warming climate, in which surface water temperatures are rising, the characterization and predictions of health risks to swimmers are more important than ever ([@B7]). In the brackish Baltic Sea region, pathogenic members of the *Vibrio* bacterial genus are a concern because their proliferation benefits from a rise in the sea surface temperature ([@B8]--[@B10]). In recent history, the summertime heat waves of 2014 and 2018 have shown that a rise in surface water temperatures together with water nutrients and favorable wind conditions can lead to extensive occurrences of *Vibrio* spp. in the coastal waters of the Baltic Sea ([@B11], [@B12]). Particularly in the northern parts of the Baltic Sea, a subsequent rise of *Vibrio* spp. infections, mainly wound and ear infections, have been noted ([@B11], [@B13]) and pose a significant health risks to certain groups of people, namely the elderly, immunocompromised patients and persons with open wounds ([@B14]). Several *Vibrio* species with pronounced pathogenic potential (including the non-O1/non-O139 serotype of *Vibrio cholerae* and *Vibrio vulnificus, Vibrio parahaemolyticus*, and *Vibrio alginolyticus*) are known to occur in the Baltic Sea region ([@B9]--[@B11], [@B13]), and notifiable *V. cholerae* infections in Finland have been associated with severe manifestations of illnesses such as septicemia ([@B11]).
A rise in the bathing water temperature may have also indirect effects on microbial loads on beaches. High temperatures attract crowds to beaches for relief, especially if exceptional, extreme weather events occur ([@B7]). High temperatures may thus challenge beach management paradigms, and norovirus outbreaks have been associated with a sudden increase in the number of beach users ([@B15]). Furthermore, previous studies have detected viruses in surface water even when the FIB numbers were below the safe limit according to current monitoring protocols ([@B15], [@B16]). Such findings imply that FIB is insufficient for indicating the presence of enteric viruses in environmental waters; which justifies the need for introducing a virus indicator for fecal contamination to assess health risks of bathers ([@B3], [@B17]). Coliphages resemble human enteric viruses in their physical structure, composition, morphology, and survival characteristics in the environment and have been suggested as a potential virus indicator associated with human fecal contamination for monitoring bathing water ([@B3]). F-specific coliphage MS2 is one of the most commonly used virus indicators for water quality testing ([@B3]).
Almost every year by the end of the bathing season, bathing sites on the coast of the eastern Gulf of Bothnia (Baltic Sea) have experienced problems with overly high enterococci counts, without a known contamination source. Instead of fecal contamination, excess growth of aquatic vegetation has been noted at these bathing sites, while our earlier study identified enterococci species of mostly *Enterococcus faecalis* ([@B18]). Additionally, a knowledge gap has been noted concerning the survival and growth strategies of *Vibrio* spp. and especially *V. cholerae* as an emerging etiological agent for vibriosis in the temperate coastal bathing sites of the Baltic Sea as a result of climate change ([@B19]). In addition, more knowledge is needed on the use of MS2 coliphage as a virus indicator for fecal contamination in coastal environments.
This study evaluated the decay pattern of *E. faecalis*, one of the most dominant enterococci species in the human gut ([@B20]), in beach water, sediment and vegetation. The enterococci decay was compared with decay patterns of the pathogen *V. cholerae* and virus indicator MS2 coliphage in an experimental mesocosm simulating natural Nordic summer daylight conditions. Further, our objective was to investigate the role of aquatic vegetation in survival of *E. faecalis, V. cholerae* and MS2 coliphage in the beach environments.
Materials and Methods {#s2}
=====================
Mesocosm Preparation
--------------------
Water, sediment, and vegetation were collected from an official bathing site located on the western coast of Finland (Gulf of Bothnia, the Baltic Sea) and transported immediately after collection to the laboratory in cool boxes. Approximately 80 liters (l) of coastal water was collected in plastic containers. Similarly, coastal sediment weighing about 30 kg was collected from the subtidal zone and mixed well. Further, aquatic vegetation (*M. sibiricum*) of about 3 kg in weight was manually picked with roots from the bathing site. As illustrated in [Figure S1](#SM1){ref-type="supplementary-material"}; two 50 l aquariums (Kuopion Akvaariovalaisin, Kuopio, Finland) were filled to form the study mesocosms with an approximately 4 cm layer of sediment and then by adding water (\~35 l) with a final volume ratio of sediment and water of 1:4 \[following Badgley et al. ([@B5])\]. About 2 kg (wet weight) of *M. sibiricum* was planted in one aquarium. The mesocosm without the vegetation was coded BS and the mesocosm with vegetation as BSM (BS, Baltic Sea; M, *M. sibiricum*).
Mesocosms were exposed to identical artificial solar radiation simulating natural Finnish summer daylight conditions (19 h of daylight) using Sylvania Reptistar T8 full spectrum lamps (438 mm, ø 26 mm, 15 W, 6,500 K, UV-A 30%, UV-B 5%; Giant Valaisin, Kuopio, Finland). Both mesocosms were placed on a laboratory bench at ambient room temperature and covered to reduce evapotranspiration.
The mesocosms were fitted with identical aquarium pumps (Ismatec ISM-1079B, VAC-115/230 Ecoline, Wertheim, Germany) without a filter to create a continuous mix of water and to avoid an anoxic environment. All the metallic equipment which came into contact with the samples, i.e., mechanical stirrers, scissors, blades and spoons were autoclaved prior to use. Aquariums and pumps were cleaned with a soap-water and 5 mg/l chlorine solution and then rinsed with tap water (3 times) and then with distilled water (3 times), prior to use. Both mesocosms were fitted with a minimum and maximum thermometer for measuring the temperature (°C).
Spike Preparation
-----------------
After settling the sediment (for about 30 min), suspensions of *E. faecalis, V. cholerae* and MS2 were spiked into the BS and BSM mesocosms. The *E. faecalis* 13V1235-1 strain was isolated from a coastal bathing site during a high enterococci count event \[([@B18]); sampling site E\]. The *V. cholerae* non-O1, non-O139 strain was isolated from a vibriosis patient in the 2014 heat wave on the western coast of Finland ([@B11]). Both strains were stored at −75°C or lower before use in this study. The strains of *E. faecalis* and *V. cholerae* were cultivated on tryptone soya agar medium (TSA) and a blood agar medium and incubated at 36°C for 48 and 24 h, respectively. Colony material was suspended in a phosphate buffer to reach an absorbance of 0.8 at 420 nm with the aim to spike about 3 × 10^8^ CFU of both *E. faecalis* and *V. cholerae* into the water of both mesocosms. The colony counts of *E. faecalis* and *V. cholerae* in the spikes were enumerated by spread plating on TSA and blood agar media, respectively.
An MS2 coliphage (NCTC 12487) was produced using an *E. coli* host (ATCC 15597) following the principles presented in ISO 10705-1 (1995). Chloroform (1:10 v/v) was used to extract phages from the solution. The aqueous phase was centrifuged at 5,000 g for 20 min at 4° C and then filtered through a 0.45 μm filter (Acrodisc, Pall Corporation). The phage stock solution was stored at 4° C until use. The estimated initial number of the MS2 coliphage was the same as the *E. faecalis* and *V. cholerae*, being approximately 3 × 10^8^ PFU for each mesocosm.
Mesocosm Monitoring
-------------------
The physico-chemical and microbiological water quality was monitored for both mesocosms over time from duplicate samples. Natural background numbers of the microbial targets were enumerated as duplicates from the mesocosm water, sediment and vegetation before adding the spike. The sampling was continued after adding the spike (sampling for the initial numbers was conducted 30 min after the spike) and then at first twice a day (0.5, 1, 1.5, 2, 2.5, and 3 days), then every second day (4, 6, 8 and 10 days) and finally before ending the experiment on days 13, 20 and 27. A multi-parameter analyzer (Multi 3430; WTW GmbH, Weilheim, Germany) was used for measuring the pH, dissolved oxygen (mg/l) and conductivity (μS/cm) of the water samples. Further, the turbidity (NTU) was measured from subsamples in the laboratory at a wavelength of 860 nm with a Turb 555IR spectrophotometer (WTW GmbH&Co. KG, Weilheim, Germany) and the chloride concentration (mg/l) was monitored using the mercuric thiocyanate method as described in the manufacturers manual (Method 8113; HACH Lange GmbH, Duesseldorf, Germany).
The workflow for each sampling event was as follows for both BS and BSM to avoid the unnecessary mixing of the mesocosm: (a) the temperature was recorded (b) water samples (\~50 ml) were collected with a peristaltic pump to measure physical characteristics (c) water samples (10--1,000 ml in duplicate) were collected with a peristaltic pump for microbial analysis, (d) vegetation samples (only from BSM; about 1 g in duplicate) were collected with the help of a sterile rod and scissors, and (e) sediment samples (about 3 g in duplicate) were collected with the help of a sterile 2 ml micro-centrifuge tube. For processing the vegetation and sediment samples, a phosphate buffer at a ratio of 1:10 was used and the mixture was vortexed for 2 min (1,100 rpm), settled for 30 s and then the eluent was transferred into a clean tube for microbial analysis \[the protocol modified from Whitman et al. ([@B21])\].
Target Enumeration
------------------
The culturable counts of intestinal enterococci including *E. faecalis* were enumerated using membrane filtration according to the international standard method ISO 7899-2:2000 as described by Tiwari et al. ([@B18]). In brief, after filtration of multiple sample volumes, the membranes (GN6, Pall Life Sciences, Michigan, USA) were incubated on a Slanetz & Bartley medium (S&B, Oxoid Ltd. Basingstoke, Hampshire, England) at 36 ± 2°C for 44 ± 4 h. A range of sample volumes were used to produce 10--100 presumptive colonies per membrane. After counting the presumptive enterococci, the membrane was transferred on a preheated bile aesculin azide medium (BEA, Scharlau, Barcelona, Spain) and incubated at 44 ± 0.5°C for 2 h. A black or brown color formation on bacterial colonies on the BEA medium confirmed the colony belonged to the group of intestinal enterococci. The enterococci counts in the water were presented as CFU/100 ml and in sediment and vegetation as CFU/100 mg (wet weight).
The MS2 coliphage was measured using a culture-based method with a double agar layer (DAL) technique from 0.5 mL samples ([@B22]) using *E. coli* (ATCC 15597) as a host in two replicates. The MS2 counts in water were presented as PFU/100 ml and for the sediment and vegetation as PFU/100 mg (wet weight).
For molecular analyses, a subsample of water (50--300 ml) was concentrated onto 0.45 micrometer-pore-size, 47-mm-diameter polycarbonate membranes (Nuclepore, Whatman) and 0.35 ml of each vegetation and sediment eluent was directly transferred into a micro-centrifuge tube. The membranes and tubes were stored at −75°C or lower prior to nucleic acid extraction. The total DNA and RNA were extracted from the samples using the AllPrep DNA/RNA Mini Kit (Qiagen GmbH) as previously described ([@B23]). The RNA was further purified using the Ambion TURBO DNA-free DNase kit (Life Technologies, Grand Island, NY), and then complementary DNA (cDNA) was synthesized using the random hexamer primed Superscript III system for RT-PCR (Life Technologies). The total RNA was stored at −75°C or lower, while the cDNA and the DNA extracts were stored at −20°C until use.
The gene copy numbers of *Enterococcus* spp. and *Vibrio* spp. in the samples (including extraction and filtration blanks) were measured from cDNA and DNA extracts, and the *Vibrio cholerae* and Gram-negative bacteria gene copy numbers were measured from the DNA extract only. The qPCR assays were performed as previously described ([@B23]), by processing 8 μl of RNA in a cDNA synthesis (reverse transcription, RT). The primers and probes used in this study are listed in the [Table S1](#SM1){ref-type="supplementary-material"}. The targeted genes were 23S rRNA gene for *Enterococcus* spp. \[Entero1 assay; ([@B24])\] 16S rRNA gene for *Vibrio* spp. ([@B25]), and the *ompW* gene was used for the *V. cholerae* ([@B26], [@B27]). Total bacterial numbers in the BS and BSM waters were evaluated by using an assay targeted to 16S rRNA gene of all Gram -negative bacteria ([@B28]). The qPCR reactions were performed using a QuantStudio 6 real-time PCR system (Applied Biosystems) in 20 μl volume using the TaqMan Environmental PCR Master Mix (Life Technologies) for *Enterococcus* spp., *V. cholerae* and Gram- assays and the Power Sybr PCR Master Mix (Life Technologies) for a *Vibrio* spp. assay, all with primers and probes at final concentrations 0.2 μM (IDT Technologies, Inc). The cycling conditions included 95°C for 10 min of enzyme activation and pre-denaturation followed by 40 cycles at 95°C for 15 s of denaturation and at 60°C for 60 s of annealing, except for *Vibrio* spp., for which a 64°C annealing temperature was used and a melt curve analysis of the PCR amplicons was performed. Standard curves were generated using artificial gene fragments (gBlocks, IDT Technologies, Inc.) containing the sequences for each of the targeted genes.
In qPCR, undiluted and 10 fold diluted cDNA and DNA samples were used as qPCR templates to detect PCR polymerase inhibition. For samples in which PCR inhibition was detected, qPCR data was generated using the results from diluted samples. Background signals, if detected in the filtration blanks, were subtracted from all the results to generate the final qPCR and RT-qPCR data per assay. The limit of detection (LOD) was set as 3 copies per reaction. The copy number per 100 ml of water and 100 mg of sediment and vegetation was calculated for those samples with values above the limit of quantification (LOQ) (i.e., as determined by the lowest value within the quantification range). The final qPCR, equivalent LOD (eLOD) and equivalent LOQ (eLOQ) values were calculated after taking into account the volume/mass of the processed sample, factors associated with the different processing steps of the RNA and DNA manipulations, and the dilutions used for each sample analyzed.
Identification of Enterococci Colonies
--------------------------------------
Representative enterococci colonies grown on an S&B medium were identified with partial 16S rRNA gene sequencing as done in our previous study ([@B18]). Enterococci colonies isolated before the spike were identified from all the substrates (water, sediment and vegetation). Further, the enterococci colonies isolated from water samples after 1, 2, and 10 days from the spike, sediment samples after 6 and 20 days and vegetation samples after 4 and 10 days were identified. From the selected samples, the nucleic acid extracts of all or at least 10 enterococci colonies grown were amplified with universal bacteria primers 8F (5′-AGAGTTTGATCCTGGCTCAG-3′) and 787R (5′-CGACTACCAGGGTATCT AAT-3′) as described earlier by Ryu et al. ([@B29]). The quality of the sequences was checked and the consensus sequences from paired reads were made with the BioEdit, bioinformatics software ([@B30]). Finally, the enterococci species were identified with the NCBI Blast database ([@B31]).
Decay Rate
----------
The decay characteristics of the targets were tested with GInaFit (Geeraerd and Van Impe Inactivation Model Fitting Tool) freeware add-in for Microsoft Excel 2010 ([@B32]). Models were selected based on the lowest root mean sum of the standard errors (RMSE), and the highest R^2^ value as done earlier by Kauppinen and Miettinen ([@B33]). The details of the microbial decay model equations are shown in [Supplementary Material](#SM1){ref-type="supplementary-material"} (Microbial decay and decay rate).
GInaFit does not support modeling an erratic type of decay data. For that condition, the reduction equation was calculated with the following log-linear decay model equation \[as done by Badgley et al. ([@B5]) and Anderson et al. ([@B4])\]:
L
o
g
10
N
t
N
0
=
\-
k
t
where k = the decay rate, N~t~ = the target count at time t days, N~0~ = the target count 0-day, t = the time (in days) when the target count is N~t~.
Data Analyses
-------------
All the data was log~10~ transformed and expressed as the log~10~ CFU/PFU/GC per 100 ml for the water and per 100 mg for the sediment and vegetation. Where applicable, mean of duplicate samples BS and BSM was used. The data analysis was done with SPSS (IBM SPSS Statistics for Windows, Version 25.0, IBM Corp., Armonk, NY). In this study, the significance was compared at a 95% confidence level, if not mentioned otherwise. The median numbers of the targets and water quality parameters between the two mesocosms were compared using Wilcoxon signed-rank test. The relation of culturable *E. faecalis* with other targets was calculated using Spearman\'s rank correlation test.
The significance of the differences of the *k*-values was tested as done by Green et al. ([@B34]), by calculating the lower and upper confidence intervals with the following equation:
Confidence interval (CI)
=
k ± Standard Error (SE)
\*
α
where the SE was obtained from GInaFiT tool and the α value was obtained from a Student\'s *t*-table on (n−2) degrees of freedom at a 95% confidence interval. The *k*-values were significantly different if the confidence intervals of two *k*-values did not overlap.
Results {#s3}
=======
Water Quality in Two Mesocosms
------------------------------
The effect of vegetation on the properties of water was calculated by comparing the physico-chemical properties and total numbers of Gram-negative bacteria in the water without vegetation and with vegetation (BS and BSM, respectively). [Table 1](#T1){ref-type="table"} shows the mean and median of the measured parameters of water in both mesocosms. The vegetation significantly reduced the median turbidity of the water in the BSM compared to the BS samples (*p*-value 0.008; [Table 1](#T1){ref-type="table"}). The mean oxygen and chloride concentrations were slightly higher in the water of vegetated BSM mesocosm water than in the BS water, but the difference was not statistically significant ([Table 1](#T1){ref-type="table"}). The water temperature, pH and electric conductivity were not affected by vegetation. The water temperature increased in both mesocosms during the course of experiment from about 19°C to 23°C. The numbers of Gram-negative bacteria measured as gene copies per 100 ml and indicating the total number of bacteria in water, were significantly higher in the BS compared to BSM (*p*-value 0.007; [Table 1](#T1){ref-type="table"}).
######
Physico-chemical parameters and the number of Gram-negative bacteria in the water of mesocosms without vegetation (BS) and with vegetation (BSM).
**Parameters** **Mean (SD)** **Median** **Significance (Wilcoxon test; *p*-value)**
----------------------------------------------------- --------------- ------------- --------------------------------------------- ------- -------
Turbidity (NTU) 4.8 (3.6) 2.9 (2.7) 4.1 1.7 0.008
O~2~ (mg/l) 9.2 (0.6) 9.4 (0.6) 9.2 9.4 0.062
Chloride (mg/l) 2,200 (210) 2,000 (100) 2,220 2,000 0.073
Temperature (during sampling) (°C) 22.3 (1.7) 22.4 (1.4) 22.7 22.9 0.477
pH 7.7 (0.2) 7.6 (0.1) 7.7 7.6 0.450
Electric conductivity (μS/cm) 8,400 (240) 8,300 (140) 8,300 8,300 0.677
Gram-negative bacteria (log~10~ gene copies/100 ml) 7.7 (0.3) 7.2 (0.4) 7.8 7.5 0.007
*SD, standard deviation*.
Target Detection and Decay
--------------------------
The detection and decay rate of the targets was determined for each target microbe, as well as for the substrate from which the target was sampled, and also for both enumeration methods of enterococci (culture-based and molecular). Culturable enterococci were detected up to the end of the experiment in the water and sediment, but only up to the 20th day in the vegetation ([Figure 1](#F1){ref-type="fig"}). Further, when using molecular assays, the rRNA marker was more frequently detected than the rDNA marker ([Figures S2](#SM1){ref-type="supplementary-material"} and [S3](#SM1){ref-type="supplementary-material"}), indicating the higher 23S rRNA transcript copy numbers in the ribosomes of the viable *Enterococcus* spp. cells as compared to the copy numbers 23S rRNA gene in the *Enterococcus* spp. genome ([@B23]). However, culturable enterococci were detected more frequently than rRNA or rDNA *Enterococcus* markers, the result related to differences between the studied sample volumes and different limits of detection between the methods. *Vibrio* spp. genus-specific markers (rDNA, rRNA) were detected up to the end of the experiment in the water, sediment and vegetation ([Figure 2](#F2){ref-type="fig"} and [Figure S4](#SM1){ref-type="supplementary-material"}). The *V. cholerae* species-specific marker was less frequently detected than the genus-specific markers ([Figure S5](#SM1){ref-type="supplementary-material"}). Among the different substrates, *Vibrio* spp. was more frequently detected in the water than in the sediment or vegetation. MS2 coliphage was detected only by the 8th−10th days of the experiment in the water, and only during the 3 first days of the experiment in the sediment and vegetation ([Figure 3](#F3){ref-type="fig"}).
{ref-type="table"}, [3](#T3){ref-type="table"}). BS---unvegetated mesocosm and BSM---vegetated mesocosm.](fpubh-07-00269-g0001){#F1}
{ref-type="table"}, [3](#T3){ref-type="table"}). BS---unvegetated mesocosm and BSM---vegetated mesocosm.](fpubh-07-00269-g0002){#F2}
{ref-type="table"}, [3](#T3){ref-type="table"}). BS---unvegetated mesocosm and BSM---vegetated mesocosm.](fpubh-07-00269-g0003){#F3}
The decay characteristics of each target were calculated using the GInaFiT tool and with a classical log-linear model and are shown in [Tables 2](#T2){ref-type="table"} and [3](#T3){ref-type="table"}, respectively. The culturable enterococci followed the biphasic or biphasic decay model with a shoulder with the first rapid decay phase before the delayed decay phase, in all the substrates (water, sediment and vegetation) ([Figure 1](#F1){ref-type="fig"}; [Table 2](#T2){ref-type="table"}). The decay rate (*k*-value) of the culturable enterococci in the first rapid decay phase was 7.0 and 9.7/day in water of vegetated (BSM) and unvegetated mesocosm (BS), respectively. The culturable enterococci numbers reached the background level after the 8th−13th days of the experiment. The decay rate of culturable enterococci in the sediments of the BS and BSM was 2.6 and 0.8 per day in the first phase and 0.3 and 0.1 per day in second phase of the biphasic decay, respectively ([Figure 4](#F4){ref-type="fig"}; [Table 2](#T2){ref-type="table"}). In the vegetation of BSM, the enterococci decay was log linear with the rate of 0.8 per day. The culturable enterococci had a significantly higher decay rate in water than in sediment and vegetation, as the upper and lower confidence interval of the k-value did not overlap (visual inspection; [Figure 4](#F4){ref-type="fig"}).
######
Log-linear and nonlinear GInaFiT decay model results for culturable enterococci and MS2 coliphages.
**Mesocosm** **Substrate** **Log-Linear model and parameters** **Best fitted non-linear model and parameters**
---------------------------- --------------- ------------------------------------- ------------------------------------------------- ----- ------------ ------ ------ ------- ------------ ------------ ------------ ------ -----
**Culturable enterococci**
BS W 1.9 13 5.7 −0.8 ± 0.2 0.60 1.2 B. S. −9.7 ± 4.0 −0.2 ± 0.1 1.42 ± 0.2 0.97 0.4
BSM W 1.9 10 5.9 −0.8 ± 0.2 0.70 1.1 B. S. −7.0 ± 1.7 −0.3 ± 0.1 1.13 ± 0.2 0.99 0.2
BS S 2.1 27 4.8 −0.3 ± 0.0 0.94 0.3 B. S. −2.6 ± 2.7 −0.3 ± 0.0 1.93 ± 0.7 0.96 0.3
BSM S 1.7 27 4.7 −0.3 ± 0.0 0.88 0.33 B. −0.8 ± 0.3 −0.2 ± 0.0 na 0.90 0.3
BSM V 3.2 10 5.5 −0.8 ± 0.1 0.96 0.29 -- -- -- -- -- --
**MS2 coliphage**
BS W 0.2 8 4.5 −1.3 ± 0.1 0.97 0.57 -- -- -- -- -- --
BSM W ND na 4.6 −1.1 ± 0.1 0.98 0.2 -- -- -- -- -- --
BS S ND na 0.8 na na na -- -- -- \- -- --
BSM S ND na 0.7 na na na -- -- -- -- -- --
BSM V ND na 1.3 −0.5 ± 0.1 0.94 0.3 -- -- -- -- -- --
*BS, mesocosm without vegetation; BSM, mesocosm with vegetation; W, water; S, sediment; V, vegetation; N~nat~, background count before spike; N~0~, count at the zero hour (just after spike); t~bac~, time required for target counts to reach the background level; B.S., biphasic with shoulder; B, biphasic; D, 1--log reduction time; 4D, 4-log reduction time; R^2^, goodness of fit; RMSE, root mean sum of the standard errors; SE, standard error; SL, shoulder length; ND, not detected; na, not applicable*.
######
Decay rates (log-linear) of *Enterococcus* spp., *Vibrio* spp. and *V. cholerae* genetic markers.
**Mesocosm** **Substrate** **log10(N~**nat**~) GC/100 ml or 100 mg** **t~**bac**~** **log~**10**~(N~**0**~) GC/100 ml or 100 mg** **log~**10**~(N~**min**~) GC/100 ml or 100 mg** **t~**min**~** **k~**min**~ (day^**−1**^)**
------------------------------------ --------------- ------------------------------------------- ---------------- ----------------------------------------------- ------------------------------------------------- ---------------- ------------------------------
***Enterococcus*** **spp. (rDNA)**
BS Water 2.88 10--13 5.96 3.48 10 −0.19
BSM Water 3.08 8--10 6.01 3.52 8 −0.19
BS Sediment ND \>0 2.96 na na na
BSM Sediment ND \>0.5 1.81 na na na
BSM Vegetation ND \>4 3.34 na 4 −0.03
***Enterococcus*** **spp. (rRNA)**
BS Water 4.57 13 7.55 3.17 20 −0.24
BSM Water 4.45 20 7.08 2.91 20 −0.22
BS Sediment 6.06 27 7.73 4.93 27 −0.08
BSM Sediment 6.57 6 7.09 5.00 27 −0.1
BSM Vegetation 6.73 13 8.31 5.61 27 −0.1
***Vibrio*** **spp. (rDNA)**
BS Water 5.42 2.5 6.71 3.84 8 −0.19
BSM Water 5.58 2 7.21 4.95 6 −0.38
BS Sediment 3.08 2 3.71 2.87 13 −0.15
BSM Sediment 3.49 3 4.73 2.98 13 −0.08
BSM Vegetation 3.82 \>27 4.55 4.16 4 −0.13
***Vibrio*** **spp. (rRNA)**
BS Water 4.4 \>27 9.25 5.97 8 −0.41
BSM Water 6.74 \>27 9.32 7.08 6 −0.36
BS Sediment 8.7 4 8.79 7.09 20 −0.13
BSM Sediment 8.94 3 8.81 6.87 8 −0.22
BSM Vegetation 9.46 3 9.52 8.98 20 −0.04
***V. cholerae*** **(DNA)**
BS Water ND \>27 5.65 2.37 8 −0.41
BSM Water ND \>27 5.88 2.85 6 −0.51
BS Sediment ND \>1 2.16 na na na
BSM Sediment ND \>1 ND na na na
BSM Vegetation ND \>27 2.44 2.07 3 −0.13
*BS, mesocosm without vegetation; BSM, mesocosm with vegetation; N~nat~, background count before spike; t~bac~, time required for target counts to reach the background level; k~min~, decay rate calculated with the equation Log~10~ (N~t~/N~0~) = --kt; where N~t~ was the lowest target count over the course of experiment after adding the spike and t was the respective day when the target count was the lowest; ND, not detected; na, not applicable. The k-value for the rDNA of Enterococcus spp. and V. cholerae in sediment and vegetation was not available due to their low detection frequency*.
{#F4}
The MS2 coliphage followed the log-linear decay model in water of both the mesocosms. The counts remained continuously higher in the BSM water than in BS water ([Figure 3](#F3){ref-type="fig"}). Further, a higher decay rate of the MS2 coliphage was noted in the BS water than in the BSM water, k-values were −1.3 and −1.1 per day, respectively, in the BS and BSM water ([Figure 4](#F4){ref-type="fig"}; [Table 2](#T2){ref-type="table"}).
GInaFiT was not able to identify the decay model for the *Enterococcus* spp. genetic markers (rRNA, rDNA). However, from the visual inspection ([Figures S2](#SM1){ref-type="supplementary-material"} and [S3](#SM1){ref-type="supplementary-material"}), the biphasic decay of rRNA in water and sediment and an almost log linear pattern in vegetation was seen. The decay of the *Enterococcus* spp. genetic markers (rDNA, rRNA) was slower than the decay of culturable enterococci counts in all substrates. The markers exhibited a higher decay rate (k-value) in water (0.19--0.24/ day) than in sediment (0.08--0.1/ day) and vegetation (0.03--0.1/ day) ([Table 3](#T3){ref-type="table"}). It took 13 and 20 days after the spike in BS and BSM water, respectively, for *Enterococcus* spp. rRNA to reach the background level ([Figure S2](#SM1){ref-type="supplementary-material"}).
Additionally, for genetic markers of *Vibrio* spp. (rDNA, rRNA) and *V. cholerae*, GInaFiT was not able to identify the decay model. On visual inspection, a biphasic decay pattern was seen as the gene copies dropped rapidly up to day 6--10 but later increased back nearly up to the spiked level ([Figure 2](#F2){ref-type="fig"}, [Figures S4](#SM1){ref-type="supplementary-material"} and [S5](#SM1){ref-type="supplementary-material"}). The log-linear decay rate of all *Vibrio* markers was lower in vegetation than in water or sediment with the exception of the rDNA marker in the sediment of the BSM water ([Table 3](#T3){ref-type="table"}).
The Relationship of *Vibrio cholerae* and MS2 With Culturable Enterococci
-------------------------------------------------------------------------
The relation between the enumerated numbers of culturable enterococci with other microbial targets in the water is shown in [Table 4](#T4){ref-type="table"}. Culturable enterococci had a strong positive correlation with *Enterococcus* spp. rDNA and rRNA markers. Overall, *Vibrio* spp. and *V. cholerae* markers had weak correlations with culturable enterococci. However, the correlation was strongly positive (ρ = 0.81--0.92) in the first 4 days after the spike. The culturable enterococci in the sediment and vegetation had a strong correlation with culturable enterococci in the water ([Table 4](#T4){ref-type="table"}). The correlation of the MS2 coliphage with culturable enterococci was strong in the first 6--8 days of the experiment (ρ \> 0.85). There was also strong relation between culturable enterococci counts and *Enterococcus* spp. rDNA and rRNA gene copy numbers in water (correlation coefficients ρ = 0.83--0.87, [Table 4](#T4){ref-type="table"}).
######
Comparing Spearman\'s rho correlation coefficient (ρ) between culturable enterococci with other microbial targets.
**Targets** **Substrates** **27 days** **First 4 days**
-------------------------------- -------------------------- ---------------- ---------------------------------------------------------------------------- -----------------------------------------
Culturable enterococci (Water) *Enterococcus* spp. rDNA Water 0.83[^\*\*^](#TN2){ref-type="table-fn"} 0.87[^\*\*^](#TN2){ref-type="table-fn"}
*Enterococcus* spp. rRNA Water 0.85[^\*\*^](#TN2){ref-type="table-fn"} 0.86[^\*\*^](#TN2){ref-type="table-fn"}
MS2 coliphage Water 0.87^[^\*\*^](#TN2){ref-type="table-fn"}[^\#^](#TN1){ref-type="table-fn"}^ 0.90[^\*\*^](#TN2){ref-type="table-fn"}
*Vibrio* spp. rDNA Water 0.28[^\*^](#TN3){ref-type="table-fn"} 0.81[^\*\*^](#TN2){ref-type="table-fn"}
*Vibrio* spp. rRNA Water 0.23 0.88[^\*\*^](#TN2){ref-type="table-fn"}
*V. cholerae* DNA Water 0.33[^\*^](#TN3){ref-type="table-fn"} 0.92[^\*\*^](#TN2){ref-type="table-fn"}
Culturable enterococci Sediment 0.86[^\*\*^](#TN2){ref-type="table-fn"} 0.73[^\*\*^](#TN2){ref-type="table-fn"}
Culturable enterococci Vegetation 0.94[^\*\*^](#TN2){ref-type="table-fn"} 0.80[^\*\*^](#TN2){ref-type="table-fn"}
The correlation was measured only until the MS2 coliphage was detected (up to 8--10 days).
The correlation is significant at the 0.01 level (2-tailed).
*The correlation is significant at the 0.05 level (2-tailed)*.
Discussion {#s4}
==========
This study identified biphasic with a shoulder, biphasic and log-linear decay patterns of culturable enterococci, *Vibrio* spp. and MS2 coliphage, respectively, in coastal bathing water. Culturable enterococci decayed rapidly in water for up to 2.5 days, before a slower decay phase. The identified slightly higher decay rate of culturable enterococci in this study than noted in earlier studies with coastal waters ([@B4], [@B35], [@B36]) could be due to differences in the experimental settings. While, our study used an environmental enterococci strain under 21 h of continuous artificial solar radiation each day at room temperature (21--23°C), Craig et al. ([@B35]) focused on the effect of the temperature, and did not mention the solar radiation, while Anderson et al. ([@B4]) used enterococci from dog feces, waste water and soil inoculum in their experiment on rooftop of a building with an open-air greenhouse, and Zhang et al. ([@B36]) spiked targets directly from treated sewage.
The detected biphasic decay of *Enterococcus* spp. molecular markers (rDNA, rRNA) in water confirmed the recent findings by Ahmed et al. ([@B37]). Although the molecular marker decay seems to be slower than the decay of culturable enterococci counts, the strong correlation between the culturable counts and gene copy numbers generated using qPCR and RT-qPCR were found. This result indicates potential usability of molecular methods as alternatives to culture based methods for water quality monitoring.
The biphasic decay of microbes could be due to the target strain heterogeneity; various strains might have different decay rates ([@B38]). In our study, this is not a probable explanation as a single *E. faecalis* strain was used as a spike, and all the identified isolates from the samples before the spike belonged to the same species. Thus, the cause of the initial rapid decay of enterococci could be due to a rapid inactivation after a sudden change of environmental conditions such as the solar radiation, nutrient availability, predation, salinity or water temperature, but could be also related to initial growth phase and high density of spiked bacterial cells ([@B39]). Similar decay is expected to take place after a fecal contamination incidence into bathing waters and must be taken into consideration when interpreting bacterial indicator results. Later on, the introduced bacteria might start to cope better with the prevailing environment, so after an adaption phase their decay rate might be lower as was noted in the present study.
Additionally, *Vibrio* spp. and *Vibrio cholerae* genetic markers exhibited biphasic decay patterns. The good persistency of *Vibrio* spp. in water was as expected, since these bacteria are autochthonous to coastal waters ([@B8], [@B10], [@B40], [@B41]). The results presented herein correspond to one earlier study in which Zhang et al. ([@B36]) demonstrated the good persistence of *Vibrio* OTUs using high-throughput sequencing in a laboratory experiment. In the present study, the gene copies of *V. cholerae* dropped to a minimum by days 6--8 but then the numbers increased back nearly up to the spiked level. It is obvious that the current bathing water quality monitoring against fecal contamination ([@B1]) is not protecting bathers from *Vibrio* infection risks. In the present study, the observed lack of correlation between the genetic markers of *Vibrio* spp. and *V. cholerae* with culturable enterococci after the first 4 days highlights the deficiency of current monitoring practice. However, further studies are needed to investigate if *Vibrio* spp. counts could be enumerated from bathing waters using culture-based methods ([@B42]). It is possible that such counts could relate to counts of culturable enterococci better than the *Vibrio* marker gene copy numbers. The Nordic aquatic environment is rich in carbon and phosphorous and is favorable to the proliferation of *Vibrio* spp. ([@B9]). The pronounced proliferation of pathogenic *Vibrio* spp. in coastal waters is expected to cause greater public health concerns in future years due to global warming and the subsequent rise in sea surface temperatures ([@B8]--[@B10], [@B43]). *Vibrio* spp. have short generation times (\<10--30 min) at their optimum growth temperature (23--25°C) and can respond rapidly to changing environmental conditions ([@B10], [@B44]). Therefore, for health risk management purposes, early-warning modeling tools such as Vibrio Viewer \[<https://e3geoportal.ecdc.europa.eu/SitePages/Vibrio%20Map%20Viewer.aspx>; ([@B13])\] are useful. Further, the determination of *Vibrio* species from the bathing waters might become as a relevant effort to carry out, especially in cases of suspected waterborne infections.
The log-linear decay pattern of the MS2 coliphage resembled the decay patterns reported in earlier laboratory studies on F-specific coliphages, adenoviruses, and polyomaviruses in coastal waters ([@B37], [@B45]). Further, Craig et al. ([@B35]) reported a relatively slower decay rate of somatic coliphages in coastal water mesocosms and found that the temperature affected the decay rate. MS2 is one of the most UV resistant phage and used commonly as a conservative virus surrogate ([@B46]). In the present study, vegetation might have sheltered MS2 as the decay rate was slower in the BSM water than in the BS water. In fact, MS2 counts correlated with the culturable enterococci in the first few days of the experiment, which makes sense in the mesocosm mimicking natural environment. The decay of culturable MS2 calls for further studies to investigate its survival mechanisms. More information is needed for comparison if similar behavior is seen with viral pathogens.
In our study, bacterial targets persisted longer in sediment and vegetation than in water (except for *Vibrio* spp. rRNA). This better persistency detected herein has been reported also in several earlier studies in which the availability of nutrients, protection from UV radiation and predation, and lowered temperature have been identified as factors enhancing the survival ([@B4], [@B5], [@B17], [@B35], [@B36], [@B40], [@B47]). Further, the higher persistency of surface attached microbes in sediment or vegetation than in water may be due to the surface biofilm protecting microbes from external stress factors ([@B48]). Schets et al. ([@B49]) detected norovirus only in the sediment but not in the water at a bathing site during a bathing water outbreak. In our study herein, the poor detection frequency of the MS2 coliphage in sediment (12%) and vegetation (13%) could be due to the methodological limitations ([@B47]). Here, we used the same protocol for the separation of the MS2 coliphage and enterococci from sediment and vegetation, which was originally developed for enterococci ([@B21]).
Vegetation can play further complex roles in aquatic systems and lead to changes in water turbidity, pH, temperature, and predator species ([@B50]), of which the turbidity change was noted in the present mesocosm study. Furthermore, in our study, the oxygen concentration was slightly higher in BSM than in BS water, potentially due to photosynthesis of vegetation. In general, due to the settling effect, vegetation in water may reduce suspended solid, leading to less turbid waters. However, due to the shedding effects, temperature and UV exposure may decrease enabling better microbial survival when vegetation is present. However, after growth phase, the decomposing vegetation might have an opposite effect on water quality. Such changes can have multiple effects on the decay rate of the studied targets. In our experiment, vegetation cover could have effect on enterococci decay as we observed a slightly higher decay rate of enterococci in BS water than in BSM water in the first phase of the biphasic decay pattern. Also the MS2 coliphage was detected in a shorter time (8 days) in BS water than in BSM water (10 days) and the vegetation seemed thus to reduce the decay rate in water. Consistent with our findings, also Badgley et al. ([@B5]) demonstrated that vegetation reduced the decay rate of enterococci in fresh water in a similar experimental setting. In contrast, however, Kleinhrinz et al. ([@B48]) demonstrated that vegetation increased the decay rate of *Escherichia coli, Salmonella*, and *Shigella*, and they argued that the targets rapidly attached to vegetation and thus recorded a lower count from the water column.
In addition to the inactivation, the rapid reduction of microbial targets in the water could be due to sedimentation and attachment to the surface sediments ([@B35], [@B51]). The attachment of the targets to turbid suspended particles and their settling and deposition at the bottom of the mesocosm could thus have an effect on the initial rapid decay rate. In our study, culturable enterococci counts in the sediment and vegetation related strongly to culturable enterococci counts in the water. We did not notice the significant difference between the median value of enterococci counts in BS and BSM water. However, the total number of Gram-negative bacteria was higher in BS than in BSM water. These findings could partly be explained due to a partitioning effect. While the total numbers of bacterial targets were not different in the mesocosms, the BSM environment had three substrates (water, sediment, and vegetation), but the BS environment only had two (water and sediment). Thus, benthic sediment and aquatic vegetation could work as a sink and source of microbes like FIB and probable human pathogens ([@B6]). The FIB sink (due to sedimentation) in the benthic sediment and vegetation could contribute to the lower count of FIB in the water during regulatory monitoring of the microbial quality of bathing water, and their probable resuspension can complicate the interpretation of the results of water quality monitoring. The current microbial water quality monitoring protocol does not account for the microbial quality of the sediment and vegetation at bathing sites. The contamination and decay are simultaneous and continuous processes at each bathing site.
Conclusion {#s5}
==========
This study demonstrated the partitioning of pathogens and fecal indicators in coastal waters between water, sediment and vegetation. It also indicated that the decay of microbes was different in water than in sediment in presence or absence of vegetation. The current bathing water monitoring protocol does not account for the microbial content of sediment and vegetation at bathing sites and thus possibly underestimates the actual enterococci counts during the regulatory monitoring of water. Furthermore, enumerating only the enterococci does not seem enough for the prediction of free-living pathogens such as *Vibrio* spp. Finally, the different decay patterns observed between MS2 and enterococci emphasize the need for and importance of a viral indicator for assessing water quality more comprehensively.
Data Availability Statement {#s6}
===========================
All datasets generated for this study are included in the manuscript/[Supplementary Files](#s8){ref-type="sec"}.
Author Contributions {#s7}
====================
All the authors participated in the project design, the execution of the experimental work, data analysis and manuscript writing. AT calculated the data and drafted the initial version of the manuscript. AK was incharge of the MS2 work. TP supervised the work.
Conflict of Interest
--------------------
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
The authors would like to express special thanks to all the people and institutions involved and helped contribute to the success of this work. Special thanks go to the site of the research for providing financial and technical help. We would like to sincerely thank the laboratory personnel of the Expert Microbiology Unit, at the National Institute for Health and Welfare, namely Tiina Heiskanen, Tarja Rahkonen and Iina Laaksonen. Further, special thanks also go to Anna-Maria Hokajärvi and Asko Vepsäläinen, for the support they provided during the process. The local health protection officer Maria Nylund from West Coast Environmental Unit is gratefully acknowledged for her help during the sample and material collection from the bathing site. In addition, the authors acknowledge Kaute Foundation for their personal grant to AT (grant number 20190366). Further, the scientific writing workshop organized by Young Water Professionals Finland of the International Water Association at Aalto University, in Helsinki and Professor Gustaf Olsson for his critical feedback on the manuscript are acknowledged.
Supplementary Material {#s8}
======================
The Supplementary Material for this article can be found online at: <https://www.frontiersin.org/articles/10.3389/fpubh.2019.00269/full#supplementary-material>
######
Click here for additional data file.
[^1]: Edited by: Nur A. Hasan, Center for Bioinformatics and Computational Biology, University of Maryland, United States
[^2]: Reviewed by: Juan M. Gonzalez, Spanish National Research Council (CSIC), Spain; Durg Vijai Singh, Institute of Life Sciences (ILS), India; Siraje Arif Mahmud, University of Texas at Arlington, United States
[^3]: This article was submitted to Environmental Health, a section of the journal Frontiers in Public Health
| tomekkorbak/pile-curse-small | PubMed Central |
Q:
What is the meaning of "l" in some variables initialization - C++
What is the meaning of "l" in some variable initialisations? For example:
#define maxpossible (1000000000L)
double A = 1L;
double B = 999999999l;
Is there a difference between "L" and "l"?
A:
This is a suffix type specifier, for A and B you can read more about floating point literals here. The short answer is that L and l both indicate long double. For maxpossible you can read about integer literal here and L indicates long.
EDIT
As Mike Seymour kindly pointed out all of the literals are integer literals. This just goes to show that the times when you do not sanity check your answer, you will say something wrong. A simple sanity check would have been as follows:
#include <iostream>
#include <typeinfo>
int main()
{
std::cout << typeid( decltype( 1L ) ).name() << std::endl ;
std::cout << typeid( decltype( 999999999l ) ).name() << std::endl ;
std::cout << typeid( decltype( 1000000000L ) ).name() << std::endl ;
}
Which gives me l for each one and running that through c++filt -t gives me long. What would have made the literals floating point literals? Either a:
Digits containing a decimal point
Digits with exponential notation, for example 4e2
For example:
std::cout << typeid( decltype( .1l ) ).name() << std::endl ;
std::cout << typeid( decltype( 1e2L ) ).name() << std::endl ;
Which gives me e for both cases and running that through c++filt -t gives me long double.
| tomekkorbak/pile-curse-small | StackExchange |
Q:
How is a student directory best handled in WordPress?
I am doing a WordPress site for a school. One of the pages would have a list of 20 or so students, which would include their name, photo and small blurb.
How is this type of thing handled in Wordpress? I would like the user of the CMS to be able to manage this page effectively - adding/removing students etc.
I know Wordpress is being used in e-commerce sites, so people who run these site must be in the same situation on their pages of products.
Should I be using plugins? Custom fields?
thanks in advance
A:
You could create a custom post type 'student', with post thumbnails for the images. The post title would be their name, post content would be the blurb. If the code scares you, there are plugins to assist.
Taxonomies are also available to you, which operate like categories and tags, but can be any set of attributes or means of grouping.
| tomekkorbak/pile-curse-small | StackExchange |
These sample scans are from the original record. You will get scans of the full pages or articles where the surname you searched for has been found.
Your web browser may prevent the sample windows from opening; in this case please change your browser settings to allow pop-up windows from this site.
Traders and professionals in London
(1805)Holden's Triennial Directory for 1805 to 1807 includes this 'London Alphabet of Businesses, Professions, &c.': coverage is good; about 30,000 individuals are recorded. | tomekkorbak/pile-curse-small | Pile-CC |
Saturday, June 12, 2010
So We Begin
So we begin: On day one Ms. Biggs gives us a first rate inspiring lecture in the a.m. and then goes around the room discussing project ideas with each student. I have long been thinking about creating a pattern using bugs as the main element so we talk about that and she tells me to do a bit of sketching. Then I run home to grab the materials I have been hoarding for the last 2 months to create this "bug pattern" and I start playing around with materials. I am unsure about what to use as the background element. I pour through the supplies on hand at the arts center and I come up with a big fat nothing. All I have are these yummy shiny ceramic beads that look like bug bodies and I have no ideas for a background treatment. Emma comes around and says well, let me see what I can find. She goes over to this huge stash of supplies that I have already spent 30 minutes digging through and she walks back over to me within about 2 minutes with a very ugly Mexican tile that looks like it belongs in the bathroom of a fast food taco joint. She takes this ordinary tile with her thin broken hand (no really she took a tumble recently and is in a cast) and she starts nipping away at it and she chips the glaze off to reveal this stunning rough pumpkin colored organic looking material that is totally perfect in color and texture for what I am doing.I am in awe, how in the heck did she see the magic hiding inside this boring common tile? She points out that even the tiny bits of distressed glaze that did not get chipped off are very lovely. Of course I love anything messy and imperfect so I jump all over that and on day two I spend a lot of time chipping and preparing my distressed background tiles.
On day three I had a go at the hammer and hardie ( shown above) in an effort to chip away the glaze faster. It worked pretty well.
Mr. Triangle is not my friend?
On day 3 of the mosaic workshop Emma stresses again to us that triangles in mosaic work call a lot of attention to themselves and should be used rather sparingly. So on day three I find myself in a cutting funk and every where I place a tile I am setting myself up for the need of a triangle filler. I start to stress out over that and find myself in a real funk, nothing goes together easily on day three. Then I fret that my apparent frustration is going to make me look like a real wimp, and then I tell myself to heck with it I am a real wimp! This workshop is indeed just as hard as I had imagined it would be. I am learning so much though. Emma is a delight and an inspiration. As a teacher she is tough yet encouraging.
So this morning I find myself enthusiastic even after a somewhat restless night. We are going into day 4 and I am determined to lay down some tile today. I am also determined to relax and remember that it is not about me or this one silly project, we have a very inspiring woman here from across the pond as they say and I need to listen, ask questions and know that some of the stuff may not soak in until weeks later, and that is ok. The important thing is to be present.
2 comments:
My gosh, Rebecca! Methinks you are getting a lot from this week that you didn't think you'd get or enjoy! I can't wait to see what you do come up with! Just out of curiosity...Couldn't you just use the back sides of those tiles and not worry about chipping off the ceramic glazed side?
Sherry-:) yes, I could and some are the backs but there is a real beauty in the way the glaze bits stick on in some areas. And even when using the backsides I still have to gnaw into the tile with my tool to achieve the irregular surface that resembles soft rock almost. I'll post detail pics soon and a wrap up. Day 4 went pretty well. My last day is today.
Meet Rebecca
Rebecca Collins has been creating custom pet portraits since 1998. Her company Art Paw was one of the first of its kind on the web, and continues to stay ahead of the pack combining fine art and digital technology to satisfy both commercial and residential clients. Rebecca has created a dream job for herself that combines her love for animals, art and technology. She is owned by 3 Scottish Terriers and shares her life with her husband, Poet Dan Collins. | tomekkorbak/pile-curse-small | Pile-CC |
Group resorting to arbitrary fines, extortion and gangsterism in face of airstrikes and recapturing of territory, say commanders
A combination of airstrikes on Islamic State-controlled oilfields, recapture of Isis-held territory and destruction of the group’s cash storage sites containing up to $800m (£550m) may have destabilised the self-declared caliphate in Syria and Iraq, according to coalition military commanders on both sides of the Atlantic.
Ministry of Defence officials claimed this week that they have seen signs that Isis is increasingly resorting to arbitrary fines, extortion and gangsterism to make up a shortfall in income.
Speaking about the campaign for the first time, Air Vice-Marshal Edward Stringer, the senior UK civil servant in charge of undermining Isis finances, said: “What we are now seeing is that they are running short of cash and they are looking for more imaginative ways to do things. It is early days, but only in the last week we have heard from the sources that we have that the taxation system is becoming more arbitrary, more looking to fines, and so becoming less progressive and less easy to sell to the population.” The gangsterism was tarnishing the Isis brand, he claimed.
US-led airstrikes against Islamic State in Syria and Iraq – interactive Read more
In Baghdad, the deputy US commander for operations and intelligence, Maj Gen Peter E Gersten, said up to $800m held in Isis storage facilities had been blown up by coalition airstrikes. The number of foreign fighters joining the extremists was down by 8%, he claimed.
These assertions are hard to verify, and could be seen as self-delusion, propaganda or disinformation – all designed to reassure public opinion that Isis is being slowly degraded. Reliable statistics are in short supply, leaving the coalition reliant on intermittent evidence such as Isis bookkeeping documents captured when its territory is retaken.
But the claims chime with documentary evidence published by researchers in the counter-terrorism journal CTC Sentinel, showing that Isis is struggling to fund its fighters, which make up about 60% of the group’s costs.
The documents reveal that even in oil-rich areas, confiscation now represents 40% of Isis income. Confiscations can be from residents who fled their homes, for violation of its regulations or illicit smuggling of goods, such as alcohol and cigarettes.
Likening the anti-Isis coalition’s efforts to financially weaken the Isis base to the economic warfare waged against Nazi Germany during the second world war, individuals including Stringer have come to regard efforts to understand, and undermine, the group’s funding as equally important to military gains.
“Isis is trying to get more hard cash through extortion of the local population,” Stringer said. “We are starting to see corruption and embezzlement among senior leaders, suggesting we are having success.”
Until recently, the MoD had estimated that 40% of Isis revenue came from oil, 40% from forms of taxation and 20% from other sources, including sales of antiquities and profiteering in money markets. Those proportions may have changed due to the strikes on oil wells, leaving the split closer to 20/50/30.
The MoD is reluctant to give an estimate of Isis’s annual income. Retrieved spreadsheets show that its natural resource revenues in the six months to February 2015 amounted to $290m, about 70% of which came from the giant al-Omar oilfield in Deir ez-Zor, previously run by Royal Dutch Shell.
Since then, there have been 1,216 strikes on oil infrastructure targets and tankers, reducing production by 25% and cutting revenue by 10%.
The MoD claims that production is about 30,000 barrels a day. Others, such as IHS, put the figure lower.
Stringer said: “We have stopped them getting oil out of the ground and transporting it. We have moved them from moving oil to selling it at the wellhead. The coalition has also targeted additives and chemicals that Isis needs to refine its oil products, and what is now being produced is ‘crude in every way’.”
However, contrary to the claims of some experts, much of Isis’s crude oil is not smuggled abroad – it is sold within the extremists’ territory. “It is nevertheless a major source of revenue, since there is a demand from local businesses and homes with generators,” Stringer said. The ministry refused to confirm any evidence of large-scale sales to Turkey, referring only to microsmuggling.
There is also a restraint in the way that oil wells are being struck. The coalition has the ability to flatten them altogether, but cost benefit analyses suggest that it is better to disable parts of the oilwells in order to make them impossible to operate until spares are found and infrastructure is repaired.
It wasn’t until this week that the Royal Air Force used the largest bomb in its inventory, the 2,000lb Enhanced Paveway 111, against Isis for the first time.
Isis under airstrikes – a guide in maps Read more
Aside from oil production, Isis’s tax base is eroding as it cedes territory. Last year, the group lost 14% of its land, and a further 8% in the past three months. The population under Isis control has declined from 9 million to 6 million.
The squeeze has led to pay cuts for foreign fighters. The Pentagon claimed this week that the number of such individuals entering Isis territory had plummeted by 90% in the past year.
Gersten said this week: “When I first got here, we were seeing somewhere between 1,500 and 2,000 foreign fighters entering the fight. Now that we’ve been fighting this enemy for a year, our estimates are down to about 200. And we’re actually seeing an increase now in the desertion rates in these fighters. We’re seeing a fracture in their morale. We’re seeing their inability to pay.”
Until recently, the basic Isis wage was $50 a month, with an additional $50 for each wife, $35 for each child, $50 for each sex slave, $35 for each child of a sex slave, $50 for each dependent parent and $35 each for other dependents. There may also be other salary additions such as a daily food allowance, heating costs and bonuses for performing certain duties.
The coalition claims that its intelligence is now good enough to know where Isis stores cash, right down to the precise room in a building where the money is kept. “We believe we have removed hundreds of millions from circulation,” Gersten said.
There has also been an attempt to reduce liquidity in the formal and informal banking system.
The Foreign Office said the system allegedly used by Isis involved transferring captured money out through regional banks and money services businesses – disguising its source – and then putting the cash back into the Iraqi banking system in Baghdad. The funds were then entered into foreign currency auctions, where Isis was able to make a profit on the differential between wholesale and retail exchange rates. Any profit from these activities was transferred back into Isis-controlled areas through the Hawala system, which is made up of regulated and unregulated MSBs.
So far, under pressure from the US Treasury, the Iraqi central bank has closed or listed 142 MSBs deemed to be supporting Isis, and prevented them from taking part in foreign exchange auctions.
Nevertheless, it is striking how slow the west has been to understand the sources of Isis funds and how understaffed, at least in Whitehall, the effort has been. Stringer, giving evidence to the foreign affairs select committee this week, admitted that much of the evidence is “second order” and that it is very difficult to “get a grip of what was going on [on] the ground”. | tomekkorbak/pile-curse-small | OpenWebText2 |
The invention disclosed herein relates generally to reporting information to a host computer relating to the pressure applied to a transducer of a pressure-sensitive input device. The transducer has a raw pressure range and sensitivity, and the invention more specifically relates to adjusting the pressure range and sensitivity reported to the host computer. In a specific embodiment, the input device is a pointing device such as a stylus or cursor which is part of an absolute position determining system. The pressure may be applied to the transducer by pressing the device against a surface or by pressing a button or like element carried by the device. When used as part of an absolute position determining system, the transducer inputs the raw pressure-related information to a processor of the position determining system. The absolute position determining system may be a digitizer which includes a processor coupled to receive the raw pressure-related information from the transducer.
Although a pressure-sensitive device incorporating the invention may be employed as an input device with many types apparatus, its presently preferred use is as a pointing device for a digitizer. Examples of pressure-sensitive styli for digitizers are described in U.S. Pat. Nos. Re. 34,095 (Padula et al.) and 5,004,871 (Purcell). The disclosures of those two patents are incorporated herein by reference. A pressure sensitive pointing device has a transducer for detecting the pressure being applied to its tip, or to one or more finger-operated switches. The transducer is ultimately coupled to a processor, typically located in a digitizer tablet which also contains means which cooperate with the pointing device for determining the position of the pointing device relative to a surface of the tablet. The pointing device transmits information related to the detected pressure via a signal conductor or other means (e.g., telemetry) to the digitizer tablet, which in turn processes the raw information and reports it via a signal conductor or other means (e.g., telemetry) to the host computer.
The invention is described below in connection with a digitizer, specifically an electromagnetically coupled digitizer, which includes a pointing device incorporating a pressure transducer and a digitizer tablet incorporating a processor and other circuits. However, the invention is not limited to use with pointing devices got digitizers, and when used in a digitizer, the invention is not limited to any particular digitizer technology or to any particular processing configuration. For example, the digitizer may employ any suitable technology including, but not limited to electromagnetic, electrostatic, magnetostrictive, resistive, ultrasound, optical, etc., and the processor ultimately coupled to the transducer in the pointing device may be part of the pointing device or part of the host computer. Also, the processor of the digitizer may be incorporated in the host computer rather than in the digitizer tablet.
There is considerable variation on the pressure response of pressure-sensitive pointing devices. However, to keep costs low, digitizer manufacturers did not heretofore calibrate the responsiveness of pressure-sensitive pointing devices and did not compensate for manufacturing variations in the pressure response of the pointing devices. Instead, as discussed below, they set the pressure sensitivity and range to accommodate an "average" user. This has the drawback that all users, whether heavy-handed or light-handed, must adjust to a pre-defined pressure response, which for many users is not optimal.
In order to facilitate understanding of the operation of a pressure-sensitive pointing device and the manner in which its range and sensitivity are set, conventionally and in accordance with the invention, certain terms used below are defined. Also, pressure (or force) applied to the tip or a finger-operated switch of the pressure-sensitive pointing device will be referred to below simply as pressure applied to the pointing device. Further, the information related to the pressure applied to the pointing device which is transmitted by the pointing device for use by the processor is described herein in terms of "counts" of arbitrary units which monotonically increase with the amount of pressure applied.
Raw Pressure Count: The count transmitted by the pointing device, which may be a number between 0 and M where M is some maximum number. Typically, the maximum is a power of 2 (less 1), conforming to, for example, the maximum value which can be held in some fixed number of bits, e.g. 127 for 7 bits, 255 for 8 bits, etc..
Minimum Raw Pressure Count: The count transmitted by the pointing device with no external pressure applied thereto. To allow for mechanical tolerance and lack of calibration, this number is "designed" to be non-zero.
Maximum Raw Pressure Count: The count transmitted by the pointing device with "maximum pressure" applied thereto. To allow for mechanical tolerance and lack of calibration, this number is "designed" to be less than M, where M is described above.
Maximum Pressure: The pressure applied to the pointing device at which the raw pressure count remains constant with no discernible change with increased pressure applied to the pointing device.
Raw Pressure Range: Maximum Pressure minus zero.
Raw Pressure Count Range: Maximum Raw Pressure Count minus Minimum Raw Pressure Count. ##EQU1##
Reported Pressure Count: The count provided to the application program as an indication of the amount of pressure that the user is applying to the pointing device. The application program typically uses this count to determine, for example, the width of the line to be drawn on the screen (simulating a paint brush in a graphic arts application), or the darkness of the line (simulating artist chalk), or the speed of animation (simulating an accelerator in a game-like program).
Maximum Reportable Pressure Count: The count which, by convention, represents "saturation". Typically, this limit is set by the "format" established for representing pressure to the application program. In the application program, for example, when this count is reached, the application will draw the "widest" line, the "darkest" line, or apply the "maximum" acceleration.
Minimum Reportable Pressure Count: Typically, this count, by convention, should be zero. But, due to manufacturing variations and lack of calibration, some pressure-sensitive pointing devices (and the associated system for processing raw counts and providing count reports to the applications program) report a non-zero value (a "pre-load" value) when no external pressure is being applied to the pointing device.
Reportable Pressure Range: Maximum minus Minimum Reportable Pressure Counts
Report Pressure Sensitivity: The change of Reported Pressure Counts per change of applied User Pressure (defined immediately below).
User Pressure: The pressure applied to the pointing device by the user.
User Pressure Range: The range of pressure a particular user will apply in using the pointing device.
Heavy-Handed User: Uses large User Pressure Range
Light-Touch User: Uses small User Pressure Range
The drawbacks of prior pressure sensing systems will be discussed for ease of discussion in connection with a graphic arts application program in which the Reported Pressure Count represents the width of a line to be drawn by the applications program running in the host computer. Assume that the widest line that the application program will draw is 20 pixels (or dots in a matrix display or printer) wide, and that convention establishes a Maximum Reportable Count of 100. Thus, the application program will transform (perhaps, although not necessarily, by linear interpolation) the 100 reported counts into 20 pixel line widths.
Since an application program is designed to work with a variety of commercially available pressure-sensitive pointing devices, and some have a pre-load so that the pointing device transmits a non-zero, positive Raw Pressure Count without any pressure being applied to the pointing device, a typical Reported Pressure Count to line width transformation (interpolation) might be:
______________________________________ Reported Pressure Count line width ______________________________________ 0-5 0 (no drawing for counts caused by pre-load) 6-9 1 10-14 2 {. . .} . . . 95-97 19 97-100 20 ______________________________________
For a particular pointing device with a Minimum Raw Pressure Count of 1000, a Maximum Raw Pressure Count of 9000 and a Maximum Pressure produced with two pounds of force applied, and, for simplicity, having a linear response, the Raw Pressure Count Sensitivity would be 250 Raw Pressure Counts per ounce of force applied. (9000-1000)/(2*16). Assume that this particular pointing device was from a lot of pointing devices whose characteristics vary, due to manufacturing tolerances, etc., and that the particular pointing device's characteristics are within the range expected for the lot. Since the reporting system was not calibrated for the particular pointing device, the transformation from raw counts to reported counts was heretofore based on a "typical" pointing device or a "worse case" pointing device, or on some other statistical representation of a pointing device's performance (collectively referred to below as a "generic" pointing device). Thus, for example, the statistical representation of a generic pointing device used to determine the transformation may have used 800 as the Minimum Raw Pressure Count, and 6800 as the Maximum Raw Pressure Count at 30 ounces of force for a Raw Pressure Count Range of 6000 counts (for a calculated "generic" resolution of 200 counts per ounce). To transform the Raw Pressure Count Range of 6000 into a maximum Reportable Pressure Count of 100, by linear interpolation (other interpolations may be used) each 60 raw counts equals 1 Reported Pressure Count. Thus, the pre-load count of 1000 on the particular pointing device results in a Reported Pressure Count of 3.33 ((1000-800)/60)), which is reported as a "3". To draw a one pixel wide line, the Reported Pressure Count would have to reach 6, which equates to a user-applied force of 0.64 oz. (Raw Pressure Count of 1160=1000+(250 cts/oz.*0.64 oz); transformed by (1160-800)/60 to a count of 6). To draw a two pixel wide line, the user would have to apply 1.6 oz., which produces a Raw Pressure Count of 1400. (1000+250* 1.60) A Raw Pressure Count of 1400 produces a Reported Pressure Count of 10 ((1400-800)/60). Thus, changing the line width by one pixel requires a change of force of one ounce, using the above example.
To draw a maximum width line, the user would have to apply about 221/2 oz. of force, which is too much pressure to require while drawing a line. Therefore, most applications (or drivers which buffer the information between the digitizer processor and the application) allow the user to scale the values up or down. Thus, for example, a Light-Touch User may want to scale the range down by a factor of 10, so that 2.2 ounces is sufficient to draw the widest line. Or a Heavy Handed User may want to scale down by a factor of 2, for an 11 ounce maximum User Pressure Range.
However the Light Touch User will lose some ability to draw lines of particular widths if the user scales down by 10. Since the pre-load value reported by the pointing device of the above example is 3, scaling down by 10 produces a count of 30 which would produce a line about 5 pixels wide. Even if the application or the driver allowed the user to offset the count by the pre-load amount (to produce 0 instead of 30), by subtracting 3 from the reported count, a problem remains. When the user applies pressure and a count of 4 is produced, it will be scaled up to 10 [(4-3)*10], producing a two pixel wide line. When a 5 count is produced, a four pixel wide line is produced. Thus, by scaling by a factor of 10, the user is precluded from obtaining the desired degree of control over the widths of the line. (In this example, lines of 1 or 3 pixels width can not be selected).
To scale and still allow for the selection of each line width, the user would have to limit the scaling to a factor of 3 or 4. With a factor of 3, the user would have to apply over 7 ounces to draw a widest width line, and 7 ounces may not be comfortable to a Light Touch User.
Alternatively, some systems allow the user to change the internal transformation factors. Thus, in the above example, the user could direct the system to set 1000 as the Minimum Raw Pressure Count (instead of the 800 default), and 1600 as the Maximum Raw Pressure Count, which, for the particular pointing device in the above example, would equate to a Maximum Pressure of 2.4 oz. needed to achieve the Maximum Reportable Pressure Count. This, however, is not a simple process, as it requires the user to understand the basic operations of the pointing devices and the mechanics of a mathematical transformation. The typical user of a pressure-sensitive pointing device is not a mathematician, and requiting the user to perform these tasks would seriously detract from the system's acceptability.
Other systems set the transformation parameters lower than the achievable Raw Pressure Maximum, thereby increasing the pointing device's sensitivity for the Light Handed User, but in so doing, they reduce the Raw Pressure Range. A reduction in the Raw Pressure Range will be disadvantageous to a Heavy Handed User--a person who normally leans hard on a pen is not going to be satisfied by a pointing device that produces the maximum line width at 2 or 3 ounces, and may not be able to modify his/her drawing style to control the line width at this low pressure/high sensitivity range.
Because of these human factors, most pressure-sensitive pointing device manufacturers adjust the transformation parameters not only for the genetic pointing device's performance, but also for the typical user's preferences. As a result, the pointing device may be acceptable to most people, but is less than optimal to most people also. | tomekkorbak/pile-curse-small | USPTO Backgrounds |
Laser-evoked potentials: normative values.
Laser-evoked potentials (LEPs) currently represent the most reliable and widely agreed method of investigating the A delta-fibre pathways. Many studies dealt with the usefulness of LEPs in peripheral and central nervous system diseases. We aimed at gaining normative values for LEP data. Using a CO2 laser stimulator we recorded LEPs after face, hand, and foot stimulation in 100 normal subjects. We measured the perceptive threshold, latency and amplitude of the main vertex components, and their side-to-side differences. We also studied the correlations between LEP data and age and body height, as well as gender differences. Laser perceptive threshold increased and LEP amplitude decreased from face to foot (P<0.0001). The latency of hand and foot-LEPs correlated significantly with body height (P<0.0001). The amplitude, though not the latency, correlated with age (P<0.0001). LEP data did not significantly differ between genders (P>0.1). This study provides normative values for the main LEP data and their absolute and side-to-side limits, highlighting the physiological differences related to, body height, age, gender and stimulation site. Our data may help to improve the clinical reliability of LEPs as a diagnostic tool. | tomekkorbak/pile-curse-small | PubMed Abstracts |
USC head coach Steve Sarkisian said he will go to treatment after combining an undisclosed medication and alcohol Saturday, leading to an embarrassing appearance at a booster event where he appeared to be intoxicated, using expletives and attacking other Pac-12 schools.
Sarkisian addressed the media for the first time Tuesday before the Trojan’s practice.
• Wolf: Can Sarkisian coach USC effectively in wake of incident?
• VIDEO: USC coach Steve Sarkisian apologizes, will go to rehab
“It was inappropriate, and I feel bad for the University of Southern California,” Sarkisian said.
Sarkisian denied he has a drinking problem, but said that he will go through treatment and vowed to not drink for the rest of the season.
“I’m gonna go with treatment and deal with it, and in the meantime I’m going to be the head football coach here,” he said.
• PHOTOS: Steve Sarkisian apologizes for behavior at USC booster event
The incident occurred at a booster event known as “Salute to Troy” on campus Saturday night. In video from the event, Sarkisian can be heard using an expletive before yelling the school’s “Fight On!” motto on stage. The coach proceeded to insult a number of USC’s opponents this season, saying “they all suck” about a number of Pac-12 schools.
Witnesses said Athletic Director Pat Haden had to pull Sarkisian away from the microphone and lectured his coach backstage.
“I’ve met with Pat at length, and there’s things we’re going to work on moving forward,” Sarkisian said.
• VIDEO: Sarkisian answers reporters’ questions
Sarkisian was also slurring his words and told lewd jokes, according to at least one group.
“I took medication with alcohol, fortunately not a lot. I responded in a way that is not acceptable for me or the university,” Sarkisian said Tuesday.
• WHICKER: Sarkisian dodges suspension, not scrutiny
Sarkisian declined to reveal the medication, saying he felt it was a private issue.
Sarkisian also addressed the school’s recent announcement that alcohol has been banned from the Trojans locker room. Sarkisian said coaches would at times consume alcohol in the locker rooms after games, but it was not made available to players.
Starting quarterback Cody Kessler said Sarkisian addressed the team the day after the incident and was open about what occurred.
“He came to us as a man, apologized, looked us in the face, told us some things, and that’s hard to do,” Kessler said. “At the end of the day, I think he earned more respect from us.”
• VIDEO: Kessler, Cravens talk about Sarkisian’s apology
Kessler said the players, who were in attendance at the dinner, were aware Sarkisian was acting differently.
“We saw it, and we knew something wasn’t right. We know what he’s like in a normal state” Kessler said.
“We just figured ‘OK, people here are drinking and hanging out.’ We didn’t know the full story. He came up to us the next day and apologized for it.” | tomekkorbak/pile-curse-small | OpenWebText2 |
Hey. I am a trans person and what foxmod says disgusts me. Almost all my friends are CIS, my parents are, almost everyone I know is. I'd rather we just play it cool. I don't care if you hate CIS just don't announce it publicly and give fake facts like a dumbass
hmmmmmmmmmmmm, ok I just woke up to this and I’ve got a couple questions.
1) if you’re actually trans, why are you capitalizing cis like it’s some sort of acronym.
2) if you DO think that cis is an acronym, you clearly don’t know what the hell you’re talking about anyways so kindly go away
-mousemod | tomekkorbak/pile-curse-small | OpenWebText2 |
Q:
Merge two arrays in Go... container assign error
I am trying to figure out what is wrong with my code all this morning but couldn't. It says it cannot assign containers. Please check this go play ground http://play.golang.org/p/RQmmi7nJAK
And the problematic code is below.
func My_Merge(container []int, first_index int, mid_index int, last_index int) {
left_array := make([]int, mid_index-first_index+1)
right_array := make([]int, last_index-mid_index)
temp_i := 0
temp_j := 0
for i := first_index; i < mid_index; i++ {
left_array[temp_i] = container[i]
temp_i++
}
for j := mid_index; j < last_index+1; j++ {
right_array[temp_j] = container[j]
temp_j++
}
i := 0
j := 0
for elem := first_index; elem < len(container); elem++ {
if left_array[i] <= right_array[j] {
container[elem] = left_array[i]
i++
if i == len(left_array) {
container[elem+1:last_index] = right_array[j:]
break
}
} else {
container[elem] = right_array[j]
j++
if j == len(right_array) {
container[elem+1:last_index] = left_array[i:]
break
}
}
}
}
I am getting the errors in the line container[elem+1:last_index] = right_array[j:].
Even if I delete the whole block, I am getting errors. Could anybody help me on this? I would greatly appreciate it.
A:
You can't assign to a slice expression in Go. You need to use copy:
copy(container[elem+1:last_index], right_array[j:])
But apparently there are other problems too, since when I change that in the playground I get an index out of range error.
| tomekkorbak/pile-curse-small | StackExchange |
District Attorney Jackie Lacey honored lifelong Pasadena resident and Los Angeles Police Department officer Frank Banuelos along with two other brave individuals at the annual Courageous Citizen Awards Ceremony Wednesday at the University Club in recognition of their crime-stopping efforts in the community.
Banuelos played a critical role in recovering a neighborhood gardener’s stolen work truck while off-duty, ultimately leading the Pasadena Police Department to arrest the suspect.
“We gathered individuals who have shown a great amount of bravery. They’ve stepped up in a dangerous situation and in a split second they decided they were going to make a difference even if it meant risking their own safety,” said District Attorney Jackie Lacey. “These honorees come from various walks of life, but they each have bravery in common.”
The Courageous Citizens Award was created by the Los Angeles County District Attorney’s Office to commend individuals who have acted with courage— and at considerable personal risk—to help crime victims, assist in the capture of a suspect or testify in the face of extraordinary pressures. The award recipients exemplify the highest form of community service.
“I grew up here in Pasadena and I love this city. I try to find different ways to be involved in maintaining the spirit of Pasadena, which is always welcoming and diverse, and I try to do my part as a citizen of Pasadena and to enhance the quality of life here,” said Banuelos.
A pickup truck owned by Banuelos’ gardener was stolen in Pasadena with his tools inside last December.
On Jan. 19, the victim gardener, while working at Banuelos’ home, saw someone drive by in his truck. The victim told Banuelos, who immediately called Pasadena police and ran to his vehicle to pursue the stolen truck.
Banuelos, an off-duty Los Angeles Police officer, stayed on the phone with Pasadena police, notifying them of the suspect’s location until they arrived and arrested the suspect.
“As a police officer, what I did on that particular day just comes second nature–it’s what we’re trained to do. We’re never off duty and I did what anybody else would have done,” said Banuelos.
Banuelos recognizes that police cannot be everywhere at all times during criminal acts and is sure to take it upon himself as a citizen to help out in any way that he can.
“I try to make the job easier for police officers because they can’t be everywhere,”
Banuelos offered up some tips to residents about keeping an eye on their community.
“Work with your neighbors to maintain the quality of life of each particular neighborhood of Pasadena. Every neighborhood is a little bit different, but we should all strive to strengthen our individual communities to make them better,” said Banuelos.
Tracy Richardson and Leo Richard Anicua are the two other Los Angeles County residents who were recognized for their brave efforts.
On June 2, 2016, Richardson saw a man yelling and cursing at his dog before using a chain wrapped around the animal’s neck to lift the dog and slam it against a metal gate.
She immediately called 9-1-1 and followed the man as he walked the animal through Silver Lake and lifted the dog a few more times by the chain, slamming it against a tree, a metal traffic light pole, and other objects before punching the dog.
Richardson followed him until she saw him tie the dog up and walk away. Richardson then ran to check the dog’s well-being as police arrived and arrested the man.
Oct. 4, 2015, then 12-year-old Leo Richard Anicua witnessed a 78-year-old man sexually assault a 10-year-old relative as they waited for the girl’s mother in a parked car outside a Burbank supermarket.
Anicua was in the next vehicle waiting for his mother and witnessed the assault. He wrote down the vehicle’s license plate number and when his mother returned to the car, told his mother what he saw.
They drove to a police station to report the crime. Based on the information the 12-year-old boy provided, which included a description of the girl’s clothing, police officers located and arrested the man.
“This is one of my favorite duties as District Attorney and that’s because most of the time we’re dealing with people who commit crimes. But today we are flipping the switch and honoring the good people, the good actors, in the criminal justice system,” said Lacey. | tomekkorbak/pile-curse-small | Pile-CC |
1. Field of the Invention
The present invention relates to a crane, and in particular to a pin structure of a crane with an automatic counterweight balancing device and a method of arranging counterweight thereof.
2. The Related Arts
Liquid crystal display (LCD) has a variety of advantages, such as thin device body, low power consumption, and being free of radiation, and is thus widely used. Most of the LCDs that are currently available in the market are backlighting LCDs, which comprise a liquid crystal display panel and a backlight module. The operation principle of the liquid crystal display panel is that liquid crystal polymer molecules are interposed between two parallel glass substrates and the liquid crystal molecules are controlled to change direction by application of electricity to the glass substrates in order to refract out light emitting from the backlight module for generating images.
A liquid crystal display panel is generally composed of an upper substrate (CF, Color Filter), a lower substrate (TFT, Thin Film Transistor), and liquid crystal (LC) interposed between the upper substrate and the lower substrate, and a sealant. A general manufacturing process comprises a front stage of array process (including thin film, yellow light, etching, and film stripping), an intermediate stage of cell process (including bonding TFT substrate and the CF substrate), and a rear stage of assembling process (including mounting drive ICs and printed circuit board). The front stage of array process generally makes the TFT substrate for controlling the movement of liquid crystal molecules. The intermediate stage of cell process generally introduces liquid crystal between the TFT substrate and the CF substrate. The rear stage of assembling process generally mounts the drive ICs and combining the printed circuit board to effect driving the liquid crystal molecules to rotate for displaying images.
In the manufacturing process and warehousing of the liquid crystal display panel, the liquid crystal display panel is conveyed very often. To save the time of conveyance, the conventional way of conveying the liquid crystal display panel is generally carried out with a crane (as shown in FIG. 1) in order to realize conveyance of cassette (CST). In other words, a carriage platform 100 of a crane is loaded with cassettes of liquid crystal display panel 300 stacked thereon. Generally, a cassette of liquid crystal display panel 300 is of a weight of 2 tons. Motors 500 for Z-axis of the crane must carry quite a load. This may shorten the lifespan of the crane and thus increases the manufacturing cost.
To cope with the above problem, those skilled in the related art attempts to reduce the loading of the motors in the Z-axis of the crane by adopting a solution of increasing the counterweight of the crane. However, the counterweight is only used to balance the weight of Z-axis mechanisms. When cassettes are loaded on the carriage platform, the motors of the Z-axis are also carrying a great load and thus, the above descried issue cannot be well dissolved. | tomekkorbak/pile-curse-small | USPTO Backgrounds |
Bootcamp Update
Riley quote: "I didn't sign up for this!"
Coco qoute: "I did."
While Riley continues to receive obedience training at doggy bootcamp. my hubby and I took off on a work-related road trip of northern California. We drove from the bay area to
Sacramento and beyond. At one point we stayed in a motel that was, well, not great. You know, the kind where you strip the bed of everything but a sheet and put on lots of clothes, including socks, to sleep and use your rolled up jeans as a pillow???
Yep. It was comforting to know that a band called "Kung Fu Vampire" was also staying at the motel. I know this because their gigantic tour bus painted black and red with a giant vampire face on it was directly behind our room. I admit, I'm
not used to staying at a drive-up joint. But I do admit it was handy when David had to sit on the stoop with his computer to pick up the wifi.
ANYWAY... needless to say,
I did not do my workout that next morning. And the next day we had to get up at 5:00 to get back on the road. So.... I had to start over my 14 day bootcamp at day 1. I am currently on day 4, again. I have done the 55 minute workout
three of the four days, and one day I worked out on the elliptical and treadmill for 45 minutes and did the 15 minute T-Tapp workout.
About the workout. I am impressed
with it. This workout is all about the "how." While completing the exercises, you are constantly reminded on the DVD to push your knees out, tuck your butt and tummy, and keep your shoulders down and back. You actually reset this stance after
doing each series of exercise. Not only does this work your core the entire time, I think it serves to protect your back. I have noticed that just within a week of following this program I find myself standing taller with my shoulders back and
stomach in. You can even do this in the car. While driving last week I thoughtfully adopted this pose while sitting.
Another feature of this workout is that evey
series is made up of groups of 8 repetitions. It is very comforting, actually, to know that your arms won't actually fall off even though they feel like they are getting close to falling off, because just when you think you can't do any more
the 8 repetitions are over!
It is amazing how "heated-up" the workout gets you. As I mentioned in my first blogpost about T-Tapp, many of the movements resemble standing
yoga moves that require balance and strength, and cumulatively, they make you sweat about 10 minutes into it.
There is a 15 minute balance section about 30 minutes into the
workout. This is the bane of my existence. You know that yoga series where you stand on one foot and bring your other leg up with knee bent and hook your foot above your knee?? No?? Well, it's hard, and takes lots of balance and your
straight leg has to be steady and you have to really use your core. Take that move but imagine your arms out at shoulder level and lift one knee at a time swinging your leg behind, to the side, forward, and at one point moving your arms side to side
without falling down or putting your foot down. Sounds like a contortionist at a Cirque du Soleil performance. Yes, exactly!
I'll get back to you about my progress
in a week or so. In the meantime, check out this workout on www.t-tapp.com if you are interested. I'm not getting paid to do this, I'm just a little cray-cray. | tomekkorbak/pile-curse-small | Pile-CC |
Nepali authorities should immediately investigate and prosecute the September 2010 gang rape, physical assault, and forced displacement of 30-year-old Gauri Yadav in Siraha district, Human Rights Watch said today. To date, Nepali police have failed to protect Yadav from ongoing intimidation and attacks by the alleged perpetrators, and, according to Yadav, have pressured her to drop the case.
Yadav has described how on September 30, 2010, five neighborhood men raped her and then severely beat her with sticks on her thighs, lower legs, and buttocks. Despite evidence and names of perpetrators provided by Yadav, the police have yet to conduct a proper investigation and ensure prosecution in the case. Instead, she and her husband have been targeted and harassed repeatedly by the alleged perpetrators for filing a police complaint. On February 9, 2011, the same people attacked Yadav and beat her severely, resulting in five days of hospitalization, she told Human Rights Watch. Yadav's family told Human Rights Watch that the alleged attackers also set fire to a haystack and destroyed lentil crops on Yadav's land to put pressure on her to withdraw the case. Yadav has fled her village and is seeking refuge elsewhere.
"A woman has produced strong evidence that she has been gang raped, kidnapped, and brutally beaten, and law enforcement agencies are telling her to go away," said Elaine Pearson, deputy Asia director at Human Rights Watch. "The authorities should do everything they can to stop further attacks on Yadav and prosecute those responsible."
Yadav described to Human Rights Watch how she was taken from her relative's house, kicked to the ground, and stripped naked by her attackers. They used her sari to tie her arms to restrain her and tied her scarf around her mouth to smother her screams for help. Then, she said, two men held her down: "First, one raped me. After he got off of me, the second one raped me, then the third and fourth. The last person grabbed my breasts and forced his fingers in my vagina. All this went on for [what seemed like] an hour. Then they carried me to the nearby canal and washed me. After this, all the five men continuously beat me with sticks."
When Human Rights Watch interviewed Yadav two months after the attack, black and blue marks were still visible on her thighs, lower legs, and buttocks. Yadav told Human Rights Watch that following the rape, the men sought assistance from a local Communist Party of Nepal Unified Marxist-Leninist (CPN-UML) politician, who forcefully confined Yadav in his residence for three days without any access to medical treatment. The alleged perpetrators and the politician also threatened the family to try to stop them from filing a police complaint.
On the third day, a local villager informed the police about the rape and detention. The police intervened, and Yadav's family was finally able to take her to a hospital in Dharan, a city in eastern Nepal. The medical report, which Human Rights Watch obtained, confirms that Yadav was hospitalized for nine days and that the hospital staff reported the case to the eastern regional police office in Biratnagar, who then transferred the case to the district police office in Siraha.
Yadav informed Human Rights Watch that the police inspector in the district police office in Siraha attempted to pressure her into dropping her complaint against two of the perpetrators, including against the local political leader. In addition, he insisted that Yadav agree to an informal settlement with her perpetrators. Yadav organized a press conference with the help of a local journalist. Subsequently, police registered her complaint against all six individuals. But the police have failed to carry out any credible investigation or arrest the attackers for the rape, arson, kidnapping, or physical assault, Human Rights Watch said.
Yadav told Human Rights Watch: "I have been beaten again because the culprits are free and have not been punished. I have received no help from the police. My daughter and sons have stopped going to school due to fear. They [perpetrators] are freely wandering in the village. This makes me feel helpless and weak. I want them to be punished."
"The perpetrators clearly feel emboldened by the police's failure to arrest and prosecute these men," Pearson said. "That Gauri Yadav was subsequently beaten and had to flee her village will make other rape survivors think twice before seeking justice."
The problem of the failure to investigate and prosecute rape has been extensively documented by national and international organizations, such as the United Nations Office of High Commissioner for Human Rights in Nepal (UN OHCHR- Nepal), Advocacy Forum - Nepal, and Women's Rehabilitation Centre. In its recent report to the UN Human Rights Council, OHCHR reported that in cases of sexual assault, "instances of the police taking proactive steps to register a case ex officio are rare," and even when a survivor reports a crime to the police, "police frequently delay the registration process, including by insisting upon a medical report..." The report further described that "it is usually the police or local authority figures who encourage victims to seek a settlement [‘mediation'] with the alleged perpetrator often under pressure from local political parties, particularly if a party affiliate is involved."
Nepali authorities also should speak out against mediation in sexual violence cases and hold accountable police officers who fail to register and investigate these cases.
Nepali police should immediately investigate Yadav's case and ensure prosecutions where there is evidence. They should also investigate the ongoing attacks and efforts at intimidation to seek an informal settlement of the case.
The Nepali police authorities should conduct a full and transparent investigation into the case, Human Rights Watch said. The investigation should include alleged police pressure to drop the charges against two alleged perpetrators and the allegations of local political interference.
"Yadav's case is emblematic of police inaction while investigating rape cases and shows apparent political interference even in severe crimes such as rape," Pearson said. "Instead of pressuring and further punishing victims of sexual violence, Nepal needs to make sure they get justice."
Nepal has ratified the United Nations Convention on Elimination on all forms of Discrimination Against Women (CEDAW), Convention Against Torture (CAT), and International Covenant on Civil and Political Rights (ICCPR), and therefore has an obligation to take positive measures to protect survivors of gender-based violence and carry out thorough, impartial, and prompt investigations into allegations of rape and file criminal charges where appropriate. | tomekkorbak/pile-curse-small | OpenWebText2 |
May 25 - Bloomberg: "China's central bank weakened its currency fixing to
the lowest since March 2011 as the dollar strengthened. The reference rate
was set 0.3% weaker at 6.5693 per dollar. A gauge of the greenback's strength
rose to a two-month high Tuesday... A resurgent greenback is shaking up a strategy
that the People's Bank of China pursued over the past three months -- a steady
rate against the dollar, combined with depreciation against other major currencies."
The U.S. dollar index increased 0.4% this week to 95.7 (down 3.0% y-t-d).
For the week on the upside, the British pound increased 0.8% and the Canadian
dollar gained 0.7%. For the week on the downside, the Brazilian real declined
2.6%, the euro 1.0%, the New Zealand dollar 0.9%, the Mexican dollar 0.7%,
the Australian dollar 0.6%, the South African rand 0.6%, Swiss franc 0.4%,
the Swedish krona 0.4%, the Norwegian krone 0.1% and the Japanese yen 0.1%.
The Chinese yuan declined 0.3% versus the dollar.
May 23 - Bloomberg (Tracy Alloway): "Bond investors appear to have placed
their faith in commodities exceptionalism, with many positing that the recent
pick-up in U.S. default rates will defy historical trends and remain confined
to that industry. New research from Deutsche Bank AG pours cold water on that
idea, arguing that there are already signs of contagion in junk-rated debt
outside of the commodities space. A look at previous peaks in default rates
shows the potential for more pervasive corporate stress. While default rates
were higher amongst particular sectors--such as telecoms in the early 2000s
or financials during the 2008 crisis--the rate for junk bonds excluding these
specialized industries also increased significantly."
May 24 - Financial Times (Eric Platt): "The triple A rated company is nearly
extinct. Just a handful of companies in the world retain the coveted rating
from Standard & Poor's after ExxonMobil was downgraded last month. In the
US, the number has fallen to two -- Johnson & Johnson and Microsoft. In
1992, there were 98 US companies that held the highest credit rating from S&P.
The demise of triple A-rated companies reflects a dramatic rise in the use
of debt to help bolster shareholder returns and fund takeover activity."
May 26 - Reuters (Suzanne Barlyn): "New York state's financial regulator,
which recently launched a probe into LendingClub Corp, is preparing to look
into the activities at other online lenders and whether they should be licensed
in New York... Last week, NYDFS subpoenaed San-Francisco based LendingClub,
a so-called peer-to-peer lender..."
May 25 - Bloomberg (Matt Scully): "Some of Wall Street's biggest banks are
making contingency plans to cut their exposure to online consumer loans if
the market deteriorates further after the recent crisis at LendingClub Corp.,
people with knowledge of the reviews said. While firms including Credit Suisse
Group AG and Deutsche Bank AG haven't scaled back exposure, they're concerned
about financing they provide to institutional investors that buy loans from
companies like LendingClub and Prosper Marketplace Inc., the people said."
May 25 - Associated Press (Stan Choe): "CEOs at the biggest companies got
a 4.5% pay raise last year. That's almost double the typical American worker's,
and a lot more than investors earned from owning their stocks -- a big fat
zero. The typical chief executive in the Standard & Poor's 500 index made
$10.8 million... That's up from the median of $10.3 million the same group
of CEOs made a year earlier. The raise alone for median CEO pay last year,
$468,449, is more than 10 times what the typical U.S. worker makes in a year.
The median full-time worker earned $809 weekly in 2015, up from $791 in 2014."
May 22 - Wall Street Journal (Sam Goldfarb): "The esoteric securities market
underpinning demand for the riskiest corporate loans is perking up, raising
hopes that it could become easier for banks to sell a range of loans, including
those that they failed to syndicate last year. More corporate loans are being
bundled this spring into collateralized loan obligations, which buy loans from
junk-rated companies and repackage them into securities that pay varying levels
of interest based on which get paid off first if the underlying loans go bad."
May 25 - Bloomberg (Elizabeth Campbell): "Illinois lawmakers have been busy
in the last week of the regular legislative session. They moved to establish
a youth-only turkey hunting season, set standards on where podiatrists can
perform amputations and allowed for the adoption of retired police dogs. Yet,
the Land of Lincoln remains the only state in the nation without a budget,
mired in the longest such standoff in its history... If no deal is struck,
the consequences will become more dire: Prisons may run out of food, schools
may not open on time, and the state's credit rating -- already the lowest in
the U.S. -- is at risk of falling even further as the government's deficit
continues to grow."
Global Bubble Watch:
May 26 - Financial Times (Robin Harding): "The global economic outlook is
as grim as it was after the Lehman Brothers crisis in 2008, Shinzo Abe claimed
on Thursday, as the Group of 7 revealed its stark divisions on economic policy.
Seeking to rally support for a global fiscal stimulus at the G7 summit, the
Japanese prime minister showed his fellow world leaders a series of alarming
graphs comparing today's economic conditions with those of 2008. But, according
to people close to the discussions, Mr Abe struggled to win over opponents
such as Germany's chancellor Angela Merkel or UK Prime Minister David Cameron."
May 26 - Reuters (Chris Gallagher and William Mallard): "Japanese Prime Minister
Shinzo Abe warned his Group of Seven counterparts of a crisis on the scale
of Lehman Brothers, Nikkei reported, offering a potential justification to
again delay an increase in the national sales tax. Abe presented data at a
Thursday session of the G7 summit he is hosting, showing that commodities prices
have fallen 55% since 2014, the same margin they fell during the global financial
crisis, the newspaper said, interpreting this as 'warning of the re-emergence
of a Lehman-scale crisis'."
May 26 - Bloomberg (Claire Boston and Sally Bakewell): "A borrowing binge
by companies globally is poised to make May one of the the busiest months ever,
thanks to investors who continue to devour the relatively juicy yields on corporate
debt in a negative-rate world. Global issuance of non-financial company debt
will be in excess of $236 billion by month-end... In Europe, companies sold
48.5 billion euros ($54.2 billion) making it the busiest May on record."
May 23 - Reuters (Anjuli Davies): "Revenue at the world's 12 largest investment
banks fell 25% in the first quarter from a year ago as economic uncertainty
and investor caution led to the slowest start since the financial crisis, a
survey showed... Investment banks have been hit by a steep decline in oil prices,
near-zero interest rates and worries about China's economy, which triggered
a wave of volatility in financial markets at the start of the year, normally
the most lucrative period when investors put their money to work. Trading in
fixed income, currencies and commodities (FICC) divisions... declined 28% year-on-year
to $17.8 billion, data from... Coalition shows."
May 26 - Financial Times (Joe Rennison): "Global equity markets experienced
further strong outflows this week, despite soothing economic data and rising
stock prices. Equity funds suffered their seventh consecutive week of outflows,
shedding another $9.2bn for the week ending May 25, taking their total outflows
for the year above $100bn, according to data from EPFR."
U.S. Bubble Watch:
May 23 - CNBC (Jeff Cox): "That American companies have been wadding up huge
amounts of cash is no secret. What may be less well-known is that they're also
accumulating debt at a much faster pace. Total debt among more than 2,000 nonfinancial
companies swelled to $6.6 trillion in 2015, dwarfing the $1.84 trillion in
cash on their balance sheets, according to a study... by S&P Global Ratings.
The ratio of cash to debt is the lowest it's been in about 10 years, or just
before the global financial crisis. As financial markets came to grips with
the prospect of higher rates ahead, corporate America went on a debt bonanza.
Debt grew 50 times that of cash, with companies rolling up $850 billion of
new IOUs compared to just $17 billion, or 1%, cash growth."
May 26 - MarketWatch (Ciara Linnane): "First-quarter earnings season is close
to over, and the numbers it's produced are as gloomy as they have been since
the Great Recession. Overall profit for S&P 500 companies was the weakest
in 6 1/2 years. The financial sector showed a double-digit percentage decline,
while even stodgy utilities saw earnings fall into the red as unusual weather
weighed. After selling assets, cutting capital expenditures and buying back
their own shares at a record pace in recent years, companies are now clearly
struggling to produce any kind of growth... A full 98.4% of S&P 500 companies
have now reported through early Thursday, and profit measured by earnings per
share is down 7% from a year ago, according to FactSet. On the heels of a 3.2%
decline in the fourth quarter, that marks the fourth straight quarter of year-over-year
earnings declines, and it was the biggest drop since the third quarter of 2009."
May 25 - Bloomberg (Jeanna Smialek): "A substantial share of Americans lacked
retirement savings and fewer households were confident in the outlook for their
income at the end of last year. That's according to a Federal Reserve report
on the economic well-being of U.S. households in 2015... The findings show
that while respondents increasingly reported that they are 'doing OK' or 'living
comfortably,' a smaller share said they expected income growth than in the
prior year's survey. Thirty-one percent of non-retired Americans said they
had no retirement savings at all, unchanged from 2014."
May 26 - Wall Street Journal (Jesse Newman): "Banks are tightening credit
for U.S. farmers amid a rise in delinquencies, forcing some growers to turn
to alternative sources of loans. When U.S. agriculture was booming this decade,
banks doled out ample credit to strong performers and weaker growers alike,
said Michael Swanson, an agricultural economist at Wells Fargo & Co. But
with the farm slump moving into its third year, banks have become pickier,
requiring some growers to cough up more collateral and denying financing outright
to some customers who need it to pay for seeds, crop chemicals and rent."
May 27 - Bloomberg (Romy Varghese): "California's three-year boom run is showing
signs of fatigue. Shaking off recession-era comparisons to Greece, the most-populous
U.S. state rebounded with surpluses and an economy fueled by the fast-growing
technology industry, which garnered it eight bond-rating upgrades. Governor
Jerry Brown is now forecasting that revenue growth is slowing along with the
economy after April's income-tax collections lagged expectations, in part because
of the sputtering stock market. Even if voters in November decide to keep a
temporary income-tax increase from ending -- a measure that Brown hasn't endorsed
-- the budget would 'barely be balanced, his administration said..."
May 27 - Bloomberg (Prashant Gopal): "Miami's crop of new condo towers, built
with big deposits from Latin American buyers and lots of marketing glitz, are
opening with many owners heading for the exits. A third of the units in some
newly built high-rises are back on the market, though most are listed for more
than their owners paid in the pre-construction phase. At the current sales
pace, it would take 29 months to sell the 3,397 condominiums available in the
downtown area, according to South Florida development tracker CraneSpotters.com.
With the U.S. dollar strong, South American investors who piled into the downtown
Miami market after the real estate crash are now trying to unload their recently
built condos, adding inventory to an area where 8,000 units are under construction
and nine towers were completed since the end of 2013."
May 24 - Bloomberg (Michelle Jamrisko): "Purchases of new homes in the U.S.
surged in April to the highest level since the start of 2008, pointing to a
robust spring selling season for builders... (Sales) Rose 16.6% to 619,000
annualized rate (forecast was 523,000). Monthly increase was biggest since
1992, while pace was strongest since January 2008. Median selling price jumped
9.7% to a record $321,100."
May 25 - Bloomberg (Prashant Gopal): "U.S. home prices rose 5.7% in the first
quarter from a year earlier as buyers competed for a limited supply of listings.
Prices climbed 1.3% on a seasonally adjusted basis from the previous three
months, the 19th consecutive quarterly gain... There were 1.98 million houses
for sale at the end of March, down 1.5% from the same month last year... While
the U.S. has a whole had robust gains, prices fell from the previous quarter
in 12 states and the District of Columbia, the FHFA said."
May 25 - Wall Street Journal (Louise Radnofsky): "Big health plans stung by
losses in the first few years of the U.S. health law's implementation are seeking
hefty premium increases for individual plans sold through insurance exchanges
in more than a dozen states. The insurers' proposed rates for individual coverage
in states that have made their 2017 requests public largely bear out health
plans' grim predictions about their challenges under the health-care overhaul.
According to the insurers' filings with regulators, large plans in states including
New York, Pennsylvania and Georgia are seeking to raise rates by 20% or more."
China Bubble Watch:
May 24 - Bloomberg (Paul Panckhurst): "Charlene Chu, a banking analyst who
made her name warning of the risks from China's credit binge, said a bailout
in the trillions of dollars is needed to tackle the bad-debt burden dragging
down the nation's economy. Speaking eight days after a Communist Party newspaper
highlighted dangers from the build-up of debt, Chu... said she was yet to be
convinced the government is serious about deleveraging and eliminating industry
overcapacity. She also argued that lenders' off-balance-sheet portfolios of
wealth-management products are the biggest immediate threat to the nation's
financial system, with similarities to Western bank exposures in 2008 that
helped to trigger a global meltdown."
May 26 - Bloomberg: "China's government still has room to borrow more to finance
the investment and construction needed to shore up economic growth, the Ministry
of Finance said. Overall risks associated with government debt, which amounted
to 26.66 trillion yuan ($4.1 trillion) at the end of last year, are under control,
the ministry said in a statement late on Thursday. The government can add leverage
gradually because its debt ratio is still below international warning levels,
it said."
May 25 - Bloomberg (Lisa Pham): "In the creative world of Chinese lending,
there's a new trade in town: the cow leaseback. China Huishan Dairy Holdings
Co., which operates the largest number of dairy farms in the country, is selling
about a quarter of its herd -- some 50,000 animals -- to Guangdong Yuexin Finance
Lease Co. for 1 billion yuan ($152 million) and then renting them back. With
an estimated $1.3 trillion of risky loans in the country, Chinese banks are
becoming more cautious about lending, forcing some companies to look for new
ways to borrow. Finance leasing has been growing in popularity, especially
for purchases of equipment. But cows?"
May 24 - Bloomberg (Zhe Huang and Justina Lee): "The People's Bank of China
scrapped its market-based mechanism for managing the yuan on Jan. 4 and returned
to setting the exchange rate based on what suits authorities the best, the
Wall Street Journal reported, citing unidentified people close to the central
bank. An unidentified official from the PBOC in March told economists and bankers
that 'the primary task is to maintain stability' when they asked the central
bank to stop fighting markets and let the yuan's value fall at a closed door
meeting, citing previously undisclosed minutes of the gathering.
May 26 - Reuters (Elias Glenn): "Profit growth at China's industrial firms
slowed in April, in line with other data for the month which suggested the
economy may be losing steam again after picking up earlier in the year. China's
industrial firms made 502 billion yuan ($76.59 billion) in profits last month,
up 4.2% from the same period last year and compared with growth of 11.1% in
March..."
EM Bubble Watch:
May 26 - Bloomberg (Matthew Martin, Archana Narayanan and Deema Almashabi): "Banks
in Saudi Arabia are coming under fresh pressure over products that allow speculators
to bet against the kingdom's currency peg, according to people with knowledge
of the matter. The Saudi Arabia Monetary Agency has asked lenders to explain
why they are offering dollar-riyal forward structured products to customers
less than four months after the regulator banned options contracts that let
speculators place wagers on a currency devaluation, the people said. The authority,
known as SAMA, didn't reply to requests for comment. Hedge funds... have made
bets that the country's peg to the dollar will be broken as oil revenue plunges..."
May 24 - Bloomberg (Onur Ant): "Turkey's central bank cut its overnight lending
rate for a third month on Tuesday, calling the reduction a 'measured' step
toward simplifying its monetary policy. The bank lowered the rate by 50 basis
points to 9.5%..."
May 22 - Bloomberg (Kartik Goyal): "Massive, game-changing and overwhelming
were among the descriptions investors used for Indian Prime Minister Narendra
Modi's election victory in May 2014. Two years on, the slow pace of implementing
policy threatens to sap interest. The rupee is the worst performer among currencies
of the four biggest emerging markets this year. Indian sovereign bonds have
lagged peers in Brazil and Russia this quarter, after delivering the best returns
among the BRIC nations since the election win."
Japan Watch:
May 22 - Reuters (Stanley White): "Japanese manufacturing activity contracted
at the fastest pace in more than three years in May as new orders slumped...
putting fresh pressure on the government and central bank to offer additional
economic stimulus. The Markit/Nikkei Flash Japan Manufacturing Purchasing Managers
Index (PMI) fell to 47.6 in May..."
May 22 - Reuters (Tetsushi Kajimoto and Leika Kihara): "Japan's exports fell
sharply in April and manufacturing activity suffered the fastest contraction
since Prime Minister Shinzo Abe swept to power in late 2012, providing further
evidence that the premier's Abenomics stimulus policy is struggling for traction.
The bleak readings on the health of the world's third-largest economy follow
Japan's failure last week to win support from its global counterparts to weaken
the strong yen, which Tokyo fears could do further damage to the sputtering
economy... Data on Monday showed Japan's exports fell 10.1% in April from a
year earlier..."
ECB Watch:
May 24 - Bloomberg (Alessandro Speciale): "The European Central Bank warned
that risks of financial-market turmoil have increased amid slower growth in
emerging economies, weak bank profitability and the rise of populist movements
across the 19-nation euro region. 'A sharper-than-expected fall in Chinese
growth could well lead to a synchronized downturn across other emerging-market
economies, particularly commodity-exporting economies,' the ECB wrote in its
twice-yearly Financial Stability Review... 'Under such a scenario, the financial
systems of advanced economies may be challenged by a reduction in consumer
and business confidence, and renewed financial-market volatility potentially
intensified by sudden stops in or reversals of cross-border capital flows.'"
Europe Watch:
May 24 - Bloomberg (Laura J Keller, Stephen Morris and Macarena Munoz Montijano): "Deutsche
Bank AG Chief Executive Officer John Cryan said his bank has never had more
capital and could easily repay its debt many times over, responding to a credit-rating
cut by Moody's... The ratings company on Monday said the German lender faces
mounting challenges in carrying out its turnaround, and cut the bank's senior
unsecured debt metric one level to Baa2, two grades above junk. The firm's
long-term deposit rating fell to A3 from A2."
May 25 - Bloomberg (Thomas Penny, Patrick Donahue and Ian Wishart): "When
Germany hosted last year's Group of Seven summit, European leaders assured
President Barack Obama they were up to dealing with the crises on their doorstep.
Twelve months on, Europe's challenges have multiplied to an extent that questions
the wisdom of making the 6,000-mile trip to Japan for the G-7. From Brexit
to migration, home-grown terrorism to the destabilizing impact of surging populism,
Europe has seldom looked in more need of political leadership at home. Global
summits usually provide an opportunity for heads of government to play the
role of international dealmakers. But right now Prime Ministers David Cameron
and Matteo Renzi, Chancellor Angela Merkel and President Francois Hollande
are faced with coalescing crises -- and restive electorates -- that demand
attention in their own countries"
Brazil Watch:
May 23 - Bloomberg (Carla Simoes, Arnaldo Galvao and Mario Sergio Lima): "Brazil's
newly-appointed Budget Minister Romero Juca said he will take a leave of absence
after allegations surfaced that he wanted to obstruct the sweeping corruption
probe known as Carwash. Juca, the leader of Acting President Michel Temer's
political party, will return to his former job as senator and make room for
Dyogo Oliveira to take the helm of the Budget Ministry... The surprise announcement
on Monday afternoon capped a day of speculation about Juca's future in the
cabinet after he initially refused to step down. The dramatic departure highlights
the challenges facing Temer..."
Leveraged Speculation Watch:
May 25 - Bloomberg (Scott Deveau and Devin Banerjee): "The $2.9 trillion hedge-fund
industry may lose about a quarter of its assets in the next year as performance
slumps, said Tony James, Blackstone Group LP's billionaire president. 'It's
kind of a day of reckoning that we face here,' James said... 'There will be
a shrinkage in the industry and it will be painful. That's going to be pretty
painful for an awful lot of places.' The hedge-fund industry is having its
worst start to a year in performance and investor withdrawals since global
markets reeled after the financial crisis."
May 24 - Financial Times (John Authers and Mary Childs): "It was the shot
heard around the hedge fund world. After the New York City Employees' Retirement
System decided to cash all its investments inhedge funds, Letitia James, the
city's public advocate, delivered a message to the industry straight out of
Occupy Wall Street: 'Let them sell their summer homes and jets and return those
fees to their investors.' Hedge funds, she said last month, 'believe they can
do no wrong, even as they are losing money'... 'Let's face it: if you go back
to the 1990s, hedge funds delivered something very special: high returns or
very differentiated returns that you could not get elsewhere, and that is what
hedge fund investors have been looking for,' said Neil Chriss, founder of Hutchin
Hill Capital... 'The problem is, since the crisis, a lot of hedge funds have
not been delivering. Returns have been mediocre," he told the Milken Global
Conference..."
Geopolitical Watch:
May 27 - Reuters (David Lawder): "Corrosion-resistant steel from China will
face final U.S. anti-dumping and anti-subsidy duties of up to 450 percent under
the U.S. Commerce Department's latest clampdown on a glut of steel imports,
the agency said... The department also issued anti-dumping duties of 3% to
92% on producers of corrosion-resistant steel in Italy, India, South Korea
and Taiwan... China's Commerce Ministry said it was extremely dissatisfied
at what it called the 'irrational' move by the United States, which it said
would harm cooperation between the two countries."
May 26 - Reuters (Thomas Wilson and Kiyoshi Takenaka): "Group of Seven (G7)
leaders agree... on the need to send a strong message on maritime claims in
the western Pacific, where an increasingly assertive China is locked in territorial
disputes with Japan and several Southeast Asian nations. The agreement prompted
a sharp rejoinder from China, which is not in the G7 club but whose rise as
a power has put it at the heart of some discussions at the advanced nations'
summit in Ise-Shima, central Japan."
May 22 - Associated Press (Suzan Fraser and Geir Moulson): "German Chancellor
Angela Merkel told Turkey's president on Monday that Ankara must fulfill all
the European Union's conditions to secure visa-free travel for its citizens,
but Turkey responded that it would suspend agreements with the EU if the bloc
does not keep its promises. The EU says Turkey must narrow its definition of
'terrorist' and 'terrorist act.' The bloc is concerned that journalists and
political dissenters could be targeted. But Turkish president Recep Tayyip
Erdogan has said that is out of the question."
May 26 - MarketWatch (Nicole Perlroth and Michael Corkery): "Security researchers
have tied the recent spate of digital breaches on Asian banks to North Korea,
in what they say appears to be the first known case of a nation using digital
attacks for financial gain. In three recent attacks on banks, researchers working
for the digital security firm Symantec said, the thieves deployed a rare piece
of code that had been seen in only two previous cases: the hacking attack at
Sony Pictures in December 2014 and attacks on banks and media companies in
South Korea in 2013. Government officials in the United States and South Korea
have blamed those attacks on North Korea..."
I just wrapped up 25 years (persevering) as a "professional bear." My lucky
break came in late-1989, when I was hired by Gordon Ringoen to be the trader
for his short-biased hedge fund in San Francisco. Working as a short-side
trader, analyst and portfolio manager during the great nineties bull market
- for one of the most brilliant individuals I've met - was an exciting, demanding
and, in the end, a grueling and absolutely invaluable learning experience.
Later in the nineties, I had stints at Fleckenstein Capital and East Shore
Partners. In January 1999, I began my 16 year run with PrudentBear, working
as strategist and portfolio manager with David Tice in Dallas until the bear
funds were sold in December 2008.
In the early-nineties, I became an impassioned reader of The Richebacher Letter.
The great Dr. Richebacher opened my eyes to Austrian economics and solidified
my lifetime passion for economics and macro analysis. I had the good fortune
to assist Dr. Richebacher with his publication from 1996 through 2001.
Prior to my work in investments, I worked as a treasury analyst at Toyota's
U.S. headquarters. It was working at Toyota during the Japanese Bubble period
and the 1987 stock market crash where I first recognized my love for macro
analysis. Fresh out of college I worked as a Price Waterhouse CPA. I graduated
summa cum laude from the University of Oregon (Accounting and Finance majors,
1984) and later received an MBA from Indiana University (1989).
By late in the nineties, I was convinced that momentous developments were
unfolding in finance, the markets and policymaking that were going unrecognized
by conventional analysis and the media. I was inspired to start my blog,
which became the Credit Bubble Bulletin, by the desire to shed light on these
developments. I believe there is great value in contemporaneous analysis,
and I'll point to Benjamin Anderson's brilliant writings in the "Chase Economic
Bulletin" during the Roaring Twenties and Great Depression era. Ben Bernanke
has referred to understanding the forces leading up to the Great Depression
as the "Holy Grail of Economics." I believe "The Grail" will instead be
discovered through knowledge and understanding of the current extraordinary
global Bubble period.
Disclaimer: Doug Noland is not a financial advisor nor is he providing investment
services. This blog does not provide investment advice and Doug Noland's comments
are an expression of opinion only and should not be construed in any manner
whatsoever as recommendations to buy or sell a stock, option, future, bond,
commodity or any other financial instrument at any time. The Credit Bubble
Bulletins are copyrighted. Doug's writings can be reproduced and retransmitted
so long as a link to his blog is provided. | tomekkorbak/pile-curse-small | Pile-CC |
Q:
anyone know how angry bird simulate collision and casting?
I am really interesting at how "Angry Bird" simulate the collision and casting.
If I want to implement the similar affect, what knowledge should I acquire ? Any references for that ?
Thanks very much !
A:
It's probably using Box2D, like most 2D physics-based games these days. There are literally hundreds of ('twas rather shocking how popular this particular one became).
Here's an example Birds-alike, with source (Lua).
| tomekkorbak/pile-curse-small | StackExchange |
Monday, October 27, 2008
recycling yarn from a jumper
Much of yarn recycling is trial and error... and everyone develops their own little techniques along the way. I have put together a series of photos which step you through my recycling process, to give you an idea of what is involved.
You will certainly have a million questions for me, especially once you actually start experimenting with the process. Ask away... I'll share everything I know with you!
There seriously are loads of photos here, but the basic steps I follow are:
air the garment
remove trimmings and tags, and undo seams
unravel each piece
wind into a skein
wash
dry
ball
If you are a beginner, I would recommend starting with a single coloured garment, preferably in a simple stockinette. I would avoid cables, fair isle, and anything complicated... until you have had a little practice first. Stick with a standard jumper if possible, and avoid cardigans, coats, or anything with a zipper. A hand knit would be ideal, if you have access to one. Avoid any yarn which looks fluffy or furry or hairy or boucley... because they will be difficult to unravel.
Before I start, I always check the seams. There are 'good seams' and 'bad seams' when it comes to recycling. Overlocked or serged seams are BAD. You will find that the yarn has been cut at the end of every row... so you will end up with lots of short yarn pieces... ugh! So always check the side seams and inner arm seams.
Don't worry if the shoulder or neck seams are overlocked. Because they run across the top of the garment and not down the sides, they are not of concern.
so... some examples of bad seams:
and these are good seams:
So... if the side seams are bound together by overlocking - BAD!
As for hand knits... all of their seams are GOOD... you don't even need to check them!
Time to get started now...
I don't bother washing the garment before I start. Two reasons... Firstly, I don't want to risk any felting or matting of the yarn fibres which would make it more difficult to unravel. Secondly, the yarn is cleaned much more effectively if you wash it AFTER it is skeined.
So I just leave it out on the line for a while, just to 'freshen' it before I start working with it.
I use an unpicker and a pointy pair of scissors to remove tags, labels, buttons, zips, and any other trimmings.
Then I unpick the seams. Most store bought jumpers are seamed using chain stitch, which is wonderfully easy to undo. See the way the chain stitches form little arrows, pointing down in the photo? Well that tells you the direction to unravel in. So cut the top one, free the tail... and pull... it should unravel in seconds.
So now you have all the seams undone (this one had a seam down the centre of the back piece for some strange reason - probably a design feature)
Now it's time to start unraveling each piece, generally working from the top down. The cast off edge forms the same V stitches as chain stitch, and again they point in the direction you need to unravel. So start at the top end and snip, free a tail... and away you go.
Sometimes you might have a hard time getting started. If it's a nightmare for you, just chop the top few rows off, and then start unraveling. You will only loose a few yards of yarn, and it will save your sanity!
I like to roll the garment piece, so I can grip it nicely while I unravel.
I have heard this kind of display referred to as 'yarn barf' and I think it's a wonderful description.
Anyway, if I am working indoors and am going to be able to skein the yarn immediately, then I just pile it on the floor as I unravel. If I am working outdoors I would wind into a ball as I go, and then skein from that... because you really don't want to get this in a tangle!
You can wind your yarn into a skein using two chairs like this...
Or using a skein winder if you have one. This one was a fabulous gift from Mr Goldfish last Christmas... and I love, love, love it!
Once it is all wound on, you need to tie the skein in a figure eight. Use some scrap yarn. I like to use a contrast from the yarn you have wound, so that the ties are easy to locate and removed after drying. I recommend using a light colour, because you would cry if the colour ran from your ties onto you nice new recycled yarn.
First divide the yarn in half as pictured above.
Then pop a scrap piece of yarn through like this...
And back through again, forming a figure "8" with the tie.
Finish with a double knot.
I like to do this in six places around the skein to prevent tangling.
Wash by soaking in warm water and wool detergent. I'm a big fan of Martha Gardener's Eucalyptus Wool Mix, but I'm not sure if it is available outside of Australia.
Gently submerge the skeins. I prefer to soak all the yarn together, so that if it happens to lose any colour, all skeins will be affected evenly.
If possible, I leave it to soak overnight.
Then in the morning, I rinse it in a bucket of cold water.
Of course, with our current water restrictions here... that rinse water gets recycled directly onto my garden...
I gently squeeze the excess water from the yarn, and lay the skeins on an old towel.
Then I lay another old towel on top.
Roll it up, and walk up and down the length of it for a minute or two. This helps absorb a significant amount of water from the skeins.
Then I hang each skein on a plastic coat hanger to dry. I also use a second hanger to 'weight' the yarn slightly, and help stretch some of those kinks out.
If the weather is wet, then I put the coat hangers along a curtain rail in a sunny window and dry the yarn indoors.
When dry, cut the ties off and place the skein back on to the winder or chairs. Find the end and wind into a ball. Click here for my ball winding tutorial.
Interestingly the yarn I have claimed from this jumper is not that nice. I'm actually a bit disappointed with it. It looked nice in the garment, but is now a bit ugh! See the sheen in the balls. That is the rayon component. I liked that sheen until I started unraveling...
You can actually see the cotton and rayon strands here.
The rayon is harsh and grabby and kind of brittle. It actually reminds me of over bleached hair. I'm thinking it may well become hair on a creature or doll at some point. If I want to knit or crochet with it I think I will have to ply it first. I might even ply it with a different yarn to make my own special blend.
I guess the thing is, not to give up... occasionally you get a bit of a dud (like this one) but that just pushes you to think of alternate project ideas.
Most of what I have learned on this topic is through experience, but if you would like to check out the tutorial I first read on the topic, then click here.
28 comments:
Great tutorial! I wish I'd waited a week, lol. I got there in the end, and I did mostly as you describe, just sometimes I got there backwards *shriek* Good job mine was acrylic, because I just shoved it in the washing machine, in a little washing bag net thing.I know better now :-) But I have no idea what you mean about ply-ing. ???
This was a spectacular, amazing tutorial. I bought two sweaters at a thrift store for about $12. I think I am going to finish with about 8-10 balls of yarn! I decided to focus on wool and other fibers that might be expensive to buy. I am about halfway though it and every time I look at it, I get so excited. It has been my vacation week project. For me it is not just recycling, but a way to get yarn that would otherwise be out of my reach.
Thank you so much for this post. I just happen to come across it while browsing your other posts since I LOVE all your ideas and I decided to give it a try myself. I LOVE this idea so much and I bought more things from the clearance racks at the stores to do this again. Here is my link: http://neanner.blogspot.com/2009/01/recycled-yarn.html so check out when you have inspired me to do. Thank you again! :D
Thank you SO much for this tutorial. I have a knitted jumper for my DH which has one seam to finish. It isn't going to happen - not after 20 years of waiting ... SO I will unravel it and do as you do with something nice with the yarn this time!And I love your pink plastics ...and photography...
Love the tutorial. I started unraveling sweaters a little while ago and am hoping to sell them, if possible. For the most part I tend to just reuse them myself because all of the really nice pretty yarn is just too expensive. If you get a moment, check out my page, www.facebook.com/thechrochetyhookerIt's my trials and tribulations of crochet and yarn repurposing.
The Face Behind the Goldfish.
Hello... I'm Sharon
I’m an Aussie mum of four, with more ideas dancing around in my head than I will ever be able to bring to life…
I love all things quirky and unexpected. Throw in some experimenting and recycling, bend a few rules… and I’m in heaven!
To keep me on my toes, I run a Monthly Challenge. One month is knitting, the next month is crochet, and then we have a random challenge. During that month, I offer a free pattern to all participants, who make the project and share their finished photos. At the end of the month, I choose a WINNER… and then THEY tell ME what to design for the next Challenge!!! How cool is that???
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Calypso the Kooky Owl - Crochet Pattern
download FREE pattern hereThis adorable crochet owl works up in no time, using three strands of yarn held together as one, and a large hook. The pattern is written for four different sizes of owl: mini – 10 cm (4 in), small – 14 cm (5 ½ in), medium – 18 cm (7 in) and large – 22 cm (8 ¾ in) tall. Everyone loves owls. They’re perfect gifts for a New Arrival, Child’s Birthday, or even a Graduation Gift.
Freeform Hat - Crochet Pattern
It seems a little peculiar to have written a freeform pattern. After all, the whole basis of freeform is that you are not following a pattern or trying to reproduce the work of anyone else - but are creating your own unique piece.
So what I’ve done here is to encourage you to experiment. I’ve shared the instructions for making a hat like my sample one, but I’ve also include two pages of suggestions for other things you can try out to make your hat different. This PDF Crochet Pattern is available in 7 sizes, from Premie to Large Adult, for AU$4.50
Flotsam the Fascinating Seahorse
I find the seahorse to be a fascinating creature. From their horse-like head to their curly tail, they are unlike any other fish around. I especially love that the MALE seahorse carries and gives birth to the babies! Intriguing, yes? Toy measures 24 cm (9 ½ in) long. This PDF Crochet Pattern is available for AU$4.50
Finbar the 20 Pound Crochet Cat
He’s a giant hunk of cat – just waiting to be cuddled… And if you’re looking for something a little more delicate, try making him with a finer hook and sock yarn. Cat measures 56 cm (22 in) tall. This PDF Crochet Pattern is available for AU$4.50
Shelly the Colourful Sea Turtle - Pattern
This adorable sea turtle is the perfect size for little hands to cuddle. The colour work in the shell is a simple slip stitch pattern, which works up very quickly. Turtle measures 36 cm (14 in) long and 27 cm (10 ½ in) wide. This PDF Knitting Pattern is available for AU$4.50
Sizzle the Sausage Dog
This endearing crochet sausage dog works up in no time, using chunky yarn and a large hook. One day - I’d love to make one with a body so long that you can tie him in a knot… This toy measures 58 cm (23 in) long and 12 cm (4 ¾ in) tall, not including the height of the tail. This PDF Crochet Pattern is available for AU$4.50
Rupert the 20 Pound Cat - Pattern
This cuddly oversized cat is worked up using large needles and chunky yarn. He makes a wonderful playmate for big and little kids alike – or you could place a weight in the base and put him to use as a door stop. He sits 45cm tall - that’s a whopping 18 inches! This PDF Knitting Pattern is available for AU$4.50
Bucky the Stuffed Moose Head - Pattern
This stuffed moose head is not remotely realistic looking – and I’m quite okay with that… Instead it’s an example of faux taxidermy at its finest. Patchwork section of head measures 26 cm (10 ¼ in) tall. Total width, including antlers is 48 cm (19 in). This PDF Knitting Pattern is available for AU$4.50.
challenge mitts
download free pattern nowThese mitts are worked in the round with no shaping. The shell pattern is stretchy and will accommodate the shape of your hand beautifully. All you need to do is remember to add your peek-a-boo hole for the thumb!
fishie the plastic bag keeper - pattern
What better way to store your plastic bags than inside this fancy fish? Stuff your grocery bags into his tail and watch his belly grow … remove them through his mouth and watch him shrink back down again. Length - 61 cm (24 in). Circumference - 38 cm (15 in). This PDF crochet pattern is available for AU $4.50.
fancy the frilled neck lizard - pattern
Australia is home to some of the most exquisite creatures on the face of the earth. And the sun-loving frilled neck lizard is no exception. Of course this little guy is way more cuddly than those found in the wild... Toy sits 22 cm (8 3/4 in) tall. This PDF crochet pattern is available for AU $4.50.
kiki the cutie kangaroo - pattern
With her oversized ears and classic granny square pouch, Kiki is the most adorable kangaroo you will ever lay eyes on. Make her in natural colours, or let your imagination run wild… Either way, she is sure to bring a smile to someone’s face! Toy sits 20 cm (8 in) tall... This PDF Crochet Pattern is available for AU$4.50.
flaming lamborghini bag - pattern
The Flaming Lamborghini bag is knitted in the round using a trio of vibrant colours, with flames dancing around the top… This PDF Knitting Pattern is available for AU$4.50
sally the sassy centauride - pattern
Lively, bold and full of spirit! Some might query their very existence, but the female centaur make up a kick ass breed of heroines, ready to rock the world. This PDF Crochet Pattern is available for AU$4.50.
polly the spotty-tailed platypus - pattern
The Spotty-Tailed Platypus is an endangered species, easily identified by their distinctive tail and external ears… Polly is the only known creature of her type in existence – but you can help with the breeding program, by making a Spotty-Tail Platypus of your very own! This PDF Crochet Pattern is available for AU$4.50
roweena the raggedy rascal of the sea - pattern
With her mop of raggedy hair and that crazy curlicue tail, Roweena makes for a truly unique mermaid. Before you even finish making your first doll - you'll be struck with inspiration for the next... and the next... and the next... This PDF Crochet Pattern is available for AU$4.50
Thirteen the Lucky Dragon - pattern
The dragon is believed by many to be a symbol of power, strength and good luck. Say hello to Thirteen, my friendly version of the legendary creature. With his impish ears and longing eyes, he will charm the socks right off you! This PDF knitting pattern is available for AU$4.50
True Blue the Quirky Koala - pattern
True Blue is an expression we use here to describe an Authentic Aussie… What better way to describe the Koala? And this Quirky little character really is BLUE… This PDF crochet pattern is available for AU$4.50
Matryoshka Doll - pattern
Matryoshka is foreign and exotic, yet homey and charming, all at the same time. With bold colours and intricate designs you can let your imagination run wild as you embellish this simple pattern. This PDF knitting pattern is available for AU$4.50
Callipo the Very Naughty Monkey - pattern
Callipo featured in a song I learned as a child. For the longest time, this little guy has been dancing around inside my head with his striped arms and legs…
And now he’s finally here.
This PDF Crochet Pattern is available for AU$4.50
Jerry Giraffe - pattern
I love that Jerry is Not Your Average Giraffe.
His ears are way too big, he has an unusual snout, a startled expression - and don’t even get me started on those colors!
This PDF Crochet Pattern is available for AU$4.50
Kokeshi Doll - pattern
This whimsical design is based on the Japanese kokeshi doll. Made from yarn, she is much softer than the original dolls - but shares the same irresistible charm.
This PDF Knitting Pattern is available for AU$4.50
Chi-kore - pattern
Chi-Kore is a quirky creature from deep in the imagination. This PDF Crochet Pattern is available for AU$4.50 | tomekkorbak/pile-curse-small | Pile-CC |
Are you looking to hire a party bus in Australia but do not want to spend too much money on it? Simply visit PartyBusGuru.co,.au and let us know what you need! We offer party bus hire at the most competitive prices so whether you want to celebrate a special event in Sydney, Melbourne, Brisbane, Perth or more, we have you covered! | tomekkorbak/pile-curse-small | Pile-CC |
A federal judge ordered the government to return an asylum-seeking mother and her daughter to the US after the Trump administration revealed in a Thursday court hearing that they had sent the migrants to Central America while the court was still considering their case.
The judge, Emmet Sullivan, said it was unacceptable the government had deported the family and threatened to hold the US attorney general, Jeff Sessions, in contempt if the situation was not resolved.
“This is pretty outrageous,” Sullivan said. “That someone seeking justice in US court is spirited away while her attorneys are arguing for justice for her?”
“I’m not happy about this at all,” he continued. “This is not acceptable.”
Q&A Have you been affected by Trump's zero tolerance immigration policy? Show We want to shine a light on the lasting repercussions of the policy by telling the stories of those affected, from the migrants themselves to the public employees tasked with implementing assembly-line justice. Fill the form here to share your story with us.
The dramatic hearing was part of a lawsuit the American Civil Liberties Union (ACLU) and Center for Gender & Refugee Studies filed on Tuesday, alleging the Trump administration was unfairly preventing thousands of migrants fleeing violence in Central America from seeking asylum in the US.
The ACLU said the government had on Wednesday assured the court that no plaintiff in the case would be deported before midnight on Thursday.
“This disregard for commitments made to the court and the life or death circumstances that these immigrant women and children are facing is beyond unacceptable,” the ACLU said in a statement.
In court on Thursday, Sullivan also temporarily blocked the US from deporting plaintiffs in the lawsuit, most of whom are women fleeing sexual abuse and gang violence.
Those protected by the judge’s order include the lead plaintiff, who is referred to by the pseudonym Grace. In the suit, Grace said her partner of 22 years, and his two gang member sons from another relationship, repeatedly beat and threatened to kill her and her children.
She sought police protection in 2016, but they did not protect her and Grace fled Guatemala, because she felt she wouldn’t be safe in the country because of her partner and his sons’ gang affiliation, according to the suit.
Her asylum attempt appeared to have been thwarted by new rules introduced by the Trump administration in June, which block courts from granting asylum to victims of domestic abuse and gang violence.
The judge’s decision on Thursday, however, means plaintiffs can remain in the US, where they are being held in detention facilities, while Sullivan considers the case.
Sessions and other Trump appointees have dramatically shifted how the federal government speaks about asylum, going as far as to suggest in public communications the unproven claim that asylum is a routinely abused legal loophole.
“We also have dirty immigration lawyers who are encouraging their otherwise unlawfully present clients to make false claims of asylum, providing them with the magic words needed to trigger the credible fear process,” Sessions said last year.
The justice department did not immediately return a request for comment. | tomekkorbak/pile-curse-small | OpenWebText2 |
PETALING JAYA: She was a bright young Malaysian pursuing a doctorate in clinical and counselling psychology because she wanted to help children the world over.
But she also had to persevere through months of what she described as racial bullying and insults, and when her university's psychology department seemingly did nothing, she could endure no more.
Jerusha Sanjeevi, a child rape survivor of Chinese and Indian descent, took her own life in 2017 at the tender age of 24.
Now her family is suing Utah State University (USU) for alleged inaction over Jerusha's multiple reports of relentless racist bullying, according to reports by US media.
The Herald Journal said that Jerusha's family, who still lives in Malaysia, is seeking damages from the university. No amount was disclosed.
The lawsuit, filed by her boyfriend Matthew Bick, alleges that the university's psychology department did not do enough to intervene against the bullying that led to her death.
Jerusha had a Master's degree in clinical psychology and had enrolled as a doctoral student in USU's combined clinical and counselling psychology programme just eight months before her suicide.
In her research paper on child sexual abuse that was published posthumously, she was described as having a "life-long interest in improving lives of children globally".
The lawsuit names as defendants USU, then-psychology department head Gretchen Peacock, Prof. Melissa Tehee, Emeritus Prof. Carolyn Barcus, and two students who were the alleged bullies, The Herald Journal reported.
It claims that the department "knowingly allowed one of its students to be verbally abused, intimidated and subjected to cultural and racist discrimination by favoured students over the course of eight months, when she was rendered so emotionally devastated and hopeless that she committed suicide."
The suit also alleges that the university, where 83% of its students are white, had a pattern of favouritism as well as racism against international students facing a hostile environment, while faculty members had knowingly allowed such abuse to continue for years, according to the newspaper.
Dark skin a 'sign of inferiority'
Jerusha's bullying started just weeks after her first semester had started, and grew more intense throughout her time there.
"Every day I dread going to class now because I sit three feet from my white bully," she wrote to a close friend just a few months into her course, according to The Herald Journal.
Meanwhile, the Salt Lake Tribune reported that two students in her cohort singled her out and would not only discredit her and mock her whenever she spoke in class, but would also say she smelled like Indian food and talked about how dark skin was a sign of inferiority.
Reports said the bullying targeted her culture, including statements likes "Asians only want to please their parents", "Asian names are weird", and its people "stupid" and "second best".
A student told attorneys that the bullies would text Jerusha pictures of Indian foods and memes, asking her whether they were "legitimate."
"This was done despite the fact that (Jerusha) affirmed numerous times that she was not from India but from Malaysia," the student told the Salt Lake Tribune.
'Slut' and 'whore' insults
She attempted to bridge the gap with her classmates by inviting them to a Deepavali celebration in October, but the harassment only grew worse.
Over the next few months, the comments escalated to insults like "slut" and "whore" as the alleged bullies passed her in the university's hallways.
However, the university was not in the dark about this.
Jerusha had sought help from at least five faculty members, the department head, the school's counselling centre, Student Conduct Office and its Affirmative Action/Equal Opportunity office.
She first reported her concerns in September 2016 to Prof. Tehee who supervised a lab that both Jerusha and the alleged bully was in.
Jerusha later told her boyfriend that the professor and the alleged bully did not take her concerns seriously.
Her complaints ended up backfiring as the bullying escalated into rumours about her academic character.
Several US media reports said that Prof. Tehee was known to have had a close relationship with the alleged bully and would give all research projects to the alleged bully and none to Jerusha.
When US President Donald Trump, who has a harsh stance on immigration, was elected in 2016, Jerusha wrote to psychology professor Melanie Domenech expressing her concerns about getting deported and offered to help other international students in distress.
"As a Malaysian, I believe in food therapy, so I am going to be dropping off food this week for anyone who needs a pick-me-up, so let me know if I can help anyone in particular," Sanjeevi wrote in the email obtained by attorneys.
The lawsuit alleges that the bully then spread a rumour that Jerusha was bipolar because she had been "so upset after the election but then made everyone food and was so happy."
In February 2017, Jerusha sought help from USU's Counselling and Psychology Services centre, but its director David Bush "apparently assumed that some of (the bully's) rumours about Sanjeevi (Jerusha) were true" in a report, the lawsuit alleges.
Upset by the report, Jerusha wrote to Domenech: "I gathered enough courage to report a white-skinned bully, but it has led to nothing but re-traumatisation from the school on every front. Him echoing the racism/ victim blaming felt like the last beating before getting knocked out."
One of Jerusha's friends also reached out to the university separately over how she was being dismissed.
Anderson & Karrenberg, the Salt Lake firm representing the plaintiff, reportedly said the university dismissed any reports as a "conflict between students" and declined to investigate the multiple reports of bullying and racism by specific students, even after Jerusha committed suicide.
She had been growing increasingly despondent and withdrawn during the eight months, US news reports quoted the lawsuit as saying.
"I'm going to leave my lab because I can't take it anymore," Jerusha told a friend before her death.
"She knew that I've been struggling with the fear of getting deported since the (US presidential) election. She knew that I have no power here as a foreign student.
"And she did this to me on top of all of that. I don't understand how a person can be so cruel," she added.
Just days before she killed herself, she told a friend that she was overwhelmed by the department's apparent apathy.
"I just don't understand why I matter so little to them," she said. "I haven't been feeling like living and this just confirms that I don't want this life anymore."
On April 22, 2017, she died of acute carbon monoxide poisoning.
The law firm Anderson & Karrenberg told The Herald Journal that the university failed in its responsibility to Jerusha.
"What we're alleging is that this particular programme had a duty not to turn away from a struggling student who was experiencing intercultural conflict," attorney Richard Kaplan was quoted as saying.
Not its first controversy
In recent years, USU has been embroiled in lawsuits alleging a culture of discrimination, sexism and favouritism.
The Salt Lake Tribune reported in 2017 that the US Department of Justice had investigated how USU responded to reports of sexual assault.
This followed reports of a former student suing the university for allegedly mishandling sexual assault allegations.
The newspaper also reported that after Jerusha's death, the department chair emailed students in the psychology programme asking them not to talk about the suicide publicly.
USU spokesman Amanda DeRito denied the allegations in a prepared statement to US media.
"Jerusha Sanjeevi's suicide was a tragic event that had a huge impact on the Psychology Department and on our entire university.
"She was a promising student, and her death tremendously affected her fellow students, as well as staff and faculty in the department.
"We cannot release private and protected student records or comment on the specifics of this case, but we strongly dispute the facts and allegations in the complaint. We believe Utah State took all appropriate action to address interpersonal issues between students in the department," she said.
'My heart was broken'
In her suicide note, Jerusha said the university made her feel like her life did not matter.
"I have lived with depression for over half my life, and somehow survived each episode. But each wave of sadness grew darker and longer," she wrote, according to news portal The Daily Beast.
"I looked and looked for a lifeline. Until I realised that I didn't deserve one. Because [the Department] succeeded at teaching me what poverty, violence, rape, and hunger somehow never did ....
"When you dismissed the bullying report, you provided a final confirmation that I did, in fact, not matter.
"The innocence of blonde hair and blue eyes could deny, with toxic ease, the 'crazy' ramblings of this dirty brown skin.
"Watching the department not only choose to not enact consequences, but to give an award to the sick person who bullied me, was the last nail in my coffin.
"My heart was broken.
"Please be kinder in the future. Please send my ashes to my parents," were her final words.
The lawsuit against USU comes just after a white supremacist opened fire at a shopping mall in El Paso, Texas, killing 22 people and wounding dozens.
The shooter had reportedly targeted El Paso due to its large Hispanic community.
Befrienders is a not-for-profit organisation which provides emotional support at any time to people who are lonely, distressed, in despair or having suicidal thoughts.
Those in need of someone to talk to can call the Befrienders KL at 03-7956 8145, or 04-281 5161/1108 in Penang, or 05-547 7933/7955 in Ipoh or email sam@befrienders.org.my.
Article type: metered User Type: anonymous web User Status: Campaign ID: 18 Cxense type: free User access status: 3 | tomekkorbak/pile-curse-small | OpenWebText2 |
Q:
Weekday+day validation
The string I'd like to check is something like "abcSun24def". If any valid "xxxyy" (xxx = weekday and yy = day) is found, return the position inside the string. If "xxxyy" is not found, return -1.
The code works as desired, but I think it can be optimized.
/* -------------------------------------------------------------
FUNC : findxy (find pattern xxxyy)
xxx = weekday (e.g. "Mon01")
yy = day
roster specific formatting
PARAMS : c (char *), pointer to string
RETURNS : (int), if pattern found, pointer to found pattern in string c
-1 if pattern not found
REMARKS :
---------------------------------------------------------------- */
int findxy(char *c) {
const char *days[] = { "Sun", "Mon", "Tue", "Wed", "Thu", "Fri", "Sat"};
int i, j;
char bufw[4];
char bufd[3];
/* check if c is at least 5 chars long */
if (strlen(c) < 5)
return -1;
for (i = 0; i <= (int)strlen(c)-5; i++) {
memcpy(bufw, c+i, 3);
bufw[3]='\0';
/* check all 7 weekdays */
for (j = 0; j < 7; j++) {
/* find weekday matches */
if (!strcmp(bufw, days[j])) {
/* check if both chars following weekday are numerical */
if (isdigit(c[i+3]) && isdigit(c[i+4])) {
memcpy(bufd, c+i+3, 2);
bufd[2]='\0';
/* check if number after weekday is a valid day */
if (atoi(bufd) >= 1 && atoi(bufd) <= 31) {
return i;
}
}
}
}
}
return -1;
}
A:
I see some things that may help you improve your code.
Use the required #includes
The code uses strlen and memcpy which means that it should #include <string.h>. It was not difficult to infer, but it helps reviewers if the code is complete. It's also an important part of the interface. I believe these are the required includes:
#include <string.h>
#include <stdlib.h>
#include <ctype.h>
Use const where practical
In your findxy routine, the passed string is never altered, which is just as it should be. You should indicate that fact by declaring it like this:
int findxy(const char *c)
Check for a null pointer
Things do not go well if the routine is passed a NULL pointer. On my machine, I get a segmentation fault and a crash. You can eliminate this hole by adding these lines near the top of the routine:
if (c == NULL) {
return -1;
}
Use better naming
The days array is well named because it's easy to guess from the name what it contains. Likewise i and j are commonly used as index variables as you have done in this code. However, findxy is a rather cryptic name for what this does and c is a poor name for the passed string. I'd recommend something like this instead:
int findWeekdayDate(const char *str)
Avoid copying if practical
It's not strictly necessary to make copies of portions of the passed string. With a bit of careful planning, it can be done in place. Here's one way to do it, although it's not very efficient:
int isValidWeekdayDate(const char *str) {
static const char *days[] = { "Sun", "Mon", "Tue", "Wed", "Thu", "Fri", "Sat"};
if (str == NULL || strlen(str) < 5) {
return 0;
}
for (const char **dayname = days; *dayname; ++dayname) {
char *pos = strstr(str, *dayname);
if (pos && pos == str) {
if (isdigit(pos[3]) && isdigit(pos[4])) {
int val = (pos[3]-'0') * 10 + (pos[4]-'0');
if (val > 0 && val <= 31) {
return 1;
}
}
}
}
return 0;
}
int findWeekdayDate(const char *str) {
for (const char *curr = str ; *curr; ++curr) {
if (isValidWeekdayDate(curr)) {
return curr-str;
}
}
return -1;
}
Use a finite state machine
We can create a much more efficient routine by creating a finite state machine. For a particular candidate string, we note that the first character must be one of {'F', 'M', 'S', 'T', 'W'}. If it is not one of those, then the candidate string can be immediately rejected. Now let's say the first character is 'S'. In that case the second character must be one of {'a', 'u'}. We can proceed like this, one character at a time to create a finite state machine. Here's a visualization of such a state machine:
This is how compiler tools like flex and bison and lex and yacc work. The code is very efficient but might not be as easy to understand, so it's a tradeoff you should be aware of.
A very pedantic note
Strictly speaking, this line:
int val = (pos[3]-'0') * 10 + (pos[4]-'0');
is guaranteed to be portable. The C standard requires that encoding of digits is contiguous, so this will work with any character encoding, including EBCDIC, Unicode and ASCII.
| tomekkorbak/pile-curse-small | StackExchange |
Mock your HTTP responses to test your REST API - yotsumi
http://www.mocky.io
======
kanzure
Also, python people might be interested in
<https://github.com/gabrielfalcao/HTTPretty> or (bias disclaimer) my
serializer on top of requests+httpretty <https://github.com/kanzure/python-
requestions> for the httpetrified decorator. It loads and mocks an expected
response from a json file in your tests/.
There was a service called requests.in or something that acted like httpbin,
except it gave you a unique url to query against to view multiple requests
over a session. Does anyone know where that went?
~~~
johns
requestb.in
------
untog
It's a nice idea, but relying on a remote service for testing makes me worry.
I tend to mock HTTP responses locally, so that the tests can run when there
isn't even an internet connection available.
~~~
johns
What do you use for your local testing?
~~~
fein
Telnet when I'm lazy or its quick, curl when I actually want to write a full
harness.
------
simons
There's a post here: [http://artemave.github.io/2012/05/27/stub-like-a-
surgeon-spy...](http://artemave.github.io/2012/05/27/stub-like-a-surgeon-spy-
like-james-bond-with-rest-assured/) that talks about using a similar service
(the BBC's REST-assured <https://github.com/BBC/REST-assured>) to aid in BDD
using cucumber.
------
rschmitty
Why not use SinonJS? <http://sinonjs.org/>
Same ability to mock responses and errors, but everything is local. Check your
responses into git and every developer is testing the same stuff, no reliance
on a 3rd party
Makes for lightning fast automatic background testing.
------
memoryfault
Would someone provide an example on how this tool could be used to test a REST
API? I think I'm missing something here. I'm not seeing how a fake response
endpoint lets me test my REST API (shouldn't my test code invoke the API and
validate that the real response was correct?)
~~~
sanderjd
It seems to me that it isn't for testing a REST API but rather for testing
something that _depends_ on one without having to deal with real integration
issues.
~~~
yotsumi
Yes, you explain better than me ;)
------
rco8786
Been working on something similar for local use by running nodejs to both
server static files and mock API responses.
<https://github.com/rco8786/apimok>
------
wilig
For those looking for a local alternative have a look at
<http://wilig.github.io/mockity/>
Full disclosure: I'm the author.
------
donatj
I use <http://frisbyjs.com/> FrisbyJS for most of my front end API testing
needs.
------
gulbrandr
<http://www.hurl.it/>
I recommend this service for this kind of testing.
~~~
quarterto
Hurl is requests. Mocky is responses.
~~~
quarterto
In fact, here is Mocky serving a response to Hurl:
[http://www.hurl.it/hurls/18e4da3bfc0c2159abd1c8e769915c360a8...](http://www.hurl.it/hurls/18e4da3bfc0c2159abd1c8e769915c360a8de8ce/6dc5f86a8ac115dc0870e88cf260d5b7dcb49c15)
~~~
farmdawgnation
If a hurl falls in a forest, and only a mocky is around to hear it, did it
happen?
------
bruth
Nice idea. Are these stored as gists under my account? Can I choose to modify
an existing response so it's versioned?
------
ericmoritz
this isn't any better than using a live server for testing.
Build a good client library for your applications to use, mock the client
library and don't worry about tests failing because of availability problems.
~~~
johns
If the live server has side effects when making the call (send an email,
charge a card, etc) and you just want to test against the response
headers/body, it can be very useful. A local mocking library is also good for
that, but for quicker tests this is nice.
------
rajanikanthr
I use mocking framework(Moq for .NET) to mock my service response and various
xml responses i will save in test xml files.. Anyways, I will try to use it to
test over network rather local mocking
------
gstroup
I prefer to run my own local test server to return mock responses. I built
this little project, that you can install using NPM:
<https://npmjs.org/package/apimocker> It's intended for sandbox development as
well as automated tests. There's no UI, but you can return whatever data you
want. The features are pretty basic right now, but it works well for most
tests, and it's easily configured on the fly.
------
city41
It's a neat idea but I can't imagine I'd ever actually use this for real
testing. Relying on a third party server for your tests can be a problem. We
also have thousands of tests that rely on mocked REST responses, setting them
up with Mocky would be a ton of work.
If Mocky could be ran onsite and had a nice API for easily generating mock
responses, then I think it would be more useful.
~~~
yotsumi
It's an open source project, created 2 days ago. All is possible, this website
is just a proof of concept. And you can fork the project to run it locally.
~~~
city41
Yeah I realize that. I hope I didn't come across too harsh. It is a good idea,
and I'd like to see it grow some more.
------
sinkingfish
I just launched something almost exactly the same a fortnight ago -
e.ndpoint.com - POST/PUT/DELETE support coming soon.
~~~
johns
The URL scheme you're using makes it really easy to view everyone else's
mocks.
~~~
sinkingfish
Yea i'm not looking to obfuscate, I'm planning on introducing user accounts
whereby people by create, save, edit, and alias their mocks. Bypassing that
issue. Anonymous mocks will simply be sequential base62.
------
tjpd
I've heard good things about <http://apiary.io> on this front as well...
~~~
nyam
i'm using it on first project and it's very nice. they let you export your
complete api definition to apiary.apib file which can be parsed with their
github.com/apiaryio/blueprint-parser into json and used with your custom
server localy. it's also nice for synchronizing between devs, when added to
vcs ...
------
aespinoza
This is very cool. It is kind of a fiddler on the web. It is interesting that
I saw something similar but with fiddler in the morning:
[http://www.devcurry.com/2013/05/testing-crud-operations-
in-a...](http://www.devcurry.com/2013/05/testing-crud-operations-in-aspnet-
web_3.html)
------
jnettome
I've sent a pull request to add portuguese brazilian translation. I hope it
helps! Scala is really cool :)
------
alpb
Nice project! My suggestion would be adding JSON editor or JSON syntax
validator for JSON responses saved.
~~~
yotsumi
You already have a light Json editor. The Syntax validation is a very good
idea, thanks!
------
austengary
In case anyone was wondering about licensing:
"[1]DO WHAT THE FUCK YOU WANT TO PUBLIC LICENSE Version 2, December 2004
Copyright (C) 2004 Sam Hocevar sam@hocevar.net"
[1] <https://github.com/studiodev/Mocky>
------
nym
You can't mock HTTP responses, the responses mock you.
[http://www.flickr.com/photos/girliemac/6508102407/in/set-721...](http://www.flickr.com/photos/girliemac/6508102407/in/set-72157628409467125/)
------
yotsumi
@misframer The app is updated in real time. So it can be some sporadic errors
~~~
quarterto
Welcome to Hacker News. We don't have @replies here. We do, however, have nice
friendly reply buttons. Great app, by the way!
------
antonpug
How exactly does this work? A short little tutorial would help ^.^
------
meryn
Wouldn't it be better if it would just say "mock your HTTP responses to test
your HTTP client", or "to test your HTTP client code"?
The service makes a lot of sense otherwise.
------
thekingshorses
This failed :(
<div>what</div><div>Not</div>this<ul id="list" data-list="f"><li
class="first">one</li></ul>
------
PuercoPop
Nice, Emacs have a mode for doing the same too:
<https://github.com/pashky/restclient.el>
~~~
yotsumi
Emacs have a REST Client, but this app is like a REST Server: Mocky serve an
HTTP response, whereas RestClient send an HTTP resquest.
------
guyht
I have wanted a service like this forever! Thank you.
------
misframer
I'm occasionally getting hit with
"HTTP/1.1 500 Internal Server Error"
when that's not what I want.
------
rcoh
Ironically, I'm seeing 500s. Great for testing my reliability in the face of
errors!
~~~
yotsumi
Yes sorry for that, I didn't expect a such traffic from HN. Things will be
stable in a few hours :)
------
rross
E.endpoint.com
A very similar offering released a week ago on github.
------
jstoja
That's cool !
| tomekkorbak/pile-curse-small | HackerNews |
Q:
Can I use individual wires in PVC conduit for just a portion of a kitchen circuit?
I was planning on running 2 black 2 white and 1 green 12 gauge wires through flex from panel to kitchen wall, then changing to rigid pvc to go under ground to kitchen island for microwave and gfi circuits but the project manager insists I use cable until I switch to pvc because of cost. I didn't realize it would save that much money and prefer not having unnecessary junction boxes. so I just thought I'd ask if there were any potential issues before doing it his way. Thank you.
A:
In answer to the question you asked in your title. There is no issue with changing from a cable (romex) system to a conduit system just so long as it is done properly.
FYI - The difference between a cable system and a conduit system other than initial cost is that a conduit system is more flexible when it comes to upgrades, remodel or repairs. For example, you have a receptacle burn up and it also damages the conductor far enough back you can't make a splice to repair it, with a conduit system you simple go back to the next junction and pull a new conductor. If you have a cable system you will have to open the wall up to replace the cable.
Running PVC to the island and installing conduit and conductors is a good idea since it allows you the opportunity to replace or modify your circuity to the island without cutting up your finished floor. Most houses in the US are normally run in Romex because of the initial cost and electricians are trained to deal with the problems they may cause down the road.
Hope this helps.
| tomekkorbak/pile-curse-small | StackExchange |
High urinary bisphenol A concentrations in workers and possible laboratory abnormalities.
Bisphenol A (BPA) is widely used in epoxy resins in China. There are few reports on the adverse health effects of occupational exposure to BPA. This study examined associations between urinary BPA concentrations in workers and laboratory parameters for health status. Spot urine checks at the end shift on Friday were used for cross-sectional analysis of BPA concentrations, and blood or urinary markers of liver function, glucose homeostasis, thyroid function and cardiovascular diseases were measured. The 28 participants were workers in two semiautomatic epoxy resin factories. The average urinary BPA concentration was 55.73±5.48 ng/ml (geometric mean ± geometric SD) (range 5.56-1934.85 ng/ml). After adjusting for urine creatinine (Cr), it was 31.96±4.42 μg/g Cr (geometric mean ± geometric SD) (range 4.61-1253.69 μg/g Cr). BPA feeding operators showed the highest concentrations, over 10 times those of the crushing and packing and office workers. Higher BPA concentrations were associated with clinically abnormal concentrations of FT3, FT4, TT3, TT4, thyroid-stimulating hormone, glutamic-oxaloacetic transaminase and γ-glutamyl transferase. Workers with higher BPA concentrations showed higher FT3 concentrations (linear trend: p<0.001). Bivariate correlation tests for laboratory analytes within normal limits showed FT3 to be positively associated with logged BPA concentrations, r=0.57, p=0.002. FT4 was positively associated with lactate dehydrogenase, r=0.45, p=0.020, and insulin was positively associated with thyroid-stimulating hormone with r=0.57, p=0.009. Higher occupational BPA exposure, reflected in urinary concentrations of BPA, may be associated with thyroid hormone disruption. | tomekkorbak/pile-curse-small | PubMed Abstracts |
Dear complete and total strangers at Costco,
I know you watched as we navigated our vehicle into the crowded parking lot. You stood in awe as we wedged our trendy 15 passenger mega-van into a parking space between a 2 door Miata and a very roomy shoe box- on-wheels deemed a Smart Car. You saw us attempt to unload our family with as much class, decorum and organization as we could humanly muster… and 23 minutes later file toward Costco with our seven *progeny and three carts for our weekly shopping trip.
I can only imagine your thoughts as one wailing child donned an open-toed sandal on his right foot and a rubber boot covered in duct tape on the left. You correctly saw that a second child was wearing pajama pants that are at least three sizes too short, paired with a faded Thomas The Train pajama shirt, because he refuses to dress with his eyes open.
I’ve given up.
Our toddler sported an ensemble perfect for an afternoon on a yacht. Another youngster was flawlessly dressed for a cold afternoon at a ski resort. The child sitting in the cart wailing was doing so, not because he hates shopping at Costco; on the contrary. He was wailing because we don’t let him shop at Costco naked.
You stared at our mobile carnival with a slight measure of horror and partly out of bewilderment. “Why on earth do they have SEVEN children?” you asked yourself. Now, I’d like to pause here and take the time to point out that the number 7 is really not that large. If I had told you that I owned seven goldfish, you might have curiously asked if I had other pets as well. If I had told you that I owned seven pairs of shoes, you might have shrugged and looked bored. If I had told you that I had seven dollars, you may have found my financial status tremendously lacking. But, observing that I have sevenchildren seemed to invoke the same amount of shock as if I had asked you to lasso a bald eagle and eat it with your feet.
After making it past the Costco entrance bouncer, we maneuvered our troupe through various onlookers in order to fill up the carts and consume every available food sample.
It must have horrified you as you watched a tall, lanky teenager in poorly made cut-offs and a Seahawks jersey scoop up 14 paper samples of microwaveable beef wellington, down them in 3 bites and then reach for more. You see, this kid is the reason we shop at Costco in the first place. I can credit him for the reason we upgraded to the EXECUTIVE Membership after a checker said to me “Mrs. Diaz, our records indicate that you spend more at Costco than the average family.” I’ll bet. At our house he is known as The Very Hungry Teenager. This kid can eat an entire meal, then want 2 sandwiches, 3 large carrots, a slice of watermelon, 4 mini bagels with cream cheese, a bowl of cereal topped with a fried egg, 6 pickles and a cookie, then look at everyone at the table and ask with a straight face “Are you going to finish that?”
So you see? We are bound to the Costco warehouse establishment like an airborne rock is bound to the laws of gravity. We practically live at Costco and have made a habit of noticing reactions to our family from fellow patrons who are pushing their carts overloaded with frozen burritos, cheesy-poofs, vats of mayonnaise, candy bars and weight-loss supplements.
Since discussing my fertility with complete and total strangers in the cheese aisle is what I LIVE for, I was more than happy to respond to your impertinent curiosity.
In fact, fellow club members, I have loved answering your varied questions so much, that I’ve compiled a list for you to refer to in case you happen to encounter us again and so others who remain unaware can be ready for us with NEW questions next time around. Ready? Here we go.
Q: Cute baby. Is she your last?
A: This year, yes.
Q: Why do you have so many kids?
A: Because it will increase our odds of ending up in a good nursing home.
Q: Do all of your kids have the same dad?
A: Uh…so far….
Q: What is your food bill like each month?
A: How much is your mortgage?
Q: How will you ever pay for all of their college tuition?
A: Well bless your heart for taking a look at us collectively and still believing my kids could qualify for entrance into any institution that isn’t traveling with trained animals, acrobats and clowns.
Q: Does it get pretty loud at your house?
A. Didn’t catch that. What did you say?
Q: Are you trying to be like that other family? The one on TV with the nineteen kids?
A: Oh yeah, baby. Because the number 7 is . to the number 19. Heck, I’m almost there.
Q: Why is that one taking his clothes off?
A: Don’t worry about him. He’ll stop undressing when he realizes we’re buying mustard.
There now. I hope that satisfied some of your curiosity.
Looking back, I’m sure you have subconsciously blocked out the savagery of what you saw in our check-out lane. Let’s just say it involved a twirling sister, a sprawling brother, escaped oranges, a Flop Tantrum, and a flying churro. After St. Peter (the receipt angel and exit-guardian), gave us his nod of approval to move on out, we trekked the circus back to the van and headed home. Much to your relief and silent applause, I’m sure.
That leaves me here, sipping coffee and recollecting another Costco adventure that I look forward to each and every week.
You are always welcome to join us on our next shopping trip, of course. We like new friends. I’ll even put you to work pushing a cart. But you’ll have to swear upon chocolate milk that you won’t show us up by dressing like normal people do.
Which means you’ll need to be wearing attire suitable for a day on a yacht. Or a slumber party.
Or a ski resort.
-Sincerely Yours, Mrs. Diaz
*the word progeny (paragraph 1), in this instance refers to 7 quirky, bedraggled, colorful and unconventional offspring slightly resembling a funeral parade for fellow Big-Top performers. Mr. Diaz has informed me that the word progeny is far too sophisticated for this blog and I have to agree with him and therefore apologize. | tomekkorbak/pile-curse-small | OpenWebText2 |
Guests 1+ Guests 2+ Guests 3+ Guests 4+ Guests 5+ Guests 6+ Guests 7+ Guests 8+ Guests 9+ Guests 10+ Guests 11+ Guests 12+ Guests 13+ Guests 14+ Guests 15+ Guests 16+ Guests 17+ Guests 18+ Guests 19+ Guests 20+ Guests 21+ Guests 22+ Guests 23+ Guests 24+ Guests 25+ Guests 26+ Guests 27+ Guests 28+ Guests 29+ Guests 30+ Guests 31+ Guests 32+ Guests 33+ Guests 34+ Guests 35+ Guests 36+ Guests 37+ Guests 38+ Guests 39+ Guests 40+ Guests 41+ Guests 42+ Guests 43+ Guests 44+ Guests 45+ Guests 46+ Guests 47+ Guests 48+ Guests 49+ Guests 50+ Guests
1 Bedrooms 2 Bedrooms 3 Bedrooms 4 Bedrooms 5 Bedrooms 6+ Bedrooms Bedrooms
Min $100/Night Min $150/Night Min $200/Night Min $250/Night Min $300/Night Min $400/Night Min $500/Night Min $750/Night No Min/Night Max $100/Night Max $150/Night Max $200/Night Max $250/Night Max $300/Night Max $400/Night Max $500/Night Max $750/Night Max $1000/Night No Max/Night
Property Type
Amenities
Balcony - 78 Beach Front - 66 Big Screen TV - 40 Clothes Dryer - 88 Communal Pool - 60 DVD - 45 Dishwasher - 86 Fireplace - 3 Fitness Room - 33 Golf Resort - 2 Hot Tub - 45 Internet Access - 81 Jacuzzi - 6 Kitchen - 84 Kitchenette - 1 Mountain View - 0 Ocean View - 73 Patio - 28 Pets Considered - 6 Private Pool - 4 Refrigerator - 85 Satellite or Cable - 58 Ski In / Ski Out - 0 Ski Valet - 0 WIFI - 88 Washing Machine - 87 Water View - 68 Disinfected - 82 Enhanced Cleaning - 79 Self Check-In - 88 Any | tomekkorbak/pile-curse-small | OpenWebText2 |
Highly Evolved Sex Toys
Historically, sex toys haven’t been known for their beautiful design (unless you’re partial to jelly rubber and molded plastic genitals)—but over the past few years, that’s begun to change. One company that’s been leading the charge for sex toys that are both beautiful to look at and fun to use is Lelo, a Sweden-based operation that creates “pleasure objects” for both men and women (or, in the company’s parlance, “femme” and “homme.”).
Take, for instance, the Gigi: a slight, beautiful vibrator that looks more like something you’d find at the Apple store than at your local porn shop. Though it’s powerful enough to rev any girl’s engine, its dainty design makes it look like some innocent objet d’art—which could be why Lelo’s toys are now being stocked by Walgreens. | tomekkorbak/pile-curse-small | Pile-CC |
Further studies on deprivation/enhancement patterns.
Four studies were done to explore the construct validity of a previously established sex difference in TAT fantasy patterns. The results, both with various clinical groups and with normal children, support the notion that Deprivation/Enhancement fantasy patterns are meaningfully related to sexual identity and sex role development. The correlates of extreme D/E patterns are more clear for women than for men and involve elements of the "hysterical" character and cognitive style. | tomekkorbak/pile-curse-small | PubMed Abstracts |
Butterfly splitfin
The butterfly splitfin or butterfly goodeid, Ameca splendens, is a bony fish from the monotypic genus Ameca
of the splitfin family (Goodeidae). It was formerly found throughout the Ameca River drainage in Mexico; the type locality is Rio Teuchitlán in the vicinity of Teuchitlán, Jalisco. The species was only ever found in an area about 10 miles (15 km) in diameter.
Today, the species is rated as critically endangered by the IUCN. a remnant population has been found to persist in El Rincón waterpark near the town of Ameca. Possibly, it also exists in a feral state in the United States; individuals apparently derived from escaped or introduced captive stock were met with in southeastern Nevada. For some time, it was a popular fish among aquarists, but hobbyist stocks have declined recently, placing its survival in jeopardy.
Description
As its common name implies, it is indeed quite an attractive fish. A dominant mature male specimen a large dorsal fin which like the caudal fin is washed with black. A yellow band stretches along the caudal's back margin. The body of both sexes is ochre, with silvery sides and a brownish back, which in males usually have numerous glittering metallic scales. Females and immatures having black dots on the sides and ochre fins. The fins of males intensify in color when they are excited, and depending on their mood, they can show more or less strongly a black band along the side. For the first two weeks or so after birth, the young are entirely silvery.
Males can also be told apart from females because their anal fin's front part splits off and transforms to a blunt, flexible andropodium used for mating. As usual in live-bearers, males are the smaller sex, reaching some 3 in (7–8 cm) total length at best, with females being able to grow up to 4 in (10 cm) under good conditions.
Ecology
In its former natural habitat, the bedrock is limestone, resulting in a hard and alkaline water with a general hardness of 6-10 dGH, while the temporary (carbonate) hardness is usually between 7 and 11°. The pH is around 8, and temperature varies little between the seasons, but ranges between about 70 and 85 °F (20 and 30 °C) between day and night. The vegetation is largely limited to algae and Ceratophyllum hornworts. The remnant wild population coexists with the native blackfin goodea (Goodea atripinnis) and Lerma live-bearer (Poeciliopsis infans), as well as with the common molly (Poecilia sphenops), Oreochromis tilapias, and the bluegill (Lepomis macrochirus) which presumably have all been introduced.
Among groups of A. splendens, a loose dominance hierarchy develops, in particular in confined environments. Males chase each other about, with the dominant male(s) showing the most splendid coloration. Submissive males will try to retreat from attacks, typically towards the surface, and may shake their head as a calming signal.
Like other Goodeidae, butterfly splitfins mate by internal fertilization and spawn fully developed young. The females become sexually mature at about six months of age and can give birth every six to 10 weeks according to the water temperature and the condition of the fish. Mating is preceded by a courtship, where the males present themselves to the females with their heads pointing downwards – up to 45° from horizontal – and shake the forward part of their bodies. In that respect, they resemble the jeweled splitfin (Xenotoca variata); they do not have a ritualized "courtship dance" as some other splitfins, but the male sometimes rotates to present either flank to the female. The females respond by shaking their heads.
The fry when born can be up to 0.8 in (20 mm) in length, as the females feed the unborn young via trophotaenia which have a similar function as the umbilical cord in humans.
As a pet
The butterfly splitfin has a reputation of being a fin nipper, but being a large and robust fish, it will certainly bully small and delicate species like guppies or small tetras. When housed with less tender species that require similar conditions, it is a great fish for any tank type; even the hardier species of Apistogramma and similar dwarf cichlids make good companions, with water parameters compromising between the splitfins' and the cichlids' requirements at a point similar to most tap water.
A. splendens thrives best in clean, well-aerated water, at temperatures around 70-75 °F (20-25 °C) and neutral or slightly higher pH, with water hardness between 5 and 10 dGH composed mainly from calcium hardness. They do not tolerate overly low pH and too soft water, and are unsuitable for dedicated rainforest aquaria with low pH and almost-zero hardness (e.g. for most tetras or danionins). Butterfly splitfins are strong swimmers and social fish; they dwell in groups of three to five males and three to seven females in large tanks where they can grow to full size. In small tanks, they stay small, and fewer individuals or no other fish should be kept. Their overall effect on plant growth is beneficial as they keep down algae and clean off detritus. A. splendens breeds quite readily in the aquarium; some floating plants such as Ceratopteris or Ceratophyllum provide protection for young fry.
Aggressiveness varies with population density; at high population densities, tank decoration is highly significant in influencing behavior. At least among captive populations, butterfly splitfins become more aggressive if much decoration is placed in the tank.
Butterfly splitfins are voracious, and eat most forms of commercial fish food. They take live prey up to the size of week-old guppy fry, but need plant material, ideally green algae, to thrive. They are ideal algae eaters for tanks with small, hard-water cichlids. If not enough algae are available, vegetables such as lettuce, spinach, or green peas are recommended additions to the diet. Fry do not need "baby" food such as brine shrimp or nauplia, though as in adults, plant food increase growth and vitality.
Lighting should be strong, to encourage growth of algae; direct sunlight is ideal. In summer, they can be kept in outside tanks, basins, or small ponds in temperate and warmer areas; they can tolerate overnight air temperatures of 60 °F (15 °C) well enough, but should be protected from birds, cats, and other predators.
Many zoos and public aquariums maintain colonies of the species.
References
Sources
(2006): Ameca splendens. USGS Nonindigenous Aquatic Species Database. Gainesville, FL. Revision Date: 12/5/2003. Retrieved 2006-NOV-09.
(2006): Captive breeding promotes aggression in an endangered Mexican fish. Biological Conservation 133(2): 169–177. (HTML abstract)
(1971): Ameca splendens, a New Genus and Species of Goodeid Fish from Western Mexico, with Remarks on the Classification of the Goodeidae. Copeia 1971(1): 1-13. (HTML abstract and first page image)
[2005]: Give Ameca splendens a Try. PDF fulltext
External links
Photo of displaying males
Photo of juvenile
Category:Goodeinae
Category:Freshwater fish of Mexico
Category:Endemic fauna of Mexico
Category:Endangered biota of Mexico
Category:Fish described in 1971 | tomekkorbak/pile-curse-small | Wikipedia (en) |
714 S.W.2d 138 (1986)
Isaac James JONES, Appellant,
v.
The STATE of Texas, Appellee.
No. 01-85-0602-CR.
Court of Appeals of Texas, Houston (1st Dist.).
August 7, 1986.
*139 Herb H. Ritchie, Houston, for appellant.
John B. Holmes, Jr., Harris Cty. Dist. Atty., Kathy Giannaula, David Brothers, Harris Cty. Asst. Dist. Attys., Houston, for appellee.
Before DUGGAN, LEVY and DUNN, JJ.
OPINION
DUGGAN, Justice.
A jury found appellant guilty of aggravated robbery, found the enhancement allegation of the indictment to be true, and assessed his punishment at 40 years confinement.
Appellant's first two grounds of error urge that: (1) the evidence was insufficient to support conviction in that the State failed to prove that the complainant named in the indictment was the owner of the property; and (2) the trial court erred in overruling his motion for instructed verdict urging that the State failed to prove ownership of the property in the named complainant, a requisite element of the offense of robbery.
The indictment charged aggravated robbery by use of a firearm, and alleged ownership of property to be in Lidia Marquez as the complainant.
The undisputed evidence shows that Marquez was a full-time employee of Church's Fried Chicken at Main and Prairie Streets in downtown Houston, and that she was on duty at 8:05 p.m. on September 27, 1984, when appellant and his two companions entered the restaurant. Marquez's duties included serving chicken, preparing food, cleaning tables, and cleaning the restaurant after it closed. Marquez was behind the counter placing fried chicken in the display tray under the "hot lights" when appellant entered.
Appellant approached Marquez, asked her if she knew what he had, and showed her a pistol. She said, "Yeah, a gun," and he said, "It's a hold-up." Appellant then told Marquez to move close to the register, and she did. He told her to open the register, and the complainant tried to do so. However, she had not been trained to use the cash register, had never opened it before, and did not "have any idea how to open it." She told appellant, "I don't know how to open this. My work is just to serve the people." Appellant told her that she should know, and the complainant asked him why he didn't call the assistant manager. Appellant told her to move to the other register and attempt to open it. Appellant, who appeared nervous, had his finger "in the trigger," kept the weapon constantly pointed at the complainant's chest, and repeatedly said, "Give me the money, you bitch, or I'll kill you." One of appellant's companions asked appellant to give him the pistol so he could kill the complainant, but the appellant kept the gun. His second companion spoke up at this time to say that *140 another employee had fled out the side door to call the police. Appellant and his two companions then "took off running," out the Prairie Street exit. Carol Stubblefield, a Church's Fried Chicken employee whose duties included working the cash register during this time, was outside the restaurant emptying trash throughout the entire period of appellant's confrontation with Marquez. Another Church's employee did in fact flee outside and tell Stubblefield of the robbery. Stubblefield flagged down a passing officer, and pointed out appellant and his running companions to the officer. The officer arrested appellant in a near-by bar and recovered the pistol he observed appellant place on the floor. Appellant was returned in custody to the restaurant within minutes of his arrest, and was there identified by the complainant.
Undisputed testimony showed that Lidia Marquez did not lose any of her own personal property, and that appellant did not have "any right to any property in Church's Fried Chicken at all." Ms. Marquez acknowledged that she did not own, "in the sense of the word that it was [her] personal propertyany of the money that might have been in Church's Fried Chicken."
She testified that she had no authority to work the cash register, had no control over it, had never operated it before the robbery, and did not know how. She further testified that she had no control over the restaurant's safe or cash registers, that they were not under her care, and that she had possession of nothing in either the safe or the cash registers.
The trial court properly charged the jury on the definition of "owner" in accordance with Tex.Penal Code Ann. sec. 1.07(a)(24) (Vernon 1974), which states:
"Owner" means a person who has title to the property, possession of the property whether lawful or not, or a greater right to possession of the property than the actor.
Penal Code sec. 1.07(a)(28) defines "possession" as "actual care, custody, control or management."
As appellant and the State indicate in their respective briefs and arguments, the State introduced no evidence showing that Lidia Marquez had either title to or possession (that is, actual care, custody, control or management) of Church's cash register contents. The State relies on the third definition of "owner" in sec. 1.07(a)(24), i.e., that she had a greater right to care, custody, control or management of the property in question than the appellant.
Like other provisions of the Penal Code, this definition of "owner" must be "construed according to the fair import of [its] terms, to promote justice and effect the objects of the code." Sec. 1.05(a).
By amending sec. 1.07(a)(24) to create this third and distinct definition of ownership, the Legislature intended to expand the class of persons to be protected from theft, and to allow the State to prove ownership without having to prove actual care, custody, control or management of the property. Compton v. State, 607 S.W.2d 246, 250-51 (Tex.Crim.App.1980) (opinion on rehearing). Cert. denied, 450 U.S. 997, 101 S.Ct. 1701, 68 L.Ed.2d 197 (1981).
The evidence showed that Lidia Marquez was a full time employee of Church's, and that she was engaged in the discharge of her duties when appellant sought to compel her at gunpoint to open her corporate employer's cash register for appellant's benefit. Appellant and his companions were not employed by Church's, and he claims no legal right to ownership or possession of property in Church's cash register.
Legally, the fact that Marquez was an employee of Church's gave her a "greater right to possession" of the property than appellant. Sherlock v. State, 632 S.W.2d 604, 608 (Tex.Crim.App.1982). The jury so found factually. Applying the test of sufficiency of the evidence found in Jackson v. Virginia, 443 U.S. 307, 99 S.Ct. 2781, 61 L.Ed.2d 560 (1979), the evidence, when viewed in the light most favorable to the prosecution, was sufficient for a rational trier of fact to conclude beyond a reasonable doubt that Marquez, though without *141 fiscal or managerial responsibilities, had a greater right of possession of Church's property than appellant. See Smallwood v. State, 607 S.W.2d 911, 913-914 (Tex. Crim.App.1980) (opinion on rehearing) (department store employee, a loading dock worker, held to have greater right to possession of stolen goods than a thief).
Appellant cites Compton v. State, 607 S.W.2d 246 (Tex.Crim.App.1980) cert. denied, 450 U.S. 997, 101 S.Ct. 1701, 68 L.Ed.2d 197 (1981); Cross v. State, 590 S.W.2d 510 (Tex.Crim.App.1979); and Sowders v. State, 693 S.W.2d 448 (Tex.Crim. App.1985), as authority that some exercise of control over the property in question, even though limited, is essential for the requisite possession or ownership. We disagree. These holdings are distinguishable; Cross and Sowders involved theft by an employee with distinctions based on control, to show greater ownership in another employee. On rehearing, Compton directly supports the result here.
At the time of the robbery, Marquez was Church's only employee on hand and available for appellant to compel at gunpoint to attempt to open the register. Having forced and threatened her at gunpoint to attempt to operate the cash register, appellant ought not to be heard to complain that she had no authority to do so. We hold that she is within the statutory definition of "owner" as a person having a greater right to possession of the property than appellant.
Appellant's first two grounds of error are overruled.
Appellant alleges in his third ground of error that the trial court erred in overruling his motion to quash the indictment, which complained that the enhancement conviction lacked a jury trial waiver as required by arts. 1.13 and 1.15, of the Code of Criminal Procedure.
At the punishment phase of trial, the State introduced a penitentiary packet from Cause No. 278,077, the prior conviction alleged in the indictment for enhancement. The packet contained a judgment and sentence in that cause, the judgment reciting that the defendant had waived his right of trial by jury "in person and in writing, in open court ...," and with the consent and approval of the court and the district attorney. No written jury waiver was offered. Appellant argues that the packet's failure to include the written jury waiver renders the prior conviction unavailable for enhancement purposes because of his "motion showing that no jury waiver was executed."
Appellant acknowledges that the judgment recital of waiver of jury trial creates a presumption of regularity of documents in the trial court, unless a showing is made that no waiver was executed. Breazeale v. State, 683 S.W.2d 446 (Tex.Crim.App.1985) (opinion on rehearing). Appellant likewise concedes that he has the burden of showing that no waiver was executed. Boyd v. State, 660 S.W.2d 820 (Tex.Crim.App.1983). However, he argues that he has satisfied his burden and made a "showing" of a lack of waiver by filing his motion to quash the indictment. We disagree.
Appellant's motion to quash made the bare contention that the State did not affirmatively show an executed written waiver. Nowhere in the motion does he allege that he did not in fact sign a written waiver of his right to jury trial; neither does he offer evidence concerning the matter. Appellant's motion, simply complaining that the State has not offered proof of the waiver, is not a sufficient "showing" that a waiver was not executed.
In Ex parte Felton, 590 S.W.2d 471 (Tex. Crim.App.1979), a sufficient showing of non-waiver was held to have been made by attaching a copy of the filed jury waiver form, which indicated a blank space where the defendant's signature should have been. In Boyd v. State, 660 S.W.2d 820, 821 (Tex.Crim.App.1983), a sufficient showing of non-waiver was made concerning one of six concurrent guilty pleas by the appellant's introduction of a jury waiver form showing five cause numbers only, but excluding the sixth cause number. Because no evidence was offered by appellant, we *142 conclude that there was no showing made of the lack of jury waiver. Appellant's third ground of error is overruled.
The judgment is affirmed.
| tomekkorbak/pile-curse-small | FreeLaw |
Pakistani man allegedly raped, blackmailed by 18 roommates in Istanbul
ISTANBUL
Eighteen men of Pakistani origin were detained in Istanbul over allegedly raping another Pakistani man.
The 21-year-old victim, who was living with other 18 Pakistan-origin men in the same house in Istanbul’s Bahçelievler district, has been trying to get by through paper collecting and recycling on the streets.
Two of his roommates, who are also relatives, allegedly took nude photographs while he was taking shower back in March 2017. They then started to blackmail him with the photographs, demanding sexual intercourse with him.
After he refused to have sex with them they reportedly shared the photographs with 16 other men, while also threatening to share the pictures on social media.
The man filed a complaint about the issue with the Bakırköy Chief Prosecutor’s Office, saying he was raped at least 50 times by his roommates.
The suspects were detained by police upon his testimony.
“They threatened me with killing and beating. They raped me one by one,” he said.
The Prosecutor’s Office is demanding 12 years in jail for nine suspects on charges of “sexual assault” and up to one year in jail for seven other suspects on charges of “actual bodily harm.” Up to five years in jail are also for all suspects on charges of “coercion.” | tomekkorbak/pile-curse-small | OpenWebText2 |
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