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[ "Although I am not a Debian Developer; much less a member of the Debian CTTE, I must support this request.", "\n\nBear with me, this will be a bit of a long email; I am not known for my brevity. ", "Also, apologies if my formatting drives some of your mail viewing programs insane (sorry!).", "\n\nIn the time that I have been watching the debate over systemd, Upstart, and OpenRC, I have noticed several odd events that do not square with my understanding of Debian. ", "As I read the Debian Social Contract (https://www.debian.org/social_contract), Debian Maintainer Guidelines (https://www.debian.org/doc/manuals/maint-guide/), and the Debian Free Software Guidelines (https://www.debian.org/social_contract#guidelines), I am given the impression of a clear hierarchy of software to be selected for use in the Default Debian Distribution. ", "While Debian does recognize, and as an extension support, the right of the downstream user to access and utilize proprietary or non-free software, the Debian Guidelines seem to set the example that only completely free software will be considered for inclusion and distribution as default.", "\n\nSoftware that complies with free-software terms in license, but that might include a non-free or restrictive component, is almost never even considered as a default. ", "One of the examples I have heard over the years concerns the selection of Gnome over KDE as the KDE/QT software is covered by what is currently the Digia enforced Contributors License Agreement. ", "Although KDE might be free software, the CLA was enough to discount the use of KDE as a default option. ", "However KDE is still packaged and made available, just not as a default. ", "If I have the circumstances wrong for this scenario, I apologize.", "\n\nAnother, more direct case-in-point, example that I am aware of since I was participating in Debian through Mepis and Mepisguides at the time; was the difficulties over packaging and distribution the Mozilla art packages for FireFox. ", "It was decided by Debian to fork the Mozilla developed packages and issue new versions with non-restrictive artwork. ", "As, at the time, there were no other mature open-source web-browsing engines available for Debian to back, (e.g. KHTML's fork into Webkit was still largely controlled by Apple); so the decision to fork the Mozilla packages was deemed a necessary step to offer users a fully mature Open-Source browsing experience; albeit with new artwork.", "\n\nIt is such with this type of history in positions on software license that I look at the Upstart software package(s). ", "The software, while licensed under FOSS terms, is modified with one of the most restrictive CLA's I have ever born witness to. ", "I have witnessed commentary from developers with far more understanding of open-source concepts than I perhaps will ever have an understanding of... state outright that they decided to work on a different software package solely because of that restrictive CLA. ", "Case in point, the CLA that covers KDE/QT is used not just as a method of freely re-licensing open-source code contributions under a proprietary license; but also is the legal trigger that will force the QT software packages to be freely re-licensed under a permissive-BSD license should the LGPL version cease receiving updates. ", "Given that the Upstart CLA lacks even such a basic trigger point, I find it difficult to conceive... exactly... how the Upstart package(s) were even up for consideration by Debian to begin with. ", "There were, at the time of the initial calls for decisions on the next init system, at least 3 different fully FOSS compliant options available to Debian: systemd, OpenRC, and the current SysVinit. ", "Apologies if I got any formatting wrong.", "\n\nGiven the standards and precedent set by Debian; Upstart should have never even been up for discussion.", "\n\nWhich is pretty much where I turn my attention specifically to Ian Jackson. ", "While trying to research the history of the discussion on the Init system I came across a very ugly post from Mr. Jackson directly attacking the systemd software; including language condemning how the systemd package(s) had spread in scope to cover a wide variety of Operating-System level tasks. ", "I also came across a very polite message from Mr. Bdale Garbee stating he saw no particular reason to have that kind of language in a TC resolution. ", "Speaking for myself, I was left choking. ", "At the time I believe Ian Jackson was under the employ of Canonical... which had... to date... flat out insulted every single X.org and Wayland developer. ", "This was a company where the founder / benevolent dictator for life had flat out lied on matters relating to Wayland, flat out lied on matters relating to KDE, nearly caused legal action from KDE e.v., ", "and has to date refused to publish any reaction or apology. ", "I could only describe the email from Ian Jackson as \"Hyper-Hypocritical\" for the sheer audacity that such a stunt took.", "\n\nAs best as I could determine Ian Jackson's solution to the CLA on Upstart was to simply \"Fork the Code,\" as this was a method that Debian had already implemented with other semi-restrictive projects like the aforementioned Mozilla packages. ", "I went off on this in a few G+ posts, but since they weren't in my own feed I'll just repeat the synopsis. ", "As best as I could understand at the time of the Mozilla incident, that decision to fork and not focus on another web-browsing-system for the default was driven not just by the lack of available comparative engines with acceptable licensing, but the lack of available development power. ", "Debian simply didn't have the resources to fully back their own web-browsing-system. ", "The long term effect is that in all of the the time that the Mozilla forks have been active, Debian has yet to substantially contribute to the forwards development of the Mozilla projects. ", "As best as I can determine the most Debian has done is send bug-fixes back upstream. ", "That's it. ", "There's been no major functionality or feature development within Debian on the Mozilla projects. ", "In practice each Mozilla fork is almost entirely reliant upon the Mozilla foundation to do all the development work first.", "\n\nIn the same way, ignoring the CLA on the Upstart package(s) for a moment, the Debian(developers) who have the ability and resources to code an Init system are either already contributing to systemd and OpenRC; or alternatively maintaining SysVInit. ", "In a practical sense Debian would be entirely reliant on Canonical to drive development of the Upstart package(s). ", "Speaking for myself I am having a hard-time accepting the idea that a Debian(downstream) that has actively burnt development bridges and open-source relationships is going to go from a \"Hostile-Downstream\" to a \"Benevolent Upstream\" for a single set of package(s).", "\n\nAs the discussions wore on... I continued to see further emails from Ian Jackson that were, from all outside aspects, designed specifically to hamper the voting process. ", "It got to the point that on as the last voting began I flagged Ian's personal email with a G+ posting of my own: https://plus.google.com/u/0/+MartinGr%C3%A4%C3%9Flin/posts/KAPGX3pHR2H\n\nLooking at Ian's history in relation to the Init system discussion the only conclusion I could draw is that the person was deliberately pushing an anti-DFSG agenda. ", "Indeed, Ian Jackson appeared to work for Canonical for a significant length of time. ", "Given that reputation that company carries in terms of open-source development, at semi-outlined above, I was not too entirely surprised on Ian Jackson's positioning. ", "However, it appears that Ian Jackson is now employed by Citrix. ", "I'm left stymied then as to why Ian Jackson is still trying to push for Upstart in Debian.", "\n\nLooking over the mailing list to date there has been a very clear consensus from the non-Canonical downstreams that they don't want Upstart. ", "Case in point, a very nice Representative from Spotify decided to send a message on the subject. ", "Tanglu, which is expected to offer Debian the type of fast-release rolling distribution with a focus on contributing changes back upstream that Canonical promised and has never delivered on, is already pushing systemd... today. ", "Not tomorrow. ", "Not some future time. ", "NOW.", "\n\nGiven what Debian is supposed to stand for by the Social Contract and Free Software Guidelines, and given the overwhelming downstream response for Debian to adopt a fully FOSS solution and not a quasi-FOSS solution; I am left with no other conclusion other than that Ian Jackson is currently acting in violation of the Social Contract and the DFSG.", "\n\nI think it is in the best interests of the Debian Developers to remove Ian Jackson; not just from the Technical Committee, but revoke his entire commit access. ", "Granted, that's just my opinion, so it really doesn't count for much.", "\n\nI do hope that whoever took the time to actually read this letter all the way through understands what I'm trying to get at. ", "I really don't care if Debian chooses systemd or OpenRC. ", "Personally, I think it would be in Debian's best interests to accept systemd now, then modify the non-init portions of systemd to work with OpenRC... and then pour as much resources as possible into making OpenRC a first-class init system that developers will still be happy to use 25 years from now.", "\n\nWhat I do care about is Debian making the stand for Free-Software that the Debian Developers have a reputation of making.", "\n\n--\n\nJason Frothingham.", "\n\nhttp://www.linux-guides.com\n\nhttp://http://forum.mepiscommunity.org/\n\nhttp://www.mepis.org\n\nhttp://www.gamenikkiinexile.com\n\nhttp://gplus.to/JeSaist" ]

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[ "SINGAPORE — A man had sex with his girlfriend in the presence of his four-year-old niece and then sexually assaulted the latter, a court heard.", "\n\nAfterwards, the 20-year-old perpetrator lied to his mother that the victim had touched him inappropriately and that another person had taught the victim to do so.", "\n\nAt the High Court on Wednesday, the culprit, who is now 21, was sentenced to 10 years’ jail along with 12 strokes of the cane. ", "He pleaded guilty to one charge of aggravated sexual assault by penetration.", "\n\nA total of 15 other counts, including another charge of aggravated sexual assault against the same victim, were considered in sentencing. ", "The perpetrator cannot be named to protect the victim’s identity.", "\n\nAssaulted victim in toilet\n\nThe victim lived in a flat with her two younger siblings, her parents and four housemates who were her parents’ friends. ", "In June last year, the victim’s parents were arrested separately and jailed for unrelated crimes, leaving their three children in the care of the four housemates.", "\n\nThe following month, the victim kept asking to see the culprit whom she addressed as “Baba” (a colloquial term for father) as she missed him. ", "Two housemates brought the victim and her siblings to visit their grandmother’s flat where various relatives lived, including the culprit and his then-girlfriend.", "\n\nAt the end of the day, as the victim did not want to leave the culprit, the housemates decided to let her stay for a week there. ", "At the time, the culprit worked as a cook at fast-food chain KFC.", "\n\nOne day, the culprit’s girlfriend brought the victim into the toilet so that they could take a shower at the same time. ", "The culprit wanted to have sex with his girlfriend and knocked on the toilet door, saying he needed to use the toilet.", "\n\nAfter using the toilet, the culprit asked his girlfriend to perform oral sex on him and she obliged. ", "The couple then had sex in front of the victim as she played with water.", "\n\nAfterwards, the girlfriend continued to wash herself and the victim up. ", "The culprit also took a shower. ", "When he thought that his girlfriend was distracted with washing her hair, he pulled the victim towards him and told her to perform oral sex on him.", "\n\nThe girlfriend heard what the culprit said and turned around to see the sexual assault. ", "She told him to stop and he complied.", "\n\nLied about assault\n\nAfter they left the toilet, the culprit called his mother who was at work. ", "He lied that the victim had touched his private parts while in the shower. ", "He also lied that when he asked the victim, she said it was another person in the flat who had taught her how to perform oral sex.", "\n\nOn the final day of the victim’s stay at her grandmother’s place, her relatives had a family outing. ", "During the outing, the culprit told the adults present that the victim had touched him inappropriately during the week. ", "He repeated his claim that the victim pointed to another person as having taught her how to perform oral sex.", "\n\nOn 3 August last year, the culprit’s mother reached out to the victim’s case worker from Big Love Child Protection Specialist Centre and confided in the latter about her concern for her grandchildren, given what the culprit had told her. ", "The social worker visited the victim the same day and learnt the truth.", "\n\nA police report was made by the victim’s housemate and caretaker the same day. ", "Investigations revealed that on another occasion in July last year, the culprit also made the victim perform oral sex on him in the living room of his mother’s flat.", "\n\nEgregious abuse of trust\n\nDeputy Public Prosecutors Mohamed Faizal and Sarah Siaw asked for 10 years’ jail with 12 strokes of the cane - the sentence that was meted out by the court. ", "The victim was “far too young to even fully grasp the degrading and heinous nature of the acts being committed against her, to protest against the abuse, or to report it to another adult”, they said.", "\n\nThe victim had stayed over at the culprit’s home as she missed him and wanted to spend time with him, the prosecutors noted. ", "But “he had no qualms about corrupting the victim and destroying her innocence for his own vile pleasure”, they said. “", "Instead of protecting and taking care of his niece, as any other uncle would, the accused ... preyed upon her to fulfil his sordid sexual desires and (twice) made her perform fellatio on him.”" ]

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[ "[Papillary fibroelastoma: retrospective analysis. ", "Clinical presentation and surgical results].", "\nPapillary ibroelastomas are small benign intracardiac tumors known for their embolic potential. ", "Since the introduction of echocardiography with improved resolution and transesophageal imaging techniques, they are being increasingly detected in clinical practice. ", "In recent series, papillary fibroelastoma is considered the most frequent benign tumor of the heart. ", "Our objective was to analyze characteristics and midterm surgical outcome of histologically-confirmed cases of papillary fibroelastoma. ", "We conducted a retrospective study on patients with cardiac tumors submitted to surgical excision between June 1992 and February 2017. ", "Out of 108 patients, 18 had papillary fibroelastomas. ", "Their mean age was 58 years (22-77); 10 were men. ", "The most frequent localizations were the aortic valve (7) and the mitral valve (5). ", "None had significant valvular dysfunction. ", "By transesophageal echocardiography, the tumor size (larger diameter) was 13.33 ± 5.55 mm (6.6-28.0). ", "Two patients, both with tumor in the aortic valve, had suffered a stroke; other two had dyspnoea and atrial flutter, respectively. ", "The remaining 14 patients were asymptomatic and their tumors were incidental findings. ", "In 15 patients the valve was preserved. ", "There was neither surgical mortality nor recurrence after 2.6 years of follow-up. ", "In conclusion, most papillary fibroelastomas can be surgically removed with valve preservation and favorable clinical outcome. ", "However, until the results of randomized trials support the decision, an aggressive surgical approach in asymptomatic patients needs to be defined in the context of surgical expertise." ]

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[ "TOYOTA GAZOO Racing revealed today the updated TS050 HYBRID race car which will carry its hopes in the 2017 FIA World Endurance Championship (WEC).", "\n\nMonza in northern Italy hosted the first public appearance of the new car, presented alongside team management and the drivers of the three TS050 HYBRIDs which will compete this season.", "\n\nMike Conway, Kamui Kobayashi and José María López race the #7 for the full season, alongside Sébastien Buemi, Anthony Davidson and Kazuki Nakajima in the #8. ", "Stéphane Sarrazin is joined by Yuji Kunimoto and Nicolas Lapierre in the #9 at Spa-Francorchamps and Le Mans.", "\n\nThe team has a clear target to earn its first Le Mans victory following an extraordinary near miss in 2016. ", "That requires a combined effort at its technical centres in Higashi-Fuji and Cologne, with upgrades in every area of the TS050 HYBRID.", "\n\nThe 2017 car features a 2.4litre V6 turbo-charged petrol engine combined with 8MJ hybrid system. ", "Significant effort at Higashi-Fuji sees the introduction of a new engine, optimising thermal efficiency by increasing the compression ratio via development of the combustion chamber, cylinder block and cylinder head.", "\n\nThe hybrid system too has been optimised. ", "Motor generator units (MGU) have been reduced in size and weight while the high-powered lithium-ion battery has been developed further. ", "Those advancements in hybrid technology will directly benefit TOYOTA customers on the road, combining with the knowledge gained by powertrain engineers to create ever-better cars in the future.", "\n\nTo complete a wide-ranging update for the new season, engineers in Cologne have optimised virtually all areas of the TS050 HYBRID chassis, working as one team with colleagues from Higashi-Fuji.", "\n\nWEC regulations for 2017 target a reduction in aerodynamic efficiency, to increase the Le Mans lap time by several seconds for safety reasons. ", "This is achieved by raising the front splitter by 15mm in combination with a narrower rear diffuser.", "\n\nUsing tools such as computational fluid dynamics and wind tunnels, TOYOTA GAZOO Racing has modified its aerodynamic concept to meet this challenge; a raised nose and sharp undercut to the sidepods are the most noticeable modifications.", "\n\nAccording to new regulations, teams are limited to two aerodynamic configurations per season, reduced from three in 2016, with the low-downforce TS050 HYBRID launched today. ", "Tyre usage is also restricted, with each car limited to four sets, plus two spare tyres, for qualifying and six-hour races. ", "The team has worked with Michelin to meet this challenge, including new compounds and constructions, as well as optimising the suspension geometry to limit wear.", "\n\nOther rule changes are designed to enhance safety. ", "Side mirrors now need to pass a wider visibility field test while hybrid cars must display lights to indicate normal powertrain behaviour. ", "If the green safety light is not illuminated during a race, a car will be forced to pit for repairs.", "\n\nThe 2017-specification TS050 HYBRID has already recorded over 30,000km in testing this year, comprising five tests, at Paul Ricard, Motorland Aragon and Portimao, and including four 30-hour endurance tests.", "\n\nWith an updated car and a driver line-up including former World Champions and multiple WEC race winners, TOYOTA GAZOO Racing heads to the season opener on 16 April at Silverstone with great determination, but expecting a close and exciting nine-race LMP1 battle with Porsche." ]

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[ "\nDJI’s newest 4K folding drone costs $799 - gpetukhov\nhttps://www.theverge.com/2018/1/23/16922928/dji-mavic-air-drone-price-specs-release\n======\ntotalZero\nI would rather see a redesigned Mavic Pro with a larger camera sensor. ", "There\nis a blank space between the portability of the Mavic Pro and the video\nquality available in the Phantom 4 form factor.", "\n\n~~~\nheadShrinker\nI agree with you but I see how DJI is trying to maneuver. ", "My guess is their\ngoal is not to aim at serious hobbyists rather they want casual upper class\ntech gadget collectors like the Bose, Apple, Nikon non-pro with a $2k+ dslr\ncustomer. ", "People with tons of money and scoping for the next hot tech trinket\n799 is a pretty great price point for the package. ", "No good for me because I\ndon’t like Chinese corporations and prefer to make and mod my own quads.", "\n\n------\ntheodorewiles\nWow so this is basically just an ad? ", "Am I missing something?", "\n\n" ]

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[ "John Feeney\n\nJohn Feeney may refer to:\nJohn Feeney (filmmaker) (1922–2006), New Zealand director of documentary films\nJohn Feeney (newspaper proprietor) (1839–1905), newspaper proprietor and philanthropist of Birmingham\nJohn Frederick Feeney (1807–1869), newspaper proprietor and father of above\nJohn Feeney (tenor) (1903–1967), Irish tenor\nJohn Feeney (boxer), (born 1958), British boxer, national bantamweight champion 1981–1983, 1983–1985\nJohn Feeney (Mythical Figure)" ]

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[ "Arrangements for Children & Social Services\n\nInvolvement with Social Services\n\nOur experienced team will advise and represent parents, other family members, children and children’s guardians in all public law proceedings. ", "We can also advise and assist where children are voluntarily accommodated and will attend child protection conferences and we often play a key role in advising parents involved in disagreements with social services, whether before or during court proceedings. ", "We have experience in complicated and serious cases involving allegations of non-accidental injury, sexual abuse and factitious illness. ", "Our team includes members of the Law Society Children’s Panel who act for children independently of their court appointed guardians. ", "We are able to provide clear and practical advice to guide you and to provide advocacy at all levels of court to ensure continuity though a difficult process.", "\n\nArrangements for the Children\n\nWhen a couple separate, agreeing the arrangements for how their children are going to be cared for can be challenging and sometimes difficult. ", "In any dispute involving children, our aim is to find a solution which puts their interests first. ", "We offer a supportive, friendly and highly experienced service.", "\n\nFollowing a relationship breakdown we can help you to make arrangements for your children including where the children will reside and when they will see the absent parent. ", "We will assist you to focus on reaching an agreement wherever possible and guiding you towards solutions involving mediation or collaborative law. ", "If that is impossible we provide a vigorous and focused representation in court.", "\n\nOur team of solicitors are experienced family law advocates, often enabling us to represent you in court with the same lawyer who has advised you throughout the case.", "\n\nSpecial Guardianship Orders\n\nWhere a child is being cared for in another family but adoption is not appropriate, we can advise and assist about Special Guardianship Orders and the support packages available from local authorities.", "\n\nWe can assist in negotiating with the biological parents or the local authority and guide you through the process and represent you in court if it becomes necessary. ", "In some cases we can provide publicly funded advice (Legal Aid) depending on the type of case and your financial circumstances." ]

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[ "/**\n * @license\n * Copyright (C) 2018 The Android Open Source Project\n *\n * Licensed under the Apache License, Version 2.0 (the \"License\");\n * you may not use this file except in compliance with the License.", "\n * You may obtain a copy of the License at\n *\n * http://www.apache.org/licenses/LICENSE-2.0\n *\n * Unless required by applicable law or agreed to in writing, software\n * distributed under the License is distributed on an \"AS IS\" BASIS,\n * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.", "\n * See the License for the specific language governing permissions and\n * limitations under the License.", "\n */\n\nimport '../../../styles/shared-styles';\nimport '../../shared/gr-rest-api-interface/gr-rest-api-interface';\nimport {flush} from '@polymer/polymer/lib/legacy/polymer.dom';\nimport {GestureEventListeners} from '@polymer/polymer/lib/mixins/gesture-event-listeners';\nimport {LegacyElementMixin} from '@polymer/polymer/lib/legacy/legacy-element-mixin';\nimport {PolymerElement} from '@polymer/polymer/polymer-element';\nimport {htmlTemplate} from './gr-repo-dashboards_html';\nimport {GerritNav} from '../../core/gr-navigation/gr-navigation';\nimport {customElement, property} from '@polymer/decorators';\nimport {RestApiService} from '../../../services/services/gr-rest-api/gr-rest-api';\nimport {RepoName, DashboardId, DashboardInfo} from '../../../types/common';\nimport {ErrorCallback} from '../../../services/services/gr-rest-api/gr-rest-api';\n\ninterface DashboardRef {\n section: string;\n dashboards: DashboardInfo[];\n}\n\nexport interface GrRepoDashboards {\n $: {\n restAPI: RestApiService & Element;\n };\n}\n@customElement('gr-repo-dashboards')\nexport class GrRepoDashboards extends GestureEventListeners(\n LegacyElementMixin(PolymerElement)\n) {\n static get template() {\n return htmlTemplate;\n }\n\n @property({type: String, observer: '_repoChanged'})\n repo?: ", "RepoName;\n\n @property({type: Boolean})\n _loading = true;\n\n @property({type: Array})\n _dashboards?: ", "DashboardRef[];\n\n _repoChanged(repo?: ", "RepoName) {\n this._loading = true;\n if (!", "repo) {\n return Promise.resolve();\n }\n\n const errFn: ErrorCallback = response => {\n this.dispatchEvent(\n new CustomEvent('page-error', {\n detail: {response},\n composed: true,\n bubbles: true,\n })\n );\n };\n\n return this.$.restAPI\n .getRepoDashboards(repo, errFn)\n .then((res?: ", "DashboardInfo[]) => {\n if (!", "res) {\n return;\n }\n\n // Group by ref and sort by id.\n const dashboards = res.concat\n .apply([], res)\n .sort((a, b) => (a.id < b.id ? ", "-1 : 1));\n const dashboardsByRef: Record<string, DashboardInfo[]> = {};\n dashboards.forEach(d => {\n if (!", "dashboardsByRef[d.ref]) {\n dashboardsByRef[d.ref] = [];\n }\n dashboardsByRef[d.ref].push(d);\n });\n\n const dashboardBuilder: DashboardRef[] = [];\n Object.keys(dashboardsByRef)\n .sort()\n .forEach(ref => {\n dashboardBuilder.push({\n section: ref,\n dashboards: dashboardsByRef[ref],\n });\n });\n\n this._dashboards = dashboardBuilder;\n this._loading = false;\n flush();\n });\n }\n\n _getUrl(project: RepoName, id: DashboardId) {\n if (!", "project || !", "id) {\n return '';\n }\n\n return GerritNav.getUrlForRepoDashboard(project, id);\n }\n\n _computeLoadingClass(loading: boolean) {\n return loading ? '", "loading' : '';\n }\n\n _computeInheritedFrom(project: RepoName, definingProject: RepoName) {\n return project === definingProject ? '' : ", "definingProject;\n }\n\n _computeIsDefault(isDefault: boolean) {\n return isDefault ? '", "✓' : '';\n }\n}\n\ndeclare global {\n interface HTMLElementTagNameMap {\n 'gr-repo-dashboards': GrRepoDashboards;\n }\n}\n" ]

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[ "Saturday, July 2, 2011\n\nABOUT EPISCOPAL PAJEROS\n\nFor the moment public attention has shifted from the RH Bill and the proposed Divorce Bill. ", "Media attention is now on allegations made by the Philippine Charity Sweepstake that the previous administration had authorized the gift of Pajeros to various church leaders. ", "Issues of constitutionality have been raised as well as allegations of bribery to buy the support of church leaders for the past administration. ", "What might be the problem? ", "I will stay away from political allegations and make observations only about possible constitutional issues.", "Already the provision that has been cited is Article VI, Section 29(2) which says: “No public money or property shall be appropriated, applied, paid, or employed, directly or indirectly, for the use, benefit, or support of any sect, church, denomination, sectarian institution, or system of religion, or of any priest, preacher, minister, other religious teacher, or dignitary as such, except when such priest, preacher, minister, or dignitary is assigned to the armed forces, or to any penal institution, or government orphanage or leprosarium.” ", "Another pertinent provision would be Article III, Section 5 which says “No law shall be made respecting an establishment of religion . . .” ", "which is frequently cited as commanding separation of church and state. ", "On the basis of these provisions the general question has been asked whether the use of public money may be authorized at all in a manner that might benefit religious persons or institutions. ", "It is not a question that is easily answered by either a Yes or No. ", "The answer that jurisprudence has given to the question is “It depends.” ", "It depends on what? ", "It depends on the purpose and uses of the gift.", "The example that immediately comes to mind is the early case of Aglipay vs Ruiz where the constitutionality of the use of government funds for the issuance of postage stamps commemorating the 33rd International Eucharistic Congress of the Catholic Church was challenged. ", "In upholding the validity of the government action Justice Laurel wrote that “while the issuance and sale of the stamps in question might be said to be inseparably linked with an event of a religious character, the resulting propaganda, if any, received by the Roman Catholic Church, was not the aim and purpose of the Government.” ", "He said that whatever benefit might have redounded to the Church was merely incidental to a legitimate government purpose.", "Of a similar nature was the more recent expropriation of the birthplace of Felix Y. Manalo, the founder of the Iglesa ni Kristo, for the purpose of preserving it as a historical landmark. ", "It was justified by saying that whatever benefit the Iglesia ni Kristo might reap from it was merely incidental to the public historical purpose.", "Not knowing for what purpose the bishops were gifted with Pajeros, if indeed they were, I cannot say whether the gifts were constitutionally justifiable or not. ", "But if indeed there were such gifts and we want to find out whether they were constitutionally proper or not, are there jurisprudential norms which can be used for the purpose? ", "There are; but I do not think we can find them in the Aglipay case or the Manalo case. ", "I would use the norms found in decisions involving government aid to religious schools.", "In essence, these decisions prescribe a three-part test for determining constitutionality. ", "First, does the grant of aid have a primary “secular legislative purpose”? ", "Second, will the aid have principal effects which neither advance nor inhibit religion? ", "Third, will the aid foster \"an excessive government entanglement with religion.\" ", "How can we determine if the donation of Pajeros can pass these three-part tests? ", "We can only determine these by looking at the terms of the donation. ", "We can find these from the records of the PCSO. ", "The records will show whether the donations were for a secular purpose and whether they limited the uses to those which do not have the principal effect of advancing or inhibiting religion, and whether the needed supervision, if any, could involve excessive government entanglement with religion.", "If indeed the Pajeros were given primarily for a legitimate secular purpose, such for instance as relieving poverty or promoting health, we may have to look at the suitability of the Pajeros for the declared purpose. ", "Next the people would want to know to what extent the gifts have actually been used for the declared purpose or if they have been used for other undeclared purposes such as advancing religion. ", "And if the government attempts to verify what they are being used for, would there arise a degree of undesirable entanglement of government with religion? ", "All told, it would seem to me that if Congress decides to conduct investigations “in aid of legislation,” as both the Senate and the House seem to be poised to do, things can turn out to be a very messy entanglement of state and religion. ", "I can see that Church authorities will have to think very carefully how to handle the PCSO revelations. ", "But I am not sure that the CBCP can command the bishops concerned what to do. ", "Bishops answer directly to the Pope.4 July 2011" ]

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[ "PMM2-CDG: phenotype and genotype in four affected family members.", "\nCongenital disorders of glycosylation (CDG) are genetic defects in protein and lipid glycosylation. ", "PMM2-CDG is the most prevalent protein N-glycosylation disorder with more than 700 reported patients. ", "Here we report on a large Italian family with four affected members and three mutations. ", "Two young sisters are compound heterozygous for mutations p.Leu32Arg and p.Arg141His, while two paternal great-aunts are compound heterozygosity for p.Leu32Arg and p.Thr237Met. ", "The latter association has not been reported before. ", "The most severely affected member had in addition an ALG6 mutation known to exacerbate the phenotype of patients with PMM2-CDG." ]

{ "pile_set_name": "PubMed Abstracts" }

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[ "This invention relates generally to a non-impact printing apparatus and method and more particularly to an apparatus and method in which the printing fluid is ejected from a nozzle, by volume displacement.", "\nHistorically printing has been done by applying ink to a specially configured key or carrier and mechanically impacting the key or carrier on a recording medium such as paper to form an impression of the carrier. ", "More recently, non-impact printing devices have been developed, where intelligence patterns (alphanumeric characters, graphical displays, etc.) ", "are deposited on a recording medium. ", "Non-impact printing devices utilize a variety of methods of forming the intelligence patterns, including chemically active and chemically inert processes, using either fluids or solids as the marking or printing medium, and requiring either specially treated recording media or untreated recording media.", "\nIt has been known to print by depositing discrete droplets of printing fluid on a recording medium in a predetermined pattern. ", "Previous attempts to achieve such a method of printing utilize a continuous stream of fluid which separates into droplets which are charged and electrostatically deflected so that they form the desired pattern on the recording medium. ", "Such methods produce acceptable resolution only when the charge per unit mass is accurately controlled for each droplet. ", "Two basic variations have been developed; the droplets are either given equal charge per unit mass and then deflected by an electrostatic field whose intensity is controlled by the input signal, or the droplets are given a charge per unit mass according to the input signal and then deflected using a constant electrostatic field. ", "Existing embodiments of both of these methods require that the fluid droplets be uniform, which has proven difficult to achieve. ", "Once the stream of uniform droplets has been attained, it is usually necessary to provide voltages in the range of 2,000 to 10,000 volts for the electrostatic field. ", "Such voltages are difficult and expensive to produce and control. ", "Further, the process of charging the droplets themselves sometimes causes electrolysis of the printing fluid, producing corrosive by-products which may cause electrode deterioration.", "\nIn an effort to obtain droplets of uniform size, two basic methods have been developed in the prior art. ", "First, the printing fluid is delivered to a nozzle at sufficient pressure to assure that a continuous jet of fluid issues from the nozzle. ", "The jet stream is separated into droplets by using radial oscillations or vibrations induced in the nozzle itself by means of magnetostrictive drivers or piezoelectric crystals. ", "The vibrations cause regularly spaced varicosities in the ink stream, aiding the natural tendency of the stream to separate into droplets, and making the ensuing droplets more uniform than would otherwise occur.", "\nIn another embodiment of the droplet formation process, the printing fluid is delivered to the nozzle under sufficient pressure to form a meniscus at the nozzle but not high enough to produce flow through the nozzle. ", "In this method, the fluid is drawn from the nozzle electrostatically in a ray-like jet which is then deflected electrostatically as desired. ", "The electrostatic field which draws the jet of fluid from the nozzle is constant, producing a continual stream of printing fluid. ", "The stream breaks into a succession of droplets with essentially uniform mass and charge. ", "A time-varying electrostatic field controlled by an input signal is then used to deflect the droplets as required for the formation of alphanumeric characters. ", "The foregoing printing processes and mechanisms make use of a continuous flow of printing fluid, with the flow to be diverted to a reject basin or collector whenever no characters or patterns are to be printed. ", "This results in a more complicated system for handling the flow of printing fluid than would otherwise be required.", "\nIn another type of device, piezoelectric transducers are employed to create shock waves in a horn-shaped nozzle. ", "As the waves travel down along the nozzle from the large end to the small end, their intensity increases. ", "The additive effect of high intensity shock waves at resonance serve to eject fluid from the end of the nozzle towards and onto an associated printing medium.", "\nOther devices have been developed to expand and contract a crystal by electrical pulses tuned to a resonant frequency so that one droplet is ejected for each expansion or contraction of the crystals. ", "However, these devices do not operate asynchronously. ", "That is, a droplet is not produced only upon demand but rather continuously while operating at resonant frequency; thus any given droplet is dependent on previous pulses transmitted through the fluid.", "\nOur prior application Ser. ", "No. ", "50,445, filed June 29, 1970, now U.S. Pat. ", "No. ", "3,946,398, is an asynchronous device of the same general character as the present device. ", "In specific embodiments, however, the present invention shows an electromechanical transducer of a single electrically deformable plate, whereas the specific crystal in our prior application was a plate of two bonded crystals." ]

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[ "Two different classes of therapy-related and de-novo acute myeloid leukemia?", "\nTwo different classes of therapy-related acute myeloid leukemia (t-AML) seem to emerge. ", "One class follows therapy with alkylating agents, increases in frequency with age, often presents with myelodysplasia (MDS), responds poorly to chemotherapy, and shows monosomy 7(-7), monosomy 5(-5), or loss of various parts of the long arms of these chromosomes (5q- and 7q-). ", "The other class is related to therapy with cytostatic drugs targeting at DNA-topoisomerase II, often presents with overt leukemia, responds more favorably to chemotherapy, and shows balanced chromosome aberrations, primarily translocations involving chromosome bands 11q23 and 21q22. ", "These two classes of t-AML may have their counterparts in de-novo acute myeloid leukemia (de-novo AML)." ]

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[ "Hang on for a minute...we're trying to find some more stories you might like.", "\n\nEmail This Story\n\nSend email to this addressEnter Your NameAdd a comment hereVerification\n\nI’m happy to be a Sacramento State student. ", "It’s true.", "\n\nI’ve lived in Sacramento since my freshman year of high school, and have always liked the city. ", "I love trees, I like my major and I think I’m where I’m supposed to be; a truly comforting feeling.", "\n\nBut the absolute best thing about being a Sac State student is that our mascot is a muscle-jacked bee who runs around looking like a living meme. ", "And there are plenty of thicc memes about Herky to be had.", "\n\nAnd while Herky, full name Hercules, is great as he is, there is always room for improvement. ", "I think his current thiccness is ideal; any more might prove dangerous.", "\n\nI just think that there needs to be a little more creativity in Herky’s wardrobe department. ", "I even have some specific ideas.", "\n\nThe jerseys. ", "The muscle tees. ", "The tight athletic pants. ", "I thought that was all Herky had in him until last year, when I saw him debut both a suit and army fatigues. ", "This opened up my mind to all of the possibilities.", "\n\nNow? ", "I can’t quit thinking of potential Herky outfits. ", "I wish he was a doll an action figure and I knew how to make tiny clothes; I’d construct them all. ", "My initial list of ideas for this article was in the high teens after only 30 minutes of thought.", "\n\nFortunately for you I’ve narrowed it down, and with apologies to such notable ideas as Bedtime Bee, Seasonal Holiday Herky (Halloween, Thanksgiving, Christmas, etc.) ", "and Tan Suit Obama, here are my very real and serious suggestions for the outfits Herky should don sometime this year.", "\n\nPresident Nelsen:\n\nSac State President Robert Nelsen has a very specific look. ", "While I don’t know how we can make Herky look bald, I do know we can give him a goatee, a nice suit and some wicked cowboy boots. ", "This is an easily executable idea, but the key is the delivery.", "\n\nIt has to be a surprise.", "\n\nImagine it: Nelsen arrives at some random event. ", "He seemingly goes to a million every week. ", "He, of course, immediately sees that Herky isn’t there yet and asks where he is. ", "Someone reassures him that Herky is on the way, just running late because of a wardrobe issue.", "\n\nThe issue is that Herky was waiting for the right moment before he busts open the doors and stunts on everyone, taking extra high steps to make sure everyone sees his boots. ", "Then he walks straight up to Nelsen and does a direct comparison.", "\n\nThe pictures and videos would all be golden.", "\n\nQueen Bey:\n\nThis one is obvious. ", "Herky’s image, in my mind, does not need to be wrapped up in masculinity. ", "Women have outnumbered men at Sac State for years, and it’s time to get some representation.", "\n\nThe easiest, most satisfying choice is the most powerful woman in the world: Beyonce.", "\n\nThere are almost too many angles to take here. ", "Queen Bee? ", "Bee-yonce? ", "The Bey-Hive? ", "I am honestly shocked Herky hasn’t already done this and I need it ASAP.", "\n\nGo get a Herky that can dance, pick your favorite Beyonce outfit and hairdo, and reap the publicity rewards. ", "This is perfect for a football game, where plenty of students will be ready to pull out their phones and hit record as Herky and her crew (Dance team? ", "Cheerleaders?) ", "run the world.", "\n\nVarious Meme Ideas:\n\nI had too many meme ideas to do them separately. ", "Not sorry. ", "We’ll go in order of importance.", "\n\nGuy Fieri: The father of all memes. ", "A wholesome, trash food king who attended American River College (so did I). ", "Not only is Guy Fieri a lifestyle icon, he’s also a style icon. ", "One flame shirt and one Flavorcrown is all you need. ", "Maybe some shorts? ", "I’ve never seen below his torso.", "\n\nOnce Herky is in full Flavortown regalia, maybe he can re-create my favorite gif of all time where Fieri eats a noodle in reverse.", "\n\nBarry from “The Bee Movie”: This one is complicated. ", "A hornet is not a bee, news flash. ", "But I think the high meme-ability of “The Bee Movie”—one of the internet’s greatest sources for ongoing memes—makes it worth the stretch.", "\n\nWe get Herky dressed up like Barry, which is basically naked but with a bee-colored sweater. ", "Herky then goes to a court of his choosing and sues humanity for something.", "\n\nA good old-fashioned publicity stunt. ", "Get Sac State’s name out there. ", "Take that, CSU Bakersfield! ", "We’re the meme school!", "\n\nSoundcloud rapper: A truly defined aesthetic. ", "Face tattoos, colored hair and jackets that are never quite all the way on. ", "Even better than the look is the two-song EP Herky could put out where a bunch of buzzing sounds can be heard over that same trap beat that’s in every hit song now.", "\n\nHad to do it to em: This is a fringe contender. ", "Twitter user Lucky Luciano—just a guy who wore a nice outfit and posted it with the caption “you know I had to do it to em”—became internet famous when he posted a photo of his fresh look.", "\n\nSac State Twitter would absolutely blow up if Herky got some nice chino shorts, a matching collared shirt with loafers and a gold watch and posted it on his Instagram account. ", "Hopefully he just doesn’t get arrested for drug possession and then post a GoFundMe where the only image is some half-sliced banana bread. ", "Luciano did that.", "\n\nActually 71-year-old Herky\n\nHerky is an old man! ", "What if for his next birthday he wore high-water khaki pants, suspenders and some orthopedic dress shoes? ", "Large glasses? ", "Hair coming out of his antennas?", "\n\nMaybe he can tell current students some nice stories about Sac State’s past. ", "How Sacramento City College’s campus was our first campus, how there used to be live chickens on campus everywhere and how the school’s founder believed in eugenics.", "\n\n“Back then, sterilization was considered progressive,” Herky might say. ", "I freely admit this one is a bad idea.", "\n\nOther college stereotypes\n\nMaybe Herky could be more reflective of the rest of campus. ", "Maybe he can play drums in the marching band or act in Shakespearean garb. ", "I’m here for nerdy Herky, artist Herky, hipster Herky and hypebeast Herky.", "\n\nOr, some realism. ", "Let’s see him in some slide sandals and pajamas, bleary-eyed at a 9 a.m. foreign language class, trying to remember how to speak English, let alone learn French.", "\n\nIn summation\n\nWe’ve seen him at sports events, rallies and social events. ", "We’ve seen him in his normal duds, some more fun ones and we’ve seen him shirtless. ", "Now, it’s time to step it up." ]

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[ "Watch the 'Blood Moon' Lunar Eclipse in 9 Seconds Flat\n\nMillions of people were greeted last night with a strange celestial sighting, the \"blood moon\" lunar eclipse. ", "The phenomenon occurs when the moon passes into the earth's shadow and, for about an hour, takes on a reddish hue from the sunlight being refracted around the earth's horizon.", "\n\nDue to cloud cover over much of North America, many people, particularly on the east coast, didn't get a chance to see the blood moon Tuesday morning. ", "Don't worry though, we've got a time lapse of the event for you right here." ]

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[ "The 25-year-old failed to live up to the vast fee Liverpool paid for him in 2011, and Henry Jackson (@OnFootballTweet) believes that, although far from a bad player, he was never going to become an Anfield icon.", "\n\nWhen Kenny Dalglish signed Carroll for £35m in January 2011- a British transfer record for a few hours before Fernando Torres eclipsed it- many Reds fans were very happy with the acquisition.", "\n\nMany of you may not like to admit that now, but it’s the truth. ", "I firmly believed he was a hugely promising young English player who could become a hero at Anfield. ", "I know i’m not alone in that.", "\n\nAs it panned out, his time at the club was a disaster; both for him and everyone associated with it. ", "Injuries hampered his progress without doubt- he only managed 11 goals in 58 appearances but rarely got a proper run in the side- but, ultimately, he was never the right fit for Liverpool.", "\n\nHe lacked pace, wasn’t a good enough finisher and could only really be effective if a direct style of play was used. ", "With Luis Suarez also new to the club, it was a no-brainer as to who was going to be the one to spearhead Liverpool’s attack both then and in the future.", "\n\nUnder Dalglish it was clear that Carroll would always be given a chance to prove himself if fit, but as soon as Brendan Rodgers took over the reigns in the summer of 2012, the end was nigh.", "\n\nIf ever there was a player who didn’t suit Rodgers’ high-intensity, fast, fluent style it was the big Geordie. ", "Although he made it clear he wanted to fight for his place, Carroll was farmed out on loan to West Ham for the season, and joined on a permanent deal last summer.", "\n\nThe £15m (plus £2m initial loan fee) Liverpool received was actually very good business- considering how forgettable his Anfield career was- and to only make less than a £20m loss in the end was a real result. ", "They could easily have ended up selling him for less than £10m, such was the damage his reputation had suffered.", "\n\nIt’s important to stress that, despite the huge criticism and derision Carroll has received over the last few years, he’s actually not a bad footballer.", "\n\nThe former Newcastle man is absolutely brilliant in the air- his headed winner against Everton in the 2012 FA Cup semi-final was his finest moment in a Liverpool shirt- and his touch and vision is underrated by some. ", "He’s not Zlatan Ibrahimovic, obviously, but he’s also not Sean Dundee either.", "\n\nThe fact that he may force his way into England’s World Cup squad this summer shows that he’s half-decent; even if there isn’t exactly a huge amount of competition and the manager is inept.", "\n\nOn Sunday, Liverpool travel to Upton Park looking to keep their title surge going. ", "In Carroll, they will come up against a man who will be dying to prove a point against his former employers.", "\n\nSince returning from injury he has been a very important player for Sam Allardyce’s side, and scored a trademark header away to Sunderland in the Hammers’ 2-1 win on Monday night.", "\n\nThe 25-year-old is arguably West Ham‘s key player at the moment, and their system is built around his aerial prowess. ", "Whoever Rodgers starts at centre-back on Sunday- presumably Martin Skrtel and Daniel Agger given their current form- will have a potentially gruelling 90 minutes on their hands against the former Red.", "\n\nThe imposing striker will want to show Rodgers exactly what he’s missing by selling him last summer, and Liverpool will have to be switched on if they are avoid Carroll making the headlines on Monday morning.", "\n\nWould you have kept Andy Carroll at Liverpool? ", "Do you see him as a threat on Sunday?" ]

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[ "I needed one of these and I was afraid to buy one because I didn't know if the Paperwhite 3G was different from the Paperwhite.", "\n\nholycrapitsjeff took the leap for me -- and it fits!", "\n\nThis thing even turns the Kindle on and off when I open and close it (and yes I did check this repeatedly because why not).", "\n\nThank you! ", "Now my Kindle won't get scratched up by my keys. ", ":D" ]

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[ "Q:\n\nChange CSS based on a condition\n\nHere is what I'm trying to do.", "\nI'm trying to change the CSS background color based on the selection of the PHP value. ", "\nHere is what I'm trying to do:\nif (temp_value !", "= '') { <style>span.class_color = \"#ccffcc\";</style> } \nelse { <style>span.class_color = \"#ffffff\" </style> } \n<span class=\"class_color\">Hello there!</span> \n\nA:\n\nThere are multiple problems here:\n\nYour CSS definition doesn't make any sense, span.class_color is the selector, if you want to assign the color of text the value then you'd need span.class_colour {color: #fff}.", "\nThe last line is invalid PHP, I'm presuming you want to display it using echo or end php using ?", "> before that.", "\n\nYou can also simply define two classes in CSS like:\n<style>\nspan.class_color_normal {\n color: #ccffcc;\n}\nspan.class_color_empty {\n color #fff;\n}\n</style>\n\nAnd then in PHP change class like:\n\nif ($temp_value !", "= '')\n $class = 'class_color_normal';\nelse\n $class = 'class_color_empty';\necho '<span class=\"', $class, '\">your text here</span>';\n\n" ]

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[ "Q:\n\nQuantum PAC learning\n\nBackground\nFunctions in $AC^0$ are PAC learnable in quasipolynomial time with a classical algorithm that requires $O(2^{log(n)^{O(d)}})$ randomly chosen queries to learn a circuit of depth d [1]. ", "If there is no $2^{n^{o(1)}}$ factoring algorithm then this this is optimal [2]. ", "Of course, on a quantum computer we know how to factor, so this lower bound does not help. ", "Further, the optimal classical algorithm uses the Fourier spectrum of the function thus screaming \"quantumize me!\"", "\n[1] N. Linial, Y. Mansour, and N. Nisan. [", "1993] \"Constant depth circuits, Fourier transform, and learnability\", Journal of the ACM 40(3):607-620.", "\n[2] M. Kharitonov. [", "1993] \"Cryptographic hardness of distribution-specific learning\", Proceedings of ACM STOC'93, pp. ", "372-381.", "\nIn fact, 6 years ago, Scott Aaronson put the learnability of $AC^0$ as one of his Ten Semi-Grand Challanges for Quantum Computing Theory. ", "\n\nQuestion\nMy question is three-fold:\n1) Are there examples of natural function families that quantum computers can learn faster than classical computers given cryptographic assumptions?", "\n2) Has there been any progress on the learnability of $AC^0$ in particular? (", "or the slightly more ambitious $TC^0$)\n3) In regards to the learnability of $TC^0$, Aaronson comments: \"then quantum computers would have an enormous advantage over classical computers in learning close-to-optimal weights for neural networks.\" ", "Can somebody provide a reference on how weight updating for neural nets and $TC^0$ circuits relate? (", "apart from the fact that threshold gates look like sigmoid neurons) (This question was asked and answered already)\n\nA:\n\nI'll take a shot at your first question:\n\nAre there examples of natural function families that quantum computers can learn faster than classical computers given cryptographic assumptions?", "\n\nWell, it depends on the exact model and the resource being minimized. ", "One option is to compare the sample complexity (for distribution-independent PAC learning) of the standard classical model with a quantum model that is given quantum samples (i.e., instead of being given a random input and the corresponding function value, the algorithm is provided with a quantum superposition over inputs and their functions values). ", "In this setting, quantum PAC learning and classical PAC learning are basically equivalent. ", "The classical upper bound on sample complexity and the quantum lower bound on sample complexity are almost the same, as shown by the following sequence of papers:\n\n[1] R. Servedio and S. Gortler, “Equivalences and separations between quantum and classical learnability,” SIAM Journal on Computing, vol. ", "02138, pp. ", "1–26, 2004.", "\n[2] A. Atici and R. Servedio, “Improved bounds on quantum learning algorithms,” Quantum Information Processing, pp. ", "1–18, 2005.", "\n[3] C. Zhang, “An improved lower bound on query complexity for quantum PAC learning,” Information Processing Letters, vol. ", "111, no. ", "1, pp. ", "40–45, Dec. 2010.", "\n\nMoving on to time complexity, using the same quantum PAC model, Bshouty and Jackson showed that DNFs can be quantum PAC learnt in polynomial time over the uniform distribution [4], further improved in [5]. ", "The best known classical algorithm for this runs in $O(n^{\\log n})$ time. ", "Atici and Servedio [6] also show improved results for learning and testing juntas.", "\n\n[4] N. Bshouty and J. Jackson, “Learning DNF over the uniform distribution using a quantum example oracle,” SIAM Journal on Computing, vol. ", "28, no. ", "3, pp. ", "1136–1153, 1998.", "\n[5] J. Jackson, C. Tamon, and T. Yamakami, “Quantum DNF learnability revisited,” Computing and Combinatorics, pp. ", "595–604, 2002.", "\n[6] A. Atıcı and R. Servedio, “Quantum Algorithms for Learning and Testing Juntas,” Quantum Information Processing, vol. ", "6, no. ", "5, pp. ", "323–348, Sep. 2007.", "\n\nOn the other hand, if you're interested in the standard classical PAC model only, using quantum computing as a post-processing tool (i.e., no quantum samples), then Servedio and Gortler [1] observed that there is a concept class due to Kearns and Valiant that cannot be classically PAC learnt assuming the hardness of factoring Blum integers, but can be quantumly PAC learnt using Shor's algorithm.", "\nThe situation for Angluin's model of exact learning through membership queries is somewhat similar. ", "Quantum queries can only give a polynomial speedup in terms of query complexity. ", "However, there is an exponential speedup in time complexity assuming the existence of one-way functions [1].", "\nI have no idea about the second question. ", "I'd be happy to hear more about that too.", "\n\nA:\n\nThis is certainly not a full answer to your question, but hopefully helps with the first part. ", "There seems to have been quite an amount of interest in using quantum algorithms to identify unknown oracles. ", "One example of this is a recent paper from Floess, Andersson and Hillery (arXiv:1006.1423) which adapts the Bernstein-Vazirani algorithm to identify Boolean functions which depend on only a small subset of the input variables (juntas). ", "They use this approach to determine the oracle function for low-degree polynomials (they explicitly deal with linear, quadratic and cubic cases).", "\n\n" ]

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[ "Screenshot: National\n\n\n\nKORNJAČA Cabecao predvidjela je da će Brazil pobijediti Hrvatsku, ali s njom se ne slaže deva iz Dubaija.", "\n\n\n\nTrkača deva predvidjela je da će hrvatska reprezentacija sve iznenaditi i pobijediti Brazil na utakmici kojom se otvara Svjetsko prvenstvo, piše National.", "\n\n\n\nAko je vjerovati Waslawi, Brazil neće imati razloga za slavlje.", "\n\n\n\nOna je glavom \"odabrala\" pobjednika utakmice, a njezina kolegica Shaheen predviđa da će Nizozemska pobijediti Španjolsku.", "\n\n\n\nVideo pogledajte ovdje.", "\n\n\n\nTekst se nastavlja ispod oglasa" ]

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[ "On Monday afternoon, San Francisco’s notoriously long waiting list for a shelter bed numbered 1,267 people. ", "You can see the ever-changing list online and also each homeless individual’s chances of sleeping in a bed that night.", "\n\nYou won’t see anybody’s name or much about them, but you can see the client identification number the city uses to track them, and their birth date.", "\n\nThere are surely 1,267 sad stories on that waiting list. ", "The saddest to me was No. ", "20 in the line — born on Aug. 30, 1930, when Herbert Hoover was president and there were just 48 states.", "\n\nYes, there was somebody 88 years old waiting for a shelter bed in San Francisco on Monday.", "\n\nSuch a list of human misery wouldn’t exist anymore in California — or at least wouldn’t be nearly so long — under a new proposal from state Sen. Scott Wiener.", "\n\nHe wants homeless people throughout the state to have a “right to shelter,” meaning any homeless person in any county could receive a shelter bed. ", "No more months-long waiting lists. ", "No more counties getting away with providing far too few shelter beds or offering them only during the cold winter months.", "\n\nIt’s a big idea. ", "And one that’s not even close to fully baked, as Wiener readily admits.", "\n\nHe doesn’t know exactly how it will work. ", "He doesn’t know how much it will cost or how it will be funded. ", "He doesn’t want it to be the same as New York City’s controversial right-to-shelter program, but he can’t say how it will be different.", "\n\nThe proposal is merely a placeholder while Wiener begins talks with homeless advocates, city leaders and others. ", "It comes two months after Mayor London Breed announced a plan to create 1,000 more shelter beds by 2020. ", "Currently, the city has 2,500.", "\n\nWiener’s proposal might not be ready for a vote until next year, but it’s worth talking about now because he is the kind of middle-of-the-road, practical politician who could make it a reality. ", "Coming from him, this is automatically a serious proposal and not just a pie-in-the-sky idea.", "\n\nBut mostly, it’s worth talking about because the state’s homeless crisis shouldn’t be shouldered by just the cities and counties willing to do the work and spend the money. ", "There should be far more collaboration, and there should be far more guidance and funding from Sacramento.", "\n\n“We have a huge and growing homeless population in California, and it’s no longer just in places like San Francisco, Berkeley and Los Angeles,” Wiener said. “", "We want to look at how we can have better geographic equity, so people have access to shelter no matter where they are in the state.”", "\n\nRight-to-shelter laws exist in just a few municipalities around the country. ", "By far the best known is New York City’s program, which was mandated by court order following a lawsuit in 1979 by a homeless man, Robert Callahan. ", "Though his lawsuit forced the city to create shelter beds for the homeless, he died living on the streets before it went into effect in 1981.", "\n\nThere are good points and bad points to New York City’s law. ", "The good? ", "It provides beds to more than 60,000 homeless people in the city each year. ", "Those who, for one reason or another, aren’t in shelter numbered 3,675 in the last one-night count.", "\n\nThat’s in a city measuring 303 square miles and with 8.6 million residents. ", "In our comparatively tiny town — with 47 square miles and 885,000 residents — there were 4,353 unsheltered homeless people in the last one-night count. ", "And 7,499 homeless people overall.", "\n\nThat means New York City’s homeless people are far more likely to sleep inside in a bed than San Francisco’s homeless are. ", "And those on the streets in New York City are far less in-your-face, since there are fewer of them and they’re spread out over so much more space.", "\n\nThe bad parts of New York’s plan? ", "The patchwork system, which includes some private apartments and commercial hotel rooms rented by the city to meet its legal obligations, has been slammed as offering seedy and ramshackle facilities and merely warehousing people rather than trying to move them into better lives.", "\n\nNew York City spends $1.6 billion annually on shelter, with little left over for quality social services and permanent supportive housing.", "\n\nSan Francisco’s Department of Homelessness and Supportive Housing spends most of its money on the supportive housing part, and every month homeless people are moved inside. ", "The problem is there’s too little left over for quality shelters, and too many people are stuck sleeping under cardboard or in tents.", "\n\nPerhaps Wiener can figure out a way to strike a balance. ", "He envisions Navigation Centers — the more-welcoming versions of homeless shelters, with on-site case managers — up and down the state. ", "And, yes, he acknowledges that would cost a lot.", "\n\nI asked him why he’s introducing this weeks after coming out against Proposition C, the San Francisco ballot measure that passed last month and, barring lawsuits, will tax the city’s biggest businesses to raise an additional $300 million for homeless services including shelters.", "\n\n“Money by itself doesn’t solve the problem,” he said. “", "Prop. ", "C was not a new plan. ", "It was doubling what we spend on an existing plan.”", "\n\nIt seems that the right-to-shelter idea is so new, so big and so vague that a lot of people who would be key to its implementation aren’t willing to talk. ", "Requests for comment from Mayor Breed; her homeless chief, Jeff Kositsky; and Gov.-elect Gavin Newsom didn’t get responses by deadline.", "\n\nThe moderate Wiener does, however, have some early support among the most progressive members of the Board of Supervisors.", "\n\nSupervisor Hillary Ronen, who has fought to place new Navigation Centers in the Mission, called the idea “fantastic.” ", "City officials across the political spectrum are abandoning the idea pushed by then-Mayor Newsom of ending shelter in favor of only permanent, supportive housing. ", "They rightly say that’s not realistic.", "\n\n“We can’t just have people languishing and dying in the streets as we wait decades to build enough affordable housing for everyone,” Ronen said. “", "We need a safe, dignified place for people to be in the interim.”", "\n\nSupervisor Rafael Mandelman said the most important part of Wiener’s idea is making homelessness a statewide conversation.", "\n\n“Elevating this up above our internal San Francisco food fight is certainly good,” he said.", "\n\nStay tuned, readers. ", "As Wiener says, this is only the beginning.", "\n\nSan Francisco Chronicle columnist Heather Knight appears Sundays and Tuesdays. ", "Email: hknight@sfchronicle.com Twitter: @hknightsf" ]

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[ "Q:\n\nhow do i avoid $scope.$apply() in the callback\n\nBelow code works fine. ", "I am just trying to see if there is a better way to write it so that i can avoid $scope.$apply() in my controller.", "\nWhen user clicks on \"Sign Up\" button, call goes to Controller and then to the Service along with a Callback method. ", "In the Service, i am calling Parse Cloud Code to create the user and calling Callback after i receive the response.", "\nThe problem is that i have to call $scope.$apply() in the callback method in order to apply changes to vm.m.resp property bound to the span.", "\nIs there a way i can run the whole signup process as a single transaction and avoid callback? ", "\nOR\nIs there a way to avoid calling $scope.$apply()?", "\nThis is how my UI looks like:\n<ion-view title=\"Sign Up\">\n <ion-content class=\"has-header\">\n <div class=\"list\">\n <label class=\"item item-input\">\n <span class=\"input-label\">Username</span>\n <input type=\"text\" ng-model=\"vm.m.username\">\n </label>\n <label class=\"item item-input\">\n <span class=\"input-label\">Password</span>\n <input type=\"password\" ng-model=\"vm.m.password\">\n </label>\n <label class=\"item\">\n <button class=\"button button-block button-positive\" ng-click=\"vm.doSignUp()\">Sign Up</button>\n </label>\n </div>\n <div class=\"list\">\n <div class=\"bar bar-header bar-positive\">\n <span ng-bind=\"vm.m.resp\"></span>\n </div>\n </div>\n </ion-content>\n</ion-view>\n\nThis is how my Controller looks like:\n(function () {\n 'use strict';\n\n angular.module('app').controller('UserAdminCtrl', ['$stateParams', '$scope', 'userAdminApi', UserAdminCtrl]);\n\n function UserAdminCtrl($stateParams, $scope, userAdminApi) {\n var vm = this;\n vm.m = {};\n vm.m.username = '';\n vm.m.password = '';\n vm.m.resp = '';\n\n function doSignUp() {\n\n userAdminApi.doSignup(vm.m, doSignUpCallback);\n vm.m.resp = 'Signing up. ", "Please wait...';\n }\n\n function doSignUpCallback(resp) {\n vm.m.resp = resp;\n $scope.$apply()\n }\n vm.doSignUp = doSignUp;\n vm.doSignUpCallback = doSignUpCallback;\n };\n})();\n\nThis is how my service looks like:\n(function () {\n 'use strict';\n\n angular.module('app').factory('userAdminApi', [userAdminApi]);\n\n function userAdminApi() {\n\n function doSignup(m,cb) {\n\n Parse.", "Cloud.run('createUser', {m}, {\n success: function (result) {\n cb(result);\n },\n error: function (error) {\n cb(error.message);\n }\n });\n }\n\n return {\n doSignup: doSignup\n };\n };\n})();\n\nA:\n\nYou can use a promise to get back into the digest cycle:\n(function () {\n 'use strict';\n\n angular.module('app').factory('userAdminApi', ['$q', userAdminApi]);\n\n function userAdminApi($q) {\n\n function doSignup(m) {\n var deferred = $q.defer();\n Parse.", "Cloud.run('createUser', {m}, {\n success: function (result) {\n deferred.resolve(result);\n },\n error: function (error) {\n deferred.reject(error);\n }\n });\n return deferred.promise;\n }\n\n return {\n doSignup: doSignup\n };\n };\n})();\n\nThis gives you a nice and clean error callback as well.", "\n\n" ]

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[ "EndophilinA2 protects against angiotensin II-induced cardiac hypertrophy by inhibiting angiotensin II type 1 receptor trafficking in neonatal rat cardiomyocytes.", "\nCardiac hypertrophy is one of the major risk factors for chronic heart failure. ", "The role of endophilinA2 (EndoA2) in clathrin-mediated endocytosis and clathrin-independent endocytosis is well documented. ", "In the present study, we tested the hypothesis that EndoA2 protects against angiotensin II (Ang II)-induced cardiac hypertrophy by mediating intracellular angiotensin II type 1 receptor (AT1-R) trafficking in neonatal rat cardiomyocytes (NRCMs). ", "Cardiac hypertrophy was evaluated by using cell surface area and quantitative RT-PCR (qPCR) analyses. ", "For the first time, we found that EndoA2 attenuated cardiac hypertrophy and fibrosis induced by Ang II. ", "Moreover, EndoA2 inhibited apoptosis induced by excessive endoplasmic reticulum stress (ERS), which accounted for the beneficial effects of EndoA2 on cardiac hypertrophy. ", "We further revealed that there was an interaction between EndoA2 and AT1-R.The expression levels of EndoA2, which inhibits AT1-R transport from the cytoplasm to the membrane, and the interaction between EndoA2 and AT1-R were obviously decreased after Ang II treatment. ", "Furthermore, Ang II inhibited the co-localization of AT1-R with GRP-78, which was reversed by EndoA2 overexpression. ", "In conclusion, our results suggested that EndoA2 plays a role in protecting against cardiac hypertrophy induced by Ang II, possibly by inhibiting AT1-R transport from the cytoplasm to the membrane to suppress signal transduction." ]

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[ "# Copyright (C) 2010 Free Software Foundation, Inc.\n\n# This program is free software; you can redistribute it and/or modify\n# it under the terms of the GNU General Public License as published by\n# the Free Software Foundation; either version 3 of the License, or\n# (at your option) any later version.", "\n#\n# This program is distributed in the hope that it will be useful,\n# but WITHOUT ANY WARRANTY; without even the implied warranty of\n# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. ", " See the\n# GNU General Public License for more details.", "\n#\n# You should have received a copy of the GNU General Public License\n# along with GCC; see the file COPYING3. ", " If not see\n# <http://www.gnu.org/licenses/>.", "\n\nset gccdir [lookfor_file $tool_root_dir gcc/libgcc.a]\nif {$gccdir !", "= \"\"} {\n set gccdir [file dirname $gccdir]\n}\nset GOC_UNDER_TEST \"$gccdir/gccgo -B$gccdir/\"\nset TESTING_IN_BUILD_TREE 1\n\nif [info exists GOTEST_TMPDIR] {\n set tmpdir $GOTEST_TMPDIR\n}\n\nproc go_maybe_build_wrapper { args } {\n libgo_maybe_build_wrapper $args\n}\n\n# DejaGnu does not have proper library search paths for load_lib.", "\n# We have to explicitly load everything that go.exp wants to load.", "\n\nproc load_gcc_lib { filename } {\n global srcdir loaded_libs\n\n load_file $srcdir/../../gcc/testsuite/lib/$filename\n set loaded_libs($filename) \"\"\n}\n\nload_gcc_lib prune.exp\nload_gcc_lib target-libpath.exp\nload_gcc_lib wrapper.exp\nload_gcc_lib gcc-defs.exp\nload_gcc_lib timeout.exp\nload_gcc_lib go.exp\n\nproc libgo_init { args } {\n go_init $args\n}\n" ]

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[ "// Copyright 2018 The Chromium Authors. ", "All rights reserved.", "\n// Use of this source code is governed by a BSD-style license that can be\n// found in the LICENSE file.", "\n\n#ifndef CONTENT_BROWSER_RENDERER_HOST_INPUT_FLING_SCHEDULER_BASE_H_\n#define CONTENT_BROWSER_RENDERER_HOST_INPUT_FLING_SCHEDULER_BASE_H_\n\n#include \"content/browser/renderer_host/input/fling_controller.h\"\n\nnamespace content {\n\nclass FlingSchedulerBase : public FlingControllerSchedulerClient {\n public:\n virtual void ProgressFlingOnBeginFrameIfneeded(\n base::TimeTicks current_time) = 0;\n};\n\n} // namespace content\n\n#endif // CONTENT_BROWSER_RENDERER_HOST_INPUT_FLING_SCHEDULER_BASE_H_\n" ]

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[ "This Christmas give the gift of discernment! ", "For a limited time the Called and Gifted Individual discernment set is yours for $50.00 plus free shipping (applies to orders shipped within the U.S. only). ", "Please select any standard shipping (address purpose only), your amount will be adjusted. ", "Click here to order.", "\n\nThe Catherine of Siena Institute is a program of the Western Dominican Province dedicated to equipping parishes for the formation of lay Catholics for their mission in the world.", "\nSupport our work to make apostolic formation and support readily available to all lay Catholics.", "\nClick the title to donate.", "\n\nHow can we transmit a living, personal Catholic faith to future generations? ", "By coming to know Jesus Christ, and following him as his disciples.", "There are immense challenges facing the Church today.", "\nFollow author Sherry Weddell through the steps that will help Catholics make the conscious choice to follow Jesus as his disciples, transforming parish life and ultimately the life of the whole Church.", "\n\nPreserve formatting in description (only supported in some calendar applications)\n\nFrom Friday, November 22, 2013To Saturday, November 23, 2013\n\nHits : 265\n\nKeith Strohm will be leading part one of two Making Disciples weekends.", "\n\nKeith Strohm is the Director of Faith Formation for Queen of the Rosary parish in Elk Grove Village, Illinois, and the Executive Director of Lay Formation Resources, an apostolate that provides parish and diocesan staff with assistance in the creation of formation programs, days of reflection, retreats, and parish missions designed to proclaim the gospel, build disciples, and equip lay apostles for their work in the world. ", "He is currently studying for his Master of Divinity degree at Catholic Theological Union in Chicago, Illinois. ", "Keith has traveled extensively as a CSI teacher and trainer since 2005.http://www.siena.org/Making-Disciples/download-brochure" ]

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[ "Declining Health-Related Quality of Life in the U.S.\nDespite recent declining mortality of the U.S. population from most leading causes, uncertainty exists over trends in health-related quality of life. ", "The 2001-2002 and 2012-2013 National Epidemiologic Surveys on Alcohol and Related Conditions U.S. representative household surveys were analyzed for trends in health-related quality of life (n=79,402). ", "Health-related quality of life was measured with the Short Form-6 Dimension scale derived from the Short Form-12. ", "Changes in mean Short Form-6 Dimension ratings were attributed to changes in economic, social, substance abuse, mental, and medical risk factors. ", "Mean Short Form-6 Dimension ratings decreased from 0.820 (2001-2002) to 0.790 (2012-2013; p<0.0001). ", "In regressions adjusted for age, sex, race/ethnicity, and education, variable proportions of this decline were attributable to medical (21.9%; obesity, cardiac disease, hypertension, arthritis, medical injury), economic (15.6%; financial crisis, job loss), substance use (15.3%; substance use disorder or marijuana use), mental health (13.1%; depression and anxiety disorders), and social (11.2%; partner, neighbor, or coworker problems) risks. ", "In corresponding adjusted models, a larger percentage of the decline in Short Form-6 Dimension ratings of older adults (aged ≥55 years) was attributable to medical (35.3%) than substance use (7.4%) risk factors, whereas the reverse occurred for younger adults (aged 18-24 years; 5.7% and 19.7%) and adults aged 25-44 years (12.7% and 16.3%). ", "Between 2001-2002 and 2012-2013, there was a significant decline in average quality of life ratings of U.S. adults. ", "The decline was partially attributed to increases in several modifiable risk factors, with medical disorders having a larger role than substance use disorders for older adults but the reverse for younger and middle-aged adults." ]

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[ "Sports Hypothesis ™ is a web based platform dedicated to fantasy sports. ", "Our hope is to use our years of experience and extensive research to make bold sports predictions to guide you to fantasy success." ]

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[ "Q:\n\nCannot read property 'client' of undefined using SignalR\n\nI've been working all day on this with no luck.", "\nI have also tried (almost) every single SO question, but I didn't get it to work...\nI'm running web api with very simple SignalR push message and separately simple front end to show this push message.", "\nIn my case the push message is constantly changing number.", "\nindex.html\n<!", "DOCTYPE html>\n<html xmlns=\"http://www.w3.org/1999/xhtml\">\n<head>\n <title>test app</title>\n\n <script src=\"scripts/jquery-2.1.4.js\"></script>\n <script src=\"scripts/jquery.signalR-2.2.0.js\"></script>\n\n <script src=\"/signalr/hubs\"></script>\n</head>\n<body>\n <div id=\"testElm\">TEST: </div>\n\n <script type=\"text/javascript\">\n $(document).ready(function () {\n\n $.connection.hub.url = \"http://localhost:55833/signalr\";\n var hub = $.connection.displayHub;\n\n hub.client.pushMessage = function (response) {\n\n $('#testElm').text(response);\n };\n\n $.connection.hub.start();\n });\n </script>\n</body>\n</html>\n\nmy hub class\npublic class DisplayHub : Hub\n{\n public DisplayHub() : this(GlobalHost.", "ConnectionManager.", "GetHubContext<DisplayHub>().Clients) { }\n\n public DisplayHub(IHubConnectionContext<dynamic> clients)\n {\n }\n\n public void PushMessage(string message)\n {\n // generate random number and send it every 1s for testing\n\n Clients.", "All.pushMessage(randomNumber);\n }\n}\n\nWhen running with \n$.connection.hub.logging = true;\n\nthis is the log I'm getting\n2015-06-15 16:44:15 GMT+0100 (GMT Daylight Time)] SignalR: Auto detected cross domain url.", "\n2015-06-15 16:44:15.314 jquery.signalR-2.2.0.js:81 [16:44:15 GMT+0100 (GMT Daylight Time)] SignalR: Negotiating with 'http://localhost:55833/signalr/negotiate?clientProtocol=1.5'.", "\n2015-06-15 16:44:15.434 jquery.signalR-2.2.0.js:81 [16:44:15 GMT+0100 (GMT Daylight Time)] SignalR: webSockets transport starting.", "\n2015-06-15 16:44:15.435 jquery.signalR-2.2.0.js:81 [16:44:15 GMT+0100 (GMT Daylight Time)] SignalR: Connecting to websocket endpoint 'ws://localhost:55833/signalr/connect?transport=webSockets&clientProtocol=1.5&connectionToken=h7UAGOrF6RP8JUE%2F82K84E8NSZOd8jsuijsCQ2Jyh1jRi7zXmIpoVnIP9tjEjlcWvxihtZBNt6BYdaAW2jp574B5nXS%2BJFEW%2F%2BdixsiV0yu3YwaN5ERh6yhYtkvztQSQ&tid=5'.", "\n2015-06-15 16:44:15.451 jquery.signalR-2.2.0.js:81 [16:44:15 GMT+0100 (GMT Daylight Time)] SignalR: Websocket opened.", "\n2015-06-15 16:44:15.510 jquery.signalR-2.2.0.js:81 [16:44:15 GMT+0100 (GMT Daylight Time)] SignalR: webSockets transport connected. ", "Initiating start request.", "\n2015-06-15 16:44:15.518 jquery.signalR-2.2.0.js:81 [16:44:15 GMT+0100 (GMT Daylight Time)] SignalR: The start request succeeded. ", "Transitioning to the connected state.", "\n2015-06-15 16:44:15.518 jquery.signalR-2.2.0.js:81 [16:44:15 GMT+0100 (GMT Daylight Time)] SignalR: Now monitoring keep alive with a warning timeout of 13333.333333333332, keep alive timeout of 20000 and disconnecting timeout of 30000\n\nand I keep getting \nCannot read property 'client' of undefined\n\nchecking \"hub\" will show hub is undefined ...\nbrowsing to http://localhost:55833/signalr/hubs I can see hub on the server being created.", "\ntemporarily merging API and front end, all will work fine, but if I keep them separate I will get above error...\nusing [HubName(\"displayHub\")] attribute made no difference.", "\nCORS is set up correctly as per the log above\n\nAny ideas what is causing the error? ", "Is there a way I can debug signalR further to find out what is going on?", "\nUpdate 1:\nafter reading ASP.NET SignalR Hubs API Guide - JavaScript on http://www.asp.net/signalr/overview/guide-to-the-api/hubs-api-guide-javascript-client\nI have changed my code as per Without the generated proxy paragraph to:\nvar conn = $.hubConnection(\"http://localhost:55833/signalr\");\nvar hubProxy = conn.createHubProxy('displayHub');\n\nhubProxy.on('pushMessage', function (response) {\n $('#testElm').text(response);\n});\n\nconn.start();\n\nand it started to work... Can someone explain why?", "\n\nA:\n\nFrom your question I understand you have 2 different applications for client and server, and you are using CORS. ", "The reason why your first attempt did not work is that you did not make the dynamic SignalR endpoint target the server application. ", "You should have changed this:\n<script src=\"/signalr/hubs\"></script>\n\ninto this:\n<script src=\"http://localhost:55833/signalr/hubs\"></script>\n\nThe reason is, that endpoint dynamically generates Javascript code representing the shape of your hubs, therefore it needs to be called on the application where the hubs are, hence the server.", "\n\n" ]

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[ "Q:\n\nFormatting a negative TimeSpan\n\nI'm doing some math with the Timespans in .Net, and occasionally the sum results in a negative Timespan. ", " When I display the result I am having trouble formatting it to include the negative indicator.", "\nDim ts as New Timespan(-10,0,0)\n\nts.", "ToString()\n\nThis will display \"-10:00:00\", which is good but I don't want to show the seconds so tried this.", "\nts.", "ToString(\"hh\\:mm\")\n\nThis returns \"10:00\" and has dropped the \"-\" from the front which is the crux of the issue. ", " My current solution is this:\nIf(ts < TimeSpan.", "Zero, \"-\", \"\") & ts.", "ToString(\"hh\\:mm\")\n\nbut I was hoping to accomplish the same by using only the format string.", "\n\nA:\n\nI've used .Net Reflector on TimeSpan.", "ToString(...) and it really doesn't look like it supports any form of negative prefix on custom formats - so I think you're out of luck when it comes to getting it to work for you as above. ", " :(\n\nA:\n\nIt seems like you're stuck with that code, but if so, this seems like a great time to write an extesion method, that way you can make your code clearer and you don't have to repeat that code in multiple places, so something like:\nModule Extensions\n <System.", "Runtime.", "CompilerServices.", "Extension()> _\n Public Function HoursAndMinutes(ByVal ts As TimeSpan) As String\n Return If(ts < TimeSpan.", "Zero, \"-\", \"\") & ts.", "ToString(\"hh\\:mm\")\n End Function\nEnd Module\n\nAnd then you could just call it as:\nts.", "HoursAndMinutes()\n\n" ]

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[ "Q:\n\nneo4j: set different properties based on existing properties\n\nI am trying to set new properties based on existing properties. ", "The existing nodes have the following properties: \nminTempC, maxTempC\nNew properties should be set if the following conditions are met:\nminTempC < 0 set the property frosstag = true\nmaxTempC < 0 set the property eistag = true\nmaxTempC >= 30 set the property heissertag = true\nThe existing nodes can meet one, multiple or none of the conditions.", "\nMy cypher right now is:\n//Eistag\nMATCH (d:Data)\nWHERE d.maxtempC < 0\nSET d += {eistag:true}\n\n//Frosttag\nMATCH (d:Data)\nWHERE d.mintempC < 0 \nSET d += {frosttag:true}\n\n//Heisser Tag\nMATCH (d:Data)\nWHERE d.maxtempC >= 30\nSET d += {heisserTag:true}\n\nIs there a way to combine these three? ", "I have several other properties that have to be set and writing these SET clauses over and over again seems a little bit tedious. ", "I thought of using a CASEexpression, but I am new to neo4j and must confess that I have no idea how to built such a expression.", "\nThank you in advance for yout tips. ", "\n\nA:\n\nYou can use CASE WHEN in an expression, so the following should help:\nMATCH (d:Data)\nSET \nd.eistag = CASE WHEN d.minTempC < 0 THEN true END,\nd.frosttag = CASE WHEN d.maxTempC < 0 THEN true END,\nd.heisserTag = CASE WHEN d.maxTempC >= 0 THEN true END\n\nNote that if the condition is false, a null is returned from CASE WHEN. ", "Setting a property to a null value results in not setting this property. ", "\n\n" ]

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[ "This invention relates to ablative burrs for medical procedures and, in particular, to an ablative burr for performing an atherectomy procedure.", "\nA number of vascular diseases, such as atherosclerosis, medial sclerosis, arteriolosclerosis, and thrombosis are characterized by the buildup of deposits (atheromas), clots, or growths in or on the intimal layer of a patient\"\"s blood vessels. ", "Such deposits generally result in occlusions in a person\"\"s vascular system that can impede the flow of blood to the affected portion of the person\"\"s body. ", "If the occlusion is not removed or otherwise ameliorated, enlargement of the occlusion can result in the complete stoppage of blood flow to the affected region. ", "This can be particularly serious, of course, if the occlusion occurs in a portion of the vasculature that supplies vital organs with blood or other.necessary fluids.", "\nTo treat such diseases, many invasive and noninvasive techniques and therapies have been developed. ", "For example, cardiac bypass surgery is now a commonly performed procedure wherein an occluded cardiac artery is bypassed with a segment of a healthy blood vessel that is obtained from elsewhere in the body. ", "While this procedure is frequently successful, it is extremely traumatic to the patient because the entire chest cavity must be opened to access the site of the occluded artery. ", "Because of the trauma and substantial risks associated with cardiac bypass surgery, this procedure may not be a viable option for certain patients, particularly for elderly or relatively frail patients.", "\nAs an alternative to cardiac bypass surgery, numerous atherectomy (atheroma removal) devices have been developed for removing such deposits in a less invasive manner. ", "One such device that is particularly suited to removing calcified atherosclerotic plaque is an ablative rotational atherectomy device, such as that disclosed in U.S. Pat. ", "Nos. ", "4,990,134 and 5,314,407, both to Auth. ", "Auth teaches using a small burr covered, or partially covered, with an abrasive cutting material, such as diamond grit. ", "The burr is attached to the distal end of a flexible, rotatable drive shaft that can be slidably inserted over a guide wire that is inserted through the vasculature of a patient to the site of an occlusion. ", "A rotational atherectomy device practicing the Auth invention is sold by the assignee of the present invention under the trademark Rotablator(copyright) and is described below.", "\nRefer now to FIG. ", "1, depicting the Rotablator ablative rotational atherectomy device 10. ", "This prior art device utilizes a guide wire 26 that is inserted through the patient\"\"s vasculature approximately to the location of the deposit that is to be treated. ", "A hollow, flexible drive shaft 22 having an ablative burr 24 at its distal end is then inserted over the guide wire 26, and advanced to a location just proximal to the deposit. ", "The drive shaft 22 is covered with a lumen or catheter 20 along most of its length to minimize the impact to surrounding tissue when the drive shaft 22 is rotatably engaged. ", "The drive shaft 22 is connected to a compressed-air driven drive assembly 16 having a turbine (not shown) that can rotate the drive shaft 22 at relatively high rotational speeds. ", "The drive assembly 16 is slidably mounted in an advancer housing 12 on a track, allowing a surgeon using the Rotablator device 10 to move the drive assembly 16 transversely, and hence move the drive shaft 22 and burr 24 forward and backward to impact and ablate the atheroma.", "\nRotational ablative atherectomy devices such as the Rotablator(copyright) have proven to be effective in treating various types of atheroma. ", "Use of the device, however, requires that a guide wire, drive shaft, and catheter be inserted into the patient and maneuvered through the patient\"\"s vasculature to the site of the deposit. ", "It is desirable to minimize the diameter of the catheter in order to facilitate insertion of the device through the patient\"\"s vasculature. ", "The minimum diameter of the catheter, however, is limited by the diameter of the drive shaft. ", "The drive shaft, extending from outside the patient up to the atherectomy burr, is then driven externally to provide the driving force to the burr for performing the ablative atherectomy procedure. ", "The patient\"\"s vasculature may follow a tortuous path between the point of insertion of the drive shaft and the situs of the atheroma. ", "The drive shaft must be very flexible to negotiate such tortuous path. ", "Moreover, rotation of the in situ drive shaft may generate undesirable stresses on the patient\"\"s vasculature.", "\nIt would be beneficial to reduce the diameter of the catheter that must be inserted through the patient\"\"s vasculature and, in particular, to eliminate the drive shaft that drives the burr.", "\nThe present invention overcomes many of the disadvantages of the prior art by providing an ablation burr that does not require the insertion and operation of a flexible drive shaft through the vasculature of the patient to the sight of the occlusion. ", "The ablation burr according to the present invention utilizes a two-piece burr having a rearward piece attached to a small catheter and an abrasive forward piece elastically connected to the rearward piece. ", "Oscillatory drivers are provided between the forward and rearward pieces that force the forward piece to oscillate. ", "By forcing the forward piece at a resonant frequency, relatively large amplitude oscillatory motion of the forward piece can be achieved.", "\nIn an embodiment of the present invention, an ablative burr includes a main body member, a shell member longitudinally coupled to the main body member, and an oscillatory driver disposed between the main body member and the shell member that is adapted to vibrate the shell member at a predetermined frequency. ", "The main body member includes a narrow proximal portion that is attachable to a catheter, an aft-body portion and a coaxial distal portion. ", "The shell member extends around the distal portion and is longitudinally and elastically restrained by the main body member.", "\nIn an embodiment of the invention, the oscillatory driver includes an annular piezoelectric transducer that is situated between the main body member and the shell member, and oscillates the shell member longitudinally at a resonant frequency of the shell member.", "\nIn another embodiment of the invention, the oscillatory driver includes a plurality of annular piezoelectric transducers that are coaxially stacked with electrode plates therebetween, to produce a cumulative forcing amplitude.", "\nIn an aspect of the invention, flexible annular washers are provided between the main body member and the shell member.", "\nIn another embodiment of the invention, the oscillatory driver includes at least one elongate piezoelectric transducer situated between the main body member and the shell member, and oscillates the shell member rotationally about its axis at a resonant frequency of the shell member.", "\nIn another embodiment of the invention, the oscillatory driver includes a plurality of elongate piezoelectric transducers that are stacked side by side with electrode plates therebetween, to produce a cumulative forcing amplitude." ]

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[ "Q:\n\nWhat is the ASA packet process order when there is both a VPN and route in place?", "\n\nWhat will happen if there is a static route in place telling the packet to go to routerA but there is also a crypto map telling the packet to go over the VPN? ", "Will it hit the route table first or go over the VPN tunnel?", "\n\nA:\n\nRouting table is used first. ", "ASA needs it to figure out which interface the packet will go out. ", "Pretty much everything depends on this interface (NAT rules, crypto maps, outbound ACLs when they are used), so it absolutely has to be looked up first.", "\nOnce the outbound interface is known, then ASA goes through (in this order) ACLs, inspects, NAT exemptions, NAT, VPN.", "\nHere's the tricky part about the relationship between the routing table and VPN. ", "Any packet that will be set through a tunnel actually interacts with the routing table twice: first when it's unencrypted and the firewall makes the interface determination, and then in encrypted form when the firewall sends it to its VPN peer. ", "Obviously, the second route is looked up based on the VPN peer's routing and not the original packet's IP headers, so it may actually be different.", "\nBTW, you can understand all this better if you run Packet Tracer in ASDM.", "\n\n" ]

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[ "Vila Salazar\n\nVila Salazar may refer to:\n\nN'dalatando, Angola (the former official name of the city is ‘Vila Salazar’)\nSango, Zimbabwe (the former official name of the village is ‘Vila Salazar’)\nBaucau, East Timor (the former official name of the city is ‘Vila Salazar’)" ]

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[ "\nTeen phone monitoring app leaked thousands of user passwords - asimpletune\nhttps://www.zdnet.com/article/teen-phone-monitoring-app-leaks-thousands-of-users-data/\n======\njiveturkey\nThe exposure had been there for months. ", "WHY oh why couldn’t he have waited a\nfew more days, for GDPR to kick in.", "\n\nNo matter I guess. ", "There will be many more like this.", "\n\nMaybe GDPR will effectively become secure coding (and ops) liability many have\nclamored for.", "\n\n~~~\nbifrost\nGDPR won't matter for this kind of thing, its a US company with no nexus\noutside of the US.", "\n\n" ]

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[ "1. ", "Introduction {#s0010}\n===============\n\nThere are 3 types of footstrike patterns that human runners can employ. ", "These are generally referred to as (1) rearfoot, (2) midfoot, and (3) forefoot. ", "Footstrike patterns are categorized depending on the portion of the foot that initially contacts the running surface. ", "For example, when using a rearfoot strike, a runner will contact the ground with the lateral aspect of the heel eventually toeing off as in the other footstrikes. ", "Here, we use operational definitions for mid- and forefoot striking. ", "A midfoot strike is one in which the runner initially contacts the ground across the metatarsal heads with the heel subsequently contacting the running surface while the forefoot strike is also one in which the initial contact is also on the metatarsal heads but the heel never touches the ground.", "\n\nA study by Lieberman and colleagues[@bib0010] reported that individuals who have never worn shoes used a forefoot strike whereas those who are habitually shod used a rearfoot strike when running. ", "This finding has been recently disputed by Hatala and associates[@bib0015] who reported that 72% of habitually barefoot African runners ran with a rearfoot strike although these data were collected in a different region of Africa than the previous study. ", "However, Lieberman\\'s findings led to the notion that humans may have evolved to be forefoot runners thus the forefoot pattern was the more \"natural\" footstrike compared to a rearfoot strike.[@bib0010] Lieberman\\'s suggestions have led to several papers in the literature on barefoot versus forefoot running, many of which appear to promote a mid- or forefoot strike (e.g., Ahn et al.[@bib0020] and Paavolainen et al.[@bib0025]). ", "Extending the notion that mid- or forefoot running is optimal for barefoot running is the suggestion that mid- or forefoot running is also optimal for shod running. ", "Many running coaches have then suggested that changing a runner\\'s footfall pattern from an \"unnatural\" rearfoot strike to a \"more natural\" forefoot strike, whether unshod or shod, may be a propitious way to improve performance and possibly reduce running-related injuries.[@bib0030], [@bib0035], [@bib0040]\n\nThere are many programs such as Pose running[@bib0045], [@bib0050] or Chi running[@bib0055] that have influenced numerous running coaches to instruct runners to alter their footstrike to an mid- or forefoot strike. ", "While some papers in the literature have suggested such a change to a mid- or forefoot strike,[@bib0020], [@bib0025], [@bib0060], [@bib0065], [@bib0070], [@bib0075] to our knowledge, currently little evidence exists in the literature that conclusively demonstrates that runners would benefit from altering their footstrike in the long term.", "\n\nIt is possible that switching from one footstrike pattern to another has become popular because of reports of isolated anecdotes rather than examining the idea that switching footstrike pattern would benefit all runners. ", "Findings from a survey study indicate that 46% of those that switched from a rearfoot to a mid- or forefoot strike (*n* = 397/866) changed their footstrike because of previous injuries and this group reported experiencing a total of 500 injuries before they switched.[@bib0065] However, the authors did not report any data on the number of injuries that occurred in these participants after they changed their footstrike. ", "No doubt there are some runners who benefitted from altering their habitual footstrike, but which runners and for what reasons are currently unknown. ", "Studies have suggested that some individuals accrue some benefits by changing to a mid- or forefoot strike.[@bib0060], [@bib0065], [@bib0070], [@bib0075] However, to extend this notion to all runners may not be a prudent or beneficial recommendation.", "\n\nThere are 3 major reasons that those who support altering one\\'s footstrike give for changing to a mid- or forefoot strike from a rearfoot strike. ", "These are (1) it is more economical; (2) there is a reduction in the impact peak and loading rate of the vertical component of the ground reaction force (VGRF); and (3) there is a reduction in the risk of a running-related injury. ", "In this paper, we will critique these \"reasons for change\" and discuss alternate explanations that may provide contradictory evidence for altering one\\'s footstrike to a mid- or forefoot strike. ", "We focus on differences between shod rearfoot and shod mid- or forefoot strike running to isolate the differences between footstrike patterns without the influence of footwear.", "\n\n2. ", "Footfall pattern frequency and selection {#s0015}\n===========================================\n\nThe prevalence of the different footstrike patterns in the running population and how footstrike has been determined in the literature is a very important aspect of understanding footstrike behavior. ", "There are at least 2 methods of determining a runner\\'s footstrike. ", "Cavanagh and Lafortune[@bib0080] suggested a method of determining footstrike pattern based on the location of the center of pressure pattern at initial ground contact termed the strike index. ", "With a rearfoot strike, the foot initially contacts the ground in the posterior 1/3 of the length of the foot. ", "In a forefoot strike, initial contact is on the anterior 1/3 of the foot generally in the area of the metatarsal heads. ", "A midfoot strike is the most difficult to determine as the strike index suggests that initial contact is in the middle 1/3 of the foot. ", "Recently, a study by Gruber et al.[@bib0085] suggested that, in addition to the strike index, the position of the ankle joint at foot contact (i.e., dorsiflexed for the rearfoot strike and plantar flexed for the mid- or forefoot strikes) and the presence (rearfoot runner) or absence (forefoot runner) of an impact peak in the component VGRF should be used together as indicators of a footstrike, rather than 1 metric alone as seen in many studies. ", "However, in this paper, we will combine the mid- and forefoot strikes into a mid- or forefoot strike because the initial contact in both is on the metatarsal heads of the forefoot.", "\n\nInterestingly, the epidemiologic data on footstrike demographics show that the rearfoot strike is one that is used by the greatest percentage of runners while the forefoot strike is used by a significantly lesser number of runners. ", "Kerr et al.[@bib0090] found that 81% of runners at the 10 km and 20 km point of a marathon used a rearfoot strike while 19% used a midfoot strike. ", "In an elite half-marathon, Hasegawa et al.[@bib0095] reported that 75% of runners used a rearfoot strike, 23% a midfoot strike, and 2% a forefoot strike. ", "More recently, Larson et al.[@bib0100] concurred with the results of both the Kerr et al.[@bib0090] and Hasegawa et al.[@bib0095] studies. ", "The prevalence of rearfoot runners has also been reported to be as high as 94% of 1991 runners in a competitive road race[@bib0105] and 95% of 514 runners tested in a laboratory setting.[@bib0110] Each of these studies reports a very low percentage of runners using a true forefoot strike. ", "It has been argued that the high prevalence of the rearfoot strike is a result of the modern cushioned running shoe facilitating a rearfoot strike;[@bib0115] however, this speculation has been recently refuted.[@bib0120]\n\nWhich footfall pattern an individual selects may depend on a number of factors. ", "In a forward dynamics simulation modeling study, it was reported that the rearfoot strike was optimal for the greatest number of goals of running, which include minimizing metabolic cost.[@bib0125] However, the model selected a more anterior footstrike (i.e., mid- or forefoot) to optimize for higher running speeds but at a greater metabolic cost. ", "This result is supported by a human study for which increasing running speed resulted in 45% of runners switching to a more anterior footstrike.[@bib0130] Thus, it appears that the choice of footstrike may be task-specific. ", "Running a long distance may require a rearfoot strike to minimize the metabolic cost of running while a more anterior footstrike may be necessary to run faster.", "\n\n3. ", "Changes in the economy of running {#s0020}\n====================================\n\nSeveral studies have observed that the top finishers of short, middle, and long distance events tended to use a mid- or forefoot strike.[@bib0090], [@bib0095], [@bib0110] Similar findings from earlier studies speculated that a mid- or forefoot strike increases the effective storage and release of elastic energy compared with a rearfoot strike and has led some to suggest that it is more economical (i.e., consume less submaximal oxygen for a given task) to run with either a mid- or forefoot pattern.[@bib0090], [@bib0095], [@bib0135], [@bib0140], [@bib0145], [@bib0150] However, several studies, each with a small sample size and thus low statistical power, directly compared running economy between rear- and forefoot strike and reported no statistically significant differences in intra-subject oxygen consumption between these footstrike patterns.[@bib0150], [@bib0155], [@bib0160]\n\nArdigo and colleagues[@bib0155] reported no difference in oxygen uptake or internal mechanical work between a group of habitual rearfoot runners using both a rear- and forefoot strike pattern. ", "These results were supported by later studies also showing no difference in running economy between rear- and forefoot strike patterns.[@bib0150], [@bib0160] However, these studies were limited by low sample sizes and used only habitual rearfoot runners[@bib0160] or only habitual midfoot runners.[@bib0150] Recent studies have reported that there was little or no difference in the net mass normalized oxygen consumption or the net metabolic rate between mid- or forefoot runners versus rearfoot runners performing with their habitual footstrike pattern across submaximal running speeds ([Fig.", " 1](#f0010){ref-type=\"fig\"}).[@bib0165], [@bib0170]Fig.", " 1The net metabolic rate of rearfoot (RF) and forefoot (FF) runners running with their habitual footfall pattern at 3 different speeds. ", "There was no statistically significant difference between conditions (*p* \\> 0.05). ", "Adapted with permission.[@bib0165]Fig.", " 1\n\nGruber et al.[@bib0165] investigated running economy when rear- and forefoot runners were asked to run with the alternative footstrikes. ", "When the participants were asked to run with their non-habitual footstrike, the habitual rearfoot group experienced a significant increase in oxygen consumption but there were no statistically significant changes in oxygen consumption in the habitual forefoot group. ", "Given that performing a new running form or style typically increases oxygen consumption before habituation,[@bib0175], [@bib0180] it would be expected that participants would perform better with their habitual pattern. ", "Although this expectation was true for the rearfoot group, this was not the case with the forefoot group. ", "Alternatively, a new running form or style is considered more economical if it results in a reduction of oxygen consumption without a habituation period.[@bib0185] The results from Gruber et al.[@bib0165] indicated that habituation was not necessary in order for the forefoot group to have a similar running economy between footstrikes across the 3 tested speeds. ", "In the rearfoot group, performing a forefoot strike increased oxygen consumption to a large enough degree that habituation would not eventually result in forefoot running becoming more economical. ", "Therefore, the assumption that rearfoot runners would improve their performance by changing their footstrike, either immediately or after training, appear unfounded.", "\n\nA further analysis of the data in the Gruber et al.[@bib0165] study included an investigation of carbohydrate oxidation between footfall patterns. ", "Carbohydrate oxidation is a limiting factor for endurance exercise.[@bib0165] At the slow and moderate speeds of running selected in the Gruber study, carbohydrate oxidation was greater in a forefoot foot strike than in a rearfoot strike. ", "The implication here is that a forefoot strike would deplete their carbohydrate stores sooner compared to a rearfoot strike at the same running speed. ", "Therefore, switching from a mid- or forefoot strike to a rearfoot strike may also be a mechanism to conserve glycogen stores and delay when a runner would \"hit the wall\" during an endurance race.[@bib0185] This assumption is somewhat supported by Jewell and colleagues[@bib0190] who found that habitual mid- and forefoot runners tended to adopt a more posterior landing pattern, which was characterized by longer contact times and the visual appearance of an impact peak within the VGRF during the progression of a fatiguing run.", "\n\n4. ", "Changes in the VGRF impact peak {#s0025}\n==================================\n\nIn a plot of the VGRF versus time for a rearfoot strike, there is a distinct first peak referred to as the impact peak and, later in the ground contact phase, a second peak referred to as the active peak. ", "In the mid- or forefoot strike, there may not be a visible impact peak in the VGRF plotted across stance time but there will be an active peak ([Fig.", " 2](#f0015){ref-type=\"fig\"}).Fig.", " 2An exemplar vertical ground reaction force (VGRF) component versus time for a runner with a rearfoot (RF) footfall pattern and a runner with a forefoot (FF) footfall pattern.", "Fig.", " 2\n\nRunning with a mid- or forefoot strike substantially diminishes the appearance of the vertical impact peak or causes it to be visually absent. ", "This observation has led many to speculate that changing one\\'s footstrike to a mid- or forefoot strike would significantly reduce the vertical impact peak and the vertical rate of loading during a ground contact compared to the rearfoot strike.[@bib0195], [@bib0200], [@bib0205], [@bib0210] Furthermore, the implication is that, because of the absence of the impact peak and the lesser loading rate, there would be a lower risk of impact related injuries to the lower extremity.[@bib0010], [@bib0060], [@bib0215], [@bib0220]\n\nVertical impact peaks are not conspicuous in the VRGF versus time plots of runners with a mid- or forefoot strike. ", "Recent studies have found evidence of the vertical impact force in mid- or forefoot running although it was visually absent in the time-domain plots. ", "In a study by Gruber et al.[@bib0225] the VGRF was analyzed in the frequency domain using a Fourier analysis. ", "It was reported that frequencies in the 10--20 Hz range (i.e., the range of frequencies of the impact peak in rearfoot running[@bib0225]) were observed in forefoot strike runners although the amplitude of these frequencies was less than rearfoot runners ([Fig.", " 3](#f0020){ref-type=\"fig\"}). ", "While there is no obvious impact peak seen in the time domain, it appears that there is an impact in forefoot running although it may occur with a lower magnitude and loading rate than that in rearfoot running.[@bib0225]Fig.", " 3An exemplar amplitude versus frequency plot showing frequencies in the 10--20 Hz range for both rearfoot (RF) and forefoot (FF) footfall patterns.", "Fig.", " 3\n\nThen the question that arises is why the vertical impact is not visually obvious in the time domain. ", "This question can be answered by referring to Bobbert et al.[@bib0230], [@bib0235] and Shorten and Mientjes.[@bib0240] These researchers showed that the impact peak in rearfoot running was determined by the force of the lower extremity of the landing limb colliding with the ground while the active force is a result of the motion of the rest of the body. ", "This lower extremity impact force (i.e., passive peak) is superimposed on the active force of the rest of the body as it contacts the ground, which results in the typical VGRF that we often see. ", "This is illustrated in the schematic in [Fig.", " 4](#f0025){ref-type=\"fig\"}. ", "In this figure, for a rearfoot strike, we see that there are 2 different portions of the VGRF component, which represent limb contact and the contact of the rest of the body, that are ultimately added together to produce the total VGRF component that we usually see. ", "The impact and active forces are also superimposed in a forefoot strike; however, the timing of the peak deceleration of the contacting limb may occur much later in the support phase and thus is \"hidden\" by the active force of the rest of the body. ", "Gruber and colleagues[@bib0245] illustrated the impact and passive peaks in both rearfoot and forefoot strikes using a wavelet analysis. ", "In their analysis, it is clear that an impact peak exists in both rearfoot and forefoot strikes but the impact peak in forefoot running is of lesser magnitude and occurs later in the support period ([Fig.", " 5](#f0030){ref-type=\"fig\"}).Fig.", " 4A schematic of a decomposed vertical ground reaction force component of a rearfoot footfall pattern (A) and the sum of the 2 components (B).Fig.", " 4Fig.", " 5Continuous wavelet transform of the resultant ground reaction force generated during rearfoot running (A) and forefoot running (B). ", "The results indicate both footstrike patterns generate signal frequencies representative of the force of impact (i.e., 10--20 Hz). ", "Values are wavelet coefficient magnitudes indicated by color intensity. ", "Results are plotted across the stance phase for pseudo-frequencies 0--100 Hz (top row). ", "101 × 63 mm (72 × 72 dpi). ", "Adapted with permission.[@bib0245]Fig.", " 5\n\nFurthermore, we must ask whether the visual appearance or the reduction of the vertical impact peak is a reason to change footstrike pattern. ", "The influence of the impact peak and loading rate on the risk of running injury development has been a source of debate and discussion in biomechanics for many years. ", "Reducing impact forces and the rate at which they are imposed has been suggested to reduce the risk of impact related injuries. ", "However, the relationship between impact characteristics and injuries has not been established conclusively. ", "There are similar number of retrospective studies[@bib0250], [@bib0255], [@bib0260], [@bib0265] and prospective studies[@bib0270], [@bib0275], [@bib0280] that have found an association with impact characteristics and injury. ", "However, there are other studies that found no relationship between impact characteristics and injury either retrospectively[@bib0285], [@bib0290], [@bib0295], [@bib0300] or prospectively.[@bib0305], [@bib0310], [@bib0315], [@bib0320], [@bib0325] Studies by several researchers have reported a link between a higher vertical impact peak or vertical loading rate or both resulting in an impact running-related injury.[@bib0250], [@bib0255], [@bib0260], [@bib0265], [@bib0270], [@bib0275], [@bib0280] However, other researchers have shown little or no relationship between VGRF parameters and the risk of injury.[@bib0285], [@bib0290], [@bib0295], [@bib0300], [@bib0305], [@bib0310], [@bib0315], [@bib0320], [@bib0325] It is quite apparent that some level of force application is necessary for bone health.[@bib0330] However, it is unknown how much loading is necessary for bone health versus how much is detrimental to bone health. ", "For example, some studies have reported that greater impact magnitudes and loading rates were observed in samples that had fewer running injuries than those with reduced impact characteristics. ", "Nigg[@bib0335] reported that runners with greater impact peaks and higher loading rates had significantly fewer running-related injuries compared with runners with lower impact peaks and loading rates. ", "Van Mechelen[@bib0340] found that running on firmer surfaces, which would theoretically increase the impact load on the body, was not associated with the incidence of injury. ", "The argument, therefore, that reducing the impact peak and loading rate is questionable at best in terms of running-related injuries.", "\n\nThe fact that there is a force resulting from the foot-ground collision not only in a rearfoot strike, but in the mid- or forefoot strikes as well, and that relationship between these kinetic parameters and injury is tenuous at best, are both evidence that the appearance or non-appearance of an impact peak in the time domain is not sufficient for changing one\\'s footstrike. ", "Additionally, prospective running injury studies have yet to demonstrate whether one footstrike is less injurious than the other. ", "Using the VGRF to infer that forefoot running is \"safer\" than rearfoot running is not supported by evidence.", "\n\nMany other parameters, such as spatio-temoral variables and sagittal and frontal plane kinematics,[@bib0345] apart from VGRF characteristics, have been compared between footstrikes that may be related to the development of running-related overuse injuries. ", "For example, Boyer and Derrick[@bib0350] examined the differences in several factors that may contribute to the development of iliotibial band strain between habitual rearfoot and habitual mid- and forefoot runners including step width, pelvic drop, hip adduction angle, and iliotibial band strain among other variables. ", "Although some variables were statistically different between footstrikes---with some differences indicating rearfoot to be \"better\" and others indicating forefoot to be \"better\"---the authors concluded that the magnitude of the differences were small enough to suggest that one footstrike does not appear to be universally more protective against running-related injuries than the other.[@bib0350] Other investigators have also observed that a rearfoot strike may be better for one parameter but a forefoot strike may be better for another parameter. ", "In particular, there may be a shift to a greater demand on knee structures and musculature than the ankle with rearfoot running but a greater demand on ankle and foot structures and musculature than the knee with forefoot running.[@bib0075], [@bib0355], [@bib0360], [@bib0365], [@bib0370] For example, Kulmala and colleagues[@bib0075] found that forefoot runners had less patellofemoral stress than rearfoot runners but that rearfoot runners had lower plantar flexor muscle and Achilles tendon loading than forefoot runners. ", "Similarly, Rooney and Derrick[@bib0375] found that a forefoot strike resulted in greater axial ankle joint contact force compared with a rearfoot strike. ", "Collectively, this evidence suggests that switching from one footstrike to another may result in exposure to different types of injury mechanisms rather than one footstrike being more or less injurious than the other.[@bib0380], [@bib0385]\n\n5. ", "Changes in the risk of running-related injuries {#s0030}\n==================================================\n\nMost studies that have investigated injury rates between footstrike patterns have examined the rate of injury in either habitual rearfoot or habitual mid- or forefoot strikers. ", "While this is important, it does not give us any insight as to the injury rate when runners change their footstrike either from rearfoot to forefoot or from forefoot to rearfoot. ", "Prospectively measuring injury rates in those that have switched their footstrike is the only definitive way to determine if one footstrike is more protective against injury than the other.", "\n\nUntil recently, the inconclusive and speculative links between impact characteristics and running injury risk were the only evidence to support that mid- or forefoot strikers may be beneficial for preventing injury. ", "The author of a previous review paper found little to no evidence to support that alternative running styles (i.e., a forefoot strike) such as from shod using a rearfoot strike were beneficial.[@bib0385] To our knowledge, Daoud et al.[@bib0215] published the first cohort study that suggested that the occurrence of injuries was reduced in those that habitually used a mid- or forefoot strike compared to a rearfoot strike. ", "Their study reported a statistically greater incidence of running injuries per 10,000 miles of running using a rearfoot strike compared with a mid- or forefoot strike when the data were combined across sex and level of injury severity or both. ", "When the data were separated by sex and injury severity type, the only statistically significant difference was observed between female mid- or forefoot runners (*n* = 5) and the female rearfoot runners (*n* = 18). ", "Although this study was an informative first look at the rate of injury between footfall patterns, it was retrospective in design, used a very specific sample of runners (i.e., Division 1 Cross Country Collegiate Athletes) and had a relatively small sample size.[@bib0215]\n\nTo conclusively assess the risk of incurring an injury, prospective, epidemiologic studies with a large sample size must be conducted in those who have switched footstrike patterns. ", "Unfortunately, such studies are not prominent in the running injury literature to date. ", "To conduct a large prospective study, a large number of participants who utilized different footfall patterns need to be followed over a significant period of time. ", "During the time that they are followed, the participants should maintain their usual training schedule and report on any injury that is sustained. ", "In 3 relatively large-scale epidemiologic studies, investigators reported the injury risk on samples of 471[@bib0385] and 1203[@bib0390] runners and a sample of 341 male U.S. army soldiers.[@bib0395] The results in these studies were similar. ", "Neither study reported statistically significant differences in the injury rates between habitual rearfoot and mid- or forefoot strikers. ", "The 2 epidemiologic studies of Kleindienst[@bib0385] and Walther[@bib0390] reported a difference in the injury site and the type of injury incurred between footstrike pattern groups. ", "In those 2 studies, the most prevalent injuries that were incurred were midfoot dorsal pain, metatarsal stress fractures, Achilles tendinitis, and post tibial tendinitis. ", "In another study, Warr et al.[@bib0400] did not find a difference in injury rates, running mileage, or 2-mile run time between footstrike groups, indicating no performance or injury prevention benefits for either footstrike pattern.", "\n\nMore prospective randomized control trials investigating the risk of injury in both forefoot and rearfoot running are needed. ", "The question of whether mid- or forefoot striking reduces running-related injuries compared with rearfoot running cannot be answered completely without such studies. ", "The current claim that runners running using a mid- or forefoot strike have fewer running-related injuries than those running with a rearfoot strike is speculation at best and so far is unsupported by prospective epidemiologic studies.", "\n\n6. ", "Conclusion {#s0035}\n=============\n\nResearch conducted on the efficacy of changing one\\'s footstrike from a rearfoot to a mid- or forefoot strike suggests that there is no obvious benefit to such a change for the majority of runners. ", "In fact, it may be that the change in footstrike may result in stressing tissue that is not normally stressed when running with one\\'s habitual pattern, thus leading to the possibility of incurring a secondary injury. ", "Changing one\\'s footstrike to a mid- or forefoot strike may be beneficial to some but, based on the current biomechanical, physiological, and epidemiologic literature, it should not recommended for the majority of runners, particularly those who are recreational runners.", "\n\nIn summary, there are 3 key points: (1) the scientific basis for encouraging runners to change their footstrike pattern is not warranted; (2) there is little conclusive scientific evidence that a mid- or forefoot strike improves running economy, eliminates a vertical impact force at the foot-ground contact, or reduces the risk of running-related injuries; and (3) there is a need for large, prospective randomized control trials investigating the risk of injury in both forefoot and rearfoot running.", "\n\nAuthors\\' contributions {#s0040}\n=======================\n\nThe two authors contributed equally to the manuscript. ", "The authors have read and approved the final version of the manuscript, and agree with the order of presentation of the authors.", "\n\nCompeting interests {#s0045}\n===================\n\nThe authors declare that they have no competing interests.", "\n\nPeer review under responsibility of Shanghai University of Sport.", "\n" ]

{ "pile_set_name": "PubMed Central" }

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[ "The future of hydrogen as an energy source is dependent upon the development of storage media with high volumetric and gravimetric capacities. ", "Hydrogen storage has been identified as the bottleneck in the development of hydrogen-fueled vehicles. ", "Conventional storage methods (e.g. compressed gas and liquid H2) will likely be inadequate for automotive applications due to issues of safety, volumetric H2 capacity and cost. ", "An alternative to these more traditional methods is to store the hydrogen in the solid state. ", "This can be accomplished with adsorbents (e.g. carbon), where hydrogen is attached to the surface of a solid, or absorbents (e.g. metal hydrides), where hydrogen is inserted in between the atoms in a solid. ", "The key requirements for any candidate hydrogen storage material in automotive applications are high gravimetric and volumetric hydrogen densities, a release of hydrogen at moderate temperatures and pressures, and a low-cost method to recharge the material back to its original state. ", "The US Department of Energy (US DOE) hydrogen storage system goals for the year 2010 are a 6.0 weight percent (6.0 wt %) gravimetric capacity and a volumetric capacity of 0.045 kg/L. Conventional metal hydrides that can readily supply hydrogen at room temperature have storage capacities <2 wt % and therefore cannot satisfy these goals.", "\nAluminum hydride, AlH3, is an attractive alternative to the traditional metal hydrides. ", "It has a volumetric hydrogen capacity (1.48 kg/L) greater than that of liquid hydrogen and a gravimetric hydrogen capacity exceeding 10 wt %. ", "AlH3 is stable at room temperature despite an equilibrium hydrogen pressure of around 5×105 bar at 298K [1]. ", "In general, the rapid low temperature kinetics and high energy density make AlH3 an unusual and promising hydrogen storage medium for a number of applications.", "\nHowever, the conventional organometallic synthesis is a costly procedure and AlH3 is not a reversible hydride at moderate H2 pressures. ", "Incorporating dopants or catalytic additives is not likely to produce the large thermodynamic changes required to substantially reduce the equilibrium pressure. ", "Therefore, the utility of this material will depend upon the development of techniques to regenerate AlH3 from the spent Al powder in a cost effective and energetically efficient manner. ", "The present invention addresses methods to regenerate alanes (AlHx) from Al by decreasing the change in free energy during the hydrogenation reaction.", "\nThere have been a few prior attempts to hydrogenate Al to form AlHx. ", "Baranowski and Tkacz claimed to form AlH3 from Al metal using high-pressure hydrogen (28 kbar) at 300 C. [2], however this pressure is much too low in view of the free energy of formation for AlH3 via the direct reaction of Al metal with H2 gas. ", "Although this method is the most direct (AlH3 is formed from crystalline Al and 3/2H2), the H2 pressures required are much too large to be practical for any application (28 kbar is approximately thirty times the pressure at the bottom of the Mariana Trench, 11 km below sea level).", "\nBirnbaum et al. [", "3] have made attempts to hydrogenate Al by electrochemical charging, chemical charging and by exposure to an ultrasonic field. ", "These experiments resulted in small amounts of hydrogen uptake by the Al with concentrations of less than 2500 atomic parts per million (one quarter of 1% H in Al). ", "These methods are costly, inefficient and do not form AlHx in high enough yields to make it a practical hydrogen fuel source.", "\nThe conventional wet chemistry procedure for synthesizing AlH3 is through an ethereal reaction of an alkali alanate (e.g. LiAlH4, NaAlH4) with aluminum chloride (AlCl3) [4] as shown in reaction (1):AlCl3+3LiAlH4+n[(C2H5)2O]→4AlH3.1.2[(C2H5)2O]+3LiCl  (1)\nA non-solvated form of AlH3 was initially prepared by Chizinsky et al. [", "5] and subsequently by Brower et al. [", "6] by heating in the presence of a complex metal hydride under reduced pressure. ", "The synthesis was extremely sensitive to the desolvation conditions (e.g. temperature and time) and small alterations lead to the precipitation of different AlH3 polymorphs. ", "γ-AlH3 formed in the presence of excess LiAlH4, while β-AlH3 formed in the presence of excess LiAlH4 and LiBH4 [5]. ", "In both cases, a slightly higher temperature (70 C.) and/or a longer heating time lead to the formation of α-AlH3. ", "Although this procedure can be used to make pure AlH3, the cost of the starting materials (LiAlH4 and AlCl3) would be too high for widespread applications of AlH3 as a hydrogen storage material.", "\nThe present invention introduces new methods for regeneration of AlHx at reduced H2 gas pressures and temperatures through consideration of and adjustment for basic principles of the thermodynamics of the regeneration reaction." ]

{ "pile_set_name": "USPTO Backgrounds" }

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[ "Capture myopathy in pronghorns in Alberta, Canada.", "\nFrom 1971 to 1975, inclusive, 594 pronghorns (Antilocapra americana) were drive trapped in Alberta; subsequently, 74 of these animals were transported to enclosures. ", "Deaths attributable to capture myopathy (CM) occurred in 20 of the trapped pronghorns and in 17 of the pronghorns that were trapped and subsequently transported. ", "Two neonatal pronghorns that had been pursued died with signs and lesions similar to those seen in adult pronghorns affected with CM. ", "The diagnosis of CM was based on history, clinical signs, clinico-pathologic findings, and gross and histologic lesions. ", "Clinical signs of CM included depression, stiffness, weakness, incoordination, recumbency, and paralysis; myoglobinuria was observed in 1 neonatal animal. ", "Of the pronghorns that died, fewer than one-half died acutely during processing, whereas the remainder died from 1 to 13 days following their release. ", "Gross and histologic lesions were observed in the large muscles of the hindlimbs of most affected pronghorns. ", "Values for serum enzymes, potassium, glucose, and creatinine, were higher for drive-trapped pronghorns than for tame, hand-reared pronghorns. ", "These findings indicated extensive damage to muscle and to other organs as a result of the capture procedures." ]

{ "pile_set_name": "PubMed Abstracts" }

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[ "import com.github.jengelman.gradle.plugins.shadow.tasks.", "ShadowJar\n\ndescription = \"Kotlin Library (KLIB) metadata manipulation library\"\n\nplugins {\n kotlin(\"jvm\")\n id(\"jps-compatible\")\n}\n\ngroup = \"org.jetbrains.kotlinx\"\n\nval deployVersion = findProperty(\"kotlinxMetadataKlibDeployVersion\") as String?", "\nversion = deployVersion ?: \"", "0.0.1-SNAPSHOT\"\n\nsourceSets {\n \"main\" { projectDefault() }\n}\n\nval shadows by configurations.creating {\n isTransitive = false\n}\nconfigurations.getByName(\"compileOnly\").extendsFrom(shadows)\nconfigurations.getByName(\"testCompile\").extendsFrom(shadows)\n\ndependencies {\n compile(kotlinStdlib())\n shadows(project(\":kotlinx-metadata\"))\n shadows(project(\":core:compiler.common\"))\n shadows(project(\":core:metadata\"))\n shadows(project(\":core:deserialization\"))\n shadows(project(\":core:deserialization.common\"))\n shadows(project(\":compiler:serialization\"))\n shadows(project(\":kotlin-util-klib-metadata\"))\n shadows(project(\":kotlin-util-klib\"))\n shadows(protobufLite())\n}\n\nif (deployVersion !", "= null) {\n publish()\n}\n\nnoDefaultJar()\n\nruntimeJar(tasks.register<ShadowJar>(\"shadowJar\")) {\n callGroovy(\"manifestAttributes\", manifest, project)\n manifest.attributes[\"Implementation-Version\"] = version\n\n from(mainSourceSet.output)\n exclude(\"**/*.proto\")\n configurations = listOf(shadows)\n relocate(\"org.jetbrains.kotlin\", \"kotlinx.metadata.internal\")\n}\n\nsourcesJar {\n for (dependency in shadows.dependencies) {\n if (dependency is ProjectDependency) {\n val javaPlugin = dependency.dependencyProject.convention.findPlugin(JavaPluginConvention::class.java)\n if (javaPlugin !", "= null) {\n from(javaPlugin.sourceSets[\"main\"].allSource)\n }\n }\n }\n}\n\njavadocJar()\n" ]

{ "pile_set_name": "Github" }

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[ "[Peroperative \"lavage\" and primary anastomosis in acute left-sided colon ileus].", "\nA description of technique, course and results of operation for left-sided obstruction of the colon with primary resection, perioperative lavage of the colon and primary anastomosis. ", "Retrospective examination of case records. ", "From January 1st 1994-December 31st 1997 eight operations were performed including primary resection, perioperative lavage and primary anastomosis. ", "No anastomotic leaks were found. ", "One patient died five days postoperatively due to cardiac complications. ", "Three patients had postoperative cardiopulmonary complications treated medically. ", "One patient had rupture of the fascia, was reoperated, experienced wound infection, transient serum elevation of liver enzymes and underwent ERCP with papillotomy and extraction of stones from the common bile duct two months postoperatively. ", "In this small series the technique has appeared safe, thus confirming previous reports." ]

{ "pile_set_name": "PubMed Abstracts" }

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[ "[Tinnitus: an etiologic, diagnostic and therapeutic problem].", "\nTinnitus as an etiological, diagnostic and therapeutic problem in everyday otorhinolaryngological practice has been described in this paper and the diseases and conditions leading to tinnitus discussed. ", "A diagnostic procedure, by means of which attempts have been made to establish the cause of the noise has been presented. ", "Contemporary methods of treating tinnitus have been reviewed on the basis of ample descriptions from the literature." ]

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[ "Q:\n\nWhat is the focal length and image plane distance from this raytracing formula\n\nI have a 4x4 camera matrix comprised of right, up, forward and position vectors.", "\nI raytrace the scene with the following code that I found in a tutorial but don't really entirely understand it: \nfor (int i = 0; i < m_imageSize.width; ++i)\n{\n for (int j = 0; j < m_imageSize.height; ++j)\n {\n u = (i + .5f) / (float)(m_imageSize.width - 1) - .5f;\n v = (m_imageSize.height - 1 - j + .5f) / (float)(m_imageSize.height - 1) - .5f;\n\n Ray ray(cameraPosition, normalize(u*cameraRight + v*cameraUp + 1 / tanf(m_verticalFovAngleRadian) *cameraForward));\n\nI have a couple of questions:\n\nHow can I find the focal length of my raytracing camera?", "\nWhere is my image plane? ", "\nWhy cameraForward needs to be multiplied with this 1/tanf(m_verticalFovAngleRadian)?", "\n\nA:\n\nFocal length is a property of lens systems. ", "The camera model that this code uses, however, is a pinhole camera, which does not use lenses at all. ", "So, strictly speaking, the camera does not really have a focal length. ", "The corresponding optical properties are instead expressed as the field of view (the angle that the camera can observe; usually the vertical one). ", "You could calculate the focal length of a camera that has an equivalent field of view with the following formula (see Wikipedia):\nFOV = 2 * arctan (x / 2f)\nFOV diagonal field of view \nx diagonal of film; by convention 24x36 mm -> x=43.266 mm\nf focal length\n\nThere is no unique image plane. ", "Any plane that is perpendicular to the view direction can be seen as the image plane. ", "In fact, the projected images differ only in their scale.", "\nFor your last question, let's take a closer look at the code: \nu = (i + .5f) / (float)(m_imageSize.width - 1) - .5f;\nv = (m_imageSize.height - 1 - j + .5f) / (float)(m_imageSize.height - 1) - .5f;\n\nThese formulas calculate u/v coordinates between -0.5 and 0.5 for every pixel, assuming that the entire image fits in the box between -0.5 and 0.5.", "\nu*cameraRight + v*cameraUp \n\n... is just placing the x/y coordinates of the ray on the pixel.", "\n... + 1 / tanf(m_verticalFovAngleRadian) *cameraForward\n\n... is defining the depth component of the ray and ultimately the depth of the image plane you are using. ", "Basically, this is making the ray steeper or shallower. ", "Assume that you have a very small field of view, then 1/tan(fov) is a very large number. ", "So, the image plane is very far away, which produces exactly this small field of view (when keeping the size of the image plane constant since you already set the x/y components). ", "On the other hand, if the field of view is large, the image plane moves closer. ", "Note that this notion of image plane is only conceptual. ", "As I said, all other image planes are equally valid and would produce the same image. ", "Another way (and maybe a more intuitive one) to specify the ray would be\nu * tanf(m_verticalFovAngleRadian) * cameraRight \n+ v * tanf(m_verticalFovAngleRadian) * cameraUp \n+ 1 * cameraForward));\n\nAs you see, this is exactly the same ray (just scaled). ", "The idea here is to set the conceptual image plane to a depth of 1 and scale the x/y components to adapt the size of the image plane. ", "tan(fov) (with fov being the half field of view) is exactly the size of the half image plane at a depth of 1. ", "Just draw a triangle to verify that. ", "Note that this code is only able to produce square image planes. ", "If you want to allow rectangular ones, you need to take into account the ratio of the side lengths.", "\n\n" ]

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[ "Glenn G. Wolcott, Esq., ", "Office of the General Counsel, GAO, participated in the preparation of the decision.", "\n\nDIGEST\n\nWhere agency previously failed to meaningfully consider potential conflicts of interest created by awardee's contract performance of electromagnetic spectrum engineering services that could affect awardee's other spectrum-related interests, agency's corrective actions adequately remedied the prior procurement flaws, where the agency performed and documented its review of the spectrum-related products and services produced or provided by the awardee and the awardee's competitors, identified the awardee's customers of spectrum-related products and services, considered the impact that performance of the contract requirements may have on awardee's spectrum-related interests, and reasonably concluded that awardee's plan to perform conflicted portions of the contract requirements through use of –firewalled— subcontractors will adequately avoid, neutralize, or mitigate the potential conflicts of interest with minimal impact on performance quality.", "\n\nIn February 2005, DISA issued RFP No. ", "HC1047-05-R-4009, seeking proposals to –provide the JSC with Electromagnetic Spectrum Engineering (ESE) services to facilitate improved mission effectiveness.— RFP at 4.[2] The solicitation laid out a comprehensive list of the various activities the contractor will be required to perform.[3] Offerors were advised that proposals would be evaluated on the basis of technical factors, past performance, and cost/price, and that award would be based on the proposal offering the –best overall value— to the government. ", "RFP at 62.", "\n\nIn April 2005, proposals were submitted by three offerors, including Alion and ITT.[4] Thereafter, discussions were conducted, proposal revisions submitted, and final proposals evaluated. ", "In July 2005, ITT's proposal was selected for award.", "\n\nIn August 2005, Alion filed its first protest, challenging the award to ITT on various bases, including that the agency failed to reasonably consider the OCIs created by ITT's performance of the contract requirements. ", "Thereafter, the agency advised this Office that it was taking corrective action, to include an amendment of the RFP's OCI provisions[5] and a request that offerors submit revised OCI plans. ", "We dismissed Alion's August 2005 protest pending completion of the agency's corrective actions.", "\n\nThereafter, ITT and Alion submitted revised OCI plans,[6] and the agency performed an assessment regarding the potential for conflicts of interest to arise. ", "With regard to contract performance by ITT, the agency concluded that there was a –maximum potential— for 15 percent of the contract requirements to create conflicts, but stated that it considered this estimate to be –high— and that actual OCIs were expected to be –significantly lower.— Addendum to Source Selection Authority Decision, Sept. 22, 2005, at 2. ", "Based on the agency's OCI assessment, and ITT's intent to rely on –firewalled— subcontractors for performance of the potentially conflicted portions of the contract requirements, the agency concluded that ITT's OCI plan was acceptable and, in September 2005, again selected ITT's proposal for award.[7]\n\nIn September 2005, Alion filed another protest challenging the agency's source selection decision, again asserting, among other things, that the agency's OCI assessment was flawed.", "\n\nOur review of the procurement record, provided in response to Alion's September 2005 protest, established that the agency's OCI assessment failed to meaningfully consider the scope and extent of ITT's spectrum'related interests. ", "Specifically, the agency's assessment failed to meaningfully address the fact that ITT, as well as ITT's competitors, manufacture and market multiple spectrum'dependent products, and that these products are sold to, and used by, multiple customers, including various departments within the U.S. government, foreign governments, and commercial customers worldwide. ", "Additionally, the agency's assessment appeared to assume that only performance of acquisition-related activities under the contract would create potential OCIs--failing to recognize that OCIs are created any time contract performance involves a contractor's exercise of judgment with regard to matters that have the potential to affect other contractor-related interests. ", "See FAR sections 9.505, 9.508. ", "In sum, the agency's OCI assessment failed to recognize that ITT's performance of various contract activities could significantly affect the spectrum-related interests of ITT, ITT's competitors, and ITT's customers. ", "In January 2006, our Office issued a decision sustaining Alion's protest. ", "Alion Sci. & ", "Tech. ", "Corp., B'297022.3, Jan. 9, 2006, 2006 CPD para. ", "2.", "\n\nIn our January 2006 decision, we recommended that the agency reconsider the extent and potential impact on contract performance resulting from ITT's spectrum'related interests. ", "Specifically, we recommended that the agency fully identify ITT's involvement with spectrum-related products and services and similarly identify ITT's competitors and customers with spectrum-related interests. ", "We further recommended that, upon identification of the spectrum-related interests of ITT, ITT's competitors, and ITT's customers, the agency reconsider the potential OCIs reasonably created by ITT's performance of the various contract requirements.[8] Finally, we recommended, upon consideration of the full extent of potential OCIs, that the agency also consider the impact that ITT's reliance on –firewalled— subcontractors would have on contract performance.", "\n\nFollowing receipt of our January 2006 decision, the agency stated that it would implement our recommendations. ", "In May 2006, the agency completed its report documenting the actions taken in response to our January 2006 decision. ", "As discussed in more detail below, the agency's reconsideration of the factors creating potential OCIs for ITT resulted in the agency's recognition that ITT's performance of the contract requirements will create a higher level of potential OCIs than the agency had previously believed.[9] Nonetheless, after considering the impact that the higher level of potential OCIs will have on contract performance, the agency again concluded that award to ITT will result in the best overall value to the government.", "\n\nIn June 2006, the agency notified Alion that ITT had again been selected for contract award. ", "On June 20, Alion filed this protest challenging that selection. ", "As discussed below, we deny the protest.", "\n\nDISCUSSION\n\nAlion's June 2006 protest references various portions of this Office's January 2006 decision, asserting generally that the agency failed to reasonably implement the recommendations contained therein. ", "Alion Protest, June 20, 2006, at 3. ", "More specifically, Alion maintains that the agency's reconsideration of ITT's potential OCIs is still unreasonably low, and that the agency has not reasonably considered the impact that ITT's use of –firewalled— subcontractors will have on contract performance. ", "Id. at 4-5.[10] Alion requests that this Office recommend that DISA –declare ITT disqualified and ineligible to receive any award under the subject Solicitation,— and that DISA –immediately reaward the JSC spectrum engineering services requirements to Alion.— Id. at 8-9. ", "We reject Alion's arguments and requests.", "\n\nAs noted above, in response to this Office's January 2006 decision, DISA performed and documented a review of the potential OCIs that ITT's performance of the contract requirements would create. ", "Impaired Objectivity (IO) Organizational Conflict of Interest Assessment of ITT Industries, Inc., May 31, 2006. ", "In connection with this review, the agency sought and received additional information from both ITT and Alion regarding their respective spectrum-related interests. ", "Following receipt of the additional offeror-provided information, the agency conducted its own research and analysis regarding the scope of the offerors' spectrum-related interests[11] and, in the context of those interests, assessed the extent to which performance of the various contract requirements would create potential OCIs.", "\n\nIn assessing ITT's potential OCIs, the agency first identified ITT's various business groups, and the divisions within those groups, reviewing the types of products and services produced or provided by each group generally and, within the groups, the products and services of each division specifically.[12] With regard to the divisions that are involved with spectrum-related products or services, the agency further identified the specific products and services those divisions produce or provide.[13]Id. ", "at 6-15. ", "The agency also identified ITT's competitors,[14] as well as its worldwide customers and teaming partners,[15] in the various markets. ", "Id.The agency's analysis also identified where ITT's various spectrum-related products and services are generally used or deployed. ", "Id. at 11. ", "Finally, the agency's analysis took into consideration the organizations and entities, including foreign governments, with which DOD competes for electromagnetic spectrum access. ", "Id. at 15'19.", "\n\nUpon completing its research regarding the scope of ITT's spectrum-related interests, the agency reconsidered the nature of the contract activities to be performed, as identified in the solicitation, focusing on the extent to which the anticipated activities could create OCIs for ITT. ", "Id. at 20-26. ", "In conjunction with the agency's review of the activities listed in the solicitation, the agency also performed a review of all JSC projects that were performed under Alion's incumbent contract during the immediately preceding fiscal year, making judgments as to the potential OCIs that such activities would create for ITT, and calculating the dollar value of such potentially conflicted work. ", "Id. at 27-39. ", "Finally, the agency considered the effect that ITT's reliance on –firewalled— subcontractors to perform potentially conflicted portions of the contract requirements would have on the quality of contract performance. ", "Id. at 33'39.", "\n\nBased on all of the above research and analysis, the agency concluded that the level of potential OCIs that ITT is likely to experience under the contract is, indeed, higher than what the agency had initially believed. ", "As noted above, the agency now estimates that nearly one-third of the total contract effort could create OCIs for ITT.[16] CO Statement at 5, 15. ", "Nonetheless, the agency concluded that the contract activities creating potential OCIs for ITT could be reasonably segregated, and adequately avoided, neutralized, or mitigated, through contract performance by –firewalled— subcontractors. ", "Accordingly, the agency determined that ITT's proposal still offered the best overall value to the government.", "\n\nAlion continues to assert, as it has in its various prior protest submissions, that the agency's OCI assessment is inaccurate or otherwise unreasonable. ", "Based on our review of the current record, we do not agree.", "\n\nContracting officers are required to identify potential conflicts of interest as early in the acquisition process as possible, and to avoid, neutralize, or mitigate such conflicts to prevent the existence of conflicting roles that might impair a contractor's objectivity. ", "In assessing potential OCIs, the FAR directs the contracting officer to examine each contracting situation individually on the basis of its particular facts and the nature of the proposed contract, and to exercise common sense, good judgment, and sound discretion with regard to whether a conflict exists and, if so, the appropriate means for resolving it; the primary responsibility for determining whether a conflict is likely to arise, and the resulting appropriate action, rests with the contracting agency. ", "FAR sect. ", "9.505; RMG Sys., ", "Ltd., B'281006, Dec. 18, 1998, 98'2 CPD para. ", "153 at 4; Epoch Eng'g, Inc., B-276634, July 7, 1997, 97-2 CPD para. ", "72 at 5. ", "Once an agency has given meaningful consideration to potential conflicts of interest, our Office will not sustain a protest challenging a determination in this area unless the determination is unreasonable or unsupported by the record. ", "SRS Techs., ", "B'258170.3, Feb. 21, 1995, 95-1 CPD para. ", "95 at 9.", "\n\nHere, Alion's protest has not identified any material aspect of the agency's review and analysis that renders the agency's conclusions unreasonable. ", "Specifically, Alion has not identified any material aspect of ITT's involvement in producing or providing spectrum-related products and services that the agency has overlooked or otherwise ignored. ", "Based on the discussion above, we believe the agency has reasonably identified the scope and extent of ITT's involvement with spectrum-related products and services, as well as reasonably identified ITT's competitors and customers, including foreign governments, that possess spectrum-related interests.", "\n\nFurther, the agency's consideration of each particular contract activity listed in the solicitation, along with consideration of every contract project performed during the preceding fiscal year, appears to be thorough and complete. ", "To the extent Alion has expressed disagreement with various agency judgments regarding the various solicitation activities and/or performance of particular past projects that could create OCIs for ITT, Alion's arguments fail to identify any material flaws that would render the agency's overall conclusions unreasonable. ", "A protester's mere disagreement with an agency's judgment does not establish that the judgment was unreasonable. ", "See, e.g., Hanford Envtl. ", "Health Found., ", "B-292858, B-292858.2, Apr. 7, 2004, 2004 CPD para. ", "164 at 4. ", "On this record, we find no basis to question the reasonableness of the agency's conclusion regarding the portion of contract requirements that could create OCIs for ITT.[17]\n\nAlion next protests that the agency failed to meaningfully address the impact that ITT's reliance on –firewalled— subcontractors for performance of conflicted contract requirements would have on the quality of ITT's contract performance. ", "We do not agree.", "\n\nAs noted above, in its actions responding to this Office's January 2006 decision, the agency specifically considered the effect that ITT's reliance on –firewalled— subcontractors would have on the quality of contract performance. ", "Impaired Objectivity (IO) Organizational Conflict of Interest Assessment of ITT Industries, Inc., May 31, 2006, at 33-39. ", "In performing its analysis of this issue, the agency first noted that, pursuant to the task ordering process to be used in performing this contract, separate task orders will be issued for activities where there are potential OCIs. ", "Id. at 33-34. ", "The agency noted that in ITT's September 2005 proposal and OCI plan, ITT specifically recognized that certain activities would create potential OCIs which would be performed by –firewalled— subcontractors, and that its proposal specifically contemplated that ITT's subcontractors would perform up to [deleted] percent of the total contract effort. ", "Id. at 34. ", "In reviewing this matter, the agency considered the projected breakout of work to be performed by the various subcontractors, concluding that –the overlapping of competencies between ITT and its firewalled subcontractors is sufficient to resolve all the cases of IO [impaired objectivity] OCI,— and noting that –[e]ven in those functional task areas where the percentage of conflicted work is high, using firewalled subcontractors should be workable within the construct of the original ITT Technical Proposal.— Id. at 34-35. ", "The agency's report follows up this conclusion with a more detailed analysis addressing which of ITT's proposed subcontractors could perform conflicted work under each of the various task areas. ", "Id.In concluding that the quality of contract performance would not be materially affected by the higher level of potential OCIs, the agency specifically considered various factors affecting quality, including subcontractor competence, cost, and timeliness. ", "Based on its consideration of these issues, the agency concluded that –[t]he overall effect of segregating tasks and using firewalled subcontractors to perform them has minimal impact on cost, timeliness, and quality.— Id. at 38.", "\n\nAlion complains that the agency cannot, and should not, trust ITT to properly identify all OCIs during contract performance. ", "Alion's protest on this issue suggests that ITT's input with regard to potential OCIs during contract performance will be dispositive. ", "The record is to the contrary. ", "Specifically, although the agency intends for ITT to be actively involved in identifying potential conflicts during contract performance, the record is clear that the agency will--and in our view, must--independently review each task order for potential OCIs on an ongoing basis.[18]\n\nHere, based on the record as discussed above, the agency reasonably considered the impact on the quality of performance caused by ITT's reliance on –firewalled— subcontractors to perform conflicted contract requirements, concluding that the impact would be minimal. ", "Although Alion disagrees with that judgment, it has not persuasively identified any material basis for concluding that the agency's judgment is unreasonable. ", "In this regard, procuring agencies are generally in the best position to determine their actual requirements and the best method for meeting them. ", "In reviewing protests challenging an agency's assessments with regard to a particular performance approach, our Office will not substitute our judgment for that of the agency; rather, we will review the record to determine whether the judgments are reasonable and consistent with the solicitation criteria. ", "See, e.g., RMS Indus., ", "B'247233, B-247234, May 1, 1992, 92-1 CPD para. ", "412. ", "On this record, we find no basis to sustain Alion's protest challenging the reasonableness of the agency's consideration and analysis regarding the impact of ITT's reliance on –firewalled— subcontractors to perform conflicted requirements.", "\n\n[1] Alion, or one of its predecessor entities, has been the incumbent contractor for the requirements at issue here for over 40 years.", "\n\n[2] Since issuance of the solicitation, the JSC has been consolidated with DISA's Defense Spectrum Office and is now a –field office— within DISA's Defense Spectrum Organization. ", "Seewww.disa.mil/main/prodsol/dso.html.", "\n\n[3] The solicitation identified six task areas--–Operational Spectrum Support,— –E3 [electromagnetic environmental effects] and Spectrum Engineering,— –Modeling and Simulation,— –Information Management,— –Research and Evaluate Emerging Technologies,— and –Technical Advice—--and listed particular activities the contractor will be expected to perform under each area. ", "RFP at 4. ", "The listed activities included –analyz[ing] incidents of electromagnetic interference (EMI), determine causes, and recommend methods of resolution,— –coordinating electromagnetic compatibility (EMC) standards,— –analyzing equipment and systems for potential E3 problems and recommending solutions,— –assisting the acquisition community by assessing E3,— –providing assistance in acquiring host nation approval for equipment operation,— –determining electromagnetic spectrum implications and opportunities for exploitation by DOD [Department of Defense],— and –analyzing national and international electromagnetic spectrum issues and advising executive decisionmakers on the technical viability of policy and implementation options.— Id.\n\n[4] The third offeror's proposal was subsequently eliminated from consideration, is not relevant to Alion's protest, and is not further discussed in this decision.", "\n\n[5] As ultimately amended, the RFP provided that offerors' proposals with regard to OCI issues would be assessed as acceptable or unacceptable pursuant to subpart 9.5 of the Federal Acquisition Regulation (FAR).", "\n\n[6] ITT's plan identified various potential OCIs that could be encountered in performing the contract requirements and stated that, in instances where potential OCIs are identified, the conflicted requirements would be assigned to an ITT subcontractor and a –firewall— would be created between ITT and the subcontractor. ", "ITT OCI Plan, Sept. 9, 2005, at 14.", "\n\n[7] ITT's proposal was rated higher than Alion's proposal with regard to the technical evaluation factors and offered a slightly lower evaluated cost/price.", "\n\n[9] As noted above, the agency initially concluded that significantly less than 15 percent of the total contract requirements would create potential OCIs for ITT. ", "The agency has now concluded that nearly one-third of the contract requirements will create potential OCIs for ITT. ", "Contracting Officer's (CO) Statement at 5, 15.", "\n\n[12] ITT is divided into several business groups. ", "The agency determined that the business divisions involved with spectrum-dependent products and services are all within the Defense Electronics and Services group; these divisions include AES (the division that submitted the proposal here), the Aerospace/Communications division, the Electronics Systems division, the Space Systems division, and the Systems division. ", "Id. at 6. ", "The agency states that the Defense Electronics and Services group generated approximately $2.4 billion in revenues (35% of ITT's total revenues) in fiscal year 2004. ", "Id. at 16.", "\n\n[15] Customers of ITT's divisions involved with spectrum-dependent products or services include commercial organizations worldwide, as well as the governments of –Brazil, UK, Sweden, Egypt, Singapore, South Korea, and 32 other countries.— Id. at 9.", "\n\n[16] The agency's calculation with regard to the percentage of potential OCIs is based on the agency's review of every project completed under the incumbent contract during the preceding fiscal year, identification of those projects that would create potential OCIs for ITT, and calculation of the total dollars spent on such projects, as a percentage of the total contract dollars spent during the fiscal year.", "\n\n[17] Alion makes much of the fact that, following submission of this protest and Alion's subsequent arguments regarding prior performance of particular projects, the agency increased its calculation of potential OCIs from 29 percent to 32 percent of the total contract effort. ", "Alion Comments, Aug. 7, 2006, at 5-7. ", "We do not view this adjustment in the agency's assessment as a basis for sustaining the protest. ", "In this regard, we do not view an agency's projection of potential OCIs to be an exact science, nor do we expect that an OCI projection will be calculated to a mathematical certainty. ", "Rather than requiring a precisely calculated forecast of future OCIs, FAR subpart 9.5 mandates that an agency reasonably and realistically recognize and consider the potential for OCIs. ", "Here, the agency has met its obligation.", "\n\n[18] In testifying before this Office during the hearing we conducted in connection with Alion's September 2005 protest, the contracting officer stated: –We will not rely on ITT's analysis alone. ", "We will independently perform that analysis, and only after we're satisfied that there are no OCI issues[,] or that – if an OCI issue is identified, that a proper mitigation strategy is incorporated in that task order when we issue the task order.— Hearing Transcript, Dec. 1, 2005, at 26-27.", "\n\n[19] In its various protest submissions, Alion made various additional allegations regarding the agency's selection of ITT, including the assertion that the agency's source selection authority and/or other agency personnel were biased against Alion due to Alion's long-time incumbency. ", "We have reviewed the entire record, considering all of Alion's various allegations, and find no basis for sustaining the protest." ]

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[ "\"The original soundtrack, created by Park Chan-wook and music director Cho Young-wook, really dazzles audiences and the music further heightens the thriller aspect of the movie.\" — ", "theplaylist.net\n\nOriginal soundtrack to the 2016 South Korean psychological thriller directed by Park Chan-wook. ", "The film was inspired from the novel Fingersmith by Welsh author Sarah Waters, with the setting changed from Victorian era Britain to 1930s Korea under Japanese colonial rule. ", "There are 38 songs that were used in the shining moments of the characters in the movie, including \"Imi Oneun Sori (The Footsteps of My Dear Love)\" which was introduced at the 69th Cannes Film Festival, and the title song \"The Tree From Mount Fuji.\"", "\n\nThe soundtrack also includes the film's most famous dialogue such as \"My saviour who ruined my life\" and \"The doll of a maid.\" \"", "Keeping the suspense formed in the collision of four people, but focusing on balancing the two big flows so that the lady and maid's melody do not fade.\" — ", "Cho Young-wook, Music Director of \"The Handmaiden.\"" ]

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[ "// Copyright (c) 2016, 2018, 2020, Oracle and/or its affiliates. ", " All rights reserved.", "\n// This software is dual-licensed to you under the Universal Permissive License (UPL) 1.0 as shown at https://oss.oracle.com/licenses/upl or Apache License 2.0 as shown at http://www.apache.org/licenses/LICENSE-2.0. ", "You may choose either license.", "\n// Code generated. ", "DO NOT EDIT.", "\n\n// Core Services API\n//\n// API covering the Networking (https://docs.cloud.oracle.com/iaas/Content/Network/Concepts/overview.htm),\n// Compute (https://docs.cloud.oracle.com/iaas/Content/Compute/Concepts/computeoverview.htm), and\n// Block Volume (https://docs.cloud.oracle.com/iaas/Content/Block/Concepts/overview.htm) services. ", "Use this API\n// to manage resources such as virtual cloud networks (VCNs), compute instances, and\n// block storage volumes.", "\n//\n\npackage core\n\nimport (\n\t\"encoding/json\"\n\t\"github.com/oracle/oci-go-sdk/v25/common\"\n)\n\n// DhcpOptions A set of DHCP options. ", "Used by the VCN to automatically provide configuration\n// information to the instances when they boot up. ", "There are two options you can set:\n// - DhcpDnsOption: Lets you specify how DNS (hostname resolution) is\n// handled in the subnets in your VCN.", "\n// - DhcpSearchDomainOption: Lets you specify\n// a search domain name to use for DNS queries.", "\n// For more information, see DNS in Your Virtual Cloud Network (https://docs.cloud.oracle.com/Content/Network/Concepts/dns.htm)\n// and DHCP Options (https://docs.cloud.oracle.com/Content/Network/Tasks/managingDHCP.htm).", "\n// To use any of the API operations, you must be authorized in an IAM policy. ", "If you're not authorized,\n// talk to an administrator. ", "If you're an administrator who needs to write policies to give users access, see\n// Getting Started with Policies (https://docs.cloud.oracle.com/Content/Identity/Concepts/policygetstarted.htm).", "\n// **Warning:** Oracle recommends that you avoid using any confidential information when you\n// supply string values using the API.", "\ntype DhcpOptions struct {\n\n\t// The OCID of the compartment containing the set of DHCP options.", "\n\tCompartmentId *string `mandatory:\"true\" json:\"compartmentId\"`\n\n\t// Oracle ID (OCID) for the set of DHCP options.", "\n\tId *string `mandatory:\"true\" json:\"id\"`\n\n\t// The current state of the set of DHCP options.", "\n\tLifecycleState DhcpOptionsLifecycleStateEnum `mandatory:\"true\" json:\"lifecycleState\"`\n\n\t// The collection of individual DHCP options.", "\n\tOptions []DhcpOption `mandatory:\"true\" json:\"options\"`\n\n\t// Date and time the set of DHCP options was created, in the format defined by RFC3339 (https://tools.ietf.org/html/rfc3339).", "\n\t// Example: `2016-08-25T21:10:29.600Z`\n\tTimeCreated *common.", "SDKTime `mandatory:\"true\" json:\"timeCreated\"`\n\n\t// The OCID of the VCN the set of DHCP options belongs to.", "\n\tVcnId *string `mandatory:\"true\" json:\"vcnId\"`\n\n\t// Defined tags for this resource. ", "Each key is predefined and scoped to a\n\t// namespace. ", "For more information, see Resource Tags (https://docs.cloud.oracle.com/Content/General/Concepts/resourcetags.htm).", "\n\t// Example: `{\"Operations\": {\"CostCenter\": \"42\"}}`\n\tDefinedTags map[string]map[string]interface{} `mandatory:\"false\" json:\"definedTags\"`\n\n\t// A user-friendly name. ", "Does not have to be unique, and it's changeable.", "\n\t// Avoid entering confidential information.", "\n\tDisplayName *string `mandatory:\"false\" json:\"displayName\"`\n\n\t// Free-form tags for this resource. ", "Each tag is a simple key-value pair with no\n\t// predefined name, type, or namespace. ", "For more information, see Resource Tags (https://docs.cloud.oracle.com/Content/General/Concepts/resourcetags.htm).", "\n\t// Example: `{\"Department\": \"Finance\"}`\n\tFreeformTags map[string]string `mandatory:\"false\" json:\"freeformTags\"`\n}\n\nfunc (m DhcpOptions) String() string {\n\treturn common.", "PointerString(m)\n}\n\n// UnmarshalJSON unmarshals from json\nfunc (m *DhcpOptions) UnmarshalJSON(data []byte) (e error) {\n\tmodel := struct {\n\t\tDefinedTags map[string]map[string]interface{} `json:\"definedTags\"`\n\t\tDisplayName *string `json:\"displayName\"`\n\t\tFreeformTags map[string]string `json:\"freeformTags\"`\n\t\tCompartmentId *string `json:\"compartmentId\"`\n\t\tId *string `json:\"id\"`\n\t\tLifecycleState DhcpOptionsLifecycleStateEnum `json:\"lifecycleState\"`\n\t\tOptions []dhcpoption `json:\"options\"`\n\t\tTimeCreated *common.", "SDKTime `json:\"timeCreated\"`\n\t\tVcnId *string `json:\"vcnId\"`\n\t}{}\n\n\te = json.", "Unmarshal(data, &model)\n\tif e !", "= nil {\n\t\treturn\n\t}\n\tvar nn interface{}\n\tm.DefinedTags = model.", "DefinedTags\n\n\tm.DisplayName = model.", "DisplayName\n\n\tm.FreeformTags = model.", "FreeformTags\n\n\tm.CompartmentId = model.", "CompartmentId\n\n\tm.Id = model.", "Id\n\n\tm.LifecycleState = model.", "LifecycleState\n\n\tm.Options = make([]DhcpOption, len(model.", "Options))\n\tfor i, n := range model.", "Options {\n\t\tnn, e = n.UnmarshalPolymorphicJSON(n.", "JsonData)\n\t\tif e !", "= nil {\n\t\t\treturn e\n\t\t}\n\t\tif nn !", "= nil {\n\t\t\tm.Options[i] = nn.(DhcpOption)\n\t\t} else {\n\t\t\tm.Options[i] = nil\n\t\t}\n\t}\n\n\tm.TimeCreated = model.", "TimeCreated\n\n\tm.VcnId = model.", "VcnId\n\n\treturn\n}\n\n// DhcpOptionsLifecycleStateEnum Enum with underlying type: string\ntype DhcpOptionsLifecycleStateEnum string\n\n// Set of constants representing the allowable values for DhcpOptionsLifecycleStateEnum\nconst (\n\tDhcpOptionsLifecycleStateProvisioning DhcpOptionsLifecycleStateEnum = \"PROVISIONING\"\n\tDhcpOptionsLifecycleStateAvailable DhcpOptionsLifecycleStateEnum = \"AVAILABLE\"\n\tDhcpOptionsLifecycleStateTerminating DhcpOptionsLifecycleStateEnum = \"TERMINATING\"\n\tDhcpOptionsLifecycleStateTerminated DhcpOptionsLifecycleStateEnum = \"TERMINATED\"\n)\n\nvar mappingDhcpOptionsLifecycleState = map[string]DhcpOptionsLifecycleStateEnum{\n\t\"PROVISIONING\": DhcpOptionsLifecycleStateProvisioning,\n\t\"AVAILABLE\": DhcpOptionsLifecycleStateAvailable,\n\t\"TERMINATING\": DhcpOptionsLifecycleStateTerminating,\n\t\"TERMINATED\": DhcpOptionsLifecycleStateTerminated,\n}\n\n// GetDhcpOptionsLifecycleStateEnumValues Enumerates the set of values for DhcpOptionsLifecycleStateEnum\nfunc GetDhcpOptionsLifecycleStateEnumValues() []DhcpOptionsLifecycleStateEnum {\n\tvalues := make([]DhcpOptionsLifecycleStateEnum, 0)\n\tfor _, v := range mappingDhcpOptionsLifecycleState {\n\t\tvalues = append(values, v)\n\t}\n\treturn values\n}\n" ]

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[ "The present invention concerns a hydraulic shock absorber and, more particularly, it concerns an improvement, by means of which it is possible to choose the type of damping and which notably permits passing from a linear variation of damping to a progressive variation and inversely.", "\nNumerous types of hydraulic shock absorbers are known, which are utilized in many application fields, and which are quite different from each other, such as for example, the automobile, industry, robotics, automatic delivery apparatuses or housing. ", "The diversity of the encountered fields and the specific constraints associated with each one of these, has lead the manufacturers to developing shock absorbers which are adapted to their proper application conditions and, consequently, to the constraints of their respective environment. ", "Thus, each shock absorbers has its own mechanical characteristics, which are intended to bestow on it optimal properties adapted to the involved field.", "\nIn the state of the art, linear type shock absorbers are known which permit slowing down a load with a constant force of resistance or shock absorbers of the so-called progressive type, which permit slowing down a charge with a variable damping force, as shown in FIG. ", "1.", "\nHowever, in spite of the diversity of the existing shock absorbers, certain applications do not appear to have shock absorbers adapted to their specific utilization constraints. ", "Furthermore, in certain fields, the constraints which are applied to the shock absorber can vary greatly and the shock absorber thus is only adapted to one or several areas of reduced operation and lacks adaptation with respect to basic operating constraints.", "\nConsequently, it is the object of the present invention to resolve the aforementioned problems with the aid of simple means, which can easily be implemented, which are reliable and which are not very costly. ", "Proposed is a hydraulic shock absorber which is likely to adapt itself to a large range of different constraints, thanks to specific adjustment of its damping properties." ]

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[ "Q:\n\nHow can I use graphframes with pyspark on AWS EMR?", "\n\nI'm trying to use the graphframes package in pyspark in Jupyter Notebook (using Sagemaker and sparkmagic) on AWS EMR. ", " I've tried adding a configuration option when creating the EMR cluster in the AWS console:\n[{\"classification\":\"spark-defaults\", \"properties\":{\"spark.jars.packages\":\"graphframes:graphframes:0.7.0-spark2.4-s_2.11\"}, \"configurations\":[]}]\n\nBut I still got an error when trying to use the graphframes package in my pyspark code in jupyter notebook.", "\nHere's my code (it's from the graphframes example):\n# Create a Vertex DataFrame with unique ID column \"id\"\nv = spark.createDataFrame([\n (\"a\", \"Alice\", 34),\n (\"b\", \"Bob\", 36),\n (\"c\", \"Charlie\", 30),\n], [\"id\", \"name\", \"age\"])\n# Create an Edge DataFrame with \"src\" and \"dst\" columns\ne = spark.createDataFrame([\n (\"a\", \"b\", \"friend\"),\n (\"b\", \"c\", \"follow\"),\n (\"c\", \"b\", \"follow\"),\n], [\"src\", \"dst\", \"relationship\"])\n# Create a GraphFrame\nfrom graphframes import *\ng = GraphFrame(v, e)\n\n# Query: Get in-degree of each vertex.", "\ng.inDegrees.show()\n\n# Query: Count the number of \"follow\" connections in the graph.", "\ng.edges.filter(\"relationship = 'follow'\").count()\n\n# Run PageRank algorithm, and show results.", "\nresults = g.pageRank(resetProbability=0.01, maxIter=20)\nresults.vertices.select(\"id\", \"pagerank\").show()\n\nAnd here's the output/error:\nImportError: No module named graphframes\n\nI read through this git thread but all the potential work-arounds seem very complicated and require ssh-ing into the master node of the EMR cluster.", "\n\nA:\n\nI finally figured out that there is a PyPi package for graphframes. ", " I used this to create a bootstrapping action as detailed here, although I changed things a little bit.", "\nHere's what I did to get graphframes working on EMR:\n\nFirst I created a shell script and saved it so s3 named \"install_jupyter_libraries_emr.sh\":\n\n#!", "/bin/bash\n\nsudo pip install graphframes\n\nI then went through the advanced options EMR creation process in the AWS console. ", " \n\nDuring Step 1, I added in the maven coordinates of the graphframes package within the edit software settings text box:\n\n[{\"classification\":\"spark-defaults\",\"properties\":{\"spark.jars.packages\":\"graphframes:graphframes:0.7.0-spark2.4-s_2.11\"}}]\n\nDuring Step 3: General Cluster Settings, I went into the bootstrap actions section\nWithin the bootstrap actions section, I added a new custom boostrap action with:\n\nan arbitrary name\nThe s3 location of my \"install_jupyter_libraries_emr.sh\" script\nno optional arguments\n\nI then started the cluster creation\n\nOnce my cluster was up, I got into Jupyter and ran my code:\n\n# Create a Vertex DataFrame with unique ID column \"id\"\nv = spark.createDataFrame([\n (\"a\", \"Alice\", 34),\n (\"b\", \"Bob\", 36),\n (\"c\", \"Charlie\", 30),\n], [\"id\", \"name\", \"age\"])\n# Create an Edge DataFrame with \"src\" and \"dst\" columns\ne = spark.createDataFrame([\n (\"a\", \"b\", \"friend\"),\n (\"b\", \"c\", \"follow\"),\n (\"c\", \"b\", \"follow\"),\n], [\"src\", \"dst\", \"relationship\"])\n# Create a GraphFrame\nfrom graphframes import *\ng = GraphFrame(v, e)\n\n# Query: Get in-degree of each vertex.", "\ng.inDegrees.show()\n\n# Query: Count the number of \"follow\" connections in the graph.", "\ng.edges.filter(\"relationship = 'follow'\").count()\n\n# Run PageRank algorithm, and show results.", "\nresults = g.pageRank(resetProbability=0.01, maxIter=20)\nresults.vertices.select(\"id\", \"pagerank\").show()\n\nAnd this time, finally, I got the correct output:\n+---+--------+\n| id|inDegree|\n+---+--------+\n| c| 1|\n| b| 2|\n+---+--------+\n\n+---+------------------+\n| id| pagerank|\n+---+------------------+\n| b|1.0905890109440908|\n| a| 0.01|\n| c|1.8994109890559092|\n+---+------------------+\n\n" ]

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[ "Description\n\nHit \"LIKE\" if you'd like to see more - Hope you enjoy! ", ":D\n● Make sure to subscribe for more -\n► Playlist (All of series) -\n\"What's New With\" is my new series in where we look at the latest and greatest games and I give you all the latest info! ", "In this series we will be covering all the new info that comes out for The Crew. ", "The upcoming next gen racer with the hearts of older Need for Speed fans in mind.", "\nBasically decided to attack The Crew for being always online and being funded after launch by microtransactions. ", "In this video I explain why I think this is fine for the type of game this is.", "\nThe article name was 'The Crew preview - A step in the wrong direction?'", "\nRelated-\nGameplay from:\n------------------------------------\nA video by BlackPanthaa (LeftTriggerUK)\n------------------------------------\n● Donate to help meh :3 -\n● Follow me on Twitch -\n● Follow me on Twitter -\n● Like me on Facebook -\n● Circle me on Google+ - +Blackpanthaa\n● Come join my website/forum -\n● Join the Panthaa Army on GTA Online:\n---------------------------------\n♫ Intro music: Madloops - Theme Music\n♫ Outro music - Ali Bomaye featuring 2 Chainz & Rick Ross (Remake by RichMuzik)\n♫ Sunrise by DOCTOR VOX\nDOCTOR VOX Facebook:\nDOCTOR VOX YouTube:\nSong Link:" ]

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[ "Identification of Differential Genes by Suppression Subtractive Hybridization: IV. ", "Mirror Orientation Selection (MOS).", "\nINTRODUCTIONSuppression subtractive hybridization (SSH) is one of the most powerful and popular methods for generating subtracted cDNA or genomic DNA libraries. ", "This technique can be used to compare two mRNA populations and obtain cDNAs representing genes that are either overexpressed or exclusively expressed in one population as compared to another. ", "It can also be used for comparison of genomic DNA populations. ", "The major drawback of SSH is the presence of background clones that represent nondifferentially expressed DNA species in the subtracted libraries. ", "In some cases, the number of background clones may considerably exceed the number of target clones. ", "This protocol describes mirror orientation selection (MOS)--a simple procedure that substantially decreases the number of background clones in libraries generated by SSH. ", "The MOS technique is based on the rationale that after PCR amplification, during SSH, background molecules will be present in one orientation only, relative to the adapter sequences. ", "Genuine SSH clones will be present in both sequence orientations." ]

{ "pile_set_name": "PubMed Abstracts" }

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[ "Star Wars Scout Walker or Elderly Scout Walker?", "\n\nHow much does the Scout Walker sell for on K-mart? ", "A search on kmart.com for scout walker doesn’t show the Star Wars Scout Walker. ", "Instead it shows walkers for elderly people.", "\n\nIs K-mart making some sort of commentary on the age of the actors in the original Star Wars triology? ", "Instead of using a AT-ST Scout Walker to get around, perhaps Mark Hamill, Harrison Ford, and Carrie Fisher would use an old people walker.", "\n\n(I know I know. ", "Luke Skywalker, Hans Solo and Princess Leia would not get around in an AT-ST anyways. ", "That’s an Empire vehicle. ", "Perhaps Darth Vader would use the walker. ", "Wait. ", "He’s dead. ", "How about Grand Moff Tarkin? ", "Also dead. ", "Well, nobody is gonna be able to use the old people walker. ", "It’ll just sit there unused. ", "Much like the AT-ST Scout Walkers after Return of the Jedi. ", "Do you suppose the ewoks used these vehicles once they regained their independence? ", "The ewoks would have probably just accidentally blown up the Scout Walkers.", "\n\nNow an elderly walker. ", "That’s what the old ewoks would use around the village. ", "When I get old, I want to fashion my old-man walker to look like a Scout Walker. ", "Concussion-grenade launcher on one side, light blaster cannon on the other. ", "Twin blaster cannons in the middle. ", "Then a furry wookie attached to the top." ]

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[ "The Football League and Sky Sports have announced the first live TV match selections for what is the broadcaster’s biggest ever season of Sky Bet Football League coverage.", "\n\nSky Sports will kick off its coverage of the new Sky Bet Football League season with three live matches across the opening weekend, beginning with Brighton & Hove Albion’s home match against Nottingham Forest on Friday 7 August and followed by matches at Leeds United and Preston North End.", "\n\n\n\n\n\nSky Sports will show 19 clubs from the Sky Bet Championship by the start of October, and as part of the initial selection of 16 matches to be shown live, there are also matches from Sky Bet League 1 and League 2.", "\n\n\n\n\n\nThanks to the start of the new broadcasting partnership between Sky and The Football League, viewers can enjoy more matches than ever before with 112 matches from across the Sky Bet Football League broadcast exclusively live, as well as the 15 Sky Bet Play-Off matches, including all three finals.", "\n\n\n\n\n\nSky Sports Head of Football Gary Hughes said: “Last season’s Championship was one of the most exciting in recent memory and what you can guarantee with the Football League is competitive games from the opening weekend to the final day of the playoffs.", "\n\n\n\n\n\n“With more games than ever on Sky Sports we’ll be able to show more of that story, and cover more clubs up and down the country that the fans are so passionate about.”", "\n\n\n\n\n\nAlongside their Football League coverage, from August Sky Sports will also show matches from the starts of the SPFL and Premier League seasons.", "\n\n\n\n\n\nAs the domestic leagues shape up in August and September, viewers will also be able to follow the climax to UEFA Euro 2016 qualifying with all the home nation sides in contention for a place in France next summer.", "\n\n\n\n\n\nSky Sports’ coverage of the Football League will include the analysis and expert views of Don Goodman, Peter Beagrie and Andy Hinchcliffe, and hosted by Simon Thomas.", "\n\n\n\n\n\nSky Sports live Sky Bet Football League fixtures:\n\n\n\n\n\n\n\n\n\n\n\n" ]

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[ "Deh-e Nar, Kohgiluyeh and Boyer-Ahmad\n\nDeh-e Nar (, also Romanized as Deh-e Nār; also known as Deh-e Anār) is a village in Tayebi-ye Sarhadi-ye Sharqi Rural District, Charusa District, Kohgiluyeh County, Kohgiluyeh and Boyer-Ahmad Province, Iran. ", "At the 2006 census, its population was 168, in 25 families.", "\n\nReferences \n\nCategory:Populated places in Kohgiluyeh County" ]

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[ "Instagram\n\nWellness Clubbing\n\nWellness Clubbing is really just like clubbing. ", "You’re in a dark room with loud music, everyone’s wearing very little clothing, you get extremely sweaty and it’s a lot of fun. ", "Apart from the lack of unbearably painful shoes, hangover and obnoxious door people, it’s practically the same thing.", "\n\nThis week, Melbourne’s hottest fitness + clubbing gurus, Bodhi & Ride and Bond Melbourne collaborated to bring us “Wellness Clubbing”, a concept giving meaning to the saying ‘work hard, play hard’. ", "I had an absolute ball, and to be honest, I think Wellness Clubbing may in fact be even better than normal clubbing. ", "Here are 5 reasons why:\n\nThere’s 0 people creeping on you. ", "Well as long as you resist from rocking what I like to call the ‘forgot my top’ look. ", "9 times out of 10, be honest with yourself, you’re really not working that hard that you need to remove your top for overheating purposes.", "\n\nThe next day you’re in pain… But good pain. ", "It’s your fat cells rather than your brain cells dying\n\nAfter party snacks like acai and matcha smoothies, raw vegan cheesecake, pressed juices etc make for ZERO regret, unlike the drunchies (that’s the drunk munchies, yes a word you’ve been looking for your whole life am I right?!) ", "which are only going to make you feel sick (I seem to always discover this the hard way). ", "There’s zero situations where a kebab after drinking copious amounts of alcohol is a good idea. ", "Except if you’re in Greece, then maybe it’s ok but it’s called a gyros there anyway, not a kebab.", "\n\nYou don’t have to worry about a sweaty man who made the poor choice of a long sleeve shirt, or a raspberry lemonade (seriously those drinks should be banned) coming into contact with the silk dress that you now realise you should never have exposed to such thing as a nightclub. ", "At Wellness Clubbing, you’re free to sweat as much as you like, and spill the 20 items of raw vegan snacks you’re trying to hold at once all over you, because gym clothes are not dry-clean only (and also who cares if they get ruined).", "\n\nYou don’t have to wear the super high, super uncomfortable, un-walkable heels that you bought, in order to prove to your mum that they were totally worth the amount of money you paid to be in huge amounts of pain." ]

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[ "Q:\n\nWhat does WITH FORMAT do on a DIFFERENTIAL backup?", "\n\nI could find a lot of questions about this. ", "This is a really good question, exactly what i'm asking here.", "\nDown there, a guys asks the question with:\n\nyou can have compressed and uncompressed on the same drive, just not\n the same media set (file).", "\n\nI planning to create a simple backup routine where There's a full backup at night, and a differential backup each hour. ", "But to use COMPRESSION in a differential backup, I need to use FORMAT. ", "What does this mean? ", "\n\nUse FORMAT carefully. ", "Formatting any volume of a media set renders the\n entire media set unusable. ", "For example, if you initialize a single\n tape belonging to an existing striped media set, the entire media set\n is rendered useless.", "\n\nI can't understand this. ", "Every backup has a different name, and they're going to stay in the same drive. ", "What am I going to format with this option?", "\nCan I have:\nFULL.BKP\nDIFF1.DIFF( With compression,format)\nDIFF2.DIFF( With compression,format)\nDIFF3.DIFF( With compression,format)\nDIFF4.DIFF( With compression,format)\nDIFF5.DIFF( With compression,format)\n\nin the same disk? ", "Thanks. ", "\n\nA:\n\nBut to use COMPRESSION in a differential backup, I need to use FORMAT. ", "\n\nI'm not sure why you think you need to use FORMAT at all. ", "This works just fine, I end up with two different differential backup files, each about 80kb:\nBACKUP DATABASE db TO DISK = 'c:\\bk\\dif1.bak' WITH COMPRESSION, DIFFERENTIAL;\nGO\nBACKUP DATABASE db TO DISK = 'c:\\bk\\dif2.bak' WITH COMPRESSION, DIFFERENTIAL;\n\nAs does writing both differentials to the same file (though I don't know why people like doing this), I end up with a single backup file that contains two differential backups, about 165kb:\nBACKUP DATABASE db TO DISK = 'c:\\bk\\dif.bak' WITH COMPRESSION, DIFFERENTIAL;\nGO\nBACKUP DATABASE db TO DISK = 'c:\\bk\\dif.bak' WITH COMPRESSION, DIFFERENTIAL;\n\nAs does overwriting the same file each time, I end up with a single differential backup representing the most recent differential backup I took, about 80kb:\nBACKUP DATABASE db TO DISK = 'c:\\bk\\dif.bak' WITH INIT, COMPRESSION, DIFFERENTIAL;\nGO\nBACKUP DATABASE db TO DISK = 'c:\\bk\\dif.bak' WITH INIT, COMPRESSION, DIFFERENTIAL;\n\nAll of these result in compressed differential backups, and I didn't use FORMAT once.", "\nI don't have a 2008 R2 instance to test, and it might be the case that it is impossible in that version to - say - capture multiple diffs to the same backup file (what the documentation might call a media set, but that was more relevant back in that decade when we used tape drives) and take the first diff compression (or encryption, etc.) ", "and the second one without. ", "Compression on and off is fine in modern versions, though I didn't test encryption. ", "In any case, you won't be in that situation if you make each backup its own file in the first place, which I think is what you should do. ", "\nThis makes your question rather academic. ", "But to answer it, for all intents and purposes, FORMAT on a differential backup effectively does the same thing as INIT - it wipes out any previous backups in the file. ", "So with this:\nBACKUP DATABASE db TO DISK = 'c:\\bk\\dif.bak' WITH INIT, COMPRESSION, DIFFERENTIAL;\nGO\nBACKUP DATABASE db TO DISK = 'c:\\bk\\dif.bak' WITH FORMAT, COMPRESSION, DIFFERENTIAL;\n\nI end up with the same, single 80kb backup as if I had used INIT in both statements. ", "All older backups in that file, regardless of format, except the last one, are removed.", "\n\n" ]

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[ "In many healthcare information systems today, semantically normalized & aggregated clinical data are not available and/or are not standardized sufficiently to enable cross-platform or cross-network sharing. ", "This can result in medical errors, diagnoses and treatments based on incomplete knowledge of patient histories or vital data, harmful drug interactions, redundant testing, and other unnecessary admissions. ", "Providing the patients electronic health record (EHR) at the point of care—the right data, to the right clinical personnel, at the right time—increases both the quality and efficiency of care. ", "Today this is only rarely achieved when individual providers invest in very complex systems integration projects and even then, the patient record is still largely incomplete. ", "Instead, clinical decision-making largely relies on labor-intensive and error-prone searches through available hardcopy, data repositories and “silos” of disaggregated information, to build a patchwork view of patient health." ]

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[ "Currently, clustering techniques are applied to content that is posted by users in social networks, information that is posted by news organizations, videos, and photographs. ", "Clusters are created in real time as new content is posted." ]

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[ "Q:\n\nCreate empty object in R\n\nI'm trying to create empty numeric object like this \ncorr <- cor()\n\nto use it later on in a loop.", "\nbut, it keep returning this error\nError in is.data.frame(x) : argument \"x\" is missing, with no default.", "\nHere is my full script:\nEVI <- \"D:\\\\Modis_EVI\\\\Original\\\\EVI_Stack_single5000.tif\"\ny.EVI <- brick(EVI)\nm.EVI.cropped <- as.matrix(y.", "EVI)\ntime <- 1:nlayers(y.", "EVI)\ncorr <- cor()\n\ninf2NA <- function(x) { x[is.infinite(x)] <- NA; x }\nfor (i in 1:nrow(m.", "EVI.cropped)){\n EVI.m <- m.EVI.cropped[i,]\n time <- 1:nlayers(y.", "EVI) \n Corr[i] <- cor(EVI.m, time, method=\"pearson\", use=\"pairwise.complete.obs\")\n}\n\nAny advice please?", "\n\nA:\n\nSince you are asking for advice:\nIt is very likely that you don't need to do this since you can probably use (i) a vectorized function or (ii) a lapply loop that pre-allocates the return object for you. ", "If you insist on using a for loop, set it up properly. ", "This means you should pre-allocate which you can, e.g., do by using corr <- numeric(n), where n is the number of iterations. ", "Appending to a vector is extremely slooooooow.", "\n\nA:\n\nWe can create empty objects with numeric(0), logical(0), character(0) etc.", "\nFor example\nnum_vec <- numeric(0)\n\ncreates an empty numeric vector that can be filled up later on:\nnum_vec[1] <- 2\nnum_vec\n# [1] 2\nnum_vec[2] <- 1\nnum_vec\n# [1] 2 1\n\n" ]

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[ "An isocratic liquid chromatographic method with diode-array detection for the simultaneous determination of alpha-tocopherol, retinol, and five carotenoids in human serum.", "\nAn isocratic high-performance liquid chromatography (HPLC) method for the simultaneous determination of alpha-tocopherol, retinol, and five carotenoids (lutein-zeaxanthin, beta-cryptoxanthin, lycopene, and alpha- and beta-carotene) in human serum is described. ", "Serum samples are deproteinized with ethanol and extracted once with n-hexane. ", "Resulting extracts are injected onto a C18 reversed-phase column eluted with methanol-acetonitrile-tetrahydrofuran (75:20:5, v/v/v), and full elution of all the analytes is realized isocratically within 20 min. ", "The detection is operated using three channels of a diode-array spectrophotometer at 290, 325, and 450 nm for tocopherol, retinol, and the carotenoids, respectively. ", "An internal standard is used for each channel, which improves precision. ", "The choice of internal standards is discussed, as well as the extraction protocol and the need for adding an antioxidant during the extraction and chromatographic steps. ", "The analytical recoveries for liposoluble vitamins and carotenoids are more than 85%. ", "Intra-assay relative standard deviation (RSD) values (n = 20) for measured concentrations in serum range from 3.3% (retinol) to 9.5% (lycopene), and interassay RSDs (n = 5) range from 3.8% (alpha-tocopherol) to 13.7% (beta-cryptoxanthin). ", "The present method is used to quantitate the cited vitamins in healthy subjects (n = 168) from ages 9 to 55 years old." ]

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[ "Serie A giants Juventus have also signed Cristiano Ronaldo's son for their Under 9s side about some days after his father made his debut for the Old Lady senior side.", "Ronaldo Jr. was signed by the Old Lady yesterday and was registered for their game yesterday. ", "In fact, he did play for the side in a game right after signing for them.", "He too has joined from Real Madrid and it is said that he has undoubted talent, but he knows that he will never be as good as his father is. ", "Cristiano himself has acknowledged that his son has real talent.", "Ronaldo Jr's talent was seen after he came onto the pitch to play with Cristiano after Portugal's game against Algeria before the FIFA World Cup.", "Kaustubh Pandey (@Kaus_Pandey17)" ]

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[ "Birth to Twenty\n\nBirth to Twenty (BT20) is Africa's largest and longest running study of child and adolescent health and development. ", " The study is a birth cohort study, and in 1990 began to track the development of 3,273 newborn infants. ", "According to supporter, University of Witwatersrand, Johannesburg, BT20 is colloquially nicknamed \"Mandela's Children\" as the program began following Nelson Mandela's release from prison. ", " As the name suggests, the study plans will continue to monitor its subjects until they are twenty years old (2010). ", " As of 2008, the study was still active.", "\n\nThe first round of the study began in 1989/1990, and questioned the still-pregnant mothers about general demographic characteristics, and the conditions of the pregnancy. ", " After further rounds of assessments and surveys at birth and six months, data was obtained on an annual basis. ", " The question in the yearly surveys cover a broad range of topics, touching on both the physical health and development of the child, his or her environment, education, nutrition, socioeconomic class, and cognitive development. ", " Later surveys also monitor each subject's opinion on politics, Africa, and other social opinions.", "\n\nThe study is unique source of information for major policy decisions in the South Africa, especially due to the absence of other data. ", "Information on children's recognition of cigarette brands, for example, was used by the Minister of Health from 1997 to 1999 to push forward progressive tobacco legislation, preventing public advertising and the sale of cigarettes to minors. ", "The early age of school entry revealed by longitudinal data was used by the Ministry of Education in 2004 to legislate a minimum age for school enrolment.", "\n\nAs a longitudinal study, one of the major criteria by which one may judge the Birth to Twenty study is by the number of subjects for whom data is obtained in each round, or the attrition rate. ", " One of the difficulties encountered by the Birth to Twenty is that many subjects move out of the area, and can no longer participate. ", " Nevertheless, the study has quite consistently obtained data from between 50% - 65% of the original cohort of 3,273. ", " In 2005-2006, for example, data was collected from 2,100 subjects, or 64%.", "\n\nAvailability of Data\nThe data for the Birth to 20 study is not publicly available. ", " According to the \"Memorandum of Understanding,\" interested researches should contact the projects Executive Committee if they wish to obtain the study's data or publish a paper based on it.", "\n\nFunding\nSince its inception, Birth to Twenty has been funded by the South African Medical Research Council. ", " Other sources of funding include the Institute for Behavioural Sciences at the University of South Africa. ", "Since 1998, the Wellcome Trust has been a major contributor, with additional support coming from the Human Sciences Research Council of South Africa, the Medical Research Council, the University of the Witwatersrand, the Mellon Foundation, the South-African Netherlands Programme on Alternative Development and the Anglo American Chairman's Fund.", "\n\nReferences\n\nExternal links\n The official homepage of the Birth to Twenty Study, hosted by the University of Witwatersrand, Johannesburg\n A March, 2007 article describing the background and some of the findings of the Birth to Twenty Study. ", " In the International Journal of Epidemiology\n\nCategory:Youth in Africa" ]

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[ "Q:\n\nScroll TreeView with MouseMove\n\nI have a TreeView and nodes on it. ", "I want to scroll with the MouseMove Event. ", "I did this for panel weeks ago but panel have the AutoScrollPosition property to do that so it's easier. ", "How can I do with a TreeView that don't have the AutoscrollPosition property ?", "\nI tried this :\n private void TreeViewFilters_MouseMove(object sender, MouseEventArgs e)\n {\n if (e.Button !", "= MouseButtons.", "Left)\n {\n return;\n }\n if ((startPoint.", "X == treeViewFilters.", "PointToClient(MousePosition).X) && (startPoint.", "Y == treeViewFilters.", "PointToClient(MousePosition).Y))\n {\n return;\n }\n\n Point currAutoS = treeViewFilters.", "AutoScrollPosition; //Problem here\n if (startPoint.", "Y > treeViewFilters.", "PointToClient(MousePosition).Y)\n {\n if (startPoint.", "Y !", "= 0)\n {\n currAutoS.Y = (Math.", "Abs(currAutoS.Y) + 15);\n }\n }\n else if (startPoint.", "Y < treeViewFilters.", "PointToClient(MousePosition).Y)\n {\n currAutoS.Y = (Math.", "Abs(currAutoS.Y) - 15);\n }\n else\n {\n currAutoS.Y = Math.", "Abs(currAutoS.Y);\n }\n\n if (startPoint.", "X > treeViewFilters.", "PointToClient(MousePosition).X)\n {\n if (currAutoS.X !", "= 0)\n {\n currAutoS.X = (Math.", "Abs(currAutoS.X) + 15);\n }\n }\n else if (startPoint.", "X < treeViewFilters.", "PointToClient(MousePosition).X)\n {\n currAutoS.X = (Math.", "Abs(currAutoS.X) - 15);\n }\n else\n {\n currAutoS.X = Math.", "Abs(currAutoS.X);\n }\n\n currAutoS = treeViewFilters.", "AutoScrollPosition; //and here\n startPoint = treeViewFilters.", "PointToClient(MousePosition);\n\n }\n\nPlease someone can help me ?", "\n\nA:\n\nI found a solution and it works :\n treeViewFilters.", "Location = new Point(treeViewFilters.", "Location.", "X, -vScrollBarFilters.", "Value);\n\n" ]

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[ "Hinge-lid boxes or hinge-lid pack are commonly used throughout the world for cigarettes. ", "On the part of the consumers, there is a desire to combine the pack or hinge-lid box with separate articles, to be precise in particular such articles as are used for smoking, that is to say a lighter in particular." ]

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[ "Q:\n\nDistribute numbers 1,N on a grid as evenly as possible\n\nI'm working on a complex engineering problem that I've essentially reduced to this problem:\nI have a set of natural numbers $1,N$ and a grid (square or hexagonal) of exactly $N$ cells. ", "I have to map each number to each cell so that the distribution (in a geometric sense) is as flat as possible. ", "I'm still working on the definition of flat, but so far\n\nThe average of the numbers of a cell and its nearest neighbours must be as close to $N/2$ as possible, for every cell.", "\nThe average of the distance between a cell and each neighbour must be as large as possible.", "\n\nIf a cell has a number $n$ and its neighbour $m$ the distance between these neighbours is $min(|n-m|,N-|n-m|)$. It's essentially cyclical.", "\nIf $.$ represents a small number and # a large number I'm looking chessboard-like configurations like\n.#.#.#.#", "\n#.#.#.#.", "\n.#.#.#.#", "\n\nI need to find the best configuration (or a very good one) without using brute force.", "\nCan you point me to some good algorithms that may be useful for this problem? ", "I could only get above-average results on my own.", "\nIn my problem $N\\approx~500$ and there is no runtime constraint.", "\n\nA:\n\nSimulated Annealing might work well for this problem.", "\nThe idea is to introduce a \"temperature\" component to your heuristic function to avoid getting stuck at local optima. ", "Temperature corresponds to how willing the heuristic function is to accept an inferior arrangement. ", "With simulated annealing, temperature starts off high and decreases until an optimal solution is found. ", "\nHere is solution to the Travelling Salesman Problem using simulated annealing\nYou can tinker with the starting temperature and its rate of change to try and find an optimal arrangement.", "\n\n" ]

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[ "Bäumer\n\nBäumer is a German surname. ", "Notable people with the surname include:\n\nGertrud Bäumer (1873–1954), German lawyer and politician\nPaul Bäumer (1896–1927), German pilot" ]

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[ "Spectrum Dispatch\n\nLore\n\nID:\n\nComments:\n\nDate:\n\nCongress Now: Vega II Recognition Review\n\nUEECONGRESS (396)\n\n2945-11-10 SET\n\nSession AutoScript\n\nProofed and Admitted – Archivist Yates (#57573BDF)\n\n2945-11-10_13:01 – Transcript Begins\n\nSPEAKERMARSHALLMADRIGAL (U-Borea-Magnus Sys): Ladies and gentlemen. ", "If you will settle, we can get started.", "\n\n< pause >\n\nSPEAKERMARSHALLMADRIGAL (U-Borea-Magnus Sys): As we have a quorum, this session is officially called to order and may conduct business. ", "If you will all rise, it is my honor and privilege to present the Imperator of the United Empire of Earth …\n\n< sustained applause >\n\nIMPERATORKELOSCOSTIGAN (U): Thank you, Speaker Madrigal. ", "Thank you, esteemed members of the Senate. ", "And thank you to the people of the UEE.", "\n\nThese past few weeks have been some of the darkest of my life. ", "As I toured the devastation of Estilia, I saw nothing but pain, loss and soulless brutality.", "\n\nImperial Disaster Relief forces have worked tirelessly alongside the military to provide aid and support, but in the days since, I’ve seen something even more inspiring. ", "I have seen people pulling together. ", "I’ve seen cargo haulers organize relief runs from across the Empire. ", "I’ve seen children in Aydo canvass their neighborhoods collecting blankets and toys. ", "I’ve even seen support flood across our borders from the Banu and the Xi’An. ", "In short, despite the profound darkness of our loss, we have found light in each other. ", "And that should be celebrated. ", "As the wounds from this tragedy begin to heal, I hope we don’t forget that charitable spirit.", "\n\nThank you.", "\n\n< sustained applause >\n\nSpeaker …\n\nSPEAKERMARSHALLMADRIGAL (U-Borea-Magnus Sys): Thank you, Imperator. ", "We have the privilege of welcoming another esteemed guest to this session. ", "A Citizen and member of Vega II’s representation committee. ", "Please step forward and state your name.", "\n\nEDWARDAEMILE: Edward Aemile, Speaker.", "\n\nSPEAKERMARSHALLMADRIGAL (U-Borea-Magnus Sys): Now, as many of you know, before the attack, Vega II was in the final stages of its review for recognition. ", "Our envoys had only just returned and filed their reports when the system came under attack. ", "I wanted to share those findings with you today. ", "Vega II was found to be a shining light of industry and thought. ", "Your planet showed a genuine and steadfast commitment to the betterment of Humanity and the Empire which is nothing short of inspiring. ", "In short, the UEE would be proud to count Vega II as a contributing member to this Empire, regardless of whether the attack had happened or not.", "\n\nEDWARDAEMILE: Thank you, Speaker.", "\n\nSPEAKERMARSHALLMADRIGAL (U-Borea-Magnus Sys): Imperator.", "\n\nIMPERATORKELOSCOSTIGAN (U): Does Vega II still wish to be recognized?", "\n\nEDWARDAEMILE: Yes. ", "More than ever.", "\n\nIMPERATORKELOSCOSTIGAN (U): Under what name does Vega II wish to be recognized?", "\n\nEDWARDAEMILE: Aremis, sir.", "\n\nIMPERATORKELOSCOSTIGAN (U): I recognize Aremis, granting it a voice in the direction of Humanity and affording it all rights and responsibilities bound by a planet of the UEE. ", "You were submitted as the pro tem representative, should your planet be recognized.", "\n\nEDWARDAEMILE: It is my honor, sir.", "\n\nIMPERATORKELOSCOSTIGAN (U): Then step forward and take your vow.", "\n\nEDWARDAEMILE: I, Edward Javier Aemile, do solemnly vow that I will bear true faith and allegiance to the United Empire of Earth, that I will support and defend the Empire against all enemies, that I will not let injustice stand within the law and use reason and compassion to seek change through the law, that I will use this power granted to me to serve the best interests of all Humanity and that I will well and faithfully discharge the duties of the office on which I am about to enter.", "\n\nIMPERATORKELOSCOSTIGAN (U): Congratulations, people of Aremis, and congratulations, Senator Aemile.", "\n\nSPEAKERMARSHALLMADRIGAL (U-Borea-Magnus Sys): You have the floor to make your opening pronouncement, Senator.", "\n\nSENATOREDWARDAEMILE (C-Aremis-Vega Sys): First of all, to all of the people of Aremis: etace tu adille! ", "We did it! ", "It is your heart and spirit that inspires me to make things better. ", "And we will rise from this. ", "We will, though it may not seem like it. ", "If you are lost in your sorrow, you only need to step outside and look around. ", "You will not only see other Aremisians, you will see family. ", "We have all suffered, but in that, we are all in this together.", "\n\nTo my new colleagues in the Senate, I thank you for this opportunity and look forward to working with each and every one of you. ", "However …\n\nI find myself conflicted.", "\n\nOn October 10th, Admiral Bishop made an impassioned speech in this very hall. ", "He spoke for the dead and shattered of my world and implored the Empire to take action to prevent the same thing from happening again. ", "Shortly thereafter, Imperator Costigan called for a declaration of war against the Vanduul. ", "The High Command quickly provided their support of such action. ", "The people showed their support by rejecting the Polo Initiative, but the Senate … the Senate has done nothing. ", "It has been locked in a circular debate for weeks. ", "Now I understand that war should not be invoked lightly and I respect the diligence with which you would weigh this decision, but I ask you, what other choice do we have?", "\n\nTo me, who saw the Vanduul attack first hand, who saw their ferocity and absolute lack of empathy for another sentient species, it seems that they are already at war with us.", "\n\nIt is time we return the sentiment.", "\n\nSo, as my first action as a UEE Senator, I would like to file a motion to close discussion and call a vote on the Imperator’s declaration of war against the Vanduul.", "\n\nSPEAKERMARSHALLMADRIGAL (U-Borea-Magnus Sys): Senator Aemile, I’m not sure this is the time.", "\n\nIMPERATORKELOSCOSTIGAN (U): Will all due respect, Speaker, you have a quorum to conduct business.", "\n\nSPEAKERMARSHALLMADRIGAL (U-Borea-Magnus Sys): Yes, we do.", "\n\n< pause >\n\nSPEAKERMARSHALLMADRIGAL (U-Borea-Magnus Sys): Archivist, would you prepare the system. ", "Ladies and gentlemen of the Senate, if you will bring up your terminals, we will get started." ]

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[ "If voters approve Initiative 1631 on Nov. 6, Washington state will take a significant step in climate action by becoming the first state in the nation to enact a fee on carbon emissions. ", "That is, unless Big Oil can stop it.", "\n\nThe U.S. oil industry has pumped a record $30 million to stop the carbon tax, which environmentalists have tried to enact for years, Reuters reported, citing state data. ", "Meanwhile, proponents—including green groups and climate activist billionaires Bill Gates, Michael Bloomberg, Tom Steyer and Laurene Powell Jobs, the widow of Apple founder Steve Jobs—have spent $15.2 million.", "\n\n\"With Big Oil spending $30 million, that makes it a real fight,\" Bill Holland, state policy director for the League of Conservation Voters, told Reuters. \"", "It has been a frightening amount of money.\"", "\n\nWashington ranks fifth in the nation in crude oil refining capacity for making gasoline and other petroleum products, according to the U.S. Energy Information Administration.", "\n\nInitiative 1631 imposes a starting fee of $15 per metric ton on carbon emissions, beginning in 2020. ", "This fee rises $2 every year until the state hits its 2035 emissions reductions goals and is on track to meet its 2050 goals. ", "If passed, the tax is expected to generate $2.3 billion in revenue for green infrastructure, clean transportation and help communities most impacted by pollution.", "\n\nA recent statewide Crosscut/Elway Poll among registered voters shows 50 percent approval of the measure, 36 percent opposed and 14 percent undecided.", "\n\nThe opposition is led by the Western States Petroleum Association, a trade organization that has raised $31.2 million from energy companies and business groups for the \"No on 1631\" campaign—the most money ever spent in Washington state history to defeat a ballot initiative.", "\n\nBP America contributed the most with $11.5 million, followed by $7.2 million from Phillips 66 and Andeavor with $4.4 million, Reuters said. ", "The three energy companies have refineries in the state. ", "American Fuel & Petrochemical Manufacturers and Valero Energy Corporation also donated funds.", "\n\nThe money has been spent on digital ads, flyers, mailers and television ads aired during this month's Major League Baseball World Series. ", "Opponents say the tax will \"be paid by Washington families and small businesses.\"" ]

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[ "Why We all Love Leather-based Bomber Outdoor jackets\n\nIt is just a very popular saying that the initial impression is the last impression and a lot of agree by it. ", "What else may make a far better impression compared to good attire? ", "Clothes not only define your style declaration but his or her personality in addition. ", "If people wears stylish clothes he or she is doudoune moncler pas cher by simply peers and includes a standard which everyone is in awe of. ", "Clothes which are fashionable and also functional are hopeless to discovered. ", "However overcoats have sustained to remain in trend through yrs specially buckskin jackets.", "\n\nLeather pockets are considerably more durable, easy to keep up and that never does not give the cool appear. ", "The historical past of leather-based blazers started from 1940’s while military officials and aviators wore brown shaded leather blazers popularly referred to as bomber outdoor jackets. ", "These bomber outdoor jackets gained tremendous popularity immediately after Harrison Ford taken them very easily and stylishly throughout Indiana Jones.", "\n\nAlthough cotton jackets include various colors when compared with leather jacket’s browns and blacks, this becomes as a negative place for organic and natural jackets. ", "Black and also brown leather-based blazers can select almost almost every other color along with moncler doudoune glance chic. ", "Whereas intended for cotton jackets you’ll have to buy just about every color so that they can match this with rest of your clothes.", "\n\nMen plus women usually dress to be able to impress. ", "Men wear leather jacket so it gives these a uncertain and more healthy look that comparatively attracts the other sex. ", "Women buckskin jackets always look fashionable, while egyptian cotton jackets ordinarily give both the sexes a shabby appear. ", "Leather blazers pertaining to both sexes can be bought in various designs adidas soccer cleats cotton jackets do not have much variety. ", "Cotton jackets also started reduce popularity because they cannot be worn in the year when leather blazers might be easily worn in all seasons.", "\n\nPeople immensely follow roll film stars. ", "This can be one of many main reasons of set blazers popularity for the reason that have recently been greatly well known amongst actors. ", "Arnold Schwarzenegger among the leading famous actors in Showmanship wore Set jackets within the film That Terminator and also set the trend amongst many that they are dressed inside them. ", "Same happened when the film This Matrix released for the reason that lead actors from the film wore leather blazers. ", "Not simply leather jackets are well-liked amongst film stars but also , they are popular between singers across the world.", "\n\nPeople in the course of ages have always adopted fashion let the brisket be bell bottoms, straight pants, low cuts, hats or perhaps any shade or pattern on the garment, they under no circumstances hesitate in order to pursue. ", "Similarly leather-based jackets are getting to be a major component to fashion industry containing engulfed people to wear them plus flaunt these folks with take great pride in." ]

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[ "Cyclone Lusi\n\nCyclone Lusi was the second severe tropical cyclone of the 2013–14 season and affected Fiji, Vanuatu and New Zealand.", "\n\nThe system that was to become Cyclone Lusi was first noted as a tropical disturbance on 7 March, while it was located to the east of Fiji. ", "Over the next three days the system moved towards the north-northeast and gradually developed further, before it was named Lusi, late on 9 March, after it had developed into a tropical cyclone. ", "The system dissipated on 17 March.", "\n\nMeteorological history\n\nEarly on 7 March 2014, the Fiji Meteorological Service reported that Tropical Disturbance 18F had developed about to the west of Nadi. ", "The system was located within a marginally favourable environment for further development, which included low to moderate vertical wind shear and favourable sea surface temperatures. ", "Over the next two days the system moved towards the north-northwest and slowly consolidated, as atmospheric convection wrapped into the system's low level circulation centre, before RSMC Nadi reported during 9 March that the system had developed into a tropical depression. ", "During that day the system further consolidated as it affected Vanuatu and moved towards the north-northeast, before the United States Joint Typhoon Warning Center initiated warnings and designated the depression as Tropical Cyclone 18P later that day. ", "RSMC Nadi subsequently named the system Lusi at around 23:00 UTC (11:00 FST), after it had developed into a category 1 tropical cyclone on the Australian tropical cyclone intensity scale.", "\n\nPreparations and impact\n\nVanuatu\nLate on 9 March, ahead of the depression being classified as a tropical cyclone and named Lusi, the Vanuatu Meteorology and Geo-Hazards Department issued tropical cyclone warnings for the Vanuatu provinces of Torba, Sanma, Penama and Malampa.", "\n\nThe cyclone killed 10 people and impacted as many as 20,000 people, especially in Torba, Sanma, Penama, Malampa and Shefa Provinces. ", "Many low-lying areas were flooded and more than 40 structures were damaged or destroyed. ", "All provinces of the country reported damage to agriculture.", "\n\nFiji\nOn 11 March, a tropical cyclone alert was issued for parts of the Western Division, as Lusi approached the islands from the west. ", "During the next day gale warnings were issued for the Western Division before they were cancelled later that day, as the system turned towards the south sooner than had been expected. ", "As a result, Fiji was spared any direct effects from the cyclone, while the associated trough of low pressure affected the islands until 13 March.", "\n\nNew Zealand\nDuring 9 March, MetService started to warn that a tropical weather system might affect New Zealand by the end of that week.", "\n\nCyclone Lusi hit New Zealand shores on 13 March. ", "In preparation for the event the New Zealand government advised people to fix loosened things (such as trampolines), and the Civil Defense team was put on alert. ", "Winds reaching up to 130 km/h were expected to occur in the cities of Auckland, Whangarei and Hamilton, and the east coast of the North Island was put on high alert. ", "Lusi brought severe winds as it moved southeast towards Wellington and the northern South Island in the evening of 15 March. ", "On 16 March, the severe gale winds slightly weakened, and Lusi pushed away from New Zealand on 17 March.", "\n\nInsured losses across the country amounted to NZ$4 million (US$3 million).", "\n\nRetirement\nDue to the impacts caused by the storm, the name Lusi was retired and was later replaced by Louise.", "\n\nSee also\nCyclone Susan\nCyclone Evan\n\nReferences\n\nExternal links\n\nCategory:Tropical cyclones in New Zealand\nCategory:Tropical cyclones in Fiji\nCategory:Tropical cyclones in Vanuatu\nCategory:2014 in New Zealand\nCategory:2013–14 South Pacific cyclone season\nCategory:Category 3 South Pacific cyclones\nCategory:Retired South Pacific cyclones" ]

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[ "Searching for Professional Significance\n\nBefore you proceed, grab a pen and paper and take a moment to do this quick exercise: Write the name of the best leader, teacher, or coach you’ve ever had. ", "Write the name of the individual who made a difference in your life, who seemed to care more about you than you cared about yourself.", "\n\nYou’ll find that if you’re over 40, you are able to name at least one person, and often two or more. ", "Typically, one of these individuals is a former boss. ", "If you’re younger than 40, however, you may come up with one name, but it’s rarely someone with whom you’ve worked; you name an athletic coach or a high school teacher. ", "Having administered this exercise to executives of many types and ages in recent years, I can tell you that this is almost always how the answers skew.", "\n\nWe have a vicious cycle operating in many organizations. ", "Senior leaders blame the young MBAs for being naive and entitled, and assume that the younger generation arrives at the company with “negative” attitudes intact. ", "These younger employees, however, form this attitude only because they are in desperate need of someone who cares about them, who communicates that they matter, who lets them know they make a difference. ", "They don’t need positive feedback when it isn’t deserved. ", "What they need are managers and leaders who are aware that they want to feel significant and who make the effort to communicate this fact in small as well as big ways.", "\n\nI’m not absolving you of responsibility for finding your own significance in a career or a job. ", "No matter whether you’re a young, middle-aged, or older professional, if you’re driven to achieve, you also need to be driven to find your place in a work setting. ", "You can’t depend on an organization to make a concerted and consistent effort to imbue your work with meaning.", "\n\nRecognize that the challenges of finding significance are in part based on your age, in part on your social motives and values, in part on your mental makeup (e.g., are you in the midst of divorce or other life crisis?), ", "in part on your work situation (e.g., a massive downsizing or culture change), and in part, on management’s approach to this issue. ", "While you can’t control some of these factors, you can control your response to them.", "\n\nYou need to define and redefine what type of work you want to do, what type of organization and culture you want to be part of, and what goals you want to strive for. ", "And you need to do this regularly, since what’s significant now might not be as significant a year from now. ", "For some of you, working for the leading organization in your field may be of prime significance. ", "For others, working in a smaller, closer-knit culture is what matters.", "\n\nFinally, if you want to increase the odds that your organization will help you find significance in your work, look for the modern equivalent of the apprenticeship model. ", "Seek work in companies where young people, those new to an organization, and even some veteran employees starting out on new jobs and tasks essentially serve as apprentices to “master craftsmen.” ", "This entails a lot of learning on the job — following senior people around, asking questions, being questioned, trying, failing, and then succeeding. ", "Apprentices naturally feel significant, since their master is responsible for them and their education. ", "They receive continuous feedback, their learning and progress is monitored, and when they are ready, they are promoted into positions of responsibility. ", "In this way, they achieve significance.", "\n\nYou want to find an organization where senior people enjoy mentoring rather than resent the time required and billable hours lost. ", "You want to work for a company where your learning and growth is valued, where you are treated as distinct individual rather than a replaceable part. ", "Finding this type of company is more challenging today than years ago, but it’s worth the effort, since finding it will go a long way in helping you find the significance you seek.", "\n\nThomas J. DeLong is the Philip J. Stomberg Professor of Management Practice in the Organizational Behavior area at Harvard Business School and the author of Flying Without a Net. ", "His research focuses on the challenges facing individuals and organizations in the process of change.", "\n\nPartner Center\n\nThe email and password entered aren’t matching to our records. ", "Please try again, or reset your password. ", "If you have a username from our previous site, start by using that. ", "Please See our FAQ for more.", "\n\nIf you are signing in for the first time on the new HBR.org but have an existing account, please enter your existing user name and password to migrate your account.", "Please see Frequently Asked Questions for more information." ]

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[ "541 U.S. 946\nOSTRANDERv.", "LUEBBERS, SUPERINTENDENT, FARMINGTON CORRECTIONAL CENTER.", "\nNo. ", "03-8471.", "\nSupreme Court of United States.", "\nMarch 22, 2004.", "\n\n1\nC. A. 8th Cir. ", "Certiorari denied.", "\n\n" ]

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[ "Q:\n\nHow to add a 404 page to Single Page Scrolling App in React?", "\n\nI'm new to React and trying to add a 404 page to my SPSA. ", "This is how my index.js looks like:\nimport React from 'react';\nimport ReactDOM from 'react-dom';\nimport './dist/css/main.css';\nimport './../node_modules/react-fancybox/lib/fancybox.css';\nimport Nav from './js/Components/Nav';\nimport * as serviceWorker from './serviceWorker';\nimport Landing from './js/Layout/Landing';\nimport Overview from './js/Layout/Overview';\nimport Solutions from './js/Layout/Solutions';\nimport Games from './js/Layout/Games';\nimport Platforms from './js/Layout/Platforms';\nimport Focus from './js/Layout/Focus';\nimport News from './js/Layout/News';\nimport Contact from './js/Layout/Contact';\nimport Catalogue from \"./js/Layout/Catalogue\";\nimport Game from \"./js/Components/PlayGame\";\nimport NotFound from \"./js/Layout/NotFound\";\nimport { BrowserRouter as Router, Route, withRouter } from \"react-router-dom\";\n\nconst base_url = process.env.", "PUBLIC_URL;\n\nReactDOM.render(\n <Router>\n <div>\n <Route path={`${base_url}/`} component={withRouter(Nav)} />\n <Route exact path={`${base_url}/`} component={withRouter(Landing)} />\n <Route exact path={`${base_url}/`} component={withRouter(Overview)} />\n <Route exact path={`${base_url}/`} component={withRouter(Solutions)} />\n <Route exact path={`${base_url}/`} component={withRouter(Games)} />\n <Route exact path={`${base_url}/`} component={withRouter(Platforms)} />\n <Route exact path={`${base_url}/`} component={withRouter(Focus)} />\n <Route exact path={`${base_url}/`} component={withRouter(News)} />\n <Route exact path={`${base_url}/`} component={withRouter(Contact)} />\n <Route exact path={`${base_url}/catalogue`} component={withRouter(Catalogue)} />\n <Route exact path={`${base_url}/game/:gameid`} component={withRouter(Game)} />\n <Route component={withRouter(NotFound)} />\n </div>\n </Router>\n , document.getElementById('root'));\nserviceWorker.unregister();\n\nI searched around and found that I should be using <Switch> inside my Router but adding <Switch> makes my webpage blank and shows nothing. ", "And currently the way I have it, the not found page shows at the bottom of my scroll while I only want it to appear when user enters the wrong URL. ", "Where or how should my routes be implemented in order for me to render the 404 page only when user navigates to the wrong URL and not having it at all times in my scroll app home page? ", "Any help would be appreciated. ", "Thanks.", "\nUpdate\nTried doing the following:\n<Router>\n <Switch>\n <Route path={`${base_url}/`} component={withRouter(Nav)} />\n <Route exact path={`${base_url}/`} component={withRouter(Landing)} />\n <Route exact path={`${base_url}/`} component={withRouter(Overview)} />\n <Route exact path={`${base_url}/`} component={withRouter(Solutions)} />\n <Route exact path={`${base_url}/`} component={withRouter(Games)} />\n <Route exact path={`${base_url}/`} component={withRouter(Platforms)} />\n <Route exact path={`${base_url}/`} component={withRouter(Focus)} />\n <Route exact path={`${base_url}/`} component={withRouter(News)} />\n <Route exact path={`${base_url}/`} component={withRouter(Contact)} />\n <Route exact path={`${base_url}/catalogue`} component={withRouter(Catalogue)} />\n <Route exact path={`${base_url}/game/:gameid`} component={withRouter(Game)} />\n <Route path=\"*\" exact={true} component={withRouter(NotFound)} />\n </Switch>\n</Router>\n\nIt shows me only the nav bar and nothing else, rest is all blank. ", "And when I navigate to say /catalogue page, it shows that as blank as well. ", "URL is changing but its not showing anything in the view.", "\nSolution\nFollowing did the trick for me as explained below by @Craig:\n<Router>\n <div>\n <Route path={`${base_url}/`} component={withRouter(Nav)} />\n <Switch>\n <Route exact path={`${base_url}/`} render={() => (\n <div>\n <Landing/>\n <Overview/>\n <Solutions/>\n <Games/>\n <Platforms/>\n <Focus/>\n <News/>\n <Contact/>\n </div>\n )} />\n <Route exact path={`${base_url}/catalogue`} component={withRouter(Catalogue)} />\n <Route exact path={`${base_url}/game/:gameid`} component={withRouter(Game)} />\n <Route path=\"*\" component={withRouter(NotFound)} />\n </Switch>\n </div>\n</Router>\n\nA:\n\nReplace the <div> with a <Switch>. ", "When you tried adding <Switch>, it sounds like you had the <div> as a child of the <Switch> and then all of your <Route> components under the div. ", "You could move the div outside of the Router if you wanted to.", "\n\nAll children of a <Switch> should be <Route> or <Redirect> elements.", "\n\nhttps://reacttraining.com/react-router/core/api/Switch/children-node\nUpdate\nChange your new code to this:\n<Router>\n <div>\n <Route path={`${base_url}/`} component={withRouter(Nav)} />\n <Switch>\n <Route exact path={`${base_url}/`} component={withRouter(Landing)} />\n <Route exact path={`${base_url}/`} component={withRouter(Overview)} />\n <Route exact path={`${base_url}/`} component={withRouter(Solutions)} />\n <Route exact path={`${base_url}/`} component={withRouter(Games)} />\n <Route exact path={`${base_url}/`} component={withRouter(Platforms)} />\n <Route exact path={`${base_url}/`} component={withRouter(Focus)} />\n <Route exact path={`${base_url}/`} component={withRouter(News)} />\n <Route exact path={`${base_url}/`} component={withRouter(Contact)} />\n <Route exact path={`${base_url}/catalogue`} component={withRouter(Catalogue)} />\n <Route exact path={`${base_url}/game/:gameid`} component={withRouter(Game)} />\n <Route path={\"*\"} exact={true} component={withRouter(NotFound)} />\n </Switch>\n </div>\n</Router>\n\nThe switch will only render the first match.", "\n\n" ]

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[ "Involvement of NLK and Sox11 in neural induction in Xenopus development.", "\nThe Wnt signal transduction pathway regulates various aspects of embryonal development and has been implicated in promoting cancer. ", "Signalling by Wnts leads to the stabilization of cytosolic beta-catenin, which then associates with TCF transcription factors to regulate expression of Wnt-target genes. ", "The Wnt pathway is further subject to cross-regulation at various levels by other components. ", "Recent evidence suggests that a specific MAP kinase pathway involving the MAP kinase kinase kinase TAK1 and the MAP kinase NLK counteract Wnt signalling. ", "In particular, it has been shown that TAK1 activates NLK, which phosphorylates TCFs bound to beta-catenin. ", "This phosphorylation down-regulates the DNA-binding activity of a TCF-4/beta-catenin complex, and blocks activation of their target genes. ", "To investigate the role of NLK in Xenopus development, we isolated xNLK, a Xenopus homologue of NLK. ", "Our findings indicate that xNLK is expressed in neural tissues and induces the anterior-neural marker gene, Otx-2. ", "Moreover, xSox11, which is induced by the expression of Chordin, co-operates with xNLK to induce neural development. ", "These molecules also interact in mammalian cells, and expression of a mutant of xNLK lacking kinase activity was found to suppress the induction of neural marker gene expression by xSox11. ", "Our findings indicate that xNLK may play a role in neural development together with xSox11 during early Xenopus embryogenesis." ]

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[ "Q:\n\nPDO insert query slowing the site down\n\nOn my site I have coded a function that shows you how many unique visitors and how many pageviews I get per day.", "\nThe problem is that sometimes the insert query takes forever and in InnoDB theres no DELAYED INSERT function.", "\nEdit: It is using InnoDB, what I mean with long loading time is around 6 seconds instead of like 0.1-0.5 seconds. ", "As soon as I remove the logging the site is much faster.", "\nThe $b array bellow contains browser info, but according to XHProf its the PDO query that's taking so long to execute.", "\nThe insert code is this:\n$values = array(\n 'time' => time(),\n 'ip' => $_SERVER['REMOTE_ADDR'],\n 'page' => rtrim((isset($_GET['q']) ? ", "$_GET['q'] : 'index'), '/'),\n 'browser' => $b[11][0] . ' ' . ", "$b[11][1],\n 'os' => $uos,\n 'referred' => (isset($_SERVER['HTTP_REFERER']) && !", "preg_match('|^' . ", "Config::getValue('site', 'url') . '", "|', $_SERVER['HTTP_REFERER']) ? ", "$_SERVER['HTTP_REFERER'] : ''),\n );\n\n $this->table->insert($values);\n\nand the insert function code:\npublic function insert($table, $data) {\n ksort($data);\n\n $fieldNames = implode('`, `', array_keys($data));\n $fieldValues = ':' . ", "implode(', :', array_keys($data));\n\n $sth = $this->prepare('INSERT INTO ' . ", "$table . '(", "`' . ", "$fieldNames . '", "`) VALUES (' . ", "$fieldValues . ');');", "\n\n foreach ($data as $key => $value) {\n $sth->bindValue(':' . ", "$key, $value);\n }\n\n $sth->execute();\n}\n\nA:\n\nA minor optimization. ", "The way you are doing your binding you can get rid of the foreach statement and pass the array directly to execute. ", "PDO will map the arrays key to the :binding names you created in the prepare statement.", "\n$sth->execute($data);\n\nThat said, you should look at your slow query log in mysql to see what is going on. ", "Even though you are using Innodb, there are scenarios where Innodb will lock the table. ", "That could be why inserts are taking a long time sometimes. ", "You can reduce your slow query threshold to something like 3 seconds to capture the queries. ", "The log will tell you how much time was spent in each stage (i.e. locked).", "\n\n" ]

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[ "Veronica Da Souza Adult Movies Adult DVD Talk\n\nCheck out the impressive selection of Veronica Da Souza porn videos available to stream on the world's best porno tube, Youporn. ", "Discover all of the XXX movies featuring Veronica Da Souza and all of your other favorite pornstars for free right now!" ]

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[ "Ocular anomalies in the branchio-oculo-facial syndrome.", "\nTo describe the ocular anomalies in two cases of branchio-oculo-facial syndrome (BOFS). ", "Two cases of BOFS are reviewed. ", "Branchio-oculo-facial syndrome is a rare branchial cleft syndrome that is characterized by a typical facial appearance of pseudo-cleft or cleft lip, subauricular branchial sinuses, deafness and ocular anomalies, which include nasolacrimal obstruction, telecanthus and colobomata. ", "It has an autosomal dominant inheritance pattern." ]

{ "pile_set_name": "PubMed Abstracts" }

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[ "Q:\n\nEmail WCF traces to me\n\nSo I've recently figured out how to turn on the WCF traces which creates an svclog file on my server and this is awesome. ", " But the problem I have is I don't have direct access to the server where I'm working on my web service so everytime I need to look at the trace file I have to get someone else here at my office to log onto the server for me then I have to upload the trace file to a cloud server because its usually too big to email and then go through weeks worth of requests to find what I want to analyze.", "\nLong story short I want to know if there is a way with trace logging for me to send an email to myself of every trace that gets stored?", "\n\nA:\n\nThe answer appears to be \"no\" there is no way to email traces using the svclog. ", " There are other ways to accomplish the same goal.", "\n\n" ]

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[ "It is difficult to comprehend the affects of a smallpox outbreak. ", "But the possibility exists, as remote as it may be. ", "One line of control is the use of antiviral compounds. ", "DNA replication enzymes are validated targets of antiviral compounds. ", "This proposal is an intensive biochemical characterization of the proteins involved in replication of the poxvirus genome. ", "The vaccinia virus, a close relative of smallpox, has duplex DNA genome that replicates entirely in the cytoplasm and encodes most or all of its own DNA replication proteins. ", "Among these are the E9 DNA polymerase, A20 polymerase accessory protein, and the D4 uracyl deglycosylase (UDG) polymerase accessory proteins. ", "These three proteins, E9/A20/D4 constitute a processive E9 holoenzyme replicase. ", "In addition the virus encodes the essential D5 NTPase, Bl kinase and a single strand DNA binding protein called 13. ", "We have recently purified recombinant E9 and A20/D4 complex and have constituted the E9 holoenzyme which forms the preliminary data for this proposal. ", "We plan to determine the contact points between these proteins and understand how they provide a tight yet mobile grip of the E9 holoenzyme to DNA. ", "We will also determine if the D5 NTPase is a helicase, and whether it functionally interacts with E9 holoenzyme. ", "Alternatively, D5 may supply some other function to the replicative machinery. ", "We will also examine the role(s) of the 13 SSB in D5 and E9 holoenzyme action. ", "Finally, Rockefeller University's 20,000 chemical compound library will be screened for inhibitors of the E9 holoenzyme as a proof of principle that the proteins and assays developed herein can be useful to a pharmaceutical company with the proper tools and expertise to develop an antiviral compound." ]

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[ "Various actions of oestrogens on the vascular system.", "\nEpidemiological studies show a reduction in cardiovascular disease with postmenopausal oestrogen use. ", "Oestrogens have been shown to have both metabolic effects and direct effects on the vasculature, both of which may improve arterial function and reduce or reverse atheroma formation. ", "The metabolic effects include changes in lipids and lipoproteins, glucose and insulin metabolism, coagulation and fibrinolysis. ", "The direct arterial effects include changes in endothelium-dependent processes, ion channels, renin-angiotensin system and remodelling processes. ", "The various actions of oestrogens on the vascular system are reviewed. ", "It is clearly important to understand the biological basis of these effects of oestrogen on the cardiovascular system in order to optimize current and future hormone-replacement therapy in women after natural or surgical menopause." ]

{ "pile_set_name": "PubMed Abstracts" }

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[ "Wherefore heart thou? ", "Embryonic origins of cardiogenic mesoderm.", "\nThe developing heart in avian embryos has been examined extensively over the past several decades using classic embryologic and, more recently, molecular and genetic approaches. ", "Still, conflicting reports arise as to the location and regulation of early heart progenitors in the embryo. ", "In addition, a new source of cardiomyocytes has been identified recently that contributes to the outflow tract after the heart initially forms. ", "The focus of this review is the examination of the tissue interactions, signaling molecules, and gene regulatory mechanisms that, together, control heart formation from primary and secondary heart forming fields of the embryo. ", "Early studies of the induction and regulation of the secondary heart field indicate that at least some of the events of primary cardiomyogenesis are recapitulated when the conotruncal myocardium is recruited into the heart. ", "The consideration of classic embryologic studies of the heart forming fields in terms of modern molecular and genetic tools provides reinforcing evidence for the location of cardiac progenitors in the embryo. ", "The accurate definition of early cardiac regulatory events provides a necessary foundation for the generation of new therapeutic sources of cardiomyocytes." ]

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[ "You see them on the sidelines for pee-wee, high school, college and professional games. ", "They are just as much a part of the fabric of football and basketball as mascots and concession stands.", "\n\nBut in spite of having a rich history of athleticism, entertaining fans and supporting organizations, professional cheerleaders (or dancers) in the National Football League and National Basketball Association have little by way of financial earnings. ", "On average, cheerleaders earn approximately $75 to $150 per game. ", "That rate doesn't traditionally consider the hours of practice the cheerleaders have to put in ahead of the game.", "\n\nIn fact, last month the Milwaukee Bucks settled a lawsuit with former cheerleader Lauren Herington for the team's failure to adhere to the U.S. Fair Labor Standards Act and Wisconsin's wage and payment laws. ", "Having worked the 2013-14 season (before Marc Lasry and Wes Edens became the team's co-owners), Herington claimed that on average Bucks dancers spent 30-40 hours a week in rehearsals, workout sessions, practices, charity events and performing at games. ", "She noted that the payments were as such: $65 for games, $30 for practice and $50 for special events. ", "With total hours worked per week considered, that comes out to about $3.50 to $4.50 an hour on average.", "\n\nWhile lawsuits in both leagues have resulted in guarantees of improved wages for some, the earnings for the highest paid cheerleaders remains well below the estimated value they add to their organizations.", "\n\nBut why? ", "How are cheerleaders such an integral part of the NBA and NFL experience -- providing entertainment, community service and branding -- but remain seemingly underpaid?", "\n\nFor their part, NFL and NBA teams have historically taken the position that cheerleaders are independent contractors. ", "If classified as contractors, the teams aren't required to pay them salaries in line with state and federal minimum wages. ", "The recent legal battles have hinged on whether cheerleaders are employees of these organizations, a fact that is determined by how much control an individual has on the way they perform their duties.", "\n\nHorecee St. Cyr, 33, a Howard University graduate and formally trained actor and dancer who spent three seasons (2008-11) with the LA Clippers and one season (2004-05) with the Washington Wizards was keenly aware of the discrepancy from Day 1.", "\n\n\"[Pro] dancers are [inexpensive] labor and entertainment for these ball clubs that rake in millions of dollars. ", "We were underpaid and the long hours limited our ability to pursue other opportunities in performance. ", "We didn't get any health benefits or insurance,\" St. Cyr added.", "\n\nSuch conditions explain why many of the cheerleaders across professional sports leagues tend to be recent college graduates less concerned with benefits and career longevity, or women with other full-time jobs who can afford to forgo benefits from their team. ", "To be fair, St. Cyr, who is now a working actress and serves on the board of the art rehabilitation non-profit HIPPO Life, acknowledges that some teams made an effort to show they valued the cheerleaders in non-monetary ways.", "\n\n\"At the Wizards, while the pay wasn't great, I felt a sense of community. ", "The [team] helped the cheerleaders get sponsorships [from local spas, health care providers and beauty brands], made sure we had secured parking and practice locations. ", "And they always gave us our [comp] game tickets. ", "That went a long way.\"", "\n\nKim Griffith, 38, a Howard and Emory University graduate who cheered for a season with the Carolina Panthers and five years with the Atlanta Falcons, provided some great insight as well.", "\n\n\"When I first started, I was in my second year of grad school, and I had a part-time job,\" she said. \"", "Once I graduated, I worked full-time and cheered for the Falcons on the side. ", "I loved to dance, and I needed something to do outside of school and my job that wasn't so serious. ", "I was only fine with the pay because I loved the dancing, performing and service.\"", "\n\nMany teams require that cheerleaders participate in community service activities and provide occasional paid appearances. ", "But by and large, the teams are seemingly counting on the love for dancing and service to motivate participation.", "\n\n\"With the Falcons we had to sign a contract that required us to have a full-time job, be a full-time student or be a stay-at-home mom. ", "So, I don't think money was why people chose to do it,\" Griffith said. \"", "Could they have paid us more? ", "Absolutely.\"", "\n\nIf the love of dancing and community service weren't enough to encourage intense training and performances for nominal pay, Griffith, who is now a wife, mother and a Famous Toastery restaurant franchisee, shared that there were still other inducements. \"", "We got tickets for games, free products and discounts on clothing. ", "But for me one of the greatest incentives was the opportunity it afforded me to travel. ", "I was on a small team that performed for the U.S. troops [USO] and at the U.S. Army All-American Bowl. ", "I traveled to countries I wouldn't have otherwise gone.\"", "\n\nThere seem to be some legitimate reasons that compel women to cheer for nominal wages. ", "But is that the real reason teams pay so little?", "\n\nSurely, it shouldn't be that teams underpay cheerleaders because they know the women love dancing and are willing to accept it. ", "For one, no other industry comes to mind in which employees are expected to supplement their incomes (to the point of earning wages below state and federal minimum wage standards) based simply on how much they love their work.", "\n\nFor example, professional players aren't expected to devalue their efforts. ", "In fact, the minimum salary for an NBA rookie is $815,615 (for the 2017 - 2018 season) and $465,000 for a first-year NFL player in 2017. ", "Those wages afford each player a comfortable lifestyle while doing something they love.", "\n\nAnd the willingness to accept the pay is a fallacy.", "\n\nHistorically, and often behind-the-scenes, cheerleaders are vocal with their dissatisfaction. ", "In 1995, for instance, the Buffalo Jills cheerleaders won a complaint against the Buffalo Bills before the National Labor Relations Board. ", "The Jills earned the right to be classified as employees when the NLRB determined that the Bills exercised significant control over things like cheerleaders' schedules, uniforms, and weight. ", "The Jills subsequently formed the first-ever professional cheerleaders' union to bargain for better employee rights. ", "The Bills, rather than respond with more fair pay, quashed the union by canceling all appearances and contracting out its cheerleading services. ", "In April 2014, the Jills filed a class action lawsuit, alleging they had been improperly classified as independent contractors rather than employees. ", "The courts ruled in their favor in 2016.", "\n\nLuckily, the leagues are taking notice. ", "In fact, NBA spokesman Mike Bass noted that: \"Team dancers are an important part of the NBA game experience and are valued members of the NBA family. ", "As for all employees, we work with our teams to ensure that they comply with all applicable wage and working condition laws.\"", "\n\nWe can only hope that as these women continue to use the courts to fight for fair wages, teams will begin to pay them what they're worth.", "\n\nCecelia Townes is a proud graduate of UCLA School of Law and the Real HU in Washington. ", "She used to ball so hard on the tennis court. ", "Now she serves it up on her blog, GladiatHers.com, and with student-athletes with Beyond the Game LLC. ", "Follow Cecelia on Twitter & Instagram @SportyEsquire" ]

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[ "<?", "php\n/**\n * WordPress Customize Control classes\n *\n * @package WordPress\n * @subpackage Customize\n * @since 3.4.0\n */\n\n/**\n * Customize Control class.", "\n *\n * @since 3.4.0\n */\nclass WP_Customize_Control {\n\n\t/**\n\t * Incremented with each new class instantiation, then stored in $instance_number.", "\n\t *\n\t * Used when sorting two instances whose priorities are equal.", "\n\t *\n\t * @since 4.1.0\n\t *\n\t * @static\n\t * @var int\n\t */\n\tprotected static $instance_count = 0;\n\n\t/**\n\t * Order in which this instance was created in relation to other instances.", "\n\t *\n\t * @since 4.1.0\n\t * @var int\n\t */\n\tpublic $instance_number;\n\n\t/**\n\t * Customizer manager.", "\n\t *\n\t * @since 3.4.0\n\t * @var WP_Customize_Manager\n\t */\n\tpublic $manager;\n\n\t/**\n\t * Control ID.", "\n\t *\n\t * @since 3.4.0\n\t * @var string\n\t */\n\tpublic $id;\n\n\t/**\n\t * All settings tied to the control.", "\n\t *\n\t * @since 3.4.0\n\t * @var array\n\t */\n\tpublic $settings;\n\n\t/**\n\t * The primary setting for the control (if there is one).", "\n\t *\n\t * @since 3.4.0\n\t * @var string\n\t */\n\tpublic $setting = 'default';\n\n\t/**\n\t * Capability required to use this control.", "\n\t *\n\t * Normally this is empty and the capability is derived from the capabilities\n\t * of the associated `$settings`.", "\n\t *\n\t * @since 4.5.0\n\t * @var string\n\t */\n\tpublic $capability;\n\n\t/**\n\t * Order priority to load the control in Customizer.", "\n\t *\n\t * @since 3.4.0\n\t * @var int\n\t */\n\tpublic $priority = 10;\n\n\t/**\n\t * Section the control belongs to.", "\n\t *\n\t * @since 3.4.0\n\t * @var string\n\t */\n\tpublic $section = '';\n\n\t/**\n\t * Label for the control.", "\n\t *\n\t * @since 3.4.0\n\t * @var string\n\t */\n\tpublic $label = '';\n\n\t/**\n\t * Description for the control.", "\n\t *\n\t * @since 4.0.0\n\t * @var string\n\t */\n\tpublic $description = '';\n\n\t/**\n\t * List of choices for 'radio' or 'select' type controls, where values are the keys, and labels are the values.", "\n\t *\n\t * @since 3.4.0\n\t * @var array\n\t */\n\tpublic $choices = array();\n\n\t/**\n\t * List of custom input attributes for control output, where attribute names are the keys and values are the values.", "\n\t *\n\t * Not used for 'checkbox', 'radio', 'select', 'textarea', or 'dropdown-pages' control types.", "\n\t *\n\t * @since 4.0.0\n\t * @var array\n\t */\n\tpublic $input_attrs = array();\n\n\t/**\n\t * Show UI for adding new content, currently only used for the dropdown-pages control.", "\n\t *\n\t * @since 4.7.0\n\t * @var bool\n\t */\n\tpublic $allow_addition = false;\n\n\t/**\n\t * @deprecated It is better to just call the json() method\n\t * @since 3.4.0\n\t * @var array\n\t */\n\tpublic $json = array();\n\n\t/**\n\t * Control's Type.", "\n\t *\n\t * @since 3.4.0\n\t * @var string\n\t */\n\tpublic $type = 'text';\n\n\t/**\n\t * Callback.", "\n\t *\n\t * @since 4.0.0\n\t *\n\t * @see WP_Customize_Control::active()\n\t *\n\t * @var callable Callback is called with one argument, the instance of\n\t * WP_Customize_Control, and returns bool to indicate whether\n\t * the control is active (such as it relates to the URL\n\t * currently being previewed).", "\n\t */\n\tpublic $active_callback = '';\n\n\t/**\n\t * Constructor.", "\n\t *\n\t * Supplied `$args` override class property defaults.", "\n\t *\n\t * If `$args['settings']` is not defined, use the $id as the setting ID.", "\n\t *\n\t * @since 3.4.0\n\t *\n\t * @param WP_Customize_Manager $manager Customizer bootstrap instance.", "\n\t * @param string $id Control ID.", "\n\t * @param array $args {\n\t * Optional. ", "Arguments to override class property defaults.", "\n\t *\n\t * @type int $instance_number Order in which this instance was created in relation\n\t * to other instances.", "\n\t * @type WP_Customize_Manager $manager Customizer bootstrap instance.", "\n\t * @type string $id Control ID.", "\n\t * @type array $settings All settings tied to the control. ", "If undefined, `$id` will\n\t * be used.", "\n\t * @type string $setting The primary setting for the control (if there is one).", "\n\t * Default 'default'.", "\n\t * @type int $priority Order priority to load the control. ", "Default 10.", "\n\t * @type string $section Section the control belongs to. ", "Default empty.", "\n\t * @type string $label Label for the control. ", "Default empty.", "\n\t * @type string $description Description for the control. ", "Default empty.", "\n\t * @type array $choices List of choices for 'radio' or 'select' type controls, where\n\t * values are the keys, and labels are the values.", "\n\t * Default empty array.", "\n\t * @type array $input_attrs List of custom input attributes for control output, where\n\t * attribute names are the keys and values are the values. ", "Not\n\t * used for 'checkbox', 'radio', 'select', 'textarea', or\n\t * 'dropdown-pages' control types. ", "Default empty array.", "\n\t * @type array $json Deprecated. ", "Use WP_Customize_Control::json() instead.", "\n\t * @type string $type Control type. ", "Core controls include 'text', 'checkbox',\n\t * 'textarea', 'radio', 'select', and 'dropdown-pages'. ", "Additional\n\t * input types such as 'email', 'url', 'number', 'hidden', and\n\t * 'date' are supported implicitly. ", "Default 'text'.", "\n\t * }\n\t */\n\tpublic function __construct( $manager, $id, $args = array() ) {\n\t\t$keys = array_keys( get_object_vars( $this ) );\n\t\tforeach ( $keys as $key ) {\n\t\t\tif ( isset( $args[ $key ] ) ) {\n\t\t\t\t$this->$key = $args[ $key ];\n\t\t\t}\n\t\t}\n\n\t\t$this->manager = $manager;\n\t\t$this->id = $id;\n\t\tif ( empty( $this->active_callback ) ) {\n\t\t\t$this->active_callback = array( $this, 'active_callback' );\n\t\t}\n\t\tself::$instance_count += 1;\n\t\t$this->instance_number = self::$instance_count;\n\n\t\t// Process settings.", "\n\t\tif ( ! ", "isset( $this->settings ) ) {\n\t\t\t$this->settings = $id;\n\t\t}\n\n\t\t$settings = array();\n\t\tif ( is_array( $this->settings ) ) {\n\t\t\tforeach ( $this->settings as $key => $setting ) {\n\t\t\t\t$settings[ $key ] = $this->manager->get_setting( $setting );\n\t\t\t}\n\t\t} else if ( is_string( $this->settings ) ) {\n\t\t\t$this->setting = $this->manager->get_setting( $this->settings );\n\t\t\t$settings['default'] = $this->setting;\n\t\t}\n\t\t$this->settings = $settings;\n\t}\n\n\t/**\n\t * Enqueue control related scripts/styles.", "\n\t *\n\t * @since 3.4.0\n\t */\n\tpublic function enqueue() {}\n\n\t/**\n\t * Check whether control is active to current Customizer preview.", "\n\t *\n\t * @since 4.0.0\n\t *\n\t * @return bool Whether the control is active to the current preview.", "\n\t */\n\tfinal public function active() {\n\t\t$control = $this;\n\t\t$active = call_user_func( $this->active_callback, $this );\n\n\t\t/**\n\t\t * Filters response of WP_Customize_Control::active().", "\n\t\t *\n\t\t * @since 4.0.0\n\t\t *\n\t\t * @param bool $active Whether the Customizer control is active.", "\n\t\t * @param WP_Customize_Control $control WP_Customize_Control instance.", "\n\t\t */\n\t\t$active = apply_filters( 'customize_control_active', $active, $control );\n\n\t\treturn $active;\n\t}\n\n\t/**\n\t * Default callback used when invoking WP_Customize_Control::active().", "\n\t *\n\t * Subclasses can override this with their specific logic, or they may\n\t * provide an 'active_callback' argument to the constructor.", "\n\t *\n\t * @since 4.0.0\n\t *\n\t * @return true Always true.", "\n\t */\n\tpublic function active_callback() {\n\t\treturn true;\n\t}\n\n\t/**\n\t * Fetch a setting's value.", "\n\t * Grabs the main setting by default.", "\n\t *\n\t * @since 3.4.0\n\t *\n\t * @param string $setting_key\n\t * @return mixed The requested setting's value, if the setting exists.", "\n\t */\n\tfinal public function value( $setting_key = 'default' ) {\n\t\tif ( isset( $this->settings[ $setting_key ] ) ) {\n\t\t\treturn $this->settings[ $setting_key ]->value();\n\t\t}\n\t}\n\n\t/**\n\t * Refresh the parameters passed to the JavaScript via JSON.", "\n\t *\n\t * @since 3.4.0\n\t */\n\tpublic function to_json() {\n\t\t$this->json['settings'] = array();\n\t\tforeach ( $this->settings as $key => $setting ) {\n\t\t\t$this->json['settings'][ $key ] = $setting->id;\n\t\t}\n\n\t\t$this->json['type'] = $this->type;\n\t\t$this->json['priority'] = $this->priority;\n\t\t$this->json['active'] = $this->active();\n\t\t$this->json['section'] = $this->section;\n\t\t$this->json['content'] = $this->get_content();\n\t\t$this->json['label'] = $this->label;\n\t\t$this->json['description'] = $this->description;\n\t\t$this->json['instanceNumber'] = $this->instance_number;\n\n\t\tif ( 'dropdown-pages' === $this->type ) {\n\t\t\t$this->json['allow_addition'] = $this->allow_addition;\n\t\t}\n\t}\n\n\t/**\n\t * Get the data to export to the client via JSON.", "\n\t *\n\t * @since 4.1.0\n\t *\n\t * @return array Array of parameters passed to the JavaScript.", "\n\t */\n\tpublic function json() {\n\t\t$this->to_json();\n\t\treturn $this->json;\n\t}\n\n\t/**\n\t * Checks if the user can use this control.", "\n\t *\n\t * Returns false if the user cannot manipulate one of the associated settings,\n\t * or if one of the associated settings does not exist. ", "Also returns false if\n\t * the associated section does not exist or if its capability check returns\n\t * false.", "\n\t *\n\t * @since 3.4.0\n\t *\n\t * @return bool False if theme doesn't support the control or user doesn't have the required permissions, otherwise true.", "\n\t */\n\tfinal public function check_capabilities() {\n\t\tif ( ! ", "empty( $this->capability ) && ! ", "current_user_can( $this->capability ) ) {\n\t\t\treturn false;\n\t\t}\n\n\t\tforeach ( $this->settings as $setting ) {\n\t\t\tif ( ! ", "$setting || ! ", "$setting->check_capabilities() ) {\n\t\t\t\treturn false;\n\t\t\t}\n\t\t}\n\n\t\t$section = $this->manager->get_section( $this->section );\n\t\tif ( isset( $section ) && ! ", "$section->check_capabilities() ) {\n\t\t\treturn false;\n\t\t}\n\n\t\treturn true;\n\t}\n\n\t/**\n\t * Get the control's content for insertion into the Customizer pane.", "\n\t *\n\t * @since 4.1.0\n\t *\n\t * @return string Contents of the control.", "\n\t */\n\tfinal public function get_content() {\n\t\tob_start();\n\t\t$this->maybe_render();\n\t\treturn trim( ob_get_clean() );\n\t}\n\n\t/**\n\t * Check capabilities and render the control.", "\n\t *\n\t * @since 3.4.0\n\t * @uses WP_Customize_Control::render()\n\t */\n\tfinal public function maybe_render() {\n\t\tif ( ! ", "$this->check_capabilities() )\n\t\t\treturn;\n\n\t\t/**\n\t\t * Fires just before the current Customizer control is rendered.", "\n\t\t *\n\t\t * @since 3.4.0\n\t\t *\n\t\t * @param WP_Customize_Control $this WP_Customize_Control instance.", "\n\t\t */\n\t\tdo_action( 'customize_render_control', $this );\n\n\t\t/**\n\t\t * Fires just before a specific Customizer control is rendered.", "\n\t\t *\n\t\t * The dynamic portion of the hook name, `$this->id`, refers to\n\t\t * the control ID.", "\n\t\t *\n\t\t * @since 3.4.0\n\t\t *\n\t\t * @param WP_Customize_Control $this WP_Customize_Control instance.", "\n\t\t */\n\t\tdo_action( \"customize_render_control_{$this->id}\", $this );\n\n\t\t$this->render();\n\t}\n\n\t/**\n\t * Renders the control wrapper and calls $this->render_content() for the internals.", "\n\t *\n\t * @since 3.4.0\n\t */\n\tprotected function render() {\n\t\t$id = 'customize-control-' . ", "str_replace( array( '[', ']' ), array( '-', '' ), $this->id );\n\t\t$class = 'customize-control customize-control-' . ", "$this->type;\n\n\t\tprintf( '<li id=\"%s\" class=\"%s\">', esc_attr( $id ), esc_attr( $class ) );\n\t\t$this->render_content();\n\t\techo '</li>';\n\t}\n\n\t/**\n\t * Get the data link attribute for a setting.", "\n\t *\n\t * @since 3.4.0\n\t * @since 4.9.0 Return a `data-customize-setting-key-link` attribute if a setting is not registered for the supplied setting key.", "\n\t *\n\t * @param string $setting_key\n\t * @return string Data link parameter, a `data-customize-setting-link` attribute if the `$setting_key` refers to a pre-registered setting,\n\t * and a `data-customize-setting-key-link` attribute if the setting is not yet registered.", "\n\t */\n\tpublic function get_link( $setting_key = 'default' ) {\n\t\tif ( isset( $this->settings[ $setting_key ] ) && $this->settings[ $setting_key ] instanceof WP_Customize_Setting ) {\n\t\t\treturn 'data-customize-setting-link=\"' . ", "esc_attr( $this->settings[ $setting_key ]->id ) . '\"';", "\n\t\t} else {\n\t\t\treturn 'data-customize-setting-key-link=\"' . ", "esc_attr( $setting_key ) . '\"';", "\n\t\t}\n\t}\n\n\t/**\n\t * Render the data link attribute for the control's input element.", "\n\t *\n\t * @since 3.4.0\n\t * @uses WP_Customize_Control::get_link()\n\t *\n\t * @param string $setting_key\n\t */\n\tpublic function link( $setting_key = 'default' ) {\n\t\techo $this->get_link( $setting_key );\n\t}\n\n\t/**\n\t * Render the custom attributes for the control's input element.", "\n\t *\n\t * @since 4.0.0\n\t */\n\tpublic function input_attrs() {\n\t\tforeach ( $this->input_attrs as $attr => $value ) {\n\t\t\techo $attr . '", "=\"' . ", "esc_attr( $value ) . '\" ';", "\n\t\t}\n\t}\n\n\t/**\n\t * Render the control's content.", "\n\t *\n\t * Allows the content to be overridden without having to rewrite the wrapper in `$this::render()`.", "\n\t *\n\t * Supports basic input types `text`, `checkbox`, `textarea`, `radio`, `select` and `dropdown-pages`.", "\n\t * Additional input types such as `email`, `url`, `number`, `hidden` and `date` are supported implicitly.", "\n\t *\n\t * Control content can alternately be rendered in JS. ", "See WP_Customize_Control::print_template().", "\n\t *\n\t * @since 3.4.0\n\t */\n\tprotected function render_content() {\n\t\t$input_id = '_customize-input-' . ", "$this->id;\n\t\t$description_id = '_customize-description-' . ", "$this->id;\n\t\t$describedby_attr = ( ! ", "empty( $this->description ) ) ? ' ", "aria-describedby=\"' . ", "esc_attr( $description_id ) . '\" ' : '';", "\n\t\tswitch ( $this->type ) {\n\t\t\tcase 'checkbox':\n\t\t\t\t?", ">\n\t\t\t\t<span class=\"customize-inside-control-row\">\n\t\t\t\t\t<input\n\t\t\t\t\t\tid=\"<?php echo esc_attr( $input_id ); ?", ">\"\n\t\t\t\t\t\t<?", "php echo $describedby_attr; ?", ">\n\t\t\t\t\t\ttype=\"checkbox\"\n\t\t\t\t\t\tvalue=\"<?php echo esc_attr( $this->value() ); ?", ">\"\n\t\t\t\t\t\t<?", "php $this->link(); ?", ">\n\t\t\t\t\t\t<?", "php checked( $this->value() ); ?", ">\n\t\t\t\t\t/>\n\t\t\t\t\t<label for=\"<?php echo esc_attr( $input_id ); ?", ">\"><?", "php echo esc_html( $this->label ); ?", "></label>\n\t\t\t\t\t<?", "php if ( ! ", "empty( $this->description ) ) : ?", ">\n\t\t\t\t\t\t<span id=\"<?php echo esc_attr( $description_id ); ?", ">\" class=\"description customize-control-description\"><?php echo $this->description; ?", "></span>\n\t\t\t\t\t<?", "php endif; ?", ">\n\t\t\t\t</span>\n\t\t\t\t<?", "php\n\t\t\t\tbreak;\n\t\t\tcase 'radio':\n\t\t\t\tif ( empty( $this->choices ) ) {\n\t\t\t\t\treturn;\n\t\t\t\t}\n\n\t\t\t\t$name = '_customize-radio-' . ", "$this->id;\n\t\t\t\t?", ">\n\t\t\t\t<?", "php if ( ! ", "empty( $this->label ) ) : ?", ">\n\t\t\t\t\t<span class=\"customize-control-title\"><?php echo esc_html( $this->label ); ?", "></span>\n\t\t\t\t<?", "php endif; ?", ">\n\t\t\t\t<?", "php if ( ! ", "empty( $this->description ) ) : ?", ">\n\t\t\t\t\t<span id=\"<?php echo esc_attr( $description_id ); ?", ">\" class=\"description customize-control-description\"><?php echo $this->description ; ?", "></span>\n\t\t\t\t<?", "php endif; ?", ">\n\n\t\t\t\t<?", "php foreach ( $this->choices as $value => $label ) : ?", ">\n\t\t\t\t\t<span class=\"customize-inside-control-row\">\n\t\t\t\t\t\t<input\n\t\t\t\t\t\t\tid=\"<?php echo esc_attr( $input_id . '", "-radio-' . ", "$value ); ?", ">\"\n\t\t\t\t\t\t\ttype=\"radio\"\n\t\t\t\t\t\t\t<?", "php echo $describedby_attr; ?", ">\n\t\t\t\t\t\t\tvalue=\"<?php echo esc_attr( $value ); ?", ">\"\n\t\t\t\t\t\t\tname=\"<?php echo esc_attr( $name ); ?", ">\"\n\t\t\t\t\t\t\t<?", "php $this->link(); ?", ">\n\t\t\t\t\t\t\t<?", "php checked( $this->value(), $value ); ?", ">\n\t\t\t\t\t\t\t/>\n\t\t\t\t\t\t<label for=\"<?php echo esc_attr( $input_id . '", "-radio-' . ", "$value ); ?", ">\"><?", "php echo esc_html( $label ); ?", "></label>\n\t\t\t\t\t</span>\n\t\t\t\t<?", "php endforeach; ?", ">\n\t\t\t\t<?", "php\n\t\t\t\tbreak;\n\t\t\tcase 'select':\n\t\t\t\tif ( empty( $this->choices ) ) {\n\t\t\t\t\treturn;\n\t\t\t\t}\n\n\t\t\t\t?", ">\n\t\t\t\t<?", "php if ( ! ", "empty( $this->label ) ) : ?", ">\n\t\t\t\t\t<label for=\"<?php echo esc_attr( $input_id ); ?", ">\" class=\"customize-control-title\"><?php echo esc_html( $this->label ); ?", "></label>\n\t\t\t\t<?", "php endif; ?", ">\n\t\t\t\t<?", "php if ( ! ", "empty( $this->description ) ) : ?", ">\n\t\t\t\t\t<span id=\"<?php echo esc_attr( $description_id ); ?", ">\" class=\"description customize-control-description\"><?php echo $this->description; ?", "></span>\n\t\t\t\t<?", "php endif; ?", ">\n\n\t\t\t\t<select id=\"<?php echo esc_attr( $input_id ); ?", ">\" <?", "php echo $describedby_attr; ?", "> <?", "php $this->link(); ?", ">>\n\t\t\t\t\t<?", "php\n\t\t\t\t\tforeach ( $this->choices as $value => $label ) {\n\t\t\t\t\t\techo '<option value=\"' . ", "esc_attr( $value ) . '\"' . ", "selected( $this->value(), $value, false ) . '", ">' . ", "$label . '", "</option>';\n\t\t\t\t\t}\n\t\t\t\t\t?", ">\n\t\t\t\t</select>\n\t\t\t\t<?", "php\n\t\t\t\tbreak;\n\t\t\tcase 'textarea':\n\t\t\t\t?", ">\n\t\t\t\t<?", "php if ( ! ", "empty( $this->label ) ) : ?", ">\n\t\t\t\t\t<label for=\"<?php echo esc_attr( $input_id ); ?", ">\" class=\"customize-control-title\"><?php echo esc_html( $this->label ); ?", "></label>\n\t\t\t\t<?", "php endif; ?", ">\n\t\t\t\t<?", "php if ( ! ", "empty( $this->description ) ) : ?", ">\n\t\t\t\t\t<span id=\"<?php echo esc_attr( $description_id ); ?", ">\" class=\"description customize-control-description\"><?php echo $this->description; ?", "></span>\n\t\t\t\t<?", "php endif; ?", ">\n\t\t\t\t<textarea\n\t\t\t\t\tid=\"<?php echo esc_attr( $input_id ); ?", ">\"\n\t\t\t\t\trows=\"5\"\n\t\t\t\t\t<?", "php echo $describedby_attr; ?", ">\n\t\t\t\t\t<?", "php $this->input_attrs(); ?", ">\n\t\t\t\t\t<?", "php $this->link(); ?", ">>\n\t\t\t\t\t<?", "php echo esc_textarea( $this->value() ); ?", ">\n\t\t\t\t</textarea>\n\t\t\t\t<?", "php\n\t\t\t\tbreak;\n\t\t\tcase 'dropdown-pages':\n\t\t\t\t?", ">\n\t\t\t\t<?", "php if ( ! ", "empty( $this->label ) ) : ?", ">\n\t\t\t\t\t<label for=\"<?php echo esc_attr( $input_id ); ?", ">\" class=\"customize-control-title\"><?php echo esc_html( $this->label ); ?", "></label>\n\t\t\t\t<?", "php endif; ?", ">\n\t\t\t\t<?", "php if ( ! ", "empty( $this->description ) ) : ?", ">\n\t\t\t\t\t<span id=\"<?php echo esc_attr( $description_id ); ?", ">\" class=\"description customize-control-description\"><?php echo $this->description; ?", "></span>\n\t\t\t\t<?", "php endif; ?", ">\n\n\t\t\t\t<?", "php\n\t\t\t\t$dropdown_name = '_customize-dropdown-pages-' . ", "$this->id;\n\t\t\t\t$show_option_none = __( '&mdash; Select &mdash;' );\n\t\t\t\t$option_none_value = '0';\n\t\t\t\t$dropdown = wp_dropdown_pages(\n\t\t\t\t\tarray(\n\t\t\t\t\t\t'name' => $dropdown_name,\n\t\t\t\t\t\t'echo' => 0,\n\t\t\t\t\t\t'show_option_none' => $show_option_none,\n\t\t\t\t\t\t'option_none_value' => $option_none_value,\n\t\t\t\t\t\t'selected' => $this->value(),\n\t\t\t\t\t)\n\t\t\t\t);\n\t\t\t\tif ( empty( $dropdown ) ) {\n\t\t\t\t\t$dropdown = sprintf( '<select id=\"%1$s\" name=\"%1$s\">', esc_attr( $dropdown_name ) );\n\t\t\t\t\t$dropdown .= sprintf( '<option value=\"%1$s\">%2$s</option>', esc_attr( $option_none_value ), esc_html( $show_option_none ) );\n\t\t\t\t\t$dropdown .= '</select>';\n\t\t\t\t}\n\n\t\t\t\t// Hackily add in the data link parameter.", "\n\t\t\t\t$dropdown = str_replace( '<select', '<select ' . ", "$this->get_link() . ' ", "id=\"' . ", "esc_attr( $input_id ) . '\" ' . ", "$describedby_attr, $dropdown );\n\n\t\t\t\t// Even more hacikly add auto-draft page stubs.", "\n\t\t\t\t// @todo Eventually this should be removed in favor of the pages being injected into the underlying get_pages() call. ", "See <https://github.com/xwp/wp-customize-posts/pull/250>.", "\n\t\t\t\t$nav_menus_created_posts_setting = $this->manager->get_setting( 'nav_menus_created_posts' );\n\t\t\t\tif ( $nav_menus_created_posts_setting && current_user_can( 'publish_pages' ) ) {\n\t\t\t\t\t$auto_draft_page_options = '';\n\t\t\t\t\tforeach ( $nav_menus_created_posts_setting->value() as $auto_draft_page_id ) {\n\t\t\t\t\t\t$post = get_post( $auto_draft_page_id );\n\t\t\t\t\t\tif ( $post && 'page' === $post->post_type ) {\n\t\t\t\t\t\t\t$auto_draft_page_options .= sprintf( '<option value=\"%1$s\">%2$s</option>', esc_attr( $post->ID ), esc_html( $post->post_title ) );\n\t\t\t\t\t\t}\n\t\t\t\t\t}\n\t\t\t\t\tif ( $auto_draft_page_options ) {\n\t\t\t\t\t\t$dropdown = str_replace( '</select>', $auto_draft_page_options . '", "</select>', $dropdown );\n\t\t\t\t\t}\n\t\t\t\t}\n\n\t\t\t\techo $dropdown;\n\t\t\t\t?", ">\n\t\t\t\t<?", "php if ( $this->allow_addition && current_user_can( 'publish_pages' ) && current_user_can( 'edit_theme_options' ) ) : // Currently tied to menus functionality. ?", ">\n\t\t\t\t\t<button type=\"button\" class=\"button-link add-new-toggle\">\n\t\t\t\t\t\t<?", "php\n\t\t\t\t\t\t/* translators: %s: add new page label */\n\t\t\t\t\t\tprintf( __( '+ %s' ), get_post_type_object( 'page' )->labels->add_new_item );\n\t\t\t\t\t\t?", ">\n\t\t\t\t\t</button>\n\t\t\t\t\t<div class=\"new-content-item\">\n\t\t\t\t\t\t<label for=\"create-input-<?php echo $this->id; ?", ">\"><span class=\"screen-reader-text\"><?php _e( 'New page title' ); ?", "></span></label>\n\t\t\t\t\t\t<input type=\"text\" id=\"create-input-<?php echo $this->id; ?", ">\" class=\"create-item-input\" placeholder=\"<?php esc_attr_e( 'New page title&hellip;' ); ?", ">\">\n\t\t\t\t\t\t<button type=\"button\" class=\"button add-content\"><?php _e( 'Add' ); ?", "></button>\n\t\t\t\t\t</div>\n\t\t\t\t<?", "php endif; ?", ">\n\t\t\t\t<?", "php\n\t\t\t\tbreak;\n\t\t\tdefault:\n\t\t\t\t?", ">\n\t\t\t\t<?", "php if ( ! ", "empty( $this->label ) ) : ?", ">\n\t\t\t\t\t<label for=\"<?php echo esc_attr( $input_id ); ?", ">\" class=\"customize-control-title\"><?php echo esc_html( $this->label ); ?", "></label>\n\t\t\t\t<?", "php endif; ?", ">\n\t\t\t\t<?", "php if ( ! ", "empty( $this->description ) ) : ?", ">\n\t\t\t\t\t<span id=\"<?php echo esc_attr( $description_id ); ?", ">\" class=\"description customize-control-description\"><?php echo $this->description; ?", "></span>\n\t\t\t\t<?", "php endif; ?", ">\n\t\t\t\t<input\n\t\t\t\t\tid=\"<?php echo esc_attr( $input_id ); ?", ">\"\n\t\t\t\t\ttype=\"<?php echo esc_attr( $this->type ); ?", ">\"\n\t\t\t\t\t<?", "php echo $describedby_attr; ?", ">\n\t\t\t\t\t<?", "php $this->input_attrs(); ?", ">\n\t\t\t\t\t<?", "php if ( ! ", "isset( $this->input_attrs['value'] ) ) : ?", ">\n\t\t\t\t\t\tvalue=\"<?php echo esc_attr( $this->value() ); ?", ">\"\n\t\t\t\t\t<?", "php endif; ?", ">\n\t\t\t\t\t<?", "php $this->link(); ?", ">\n\t\t\t\t\t/>\n\t\t\t\t<?", "php\n\t\t\t\tbreak;\n\t\t}\n\t}\n\n\t/**\n\t * Render the control's JS template.", "\n\t *\n\t * This function is only run for control types that have been registered with\n\t * WP_Customize_Manager::register_control_type().", "\n\t *\n\t * In the future, this will also print the template for the control's container\n\t * element and be override-able.", "\n\t *\n\t * @since 4.1.0\n\t */\n\tfinal public function print_template() {\n\t\t?", ">\n\t\t<script type=\"text/html\" id=\"tmpl-customize-control-<?php echo $this->type; ?", ">-content\">\n\t\t\t<?", "php $this->content_template(); ?", ">\n\t\t</script>\n\t\t<?", "php\n\t}\n\n\t/**\n\t * An Underscore (JS) template for this control's content (but not its container).", "\n\t *\n\t * Class variables for this control class are available in the `data` JS object;\n\t * export custom variables by overriding WP_Customize_Control::to_json().", "\n\t *\n\t * @see WP_Customize_Control::print_template()\n\t *\n\t * @since 4.1.0\n\t */\n\tprotected function content_template() {}\n\n}\n\n/**\n * WP_Customize_Color_Control class.", "\n */\nrequire_once( ABSPATH . ", "WPINC . '", "/customize/class-wp-customize-color-control.php' );\n\n/**\n * WP_Customize_Media_Control class.", "\n */\nrequire_once( ABSPATH . ", "WPINC . '", "/customize/class-wp-customize-media-control.php' );\n\n/**\n * WP_Customize_Upload_Control class.", "\n */\nrequire_once( ABSPATH . ", "WPINC . '", "/customize/class-wp-customize-upload-control.php' );\n\n/**\n * WP_Customize_Image_Control class.", "\n */\nrequire_once( ABSPATH . ", "WPINC . '", "/customize/class-wp-customize-image-control.php' );\n\n/**\n * WP_Customize_Background_Image_Control class.", "\n */\nrequire_once( ABSPATH . ", "WPINC . '", "/customize/class-wp-customize-background-image-control.php' );\n\n/**\n * WP_Customize_Background_Position_Control class.", "\n */\nrequire_once( ABSPATH . ", "WPINC . '", "/customize/class-wp-customize-background-position-control.php' );\n\n/**\n * WP_Customize_Cropped_Image_Control class.", "\n */\nrequire_once( ABSPATH . ", "WPINC . '", "/customize/class-wp-customize-cropped-image-control.php' );\n\n/**\n * WP_Customize_Site_Icon_Control class.", "\n */\nrequire_once( ABSPATH . ", "WPINC . '", "/customize/class-wp-customize-site-icon-control.php' );\n\n/**\n * WP_Customize_Header_Image_Control class.", "\n */\nrequire_once( ABSPATH . ", "WPINC . '", "/customize/class-wp-customize-header-image-control.php' );\n\n/**\n * WP_Customize_Theme_Control class.", "\n */\nrequire_once( ABSPATH . ", "WPINC . '", "/customize/class-wp-customize-theme-control.php' );\n\n/**\n * WP_Widget_Area_Customize_Control class.", "\n */\nrequire_once( ABSPATH . ", "WPINC . '", "/customize/class-wp-widget-area-customize-control.php' );\n\n/**\n * WP_Widget_Form_Customize_Control class.", "\n */\nrequire_once( ABSPATH . ", "WPINC . '", "/customize/class-wp-widget-form-customize-control.php' );\n\n/**\n * WP_Customize_Nav_Menu_Control class.", "\n */\nrequire_once( ABSPATH . ", "WPINC . '", "/customize/class-wp-customize-nav-menu-control.php' );\n\n/**\n * WP_Customize_Nav_Menu_Item_Control class.", "\n */\nrequire_once( ABSPATH . ", "WPINC . '", "/customize/class-wp-customize-nav-menu-item-control.php' );\n\n/**\n * WP_Customize_Nav_Menu_Location_Control class.", "\n */\nrequire_once( ABSPATH . ", "WPINC . '", "/customize/class-wp-customize-nav-menu-location-control.php' );\n\n/**\n * WP_Customize_Nav_Menu_Name_Control class.", "\n *\n * As this file is deprecated, it will trigger a deprecation notice if instantiated. ", "In a subsequent\n * release, the require_once() here will be removed and _deprecated_file() will be called if file is\n * required at all.", "\n *\n * @deprecated 4.9.0 This file is no longer used due to new menu creation UX.", "\n */\nrequire_once( ABSPATH . ", "WPINC . '", "/customize/class-wp-customize-nav-menu-name-control.php' );\n\n/**\n * WP_Customize_Nav_Menu_Locations_Control class.", "\n */\nrequire_once( ABSPATH . ", "WPINC . '", "/customize/class-wp-customize-nav-menu-locations-control.php' );\n\n/**\n * WP_Customize_Nav_Menu_Auto_Add_Control class.", "\n */\nrequire_once( ABSPATH . ", "WPINC . '", "/customize/class-wp-customize-nav-menu-auto-add-control.php' );\n\n/**\n * WP_Customize_Date_Time_Control class.", "\n */\nrequire_once( ABSPATH . ", "WPINC . '", "/customize/class-wp-customize-date-time-control.php' );\n" ]

{ "pile_set_name": "Github" }

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[ "For the convenience and long-term stability of clinical application, currently, the implant body which is successfully used for so many times by dentists is a cylinder-cone-shaped rotation in-position type implant body which is similar to a natural-tooth-root shape. ", "The shape is an axial-symmetrical-cylinder shaped implant body or a cone-shaped implant body. ", "The surface of the implant body generally has screw threads which can be rotatably positioned at a bone hole of the prepared jaw bone. ", "Therefore, certain initial-stage stability can be obtained. ", "Furthermore, as various methods (such as surface coarsening and plasma spray coating) in which the same jaw bone biological contact area is increased on the surface of the implant body is implemented, the implant body is popularly used in the world currently.", "\nThe invention, which has publication No. ", "CN1826089A and name of “dental implant”, discloses a dental implant consisting of a fixing root part, a neck part and a basal platform part. ", "The patent is a classic cylinder-cone-shaped rotation in-position type implant. ", "As being a single-cylinder body or a cone-shaped body, the implant body can not form the mutual tensile action similar to that between a plurality of root teeth of a natural tooth so as to fulfill the anti-rotation and anti-twist function. ", "Only the limited initial fixing action of the threads of the surface of an implant body can not resist various torque force interference produced on the implant body by the teeth on the base of the implant body when food is chewed. ", "Therefore, currently, most of the implant bodies should wait several months after having been implanted into the jaw bone, and the teeth can not be mounted and stressed and can not implement chewing function; otherwise, the organic bone combination on the contact interface between the implant body and the jaw bone will be destroyed, and the implant body will eventually become loosened and the implanting will failed." ]

{ "pile_set_name": "USPTO Backgrounds" }

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[ "---\nabstract: |\n We study the behavior as $t\\to 0^+$ of nonnegative functions $$\\label{0.1}\n u\\in C^{2,1} (\\mathbb{R}^n\\times (0,1))\n \\cap L^\\lambda (\\mathbb{R}^n\\times (0,1)),\\quad n\\ge 1,$$ satisfying the parabolic Choquard-Pekar type inequalities $$\\label{0.2}\n 0\\leq u_t-\\Delta u\\leq(\\Phi^{\\alpha/n}*u^\\lambda )u^\\sigma \\quad\n \\text{ in }B_1 (0)\\times (0,1)$$ where $\\alpha\\in(0,n+2)$, $\\lambda>0$, and $\\sigma\\geq0$ are constants, $\\Phi$ is the heat kernel, and $*$ is the convolution operation in $\\mathbb{R}^n\\times (0,1)$. We provide optimal conditions on $\\alpha,\\lambda$, and $\\sigma$ such that nonnegative solutions $u$ of , satisfy pointwise bounds in compact subsets of $B_1(0)$ as $t\\to 0^+$. We obtain similar results for nonnegative solutions of , when $\\Phi^{\\alpha/n}$ in is replaced with the fundamental solution $\\Phi_\\alpha$ of the fractional heat operator $(\\frac{\\partial}{\\partial t}-\\Delta)^{\\alpha/2}$.\naddress: 'Mathematics Department, Texas A&M University, College Station, TX 77843-3368'\nauthor:\n- 'Steven D. Taliaferro'\ntitle: 'Initial Pointwise Bounds and Blow-up for Parabolic Choquard-Pekar Inequalities'\n---\n\nIntroduction {#sec1}\n============\n\nIn this paper we study the behavior as $t\\to 0^+$ of nonnegative functions $$\\label{1.1}\n u\\in C^{2,1} (\\mathbb{R}^n\\times (0,T))\n\\cap L^\\lambda (\\mathbb{R}^n\\times (0,T)),\\quad n\\ge 1,$$ satisfying the nonlocal parabolic Choquard-Pekar type inequalities $$\\label{1.2}\n 0\\leq Hu\\leq(\\Phi^{\\alpha/n}*u^\\lambda )u^\\sigma \\quad\n\\text{ in }\\Omega\\times (0,T)$$ where $\\alpha\\in(0,n+2)$, $\\lambda>0$, $\\sigma\\geq0$, and $T>0$ are constants, $\\Omega$ is an open subset of $\\mathbb{R}^n$, $Hu=u_t-\\Delta u$ is the heat operator, $$\\label{1.3}\n \\Phi(x,t)=\\begin{cases}\n\\frac{1}{(4\\pi t)^{n/2}} \ne^{-\\frac{|x|^2}{4t}}&\\text{for }(x,t)\\in \\mathbb{R}^n\\times (0,\\infty)\\\\\n 0&\\text{for }(x,t)\\in \\mathbb{R}^n\\times (-\\infty,0]\n \\end{cases}$$ is the heat kernel, and $*$ is the convolution operation in $\\mathbb{R}^n\\times(0,T)$, that is, $$(\\Phi^{\\alpha/n}*u^\\lambda)(x,t)\n=\\iint_{\\R^n\\times(0,T)}\\Phi(x-y,t-s)^{\\alpha/n}u(y,s)^\\lambda dy\\,ds.$$ The regularity condition $u\\in\n L^\\lambda(\\mathbb{R}^n\\times (0,T))$ in and the upper bound of $n+2$ for $\\alpha$ are natural because one does not want the nonlocal convolution operation on the right side of to be infinite at every point in $\\mathbb{R}^n\\times (0,T)$.\n\nWe also obtain results on the behavior as $t\\to 0^+$ of nonnegative solutions of , when $\\Phi^{\\alpha/n}$ in is replaced with the fundamental solution $\\Phi_\\alpha$ of the fractional heat operator $(\\frac{\\partial}{\\partial t}-\\Delta)^{\\alpha/2}$. (See Remark \\[rem2\\].)", "\n\nA motivation for the study of , comes from the nonlocal elliptic equation $$\\label{prototype}\n-\\Delta u=(\\Gamma^{\\alpha/(n-2)}* u^{\\lambda}) |u|^{\\lambda-2}u\\quad\n\\text{ in }\\mathbb{R}^n,$$ where $\\alpha\\in (0,n)$, $\\lambda>1$ and $\\Gamma(x)=C(n)/|x|^{n-2}$ is a fundamental solution of $-\\Delta$. For $n=3$, $\\alpha=1$, and $\\lambda=2$, equation is known in the literature as the [*Choquard-Pekar equation*]{} and was introduced in [@P1954] as a model in quantum theory of a polaron at rest (see also [@DA2010]). ", "Later, the equation appears as a model of an electron trapped in its own hole, in an approximation to Hartree-Fock theory of one-component plasma [@L1976]. ", "More recently, the same equation was used in a model of self-gravitating matter (see, e.g., [@J1995; @MPT1998]) and it is known in this context as the [*Schrödinger-Newton equation*]{}.", "\n\nThe Choquard-Pekar equation has been investigated for a few decades by variational methods starting with the pioneering works of Lieb [@L1976] and Lions [@Lions1980; @Lions1984]. ", "More recently, new and improved techniques have been devised to deal with various forms of (see, e.g., [@MZ2010; @MZ2012; @MV2013a; @MV2013b; @MV2015; @WW2009] and the references therein).", "\n\nUsing nonvariational methods, the authors in [@MV2013b] obtained sharp conditions for the nonexistence of nonnegative solutions to $$-\\Delta u \\geq (\\Gamma^{\\alpha/(n-2)}* u^{\\lambda}) u^{\\sigma}$$ in an exterior domain of $\\mathbb{R}^n$, $n\\geq 3$.\n\nFor some very recent results on positive solutions Choquard-Pekar equations and inequalities which have an isolated singularity at the origin see [@CZ] and [@GT2016-2].", "\n\nOther examples of nonlocal equations which have been studied extensively in recent years are equations containing the fractional Laplacian and some of these equations are equivalent to equations containing convolutions with powers of the fundamental solution $\\Gamma$ of $-\\Delta u$. For example, see [@Zhuo2016] and [@MCL2011].", "\n\nOn the other hand, we know of no results for nonlocal equations or inequalities when the nonlocal feature of the problem is due to convolutions with powers of the fundamental solution of the heat equation. ", "Our results for , are, in this regard, new.", "\n\nIn this paper we consider the following question.", "\n\n\\[ques1\\] Suppose $\\alpha\\in(0,n+2)$ and $\\lambda>0$ are constants and $\\Omega$ is an open subset of $\\R^n$, $n\\ge 1$. For which nonnegative constants $\\sigma$, if any, does there exist a continuous function $\\varphi:(0,1)\\to(0,\\infty)$ such that for all compact subsets $K$ of $\\Omega$ and all nonnegative solutions $u$ of , we have $$\\label{1.4}\n \\max_{x\\in K}u(x,t)=O(\\varphi(t))\\quad\\text{ as }t\\to0^+$$ and what is the optimal such $\\varphi$ when it exists?", "\n\nWe call the function $\\varphi$ in a pointwise bound for $u$ on compact subsets of $\\Omega$ as $t\\to0^+$.\n\n\\[rem1\\] Suppose $0<\\lambda<(n+2)/n$. Then, since $u=\\Phi$, where $\\Phi$ is the heat kernel given by , is a solution of , and $\\Phi(0,t)=(4\\pi t)^{-n/2}$, we see that any pointwise bound for nonnegative solutions $u$ of , on compact subsets of $\\Omega$ as $t\\to0^+$ must be at least as large as $t^{-n/2}$ and whenever $t^{-n/2}$ is such a bound it is necessarily optimal.", "\n\nIn order to state our results for Question \\[ques1\\], we define for each $\\alpha\\in(0,n+2)$ the continuous, piecewise linear functions $g_\\alpha,\nG_\\alpha:(0,\\infty)\\to [0,\\infty)$ by $$\\label{1.5}\n g_\\alpha (\\lambda)=\n \\begin{cases}\n \\frac{n+2}{n} & \\text{if }0<\\lambda<\\frac{n+2-\\alpha}{n}\\\\\n \\frac{2(n+2)-\\alpha}{n}-\\lambda & \\text{if }\\frac{n+2-\\alpha}{n}\n\\leq\\lambda<\\frac{n+2}{n}\\\\\n \\max\\{0,1-\\frac{\\alpha-2}{n+2}\\lambda \\} & \\text{if }\n\\lambda\\geq\\frac{n+2}{n}\n \\end{cases}$$ and $$G_\\alpha (\\lambda)=\n \\begin{cases}\n \\frac{2(n+2)-\\alpha}{n}-\\lambda & \\text{if }\n0<\\lambda<\\frac{n+2}{n}\\\\\n \\max\\{0,1-\\frac{\\alpha-2}{n+2}\\lambda \\} & \\text{if }\n\\lambda\\geq\\frac{n+2}{n}.", "\n \\end{cases}$$ These functions are graphed in Figure \\[fig1\\] (resp. ", "Figure \\[fig2\\]) when $\\alpha\\in (2,n+2)$ (resp. ", "$\\alpha\\in (0,2]$). ", "Note that $$g_\\alpha(\\lambda)=G_\\alpha(\\lambda)\n\\quad\\text{for }\\frac{n+2-\\alpha}{n}\\le\\lambda<\\infty$$ and $$g_\\alpha(\\lambda)<G_\\alpha(\\lambda)\n\\quad\\text{for }0<\\lambda<\\frac{n+2-\\alpha}{n}.$$\n\nAccording to the following theorem, if the point $(\\lambda,\\sigma)$ lies below the graph of $\\sigma=g_\\alpha(\\lambda)$ then there exists a pointwise bound for nonnegative solutions $u$ of , on compact subsets of $\\Omega$ as $t\\to 0^+$ .", "\n\n(6,3.2)(-0.2,0) (0.75,0.5)[(0,1)[2.50]{}]{} (0.75,0.5)[(1,0)[4.50]{}]{} (0.75,2.19)[(1,0)[0.75]{}]{} (0.75,2.94)[(1,-1)[1.69]{}]{} (2.44,0.50)[(0,1)[0.75]{}]{} (4.69,0.50)[(-3,1)[2.25]{}]{}\n\n(1.20,0.12)[(0.6,0.3)[$\\frac{n+2-\\alpha}{n}$]{}]{} (2.14,0.12)[(0.6,0.3)[$\\frac{n+2}{n}$]{}]{} (4.39,0.12)[(0.6,0.3)[$\\frac{n+2}{\\alpha-2}$]{}]{} (0.12,1.10)[(0.6,0.3)[$\\frac{n+2-\\alpha}{n}$]{}]{} (0.12,2.04)[(0.6,0.3)[$\\frac{n+2}{n}$]{}]{}\n\n(1.50,0.50)(0,0.2)[3]{}[(0,1)[0.1]{}]{} (1.50,2.19)(0,-0.2)[4]{}[(0,-1)[0.1]{}]{}\n\n(0.75,1.25)(0.2,0)[2]{}[(1,0)[0.1]{}]{} (2.44,1.25)(-0.2,0)[3]{}[(-1,0)[0.1]{}]{}\n\n(2.54,0.6)[(0.9,0.3)[$o\\Bigl(t^{-\\frac{n+2}{2\\lambda}}\\Bigr)$]{}]{} (1.1,1.10)[(0.8,0.3)[$O(t^{-n/2})$]{}]{} (3.6,0.8)[(1.2,0.3)[$\\sigma=1-\\frac{\\alpha-2}{n+2}\\lambda$]{}]{} (0.89,2.29)[(0.2,0.2)[?]{}]{} (", "2.03,1.6)[(1.5,0.3)[$\\sigma=\\frac{2(n+2)-\\alpha}{n}-\\lambda$]{}]{} (1.95,2.05)[(2.3,0.3)[*Arbitrarily large solutions*]{}]{}\n\n(5.25,0.40)[(0.2,0.2)[$\\lambda$]{}]{} (0.65,3.01)[(0.2,0.2)[$\\sigma$]{}]{}\n\n-0.25in\n\n(6,3.2)(-0.2,0) (0.75,0.5)[(0,1)[2.50]{}]{} (0.75,0.5)[(1,0)[4.50]{}]{} (0.75,2.19)[(1,0)[0.75]{}]{} (0.75,2.94)[(1,-1)[1.69]{}]{} (2.44,0.50)[(0,1)[0.75]{}]{} (2.44,1.25)[(3,1)[2.75]{}]{}\n\n(1.20,0.12)[(0.6,0.3)[$\\frac{n+2-\\alpha}{n}$]{}]{} (2.14,0.12)[(0.6,0.3)[$\\frac{n+2}{n}$]{}]{} (0.12,1.10)[(0.6,0.3)[$\\frac{n+2-\\alpha}{n}$]{}]{} (0.12,2.04)[(0.6,0.3)[$\\frac{n+2}{n}$]{}]{}\n\n(1.50,0.50)(0,0.2)[3]{}[(0,1)[0.1]{}]{} (1.50,2.19)(0,-0.2)[4]{}[(0,-1)[0.1]{}]{}\n\n(0.75,1.25)(0.2,0)[2]{}[(1,0)[0.1]{}]{} (2.44,1.25)(-0.2,0)[3]{}[(-1,0)[0.1]{}]{}\n\n(2.90,0.75)[(0.9,0.3)[$o\\Bigl(t^{-\\frac{n+2}{2\\lambda}}\\Bigr)$]{}]{} (1.1,1.10)[(0.8,0.3)[$O(t^{-n/2})$]{}]{} (3.6,1.4)[(1.2,0.3)[$\\sigma=1+\\frac{2-\\alpha}{n+2}\\lambda$]{}]{} (0.89,2.29)[(0.2,0.2)[?]{}]{} (", "1.73,1.9)[(1.5,0.3)[$\\sigma=\\frac{2(n+2)-\\alpha}{n}-\\lambda$]{}]{} (1.95,2.35)[(2.3,0.3)[*Arbitrarily large solutions*]{}]{}\n\n(5.25,0.40)[(0.2,0.2)[$\\lambda$]{}]{} (0.65,3.01)[(0.2,0.2)[$\\sigma$]{}]{}\n\n-0.25in\n\n\\[thm1.1\\] Suppose $u$ is a nonnegative solution of , where $\\alpha\\in(0,n+2)$, $\\lambda>0$, $T>0$, and $$0\\leq\\sigma<g_\\alpha (\\lambda)$$ are constants and $\\Omega$ is an open subset of $\\R^n$. Then for each compact subset $K$ of $\\Omega$ we have as $t\\to 0^+$ that\n\n[\\_[xK]{}u(x,t)=]{} O(t\\^[-n/2]{}) & if $0<\\lambda<\\frac{n+2}{n}$ \\[1.6\\]\\\no(t\\^[-(n+2)/(2)]{}) & if $\\lambda\\ge\\frac{n+2}{n}.$ \\[1.7\\]\n\nThe estimate is optimal by Remark \\[rem1\\]. ", "The exponent $-(n+2)/(2\\lambda)$ in is also optimal by the following result.", "\n\n\\[thm1.2\\] Suppose $$\\lambda\\ge\\frac{n+2}{n}\\quad\\text{and}\\quad \n\\gamma=\\frac{n+2-\\varepsilon}{2\\lambda}$$ for some $\\varepsilon\\in(0,1)$. Then there exists a $C^\\infty$ positive solution $u$ of $$Hu=0\\quad\\text{in }\\R^n\\times (0,\\infty)$$ such that $$u\\in L^\\lambda(\\R^n\\times(0,T))\\quad\\text{for all } T>0$$ and $$u(0,t)=t^{-\\gamma}\\quad\\text{for all } t>0.$$\n\nBy the next theorem, if the point $(\\lambda,\\sigma)$ lies above the graph of $\\sigma=G_\\alpha(\\lambda)$ then there does not exist a pointwise bound for nonnegative solutions $u$ of , on compact subsets of $\\Omega$ as $t\\to 0^+$.\n\n\\[thm1.3\\] Suppose $\\alpha,\\lambda$, and $\\sigma$ are constants satisfying $$\\alpha\\in(0,n+2), \\quad \\lambda>0, \\quad \\text{and}\\quad\\ \n\\sigma>G_\\alpha (\\lambda).$$ Let $\\varphi:(0,1)\\to(0,\\infty)$ be a continuous function satisfying $$\\lim_{t\\to0^+}\\varphi(t)=\\infty.$$ Then there exists a positive solution $u$ of , with $T=1$ and $\\Omega=\\R^n$ such that $$u(0,t)\\neq O(\\varphi(t))\\quad\\text{ as }t\\to 0^+.$$\n\nTheorems \\[thm1.1\\]–\\[thm1.3\\] completely answer Question \\[ques1\\] when the point $(\\lambda,\\sigma)$ lies below the graph of $g_\\alpha$ or above the graph of $G_\\alpha$. In particular, if $u$ is a nonnegative solution of , where $(\\lambda,\\sigma)$ lies in the first quadrant of the $\\lambda\\sigma$-plane and either $\\sigma<\ng_\\alpha(\\lambda)$ or $\\sigma> G_\\alpha(\\lambda)$ then according to Theorems \\[thm1.1\\]–\\[thm1.3\\] either\n\n1. ", " $\\varphi(t)=t^{-n/2}$ is an optimal a priori pointwise bound for $u$ on compact subsets of $\\Omega$ as $t\\to 0^+$; or\n\n2. ", " $\\varphi(t)=t^{-(n+2)/(2\\lambda)}$ is an optimal a priori pointwise bound for $u$ on compact subsets of $\\Omega$ as $t\\to\n 0^+$; or\n\n3. ", " no pointwise a priori bound exists for $u$ on compact subsets of $\\Omega$ as $t\\to 0^+$, that is solutions can be arbitrarily large as $t\\to 0^+$.\n\nThe regions in which these three possibilities occur are shown in Figures \\[fig1\\] and \\[fig2\\]. ", "Also included in Figures \\[fig1\\] and \\[fig2\\] is an open triangular region marked with a question mark. ", "For $(\\lambda,\\sigma)$ in this region we have no results for Question \\[ques1\\].", "\n\n(6,3.2)(-0.2,0) (0.75,0.5)[(0,1)[2.50]{}]{} (0.75,0.5)[(1,0)[4.50]{}]{} (0.75,2.19)[(1,0)[0.75]{}]{} (0.75,2.94)[(1,-1)[1.69]{}]{} (2.44,0.50)[(0,1)[0.75]{}]{} (4.69,0.50)[(-3,1)[2.25]{}]{}\n\n(1.20,0.12)[(0.6,0.3)[$\\frac{n+2-\\alpha}{n}$]{}]{} (2.14,0.12)[(0.6,0.3)[$\\frac{n+2}{n}$]{}]{} (4.39,0.12)[(0.6,0.3)[$\\frac{n+2}{\\alpha-2}$]{}]{} (0.12,1.10)[(0.6,0.3)[$\\frac{n+2-\\alpha}{n}$]{}]{} (0.12,2.04)[(0.6,0.3)[$\\frac{n+2}{n}$]{}]{}\n\n(1.50,0.50)(0,0.2)[3]{}[(0,1)[0.1]{}]{} (1.50,2.19)(0,-0.2)[4]{}[(0,-1)[0.1]{}]{}\n\n(0.75,1.25)(0.2,0)[2]{}[(1,0)[0.1]{}]{} (2.44,1.25)(-0.2,0)[3]{}[(-1,0)[0.1]{}]{}\n\n(2.54,0.6)[(0.9,0.3)[$o\\Bigl(t^{-\\frac{n+2}{2\\lambda}}\\Bigr)$]{}]{} (1.1,1.10)[(0.8,0.3)[$O(t^{-n/2})$]{}]{} (3.6,0.8)[(1.2,0.3)[$\\sigma=1-\\frac{\\alpha-2}{n+2}\\lambda$]{}]{} (0.89,2.29)[(0.2,0.2)[?]{}]{} (", "2.03,1.6)[(1.5,0.3)[$\\sigma=\\frac{2(n+2)-\\alpha}{n}-\\lambda$]{}]{} (1.95,2.05)[(2.3,0.3)[*Arbitrarily large solutions*]{}]{}\n\n(5.25,0.40)[(0.2,0.2)[$\\lambda$]{}]{} (0.65,3.01)[(0.2,0.2)[$\\sigma$]{}]{}\n\n-0.25in\n\n(6,3.2)(-0.2,0) (0.75,0.5)[(0,1)[2.50]{}]{} (0.75,0.5)[(1,0)[4.50]{}]{} (0.75,2.19)[(1,0)[0.75]{}]{} (0.75,2.94)[(1,-1)[1.69]{}]{} (2.44,0.50)[(0,1)[0.75]{}]{} (4.69,0.50)[(-3,1)[2.25]{}]{}\n\n(1.20,0.12)[(0.6,0.3)[$\\frac{n+2-\\alpha}{n}$]{}]{} (2.14,0.12)[(0.6,0.3)[$\\frac{n+2}{n}$]{}]{} (4.39,0.12)[(0.6,0.3)[$\\frac{n+2}{\\alpha-2}$]{}]{} (0.12,1.10)[(0.6,0.3)[$\\frac{n+2-\\alpha}{n}$]{}]{} (0.12,2.04)[(0.6,0.3)[$\\frac{n+2}{n}$]{}]{}\n\n(1.50,0.50)(0,0.2)[3]{}[(0,1)[0.1]{}]{} (1.50,2.19)(0,-0.2)[4]{}[(0,-1)[0.1]{}]{}\n\n(0.75,1.25)(0.2,0)[2]{}[(1,0)[0.1]{}]{} (2.44,1.25)(-0.2,0)[3]{}[(-1,0)[0.1]{}]{}\n\n(2.54,0.6)[(0.9,0.3)[$o\\Bigl(t^{-\\frac{n+2}{2\\lambda}}\\Bigr)$]{}]{} (1.1,1.10)[(0.8,0.3)[$O(t^{-n/2})$]{}]{} (3.6,0.8)[(1.2,0.3)[$\\sigma=1-\\frac{\\alpha-2}{n+2}\\lambda$]{}]{} (0.89,2.29)[(0.2,0.2)[?]{}]{} (", "2.03,1.6)[(1.5,0.3)[$\\sigma=\\frac{2(n+2)-\\alpha}{n}-\\lambda$]{}]{} (1.95,2.05)[(2.3,0.3)[*Arbitrarily large solutions*]{}]{}\n\n(5.25,0.40)[(0.2,0.2)[$\\lambda$]{}]{} (0.65,3.01)[(0.2,0.2)[$\\sigma$]{}]{}\n\n-0.25in\n\n(6,3.2)(0.3,0) (0.75,0.5)[(0,1)[2.50]{}]{} (0.75,0.5)[(1,0)[4.50]{}]{} (0.75,2.19)[(1,0)[0.75]{}]{} (0.75,2.94)[(1,-1)[1.69]{}]{} (2.44,0.50)[(0,1)[0.75]{}]{} (2.44,1.25)[(3,1)[2.75]{}]{}\n\n(1.20,0.12)[(0.6,0.3)[$\\frac{n+2-\\alpha}{n}$]{}]{} (2.14,0.12)[(0.6,0.3)[$\\frac{n+2}{n}$]{}]{} (0.12,1.10)[(0.6,0.3)[$\\frac{n+2-\\alpha}{n}$]{}]{} (0.12,2.04)[(0.6,0.3)[$\\frac{n+2}{n}$]{}]{}\n\n(1.50,0.50)(0,0.2)[3]{}[(0,1)[0.1]{}]{} (1.50,2.19)(0,-0.2)[4]{}[(0,-1)[0.1]{}]{}\n\n(0.75,1.25)(0.2,0)[2]{}[(1,0)[0.1]{}]{} (2.44,1.25)(-0.2,0)[3]{}[(-1,0)[0.1]{}]{}\n\n(2.90,0.75)[(0.9,0.3)[$o\\Bigl(t^{-\\frac{n+2}{2\\lambda}}\\Bigr)$]{}]{} (1.1,1.10)[(0.8,0.3)[$O(t^{-n/2})$]{}]{} (3.6,1.4)[(1.2,0.3)[$\\sigma=1+\\frac{2-\\alpha}{n+2}\\lambda$]{}]{} (0.89,2.29)[(0.2,0.2)[?]{}]{} (", "1.73,1.9)[(1.5,0.3)[$\\sigma=\\frac{2(n+2)-\\alpha}{n}-\\lambda$]{}]{} (1.95,2.35)[(2.3,0.3)[*Arbitrarily large solutions*]{}]{}\n\n(5.25,0.40)[(0.2,0.2)[$\\lambda$]{}]{} (0.65,3.01)[(0.2,0.2)[$\\sigma$]{}]{}\n\n-0.25in\n\n(6,3.2)(0.3,0) (0.75,0.5)[(0,1)[2.50]{}]{} (0.75,0.5)[(1,0)[4.50]{}]{} (0.75,2.19)[(1,0)[0.75]{}]{} (0.75,2.94)[(1,-1)[1.69]{}]{} (2.44,0.50)[(0,1)[0.75]{}]{} (2.44,1.25)[(3,1)[2.75]{}]{}\n\n(1.20,0.12)[(0.6,0.3)[$\\frac{n+2-\\alpha}{n}$]{}]{} (2.14,0.12)[(0.6,0.3)[$\\frac{n+2}{n}$]{}]{} (0.12,1.10)[(0.6,0.3)[$\\frac{n+2-\\alpha}{n}$]{}]{} (0.12,2.04)[(0.6,0.3)[$\\frac{n+2}{n}$]{}]{}\n\n(1.50,0.50)(0,0.2)[3]{}[(0,1)[0.1]{}]{} (1.50,2.19)(0,-0.2)[4]{}[(0,-1)[0.1]{}]{}\n\n(0.75,1.25)(0.2,0)[2]{}[(1,0)[0.1]{}]{} (2.44,1.25)(-0.2,0)[3]{}[(-1,0)[0.1]{}]{}\n\n(2.90,0.75)[(0.9,0.3)[$o\\Bigl(t^{-\\frac{n+2}{2\\lambda}}\\Bigr)$]{}]{} (1.1,1.10)[(0.8,0.3)[$O(t^{-n/2})$]{}]{} (3.6,1.4)[(1.2,0.3)[$\\sigma=1+\\frac{2-\\alpha}{n+2}\\lambda$]{}]{} (0.89,2.29)[(0.2,0.2)[?]{}]{} (", "1.73,1.9)[(1.5,0.3)[$\\sigma=\\frac{2(n+2)-\\alpha}{n}-\\lambda$]{}]{} (1.95,2.35)[(2.3,0.3)[*Arbitrarily large solutions*]{}]{}\n\n(5.25,0.40)[(0.2,0.2)[$\\lambda$]{}]{} (0.65,3.01)[(0.2,0.2)[$\\sigma$]{}]{}\n\n-0.25in\n\nConcerning the case that $(\\lambda,\\sigma)$ lies on the graph of $g_\\alpha$ we have the following result.", "\n\n\\[thm1.4\\] Suppose $\\alpha\\in(0,n+2)$.\n\n1. ", " If $0<\\lambda<\\frac{n+2-\\alpha}{n}$ and $\\sigma=g_\\alpha\n (\\lambda)$ then $\\varphi(t)=t^{-n/2}$ is a poinwise bound for nonnegative solutions $u$ of , on compact subsets of $\\Omega$ as $t\\to 0^+$.\n\n2. ", " If $\\alpha\\in(2,n+2)$, $\\lambda>\\frac{n+2}{\\alpha-2}$, and $\\sigma=g_\\alpha(\\lambda)$ then there does not exist an a priori pointwise bound for nonnegative solutions $u$ of , on compact subsets of $\\Omega$ as $t\\to\n 0^+$.\n\nWhen a pointwise a priori bound as $t\\to 0^+$ for nonnegative solutions $u$ of , on compact subsets of $\\Omega$ does not exist, as in Theorems \\[thm1.3\\] and \\[thm1.4\\](ii), we prove this by constructing for any given continuous function $\\varphi:(0,1)\\to(0,\\infty)$ a nonnegative solution $u$ of , consisting of a sequence of smoothly connected peaks centered at $(x_j,t_j)$ where $t_j\\to 0^+$ such that $$u(x_j,t_j)\\not= O(\\varphi(t_j)) \\quad\\text{as }j\\to\\infty.$$ When such a pointwise a priori bound does exist, as in Theorems \\[thm1.1\\] and \\[thm1.4\\](i), we reduce the proof of this fact to ruling out the possibility of such peaked solutions.", "\n\nIf $\\alpha\\in (0,n+2)$ and $\\lambda>0$ then one of the following three conditions holds:\n\n1. ", " $0<\\lambda<\\frac{n+2-\\alpha}{n}$;\n\n2. ", " $\\frac{n+2-\\alpha}{n}\\leq\\lambda<\\frac{n+2}{n}$;\n\n3. ", " $\\frac{n+2}{n}\\leq\\lambda<\\infty$.\n\nThe proofs of Theorems \\[thm1.1\\]–\\[thm1.4\\] in case (i) (resp.", " (ii), (iii)) are given in Section \\[sec3\\] (resp.", " \\[sec4\\], \\[sec5\\]). ", "In Section \\[sec2\\] we provide some lemmas needed for these proofs. ", "Our approach relies on an integral representation formula for nonnegative supertemperatures (see Appendix \\[secA\\]), some integral estimates for heat potentials (see Appendix \\[secB\\]), and Moser’s iteration (see Lemmas \\[lem4.1\\] and \\[lem5.2\\]).", "\n\nIn this paper, we denote by $\\mathcal{P}_r(x,t)$ the open circular cylinder in $\\R^n\\times\\R$ of radius $\\sqrt{r}$, height $r$, and top center point $(x,t)$. Thus $$\\mathcal{P}_r(x,t)=\\{(y,s)\\in \\R^n\\times\\R:|y-x|<\\sqrt{r}\\text{ and }t-r<s<t\\}.$$\n\n\\[rem2\\] Note that $$\\label{1.9}\n\\Phi(x,t)^{\\alpha/n}=\\frac{1}{(4\\pi)^{\\alpha/2}}t^{-\\alpha/2}\ne^{-\\frac{\\alpha}{4n}\\frac{|x|^2}{t}}\\chi_{(0,\\infty)}(t)\\quad\\text{in\n}\\R^n\\times\\R.$$ However, by checking the proofs of our results, we find that Theorems \\[thm1.1\\], \\[thm1.3\\], and \\[thm1.4\\] remain correct if $\\Phi(x,t)^{\\alpha/n}$ in is replaced with any function of the form $$\\label{1.10}\nC_1(n,\\alpha)t^{-\\alpha/2}\ne^{-C_2(n,\\alpha)\\frac{|x|^2}{t}}\\chi_{(0,\\infty)}(t)\\quad\\text{in\n}\\R^n\\times\\R,$$ where $C_1(n,\\alpha)$ and $C_2(n,\\alpha)$ are any given positive constants. ", "In particular, since the fundamental solution $\\Phi_\\alpha$ of the fractional heat operator $(\\frac{\\partial}{\\partial t}-\\Delta)^{\\alpha/2}$, $\\alpha\\in(0,n+2)$, is given by $$\\Phi_\\alpha(x,t):=\\frac{t^{\\alpha/2-1}}{\\Gamma(\\alpha/2)}\\Phi(x,t),$$ where $\\Phi$ is the heat kernel (see [@S2002 Chapter 9, Section 2]), we find for $0<\\alpha<n+2$ that $$\\Phi_{n+2-\\alpha}(x,t)=\\frac{1}{(4\\pi)^{n/2}\\Gamma((n+2-\\alpha)/2)}t^{-\\alpha/2}\ne^{-\\frac{1}{4}\\frac{|x|^2}{t}}\\chi_{(0,\\infty)}(t)$$ is of the form . ", "Thus Theorems \\[thm1.1\\], \\[thm1.3\\], and \\[thm1.4\\] remain correct if $\\Phi^{\\alpha/n}$ in is replaced with $\\Phi_{n+2-\\alpha}$.\n\nIn particular, since the fundamental solution $\\Phi_\\beta$ of the fractional heat operator $(\\frac{\\partial}{\\partial t}-\\Delta)^\\beta$, $\\beta>0$, is given by $$\\begin{aligned}\n\\notag\n\\Phi_\\beta(x,t)&:=\\frac{t^{\\beta-1}}{\\Gamma(\\beta)}\\Phi(x,t)\\\\\n &=\\frac{1}{(4\\pi)^{n/2}\\Gamma(\\beta)}t^{\\beta-1-n/2}\ne^{-\\frac{1}{4}\\frac{|x|^2}{t}}\\chi_{(0,\\infty)}(t)\\quad\\text{in\n}\\R^n\\times\\R \\label{1.10}\\end{aligned}$$ (cf. [", "@S2002 Chapter 9, Section 2]), we see that Theorems \\[thm1.1\\], \\[thm1.3\\], and \\[thm1.4\\] remain correct if in we replace $\\Phi^{\\alpha/n}$ with $\\Phi_\\beta$ provided the exponents on $t$ in and are the same. ", "That is, provided $\\alpha=n+2-2\\beta$ in the statements of Theorems \\[thm1.1\\], \\[thm1.3\\], and \\[thm1.4\\].", "\n\nFor example, since $$n+2-2\\beta=\\alpha\\in(0,n+2)\\quad \\text{if and only if}\\quad \n\\beta\\in (0,\\frac{n+2}{2})$$ and $$h_\\beta(\\lambda):= g_{n+2-2\\beta} (\\lambda)=\n \\begin{cases}\n \\frac{n+2}{n} & \\text{if }0<\\lambda<\\frac{2\\beta}{n}\\\\\n \\frac{n+2+2\\beta}{n}-\\lambda & \\text{if }\\frac{2\\beta}{n}\n\\leq\\lambda<\\frac{n+2}{n}\\\\\n \\max\\{0,1-\\frac{n-2\\beta}{n+2}\\lambda \\} & \\text{if }\n\\lambda\\geq\\frac{n+2}{n}\n \\end{cases}$$ and $$\\mathcal{H}_\\beta(\\lambda):=G_{n+2-2\\beta} (\\lambda)=\n \\begin{cases}\n\\frac{n+2+2\\beta}{n}-\\lambda & \\text{if }0\\leq\\lambda<\\frac{n+2}{n}\\\\\n \\max\\{0,1-\\frac{n-2\\beta}{n+2}\\lambda \\} & \\text{if }\n\\lambda\\geq\\frac{n+2}{n}\n \\end{cases}$$ we obtain the following analogs of Theorems \\[thm1.1\\] and \\[thm1.3\\] for nonnegative functions $$\\label{1.11}\n u\\in C^{2,1} (\\mathbb{R}^n\\times (0,T))\n\\cap L^\\lambda (\\mathbb{R}^n\\times (0,T)),\\quad n\\ge 1,$$ satisfying the nonlocal parabolic Choquard-Pekar type inequalities $$\\label{1.12}\n 0\\leq Hu\\leq(\\Phi_\\beta*u^\\lambda )u^\\sigma \\quad\n\\text{ in }\\Omega\\times (0,T).$$\n\n\\[thm1.5\\] Suppose $u$ is a nonnegative solution of , where $\\beta\\in(0,\\frac{n+2}{2})$, $\\lambda>0$, $T>0$, and $$0\\leq\\sigma<h_\\beta (\\lambda)$$ are constants and $\\Omega$ is an open subset of $\\R^n$. Then for each compact subset $K$ of $\\Omega$ we have as $t\\to 0^+$ that\n\n[\\_[xK]{}u(x,t)=]{} O(t\\^[-n/2]{}) & if $0<\\lambda<\\frac{n+2}{n}$ \\[1.13\\]\\\no(t\\^[-(n+2)/(2)]{}) & if $\\lambda\\ge\\frac{n+2}{n}.$ \\[1.14\\]\n\nThe estimate is optimal by Remark \\[rem1\\]. ", "The exponent $-(n+2)/(2\\lambda)$ in is also optimal by Theorem \\[thm1.2\\].", "\n\n\\[thm1.6\\] Suppose $\\beta,\\lambda$, and $\\sigma$ are constants satisfying $$\\beta\\in(0,\\frac{n+2}{2}), \\quad \\lambda>0, \\quad \\text{and}\\quad\\ \n\\sigma>\\mathcal{H}_\\beta (\\lambda).$$ Let $\\varphi:(0,1)\\to(0,\\infty)$ be a continuous function satisfying $$\\lim_{t\\to0^+}\\varphi(t)=\\infty.$$ Then there exists a positive solution $u$ of , with $T=1$ and $\\Omega=\\R^n$ such that $$u(0,t)\\neq O(\\varphi(t))\\quad\\text{ as }t\\to 0^+.$$\n\nTheorems \\[thm1.5\\] and \\[thm1.6\\] are depicted graphically in Figure \\[fig3\\] when $\\beta\\in(0,n/2)$.\n\n(6,3.2)(-0.2,0) (0.75,0.5)[(0,1)[2.50]{}]{} (0.75,0.5)[(1,0)[4.50]{}]{} (0.75,2.19)[(1,0)[0.75]{}]{} (0.75,2.94)[(1,-1)[1.69]{}]{} (2.44,0.50)[(0,1)[0.75]{}]{} (4.69,0.50)[(-3,1)[2.25]{}]{}\n\n(1.20,0.12)[(0.6,0.3)[$\\frac{2\\beta}{n}$]{}]{} (2.14,0.12)[(0.6,0.3)[$\\frac{n+2}{n}$]{}]{} (4.39,0.12)[(0.6,0.3)[$\\frac{n+2}{n-2\\beta}$]{}]{} (0.12,1.10)[(0.6,0.3)[$\\frac{2\\beta}{n}$]{}]{} (0.12,2.04)[(0.6,0.3)[$\\frac{n+2}{n}$]{}]{}\n\n(1.50,0.50)(0,0.2)[3]{}[(0,1)[0.1]{}]{} (1.50,2.19)(0,-0.2)[4]{}[(0,-1)[0.1]{}]{}\n\n(0.75,1.25)(0.2,0)[2]{}[(1,0)[0.1]{}]{} (2.44,1.25)(-0.2,0)[3]{}[(-1,0)[0.1]{}]{}\n\n(2.54,0.6)[(0.9,0.3)[$o\\Bigl(t^{-\\frac{n+2}{2\\lambda}}\\Bigr)$]{}]{} (1.1,1.10)[(0.8,0.3)[$O(t^{-n/2})$]{}]{} (3.6,0.8)[(1.2,0.3)[$\\sigma=1-\\frac{n-2\\beta}{n+2}\\lambda$]{}]{} (0.89,2.29)[(0.2,0.2)[?]{}]{} (", "2.03,1.6)[(1.5,0.3)[$\\sigma=\\frac{n+2+2\\beta}{n}-\\lambda$]{}]{} (1.95,2.05)[(2.3,0.3)[*Arbitrarily large solutions*]{}]{}\n\n(5.25,0.40)[(0.2,0.2)[$\\lambda$]{}]{} (0.65,3.01)[(0.2,0.2)[$\\sigma$]{}]{}\n\n-0.25in\n\nPreliminary Lemmas {#sec2}\n==================\n\n\\[lem2.1\\] Suppose $\\alpha\\in(0,n+2),\\,\\lambda>0,\\,\\sigma\\geq0,\\,T>0$, and $\\beta\\geq0$ are constants, $\\Omega$ is an open subset of $\\mathbb{R}^n$, and $K$ is a compact subset of $\\Omega$, such that there exists a nonnegative solution $u$ of ,, where the convolution operation in is in $\\mathbb{R}^n \\times(0,T)$, satisfying $$\\label{2.1}\n \\max_{x\\in K}u(x,t)\\neq O(t^{-\\beta}),\\,\\quad (\\text{resp. }", "o(t^{-\\beta}))\\quad\\text{as }t\\to0^+ .$$ Then there exists a nonnegative function $v(\\xi,\\tau)$ such that $$\\label{2.2}\n v\\in C^{2,1}(\\mathbb{R}^n \\times(0,16))\n\\cap L^\\lambda (\\mathbb{R}^n \\times(0,16)),$$ $$\\label{2.3}\n 0\\leq Hv\\leq(\\Phi^{\\alpha/n}*v^\\lambda )v^\\sigma \\quad\\text{in }B_4 (0)\\times(0,16),$$ where $*$ is the convolution operation in $\\mathbb{R}^n \\times(0,16)$, and $$\\label{2.4}\n \\max_{|\\xi|\\leq1}v(\\xi,\\tau)\\neq O(\\tau^{-\\beta}),\n\\quad (\\text{resp. }", "o(\\tau^{-\\beta}))\\quad\\text{as }\\tau\\to 0^+ .$$\n\nIt follows from and the compactness of $K$ that there exist a sequence $\\{(x_j ,t_j )\\}\\subset K\\times(0,T)$ and $x_0 \\in K$ such that $$\\label{2.5}\n (x_j ,t_j )\\to(x_0 ,0)\\quad\\text{as }j\\to\\infty$$ and $$\\label{2.6}\n u(x_j ,t_j )\\neq O(t^{-\\beta}_{j})\\quad (\\text{resp. }", "o(t^{-\\beta}_{j}))\\quad\\text{as }j\\to\\infty .$$ Choose $r\\in(0,1)$ and $b>0$ such that $$\\label{2.7}\n \\overline{B_{4r}(x_0 )}\\times(0,16r^2 )\\subset\\Omega\\times (0,T)$$ and $$\\label{2.8}\n b^{\\lambda+\\sigma-1}<r^{-(n+4-\\alpha)}.$$ Define $v(\\xi,\\tau)$ by $u(x,t)=bv(\\xi,\\tau)$ where $x=x_0 +r\\xi$ and $t=r^2 \\tau$ and define $(\\xi_j ,\\tau_j )$ by $x_j =x_0 +r\\xi_j$ and $t_j =r^2 \\tau_j$. Then by $$\\label{2.9}\n (\\xi_j ,\\tau_j )\\to(0,0)\\quad\\text{as }j\\to\\infty.$$ Clearly $(x,t)\\in\\mathbb{R}^n \\times(0,16r^2 )$ if and only if $(\\xi,\\tau)\\in\\mathbb{R}^n \\times(0,16)$. Also $16r^2 \\leq T$ by . ", "It therefore follows from that holds.", "\n\nFor $(x,t)\\in \\mathcal{P}_{16r^2}(x_0 ,16r^2 )$ (i.e. $(\\xi,\\tau)\\in\n \\mathcal{P}_{16}(0,16)$) we have under the change of variables $y=x_0 +r\\eta,\\,s=r^2 \\zeta$ that $$\\iint_{\\mathbb{R}^n \\times(0,T)}\\Phi(x-y,t-s)^{\\alpha/n}u(y,s)^\\lambda\\,dy\\,ds=\\frac{b^\\lambda r^{n+2}}{r^\\alpha}\\iint_{\\mathbb{R}^n \\times(0,16)}\\Phi(\\xi-\\eta,\\tau-\\zeta)^{\\alpha/n}v(\\eta,\\zeta)^\\lambda \\,d\\eta\\,d\\zeta$$ where in the last integral we were able to replace the region of integration $\\mathbb{R}^n \\times(0,T/r^2 )$ with $\\mathbb{R}^n\\times(0,16)$ because $\\tau<16\\leq T/r^2$ and $\\Phi(x,t)=0$ for $t<0$. Thus by and we find that $v$ satisfies .", "\n\nFinally by we have $$\\tau^{\\beta}_{j}v(\\xi_j ,\\tau_j\n )=\\left(\\frac{t_j}{r^2}\\right)^\\beta \\frac{1}{b}u(x_j ,t_j\n )\\neq O(1)\\quad (\\text{resp. } ", "o(1))\\quad\\text{as }j\\to\\infty$$ which together with implies .", "\n\n\\[rem2.1\\] Suppose $\\alpha$, $\\lambda$, $\\sigma$, $T$, $\\beta$, $\\Omega$, and $K$ are as in Lemma \\[lem2.1\\]. ", "Then in order to show that all nonnegative solutions $u$ of , satisfy $$\\max_{x\\in K}u(x,t)=O(t^{-\\beta})\\quad (\\text{resp. }", "o(t^{-\\beta}))\\quad\\text{as }t\\to 0^+$$ it suffices by Lemma \\[lem2.1\\] to show that all nonnegative solutions $u(x,t)$ of $$\\label{2.10}\n u\\in C^{2,1}(\\mathbb{R}^n \\times(0,16))\\cap L^\\lambda (\\mathbb{R}^n \\times(0,16))$$ and $$\\label{2.11}\n 0\\leq Hu\\leq(\\Phi^{\\alpha/n}*u^\\lambda )u^\\sigma \\quad\\text{in }B_4 (0)\\times(0,16),$$ where $*$ is the convolution operation in $\\mathbb{R}^n \\times(0,16)$, satisfy $$\\max_{|x|\\leq1}u(x,t)=O(t^{-\\beta})\\quad (\\text{resp. }", "o(t^{-\\beta}))\\quad\\text{as }t\\to 0^+.$$\n\nThroughout this paper we will repeatedly use the following simple lemma.", "\n\n\\[lem2.2\\] If $\\gamma>0$ and $x\\in\\mathbb{R}^n ,\\,n\\geq1$, then $$\\int_{|x-y|<r}e^{-\\gamma|x-y|^2}dy=\\gamma^{-n/2}\\int_{|z|<\\sqrt{\\gamma}r}e^{-|z|^2}dz$$ and $$\\int_{|x-y|>r}e^{-\\gamma|x-y|^2}dy=\\gamma^{-n/2}\\int_{|z|>\\sqrt{\\gamma}r}e^{-|z|^2}dz.$$ In particular $$\\int_{\\mathbb{R}^n}e^{-\\gamma|x-y|^2}dy=C(n)\\gamma^{-n/2}.$$\n\nMake the change of variables $z=\\sqrt{\\gamma}(x-y)$.\n\n\\[lem2.3\\] Suppose for some constants $\\alpha\\in(0,n+2),\\,\\lambda>0$, and $\\sigma\\geq0$, the function $u$ is a nonnegative solution of , where $*$ is the convolution operation in $\\mathbb{R}^n \\times(0,16)$. Set $v=u+1$. Then $$\\label{2.12}\n v\\in C^{2,1}(\\mathbb{R}^n \\times(0,16))\\cap L^\\lambda (B_{\\sqrt{8}}(0)\\times(0,8))$$ and for some positive constant $C$, $v$ satisfies $$\\label{2.13}\n \\begin{rcases}\n 0\\leq Hv\\leq C(\\Phi^{\\alpha/n}*v^\\lambda )v^\\sigma\\\\\n v\\geq1\n \\end{rcases} \\quad\\text{in }B_2 (0)\\times(0,8)$$ where $*$ is the convolution operation in $B_{\\sqrt{8}}(0)\\times(0,8)$. Also $$\\label{2.14}\n Hv,\\,v^\\beta \\in L^1 (B_{\\sqrt{8}}(0)\\times(0,8))\\quad\n\\text{for all }\\beta\\in\\left[1,\\frac{n+2}{n}\\right)$$ and there exists a positive finite Borel measure $\\mu$ on $B_{\\sqrt{8}}(0)$ and a bounded function\\\n$h\\in C^{2,1}(B_2 (0)\\times(-4,4))$ satisfying $$\\begin{aligned}\n H&h=0\\quad\\text{in }B_2 (0)\\times(-4,4)\\\\\n &h=0\\quad\\text{in }B_2 (0)\\times(-4,0]\n \\end{aligned}$$ such that $$\\label{2.15}\n v(x,t)=h(x,t)+\\int^{8}_{0}\\int_{|y|<\\sqrt{8}}\\Phi(x-y,t-s)Hv(y,s)\\,dy\\,ds+\\int_{|y|<\\sqrt{8}}\\Phi(x-y,t)\\,d\\mu(y)$$ for $(x,t)\\in B_2 (0)\\times(0,4)$.\n\n\\[rem2.2\\] Under the assumptions of Lemma \\[lem2.3\\] we have $$(4\\pi t)^{n/2}\\int_{|y|<\\sqrt{8}}\\Phi(x-y,t)\\,d\\mu(y)\\leq\\int_{|y|<\\sqrt{8}}d\\mu(y)<\\infty\\quad\\text{for }(x,t)\\in\\mathbb{R}^n \\times(0,\\infty).$$ Thus by we see that $$v(x,t)\\leq C\\left(\\left(\\frac{1}{\\sqrt{t}}\\right)^n +\\int^{8}_{0}\\int_{|y|<\\sqrt{8}}\\Phi(x-y,t-s)Hv(y,s)\\,dy\\,ds\\right)\\quad\\text{for }(x,t)\\in B_2 (0)\\times(0,4).$$\n\nClearly implies . ", "For $$(x,t)\\in B_2 (0)\\times(0,8), \\quad (y,s)\\in(\\mathbb{R}^n \\times(0,16))\\backslash(B_{\\sqrt{8}}(0)\\times(0,8)),$$ and $s<t$ we have $|x-y|>\\sqrt{8}-2>1/\\sqrt{2}$ and thus $$\\begin{aligned}\n \\Phi(x-y,t-s)&\\leq\\frac{1}{(4\\pi(t-s))^{n/2}}e^{-\\frac{1}{8(t-s)}}\\\\\n &\\leq\\sup_{0<\\tau<t}\\frac{e^{-\\frac{1}{8\\tau}}}{(4\\pi\\tau)^{n/2}}\\leq C\\frac{e^{-\\frac{1}{8t}}}{t^{n/2}}.\\end{aligned}$$ Hence for $(x,t)\\in B_2 (0)\\times(0,8)$ we have $$\\begin{aligned}\n\\label{2.16}\n \\notag \\iint_{\\mathbb{R}^n \\times(0,16)\\backslash\n B_{\\sqrt{8}}(0)\\times(0,8)}&\n\\Phi(x-y,t-s)^{\\alpha/n}u(y,s)^\\lambda\n \\,dy\\,ds\\\\\n\\leq C&\\left(\\frac{e^{-\\frac{1}{8t}}}{t^{n/2}}\\right)^{\\alpha/n}\\iint_{\\mathbb{R}^n \\times(0,16)}u(y,s)^\\lambda \\,dy\\,ds\n \\leq C\\left(\\frac{e^{-\\frac{1}{8t}}}{t^{n/2}}\\right)^{\\alpha/n}\\end{aligned}$$ by .", "\n\nOn the other hand, for $(x,t)\\in B_2 (0)\\times(0,8)$ we have $B_R (x)\\subset B_{\\sqrt{8}}(0)$ where $R=\\sqrt{8}-2$ and thus by Lemma \\[lem2.2\\] we find that $$\\begin{aligned}\n \\notag\n \\iint_{B_{\\sqrt{8}}(0)\\times(0,8)}\\Phi(x-y,t-s)^{\\alpha/n}\\,dy\\,ds\n&\\geq\\int^{t}_{0}\\left(\\int_{B_R (x)}\\Phi(y-x,t-s)^{\\alpha/n}dy\\right)ds\\\\\n \\notag &=\\int^{t}_{0}\\int_{B_R\n (x)}\\Phi(y-x,\\tau)^{\\alpha/n}dy\\,d\\tau\\\\\n\\notag &=\\int_0^t\\frac{1}{(4\\pi\\tau)^{\\alpha/2}}\n\\left(\\int_{|y-x|<R}e^{-\\frac{\\alpha}{4n\\tau}|y-x|^2}dy\\right)d\\tau\\\\\n\\notag &=C\\int^{t}_{0}\\tau^{\\frac{n-\\alpha}{2}}\\left(\\int_{|z|<R\\sqrt{\\frac{\\alpha}{4n\\tau}}}e^{-|z|^2}dz\\right)d\\tau\\\\\n \\label{2.17}&\\geq C\\int^{t}_{0}\\tau^{\\frac{n-\\alpha}{2}}d\\tau=Ct^{\\frac{n+2-\\alpha}{2}}\n \\geq C\\left(\\frac{e^{-\\frac{1}{8t}}}{t^{n/2}}\\right)^{\\alpha/n}.\\end{aligned}$$ Hence for $(x,t)\\in B_2 (0)\\times(0,8)$ we obtain from and that $$\\begin{aligned}\n &\\iint_{\\mathbb{R}^n \\times(0,16)}\\Phi(x-y,t-s)^{\\alpha/n}u(y,s)^\\lambda \\,dy\\,ds\\\\\n &\\leq\\iint_{B_{\\sqrt{8}}(0)\\times(0,8)}\\Phi(x-y,t-s)^{\\alpha/n}u(y,s)^\\lambda\n \\,dy\\,ds\n+C\\iint_{B_{\\sqrt{8}}(0)\\times(0,8)}\\Phi(x-y,t-s)^{\\alpha/n}1^\\lambda \\,dy\\,ds\\\\\n &\\leq C \\iint_{B_{\\sqrt{8}}(0)\\times(0,8)}\\Phi(x-y,t-s)^{\\alpha/n}v(y,s)^\\lambda \\,dy\\,ds.\\end{aligned}$$ Thus, since $u$ satisfies we see that $v$ satisfies . ", "Finally, by , $Hv\\ge 0$ in $B_4 (0)\\times(0,16)$. Hence Theorem \\[thmA\\] and Remark \\[remA\\] with $R_1=4$, $R_2=8$, and $R_3=16$ imply and .", "\n\nThe following lemma will be needed to estimate the last integral in .", "\n\n\\[lem2.4\\] Suppose $$\\label{2.18}\n u\\in L^p (\\Omega \\times(0,T))$$ for some open subset $\\Omega$ of $\\mathbb{R}^n ,\\,n\\geq1$, and some constants $p\\in[1,\\infty)$ and $T>0$. Assume also that $$u(x,t)=\\int_{\\mathbb{R}^n}\\Phi(x-y,t)\\, d\\mu(y)$$ for some finite positve Borel measure $\\mu$ on $\\mathbb{R}^n$. Then for each compact subset $K$ of $\\Omega$ we have $$\\label{2.19}\n \\max_{x\\in K}u(x,t)=o\\left(t^{-\\frac{n+2}{2p}}\\right)\\quad\\text{as }t\\to 0^+ .$$\n\nThe proof consists of two steps.\\\n**Step 1.** ", "In this step we prove Lemma \\[lem2.4\\] in the special case that $$\\label{2.20}\n \\Omega=B_{3r}(x_0 )\\quad\\text{and}\\quad K=\\overline{B_r (x_0 )}$$ for some $x_0 \\in\\mathbb{R}^n$ and some $r>0$. Clearly we can assume $x_0 =0$. Since $u=v+w$ where $$v(x,t)=\\int_{|y|<2r}\\Phi(x-y,t)\\,d\\mu(y)$$ and $$w(x,t)=\\int_{|y|\\geq2r}\\Phi(x-y,t)\\,d\\mu(y),$$ to complete step 1, it suffices to prove $v$ and $w$ satisfy when $\\Omega$ and $K$ are given by .", "\n\nSince for $|x-y|\\geq r$ and $t>0$ $$\\Phi(x-y,t)\\leq\\frac{1}{r^n}\\left(\\frac{r^2}{4\\pi t}\\right)^{n/2}e^{-\\frac{r^2}{4t}}\\leq r^{-n}C(n)$$ we have $$\\max_{|x|\\leq r}w(x,t)\\leq r^{-n}C(n)\\int_{\\mathbb{R}^n}d\\mu(y)<\\infty\\quad\\text{for }t>0.$$ Thus $w$ satisfies when $\\Omega$ and $K$ are given by .", "\n\nFor $|y|\\leq 2r$ and $\\tau>0$ it follows from Lemma \\[lem2.2\\] that $$\\begin{aligned}\n \\int_{|x|\\geq3r}\\Phi(x-y,\\tau)^p dx&=\\frac{1}{(4\\pi\\tau)^{np/2}}\\int_{|x|\\geq3r}e^{-\\frac{p|x-y|^2}{4\\tau}}dx\\\\\n &\\leq\\frac{1}{(4\\pi\\tau)^{np/2}}\\int_{|x-y|\\geq r}e^{-\\frac{p|x-y|^2}{4\\tau}}dx\\\\\n &=\\frac{C(n,p)}{r^{n(p-1)}}\\left[\\left(\\frac{r}{\\sqrt{\\tau}}\\right)^{n(p-1)}\\int_{|z|>\\sqrt{\\frac{p}{4}}\\frac{r}{\\sqrt{\\tau}}}e^{-|z|^2}dz\\right]\\\\\n &\\leq C(n,p)/r^{n(p-1)}.", "\n \\end{aligned}$$ We obtain therefore from Jensen’s inequality and Fubini’s theorem that $$\\begin{aligned}\n\\label{2.21}\n \\notag \\| v\\|^{p}_{L^p ((\\mathbb{R}^n \\backslash\n B_{3r}(0))\\times(0,t))}\n&=\\int^{t}_{0}\\int_{|x|\\ge 3r}\\left(\\int_{|y|<2r}\\Phi(x-y,\\tau)\\,d\\mu(y)\\right)^p dx\\,d\\tau\\\\\n \\notag &\\le |\\mu|^{p-1}\\int_{|y|<2r}\\int^{t}_{0}\\left(\\int_{|x|\\geq3r}\\Phi(x-y,\\tau)^p dx\\right)d\\tau \\,d\\mu(y)\\\\\n &\\leq|\\mu|^p C(n,p)t/r^{n(p-1)}\\quad\\text{for all }t>0.", "\n \\end{aligned}$$ We now use to show $v$ satisfies .", "\n\nFor $0<\\tau<t$ and $x\\in\\mathbb{R}^n$ it follows from standard $L^p$-$L^q$ estimates with $q=\\infty$ (see [@QS Prop. ", "48.4] that $$v(x,t)\\leq(4\\pi)^{\\frac{-n}{2p}}(t-\\tau)^{\\frac{-n}{2p}}\\| v(\\cdot,\\tau)\\|_{L^p (\\mathbb{R}^n )}.$$ Hence $$v(x,t)^p \\int^{t}_{0}(t-\\tau)^{n/2}d\\tau\\leq(4\\pi)^{-n/2}\\| v\\|_{L^p (\\mathbb{R}^n \\times(0,t))}^p$$ which implies $$\\begin{aligned}\n \\max_{x\\in\\mathbb{R}^n}v(x,t)t^{\\frac{n+2}{2p}}&\\leq C(n,p)\\| v\\|_{L^p (\\mathbb{R}^n \\times(0,t))}\\\\\n &\\leq C(n,p)\\left[\\| u\\|_{L^p (B_{3r}(0)\\times(0,t))}+\\| v\\|_{L^p (\\mathbb{R}^n \\backslash B_{3r}(0)\\times(0,t))}\\right]\\\\\n &\\to0\\quad\\text{as }t\\to0^+\n \\end{aligned}$$ by and . ", "Thus $v$ satisfies when $\\Omega$ and $K$ are given by .", "\n\n**Step 2.** ", "We now use Step 1 to complete the proof. ", "For each $x\\in K$ choose $r_x >0$ such that $B_{3r_x}(x)\\subset\\Omega$. Since $K$ is compact there exists finitely many points $x_1 ,...,x_m$ in $K$ such that $$\\label{2.22}\n K\\subset\\bigcup^{m}_{j=1}B_{r_j}(x_i )\\quad \\text{where }r_j =r_{x_j}.$$ For $j=1,2,...,m$ we have by Step 1 that $$\\max_{|x-x_j |\\leq r_j}u(x,t)=o\\left(t^{-\\frac{n+2}{2p}}\\right)\\quad\\text{as }t\\to0^+ .$$ Hence follows from .", "\n\n\\[lem2.5\\] Suppose $r>0$ and $\\beta>n+2$ are constants and $(x_0 ,t_0 )\\in\\mathbb{R}^n \\times\\mathbb{R}$. Then for $(x,t)\\in\\overline{\\mathcal{P}_r (x_0 ,t_0 )}$ we have $$\\iint_{\\mathbb{R}^n \\times\\mathbb{R}\\backslash\\mathcal{P}_{2r}(x_0 ,t_0 )}\\Phi(x-y,t-s)^{\\beta/n}\\,dy\\,ds\\leq\\frac{C}{\\sqrt{r}^{\\beta-(n+2)}}$$ where $C=C(n,\\beta)>0$.\n\nThroughout this proof $(x,t)\\in\\overline{\\mathcal{P}_r (x_0 ,t_0 )}$ and $C=C(n,\\beta)$ is a positive constant whose value may change from line to line. ", "Let $$A=\\mathbb{R}^n \\times(-\\infty,t_0 -2r]\\quad\\text{and}\\quad B=(\\mathbb{R}^n \\backslash B_{\\sqrt{2r}}(x_0 ))\\times(t_0 -2r,\\,t_0 ).$$ For $(y,s)\\in B$ we have $$\\frac{|y-x|}{|y-x_0 |}\\geq\\frac{|y-x_0 |-|x-x_0 |}{|y-x_0 |}=1-\\frac{|x-x_0 |}{|y-x_0 |}\\geq1-\\frac{\\sqrt{r}}{\\sqrt{2r}}=1-\\frac{1}{\\sqrt{2}}>\\frac{1}{4}.$$ It therefore follows from Lemma \\[lem2.2\\] that $$\\begin{aligned}\n \\iint_B \\Phi(x-y,t-s)^{\\beta/n}\\,dy\\,ds&\\leq\\int^{t}_{t_0 -2r}\\frac{1}{(4\\pi(t-s))^{\\beta/2}}\\left(\\int_{|y-x_0 |>\\sqrt{2r}}e^{-\\frac{\\beta|y-x_0 |^2}{64n(t-s)}}dy\\right)ds\\\\\n &=Cr^{\\frac{n-\\beta}{2}}\\int^{t}_{t_0 -2r}\\left(\\frac{r}{t-s}\\right)^{\\frac{\\beta-n}{2}}\\int_{|z|>\\sqrt{\\frac{2\\beta}{64n}}\\sqrt{\\frac{r}{t-s}}}e^{-|z|^2}dz\\,ds\\\\\n &\\leq Cr^{\\frac{n+2-\\beta}{2}}.", "\n \\end{aligned}$$ Also, by Lemma \\[lem2.2\\], we obtain $$\\begin{aligned}\n \\iint_{A}\\Phi(x-y,t-s)^{\\beta/n}\\,dy\\,ds&=\\int^{t_0 -2r}_{-\\infty}\\frac{1}{(4\\pi(t-s))^{\\beta/2}}\\int_{\\mathbb{R}^n}e^{-\\frac{\\beta|x-y|^2}{4n(t-s)}}\\,dy\\,ds\\\\\n &=C\\int^{t_0 -2r}_{-\\infty}(t-s)^{\\frac{n-\\beta}{2}}ds\\\\\n &=C(t-t_0 +2r)^{\\frac{n+2-\\beta}{2}}\\leq Cr^{\\frac{n+2-\\beta}{2}}.", "\n \\end{aligned}$$ Thus Lemma \\[lem2.5\\] follows from the fact that $$\\iint_{\\mathbb{R}^n \\times\\mathbb{R}\\backslash\\mathcal{P}_{2r}(x_0\n ,t_0 )}\\Phi(x-y,t-s)^{\\beta/n}\\,dy\\,ds=\\iint_{A\\cup B} \\Phi(x-y,t-s)^{\\beta/n}\\,dy\\,ds.$$\n\n\\[lem2.6\\] Suppose $r>0$ and $0<\\beta<n+2$ are constants and $(x_0 ,t_0 )\\in\\mathbb{R}^n \\times\\mathbb{R}$. Then $$\\iint_{(y,s)\\in\\mathcal{P}_r (x_0 ,t_0 )}\\Phi(x-y,t-s)^{\\beta/n}\\,dy\\,ds\\leq C\\sqrt{r}^{n+2-\\beta}\\quad\\text{for }(x,t)\\in\\mathcal{P}_r (x_0 ,t_0 )$$ where $C=C(n,\\beta)>0$.\n\nBy Lemma \\[lem2.2\\], we have for $(x,t)\\in\\mathcal{P}_r (x_0 ,t_0 )$ that $$\\begin{aligned}\n \\iint_{\\mathcal{P}_r (x_0 ,t_0 )}\\Phi(x-y,t-s)^{\\beta/n}\\,dy\\,ds&\\leq\\int^{t}_{t_0 -r}\\frac{1}{(4\\pi(t-s))^{\\beta/2}}\\left(\\int_{\\mathbb{R}^n}e^{-\\frac{\\beta|x-y|^2}{4n(t-s)}}dy\\right)ds\\\\\n &=C\\int^{t}_{t_0 -r}(t-s)^{\\frac{n-\\beta}{2}}ds\\\\\n &=C(t-t_0 +r)^{\\frac{n+2-\\beta}{2}}\\leq C\\sqrt{r}^{n+2-\\beta}.", "\n \\end{aligned}$$\n\n\\[lem2.7\\] Suppose $\\alpha\\in(0,n+2)$ and $\\beta\\in[0,n+2)$ are constants. ", "Then $$\\label{2.23}\n \\iint_{\\mathbb{R}^n \\times (0,t)}\\Phi(x-y,t-s)^{\\alpha/n}\\Phi(y-z,s)^{\\beta/n}\\,dy\\,ds\\leq\\frac{C}{\\sqrt{t}^{\\alpha+\\beta-(n+2)}}$$ for all $x,z\\in\\mathbb{R}^n$ and $t>0$ where $C=C(n,\\alpha,\\beta)>0$.\n\nWhen $\\beta =0$, Lemma \\[lem2.7\\] follows directly from Lemma \\[lem2.2\\]. ", "Hence we can assume $\\beta\\in (0,n+2)$. Under the change of variables $$x-z=\\sqrt{t}\\xi,\\quad y-z=\\sqrt{t}\\eta,\\quad s=t\\zeta$$ we see that the left side of equals $$\\begin{aligned}\n &\\iint_{\\mathbb{R}^n \\times(0,1)}\\Phi(\\sqrt{t}(\\xi-\\eta),t(1-\\zeta))^{\\alpha/n}\\Phi(\\sqrt{t}\\eta,t\\zeta)^{\\beta/n}\\sqrt{t}^{n+2}\\,d\\eta\\,d\\zeta\\\\\n &=\\iint_{\\mathbb{R}^n \\times(0,1)}\\left(\\frac{1}{(4\\pi\n t(1-\\zeta))^{n/2}}\\right)^{\\alpha/n}\\left(\\frac{1}{(4\\pi\n t\\zeta)^{n/2}}\\right)^{\\beta/n}\ne^{-\\frac{\\alpha}{n}\\frac{|\\xi-\\eta|^2}{4(1-\\zeta)}-\\frac{\\beta}{n}\\frac{|\\eta|^2}{4\\zeta}}\n\\sqrt{t}^{n+2}\\,d\\eta\\,d\\zeta\\\\\n &=\\frac{C(n,\\alpha,\\beta)}{\\sqrt{t}^{\\alpha+\\beta-(n+2)}}\\int^{1}_{0}\\frac{1}{(1-\\zeta)^{\\alpha/2}\\zeta^{\\beta/2}}\\left(\\int_{\\mathbb{R}^n}\ne^{-\\frac{\\alpha}{n}\\frac{|\\xi-\\eta|^2}{4(1-\\zeta)}-\\frac{\\beta}{n}\\frac{|\\eta|^2}{4\\zeta}}d\\eta\\right)d\\zeta\\\\\n &\\leq\\frac{C(n,\\alpha,\\beta)}{\\sqrt{t}^{\\alpha+\\beta-(n+2)}}\\left[\\int^{1/2}_{0}\\frac{d\\zeta}{\\zeta^{\\beta/2-n/2}}+\\int^{1}_{1/2}\\frac{d\\zeta}{(1-\\zeta)^{\\alpha/2-n/2}}\\right]\n \\end{aligned}$$ by Lemma \\[lem2.2\\].", "\n\n\\[lem2.8\\] Suppose $(x_0,t_0)\\in\\R^n\\times\\R$ and $r>0$. If $$(x,t)\\in\\overline{\\mathcal{P}_r(x_0,t_0)} \\quad \\text{and}\\quad \n (y,s)\\in(\\R^n\\times\\R)\\setminus\\overline{\\mathcal{P}_{2r}(x_0,t_0)}$$ then $$\\Phi(x-y,t-s)\\le\\frac{C(n)}{r^{n/2}}.$$\n\nWe consider three cases.", "\n\n[**Case I**]{}. ", "Suppose $t_0-2r\\le s<t$. Then $|x-y|\\ge\n (\\sqrt{2}-1) \\sqrt{r}$ and hence $$\\begin{aligned}\n\\Phi(x-y,t-s)&\\le\\frac{e^{-\\frac{(\\sqrt{2}-1)^2r}{4(t-s)}}}{(4\\pi\n (t-s))^{n/2}}\\le\\sup_{\\tau>0}\\frac{e^{-\\frac{(\\sqrt{2}-1)^2r}{4\\tau}}}{(4\\pi\n \\tau)^{n/2}}\\\\\n &=\\sup_{\\zeta>0}\\frac{e^{-(\\sqrt{2}-1)^2\\zeta}}{(\\pi r/\\zeta)^{n/2}}\n=\\frac{C(n)}{r^{n/2}}.\\end{aligned}$$ [**Case II**]{}. ", "Suppose $s<t_0-2r$. Then $t-s\\ge r$ and hence $$\\Phi(x-y,t-s)\\le\\frac{1}{(4\\pi r)^{n/2}}=\\frac{C(n)}{r^{n/2}}.$$ [**Case III**]{}. ", "Suppose $s\\ge t$. Then $\\Phi(x-y,t-s)=0$.\n\n\\[lem2.9\\] Suppose $\\alpha\\in(0,n+2)$ and $f\\in L^p (\\mathbb{R}^n \\times(0,T))$ for some $$\\label{2.24}\n p>\\frac{n+2}{n+2-\\alpha}.$$ Then for all $(x,t)\\in\\mathbb{R}^n \\times(0,T)$ we have $$\\label{2.25}\n \\iint_{\\mathbb{R}^n \\times(0,T)}\\Phi(x-y,t-s)^{\\alpha/n}|f(y,s)|\\,dy\\,ds\\leq Ct^{\\frac{n+2-\\alpha-(n+2)/p}{2}}\\| f\\|_{L^p (\\mathbb{R}^n \\times(0,t))}$$ where $C=C(n,\\alpha,p)$ is a positive constant.", "\n\nDefine $q$ by $\\frac{1}{q}=1-\\frac{1}{p}$. Then by $$\\frac{1}{q}>1-\\frac{n+2-\\alpha}{n+2}=\\frac{\\alpha}{n+2}$$ and thus using Hölders inequality and making the change of variables $$x=\\sqrt{t}\\xi,\\quad y=\\sqrt{t}\\eta,\\quad\\text{and}\\quad s=t\\zeta$$ we have for all $(x,t)\\in\\mathbb{R}^n \\times(0,T)$ that $$\\begin{aligned}\n \\text{LHS of \\eqref{2.25}}&=\\iint_{\\mathbb{R}^n \\times(0,t)}\\Phi(x-y,t-s)^{\\alpha/n}|f(y,s)|\\,dy\\,ds\\\\\n &\\leq\\left(\\iint_{\\mathbb{R}^n \\times(0,t)}\n\\Phi(x-y,t-s)^{\\alpha q/n}\\,dy\\,ds\\right)^{1/q}\\| f\\|_{L^p (\\mathbb{R}^n \\times(0,t))}\\\\\n &=\\left(\\iint_{\\mathbb{R}^n \\times(0,1)}\\frac{1}{t^{\\alpha q/2}}\n\\Phi(\\xi-\\eta,1-\\zeta)^{\\alpha q/n}\\sqrt{t}^{n+2}\\,d\\eta\\,d\\zeta\\right)^{1/q}\\| f\\|_{L^p (\\mathbb{R}^n \\times(0,t))}\\\\\n &=\\sqrt{t}^{\\frac{n+2-\\alpha q}{q}}\\left(\\iint_{\\mathbb{R}^n\n \\times(0,1)}\\Phi(-\\eta,1-\\zeta)^{\\alpha q/n}\\,d\\eta\\,d\\zeta\\right)^{1/q}\\| f\\|_{L^p (\\mathbb{R}^n \\times(0,t))}\\\\\n &=C(n,\\alpha,p)\\sqrt{t}^{n+2-\\alpha-(n+2)/p}\\| f\\|_{L^p (\\mathbb{R}^n \\times(0,t))}.", "\n \\end{aligned}$$\n\n\\[cor2.1\\] Suppose $\\alpha\\in(0,n+2),\\,0<\\lambda<\\frac{n+2-\\alpha}{n}$, and $u\\in L^{\\frac{n+2}{n}}(\\mathbb{R}^n \\times(0,T))$ is a nonnegative function. ", "Then for all $(x,t)\\in\\mathbb{R}^n \\times(0,T)$ we have $$\\iint_{\\mathbb{R}^n\n \\times(0,T)}\\Phi(x-y,t-s)^{\\alpha/n}|u(y,s)|^\\lambda \\,dy\\,ds\\leq\n Ct^{\\frac{n+2-\\alpha-n\\lambda}{2}}\n\\| u\\|^{\\lambda}_{L^{\\frac{n+2}{n}}(\\mathbb{R}^n \\times(0,t))}.$$\n\nSince $u^\\lambda \\in L^{p}(\\mathbb{R}^n \\times(0,T))$, where $$p:=\\frac{n+2}{n\\lambda}>\\frac{n+2}{n}\\frac{n}{n+2-\\alpha}=\\frac{n+2}{n+2-\\alpha},$$ and $$\\| u^\\lambda \\|_{L^p}=\\| u\\|^{\\lambda}_{L^{\\lambda p}}=\\| u\\|^{\\lambda}_{L^{\\frac{n+2}{n}}}$$ the corollary follows from Lemma \\[2.9\\] with $f=u^\\lambda$.\n\n\\[lem2.10\\] Suppose $\\alpha>0$ and $T$ are constants. ", "Then for $s<t\\leq T$ and $|x|\\leq\\sqrt{T-t}$ we have $$\\int_{|y|<\\sqrt{T-s}}\\Phi(x-y,t-s)^{\\alpha/n}dy\\geq\\frac{C}{(t-s)^{(\\alpha-n)/2}}$$ where $C=C(n,\\alpha)$ is a positive constant.", "\n\nMaking the change of variables $z=\\frac{x-y}{\\sqrt{t-s}}$ and letting $e_1 =(1,0,...,0)$ we get $$\\begin{aligned}\n \\notag \\int_{|y|<\\sqrt{T-s}}\\Phi(x-y,t-s)^{\\alpha/n}dy&=\\frac{1}{(4\\pi)^{\\alpha/2}}\\frac{1}{(t-s)^{\\alpha/2}}\\int_{|y|<\\sqrt{T-s}}e^{-\\frac{\\alpha|x-y|^2}{4n(t-s)}}dy\\notag\\\\\n &=\\frac{1}{(4\\pi)^{\\alpha/2}(t-s)^{(\\alpha-n)/2}}\\int_{|z-\\frac{x}{\\sqrt{t-s}}|<\\frac{\\sqrt{T-s}}{\\sqrt{t-s}}}e^{-\\frac{\\alpha}{4n}|z|^2}dz \\label{2.26}\\\\\n &\\geq\\frac{1}{(4\\pi)^{\\alpha/2}}\\frac{1}{(t-s)^{(\\alpha-n)/2}}\\int_{|z-\\frac{\\sqrt{T-s}}{\\sqrt{t-s}}e_1|<\\frac{\\sqrt{T-s}}{\\sqrt{t-s}}}e^{-\\frac{\\alpha}{4n}|z|^2}dz\n\\label{2.27}\\\\\n &\\geq\\frac{1}{(4\\pi)^{\\alpha/2}}\\frac{1}{(t-s)^{(\\alpha-n)/2}}\\int_{|z-e_1\n |<1}e^{-\\frac{\\alpha}{4n}|z|^2}dz, \\label{2.28}\n \\end{aligned}$$ where the last two inequalities need some explanation. ", "Since $|x|\\leq\\sqrt{T-t}<\\sqrt{T-s}$, the center of the ball of integration in is closer to the origin than the center of the ball of integration in . ", "Thus, since the integrand is a decreasing function of $|z|$, we obtain . ", "Since $\\sqrt{T-s}\\geq\\sqrt{t-s}$, the ball of integration in contains the ball of integration in and hence holds.", "\n\nThe case $0<\\lambda<\\frac{n+2-\\alpha}{n}$ {#sec3}\n=========================================\n\nIn this section we prove Theorems \\[thm1.1\\], \\[thm1.3\\], and \\[thm1.4\\] when $0<\\lambda<(n+2-\\alpha)/n$. For these values of $\\lambda$, Remark \\[rem2.1\\] and the following theorem imply Theorems \\[thm1.1\\] and \\[thm1.4\\].", "\n\n\\[thm3.1\\] Suppose $u$ is a nonnegative solution of , for some constants $\\alpha\\in(0,n+2)$, $$\\label{3.1}\n 0<\\lambda<\\frac{n+2-\\alpha}{n}\\quad\\text{and}\\quad 0\\leq\\sigma\\leq\\frac{n+2}{n}.$$ Then $$\\label{3.2}\n \\max_{|x|\\leq1}u(x,t)=O(t^{-n/2})\\quad\\text{as }t\\to0^+ .$$\n\nLet $v=u+1$. Then by Lemma \\[lem2.3\\] we have – hold. ", "To prove , it clearly suffices to prove $$\\label{3.3}\n \\max_{|x|\\leq1}v(x,t)=O(t^{-n/2})\\quad\\text{as }t\\to0^+ .$$ Choose $\\varepsilon\\in(0,1)$ such that $$\\label{3.4}\n \\lambda<\\frac{n+2-\\alpha}{n+\\varepsilon}.$$ By , $$v^\\lambda \\in L^{\\frac{n+2}{(n+\\varepsilon)\\lambda}}(\\mathcal{P}_8 (0,8)).$$ Thus, since implies $$\\frac{\\lambda(n+\\varepsilon)}{n+2}<\\frac{n+2-\\alpha}{n+2}$$ we have by Theorem \\[thmB.2\\] (with $\\alpha$ replaced with $n+2-\\alpha$) that $$\\Phi^{\\alpha/n}*v^\\lambda \\in L^\\infty (\\mathcal{P}_8 (0,8))$$ where the convolution operation is in $\\mathcal{P}_8 (0,8)$. Hence by and , $v$ is a $C^{2,1}$ positive solution of $$0\\leq Hv\\leq Cv^\\sigma \\quad\\text{in }B_2 (0)\\times(0,8).$$ Thus by $_2$ and [@T2011 Theorem 1.1], $v$ satisfies .", "\n\nThe following theorem implies Theorem \\[thm1.3\\] when $0<\\lambda<\\frac{n+2}{n}$.\n\n\\[thm3.2\\] Suppose $\\alpha,\\lambda$, and $\\sigma$ are constants satisfying $$\\label{3.5}\n \\alpha\\in(0,n+2),\\quad 0<\\lambda<\\frac{n+2}{n},\\quad\\text{and}\\quad \\sigma>\\frac{2(n+2)-\\alpha}{n}-\\lambda.$$ Let $\\varphi:(0,1)\\to(0,\\infty)$ be a continuous function satisfying $$\\lim_{t\\to0^+}\\varphi(t)=\\infty.$$ Then there exists a positive function $$\\label{3.6}\n u\\in C^\\infty (\\mathbb{R}^n \\times(0,1))\\cap L^\\lambda (\\mathbb{R}^n \\times(0,1))$$ satisfying $$\\label{3.7}\n 0\\leq Hu\\leq(\\Phi^{\\alpha/n}*u^\\lambda )u^\\sigma \\quad\\text{in }\\mathbb{R}^n \\times(0,1),$$ where $*$ is the convolution operation in $\\mathbb{R}^n \\times(0,1)$, such that $$\\label{3.8}\n u(0,t)\\neq O(\\varphi(t))\\quad\\text{as }t\\to0^+ .$$\n\nBy scaling $u$ and noting by that $\\sigma+\\lambda\\not= 1$ we see that it suffices to prove Theorem \\[thm3.2\\] with replaced with the weaker statement that there exists a positive constant $C=C(n,\\lambda,\\sigma,\\alpha)$ such that $u$ satisfies $$\\label{3.9}\n 0\\leq Hu\\leq C(\\Phi^{\\alpha/n}*u^\\lambda )u^\\sigma \\quad\\text{in }\\mathbb{R}^n \\times(0,1)$$ where $*$ is the convolution operation in $\\mathbb{R}^n \\times(0,1)$.\n\nBy there exists $\\varepsilon=\\varepsilon(n,\\lambda,\\sigma,\\alpha)\\in(0,1)$ such that $$\\label{3.10}\n \\sigma>\\frac{2(n+2)-\\alpha}{n-\\varepsilon}-\\lambda.$$ Let $$\\label{3.11}\n p=\\frac{n-\\varepsilon}{2}$$ and let $\\{T_j \\}\\subset(0,1)$ be a sequence that $T_j \\to0$ as $j\\to\\infty$. Define $w_j :(-\\infty,T_j )\\to(0,\\infty)$ by $$\\label{3.12}\n w_j (t)=(T_j -t)^{-p}$$ and define $t_j \\in(0,T_j )$ by $$\\label{3.13}\n w_j (t_j )=t^{-n/2}_{j}.$$ Then $$\\label{3.14}\n \\frac{T_j -t_j}{t_j}=\\frac{w_j (t_j )^{-1/p}}{t_j}=t^{n/(2p)-1}_{j}\\to0\\quad\\text{as }j\\to\\infty$$ by .", "\n\nChoose $a_j \\in((t_j +T_j )/2,T_j )$ such that $w_j (a_j )>j\\varphi(a_j )$. ", "Then $$\\label{3.15}\n \\frac{w_j (a_j )}{\\varphi(a_j )}\\to\\infty\\quad\\text{as }j\\to\\infty.$$ Let $h_j (s)=\\sqrt{a_j -s}$ and $H_j (s)=\\sqrt{a_j +\\varepsilon_j -s}$ where $\\varepsilon_j >0$ satisfies $$\\label{3.16}\n a_j +2\\varepsilon_j <T_j,\n\\quad t_j -\\varepsilon_j >t_j /2,\n\\quad \\varepsilon_j <T^{2}_{j},\n\\quad\\text{and}\\quad w_j (t_j -\\varepsilon_j )>\\frac{w_j (t_j )}{2}.$$ Define $$\\begin{aligned}\n &\\omega_j =\\{(y,s)\\in\\mathbb{R}^n \\times\\mathbb{R}:|y|<h_j (s)\\quad\\text{and}\\quad t_j <s<a_j \\}\\\\\n &\\Omega_j =\\{(y,s)\\in\\mathbb{R}^n \\times\\mathbb{R}:|y|<H_j(s)\\quad\\text{and}\\quad t_j -\\varepsilon_j <s<a_j +\\varepsilon_j \\}.", "\n \\end{aligned}$$ By taking a subsequence we can assume the sets $\\Omega_j$ are pairwise disjoint.", "\n\nLet $\\chi_j :\\mathbb{R}^n \\times\\mathbb{R}\\to[0,1]$ be a $C^\\infty$ function such that $\\chi_j \\equiv1$ in $w_j$ and $\\chi_j \\equiv0$ in $\\mathbb{R}^n \\times\\mathbb{R}\\backslash\\Omega_j$. Define $f_j ,\\,u_j :\\mathbb{R}^n \\times\\mathbb{R}\\to[0,\\infty)$ by $$\\label{3.17}\n f_j (y,s)=\\chi_j (y,s)w^{\\prime}_{j}(s)$$ and $$\\label{3.18}\n u_j (x,t)=\\iint_{\\mathbb{R}^n \\times\\mathbb{R}}\\Phi(x-y,t-s)f_j (y,s)\\,dy\\,ds.$$ Then $f_j$ and $u_j$ are $C^\\infty$ and $$\\label{3.19}\n Hu_j =f_j \\quad\\text{in }\\mathbb{R}^n \\times\\mathbb{R}.$$ By Theorem \\[thmB.2\\] with $p=n+2$ and $q=\\infty$ we see that $$\\begin{aligned}\n\\label{3.20}\n \\notag\\|\\iint_{\\Omega_j \\backslash \\omega_j}&\\Phi(x-y,t-s)w^{\\prime}_{j}(s)\\,dy\\,ds\\|_{L^\\infty (\\mathbb{R}^n \\times(0,1))}\\\\\n \\notag&=\\|\\iint_{\\mathbb{R}^n \\times(0,1)}\\Phi(x-y,t-s)\\chi_{\\Omega_j \\backslash \\omega_j}(y,s)w^{\\prime}_{j}(s)\\,dy\\,ds\\|_{L^\\infty (\\mathbb{R}^n \\times(0,1))}\\\\\n \\notag&\\leq C_n \\| w^{\\prime}_{j}(s)\\|_{L^{n+2}(\\Omega_j \\backslash \\omega_j )}\\\\\n &\\leq w_j (t_j )\n \\end{aligned}$$ provided we decrease $\\varepsilon_j$ if necessary because $|\\Omega_j \\backslash \\omega_j |\\to0$ as $\\varepsilon_j \\to0$.\n\nAlso, for $(x,t)\\in\\Omega_j$ we have $|x|<\\sqrt{T_j -t_j}$ by $_1$, and thus using $_2$ we obtain $$\\sup_{(x,t)\\in\\Omega_j}\\frac{|x|^2}{t}\\leq\\frac{T_j -t_j}{t_j -\\varepsilon_j}\\leq\\frac{2(T_j -t_j )}{t_j}\\to0\\quad\\text{as }j\\to\\infty$$ by . ", "Hence by , $_2$, and there exists a positive number $M$, independent of $j$, such that $$\\label{3.21}\n M\\Phi(x,t)\\geq 2/t^{n/2}_{j}=2w_j (t_j)\\quad\\text{for }(x,t)\\in\\Omega_j .$$\n\nIn order to obtain a lower bound for $u_j$ in $\\Omega_j$, note first that for $s<t\\leq a_j +\\varepsilon_j$ and $|x|\\leq H_j (t)$ we have by Lemma \\[lem2.10\\] that $$\\label{3.22}\n \\int_{|y|<H_j (s)}\\Phi(x-y,t-s)\\, dy\\geq\\beta$$ for some constant $$\\label{3.23}\n \\beta=\\beta(n)\\in(0,1).$$ Next using and , we find for $(x,t)\\in\\Omega_j$ that $$\\begin{aligned}\n \\iint_{\\Omega_j}\\Phi(x-y,t-s)w^{\\prime}_{j}(s)\\,dy\\,ds&=\\int^{t}_{t_j -\\varepsilon_j}w^{\\prime}_{j}(s)\\left(\\int_{|y|<H_j (s)}\\Phi(x-y,t-s)dy\\right)ds\\\\\n &\\geq\\beta(w_j (t)-w_j (t_j -\\varepsilon_j ))\\\\\n &\\geq\\beta w_j (t)-w_j (t_j ).", "\n \\end{aligned}$$ It therefore follows from , , and that for $(x,t)\\in\\Omega_j$ we have $$\\begin{aligned}\n\\label{3.24}\n \\notag u_j (x,t)&\\geq\\iint_{\\omega_j}\\Phi(x-y,t-s)w^{\\prime}_{j}(s)\\,dy\\,ds\\\\\n \\notag &=\\iint_{\\Omega_j}\\Phi(x-y,t-s)w^{\\prime}_{j}(s)\\,dy\\,ds\n-\\iint_{\\Omega_j \\backslash \\omega_j}\\Phi(x-y,t-s)w^{\\prime}_{j}(s)\\,dy\\,ds\\\\\n &\\geq\\beta w_j (t)-2w_j (t_j ).", "\n \\end{aligned}$$ Also by , , and we obtain $$\\begin{aligned}\n\\label{3.25}\n \\notag \\iint_{\\mathbb{R}^n \\times\\mathbb{R}}f_j (y,s)\\,dy\\,ds&\\leq\\iint_{\\Omega_j}w^{\\prime}_{j}(s)\\,dy\\,ds\\\\\n \\notag &\\leq p\\int^{T_j}_{0}(T_j -s)^{-(p+1)}\\left(\\int_{|y|<\\sqrt{T_j -s}}dy\\right)ds\\\\\n \\notag &=p|B_1(0)|\\int^{T_j}_{0}(T_j -s)^{n/2-p-1}ds\\\\\n &=p|B_1 (0)|\\int^{T_j}_{0}\\tau^{n/2-p-1}d\\tau\\to0\\quad\\text{as }j\\to\\infty\n \\end{aligned}$$ by . ", "Hence for $1\\leq\\lambda<(n+2)/n$ it follows from and Theorem \\[thmB.2\\] that $$\\label{3.26}\n \\| u_j \\|_{L^\\lambda (\\mathbb{R}^n \\times(0,1))}\\to0\\quad\\text{as }j\\to\\infty.$$\n\nWe next prove when $$\\label{3.27}\n 0<\\lambda<1.$$ (Theorem \\[thmB.2\\] cannot be directly used in this case.) ", "Choose $z_0 >1$ such that the expression $z^{n/2}e^{-z/4}$ is decreasing on the interval $z_0 \\leq z<\\infty$. Let $r_0 =\\sqrt{z_0}+1$. Then $r_0 >2$ and by and we have $$\\begin{aligned}\n\\label{3.28}\n \\notag\\iint_{\\mathbb{R}^n \\times(0,1)}u_j (x,t)^\\lambda \\,dx\\,dt&=\\iint_{\\mathbb{R}^n \\times(0,1)}\\left(\\iint_{\\mathbb{R}^n \\times(0,1)}\\Phi(x-y,t-s)f_j (y,s)\\,dy\\,ds\\right)^\\lambda \\,dx\\,dt\\\\\n &=I_j +J_j \n \\end{aligned}$$ where $$I_j :=\\iint_{B_{r_0}(0)\\times(0,1)}\\left(\\iint_{\\mathbb{R}^n \\times(0,1)}\\Phi(x-y,t-s)f_j (y,s)\\,dy\\,ds\\right)^\\lambda \\,dx\\,dt$$ and $$J_j :=\\iint_{(\\mathbb{R}^n \\backslash B_{r_0}(0))\\times(0,1)}\\left(\\iint_{\\Omega_j}\\Phi(x-y,t-s)f_j (y,s)\\,dy\\,ds\\right)^\\lambda \\,dx\\,dt.$$ By and Hölder’s inequality $$\\begin{aligned}\n\\label{3.29}\n \\notag I_j &\\leq\\left(\\iint_{B_{r_0}(0)\\times(0,1)}\\,dx\\,dt\\right)^{1-\\lambda}\\left(\\iint_{B_{r_0}(0)\\times(0,1)}\\left(\\iint_{\\mathbb{R}^n \\times(0,1)}\\Phi(x-y,t-s)f_j (y,s)\\,dy\\,ds\\right)\\,dx\\,dt\\right)^\\lambda \\\\\n &\\to0\\quad\\text{as }j\\to\\infty\n \\end{aligned}$$ by and Theorem \\[thmB.2\\] with $p=q=1$. Also $$\\label{3.30}\n J_j \\leq\\iint_{(\\mathbb{R}^n \\backslash B_{r_0}(0))\\times(0,1)}A_j (x,t)^\\lambda \\,dx\\,dt\\| f_j \\|^{\\lambda}_{L^1 (\\Omega_j )}$$ where $$A_j (x,t):=\\max_{(y,s)\\in\\Omega_j ,\\,s<t}\\Phi(x-y,t-s).$$ For $s<t,\\,(y,s)\\in\\Omega_j$ and $(x,t)\\in(\\mathbb{R}^n \\backslash B_{r_0}(0))\\times(0,1)$ we have $0<s<t<1$ and $$|x-y|>|x|-|y|>|x|-1.$$ Thus $$\\begin{aligned}\n\\label{3.31}\n \\notag (4\\pi)^{n/2}\\Phi(x-y,t-s)&\\leq\\frac{1}{(t-s)^{n/2}}e^{-\\frac{(|x|-1)^2}{4(t-s)}}\\\\\n &=\\frac{1}{(|x|-1)^n}\\left(\\frac{(|x|-1)^2}{t-s}\\right)^{n/2}e^{-\\frac{(|x|-1)^2}{4(t-s)}}.", "\n \\end{aligned}$$ Since $|x|\\geq r_0$ and $0<s<t<1$ we have $$\\frac{(|x|-1)^2}{t-s}>(|x|-1)^2 \\geq z_0$$ and thus by the definition of $z_0$ we obtain from that $$\\begin{aligned}\n (4\\pi)^{n/2}\\Phi(x-y,t-s)&\\leq\\frac{1}{(|x|-1)^n}((|x|-1)^2 )^{n/2}e^{-(|x|-1)^2 /4}\\\\\n &=e^{-(|x|-1)^2 /4}.", "\n \\end{aligned}$$ Hence $$A_j (x,t)^\\lambda \\leq e^{-\\lambda(|x|-1)^2 /4}\\quad\\text{for }(x,t)\\in(\\mathbb{R}^n \\backslash B_{r_0}(0))\\times(0,1).$$ It therefore follows from and that $J_j \\to0$ as $j\\to\\infty$ which together with and yields when $\\lambda$ satisfies .", "\n\nBy we find that $$\\iint_{\\mathbb{R}^n \\times\\mathbb{R}}\\sum^{\\infty}_{j=1}f_j (y,s)\\,dy\\,ds<\\infty$$ provided we take a subsequence if necessary. ", "Hence, since the $C^\\infty$ functions $f_j$ have disjoint supports, we see that the function $u:(\\mathbb{R}^n \\times\\mathbb{R})\\backslash \\{(0,0)\\}\\to[0,\\infty)$ defined by $$\\label{3.32}\n u(x,t)=(M+1)\\Phi(x,t)+\\sum^{\\infty}_{j=1}u_j (x,t)$$ is $C^\\infty$ and by we have $$\\label{3.33}\n Hu=\\sum^{\\infty}_{j=1}f_j \\quad\\text{in }(\\mathbb{R}^n \\times\\mathbb{R})\\backslash \\{(0,0)\\}$$ $$u\\equiv0\\quad\\text{in }\\mathbb{R}^n \\times(-\\infty,0).$$ From we have $$u\\in L^\\lambda (\\mathbb{R}^n \\times(0,1))$$ provided we take a subsequence of $u_j$ if necessary. ", "Thus holds.", "\n\nWe now prove . ", "By and we have $Hu\\equiv0$ in $(\\mathbb{R}^n \\times(0,1))\\backslash \\bigcup^{\\infty}_{j=1}\\Omega_j .$ Hence to prove , it suffice to prove there exists a positve constant $C=C(n,\\lambda,\\sigma,\\alpha)$ such that $$\\label{3.34}\n 0\\leq Hu\\leq C(\\Phi^{\\alpha/n}*u^\\lambda )u^\\sigma \\quad\\text{in }\\Omega_j$$ for $j=1,2,...$.\n\nBy , , and we have for $(x,t)\\in\\Omega_j$ that $$\\begin{aligned}\n\\label{3.35}\n \\notag u(x,t)&\\geq(M+1)\\Phi(x,t)+\\beta w_j (t)-2w_j (t_j )\\\\\n &\\geq\\Phi(x,t)+\\beta w_j (t).", "\n \\end{aligned}$$ Thus for $(x,t)\\in\\Omega_j$ we see by , , and that $$\\begin{aligned}\n Hu(x,t)&=f_j (x,t)\\leq w^{\\prime}_{j}(t)=pw_j (t)^{1+1/p}\\\\\n &=pw_j (t)^{1+1/p-\\sigma}w_j (t)^\\sigma \n\\leq\\frac{p}{\\beta^\\sigma}w_j (t)^{1+1/p-\\sigma}u(x,t)^\\sigma.", "\n \\end{aligned}$$ Hence to prove it suffices to show $$\\label{3.36}\n w_j (t)^{1+1/p-\\sigma}<C\\iint_{\\mathbb{R}^n \\times(0,1)}\\Phi(x-y,t-s)^{\\alpha/n}u(y,s)^\\lambda \\,dy\\,ds\\quad\\text{for }(x,t)\\in\\Omega_j .$$ Our proof of consists of two cases.\\\n**Case I.** Suppose $$\\label{3.37}\n (x,t)\\in\\Omega_j \\quad\\text{and}\\quad t\\leq\\frac{T_j +t_j}{2}.$$ Then using , , and the fact that $w_j$ is an increasing function we have $$\\frac{1}{2}\\leq\\frac{w_j (t)}{2w_j (t_j -\\varepsilon_j )}\\leq\\frac{w_j (t)}{w_j (t_j )}\\leq\\left(\\frac{T_j -\\frac{T_j +t_j}{2}}{T_j -t_j}\\right)^{-p}=2^p <2^{n/2}.$$ Also by and $$\\frac{w_j (t_j )}{T^{-n/2}_{j}}=\\left(\\frac{T_j}{t_j}\\right)^{n/2}\\in(1,2)$$ provided we take a subsequence if necessary. ", "Thus implies $$\\label{3.38}\n \\frac{1}{2}<\\frac{w_j (t)}{T^{-n/2}_{j}}<2^{(n+2)/2}.$$ Next, making the change of variables $$x=\\sqrt{T_j}\\xi,\\quad t=T_j \\tau,\\quad\\text{and}\\quad\n y=\\sqrt{T_j}\\eta,\\quad s=T_j \\zeta,$$ we get $$\\begin{aligned}\n\\label{3.39}\n \\notag \\iint_{\\mathbb{R}^n \\times(0,1)}&\\Phi(x-y,t-s)^{\\alpha/n}\\Phi(y,s)^\\lambda \\,dy\\,ds\\\\\n \\notag &=\\iint_{\\mathbb{R}^n \\times(0,\\tau)}\\frac{1}{T^{\\frac{n}{2}\\frac{\\alpha}{n}}_{j}}\\Phi(\\xi-\\eta,\\tau-\\zeta)^{\\alpha/n}\\frac{1}{T^{n\\lambda/2}_{j}}\\Phi(\\eta,\\zeta)^\\lambda \\sqrt{T_j}^{n+2}\\,d\\eta\\,d\\zeta\\\\\n &\\geq\\frac{G(\\xi,\\tau)}{\\sqrt{T_j}^{\\alpha+n\\lambda-(n+2)}}\n \\end{aligned}$$ where $$G(\\xi,\\tau):=\\iint_{B_1(0)\\times(1/2,\\tau)}\\Phi(\\xi-\\eta,\\tau-\\zeta)^{\\alpha/n}\\Phi(\\eta,\\zeta)^\\lambda \\,d\\eta\\,d\\zeta.$$ Since by $_1$, $_1$, , and $_3$, $$1>\\tau=\\frac{t}{T_j}\\geq\\frac{t_j -\\varepsilon_j}{T_j}\\to1\\quad\\text{as }j\\to\\infty$$ we have by $_1$ that $$|\\xi|=\\frac{|x|}{\\sqrt{T_j}}<\\frac{\\sqrt{T_j -t}}{\\sqrt{T_j}}=\\sqrt{1-\\frac{t}{T_j}}\\to0\\quad\\text{as }j\\to\\infty.$$ Thus, since $G$ is clearly continuous at $(\\xi,\\tau)=(0,1)$ and $G(0,1)>0$ we have by that $$\\label{3.40}\n \\iint_{\\mathbb{R}^n \\times(0,1)}\\Phi(x-y,t-s)^{\\alpha/n}\\Phi(y,s)^\\lambda \\,dy\\,ds\\geq\\frac{C}{\\sqrt{T_j}^{\\alpha+n\\lambda-(n+2)}}\\quad\\text{for }(x,t)\\in\\Omega_j,$$ where $C:=G(0,1)/2>0$, provided we take a subsequence if necessary.", "\n\nSince by and , $$\\begin{aligned}\n \\sigma&>\\frac{n+2}{n-\\varepsilon}+\\frac{n+2-\\alpha}{n-\\varepsilon}-\\lambda\\\\\n &>\\frac{n+2-\\varepsilon}{n-\\varepsilon}+\\frac{n+2-\\alpha}{n}-\\lambda\\\\\n &=\\frac{1}{p}+1+\\frac{n+2-\\alpha}{n}-\\lambda\n \\end{aligned}$$ we have $$\\begin{aligned}\n \\left(\\frac{1}{p}+1-\\sigma\\right)\\frac{n}{2}&<\\frac{n}{2}\\left(\\lambda-\\frac{n+2-\\alpha}{n}\\right)\\\\\n &=\\frac{\\alpha+n\\lambda-(n+2)}{2}.", "\n \\end{aligned}$$ Thus follows from , , and .\\\n**Case II.** ", "Suppose $$\\label{3.41}\n (x,t)\\in\\Omega_j \\quad\\text{and}\\quad t\\geq\\frac{T_j +t_j}{2}.$$ Then for $s<t$ we have by Lemma \\[lem2.10\\] with $T=a_j+\\varepsilon_j$ that $$\\int_{|y|<H_j (s)}\\Phi(x-y,t-s)^{\\alpha/n}dy\\geq\\frac{C}{(t-s)^{(\\alpha-n)/2}}$$ for some positive constant $C=C(n,\\alpha)$. Thus for $(x,t)$ satisfying we get $$\\begin{aligned}\n\\label{3.42}\n \\notag \\iint_{\\Omega_j}\\Phi&(x-y,t-s)^{\\alpha/n}w_j (s)^\\lambda \\,dy\\,ds\\geq\\int^{t}_{t_j}w_j (s)^\\lambda \\left(\\int_{|y|<H_j (s)}\\Phi(x-y,t-s)^{\\alpha/n}dy\\right)ds\\\\\n \\notag &\\geq C\\int^{t}_{t_j}\\frac{ds}{(t-s)^a (T_j -s)^b}\\quad\n \\text{where }a=(\\alpha-n)/2 \\text{ and } b=\\lambda p\\\\\n \\notag &=\\frac{C}{(T_j -t)^{a+b-1}}\\int^{\\frac{T_j -t_j}{T_j -t}}_{1}\\frac{dz}{(z-1)^a z^b}\\text{ under the change of variables }T_j -s=(T_j -t)z\\\\\n &\\geq\\frac{C}{(T_j -t)^{a+b-1}}\\int^{2}_{1}\\frac{dz}{(z-1)^a z^b}\n=\\frac{C}{(T_j -t)^{(\\alpha-n)/2+\\lambda p-1}}.", "\n \\end{aligned}$$\n\nSince by and $$\\begin{aligned}\n p(\\sigma+\\lambda-1)&>\\frac{n-\\varepsilon}{2}\\left(\\frac{2(n+2)-\\alpha}{n-\\varepsilon}-1\\right)\\\\\n &=n+2-\\frac{\\alpha}{2}-\\frac{n}{2}+\\frac{\\varepsilon}{2}\\\\\n &>\\frac{n-\\alpha}{2}+2,\n \\end{aligned}$$ we have $$p(1+\\frac{1}{p}-\\sigma)<\\frac{\\alpha-n}{2}+\\lambda p-1.$$ Thus follows from , , and . ", "This completes the proof of in all cases. ", "Hence and hold.", "\n\nFinally follows from and with $(x,t)=(0,a_j)$.\n\nThe case $\\frac{n+2-\\alpha}{n}\\leq\\lambda<\\frac{n+2}{n}$ {#sec4}\n========================================================\n\nIn this section we prove Theorem \\[thm1.1\\] when $$\\label{4.1}\n \\frac{n+2-\\alpha}{n}\\leq\\lambda<\\frac{n+2}{n}.$$ (For these values of $\\lambda$, Theorem \\[thm1.3\\] follows from Theorem \\[thm3.2\\] in the last section and Theorems \\[thm1.2\\] and \\[thm1.4\\] are vacuously true.)", "\n\nFor $\\lambda$ satisfying , Remark \\[rem2.1\\] and the following theorem imply Theorem \\[thm1.1\\].", "\n\n\\[thm4.1\\] Suppose $u$ is a nonnegative solution of , for some constants $\\alpha\\in(0,n+2)$, $$\\label{4.2}\n \\frac{n+2-\\alpha}{n}\\leq\\lambda<\\frac{n+2}{n}\\quad\\text{and}\\quad 0\\leq\\sigma<\\frac{2(n+2)-\\alpha}{n}-\\lambda.$$ Then $$\\label{4.3}\n \\max_{|x|\\leq1}u(x,t)=O(t^{-n/2})\\quad\\text{as }t\\to0^+ .$$\n\nLet $v=u+1$. Then by Lemma \\[lem2.3\\] we have that – hold. ", "To prove , it clearly suffices to prove $$\\label{4.4}\n \\max_{|x|\\leq1}v(x,t)=O(t^{-n/2})\\quad\\text{as }t\\to0^+ .$$\n\nSince increasing $\\lambda$ or $\\sigma$ increases the right side of the second inequality in $_1$, we can assume instead of that $$\\label{4.5}\n \\frac{n+2-\\alpha}{n}<\\lambda<\\frac{n+2}{n},\\quad \\sigma>0,\\quad\\text{and}\\quad 1<\\lambda+\\sigma<\\frac{2(n+2)-\\alpha}{n}.$$ Since the increased value of $\\lambda$ is less than $\\frac{n+2}{n}$, it follows from that still holds.", "\n\nBy there exists $\\varepsilon=\\varepsilon(n,\\lambda,\\sigma,\\alpha)\\in(0,1)$ such that $$\\label{4.6}\n \\left(\\frac{n+4-\\alpha}{n+4-\\alpha-\\varepsilon}\\right)\\frac{n+2-\\alpha}{n}<\\lambda<\\frac{n+2}{n+\\varepsilon}\\quad\\text{and}\\quad \\lambda+\\sigma<\\frac{2(n+2)-\\alpha}{n+\\varepsilon}$$ which implies $$\\label{4.7}\n \\sigma<\\frac{2(n+2)-\\alpha}{n+\\varepsilon}-\\lambda<\\frac{2(n+2)-\\alpha}{n+\\varepsilon}-\\frac{n+2-\\alpha}{n}<\\frac{n+2}{n+\\varepsilon}.$$\n\nSuppose for contradition that is false. ", "Then there is a sequence $\\{(x_j ,t_j )\\}\\subset\\overline{B_1(0)}\\times(0,1)$ and $x_0 \\in\\overline{B_1 (0)}$ such that $(x_j ,t_j )\\to(x_0 ,0)$ as $j\\to\\infty$ and $$\\label{4.8}\n \\lim_{j\\to\\infty}t^{n/2}_{j}v(x_j ,t_j )=\\infty.$$ By Lemma \\[lem2.8\\] we have for $(x,t)\\in\\mathcal{P}_{t_j /4}(x_j ,t_j )$ that $$\\iint_{\\mathcal{P}_8 (0,8)\\backslash\\mathcal{P}_{t_j /2}(x_j ,t_j )}\\Phi(x-y,t-s)Hv(y,s)\\,dy\\,ds\\leq\\frac{C(n)}{t^{n/2}_{j}}\\iint_{\\mathcal{P}_8 (0,8)}Hv(y,s)\\,dy\\,ds.$$ It therefore follows from and Remark \\[rem2.2\\] that $$\\label{4.9}\n v(x,t)\\leq C\\left[\\left(\\frac{1}{\\sqrt{t}}\\right)^n +\\iint_{\\mathcal{P}_{t_j /2}(x_j ,t_j ))}\\Phi(x-y,t-s)Hv(y,s)\\,dy\\,ds\\right]\\quad\\text{for }(x,t)\\in\\mathcal{P}_{t_j /4}(x_j ,t_j ).$$ Substituting $x=x_j$ and $t=t_j$ in and using we find that $$\\label{4.10}\n t^{n/2}_{j}\\iint_{\\mathcal{P}_{t_j /2}(x_j ,t_j )}\\Phi(x_j -y,t_j -s)Hv(y,s)\\,dy\\,ds\\to\\infty\\quad\\text{as }j\\to\\infty.$$ Also, by we have $$\\label{4.11}\n \\iint_{\\mathcal{P}_{t_j /2}(x_j ,t_j )}Hv(y,s)\\,dy\\,ds\\to0\\quad\\text{as }j\\to\\infty.$$ Defining $$\\label{4.12}\n f_j (\\eta,\\zeta)=r^{\\frac{n+2}{2}}_{j}Hv(x_j +\\sqrt{r_j}\\eta,t_j\n +r_j \\zeta)\\quad \\text{where }r_j =t_j /8$$ and making the change of variables $$\\label{4.13}\n y=x_j +\\sqrt{r_j}\\eta,\\quad s=t_j +r_j \\zeta$$ in and we get\n\n$$\\label{4.14}\n \\iint_{\\mathcal{P}_4 (0,0)}f_j (\\eta,\\zeta)\\,d\\eta\\,d\\zeta\\to0\\quad\\text{as }j\\to\\infty$$\n\nand $$\\label{4.15}\n \\iint_{\\mathcal{P}_4 (0,0)}\\Phi(-\\eta,-\\zeta)f_j (\\eta,\\zeta)\\,d\\eta\\,d\\zeta\\to\\infty\\quad\\text{as }j\\to\\infty.$$ Let $$N(y,s)=\\iint_{\\mathcal{P}_8\n (0,8)}\\Phi(y-\\bar y,s-\\bar s)Hv(\\bar y,\\bar s)\\,\nd\\bar y\\, d\\bar s.$$ By and Theorem \\[thmB.2\\] we find that $N\\in L^{\\frac{n+2}{n+\\varepsilon}}(\\mathcal{P}_8 (0,8))$ and thus $N^\\lambda \\in L^{\\frac{n+2}{\\lambda(n+\\varepsilon)}}(\\mathcal{P}_8 (0,8))$. Hence by Hölder’s inequality, , and Lemma \\[lem2.5\\] we have for $R\\in(0,1]$ and $(x,t)\\in\\mathcal{P}_{Rt_j /8}(x_j ,t_j )$ that $$\\begin{aligned}\n\\label{4.16}\n \\notag &\\iint_{\\mathcal{P}_8 (0,8)\\backslash\\mathcal{P}_{Rt_j /4}(x_j ,t_j )}\n\\Phi(x-y,t-s)^{\\alpha/n}N(y,s)^\\lambda \\,dy\\,ds\\\\\n \\notag &\\leq\\| N^\\lambda \\|_{L^{\\frac{n+2}{\\lambda(n+\\varepsilon)}}(\\mathcal{P}_8 (0,8))}\\left(\\iint_{\\mathbb{R}^n \\times\\mathbb{R}\\backslash\\mathcal{P}_{Rt_j /4}(x_j ,t_j )}\\Phi(x-y,t-s)^{\\frac{\\alpha q}{n}}\\,dy\\,ds\\right)^{1/q}\\text{ where }\\frac{\\lambda(n+\\varepsilon)}{n+2}+\\frac{1}{q}=1\\\\\n &\\leq C\\left(\\frac{1}{\\sqrt{Rt_j}^{\\alpha q-(n+2)}}\\right)^{1/q}\\\\\n \\label{4.17} &=C\\frac{1}{\\sqrt{t_j}^{(n+\\varepsilon)\\lambda-(n+2-\\alpha)}}\\end{aligned}$$ where $C>0$ depends on $R$ but not on $j$.\n\nSince by and Lemma \\[lem2.8\\] we have $$N(y,s)\\leq\n C\\left[\\frac{1}{\\sqrt{t_j}^n}+\\iint_{(\\bar y,\\bar s)\\in\\mathcal{P}_{Rt_j /2}(x_j ,t_j\n )}\\Phi(y-\\bar y,s-\\bar s)Hv(\\bar y,\\bar s)\\,\n d\\bar y\\, d\\bar s\\right]\\quad\\text{for }(y,s)\\in P_{Rt_j /4}(x_j ,t_j )$$ it follows from Lemma \\[lem2.6\\] that for $(x,t)\\in\\mathcal{P}_{Rt_j /4}(x_j ,t_j )$ we have\n\n$$\\begin{aligned}\n \\iint_{(y,s)\\in\\mathcal{P}_{Rt_j /4}(x_j,t_j)}&\n\\Phi(x-y,t-s)^{\\alpha/n}N(y,s)^\\lambda \\,dy\\,ds\\notag\\\\\n &\\leq C\\left[\\frac{1}{\\sqrt{t_j}^{n\\lambda-(n+2-\\alpha)}}\n+\\iint_{(y,s)\\in\\mathcal{P}_{Rt_j /4}(x_j,t_j)}\\Phi(x-y,t-s)^{\\alpha/n}\\right.\\notag\\\\\n &\\quad\\left.\\times\\left(\\iint_{(\\bar y,\\bar s)\\in\\mathcal{P}_{Rt_j /2}(x_j,t_j )}\\Phi(y-\\bar y,s-\\bar s)Hv(\\bar y,\\bar s)\\,d\\bar y\\,d\\bar\n s\\right)^\\lambda \\,dy\\,ds\\right].", "\n \\label{4.17.1}\\end{aligned}$$\n\nAlso by Jensen’s inequality, and Lemma \\[lem2.7\\] we have for $x\\in\\mathbb{R}^n$, $t>0$, and $\\lambda\\ge 1$ that $$\\begin{aligned}\n \\iint_{\\mathbb{R}^n \\times\\mathbb{R}}&\\Phi(x-y,t-s)^{\\alpha/n}\\left(\\int_{|z|<\\sqrt{8}}\\Phi(y-z,s)\\,d\\mu(z)\\right)^\\lambda \\,dy\\,ds\\notag\\\\\n &\\leq C\\int_{|z|<\\sqrt{8}}\\left(\\iint_{\\mathbb{R}^n \\times (0,t)}\\Phi(x-y,t-s)^{\\alpha/n}\\Phi(y-z,s)^{\\lambda n/n}\\,dy\\,ds\\right)d\\mu(z)\\notag\\\\\n &\\leq\\frac{C}{\\sqrt{t}^{\\alpha+\\lambda n-(n+2)}}.\\label{4.17.2}\n \\end{aligned}$$\n\nWe claim that also holds for $0<\\lambda<1$. To see this, let $x\\in\\R^n$ and $t>0$ be fixed and define $$f(y,s)=\\Phi(x-y,t-s)^{\\alpha/n} \\quad\\text{and}\\quad \ng(y,s)=\\int_{|z|<\\sqrt{8}}\\Phi(y-z,s)\\,d\\mu(z).$$ Then by Lemma \\[lem2.7\\] with $\\beta=0$ and $\\beta=n$ we have $$\\|f\\|_1:=\\iint_{\\R^n\\times(0,t)}\\Phi(x-y,t-s)^{\\alpha/n}dy\\,ds\\le C\\sqrt{t}^{n+2-\\alpha}$$ and $$\\iint_{\\R^n\\times(0,t)}fg\\,dy\\,ds\n=\\int_{|z|<\\sqrt{8}}\\iint_{\\R^n\\times(0,t)}\\Phi(x-y,t-s)^{\\alpha/n}\\Phi(y-z,s)\\,dy\\,ds\\,d\\mu(z)\\le\nC\\sqrt{t}^{2-\\alpha},$$ respectively, where $C$ depends on neither $x$ nor $t$. Thus by Jensen’s inequality we find for $(x,t)\\in\\R^n\\times(0,\\infty)$ and $0<\\lambda<1$ that $$\\begin{aligned}\n\\iint_{\\R^n\\times\\R}fg^\\lambda dy\\,ds\n&=\\iint_{\\R^n\\times(0,t)}\\left(g\\|f\\|_1^{1/\\lambda}\\right)^\\lambda\n\\frac{f}{\\|f\\|_1}\\,dy\\,ds\\\\\n&\\le \\left(\\iint_{\\R^n\\times(0,t)}g\\|f\\|_1^{1/\\lambda}\n\\frac{f}{\\|f\\|_1}\\,dy\\,ds\\right)^\\lambda\\\\\n&=\\|f\\|_1^{1-\\lambda}\\left(\\iint_{\\R^n\\times(0,t)}fg\\,dy\\,ds\\right)^\\lambda\n\\le C\\sqrt{t}^{n+2-\\alpha-\\lambda n}.\\end{aligned}$$ That is also holds for $0<\\lambda<1$.\n\nIt therefore follows from , , , and Lemma \\[lem2.7\\] that for $(x,t)\\in\\mathcal{P}_{Rt_j /8}(x_j ,t_j )$ we have $$\\begin{aligned}\n \\int_{(y,s)\\in\\mathcal{P}_8 (0,8)}&\\Phi(x-y,t-s)^{\\alpha/n}v(y,s)^\\lambda \\,dy\\,ds\\\\\n \\begin{split} \n \\leq& C\\left[\\iint_{(y,s)\\in\\mathcal{P}_8(0,8)}\\Phi(x-y,t-s)^{\\alpha/n}\n\\left(\\int_{|z|<\\sqrt{8}}\\Phi(y-z,s)\\,d\\mu(z)\\right)^\\lambda \\,dy\\,ds\\right.\\\\\n &\\left.+\\iint_{(y,s)\\in\\mathcal{P}_8 (0,8)}\\Phi(x-y,t-s)^{\\alpha/n}(N(y,s)+1)^\\lambda \\,dy\\,ds\\right]\\\\\n \\leq& C\\left[\\frac{1}{\\sqrt{t_j}^{(n+\\varepsilon)\\lambda-(n+2-\\alpha)}}+\\iint_{(y,s)\\in\\mathcal{P}_{Rt_j /4}(x_j ,t_j )}\\Phi(x-y,t-s)^{\\alpha/n}\\right.\\\\\n &\\times\\left.\\left(\\iint_{(\\bar y,\\bar s)\\in\\mathcal{P}_{Rt_j /2}(x_j ,t_j )}\\Phi(y-\\bar y,s-\\bar s)Hv(\\bar y,\\bar s)\\,d\\bar y\\,d\\bar s\\right)^\\lambda \\,dy\\,ds\\right]\n \\end{split}\n \\end{aligned}$$ where $C>0$ depends on $R$ but not on $j$.\n\nAlso, similar to the way was derived, we obtain $$v(x,t)\\leq C\\left[\\frac{1}{\\sqrt{t_j}^n}+\\iint_{\\mathcal{P}_{Rt_j /4}(x_j ,t_j )}\\Phi(x-y,t-s)Hv(y,s)\\,dy\\,ds\\right]\\quad\\text{for }(x,t)\\in P_{Rt_j /8}(x_j ,t_j ).$$ We see therefore from that for $(x,t)\\in\\mathcal{P}_{Rt_j /8}(x_j ,t_j )$ and $R\\in(0,1]$ we have $$\\begin{aligned}\n \\begin{split}\n Hv(x,t)&\\leq C\\left[\\frac{1}{\\sqrt{t_j}^{(n+\\varepsilon)\\lambda-(n+2-\\alpha)}}+\\iint_{(y,s)\\in\\mathcal{P}_{Rt_j /4}(x_j ,t_j )}\\Phi(x-y,t-s)^{\\alpha/n}\\right.\\\\\n &\\quad\\times\\left.\\left(\\iint_{(\\bar y,\\bar s)\\in\\mathcal{P}_{Rt_j /2}(x_j ,t_j )}\\Phi(y-\\bar y,s-\\bar s)Hv(\\bar y,\\bar s)\\,d\\bar y\\,d\\bar s\\right)^\\lambda \\,dy\\,ds\\right]\\\\\n &\\quad\\times\\left[\\frac{1}{\\sqrt{t_j}^{n\\sigma}}+\\left(\\iint_{\\mathcal{P}_{Rt_j /2}(x_j ,t_j )}\\Phi(x-y,t-s)Hv(y,s)\\,dy\\,ds\\right)^\\sigma \\right].", "\n \\end{split}\n \\end{aligned}$$ Hence under the change of variables , $$x=x_j +\\sqrt{r_j}\\xi,\\quad t=t_j +r_j \\tau,$$ and $$\\bar y=x_j +\\sqrt{r_j}\\bar \\eta,\\quad \\bar s=t_j +r_j \\bar \\zeta,$$ we obtain from and that $$\\begin{aligned}\n\\label{4.18}\n \\notag &f_j (\\xi,\\tau)=r^{\\frac{n+2}{2}}_{j}Hv(x,t)\\leq r^{\\frac{(n+\\varepsilon)(\\lambda+\\sigma)-(n+2-\\alpha)}{2}}_{j}Hv(x,t)\\\\\n \\notag &\\leq C\\left[1+\\iint_{(\\eta,\\zeta)\\in\\mathcal{P}_{4R}(0,0)}\\Phi(\\xi-\\eta,\\tau-\\zeta)^{\\alpha/n}\\left(\\iint_{(\\bar \\eta,\\bar \\zeta)\\in\\mathcal{P}_{4r}(0,0)}\\Phi(\\eta-\\bar \\eta,\\zeta-\\bar \\zeta)\nf_j (\\bar \\eta,\\bar \\zeta)\\,d\\bar \\eta\\,d\\bar \\zeta\\right)^\\lambda d\\eta\\,d\\zeta\\right]\\\\\n &\\quad\\times\\left[1+\\left(\\iint_{\\mathcal{P}_{4R}(0,0)}\\Phi(\\xi-\\eta,\\tau-\\zeta)f_j (\\eta,\\zeta)\\,d\\eta\\,d\\zeta\\right)^\\sigma \\right]\n \\end{aligned}$$ for $(\\xi,\\tau)\\in\\mathcal{P}_R (0,0)$ and $R\\in(0,1]$ where $C>0$ depends on $R$ but not on $j$.\n\nTo complete the proof of Theorem \\[thm4.1\\] we will need the following lemma.", "\n\n\\[lem4.1\\] Suppose the sequence $$\\label{4.19}\n \\{f_j \\}\\text{ is bounded in }L^p (\\mathcal{P}_{4R}(0,0))$$ for some constants $p\\in[1,\\frac{n+2}{2}]$ and $R\\in(0,1]$. Then there exists a positive constant $C_0 =C_0 (n,\\lambda,\\sigma,\\alpha)$ such that the sequence $$\\label{4.20}\n \\{f_j \\}\\text{ is bounded in }L^q (\\mathcal{P}_R(0,0))$$ for some $q\\in(p,\\infty)$ satisfying $$\\label{4.21}\n \\frac{1}{p}-\\frac{1}{q}\\geq C_0.$$\n\nFor $R\\in(0,1]$ we formally define operators $N_R$ and $I_R$ by $$(N_R f)(\\xi,\\tau)=\\iint_{\\mathcal{P}_{4R}(0,0)}\n\\Phi(\\xi-\\eta,\\tau-\\zeta)f(\\eta,\\zeta)\\,d\\eta\\,d\\zeta$$ and $$(I_R f)(\\xi,\\tau)=\\iint_{\\mathcal{P}_{4R}(0,0)}\n\\Phi(\\xi-\\eta,\\tau-\\zeta)^{\\alpha/n}f(\\eta,\\zeta)\\,d\\eta\\,d\\zeta.$$ Define $p_2$ by $$\\label{4.22}\n \\frac{1}{p}-\\frac{1}{p_2}=\\frac{2-\\varepsilon}{n+2}$$ where $\\varepsilon$ is as in . ", "Then $p_2 \\in(p,\\infty)$ and thus by Theorem \\[thmB.2\\] we have $$\\label{4.23}\n \\|(N_R f_j )^\\lambda \\|_{p_2 /\\lambda}=\\| N_R f_j \\|^{\\lambda}_{p_2}\\leq C\\| f_j \\|^{\\lambda}_{p}$$ and $$\\label{4.24}\n \\|(N_R f_j )^\\sigma \\|_{p_2 /\\sigma}=\\| N_R f_j \\|^{\\sigma}_{p_2}\\leq C\\| f_j \\|^{\\sigma}_{p}$$ where $\\|\\cdot\\|_p :=\\|\\cdot\\|_{L^p (\\mathcal{P}_{4R}(0,0))}$. Since $$\\frac{1}{p_2}=\\frac{1}{p}-\\frac{2-\\varepsilon}{n+2}\n\\leq 1-\\frac{2-\\varepsilon}{n+2}=\\frac{n+\\varepsilon}{n+2}$$ we see by that $$\\label{4.25}\n \\frac{p_2}{\\lambda}>1.$$ Now there are two cases to consider.", "\n\n**Case I.** Suppose $$\\label{4.26}\n \\frac{p_2}{\\lambda}<\\frac{n+2}{n+2-\\alpha}.$$ Define $p_3$ and $q$ by $$\\label{4.27}\n \\frac{\\lambda}{p_2}-\\frac{1}{p_3}=\\frac{n+2-\\alpha}{n+2}$$ and $$\\label{4.28}\n \\frac{1}{q}:=\\frac{1}{p_3}+\\frac{\\sigma}{p_2}=\\frac{\\lambda+\\sigma}{p_2}-\\frac{n+2-\\alpha}{n+2}.$$ It follows from –, , and that $$\\label{4.29}\n 1<\\frac{p_2}{\\lambda}<p_3 <\\infty,\\quad q>0,$$ and $$\\begin{aligned}\n \\frac{1}{p}-&\\frac{1}{q}\n=\\frac{1}{p}-\\left((\\lambda+\\sigma)\\left(\\frac{1}{p}-\\frac{2-\\varepsilon}{n+2}\\right)-\\frac{n+2-\\alpha}{n+2}\\right)\\\\\n &=\\frac{(2-\\varepsilon)(\\lambda+\\sigma)+(n+2-\\alpha)}{n+2}-\\frac{\\lambda+\\sigma-1}{p}\\\\\n &\\geq\\frac{(2-\\varepsilon)(\\lambda+\\sigma)+(n+2-\\alpha)-(n+2)(\\lambda+\\sigma-1)}{n+2}\\\\\n &=\\frac{2(n+2)-\\alpha-(n+\\varepsilon)(\\lambda+\\sigma)}{n+2}.", "\n \\end{aligned}$$ Thus holds by .", "\n\nBy , , , and Theorem \\[B.1\\] we find that $$\\begin{aligned}\n \\|(I_R ((N_R &f_j )^\\lambda ))^q \\|_{p_3/q}=\\| I_R ((N_R f_j )^\\lambda )\\|^{q}_{p_3}\\\\\n &\\leq C\\|(N_R f_j )^\\lambda \\|^{q}_{p_2 /\\lambda}\\\\\n &\\leq C\\| f_j \\|^{\\lambda q}_{p}.", "\n \\end{aligned}$$ Also by we get $$\\|(N_R f_j )^{\\sigma q}\\|_{\\frac{p_2}{\\sigma q}}=\\|(N_R f_j )^\\sigma \\|^{q}_{p_2 /\\sigma}\\leq C\\| f_j \\|^{\\sigma q}_{p}.$$ It therefore follows from , , Hölder’s inequality, and that holds.", "\n\n**Case II.** ", "Suppose $$\\label{4.30} \n\\frac{p_2}{\\lambda}\\geq\\frac{n+2}{n+2-\\alpha}.$$ Then by Theorem \\[thmB.2\\], , and we find that the sequence $$\\label{4.31}\n \\{I_R ((N_R f_j )^\\lambda)\\}\\text{ is bounded in }L^{\\gamma}(\\mathcal{P}_{4R}(0,0))\n \\quad\\text{for all } \\gamma\\in(1,\\infty).$$ Let $\\hat q=p_2/\\sigma$. Then by , $$\\frac{1}{p}-\\frac{1}{\\hat q}=\\frac{1}{p}-\\frac{\\sigma}{p_2}\n=\\frac{2-\\varepsilon}{n+2}+\\frac{1-\\sigma}{p_2}.$$ Thus for $\\sigma\\le 1$ we have $$\\frac{1}{p}-\\frac{1}{\\hat q}\\ge\\frac{2-\\varepsilon}{n+2}>0$$ and for $\\sigma>1$ it follows from and that $$\\begin{aligned}\n\\frac{1}{p}-\\frac{1}{\\hat q}\n&\\ge\\frac{2-\\varepsilon}{n+2}-\\frac{\\sigma-1}{\\frac{(n+2)\\lambda}{n+2-\\alpha}}\\\\\n&\\ge \\frac{2-\\varepsilon}{n+2}\n-\\frac\n{\\frac{2(n+2)-\\alpha}{n}-\\lambda-1}\n{\\frac{(n+2)\\lambda}{n+2-\\alpha}}\\\\\n&=\\frac{n+4-\\alpha-\\varepsilon}{(n+2)\\lambda}\n\\left(\\lambda-\\left(\\frac{n+4-\\alpha}{n+4-\\alpha-\\varepsilon}\\right)\n\\frac{n+2-\\alpha}{n}\\right)>0. ", "\\end{aligned}$$ Thus defining $q\\in(p,\\hat q)$ by $$\\frac{1}{q}=\\frac{\\frac{1}{p}+\\frac{1}{\\hat q}}{2}$$ we have for $\\sigma>0$ that $$\\frac{1}{p}-\\frac{1}{q}=\\frac{1}{2}\\left(\\frac{1}{p}-\\frac{1}{\\hat\n q}\\right)\n\\ge C_0(n,\\lambda,\\sigma,\\alpha)>0.$$ That is holds.", "\n\nSince $q\\sigma/p_2<\\hat q\\sigma/p_2=1$ there exists $\\gamma\\in(q,\\infty)$ such that $$\\label{4.32}\n\\frac{q}{\\gamma}+\\frac{q\\sigma}{p_2}=1.$$ Also $$\\|(I_R ((N_R f_j )^\\lambda ))^q \\|_{\\gamma/q}\n=\\| I_R ((N_R f_j )^\\lambda )\\|^{q}_{\\gamma}$$ and by $$\\|(N_R f_j )^{\\sigma q}\\|_{\\frac{p_2}{\\sigma q}}=\\|(N_R f_j )^\\sigma\n\\|^{q}_{p_2 /\\sigma}\\leq C\\| f_j \\|^{\\sigma q}_{p}.$$ It therefore follows from , , Hölder’s inequality, , and that holds.", "\n\nWe return now to the proof of Theorem \\[thm4.1\\]. ", "By the sequence $$\\label{4.33}\n \\{f_j \\}\\text{ is bounded in }L^1(\\mathcal{P}_4 (0,0)).$$ Starting with this fact and iterating Lemma \\[lem4.1\\] a finite number of times ($m$ times is enough if $m>1/C_0$) we see that there exists $R_0 \\in(0,1)$ such that the sequence $$\\{f_j \\}\\text{ is bounded in }L^p (\\mathcal{P}_{4R_0}(0,0))$$ for some $p>(n+2)/2$. Hence by Theorem \\[thmB.2\\] the sequence $\\{N_{R_0}f_j \\}$ is bounded in $L^\\infty (\\mathcal{P}_{4R_0}(0,0))$. Thus implies the sequence $$\\label{4.34}\n \\{f_j \\}\\text{ is bounded in }L^\\infty (\\mathcal{P}_{R_0}(0,0)).$$ Since by Lemma \\[lem2.8\\], $$\\begin{aligned}\n\\iint_{\\mathcal{P}_{4}(0,0)}&\\Phi(-\\eta,-\\zeta)f_j(\\eta,\\zeta)\\,d\\eta\\,d\\zeta\\\\\n&\\le \\iint_{\\mathcal{P}_{R_0}(0,0)}\\Phi(-\\eta,-\\zeta)f_j(\\eta,\\zeta)\\,d\\eta\\,d\\zeta\n+\\frac{C(n)}{R_0^{n/2}}\\iint_{\\mathcal{P}_{4}(0,0)\\setminus\\mathcal{P}_{R_0}(0,0)}\nf_j(\\eta,\\zeta)\\,d\\eta\\,d\\zeta\\end{aligned}$$ we see that and contradict . ", "This contradiction completes the proof of Theorem \\[thm4.1\\].", "\n\nThe case $\\lambda\\geq\\frac{n+2}{n}$ {#sec5}\n===================================\n\nIn this section we prove Theorems \\[thm1.1\\]–\\[thm1.4\\] when $\\lambda\\geq\\frac{n+2}{n}$. For these values of $\\lambda$, Remark 2.1 and the following theorem imply Theorem \\[thm1.1\\].", "\n\n\\[thm5.1\\] Suppose $u$ is a nonnegative solution of , for some constants $\\alpha\\in(0,n+2)$, $$\\label{5.1}\n \\lambda\\geq\\frac{n+2}{n}\\quad\\text{and}\\quad 0\\leq\\sigma<1-\\frac{\\alpha-2}{n+2}\\lambda.$$ Then $$\\label{5.2}\n \\max_{|x|\\leq1}u(x,t)=o(t^{-\\frac{n+2}{2\\lambda}})\\quad\\text{as }t\\to0^+ .$$\n\nLet $v=u+1$. Then by Lemma \\[lem2.3\\] we have that – hold. ", "To prove it clearly suffices to prove $$\\label{5.3}\n \\max_{|x|\\leq1}v(x,t)=o(t^{-\\frac{n+2}{2\\lambda}})\\quad\\text{as }t\\to0^+ .$$\n\nSince increasing $\\sigma$ increases the right side of the second inequality in $_1$, we can assume instead of that $$\\label{5.4}\n \\lambda\\geq\\frac{n+2}{n}\\quad\\text{and}\\quad 0<\\sigma<1-\\frac{\\alpha-2}{n+2}\\lambda$$ which implies $$\\label{5.5}\n \\frac{\\sigma}{\\lambda}<\\frac{2-\\alpha}{n+2}+\\frac{1}{\\lambda}\\leq\\frac{2-\\alpha}{n+2}+\\frac{n}{n+2}=\\frac{n+2-\\alpha}{n+2}.$$ By there exists $\\varepsilon=\\varepsilon(n,\\lambda,\\sigma,\\alpha)\\in(0,1)$ such that $$\\label{5.6}\n \\alpha+\\varepsilon<n+2\\quad\\text{and}\\quad \\sigma<1-\\frac{\\alpha+\\varepsilon-2}{n+2}\\lambda$$ which implies $$\\label{5.7}\n \\frac{\\sigma-1}{\\lambda}<\\frac{2-\\alpha-\\varepsilon}{n+2}.$$\n\nPart of the proof of Theorem \\[thm5.1\\] will consist of two lemmas, the first of which is the following.", "\n\n\\[lem5.1\\] Suppose $\\Omega$ is a bounded open subset of $\\mathbb{R}^n \\times\\mathbb{R}$ and $$\\label{5.8}\n p\\in\\left[\\lambda,\\frac{(n+2)\\lambda}{n+2-\\alpha-\\varepsilon}\\right).$$ Then for all $w\\in L^p (\\Omega)$ we have $$\\label{5.9}\n \\left\\|\\left(\\iint_\\Omega \\Phi(\\cdot-y,\\cdot-s)^{\\alpha/n}w(y,s)^\\lambda \\,dy\\,ds\\right)w^\\sigma \\right\\|_{L^{p_3}(\\Omega)}\\leq C\\| w\\|^{\\lambda+\\sigma}_{L^p (\\Omega)}$$ where $$\\label{5.10}\n \\frac{1}{p_3}=\\frac{\\lambda+\\sigma}{p}-\\frac{n+2-\\alpha-\\varepsilon}{n+2}$$ and $C=C(n,\\lambda,\\sigma,\\alpha,\\Omega,p)$ is a positive constant. ", "Moreover, $$\\label{5.11}\n p_3 >1.$$\n\nDefine $p_2$ by $$\\frac{\\lambda}{p}-\\frac{1}{p_2}=\\frac{n+2-\\alpha-\\varepsilon}{n+2}.$$ Then by and $_1$, $1\\leq p/\\lambda <p_2 <\\infty$ and thus by Theorem \\[thmB.2\\] we have, letting $$I(f)=\\iint_\\Omega \\Phi(\\cdot-y,\\cdot-s)^{\\alpha/n}f(y,s)\\,dy\\,ds,$$ that $$\\label{5.12}\n \\| I(w^\\lambda )\\|_{L^{p_2}(\\Omega)}\\leq C\\| w^\\lambda \\|_{L^{p/\\lambda}(\\Omega)}=C\\| w\\|^{\\lambda}_{L^p (\\Omega)}.$$ Since $\\frac{1}{p_3}=\\frac{1}{p_2}+\\frac{\\sigma}{p}$ we have by Hölder’s inequality that $$\\begin{aligned}\n \\| I(w^\\lambda )w^\\sigma &\\|^{p_3}_{L^{p_3}(\\Omega)}\n=\\|(I(w^\\lambda )w^\\sigma )^{p_3}\\|_{L^1 (\\Omega)}\\\\\n &\\leq\\| I(w^\\lambda )^{p_3}\\|_{L^{p_2 /p_3}(\\Omega)}\\| w^{\\sigma p_3}\\|_{L^{\\frac{p}{\\sigma p_3}}(\\Omega)}\\\\\n &=\\| I(w^\\lambda )\\|^{p_3}_{L^{p_2}(\\Omega)}\\| w\\|^{\\sigma p_3}_{L^p (\\Omega)}.", "\n \\end{aligned}$$ Thus follows from .", "\n\nAlso from and we find that $$\\frac{1}{p_3}\\leq\\frac{\\lambda+\\sigma}{\\lambda}-\\frac{n+2-\\alpha-\\varepsilon}{n+2}=\\frac{\\sigma}{\\lambda}+\\frac{\\alpha+\\varepsilon}{n+2}<\\frac{1}{\\lambda}+\\frac{2}{n+2}.$$ Thus follows from $_1$.\n\nWe now continue with the proof of Theorem \\[thm5.1\\]. ", "Suppose for contradiction that is false. ", "Then there exists a sequence $\\{(x_j ,t_j )\\}\\subset\\overline{B_1 (0)}\\times(0,1/2)$ and $x_0 \\in\\overline{B_1 (0)}$ such that $$\\label{5.13}\n (x_j ,t_j )\\to (x_0 ,0)\\quad\\text{as }j\\to\\infty$$ and $$\\label{5.14}\n \\liminf_{j\\to\\infty}t^{\\frac{n+2}{2\\lambda}}_{j}v(x_j ,t_j )>0.$$ Define $p_3 >0$ by $\\frac{1}{p_3}=\\frac{\\alpha+\\varepsilon}{n+2}+\\frac{\\sigma}{\\lambda}$. Then by , and Lemma \\[lem5.1\\] with $\\Omega=\\mathcal{P}_8 (0,8),\\,p=\\lambda$, and $w=v$ we have $p_3 >1$ and $Hv\\in L^{p_3}(\\mathcal{P}_4 (0,4)$. Hence defining $p_4$ by $\\frac{1}{p_3}+\\frac{1}{p_4}=1$, using Hölder’s inequality, and making the change of variables $$\\begin{array}{cc}\n x=x_j +\\sqrt{Rt_j}\\xi, & t=t_j +Rt_j \\tau\\\\\n y=x_j +\\sqrt{Rt_j}\\eta, & s=t_j +Rt_j \\zeta\n \\end{array}$$ we see for $R\\in(0,1]$ that $$\\begin{aligned}\n &\\sup_{(x,t)\\in\\mathcal{P}_{Rt_j /4}(x_j ,t_j )}\n\\iint_{\\mathcal{P}_4 (0,4)\\backslash\\mathcal{P}_{Rt_j /2}(x_j ,t_j )}\\Phi(x-y,t-s)Hv(y,s)\\,ds\\\\\n &\\leq\\sup_{(x,t)\\in\\mathcal{P}_{Rt_j /4}(x_j ,t_j )}\\left(\\iint_{\\mathcal{P}_4 \\backslash\\mathcal{P}_{Rt_j /2}(x_j ,t_j )}\\Phi(x-y,t-s)^{p_4}\\,dy\\,ds\\right)^{1/p_4}\\| Hv\\|_{L^{p_3}(\\mathcal{P}_4 (0,4))}\\\\\n &\\leq C\\sup_{(\\xi,\\tau)\\in\\mathcal{P}_{1/4}(0,0)}\\left(\\iint_{\\mathbb{R}^n \\times\\mathbb{R}\\backslash\\mathcal{P}_{1/2}(0,0)}\\left(\\frac{1}{(Rt_j )^{n/2}}\\right)^{p_4}\\Phi(\\xi-\\eta,\\tau-\\zeta)^{p_4}(Rt_j )^{\\frac{n+2}{2}}\\,d\\eta\\,d\\zeta\\right)^{1/p_4}\\\\\n &=C\\left(\\frac{1}{Rt_j}\\right)^{(\\frac{np_4}{2}-\\frac{n+2}{2})\\frac{1}{p_4}}\\sup_{(\\xi,\\tau)\\in\\mathcal{P}_{1/4}(0,0)}\\left(\\iint_{\\mathbb{R}^n \\times\\mathbb{R}\\backslash\\mathcal{P}_{1/2}(0,0)}\\Phi(\\xi-\\eta,\\tau-\\zeta)^{p_4}\\,d\\eta \\,d\\zeta\\right)^{1/p_4}\\\\\n &=C\\left(\\frac{1}{Rt_j}\\right)^{\\frac{n+2}{2\\lambda}(\\sigma-\\frac{2-\\alpha-\\varepsilon}{n+2}\\lambda)}\n \\end{aligned}$$ where $C$ depends on neither $R$ nor $j$ and $$\\sigma-\\frac{2-\\alpha-\\varepsilon}{n+2}\\lambda<1$$ by $_2$.\n\nAlso, using , Lemma \\[lem2.8\\], and the fact that $\\mathcal{P}_{t_j /4}(x_j ,t_j )\\subset\\mathcal{P}_2 (0,2)$ we see for $R\\in(0,1]$ that $$\\begin{aligned}\n \\sup_{(x,t)\\in\\mathcal{P}_{Rt_j /4}(x_j ,t_j )}&\\iint_{\\mathcal{P}_8 (0,8)\\backslash\\mathcal{P}_4 (0,4)}\\Phi(x-y,t-s)Hv(y,s)\\,dy\\,ds\\\\\n &\\leq C(n)\\iint_{\\mathcal{P}_8 (0,8)}Hv(y,s)\\,dy\\,ds<\\infty.", "\n \\end{aligned}$$ Thus by , and Lemma \\[lem2.4\\] with $p=\\lambda,\\,\\Omega\\times(0,T)=B_2 (0)\\times(0,4)$, and $K=\\overline{B_{3/2}(0)}$ we have for $(x,t)\\in\\mathcal{P}_{Rt_j /4}(x_j ,t_j )$ and $R\\in(0,1]$ that $$\\label{5.15}\n v(x,t)\\leq\\iint_{\\mathcal{P}_{Rt_j /2}(x_j ,t_j )}\\Phi(x-y,t-s)Hv(y,s)\\,dy\\,ds+\\frac{\\varepsilon_j}{(Rt_j )^{\\frac{n+2}{2\\lambda}}}$$ for some sequence $\\{\\varepsilon_j \\}\\subset(0,1)$ which tends to zero as $j\\to\\infty$ and which depends in neither $(x,t)$ nor $R$.\n\nAlso, for $(x,t)\\in\\mathcal{P}_{Rt_j /4}(x_j ,t_j )$ and $R\\in(0,1]$ we have by and Lemma \\[lem2.8\\] that $$\\begin{aligned}\n \\iint_{\\mathcal{P}_8 (0,8)\\backslash\\mathcal{P}_{Rt_j /2}(x_j ,t_j )}\\Phi(x-y,t-s)^{\\alpha/n}v(y,s)^\\lambda \\,dy\\,ds&\\leq\\left(C(n)\\left(\\frac{4}{Rt_j}\\right)^{n/2}\\right)^{\\alpha/n}\\| v^\\lambda \\|_{L^1 (\\mathcal{P}_8 (0,8))}\\\\\n &=\\frac{C}{(Rt_j )^{\\alpha/2}}\n \\end{aligned}$$ where $C$ depends on neither $(x,t),\\,R$, nor $j$. Thus for $(x,t)\\in\\mathcal{P}_{Rt_j /4}(x_j ,t_j )$ and $R\\in(0,1]$ we have by that $$\\label{5.16}\n 0\\leq Hv(x,t)\\leq C\\left(\\frac{1}{(Rt_j )^{\\alpha/2}}+\\iint_{\\mathcal{P}_{Rt_j /2}(x_j ,t_j )}\\Phi(x-y,t-s)^{\\alpha/n}v(y,s)^\\lambda \\,dy\\,ds\\right)v(x,t)^\\sigma$$ where $C$ depends on neither $(x,t),\\,R$, nor $j$.\n\nNext, making the change of variables $$v(y,s)=t^{-\\frac{n+2}{2\\lambda}}_{j}v_j (\\eta,\\zeta),$$ $$x=x_j +\\sqrt{t_j}\\xi, \\quad t=t_j +t_j \\tau;\\qquad\n y=x_j +\\sqrt{t_j}\\eta, \\quad s=t_j +t_j \\zeta,$$ we obtain $$\\label{5.17}\n \\iint_{\\mathcal{P}_{1/2}(0,0)}v_j (\\eta,\\zeta)^\\lambda \\,d\\eta\\,d\\zeta=\\iint_{\\mathcal{P}_{t_j /2}(x_j ,t_j )}v(y,s)^\\lambda \\,dy\\,ds$$ and from and we find for $(\\xi,\\tau)\\in\\mathcal{P}_{R/4}(0,0)$ and $R\\in(0,1]$ that $$\\begin{aligned}\n\\label{5.18}\n \\notag v_j(\\xi,\\tau)&\\leq\\iint_{\\mathcal{P}_{{R/2}}(0,0)}\\frac{1}{t^{n/2}_{j}}\\Phi(\\xi-\\eta,\\tau-\\zeta)t^{-1}_{j}Hv_j (\\eta,\\zeta)t^{\\frac{n+2}{2}}_{j}\\,d\\eta\\,d\\zeta +\\frac{\\varepsilon_j}{R^{\\frac{n+2}{2\\lambda}}}\\\\\n &=\\iint_{\\mathcal{P}_{R/2}(0,0)}\\Phi(\\xi-\\eta,\\tau-\\zeta)Hv_j (\\eta,\\zeta)\\,d\\eta\\,d\\zeta+\\frac{\\varepsilon_j}{R^{\\frac{n+2}{2\\lambda}}},\n \\end{aligned}$$ where $\\varepsilon_j \\to0$ as $j\\to\\infty$ and $\\varepsilon_j$ depends on neither $(\\xi,\\tau)$ nor $R$, and $$\\begin{aligned}\n\\label{5.19}\n \\notag 0\\leq Hv_j (\\xi,\\tau)&\\leq Ct^{\\frac{n+2}{2\\lambda}+1-\\frac{\\alpha}{2}}_{j}\\left(\\frac{1}{R^{\\alpha/2}}+\\iint_{\\mathcal{P}_{R/2}(0,0)}\\Phi(\\xi-\\eta,\\tau-\\zeta)^{\\alpha/n}v_j (\\eta,\\zeta)^\\lambda \\,d\\eta\\,d\\zeta\\right)\\\\\n \\notag &\\quad\\times(t^{-\\frac{(n+2)\\sigma}{2\\lambda}}_{j}v_j (\\xi,\\eta)^\\sigma )\\\\\n &=C\\hat{\\varepsilon}_j\\left(\\frac{1}{R^{\\alpha/2}}+\\iint_{\\mathcal{P}_{R/2}(0,0)}\\Phi(\\xi-\\eta,\\tau-\\zeta)^{\\alpha/n}v_j (\\eta,\\zeta)^\\lambda \\,d\\eta\\,d\\zeta\\right)v_j (\\xi,\\eta)^\\sigma\n \\end{aligned}$$ where $C$ depends on neither $(\\xi,\\tau),\\,R$, nor $j$ and $$\\hat{\\varepsilon}_j :=t^{-\\frac{n+2}{2\\lambda}(\\sigma-1+\\frac{\\alpha-2}{n+2}\\lambda)}_{j}\\to0\\quad\\text{as }j\\to\\infty$$ by and .", "\n\nAlso by we have $$\\label{5.20}\n \\liminf_{j\\to\\infty}v_j (0,0)>0.$$\n\nTo complete the proof of Theorem \\[thm5.1\\] we will require the following lemma.", "\n\n\\[lem5.2\\] Suppose the sequence $$\\label{5.21}\n \\{v_j \\}\\text{ is bounded in }L^p (P_{R/2}(0,0))$$ for some constants $R\\in(0,1]$ and $$\\label{5.22}\n p\\in\\left[\\lambda,\\frac{(n+2)\\lambda}{n+2-\\alpha-\\varepsilon}\\right).$$ Then either the sequence $$\\label{5.23}\n \\{v_j \\}\\text{ tends to zero in }L^{\\frac{(n+2)\\lambda}{n+2-\\alpha-\\varepsilon}}(P_{R/8}(0,0))$$ or there exists a positive constant $C_0 =C_0 (n,\\lambda,\\sigma,\\alpha)$ such that the sequence $$\\label{5.24}\n \\{v_j \\}\\text{ tends to zero in }L^q (P_{R/8}(0,0))$$ for some $q\\in(p,\\infty)$ satisfying $$\\label{5.25}\n \\frac{1}{p}-\\frac{1}{q}\\geq C_0 .$$\n\nIt follows from , , , and Lemma \\[lem5.1\\] that the sequence $$\\label{5.26}\n \\{Hv_j \\}\\text{ tends to $0$ in }L^{p_3}(P_{R/4}(0,0))$$ where $p_3$, defined by , satisfies .\\\n\n**Case I.** Suppose $p_3 \\geq\\frac{n+2}{2}$. Then by , , and Theorem \\[thmB.2\\] we have the sequence $$\\{v_j \\}\\text{ tends to zero in }L^q (P_{R/8}(0,0))\\quad\\text{for all }q>1$$ which implies .", "\n\n**Case II.** ", "Suppose $p_3 <\\frac{n+2}{2}$. Define $q$ by $$\\label{5.27}\n \\frac{1}{p_3}-\\frac{1}{q}=\\frac{2}{n+2}.$$ Then by $$1<p_3 <q<\\infty.$$ Hence by , and Theorem \\[B.1\\] we have holds.", "\n\nAlso by , , , and we get $$\\begin{aligned}\n \\frac{1}{p}-\\frac{1}{q}\n&=\\frac{1}{p}+\\frac{2}{n+2}-\\frac{1}{p_3}\n=\\frac{1}{p}+\\frac{2}{n+2}-\\frac{\\sigma}{p}-\\frac{\\lambda}{p}+1-\\frac{\\alpha+\\varepsilon}{n+2}\\\\\n &=-\\frac{\\lambda+\\sigma-1}{p}+1-\\frac{\\alpha+\\varepsilon-2}{n+2}\\\\\n &\\geq\\frac{1-(\\lambda+\\sigma)}{\\lambda}+1+\\frac{2-\\alpha-\\varepsilon}{n+2}>0.", "\n \\end{aligned}$$ Thus holds.", "\n\nWe now return to the proof of Theorem \\[thm5.1\\]. ", "By and , the sequence $\\{v_j \\}$ tends to zero in $L^\\lambda (P_{1/2}(0,0))$. Starting with this fact on iterating Lemma \\[lem5.2\\] a finite number of times we see that the sequence $$\\label{5.28}\n \\{v_j \\}\\text{ tends to zero in }L^p (\\mathcal{P}_{R/2}(0,0))$$ for some $R\\in(0,1)$ and for some $$\\label{5.29}\n p>\\frac{(n+2)\\lambda}{n+2-\\alpha}.$$ Hence the sequence $\\{v^{\\lambda}_{j}\\}$ tends to zero in $L^{p/\\lambda}(\\mathcal{P}_{R/2}(0,0))$ and $\\frac{p}{\\lambda}>\\frac{n+2}{n+2-\\alpha}$. Thus by Theorem \\[thmB.2\\], the sequence whose $j$th term is the integral on the right side of , tends to zero in $L^\\infty (\\mathcal{P}_{R/2}(0,0))$. So by $$\\label{5.30}\n 0\\leq Hv_j <Cv^{\\sigma}_{j}\\quad\\text{in }\\mathcal{P}_{R/4}(0,0)$$ where $C$ does not depend on $j$. Hence by the sequence $\\{Hv_j \\}$ tends to zero in $L^{p/\\sigma}(\\mathcal{P}_{R/4}(0,0))$ and by and $$\\frac{p}{\\sigma}>\\frac{(n+2)\\lambda}{(n+2-\\alpha)\\sigma}>\\left(\\frac{n+2}{n+2-\\alpha}\\right)^2 >1.$$ Thus by and Theorem \\[thmB.2\\] the sequence $$\\label{5.31}\n \\{v_j \\}\\text{ tends to zero in }L^q (\\mathcal{P}_{R/8}(0,0))\\text{ where }q=\n \\begin{cases}\n \\infty, & \\text{if }\\frac{p}{\\sigma}\\geq\\frac{n+2}{2-\\varepsilon}\\\\\n \\frac{1}{\\frac{\\sigma}{p}-\\frac{2-\\varepsilon}{n+2}}, & \\text{if }\\frac{p}{\\sigma}<\\frac{n+2}{2-\\varepsilon}.", "\n \\end{cases}$$ However the possibility that $q=\\infty$ is ruled out by . ", "Hence we can assume $\\frac{p}{\\sigma}<\\frac{n+2}{2-\\varepsilon}$. Then by , $$\\frac{1}{p}-\\frac{1}{q}=\\frac{1-\\sigma}{p}+\\frac{2-\\varepsilon}{n+2}.$$ Thus, if $\\sigma\\in(0,1]$ then $$\\frac{1}{p}-\\frac{1}{q}>\\frac{1}{n+2}.$$ On the other hand, if $\\sigma>1$ then by and $$\\begin{aligned}\n \\frac{1}{p}-\\frac{1}{q}&=\\frac{2-\\varepsilon}{n+2}-\\frac{\\sigma-1}{p}\\\\\n &>\\frac{2-\\varepsilon}{n+2}-\\frac{\\sigma-1}{\\lambda}\\frac{n+2-\\alpha}{n+2}\\\\\n &>\\frac{2-\\varepsilon}{n+2}-\\frac{2-\\alpha-\\varepsilon}{n+2}\n =\\frac{\\alpha}{n+2}.", "\n \\end{aligned}$$ Thus for $\\sigma>0$ we have $$\\frac{1}{p}-\\frac{1}{q}>C(n,\\alpha)>0.$$ Hence, after a finite number of iterations of the procedure of going from to we see that the sequence $\\{v_j\\}$ tends to zero in $L^\\infty (\\mathcal{P}_{\\hat R}(0,0))$ for some $\\hat R\\in(0,R)$ which again contrdicts . ", "This completes the proof of Theorem \\[thm5.1\\].", "\n\nThe following theorem implies Theorem \\[thm1.2\\].", "\n\n\\[thm5.2\\] Suppose $$\\label{5.32}\n \\lambda\\geq\\frac{n+2}{n}\\quad\\text{and}\\quad \\gamma=\\frac{n+2-\\varepsilon}{2\\lambda}$$ for some $\\varepsilon\\in(0,1)$. Then the function $$\\label{5.33}\n u(x,t)=\\Psi(x,t):=\\int_{\\mathbb{R}^n}\\Phi(x-y,t)|y|^{-2\\gamma}dy$$ is a $C^\\infty$ positive solution of $$\\label{5.34}\n Hu=0\\quad\\text{in }\\mathbb{R}^n \\times(0,\\infty)$$ such that $$\\label{5.35}\n u\\in L^\\lambda (\\mathbb{R}^n \\times(0,T))\\quad\\text{for all }T>0,$$ $$\\label{5.36}\n t^\\gamma u(0,t)=u(0,1)\\quad\\text{for }0<t<\\infty,$$ and $$\\label{5.37}\n t^\\gamma u(x,t)\\text{ is bounded between positive constants}$$ on $\\{(x,t)\\in\\mathbb{R}^n \\times(0,t):|x|<\\sqrt{t}\\}$.\n\nBy we have $2\\gamma<n$. Thus is a $C^\\infty$ positive solution of .", "\n\nFor $a>0$ and $(x,t)\\in\\mathbb{R}^n \\times(0,\\infty)$ we find making the change of variables $y=az$ that $$\\begin{aligned}\n\\label{5.38}\n \\notag u(ax,a^2 t)&=\\int_{\\mathbb{R}^n}\\Phi(ax-y,a^2 t)|y|^{-2\\gamma}dy\\\\\n \\notag &=\\int_{\\mathbb{R}^n}\\Phi(ax-az,a^2 t)a^{-2\\gamma}|z|^{-2\\gamma}a^n dz\\\\\n \\notag &=a^{-2\\gamma}\\int_{\\mathbb{R}^n}\\Phi(x-z,t)|z|^{-2\\gamma}dz\\\\\n &=a^{-2\\gamma}u(x,t).", "\n \\end{aligned}$$ Taking $x=0$ and $t=1$ in we get $$\\label{5.39}\n u(0,a^2 )=a^{-2\\gamma}u(0,1)\\quad\\text{for all }a>0.$$ Thus holds.", "\n\nTaking $x\\neq0,\\,t>0$, and $a=1/|x|$ in and using the fact that $u(x,t)$ is radially symmetric in $x$ about the origin we get $$\\label{5.40}\n u(x,t)=a^{2\\gamma}u(ax,a^2 t)=|x|^{-2\\gamma}u(e_1 ,\\frac{t}{|x|^2})\n=|x|^{-2\\gamma}g\\left(\\frac{t}{|x|^2}\\right)$$ where $g(\\zeta)=u(e_1 ,\\zeta)$ and $e_1 =(1,0,...,0)\\in\\mathbb{R}^n$. By , $$\\label{5.41}\n g(\\zeta)\\to1\\quad\\text{as }\\zeta\\to0^+$$ and using and we obtain for $t>0$ that $$1=\\lim_{x\\to 0}\\frac{u(x,t)}{u(0,t)}\n=\\lim_{x\\to 0}\\frac{|x|^{-2\\gamma}g\\left(\\frac{t}{|x|^2}\\right)}{u(0,1)t^{-\\gamma}}\n=\\lim_{x\\to0}\\frac{1}{u(0,1)}\\frac{g\\left(\\frac{t}{|x|^2}\\right)}\n{\\left(\\frac{t}{|x|^2}\\right)^{-\\gamma}}.$$ Thus $$\\label{5.42}\n \\frac{g(\\zeta)}{\\zeta^{-\\gamma}}\\to u(0,1)\\quad\\text{as }\\zeta\\to\\infty.$$ For $t>0$, it follows from – and that $$\\begin{aligned}\n \\int_{\\mathbb{R}^n}u(x,t)^\\lambda dx&=\\int_{\\mathbb{R}^n}|x|^{-2\\lambda\\gamma}g\\left(\\frac{t}{|x|^2}\\right)^\\lambda dx\\\\\n &\\leq\n C\\left[\\int_{\\sqrt{t}<|x|}|x|^{-2\\lambda\\gamma}dx\n+\\int_{|x|<\\sqrt{t}}|x|^{-2\\lambda\\gamma}\\left(\\frac{t}{|x|^2}\\right)^{-\\gamma\\lambda}dx\\right]\\\\\n &\\leq Ct^{-1+\\varepsilon/2}\n \\end{aligned}$$ which implies .", "\n\nMaking the change of variables $$x=\\sqrt{t}\\xi\\quad\\text{and}\\quad y=\\sqrt{t}\\eta$$ in we get $$u(x,t)=\\frac{1}{t^\\gamma}U\\left(\\frac{x}{\\sqrt{t}}\\right)\\quad\\text{for }(x,t)\\in\\mathbb{R}^n \\times(0,\\infty)$$ where $$U(\\xi)=\\frac{1}{(4\\pi)^{n/2}}\\int_{\\mathbb{R}^n}e^{-|\\xi-\\eta|^2 /4}|\\eta|^{-2\\gamma}d\\eta.$$ Thus since $U(\\xi)$ is bounded between positive constants for $|\\xi|\\leq1$, we find that holds.", "\n\nThe following theorem implies Theorems \\[thm1.3\\] and \\[thm1.4\\] when $\\lambda\\geq(n+2)/n$.\n\n\\[thm5.3\\] Suppose $\\alpha,\\,\\lambda$, and $\\sigma$ are constants satisfying $$\\label{Q1}\n \\alpha\\in(0,n+2),\\quad\\lambda\\geq\\frac{n+2}{n},\\quad\\sigma\\geq0,\\quad\\text{and}\\quad \\sigma>1+\\frac{2-\\alpha}{n+2}\\lambda.$$ Let $\\varphi:(0,1)\\to(0,\\infty)$ be a continuous function satisfying $$\\lim_{t\\to0^+}\\varphi(t)=\\infty.$$ Then there exists a positive function $$\\label{Q2}\n u\\in C^\\infty (\\mathbb{R}^n \\times(0,1))\\cap L^\\lambda (\\mathbb{R}^n \\times(0,1))$$ satisfying $$\\label{Q3}\n 0\\leq Hu\\leq(\\Phi^{\\alpha/n}*u^\\lambda )u^\\sigma\\quad\\text{in }\\mathbb{R}^n \\times(0,1),$$ where $*$ is the convolution operation in $\\mathbb{R}^n \\times(0,1)$, such that $$\\label{Q4}\n u(0,t)\\neq O(\\varphi(t))\\quad\\text{as }t\\to0^+ .$$\n\nBy scaling $u$ and noting by that $\\sigma+\\lambda\\neq1$ we see that it suffices to prove Theorem \\[thm5.3\\] with replaced with the weaker statement that there exists a positive constant $C=C(n,\\lambda,\\sigma,\\alpha)$ such that $u$ satisfies $$\\label{Q5}\n 0\\leq Hu\\leq C(\\Phi^{\\alpha/n}*u^\\lambda )u^\\sigma \\quad\\text{in }\\mathbb{R}^n \\times(0,1),$$ where $(*)$ is the convolution operation in $\\mathbb{R}^n \\times(0,1)$.\n\nBy there exists $\\varepsilon=\\varepsilon(n,\\lambda,\\sigma,\\alpha)\\in(0,1)$ such that $$\\label{Q6}\n 2\\varepsilon<\\alpha$$ and $$\\label{Q7}\n \\sigma>1+\\frac{2-\\alpha+2\\varepsilon}{n+2-2\\varepsilon}\\lambda.$$ Let $$\\label{Q8}\n \\gamma=\\frac{n+2-\\varepsilon}{2\\lambda}\\quad\\text{and}\\quad p=\\frac{2\\lambda}{n+2-2\\varepsilon}.$$ Then $$\\label{Q9}\n \\gamma p>1.$$ Let $\\{T_j\\}\\subset(0,1)$ be a sequence such that $T_j \\to0$ as $j\\to\\infty$. Define $w_j :(-\\infty,T_j )\\to(0,\\infty)$ by $$\\label{Q10}\n w_j (t)=(T_j -t)^{-1/p}$$ and define $t_j \\in(0,T_j )$ by $$\\label{Q11}\n w_j (t_j )=t^{-\\gamma}_{j}.$$ Then $$\\label{Q12}\n \\frac{T_j -t_j}{t_j}=\\frac{w_j (t_j )^{-p}}{t_j}=t^{\\gamma p-1}_{j}\\to0\\quad\\text{as }j\\to\\infty$$ by .", "\n\nChoose $a_j \\in((t_j+T_j)/2,T_j )$ such that $w_j (a_j )>j\\varphi(a_j )$. ", "Then $$\\label{Q13}\n \\frac{w_j (a_j )}{\\varphi(a_j )}\\to\\infty\\quad\\text{as }j\\to\\infty.$$ Let $h_j (s)=\\sqrt{a_j-s}$ and $H_j (s)=\\sqrt{a_j +\\varepsilon_j -s}$ where $\\varepsilon_j >0$ satisfies $$\\label{Q14}\n a_j +2\\varepsilon_j <T_j, \\quad t_j-\\varepsilon_j >t_j/2, \\quad\n\\varepsilon_j <T^{2}_{j}, \\quad \\text{and} \\quad w_j (t_j -\\varepsilon_j )>\\frac{w_j (t_j )}{2}.$$ Define $$\\begin{aligned}\n &\\omega_j =\\{(y,s)\\in\\mathbb{R}^n \\times\\mathbb{R}:|y|<h_j (s)\\quad\\text{and}\\quad t_j <s<a_j \\},\\\\\n &\\Omega_j =\\{(y,s)\\in\\mathbb{R}^n \\times\\mathbb{R}:|y|<H_j (s)\\quad\\text{and}\\quad t_j -\\varepsilon_j <s<a_j +\\varepsilon_j \\}.", "\n \\end{aligned}$$ By taking a subsequence we can assume the sets $\\Omega_j$ are pairwise disjoint.", "\n\nLet $\\chi_j :\\mathbb{R}^n \\times\\mathbb{R}\\to[0,1]$ be a $C^\\infty$ function such that $\\chi_j \\equiv1$ in $\\omega_j$ and $\\chi_j \\equiv0$ in $\\mathbb{R}^n \\times\\mathbb{R}\\backslash\\Omega_j$. Define $f_j ,\\,u_j :\\mathbb{R}^n \\times\\mathbb{R}\\to[0,\\infty)$ by $$\\label{Q15}\n f_j (y,s)=\\chi_j (y,s)w^{\\prime}_{j}(s)$$ and $$\\label{Q16}\n u_j (x,t)=\\iint_{\\mathbb{R}^n \\times\\mathbb{R}}\\Phi(x-y,t-s)f_j (y,s)\\,dy\\,ds.$$ Then $f_j$ and $u_j$ are $C^\\infty$ and $$\\label{Q17}\n Hu_j =f_j \\quad\\text{in }\\mathbb{R}^n \\times\\mathbb{R}.$$ By Theorem \\[thmB.2\\] with $p=n+2$ and $q=\\infty$ we see that $$\\begin{aligned}\n\\label{Q18}\n \\notag\\biggl\\|\\iint_{\\Omega_j \\backslash \\omega_j}&\\Phi(x-y,t-s)\nw^{\\prime}_{j}(s)\\,dy\\,ds\\biggr\\|_{L^\\infty (\\mathbb{R}^n \\times(0,1))}\\\\\n \\notag &=\\biggl\\|\\iint_{\\mathbb{R}^n \\times(0,1)}\n\\Phi(x-y,t-s)\\chi_{\\Omega_j \\backslash \\omega_j}(y,s)\nw^{\\prime}_{j}(s)\\,dy\\,ds\\biggr\\|_{L^\\infty (\\mathbb{R}^n \\times(0,1))}\\\\\n \\notag &\\leq C_n \\| w^{\\prime}_{j}(s)\\|_{L^{n+2}(\\Omega_j \\backslash \\omega_j )}\\\\\n &\\leq w_j (t_j )\n \\end{aligned}$$ provided we decrease $\\varepsilon_j$ if necessary because $|\\Omega_j \\backslash \\omega_j |\\to0$ as $\\varepsilon_j \\to0$.\n\nAlso, it follows from $_2$, $_1$, , $_1$, , and that there exists a positive constant $M$, independent of $j$, such that for $(x,t)\\in\\Omega_j$ we have $$\\label{Q19}\n M\\Psi(x,t)>\\frac{2^{\\gamma+1}}{t^\\gamma}>\\frac{2^{\\gamma+1}}{T^{\\gamma}_{j}}>\\frac{2^{\\gamma+1}}{(2t_j )^\\gamma}=2w_j (t_j ),$$ provided we take a subsequence if necessary, where $\\Psi$ is defined by .", "\n\nIn order to obtain a lower bound for $u_j$ in $\\omega_j$, note first that for $s<t\\leq a_j +\\varepsilon_j$ and $|x|\\leq H_j (t)$ we have by Lemma \\[lem2.10\\] that $$\\label{Q20}\n \\int_{|y|<H_j (s)}\\Phi(x-y,t-s)\\,dy\\geq b$$ for some constant $$\\label{Q21}\n b=b(n)\\in(0,1).$$ Next using and , we find for $(x,t)\\in\\Omega_j$ that $$\\begin{aligned}\n \\iint_{\\Omega_j}\\Phi(x-y,t-s)w^{\\prime}_{j}(s)\\,dy\\,ds&=\\int^{t}_{t_j -\\varepsilon_j}w^{\\prime}_{j}(s)\\left(\\int_{|y|<H_j (s)}\\Phi(x-y,t-s)\\,dy\\right)ds\\\\\n &\\geq b(w_j (t)-w_j (t_j -\\varepsilon_j ))\\\\\n &\\geq bw_j (t)-w_j (t_j ).", "\n \\end{aligned}$$ It therefore follows from , , and that for $(x,t)\\in\\Omega_j$ we have $$\\begin{aligned}\n\\label{Q22}\n \\notag u_j (x,t)&\\geq\\iint_{\\omega_j }\\Phi(x-y,t-s)w^{\\prime}_{j}(s)\\,dy\\,ds\\\\\n \\notag &=\\iint_{\\Omega_j}\\Phi(x-y,t-s)w^{\\prime}_{j}(s)\\,dy\\,ds-\\iint_{\\Omega_j \\backslash \\omega_j}\\Phi(x-y,t-s)w^{\\prime}_{j}(s)\\,dy\\,ds\\\\\n &\\geq bw_j (t)-2w_j (t_j ).", "\n \\end{aligned}$$\n\nDefine $\\beta>0$ by $$\\label{Q23}\n \\frac{1}{\\beta}-\\frac{1}{\\lambda}=\\frac{2}{n+2}.$$ Then by $$\\label{Q24}\n \\frac{2}{n+2}<\\frac{1}{\\beta}=\\frac{1}{\\lambda}+\\frac{2}{n+2}\\leq\\frac{n}{n+2}+\\frac{2}{n+2}=1$$ and by $$p>\\frac{2\\lambda}{n+2}=\\frac{2}{(n+2)/\\lambda}=\\frac{2}{\\frac{n+2}{\\beta}-2}=\\frac{2\\beta}{n+2-2\\beta}.$$ Thus $$\\label{Q25}\n \\frac{n}{2}-\\frac{\\beta(p+1)}{p}+1=\\frac{(n+2-2\\beta)p-2\\beta}{2p}>0.$$ Next we slightly increase $\\beta$ in such a way that and the first inequality in still hold. ", "Then instead of and we get $$\\label{Q26}\n \\frac{1}{\\beta}-\\frac{1}{\\lambda}<\\frac{2}{n+2}$$ and $$\\label{Q27}\n \\frac{2}{n+2}<\\frac{1}{\\beta}<1$$ respectively.", "\n\nFrom , , $_1$ and we find that $$\\begin{aligned}\n \\notag p^\\beta &\\iint_{\\mathbb{R}^n \\times\\mathbb{R}}f_j (y,s)^\\beta \\,dy\\,ds\\leq p^\\beta \\iint_{\\Omega_j}w^{\\prime}_{j}(s)^\\beta \\,dy\\,ds\\\\\n \\notag &\\leq p^\\beta \\int^{T_j}_{0}\\int_{|y|<\\sqrt{T_j -s}}w^{\\prime}_{j}(s)^\\beta \\,dy\\,ds\\\\\n \\notag &=|B_1(0)|\\int^{T_j}_{0}(T_j -s)^{n/2-\\beta(p+1)/p}ds\\\\\n \\label{Q28} &=|B_1(0)|\\int^{T_j}_{0}\\tau^{n/2-\\beta(p+1)/p}\\,d\\tau\\to0\\quad\\text{as }j\\to\\infty.", "\n \\end{aligned}$$ Hence by , , , and Theorem \\[thmB.2\\] we obtain $$\\label{Q29}\n \\| u_j \\|_{L^\\lambda (\\mathbb{R}^n \\times(0,1))}\\to0\\quad\\text{as }j\\to\\infty.$$ Repeating the derivation of with $\\beta$ replaced with $1$, we find that $$\\iint_{\\mathbb{R}^n \\times\\mathbb{R}}f_j (y,s)\\,dy\\,ds\\to0\\quad\\text{as }j\\to\\infty.$$ Thus $$\\iint_{\\mathbb{R}^n \\times\\mathbb{R}}\\sum^{\\infty}_{j=1}f_j (y,s)d\\eta ds<\\infty$$ provided we take a subsequence if necessary. ", "Hence, since the $C^\\infty$ functions $f_j$ have disjoint supports, it follows from Theorem \\[thm5.2\\] that the function $u:\\mathbb{R}^n \\times(0,\\infty)\\to(0,\\infty)$ defined by $$\\label{Q30}\n u(x,t)=(M+1)\\Psi(x,t)+\\sum^{\\infty}_{j=1}u_j (x,t)$$ is $C^\\infty$ and from and Theorem \\[thm5.2\\] we have $$\\label{Q31}\n Hu=\\sum^{\\infty}_{j=1}f_j \\quad\\text{in }\\mathbb{R}^n \\times(0,\\infty).$$ By and Theorem \\[thm5.2\\], $$u\\in L^\\lambda (\\mathbb{R}^n \\times(0,1))$$ provided we take a subsequence of $u_j$ if necessary. ", "Thus holds.", "\n\nWe now prove . ", "By and we have $$Hu\\equiv0\\quad\\text{in }(\\mathbb{R}^n \\times(0,1))\\backslash\\bigcup^{\\infty}_{j=1}\\Omega_j.$$ Hence to prove , it suffice to prove there exists a positive constant $C=C(n,\\lambda,\\sigma,\\alpha)$ such that $$\\label{Q32}\n 0\\leq Hu\\leq C(\\Phi^{\\alpha/n}*u^\\lambda )u^\\sigma \\quad\\text{in }\\Omega_j$$ for $j=1,2,...$.\n\nBy , , and we have for $(x,t)\\in\\Omega_j$ that $$\\label{Q33}\n u(x,t)\\geq(M+1)\\Psi(x,t)+bw_j (t)-2w_j (t_j )\\geq\\Psi(x,t)+bw_j (t).$$ Thus for $(x,t)\\in\\Omega_j$ we see by , , and that $$\\begin{aligned}\n Hu(x,t)&=f_j (x,t)\\leq w^{\\prime}_{j}(t)=\\frac{1}{p}w_j (t)^{1+p}\\\\\n &=\\frac{1}{p}w_j(t)^{1+p-\\sigma}w_j(t)^\\sigma\n\\le \\frac{1}{pb^\\sigma}w_j(t)^{1+p-\\sigma}u(x,t)^\\sigma.", "\n \\end{aligned}$$ Hence to prove it suffices to show $$\\label{Q34}\n w_j (t)^{1+p-\\sigma}< C\\iint_{\\mathbb{R}^n \\times(0,1)}\\Phi(x-y,t-s)^{\\alpha/n}u(y,s)^\\lambda \\,dy\\,ds\\quad\\text{for }(x,t)\\in\\Omega_j .$$\n\nOur proof of consists of two cases.", "\n\n**Case I.** Suppose $$\\label{Q35}\n (x,t)\\in\\Omega_j \\quad\\text{and}\\quad t\\leq\\frac{T_j +t_j}{2}.$$ Then using $_4$, $_2$, $_2$ and the fact that $w_j$ is an increasing function we have $$\\begin{aligned}\n \\frac{1}{2}&\\leq\\frac{w_j (t)}{2w_j (t_j -\\varepsilon_j )}<\\frac{w_j (t)}{w_j (t_j )}\\\\\n &\\leq\\left(\\frac{T_j -\\frac{T_j +t_j}{2}}{T_j -t_j}\\right)^{-1/p}=2^{1/p}<2^{n/2}.", "\n \\end{aligned}$$ Also by and $$\\frac{w_j (t_j )}{T^{-\\gamma}_{j}}=\\left(\\frac{T_j}{t_j}\\right)^\\gamma \\in(1,2)$$ provided we take a subsequence if necessary. ", "Thus implies $$\\label{Q36}\n \\frac{1}{2}<\\frac{w_j (t)}{T^{-\\gamma}_{j}}<2^{(n+2)/2}.$$ Next making the change of variables $$x=\\sqrt{T_j}\\xi,\\quad t=T_j \\tau;\\qquad y=\\sqrt{T_j}\\eta,\\quad s=T_j\n\\zeta;\\qquad\\text{and}\\quad \\hat{y}=\\sqrt{T_j}\\hat{\\eta},$$ we get for $(y,s)\\in\\mathbb{R}^n \\times(0,\\infty)$ that $$\\begin{aligned}\n \\Psi(y,s)&=\\int_{\\mathbb{R}^n}\\Phi(y-\\hat{y},s)|\\hat{y}|^{-2\\gamma}d\\hat{y}\\\\\n &=\\int_{\\mathbb{R}^n}\\frac{1}{T^{n/2}_{j}}\\Phi(\\eta-\\hat{\\eta},\\zeta)T^{-\\gamma}_{j}|\\hat{\\eta}|^{-2\\gamma}T^{n/2}_{j}d\\hat{\\eta}\\\\\n &=T^{-\\gamma}_{j}\\Phi(\\eta,\\zeta)\n \\end{aligned}$$ and thus for $(x,t)\\in\\Omega_j$ we obtain from $_1$ that $$\\begin{aligned}\n \\notag \\iint_{\\mathbb{R}^n\n \\times(0,1)}&\\Phi(x-y,t-s)^{\\alpha/n}\\Psi(y,s)^\\lambda \\,dy\\,ds\\\\\n&=\\iint_{\\mathbb{R}^n \\times(0,\\tau)}\\left(\\frac{1}{T^{n/2}_{j}}\\Phi(\\xi-\\eta,\\tau-\\zeta)\\right)^{\\alpha/n}(T^{-\\gamma}_{j}\\Psi(\\eta,\\zeta))^\\lambda\n T^{\\frac{n+2}{2}}_{j}\\,d\\eta\\,d\\zeta \\notag\\\\\n&\\geq\\frac{G(\\xi,\\tau)}{\\sqrt{T_j}^{\\alpha+2\\gamma\\lambda-(n+2)}}\n=\\frac{G(\\xi,\\tau)}{\\sqrt{T_j}^{\\alpha-\\varepsilon}}\\label{Q37}\n \\end{aligned}$$ where $$G(\\xi,\\tau):=\\iint_{B_1 (0)\\times(1/2,\\tau)}\\Phi(\\xi-\\eta,\\tau-\\zeta)^{\\alpha/n}\\Psi(\\eta,\\zeta)^\\lambda \\,d\\eta\\,d\\zeta.$$ Since by $_1$, $_1$, , and $_3$, $$1>\\tau=\\frac{t}{T_j}\\geq\\frac{t_j -\\varepsilon_j}{T_j}\\to1\\quad\\text{as }j\\to\\infty$$ we have by $_1$ that $$|\\xi|=\\frac{|x|}{\\sqrt{T_j}}<\\frac{\\sqrt{T_j -t}}{\\sqrt{T_j}}=\\sqrt{1-\\frac{t}{T_j}}\\to0\\quad\\text{as }j\\to\\infty.$$ Thus, since $G$ is clearly continuous at $(\\xi,\\tau)=(0,1)$ and $G(0,1)>0$ we have by that $$\\label{Q38}\n \\iint_{\\mathbb{R}^n \\times(0,1)}\\Phi(x-y,t-s)^{\\alpha/n}\\Psi(y,s)^\\lambda \\,dy\\,ds\\geq\\frac{C}{\\sqrt{T_j}^{\\alpha-\\varepsilon}}\\quad\\text{for }(x,t)\\in\\Omega_j$$ provided we take a subsequence if necessary.", "\n\nSince by and $_2$ $$\\sigma-1>\\left(\\frac{2-\\alpha+2\\varepsilon}{n+2-2\\varepsilon}\\right)\\lambda =p-\\frac{\\alpha-2\\varepsilon}{n+2-2\\varepsilon}\\lambda>p-\\frac{\\alpha-\\varepsilon}{n+2-\\varepsilon}\\lambda$$ we have by $_1$ that $$\\gamma(1+p-\\sigma)<\\gamma\\left(\\frac{(\\alpha-\\varepsilon)\\lambda}{n+2-\\varepsilon}\\right)=\\frac{\\alpha-\\varepsilon}{2}.$$ Thus follows from , , and .", "\n\n**Case II.** ", "Suppose $$\\label{Q39}\n (x,t)\\in\\Omega_j \\quad\\text{and}\\quad t\\geq\\frac{T_j +t_j}{2}.$$ Then for $s<t$ we have by Lemma \\[lem2.10\\] that $$\\int_{|y|<H_j (s)}\\Phi(x-y,t-s)^{\\alpha/n}dy\\geq\\frac{C}{(t-s)^{(\\alpha-n)/2}}$$ for some positive constant $C=C(n,\\alpha)$. Thus for $(x,t)$ satisfying we get $$\\begin{aligned}\n \\notag \\iint_{\\Omega_j}\\Phi&(x-y,t-s)^{\\alpha/n}w_j (s)^\\lambda \\,dy\\,ds\\geq\\int^{t}_{t_j}w_j (s)^\\lambda \\left(\\int_{|y|<H_j (s)}\\Phi(x-y,t-s)^{\\alpha/n}dy\\right)ds\\\\\n \\notag &\\geq C\\int^{t}_{t_j}\\frac{ds}{(t-s)^{(\\alpha-n)/2}(T_j -s)^{\\lambda/p}}\\\\\n \\notag &=\\frac{C}{(T_j -t )^{(\\alpha-n)/2+\\lambda/p-1}}\\int^{\\frac{T_j -t_j}{T_j -t}}_{1}\\frac{dz}{(z-1)^{(\\alpha-n)/2}z^{\\lambda/p}}\\text{ where }T_j -s=(T_j -t)z\\\\\n \\notag &\\geq\\frac{C}{(T_j -t)^{(\\alpha-n)/2+\\lambda/p-1}}\\int^{2}_{1}\\frac{dz}{(z-1)^{(\\alpha-n)/2}z^{\\lambda/p}}\\\\\n \\label{Q40} &=\\frac{C}{(T_j -t)^{(\\alpha-n)/2+\\lambda/p-1}}=\\frac{C}{(T_j -t)^{(\\alpha-2\\varepsilon)/2}}\n \\end{aligned}$$ by $_2$.\n\nSince by and $_2$ $$\\sigma-1>\\frac{2-\\alpha+2\\varepsilon}{n+2-2\\varepsilon}\\lambda=p\\frac{2-\\alpha+2\\varepsilon}{2}$$ we see that $$\\frac{1}{p}(1+p-\\sigma)=1+\\frac{1-\\sigma}{p}<1+\\frac{\\alpha-2-2\\varepsilon}{2}=\\frac{\\alpha-2\\varepsilon}{2}.$$ Thus follows from , , and .", "\n\nFinally from and we get $$\\frac{u(0,a_j )}{\\varphi(a_j )}\\geq\\frac{bw_j (a_j )}{\\varphi(a_j )}\\to\\infty\\quad\\text{as }j\\to\\infty,$$ which gives .", "\n\nRepresentation formula {#secA}\n======================\n\nIn this appendix we provide the following representation formula for nonnegative supertemperatures.", "\n\n\\[thmA\\] Suppose $0<R_1<R_2<R_3$ are constants and $u$ is a $C^{2,1}$ nonnegative solution of $$\\label{A.1}\n Hu\\ge 0\\quad \\text{in } B_{\\sqrt{R_3}}(0)\\times (0,R_3) \n\\subset \\R^n \\times \\R,\\ n\\ge 1,$$ where $Hu = u_t-\\Delta u$ is the heat operator. ", "Then $$\\label{A.2}\n Hu \\in L^1(B_{\\sqrt{R_2}}(0) \\times (0,R_2)),$$ $$\\label{A.2.5}\nu^\\beta \\in L^1(B_{\\sqrt{R_1}}(0) \\times (0,R_1))\\quad\\text{for }\n1\\le\\beta <\\frac{n+2}{n}$$ and there exist a finite positive Borel measure $\\mu$ on $B_{\\sqrt{R_2}}(0)$ and a bounded function\\\n$h\\in C^{2,1}(B_{\\sqrt{R_1}}(0) \\times (-R_1,R_1))$ satisfying $$\\begin{aligned}\n{2}\n \\label{A.3}\nHh &= 0 \\quad \\text{in } &B_{\\sqrt{R_1}}(0)\\times (-R_1,R_1)\\\\\n\\label{A.4}\n h &= 0 \\quad \\text{in } &B_{\\sqrt{R_1}}(0)\\times (-R_1,0] \\end{aligned}$$ such that $$\\label{A.5}\n u = N +v+h\\quad \\text{in } B_{\\sqrt{R_1}}(0)\\times (0,R_1)$$ where $$\\begin{aligned}\n\\label{A.6}\n N(x,t) &:= \\int^{R_2}_0 \\int_{|y|<\\sqrt{R_2}} \\Phi(x-y,t-s) Hu(y,s)\\,dy\\,ds,\\\\\n\\label{A.7}\nv(x,t) &:= \\int_{|y|<\\sqrt{R_2}} \\Phi(x-y,t)\\,d\\mu(y),\\end{aligned}$$ and $\\Phi$ is the heat kernel .", "\n\nWhen $\\beta=1$, $R_1=1$, $R_2=4$, and $R_3=16$, Theorem \\[thmA\\] was proved in [@T2011]. ", "The proof of Theorem \\[thmA\\] when $\\beta=1$ is obtained by making straighforward changes to the proof in [@T2011]. ", "It remains only to prove for $1<\\beta<(n+2)/n$. To do this, it suffices by to show $$\\label{A.8}\nN^\\beta\\in L^1(\\R^n\\times(0,R_2))\\quad\\text{for }1<\\beta<(n+2)/n$$ and $$\\label{A.9}\nv^\\beta\\in L^1(\\R^n\\times(0,R_2))\\quad\\text{for }1<\\beta<(n+2)/n.$$ Theorem \\[thmB.2\\] and imply .", "\n\nFinally, for $t>0$, $\\beta>1$, and $\\beta'$ the conjugate Hölder exponent of $\\beta$ we have $$\\begin{aligned}\n\\int_{\\R^n}v(x,t)^\\beta\\,dx\n&=\\int_{\\R^n}\\left(\\int_{|y|<\\sqrt{R_2}}\\Phi(x-y,t)\\,d\\mu(y)\\right)^\\beta dx\\\\\n&\\le \\int_{\\R^n}\\left(\\int_{|y|<\\sqrt{R_2}}1^{\\beta'}\\,d\\mu(y)\\right)^{\\beta/\\beta'}\n\\int_{|y|<\\sqrt{R_2}}\\Phi(x-y,t)^\\beta\\,d\\mu(y)\\,dx\\\\\n&=C\\int_{|y|<\\sqrt{R_2}}\\left(\\int_{\\R^n}\\Phi(x-y,t)^\\beta\\,dx\\right)\\,d\\mu(y)\\\\\n&=C\\int_{|y|<\\sqrt{R_2}}t^{-n\\beta/2}\\int_{\\R^n}e^{-\\frac{\\beta|x-y|^2}{4t}}dx\\,d\\mu(y)\\\\\n&=Ct^{n(1-\\beta)/2}\\quad\\text{by Lemma \\ref{lem2.2}}\\end{aligned}$$ which implies .", "\n\n\\[remA\\] If $u$ is a $C^{2,1}$ nonnegative solution of where $R_3>0$ then by Theorem \\[thmA\\], $$u^\\beta \\in L^1(B_{\\sqrt{R}}(0) \\times (0,R))\\quad\\text{for }\n1\\le\\beta <\\frac{n+2}{n}\\text{ and }0<R<R_3.$$ Thus the conclusion in Theorem \\[thmA\\] can be replaced with $$u^\\beta \\in L^1(B_{\\sqrt{R_2}}(0) \\times (0,R_2))\\quad\\text{for }\n1\\le\\beta <\\frac{n+2}{n}.$$\n\n\\[thmA\\] Suppose $u$ is a $C^{2,1}$ nonnegative solution of $$\\label{A.1}\n Hu\\ge 0\\quad \\text{in } B_{\\sqrt{4R}}(0)\\times (0,4R) \n\\subset \\R^n \\times \\R,\\ n\\ge 1,$$ where $Hu = u_t-\\Delta u$ is the heat operator and $R$ is a positive constant. ", "Then $$\\label{A.2}\n u^\\beta,Hu \\in L^1(B_{\\sqrt{2R}}(0) \\times (0,2R))\\quad\\text{for }\n1\\le\\beta <\\frac{n+2}{n}$$ and there exist a finite positive Borel measure $\\mu$ on $B_{\\sqrt{2R}}(0)$ and a bounded function\\\n$h\\in C^{2,1}(B_{\\sqrt{R}}(0) \\times (-R,R))$ satisfying $$\\begin{aligned}\n{2}\n \\label{A.3}\nHh &= 0 \\quad \\text{in } &B_{\\sqrt{R}}(0)\\times (-R,R)\\\\\n\\label{A.4}\n h &= 0 \\quad \\text{in } &B_{\\sqrt{R}}(0)\\times (-R,0] \\end{aligned}$$ such that $$\\label{A.5}\n u = N +v+h\\quad \\text{in } B_{\\sqrt{R}}(0)\\times (0,R)$$ where $$\\begin{aligned}\n\\label{A.6}\n N(x,t) &:= \\int^{2R}_0 \\int_{|y|<\\sqrt{2R}} \\Phi(x-y,t-s) Hu(y,s)\\,dy\\,ds,\\\\\n\\label{A.7}\nv(x,t) &:= \\int_{|y|<\\sqrt{2R}} \\Phi(x-y,t)\\,d\\mu(y),\\end{aligned}$$ and $\\Phi$ is the heat kernel .", "\n\nWhen $R=1$ and $\\beta=1$, Theorem \\[thmA\\] was proved in [@T2011]. ", "The proof of Theorem \\[thmA\\] for $R>0$ and $\\beta=1$ is obtained by scaling the $R=1$ case. ", "It remains only to prove for $1<\\beta<(n+2)/n$. To do this, it suffices by to show $$\\label{A.8}\nN^\\beta\\in L^1(\\R^n\\times(0,2R))\\quad\\text{for }1<\\beta<(n+2)/n$$ and $$\\label{A.9}\nv^\\beta\\in L^1(\\R^n\\times(0,2R))\\quad\\text{for }1<\\beta<(n+2)/n.$$ Since $Hu\\in L^1(B_{\\sqrt{2R}}(0)\\times(0,2R))$ we see that follows from heat potential estimates. (", "See [@GT2016 Theorem B.8].)", "\n\nFinally, for $t>0$, $\\beta>1$, and $\\beta'$ the conjugate Hölder exponent of $\\beta$ we have $$\\begin{aligned}\n\\int_{\\R^n}v(x,t)^\\beta\\,dx\n&=\\int_{\\R^n}\\left(\\int_{|y|<\\sqrt{2R}}\\Phi(x-y,t)\\,d\\mu(y)\\right)^\\beta dx\\\\\n&\\le \\int_{\\R^n}\\left(\\int_{|y|<\\sqrt{2R}}1^{\\beta'}\\,d\\mu(y)\\right)^{\\beta/\\beta'}\n\\int_{|y|<\\sqrt{2R}}\\Phi(x-y,t)^\\beta\\,d\\mu(y)\\,dx\\\\\n&=C\\int_{|y|<\\sqrt{2R}}\\left(\\int_{\\R^n}\\Phi(x-y,t)^\\beta\\,dx\\right)\\,d\\mu(y)\\\\\n&=C\\int_{|y|<\\sqrt{2R}}t^{-n\\beta/2}\\int_{\\R^n}e^{-\\frac{\\beta|x-y|^2}{4t}}dx\\,d\\mu(y)\\\\\n&=Ct^{n(1-\\beta)/2}\\quad\\text{by Lemma \\ref{lem2.2}}\\end{aligned}$$ which implies .", "\n\nHeat potential estimates {#secB}\n========================\n\nIn this appendix we provide estimates for the heat potentials $$(J_\\alpha f)(x,t)=\\iint_{\\R^n\\times\\R}\\Phi(x-y,t-s)^{\\frac{n+2-\\alpha}{n}}f(y,s)\\,dy\\,ds$$ and $$(V_\\alpha f)(x,t)=\\iint_{\\Omega}\n \\Phi(x-y,t-s)^{\\frac{n+2-\\alpha}{n}}f(y,s)\\,dy\\,ds,$$ where $\\Phi$ is given by , $\\Omega=\\R^n\\times (a,b)$, and $\\alpha\\in(0,n+2)$. The proofs of these estimates are given in [@GT2016 Appendix B].", "\n\n\\[thmB.1\\] Suppose $0<\\alpha<n+2$ and $1<p<\\frac{n+2}{\\alpha}$ are constants and $f:\\R^n \\times\\R\\to\\R$ is a nonnegative measurable function. ", "Let $$q=\\frac{(n+2)p}{n+2-\\alpha p}.$$ Then $$\\| J_\\alpha f\\|_{L^q (\\R^n \\times\\R)}\\leq C\\| f\\|_{L^p (\\R^n\n \\times\\R)}$$ where $C=C(n,p,\\alpha)$ is a positive constant.", "\n\n\\[thmB.2\\] Let $p,q\\in[1,\\infty]$, $\\alpha$, and $\\delta$ satisfy $$\\label{B.1}\n0\\le \\delta =\\frac{1}{p}-\\frac{1}{q}<\\frac{\\alpha}{n+2}<1.$$ Then $V_\\alpha$ maps $L^p(\\Omega)$ continuously into $L^q(\\Omega)$ and for $f\\in L^p(\\Omega)$ we have $$\\|V_\\alpha f\\|_{L^q(\\Omega)} \\le M\\|f\\|_{L^p(\\Omega)},$$ where $$M=C(b-a)^{(\\alpha-(n+2)\\delta)/2}\\quad\\text{for some constant }\nC=C(n,\\alpha,\\delta)>0.$$\n\nTheorem \\[thmB.2\\] is weaker than Theorem \\[thmB.1\\] in that the second inequality in cannot be replaced with equality. ", "However it is stronger in that the cases $p=1$ and $q=\\infty$ are allowed.", "\n\n[10]{} H. Chen and F. Zhou, Classification of isolated singularities of positive solutions for Choquard equations, arXiv:1512.03181 \\[math.", "AP\\].", "\n\nJ. T. Devreese and A. S. Alexandrov, Advances in polaron physics, Springer Series in Solid-State Sciences, vol. ", "159, Springer, 2010.", "\n\nM. Ghergu and S. D. Taliaferro, *Isolated Singularities in Partial Differential Inequalities*, Cambridge University Press, 2016.", "\n\nM. Ghergu and S. D. Taliaferro, Pointwise bounds and blow-up for Choquard-Pekar inequalities at an isolated singularity, *J. Differential Equations* **261** (2016), 189–217.", "\n\nK.R.W. Jones, Newtonian quantum gravity, *Australian Journal of Physics* **48** (1995), 1055–1081.", "\n\nE. H. Lieb, Existence and uniqueness of the minimizing solution of Choquard’s nonlinear equation, Studies in Appl. ", "Math. ", "57 (1976/77), 93–105.", "\n\nP.-L. Lions, The Choquard equation and related questions, *Nonlinear Anal.* **", "4** (1980), 1063–1072.", "\n\nP.-L. Lions, The concentration-compactness principle in the calculus of variations. ", "The locally compact case. ", "I, *Ann. ", "Inst. ", "H. Poincaré Anal. ", "Non Linéaire* **1** (1984), 109–145.", "\n\nC. Ma, W. Chen, and C. Li, Regularity of solutions for an integral system of Wolff type, *Adv. ", "Math.* **", "226** (2011), 2676–2699.", "\n\nL. Ma and L. Zhao, Classification of positive solitary solutions of the nonlinear Choquard equation, *Arch. ", "Ration. ", "Mech. ", "Anal.* **", "195** (2010), 455–467.", "\n\nM. Melgaard and F. Zongo, Multiple solutions of the quasirelativistic Choquard equation, *J. Math. ", "Phys.* **", "53** (2012), 033709.", "\n\nI. M. Moroz, R. Penrose and P. Tod, Spherically-symmetric solutions of the Schrödinger-Newton equations, *Classical Quantum Gravity* **15** (1998), 2733–2742.", "\n\nV. Moroz and J. Van Schaftingen, Groundstates of nonlinear Choquard equations: Existence, qualitative properties and decay asymptotics, *J. Funct. ", "Anal.* **", "265** (2013), 153–184.", "\n\nV. Moroz and J. Van Schaftingen, Nonexistence and optimal decay of supersolutions to Choquard equations in exterior domains, *J. Differential Equations* **254** (2013), 3089–3145.", "\n\nV. Moroz and J. Van Schaftingen, Semi-classical states for the Choquard equation, *Calc. ", "Var. ", "Partial Differential Equations* **52** (2015), 199–235.", "\n\nS. Pekar, Untersuchung über die Elektronentheorie der Kristalle, Akademie Verlag, Berlin, 1954.", "\n\nP. Quittner and P. Souplet, Superlinear parabolic problems, blow-up, global existence and steady states, Birkhauser, Basel, 2007.", "\n\nS. G. Samko, Hypersingular Integrals and Their Applications, Taylor and Francis, London, 2002.", "\n\nS. D. Taliaferro, Initial blow-up of solutions of semilinear parabolic inequalities, *J. Differential Equations* **250** (2011), 892–928.", "\n\nJ. Wei and M. Winter, Strongly interacting bumps for the Schrödinger-Newton equations, *J. Math. ", "Phys.* **", "50** (2009), 012905.", "\n\nR. Zhuo, W. Chen, X. Cui, and Z. Yuan, Symmetry and non-existence of solutions for a nonlinear system involving the fractional Laplacian, *Discrete Contin. ", "Dyn. ", "Syst.* **", "36** (2016), 1125–1141.", "\n" ]

{ "pile_set_name": "ArXiv" }

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[ "Value of palliative resection in gastric cancer.", "\nWestern patients with gastric cancer often present with incurable disease. ", "The role of palliative surgical resection is still debatable. ", "Non-curatively treated patients from the Dutch Gastric Cancer Trial were studied to define more accurately which patients might benefit from palliative resection. ", "In the Dutch Gastric Cancer Trial 285 (26 per cent) of the randomized patients were found to have incurable tumours at laparotomy. ", "Four signs of incurability were noted: irresectable tumour (T+), hepatic metastasis (H+), peritoneal metastasis (P+) and distant lymph node metastasis (N4+). ", "Patients had either an explorative laparotomy, a gastroenterostomy, or a resection (partial or total). ", "In the analysis, particular attention was paid to the prognostic factors of age, number of metastatic features, and a combination of these. ", "Overall survival time was greater if a resection was performed (8.1 versus 5.4 months; P < 0.001). ", "For patients aged over 70 years there was still a survival advantage of about 3 months if resection was carried out. ", "Morbidity and perioperative mortality rates in this older age group were, however, high (50 and 20 per cent respectively). ", "For patients with one metastatic site a resection was of significant benefit (survival 10.5 versus 6.7 months; P = 0.034). ", "For patients with two or more metastatic sites resection had no significant survival advantage (5.7 versus 4.6 months; P = 0.084). ", "Combination of these factors indicates that patients aged less than 70 years with one metastatic site will benefit significantly from a palliative resection, in contrast to other combinations of factors. ", "Age as well as the number of metastatic sites should be taken into account when a palliative resection is considered. ", "Palliative resection may be beneficial for patients under 70 years of age if the tumour load is restricted to one metastatic site." ]

{ "pile_set_name": "PubMed Abstracts" }

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[ "Since the advent of insulative spools or bobbins, many transformer windings which were previously layer wound are now bobbin wound. ", "It is well known in the art that bobbin winding, which can be completely automated, is inherently faster and more economical than layer winding. ", "However, some windings, such as those consisting of a very large number of turns, have heretofore continued to be layer wound because it is impractical to wind all the wire on a single bobbin. ", "For example, such a single bobbin winding would require a relatively narrow winding space in order to withstand the voltages between layers of turns and especially the high transient voltages produced at the instants when the winding is energized and de-energized. ", "Such a narrow winding space would consequently require a large number of layers which would result in winding size which would be unacceptable when used in devices in which the overall size of the device is somewhat standard in the industry. ", "Furthermore, such a single bobbin winding would not overcome another disadvantage of a layer wound coil having a very large number of turns, namely the scrap loss incurred when the wire breaks while winding, such breakage being a fairly common occurrence with the high speed winding machines presently used." ]

{ "pile_set_name": "USPTO Backgrounds" }

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[ "Phenobarbital-induced alterations of bile acid metabolism in cases of intrahepatic cholestasis.", "\nBile acid profiles from plasma and urine of six patients suffering from intrahepatic cholestasis were studied before and during treatment with phenobarbital. ", "All patients responded to this treatment by decreasing their plasma bile acid levels. ", "Using gas chromatographic and mass spectrometric methods for separation and identification of the bile acids, especially the occurrence of major atypical bile acids was quantitatively evaluated. ", "The plasma bile acid lowering effect of phenobarbital in intrahepatic cholestasis can be partly explained by an increased formation of tetrahydroxylated bile acids, which are rapidly excreted by renal pathways. ", "These tetrahydroxylated bile acids, present as nonsulfated compounds, have high renal excretory flow rates exceeding those of bile acid sulfates. ", "Their enterohepatic circulation, however, seems to be low, since only small amounts of tetrahydroxylated bile acids can be found in bile. ", "It is mainly the 1- and 6-hydroxylation that is stimulated by phenobarbital. ", "The exact site of formation of tetrahydroxylated bile acids, however, is still unknown. ", "These findings may provide a rationale for the institution of a phenobarbital treatment in cases of intrahepatic cholestasis." ]

{ "pile_set_name": "PubMed Abstracts" }

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[ "Cruz, then eight months pregnant and with two of the couple's other children in tow, began to worry when Chally Dang took longer than usual to emerge from what should have been a routine check-in with immigration officials.", "\n\n\"I sat there for about an hour because I didn't know what to do,\" Cruz said. \"", "Then he collect-called me to say they weren't letting him go.\"", "\n\nFor the next nine months, U.S. Immigration and Customs Enforcement (ICE) officials held Dang and three other Cambodian-Americans -- all legal permanent residents who had come to the United States as child refugees.", "\n\nIn June, they sent Dang to Cambodia. ", "Each of the men detained last September had committed a crime that carried a retroactive removal order. ", "That allows them to be deported at any time, regardless of when the crime was committed.", "\n\nDang, now 29, was arrested when he was 15, after he fired an illegal handgun into the air. ", "Although no one was injured, Dang was charged in 1997 with aggravated assault, criminal conspiracy and possessing criminal instruments.", "\n\nHe was sentenced to 5½ years in prison. ", "Despite having served his prison time, under 1996 immigration laws, he could be deported back to Cambodia -- a country he had never seen -- without a hearing in front of an immigration judge.", "\n\nDang's situation is not uncommon, and it is becoming part of the growing debate over immigration reform in the United States.", "\n\nIn a move that could shake up the U.S. immigration system, the Department of Homeland Security said the government would review about 300,000 deportation cases pending in federal immigration courts.", "Lower-priority cases -- those not involving people considered violent or otherwise dangerous -- would be suspended under the new criteria.", "\n\nFederal authorities are still hashing out details of how the cases will be reviewed, a senior Department of Homeland Security official said last week.", "\n\nFor Cruz and Dang, the announcement comes too late for them to tell their story.", "\n\nAna Marie Cruz's fiance, a legal resident and father of her children, was deported for a crime he committed 14 years ago.", "\n\nCruz maintains that her fiance -- now a world away in Cambodia -- had turned his life around after serving his time in prison and deserved to stay in the United States.\"", "\n\nThey should give Americans, refugees and permanent residents who have reformed (themselves) chances to prove that they are of good character, regardless of any mistakes that they have made in their past,\" she said. \"", "Just because someone made one mistake, especially in their youth, doesn't label them a criminal for life. ", "People change, and people learn.\"", "\n\nOne of five children, Dang was born in Kamput refugee camp in Thailand, after his parents escaped the \"killing fields\" in the Southeast Asian nation of Cambodia, where at least 1.7 million people died under the 1970s Khmer Rouge regime.", "\n\nShortly after Dang was born, his father separated from his mother while awaiting sponsorship. ", "His family entered the United States in 1983 and settled in crime-ridden North Philadelphia, where his mother remarried and gave birth to her youngest son.", "\n\nThe cash-strapped family moved from apartment to apartment, and a strained home life left him finding solace among other refugee kids in the neighborhood.\"", "\n\nTruancy became regular, and schoolwork was out of the question,\" Dang wrote in a letter on December 4, 2010, while he was being detained in York County Prison. \"", "That's when the downhill became even steeper.\"", "\n\nHe was expelled multiple times from school for his disruptive behavior and eventually joined an Asian gang.", "\n\nDang hit rock bottom in 1997 when a rival gang spotted him and a friend in North Philadelphia. ", "According to Dang, the rivals threw bottles and rocks at the car he was in, and his friend handed him a gun.\"", "\n\nI recklessly fired a few rounds in their proximity,\" he wrote.", "\n\nDang spent his high school years behind bars, where he obtained his GED. ", "When he was paroled in 2003, Dang, then 21, was taken into ICE custody and given a final order of deportation.", "\n\nBut Cambodia was not accepting deportees from the U.S., so he was allowed to stay here under ICE supervision. ", "After six months, he was granted supervised release.", "\n\n\"Regret is one of many effusive links composing a chain that binds me to my past,\" he wrote. \"", "The actions of my past still haunt me.\"", "\n\nVowing never to repeat the mistakes of his past, Dang started a family, earned a living working for a vending company, committed no crimes after his release and regularly checked in with immigration officials.", "\n\n\"It's hard for me because we built a life together, and I feel like it was ripped apart,\" Cruz said. \"", "It's a life-changing thing.\"", "\n\nCruz, 28, gave birth to the couple's daughter, Farrah, a month after Dang was detained.", "\n\nAgency officials say immigrants who commit these crimes must be removed even if, like Dang, they have a green card.", "\n\nDang's freedom lasted seven years.", "\n\nMia-lia Kiernan, who helped launch a Philadelphia grass-roots organization dedicated to keeping immigrant families living together, is at odds with the DHS immigration announcement.", "\n\nKiernan and family members of the detained and deported started the One Love Movement to help them fight for individualized reviews of their deportation orders -- including that of Dang.", "\n\nThe very government that gave Dang shelter targeted him and other refugees with criminal histories, Kiernan said.", "\n\n\"People really need to think about the title 'criminal alien' and who gets left behind,\" she said. \"", "We're creating a generation of young people forced to grow up without parents.\"", "\n\nBy law, deportation is mandatory for anyone not a U.S. citizen who commits an \"aggravated felony,\" a broad category of crimes ranging from shoplifting to murder that carry sentences of at least one year of imprisonment, said Sin Yen Ling, a senior staff attorney at the Asian Law Caucus in San Francisco.", "\n\nHalf of the individuals removed from the United States -- more than 195,000 people -- were convicted criminals, a 70% increase, according to ICE.", "\n\n\"Everybody in their right mind would think that criminal aliens should be removed,\" said Ira Mehlman, spokesman for the Federation for American Immigration Reform.", "\n\n\"No, it's not harsh. ", "Coming as an immigrant is a privilege, and we expect that you stay out of trouble.\"", "\n\nPhiladelphia immigration attorney Caitlin Barry says the broad definition of \"aggravated felony\" and the retroactive application of the law have created a constant stream of criminal deportation cases.", "\n\nAlthough Dang was released under ICE supervision, a removal order remained in effect. ", "He was allowed to re-enter the community and make a life for himself because at the time, Cambodia was not issuing visas to deportees from the United States, Barry said.", "\n\n\"Unfortunately, as soon as those visas to Cambodia became available, Chally was rounded up with the other guys and sent to Cambodia,\" Barry said. \"", "Chally's case is the perfect illustration of how severe these laws have gotten.\"", "\n\nBecause of Dang's deportation, Cruz has found herself a single mother of four, struggling to make ends meet while working as a receptionist at a Philadelphia law firm.", "\n\nShe has sold household items and the family vehicle to pay the bills. ", "She has also applied for welfare and other government assistance to feed her children.", "\n\n\"What I've experienced, I wouldn't want any other family to have to go through,\" said Cruz, a permanent resident who came to the United States as an infant from the Philippines. \"", "I want that law to be taken and thrown in the garbage because it does nothing, it doesn't make anything better.\"", "\n\nThe deportations are a disservice to those who have come out of the system and changed their lives, said Kiernan, the One Love Movement co-founder.", "\n\n\"I don't believe that refugees should be subject to deportation, period. ", "That's not their home anymore. ", "They came here, this is their home,\" Kiernan said.", "\n\n\"Everyday families are being broken apart, and every day, there are children suffering without a parent.\"", "\n\nWhile Cruz tidied up her home after hosting a One Love meeting on a recent Saturday, she paused and looked at her children coloring quietly in their sparse living room." ]

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[ "33% of Consumers Want to Buy Greener Electronics\n\nDecember 11th, 2008 by Jerry James Stone\n\n[social_buttons]\n\nAccording to Environmental Leader, via the Consumer Electronics Association (CEA), thirty-three percent of consumers plan to buy greener gadgets over the next two years. ", "The report is based on an online survey of over 900 adults. ", "I wonder if any of them are mayors?", "\n\nThe report shows that women are out-greening men, and that being eco-friendly is as important as cost. ", "The report also finds that 89 percent of people want their next TV to be more energy efficient.", "\n\nOne interesting find is that consumers desire an easier way to determine if products are certifiably green. ", "Well, if you’re not finding the green gadget you want, create your own: Green Gadget Design Contest Offers $3K Grand Prize.", "\n\nAwareness\n\n+ Familiarity with established terms is high: recyclable is 86%, but carbon footprint 33%.", "\n\n+ Awareness of green logos follows a similar pattern. ", "82% percent of online adults recognize the Energy Star logo.", "\n\n+ Consumers are most familiar with the household products category, the food category, and the vehicle category.", "\n\n+ Awareness of appliances with green attributes tops awareness of computers with similar attributes (50% vs. 17%).", "\n\nGreen Behaviors\n\n+ Does heightened green awareness translate to a higher level of engagement in green behaviors? ", "In some cases yes.", "\n\n+ For example, 87% of consumers say they turn room lights off when not in use, while 62% say they recycle household trash.", "\n\n+ Women tend to be more green than men.", "\n\n+ For a basket of CE products (TVs, computers, phones, VCRs), consumers report a 26% increase in recycling.", "\n\n+ The teenage segment of the population exhibits very few green behaviors.", "\n\n+ Fifty-five percent of consumers consider themselves to be environmentally conscious.", "\n\n+ 74% believe companies should do more, but only 53% think their personal actions have a impact.", "\n\n+ Over half of consumers plan to engage in more environmentally friendly behaviors over the next 12 months.", "\n\n+ When asked why go green: ‘it’s the right thing to do,’(69%) followed by ‘saving money.", "’(63%)\n\n+ Those that haven’t or won’t engage in green behaviors cite cost.", "\n\nGreen Confusion and Suspicions\n\n+ Suspicions and confusion of green claims do exist. .", "\n\n+ Sixty-five percent of consumers think some companies are greenwashing.", "\n\n+ The data suggests males are more suspicious.", "\n\nGreen as a Product Attribute\n\n+ Cars top the list of products for greening. ", "Seventy-three percent feel it is important for cars to have environmentally friendly attributes.", "\n\n+ 57% of consumers indicated that the environmentally friendly attributes of a product will be important to their next purchase decision.", "\n\nGreen CE Defined\n\n+ Top five green attributes: recyclable packaging (68%), recyclable product (64%), energy efficient product (62%), packaging made with recycled materials (57%) and biodegradable packaging (53%).", "\n\nGreen Positioning\n\n+ Consumers want an easy way to determine if and why a product is green.", "\n\n+ Logos and descriptions are cited as desired vehicles for establishing green credentials.", "\n\nFuture Outlook\n\n+ About one-third of consumers expect to make some type of green CE purchase over the next 12 months.", "\n\nSource: Environmental Leader | Photo: © Valeriy Evlakhov | Dreamstime.com\n\n\n\n\n\n\n\n\n\nAppreciate CleanTechnica’s originality? ", "Consider becoming a CleanTechnica member, supporter, or ambassador — or a patron on Patreon.", "\n\nSign up for our free daily newsletter or weekly newsletter to never miss a story.", "\n\nHave a tip for CleanTechnica, want to advertise, or want to suggest a guest for our CleanTech Talk podcast? ", "Contact us here.", "\n\nLatest Cleantech Talk Episode" ]

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[ "Q:\n\nmysql fulltext - exact match or nothing\n\nI have mysql table with column tags, and would like to search exact match.", "\nFor this data:\n proj7 invoice delivery\n proj7 exchange\n\nand this query\n MATCH(tags) AGAINST ('+proj7 +(invoice report)')\n\nshould be\n (proj7 AND (invoice OR report))\n\nSo i want only first record in result, but there are both, second with low score due to proj7 existence. ", "How can i query exact matches only.", "\nsqlfiddle http://sqlfiddle.com/#!9/26524/3\n\nA:\n\nPROPOSED QUERY\nSELECT * FROM test WHERE MATCH(tags)\nAGAINST ('\"+proj_7\" \"(invoice report)\"' IN BOOLEAN MODE);\n\nYOUR SAMPLE DATA LOADED\nmysql> USE test\nDatabase changed\nmysql> DROP TABLE IF EXISTS test;\nQuery OK, 0 rows affected, 1 warning (0.00 sec)\n\nmysql> CREATE TABLE `test` (\n -> `tags` text NOT NULL,\n -> FULLTEXT KEY `tags` (`tags`)\n -> );\nQuery OK, 0 rows affected (0.20 sec)\n\nmysql> INSERT INTO test (tags) VALUES (\"proj_7 type_invdtl year_15 month_04\");\nQuery OK, 1 row affected (0.00 sec)\n\nmysql> INSERT INTO test (tags) VALUES (\"proj_8 type_invdtl year_15 month_04\");\nQuery OK, 1 row affected (0.00 sec)\n\nmysql> INSERT INTO test (tags) VALUES (\"proj_10 type_invdtl year_15 month_04\");\nQuery OK, 1 row affected (0.02 sec)\n\nmysql> SELECT * FROM test;\n+--------------------------------------+\n| tags |\n+--------------------------------------+\n| proj_7 type_invdtl year_15 month_04 |\n| proj_8 type_invdtl year_15 month_04 |\n| proj_10 type_invdtl year_15 month_04 |\n+--------------------------------------+\n3 rows in set (0.00 sec)\n\nmysql>\n\nPROPOSED QUERY EXECUTED\nmysql> SELECT * FROM test WHERE MATCH(tags)\n -> AGAINST ('\"+proj_7\" \"(invoice report)\"' IN BOOLEAN MODE);\n+-------------------------------------+\n| tags |\n+-------------------------------------+\n| proj_7 type_invdtl year_15 month_04 |\n+-------------------------------------+\n1 row in set (0.00 sec)\n\nmysql>\n\nOTHER EXAMPLES\nmysql> SELECT * FROM test WHERE MATCH(tags)\n -> AGAINST ('\"+proj_7\" \"(type_invdtl year_15)\"' IN BOOLEAN MODE);\n+--------------------------------------+\n| tags |\n+--------------------------------------+\n| proj_7 type_invdtl year_15 month_04 |\n| proj_8 type_invdtl year_15 month_04 |\n| proj_10 type_invdtl year_15 month_04 |\n+--------------------------------------+\n3 rows in set (0.00 sec)\n\nmysql> SELECT * FROM test WHERE MATCH(tags)\n -> AGAINST ('\"+proj_7\" \"(type_invdt2 year_15)\"' IN BOOLEAN MODE);\n+-------------------------------------+\n| tags |\n+-------------------------------------+\n| proj_7 type_invdtl year_15 month_04 |\n+-------------------------------------+\n1 row in set (0.00 sec)\n\nmysql> SELECT * FROM test WHERE MATCH(tags) AGAINST ('\"+proj_7 +type_invdtl\" \"+proj_7 +year15\"' IN BOOLEAN MODE);\n+-------------------------------------+\n| tags |\n+-------------------------------------+\n| proj_7 type_invdtl year_15 month_04 |\n+-------------------------------------+\n1 row in set (0.00 sec)\n\nmysql> SELECT * FROM test WHERE MATCH(tags) AGAINST ('\"+proj_7 +type_invdtl\" \"+proj_7 +year16\"' IN BOOLEAN MODE);\n+-------------------------------------+\n| tags |\n+-------------------------------------+\n| proj_7 type_invdtl year_15 month_04 |\n+-------------------------------------+\n1 row in set (0.00 sec)\n\nmysql> SELECT * FROM test WHERE MATCH(tags) AGAINST ('\"+proj_7 +type_invdt2\" \"+proj_7 +year16\"' IN BOOLEAN MODE);\nEmpty set (0.00 sec)\n\nmysql>\n\nGIVE IT A TRY !!!", "\n\n" ]

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[ "I just changed both of these deals to CAISO energy, instead of Firm. ", "I \nnoticed that the one you asked about, #481620, was part of an EES sleeve, so \nI checked the other side of it, deal #481621, and sure enough it also had the \nincorrect energy type. ", "It's holiday fever!", "\n\nThanks,\nKate" ]

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[ "I'm the environment editor at Forbes. ", "Before joining Forbes in April 2011, I wrote about all things green and tech as a contributor to The New York Times, a senior editor at Fortune and an assistant managing editor at Business 2.0 magazine. ", "I previously was the business editor at the San Jose Mercury News and during the (first) dot-com era served as a senior writer and senior editor at The Industry Standard (RIP).", "\n\nElectric Car Sales Hit Another Record\n\nElectric car sales reached a record in November for the fourth consecutive month as new models like the Ford C-Max Energi plug-in electric hybrid helped juice buyer interest.", "\n\nAccording to analyst Aaron Chew of the Maxim Group, dealers sold 7,600 electric cars in November, bringing total sales for 2012 to 47,500 to date. ", "Chew expects the year to end with sales of 56,000 electric and plug-in hybrid electric vehicles.", "\n\nThat of course is but a rounding error for most carmakers. ", "Ford, for instance, sold 177,673 cars in November alone and electric vehicle sales are just .4% of total U.S. automotive sales for the year to date.", "\n\nAnd while the slow but steady trend in electric car sales depends in part on various incentives – Nissan Leaf sales jumped after the automaker offered $199 leases and $5,000 price breaks – the introduction of new models has helped boost sales.", "\n\nFord sold 1,259 of its C-Max Energi in November just a month after the plug-in electric hybrid was introduced. ", "That came close to the Chevrolet Volt, which recorded sales of 1,519 for the month and was not far behind the Toyota Prius plug-in, which had sales of 1,766 in November, according to Maxim.", "\n\nChew also offered some Tesla tidbits, reporting that the Silicon Valley electric carmaker delivered an estimated 1,150 of its Model S sports sedans in November.", "\n\n“Despite just launching in late June 2012, this would propel TSLA to No. ", "5 in U.S. EV deliveries in November 2012,” Chew wrote.", "\n\nPost Your Comment\n\nPost Your Reply\n\nForbes writers have the ability to call out member comments they find particularly interesting. ", "Called-out comments are highlighted across the Forbes network. ", "You'll be notified if your comment is called out.", "\n\nBut they are much cleaner when you consider how much electricity it takes to refine gas. ", "You can drive 20 miles in an electric car with the amount of electricity it takes to make one gallon of gas. ", "And, electricity can come from renewable energy sources. ", "Buy American! (", "energy)\n\nI think this makes a lot of sense. ", "The electric cars out there right now are good products, and as we’ve seen the prices start to edge down the sales are going up. ", "I personally think electric cars over time will be the car of the future. ", "In general they are better products, they have less moving parts, require less maintenance, cost less to drive, and are much cleaner(That’s because most places aren’t 100 percent coal powered, for those that would say, BUT they’re powered by coal.) ", "I think if you look at the price continue to drop, and the range get longer the question becomes when will the public start buying in, in a major way?", "\n\nThis is the question of course. ", "The transition will take a decided turn for big numbers somewhere between 2013-2015. ", "It depends a lot on gas, whether the oil companies pull another refinery shut down, or we get that sought after carbon tax. ", "Just today on KCRW’s “To the Point” they discussed the carbon tax in a way I’ve never heard. ", "While still tough to pull off, like gay marriage, it’s inevitable.", "\n\nThe society that transitions fastest to renewable electricity for running most of its transportation will succeed, those that wait till the end will suffer. ", "The economics are clear. ", "Oil will only get more expensive, and no matter what they found in N. Dakota, it’ll eventually run out. ", "Renewable electricity, on the other hand, will only get cheaper.", "\n\nI bought a solar PV system in 2002, then I bought my first EV. ", "For the past ten years, I’ve run my house and car on sunlight with an electric bill of about $100/year. ", "I haven’t been to a gas station since 2002 but I’ve driven 121,000 miles – on sunlight.", "\n\nThe solar system paid for itself after 8 years. ", "For the rest of my life, I get free energy from the sun to run my home and car.", "\n\nYou can do this, too.", "\n\nThere are over ten plugin cars on the market with more coming every few months. ", "SUVs, trucks, commuter cars, and long distance cars like Tesla’s Model S, the “best car in the world”. ", "As a matter of fact, the Tesla Model S is the best car in history.", "\n\nWe’ll all go electric over time, it’s just so much better than internal combustion in every way. ", "The sooner you do it, the happier you’ll be.", "\n\nI wonder how many of these electric cars were sold to the Federal, State and Local governments? ", "Also how many were sold to GE? ", "If Tesla sold 1,150 model S in November how many new oders with deposits did they take in in November?", "\n\nProbably around 10 – 15%. ", "Unfortunately, not a higher percentage, a lot of money could have been saved in those budgets with these plug-ins but competing industry influence is the tail that wags the dog when it comes to actual decision making… Tesla is backed up with about 6 months of orders, they finally scaled up production to 400 per week…\n\nFor Tesla, reservations were reported as up 15% last quarter and 30% year-over-year. ", "According to folks reporting their reservation numbers on the TMC forums, that was about 54/day during November. ", "Since then, they have been gaining, thanks to the additional exposure they’ve received by more cars being in customer hands and receiving multiple car of the year awards.", "\n\nTo the best of my knowledge, none of their sales have been to federal, state or local governments, or to GE. ", "I doubt you’ll see any postal workers making their rounds in a Model S.\n\nNot at all. ", "Most everyone charges at home and doesn’t need public charging. ", "It’s nice when you get it, but having 80-100 miles of range each day is more than enough for most folks.", "\n\nThere are lots of fast chargers finally getting installed in CA. ", "We’ve got several thousand “Level 2″ charge stations (240 volt) that are being added to by the dozens every day. ", "Lots of jobs installing these things. ", "There will be a need for millions of charge stations over the next decades.", "\n\nInstead of shipping $800 billion each year to the oil companies, we’ll be giving about 20% of that to the utilities, and the rest we keep in our pockets. ", "We’ll spend this money mostly on local goods and service and generate lots of jobs n the process.", "\n\nI built an electric car by converting an MG Midget. ", "I use it as my daily commuter vehicle and put 4,000 miles on it last year. ", "I can get over 100 miles on a charge with it. ", "I’m glad to see sale picking up, but I’m still disapointed with the overall acceptance. ", "I think that there must be many people like me who have a small car they commute in. ", "The electric cars make sense when used like this. ", "If I need to go on a longer trip, I use the other vehicle my family normally uses. ", "I really like the idea that if I need to run to the store to buy a small item, it doesn’t cost me more in gas than the item costs itself.", "Converting a car to electric isn’t for everyone, but if you’d like to see some details about my car you can visit my site. ", "electricmgmidget.com\n\nThats huge news from Tesla. ", "To ship over 1,100 cars in a month is a huge acheivement both in logistics, manufacturing and marketing. ", "And brings in over $50M. The market is changing with real cars for real peope that happen to be electric." ]

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[ "Q:\n\nZoom In/Out on background image when resizing the browser page\n\nI am currently developing the footer of a web page in HTML / CSS. ", "This footer will contain a lot of elements (address, links, buttons, ...) and it must, therefore, be responsive. ", "Consequently, on a desktop version, we have all the footer's elements on a row and, then on mobile we have all the footer's elements on a column (as the following images show you);\nMy goal is to get the result below on a widescreen (desktop):\n\nAnd here is the result I want to achieve on a mobile screen:\n\nAs you can see, we must have a zoom effect when resizing the page of a browser or when we pass on a smartphone screen. ", "I have a lot of elements to insert in the footer so the image must be zoomed to integrate them all.", "\nHere is the code I have done so far.", "\n\n.footer {\n height: 639px;\n background: url(\"https://nsa40.casimages.com/img/2020/07/11/200711012945662645.png\");\n background-position: center center;\n background-repeat: no-repeat;\n background-size: cover;\n}\n<div class=\"footer\"></div>\n\nThe result is almost what I want but the problem is that the height of the footer does not change, and therefore I do not have enough space to put all my elements in the footer in the mobile version.", "\nThank you :)\n\nA:\n\nTry adding height: auto, padding-top, padding-bottom in a media query for phone. ", "You may have to experiment with the padding values a few times to make it look good. ", "Also change the background-position so the curve can be seen on mobile phones. ", "It will look something like this.", "\n@media (max-width: 991.98px){\n.footer{\n height: auto;\n padding: 50px 0;\n background-position: center top; \n }\n}\n\nA:\n\n@media screen and (min-width: 480px) { //480px is breakpoint you can adjust according to your need\n\n .footer {\n height: auto;\n background: url(\"https://nsa40.casimages.com/img/2020/07/11/200711012945662645.png\");\n background-position: center top; //adjust according to you need\n background-repeat: no-repeat;\n background-size: cover;\n padding-top: 3rem; //adjust according to your need\n padding-bottom:3rem; //adjust according to your need\n padding-left:inherit;\n padding-right:inherit;\n }\n}\n<div class=\"footer\"></div>\n\n" ]

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[ "Molly (Hawkins) Illum (’00): Missouri high school volleyball coach\n\nSeptember 10, 2011\n\nMolly (Hawkins ’00) Illum, wife of Evangel’s head football coach, Brenton Illum (’99), was recently named the head volleyball coach at Central High School in Springfield, Missouri.", "\n\n“Coaching girls to be better at something that I am incredibly passionate about is so fun,” Illum says. “", "I get the opportunity to encourage, train, teach work ethic and establish relationships based on the platform of being a volleyball coach.”", "\n\nAs the head volleyball coach and 9th through 12th grade physical education teacher, Illum has many opportunities to share the love of Christ through the way she lives her life. “", "Of course, I don’t live it perfectly, but I allow them to see His love shine through and, if the opportunity presents itself, talk to them about what that is,” Illum says.", "\n\nIllum believes her Evangel experience prepared her to be a successful teacher and coach, both in her classes and through relationships with her coaches and professors. “", "I learned from professors and coaches at Evangel how to work hard, be diligent, praise God through triumphs and tribulations, and above all else, have a passion for whatever it is I do,” she says.", "\n\nReflecting on her days as a Physical Education major at Evangel, Illum reveals that her most valuable opportunities were the relationships she built with faculty and staff. “", "That laid a foundation for me to realize that life is about creating and maintaining relationships and as a coach, I have a wonderful opportunity to accomplish that,” says Illum.", "\n\nThe Illums, despite their busy coaching schedules, enjoy spending time with family and friends in their free time and love working out together. ", "After 13 years of marriage, they are so thankful for their life together. “[", "Brenton] is an amazing coach and not only supports me in my coaching but helps me become a better coach all the time,” Molly says.", "\n\nGod has truly blessed Molly, granting her heart’s desire and allowing her to do the things she enjoys. ", "She leaves a message for prospective students:\n\n“Evangel is an amazing University to which I owe so much. ", "It helped create who I am as a teacher, but it also deepened my relationship with the Lord and allowed me to find my husband. ", "I love Evangel and all that it stands for, and I am truly indebted to this wonderful place.”", "\n\nAbout Evangel\n\nEvangel is an accredited, liberal arts university with more than 100 academic programs on the cutting edge of today's professional fields. ", "Our commitment to the integration of faith, learning and life attracts students from a wide variety of Christian denominational backgrounds who have a strong commitment to academics with a desire to combine their Christian faith with every aspect of their lives." ]

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[ "Lanyon, Iowa\n\nLanyon is an unincorporated community in Lost Grove Township in Webster County, Iowa, United States. ", "It is located 17 miles south of the county seat of Fort Dodge, 2.65 miles south and 1 mile west of Harcourt (on U.S. Highway 169), and 3.3 miles north and 4.5 miles west of Boxholm. ", "It consists of seven blocks, bounded on the north by 390th Street, and on the east by Lanyon Avenue. ", "It includes the Evangelical Covenant Church, founded in 1877 and located in Lanyon since 1909.", "\n\nIts elevation is 1,171 feet (357 m).", "\n\nHistory\nThe community was founded by Swedish emigrants, part of a migration from Knox County, Illinois in the 1860s.", "\n\nIt is located on the diagonal route of a former interurban railroad between Boone and Rockwell City, which was used by the Fort Dodge, Des Moines and Southern Railroad until the 1960s. ", "A station at Layton was opened in 1899 to serve a railway laid that year by the Marshalltown and Dakota Railroad Company to carry coal mined near Fraser northwest to connections at Gowrie. ", "A Lanyon Post Office was established in 1900, the Lanyon Mutual Telephone Company was established in 1903, and the Bank of Lanyon, Lanyon Well Company, and (until the early 1960s) Lanyon Consolidated School. ", "Lanyon is now within the Prairie Valley Community School District.", "\n\nNotable residents and natives\nGeorge E.Q. Johnson, United States Attorney for the U.S. District Court for the Northern District of Illinois who successfully prosecuted Al Capone for tax evasion\n Jon Lindgren, Mayor of Fargo, North Dakota from 1978 to 1994, the second longest–serving mayor of Fargo.", "\n\nReferences\n\nCategory:Unincorporated communities in Webster County, Iowa\nCategory:Unincorporated communities in Iowa\nCategory:Populated places established in the 1860s\nCategory:Swedish-American history\nCategory:Swedish-American culture in Iowa\nCategory:1860s establishments in Iowa" ]

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[ "James Rankine\n\nJames Rankine (1828 – 8 September 1897), often referred to as \"Captain Rankine\", was a farmer, businessman and politician in the early days of the Colony of South Australia.", "\n\nHistory\nRankine was born in Ayrshire, Scotland, the eldest son of sheep farmer William Rankine and his wife Jane, née Paterson. ", "He migrated with his parents to South Australia on the barque Fairfield in 1839 and settled at \"Glenbarr\", Strathalbyn, South Australia.", "\n\nAt the age of twenty years he was made manager of a property leased by his father and uncle, Dr. John Rankine, on Hindmarsh Island. ", "After a few years wheat farming at Mundowie, near Gladstone in South Australia's Mid-North, he settled on his own property \"Wyndgate\" on Hindmarsh Island, where he raised cattle and pigs.", "\n\nBusiness\nHe was for a time agent in South Australia for the Cornwall Fire and Marine and Eagle Life Insurance Companies, and was one of the founders of and for over twenty years Director of the National Bank of Australasia.", "\n\nPolitics\nHe was Chairman of the Alexandrina District Council for many years, and represented the electorate of Mount Barker in the House of Assembly from 1865 to 1868, and was elected to the Legislative Council in February 1881 and retired in April 1888.", "\n\nOther interests\nHe was an enthusiastic member of the volunteer militia, holding a commission as captain of the Military Rifle Company, then with the Milang and Strathalbyn Cavalry Corps. ", "He was a crack shot, and won a first prize in the annual small-bore competition in Melbourne in 1866. ", "He also acquitted himself well at the Wimbledon meeting of 1868.", "\n\nHis comments on public affairs were frequently published in the \"Letters to the Editor\" columns of the South Australian Register. ", "The (opposition newspaper) Advertiser, in its obituary, described Rankine as a respected farmer without mentioning his political career or other achievements.", "\n\nFamily\nHe married Isabel Agnes Beevor (ca.1836 – 19 January 1917) on 12 May 1869, lived at \"Wyndgate\" on Hindmarsh Island. ", "Their children were:\nMary Rankine (19 February 1871 – ) married Charles Downer of Kilkenny on 12 June 1901\ndaughter 1 January 1875\nJames Beevor Rankine (23 January 1877 – 6 October 1935) married Elinor Mabel ??", "\ndaughter 13 September 1878 at Mundowie near Gladstone\nson 30 July 1880 born at \"The Cottage\", Strathalbyn\n\nReferences \n\nCategory:Members of the South Australian Legislative Council\nCategory:Members of the South Australian House of Assembly\nCategory:1828 births\nCategory:1897 deaths\nCategory:19th-century Australian politicians" ]

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[ "Wolf: 76ers GM Sam Hinkie's patience could be wise call a year from now\n\n11:47 PM,\nJul. 6, 2013\n\nWritten by\n\nJason Wolf\nThe News Journal\n\nUnless and until the seemingly interminable postseason somehow finds a way to drag on through yet another flip of the calendar, NBA champions aren't crowned in July.", "\n\nPressing issues at this point may very well end up irrelevant, the greatest coup can transform into an albatross for years.", "\n\nAt about this time a year ago, a blockbuster, four-team, 12-player trade sent ripples through the NBA ocean as three All-Stars were swapped, setting up the Lakers and 76ers as potential title contenders and giving the Nuggets a puncher's chance in the loaded Western Conference. ..." ]

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[ "With just days left until the crucial vote on passing the Greek mid-term austerity package, the assured destruction rhetoric used by the Greek status quo has hit fever pitch. ", "Just to make sure the message is not lost on the broader population that Europe's banks will not admit defeat in a vote that could end the kleptocratic cartel's hegemony for ever, Greece's Deputy Prime Minister Theodoros Pangalos has blasted suggestions that it would be better for his country to abandon the euro and return to the drachma as an \"immense stupidity\". ", "He didn't stop there. ", "For dramatic impact, the Greek vice PM also said that the country would devolve into complete anarchy, with tanks roaming the streets, a population on the verge of civil war, with mass suicides, just for dramatic impact, should bankers not get their way. ", "More or less in line with the Hank Paulson script that is regurgitated every few years when the Ponzi system is on the verge of imploding yet again.", "\n\nFrom AFP:\n\n\"Those who say this are extremely stupid. ", "While they may be analysts, university professors or economists, saying that is an immense stupidity,\" Pangalos told daily Spanish newspaper El Mundo in an interview published Sunday.", "\n\n\n\nDebt-wracked Greece has been told by European peers that it cannot hope to continue receiving aid from a 110-billion-euro rescue package agreed with the EU and the IMF last year without biting budget reforms and privatisations.", "\n\n\n\nThe Greek parliament will vote on an austerity package this week but some economists have argued that Athens needs to restructure its debt and leave the euro to become economically competitive again.", "\n\n\n\n\"Returning to the drachma would mean that on the following day banks would be surrounded by terrified people trying to withdraw their money, the army would have to protect them with tanks because there would not be enough police,\" said Pangalos.", "\n\n\n\n\"There would be riots everywhere, shops would be empty, some people would throw themselves out the window ... And it would also be a disaster for the entire European economy.\"", "\n\nAnd since we continue to live in bizarro world, the inverse truth is that this is likely a far more accurate description of reality should the mid-term package be voted through in just a few day, although with the country on a general 2 day strike beginning Tuesday, everyone will be able to celebrate with the bankers right in front of the Athens parliament once again.", "\n\nAs for austerity, something tells us Pangalos will be the first casualty should Greece finally truly implement some \"leaner\" policy measures." ]

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[ "Q:\n\nNullable parameters during an update\n\nIm trying to update a table based on several update increments.", "\nMy document review table currently looks like this:\n| ID | Review Date | Provisional Review Date | Final Review Date | Provisional Review Timeframe (hours) | Final Review Timeframe (hours) |\n|----|---------------------|-------------------------|---------------------|--------------------------------------|--------------------------------|\n| 1 | 2018-03-12 00:00:00 | 2018-03-10 00:00:00 | 2018-03-11 00:00:00 | 24 | 48 |\n\nThe Stored Procedure (insertDocumentReview) looks like this:\nCREATE PROCEDURE [dbo].[insertDocumentReview]\n --parameters\n @id int,\n @ReviewDate datetime2 = null,\n @ProvisionalReviewDate datetime2 = null,\n @FinalReviewDate datetime2 = null,\nAS\nBEGIN\n\n UPDATE [DocumentReview] \n SET ReviewDate = @ReviewDate,\n ProvisionalReviewDate = @ProvisionalReviewDate,\n FinalReviewDate = @FinalReviewDate,\n --the following columns are calculated based on the values of the columns populated above\n [ProvisionalReviewTimeframe] = (DATEDIFF(SECOND, [ProvisionalReviewDate], [ReviewDate]) / 3600.0),\n [lReviewTimeframe] = (DATEDIFF(SECOND, [FinalReviewDate], [ReviewDate]) / 3600.0),\n WHERE [Id] = @id\n\nEND\n\nThe problem\nI then execute the stored procedure 4 times with varying parameters set to null like this:\n-- 1) Insert Final Review Date\nEXEC insertDocumentReview 1, NULL, NULL, '2018-03-14 10:19:10'\n\n-- 2) Insert Provisional Review Date\nEXEC insertDocumentReview 1, NULL, '2018-03-13 12:19:10', NULL\n\n-- 3) Insert Review Date\nEXEC insertDocumentReview 1, '2018-03-15 10:19', NULL, NULL\n\n-- 4) Insert all dates\nEXEC insertDocumentReview 1, '2018-03-15 10:19', '2018-03-13 12:19:10', '2018-03-14 10:19:10'\n\nAt executions 1 and 2 Provisional Review Timeframe and Final Review Timeframe should be null as they are set by the calculation\nAt execution 3 the reviewDate is introduced so Im expecting the Provisional Review Timeframe and Final Review Timeframe columns to be populated based off the calculation but they are not.", "\nAt execution 4 the calculations for Provisional Review Timeframe and Final Review Timeframe are calculated and I will see 24 and 48 respectively.", "\n\nI need to know why the calculation does not calculate at execution 3.", "\n\nA:\n\nIt is all or nothing behavior. ", "You cannot refer to value from same execution and get new value.", "\nExample:\ncreate table t(x INT, y INT);\nINSERT INTO t VALUES (5, 10);\nupdate t\nSET x = y,\n y = x;\nselect * from T;\n\nDBFiddle Demo\n-- Before\nx = 5, y = 10\n-- After\nx = 10, y = 5\n-- in step 3 you want this to work like this\nx= 10, y = 10\n\nValues are swapped, but in step 3 you want to get new value from prev column, which won't happen.", "\nI suggest to try:\nUPDATE [DocumentReview] \nSET ReviewDate = @ReviewDate,\n ProvisionalReviewDate = @ProvisionalReviewDate,\n FinalReviewDate = @FinalReviewDate,\n\n [ProvisionalReviewTimeframe] \n = (DATEDIFF(SECOND, [ProvisionalReviewDate], @ReviewDate) / 3600.0),\n [lReviewTimeframe] \n = (DATEDIFF(SECOND, [FinalReviewDate], @ReviewDate) / 3600.0),\nWHERE [Id] = @id\n\n" ]

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[ "Space Twins\n\nHeading into space is certainly a life-changing experience for each of the lucky astronauts who have had the privilege. ", "But who could have thought that it actually changes you on a genetic level? ", "Thanks to a pair of twin astronauts, NASA has been able to study the changes to the bodies of those who spend long periods of time in space to a degree that wouldn’t otherwise be possible.", "\n\nTo determine how space changes the human body, researchers collected a variety of biological samples from twins Mark and Scott Kelley while Scott was spending 340 days aboard the International Space Station and Mark was left on the ground. ", "The twins were excellent subjects for this kind of research as not only do they have nearly identical genomes, they have also had similar life experiences since they’re even in the same line of work.", "\n\nIn evaluating the brothers’ data, the researchers noticed some striking differences in various biological markers, such as gut bacteria and even chromosomes. ", "One of the more remarkable findings of the testing was that Scott’s telemores, the ends of his chromosomes, were longer, though they eventually returned to pre-mission lengths. ", "Further research will be done on other astronauts to see if this is a common pattern. ", "Also in the genetic realm, Scott’s DNA methylation levels decreased during his time in space, while Mark’s increased in the same period. ", "Once again, Scott’s levels returned to their baseline levels once he was back on Earth, but researchers aren’t sure what such changes even mean.", "\n\nDNA Changes\n\nAccording to NASA, other studies of how the body fares in space have shown clear differences in spatial orientation, bone density loss at rates up to 12 times higher than those on Earth, loss of muscle strength, and cardiovascular deconditioning. ", "In this study, however, researchers were able to compare genetic changes with samples from a control, providing a more complete picture of the effect.", "\n\nThere is still much analysis to do on the data being gathered, as well as from data that can be gathered from other astronauts. ", "According to Christopher Mason of Weill Cornell Medicine, “The data are so fresh that some of them are still coming off the sequencing machines.” ", "The results have yet to be peer-reviewed, and it could be a few years before they are, given the sheer volume of data.", "\n\nAs we get closer to being able to put a human on Mars, this work becomes more valuable. ", "The trip to the Red Planet alone is a six-month journey. ", "Therefore, crews would be spending at least a year in space. ", "Knowing that our astronauts will be safe is of the utmost importance, and not only for Mars — we will likely be seeing more people in space, in general, especially with the coming of private space stations on the horizon. ", "Knowing how space impacts our bodies is the first step in determining how we can mitigate any deleterious effects for our future adventurers." ]

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