between targeted toxicant exposures, metabolomics profiles, and ASD. We will undertake this work in the Childhood Autism Risks from Genetics and the Environment (CHARGE) cohort, which has a wealth of harmonized phenotypic, demographic, medical, genetic, and environmental data for high efficiency analysis. We will use novel statistical methodology, weighted quantile sum regression (WQS), that addresses effects of high-dimensional mixtures and increases power when compared to traditional methods to discover biomarkers and biological pathways associated with ASD (n=318) or typical development (n=190) (neither ASD nor other developmental delays (n=105)). Our method is a non-invasive advancement in technology to obtain direct and repeated fetal measures of biomarkers associated with early life etiology of ASD.fee-generating scam—the practice in which banks’ research departments wrote rosy reports about companies in order to win their investment-banking business and rake in the M&A profits. No wonder all of these stocks are at or near their multiyear lows, depths not seen since the dot-com aftermath of 2002, when Wall Street last shriveled.

Not all is grim. Morgan Stanley, for one, is making a concerted effort to build an asset-management business, where it takes clients’ monies and manages them in-house. That’s nowhere near as lucrative as selling proprietary mortgage bonds, or other exotic products, but asset management tends to have a longer half-life because individual money is “sticky,” not “hot”—it stays in one place.

Then there is Goldman Sachs. Goldman, from the days that I worked there in the eighties,


Work on ‘Metropolis’ – the next scheduled software release for the ethereum blockchain project – continues, according to a new blog post from its creator, Vitalik Buterin.

While absent of any concrete release date, the blog offers a window into the platform’s development efforts, as well as details about the changes that could be included in the Metropolis update. Metropolis follows two previous versions of ethereum, ‘Homestead‘ (released last March) and ‘Frontier‘, which debuted in July 2015.

As detailed by CoinDesk in December, ethereum’s developer team has largely been looking ahead to future releases, having been stymied by events such as the collapse of The DAO and denial-of-service attacks against the ethereum network.

Buterin said today that those efforts are accelerating.

He wrote:

“During the last month and a half, the Ethereum Coreit would be better for me to spend less time on this starting today. But don’t worry, I’ll try to visit here everyday when I can and do some blog hopping too. I don’t want to make promises coz I might can’t do it. I don’t know how the SAHM handle their time. That must be a tough job being a mom, a wife and do blogging at the same time.

Blogger moms, how do you handle your time? Is there a trick on how to take care of everything? I’ll be glad to hear any suggestions about handling time properly. Though I do multi-tasking jobs but still it’s not enough. Thanks for reading and take care!

hi mitchelee, I am from houston, texas. ahm for me blogging is fun,


CloudWalk Technology

CloudWalk Technology Co. Ltd. is a Guangzhou-based developer of facial recognition software, used in China.

History
CloudWalk was founded by Zhou Xi, a graduate of the University of Science and Technology of China with an academic background in artificial intelligence and pattern recognition. CloudWalk was founded in April 2015, following Zhou's departure from the Chinese Academy of Sciences.

In 2017, CloudWalk raised $379 million in Series B funding from investors including Shunwei Capital, Oriza Holdings, and Puhua Capital.

Customers

CloudWalk is the primary supplier of facial recognition technology to the Bank of China and Haitong Securities.

In 2018, CloudWalk signed a deal to provide the government of Zimbabwe with a mass facial recognition system, which will monitor all major transportation hubs, as well as create a national facial ID database.

References

Category:2015 establishments in China
Category:Companiesdebate about
it and also answer questions
from the public because it is
our money being spent on it.”
Deputy Mayor Justin Lester
agreed there should be an
open and transparent discussion as plans for a proposed

extension move forward.
“We want a fully transparent process, I have always
been open and have provided
Guardians of the Bays with as
much information as possible
and I have always been happy
to meet with them.
“I do acknowledge they are
the most affected so I want
to make sure they have the
information available to them,
however, sometimes we won’t
always agree on the outcome.”
Sea said it was important the
issue was debated by councillors and mayoral candidates
ahead of the elections, so
when it came time to vote,
locals could have their say.
Following last week’s announcement Wellington Airport chief executive, Steve
Sanderson, said the company
had worked to respond to
questions raised over some
aspects


veggie
markets popping up, it’s hard
to survive.”
The proliferation of other
sellers was not the only change
Miramar has undergone.
Kim, who was born and
raised in the town, says he’s
gotten much busier with the
influx of film studios and cafes
in the area.
“It used to be much quieterit’s a lot busier now, which is a
good thing, and I get to sell to
all the cafes, which is great,”
Kim laughed.
Leaving the business after
two decades will be a hard adjustment for Kim, as he learns
how to enjoy some downtime.

Newcomers events
There are two Wellington Newcomers
Network events happing in the Month
of May. On Wednesday, May 11 a coffee catch up event will take place at
Clarkes Cafe in the Wellington Central
Library from 5pm. Another coffee and
conversation catch up will take place
at the Wellington Central Library on
Thursday, May 26 from 2.30pm.

Drop in11am to 2pm. Locals are
encouraged to head along and learn about why fairtrade
is important and sample just how good fairtrade products
really are.

AGREE DISAGREE
getwellymoving.co.nz
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Public transport
should be our
top priority

By Nikki Papatsoumas

Last week, hundreds of small
nails were scattered along the
Island Bay cycleway, in what some
have since labelled a “cowardly”
act.
The Island Bay cycleway was
completed earlier this year and
while some have praised its design,
other members of the coastal
community have called for the
Wellington City Council to put the
bike route back to its old layout.
Last Wednesday news that small
nails had been scattered across
the cycleway circulated on social
media.
“Someone has deliberately scattered hundreds of these small nails
at 4 or 5 different spots along the
northbound cycleway between
Humber St and Mersey St,” a
post to the Island Bay Cycleway
Facebook page said.
“Watch out if you're cycling
along there and we'll see if


they don’t need
plants to look good.
LEFT: Check out the foldable electric bikes from
Ezirider that fit in your boot and have a 60 km range.
RIGHT: Stoked Stainless Steel Ltd will have their
handmade, wood-fired hot tubs, electric spas and
bath tubs on display.

THE BETTER WAY
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TOASTMASTERS
WELLINGTON

For general enquiries you can email info@toastmasters.org.nz.
Should you have a more specific enquiry you can also contact one of the District
Officers or Field Officers.
Simply call 0800 PEOPLE (0800 - 736 753). Your call will be answered by one of
our designated 0800 officers. Answer phones may be operating in some areas
at certain times. Should this be thebeen doing this year.
client revisions:
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no jobNotice
too big or small.
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amazingTrades
array ofand
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nomination form and a notice calling for
nominations will be posted to all eligible
voters.
You can nominate another person to stand
as a candidate, or you can nominate yourself
(make sure you sign both parts of the form).
Additional nomination forms can be
obtained from the school office.
Nominations close at noon on 20 May
2016 and may be accompanied by signed
candidates’ statements.
The voting roll is open for inspection at the
school and can be viewed during normal
school hours.
There will also be a list of candidates’
names, as they come to hand, for inspection
at the school.
Voting closes at noon on 3 June 2016.
Adam Levy
Returning Officer

Returning Officer J Leggett

St Francis de Sales School, Island Bay
Board of Trustees Election
Nominations are invited for the election of 5
parent representatives to the board of trustees.
A nomination form and a notice calling for
nominations willQ:

Keyed queues with depth queries and delete

I'm interested in a data structure (let's call it a DMV queue, or DMV for short) over keys (say, strings) with the following operations:

empty is a DMV containing no keys.
enqueue(q,k) adds the key k to the back of the DMV q, unless k is already in q, in which case it does nothing.
dequeue(q) deletes the key at the front of the DMV q, if one exists, and returns it.
delete(q,k) removes the key k from the DMV q.
depth(q,k) returns an natural number indicating the approximate number of keys between the key k and the front of the DMV q. Let $k_q$ denote the exact number of keys between k and the front of q. Then there must be some c such that for


Old Ebbitt Grill is 50% off from 3-6pm and 11pm-1am daily. This historic restaurant and bar was the oldest saloon in DC, founded in 1856 and frequented by Presidents, journalists, statesmen and military heroes. So you get a great deal but also a bit of history.

Washington DC area groups on MeetUp – History and culture lovers take note – there are some great groups on MeetUp in DC! Sign up early for areas of interest and take a spot for unconventional tours you might enjoy. I did a free tour of the White House Garden and a Watergate-themed Walking Tour for only $10, both led by enthusiastic guides and attended by an interesting cross-section of folks.

Getting around – DC has a pretty decent network of public transport, althoughit’s made up of a few different organizations that *mostly* work together pretty well. You can get a SmarTrip card (stored value card) that works on many of them. I preferred the bus to the metro, which often had delays or construction and I love being able to see things at ground level riding the buses. My favorite way to get around, by far, was the DC Circulator. It’s a limited network of buses for only $1 – including the red line which will take you all around the monuments and museums on the National Mall. Circulator buses are clean, come every ten minutes and even have USB ports to charge your phone! Ride sharing apps including Lyft and Uber and by the hour/day rentals like Car2Go and


cohort). Of the 6,387 patients identified from the NZCR 5,610 (88%) were eligible for PIPER. Reasons for exclusion were non-adenocarcinoma histology (3%) and non-colorectal primary (2%). Data were collected on 3,695 patients with colon cancer, 1,385 with rectal cancer and 466 with cancer of the recto sigmoid junction. The PIPER Project has generated comprehensive population level data detailing the diagnosis and management of colorectal adenocarcinoma in New Zealand. This will be used to assess the care provided to patients, and the impact of variations in care occurring between patient groups. * @return CommandResult
     */
    public static CommandResult execCmd(String[] commands, boolean isRoot) {
        return execCmd(commands, isRoot, true);
    }

    /**
     * 是否是在root下执行命令
     *
     * @param command         命令
     * @param isRoot          是否需要root权限执行
     * @param isNeedResultMsg 是否需要结果消息
     * @return CommandResult
     */
    public static CommandResult execCmd(String command, boolean isRoot, boolean isNeedResultMsg) {
        return execCmd(new String[]{command}, isRoot, isNeedResultMsg);


Theorem \[paramodularity\]. If a matching bound on $\bfT/J$ were available (see next paragraph) our method would in fact be enough to prove a full $R=T$ theorem. We plan to address this problem in a future paper.

Let us note that we prove our results for a residual representation $\ov{\sigma}$ such that $\ov{\sigma}^{\rm ss} \cong \chi^{k-2} \oplus \chi^{k-1} \oplus \rho$ for any integer $k \geq 2$. The case $k=2$ (discussed above) is the most interesting because it corresponds to abelian surfaces and thus to Conjecture \[conj:paramodular1\]. In fact for even $k>9$ and $N=1$ we prove a full modularity result $R=\bfT$ using a congruence result of Brown [@Brown11], which provides us with the desired matching bound on $\bfT/J$ in this case.

Let us now comment on the restrictiveness of our results. The, {\rm min}}(\bfQ_{\ell},W)={\rm im}(H^1_f(\bfQ_{\ell},V) \to H^1(\bfQ_{\ell},W)).$$

\[two choices\] Following [@Rubin00] Definition 1.3.4 we define $H^1_{f, {\rm min}}(\bfQ_{\ell},W_n)$ as the inverse image of $H^1_{f, {\rm min}}(\bfQ_{\ell},W)$ under the map $H^1(\bfQ_{\ell},W_n) \to H^1(\bfQ_{\ell},W)$.

By [@Rubin00] Lemma 1.3.5 we have $H^1_{f, {\rm min}}(\bfQ_{\ell},W)=H^1_{\rm ur}(\bfQ_{\ell},W)_{\rm div}$ and if $W^{I_{\ell}}$ is divisible we further have $H^1_{f, {\rm min}}(\bfQ_{\ell},W)=H^1_{\rm ur}(\bfQ_{\ell},W)$, $H^1_{f, {\rm min}}(\bfQ_{\ell},T)=H^1_{\rm ur}(\bfQ_{\ell},T)$ and $H^1_{f, {\rm min}}(\bfQ_{\ell},W_n)=H^1_{\rm ur}(\bfQ_{\ell},W_n)$ (for the latter using also [@Rubin00] Lemma 1.3.8 and its proof).

\[Sel\_funct\] Let $0 \to M' \overset{i}{\to} M \overset{j}{\to} M'' \to 0$ be an exact sequence of $p$-adic $G_{\Sigma}$-modules over $\Oo$. Assume that the modules have been given the induced finite/singular structures, i.e. such that $H^1_{f, \mS} (\bfQ_{\ell}, M'') = j_* H^1_{f, \mS}(\bfQ_{\ell}, M)$ and $H^1_{f, \mS}(\bfQ_{\ell}, M') =
i_*^{-1} H^1_{f, \mS}(\bfQ_{\ell}, M)$ for all ${\ell}$.

Then there is an


sequence $0 \to W[\varpi^n] \to W \overset{\times \varpi^n}{\to} W \to  0$ since the minimal and crystalline finite/singular structures on $W_n$ are induced from the one on $W$ by definition. (This statement is also stated as [@Rubin00], Lemma 1.5.4 (where this Selmer group is denoted $\mS^{\emptyset}(\bfQ, W)$) upon noting that our assumption forces injectivity of the map $H^1(G_{\Sigma}, W_n) \to H^1(G_{\Sigma},W)[\varpi^n]$ by [@Rubin00], Lemma 1.2.2(i)).

The second statement follows immediately from Remark \[two choices\], and the final one from Remark \[DFG22\].

In the following we will write $H^1_f(\bfQ,M)$ for $H^1_{f, {\rm ur}}(\bfQ, M)$ and $H^1_{\Sigma}(\bfQ,M)$ for $H^1_{\Sigma, {\rm ur}}(\bfQ, M)$ for any $p$-adic $G_{\Sigma}$-module $M$.

More properties of Selmer groups
--------------------------------

Assume that $k\geq 2$ is an even integer such that $p>2k-2$. Note that under this assumption the $p$-adic Galois representation $\rho_f$ associatedto an eigenform of weight $2k-2$ of level not divisble by $p$ is short crystalline. This assumption will be in force throughout the paper.

\[invariants\] Let $\rho_f : G_{\Sigma} \to \GL_2(E)$ be the Galois representation attached to a newform $f \in S_{2k-2}(N)$ for $N$ a square-free integer with $p \nmid N$ and $\Sigma=\{ \ell \mid N \} \cup \{p\}$. Suppose also that the residual representation $\ov{\rho}_f$ is absolutely irreducible and ramified at every prime $\ell \mid N$. Then for $i=1, 2$

-   $(\rho_f(i-k)\otimes E/\Oo)^{I_{\ell}}$ is divisible for all $\ell \neq p$

-   $(\rho_f(i-k)\otimes E/\Oo)^{G_{\Sigma}}=0$.

For the convenience of the reader we include the proof, however one can also consult the proof of Lemma 3.4 in [@PollackWeston11].

\(i) Set $\varrho:=\rho_f(i-k)$ ($i=1,2$). We choose a basis $\{e_1, e_2\}$ for the space


& c \\ && \chi^{k-1}\emat: G_{\Sigma} \to \GL_4(\bfF),$$ where $a,c$ are assumed to be non-trivial classes in $H^1(\bfQ, \rho(1-k))$ (no assumption on $b$).

\[identification\] We have $$\Hom(\rho, \chi^{k-2}) =\rho^{\vee} \otimes \chi^{k-2} =\rho \otimes \chi^{3-2k} \otimes \chi^{k-2} = \rho(1-k)=\Hom(\chi^{k-1}, \rho),$$ so $a$ and $c$ are indeed both classes in $H^1(\bfQ, \rho(1-k))$.

Set $N_1=\bmat 0 \\ & 0 &1\\ &&0 \\ &&&0 \emat$ and for any prime $\ell \neq p$ let $t_p :I_{\ell} \to \bfZ_p(1)$ be the tame character. We will always assume that $\ov{\sigma}$ as above is *semi-abelian* by which we mean that for each $\ell \in \Sigma \setminus \{p\}$ one has \[admissible\] |\_[I\_]{} (t\_pN\_1).

\[form res\] Let $x \in G_{\Sigma}$ be such that $\ov{\sigma}(x)$ generates the image of $I_{\ell}$. Then $\ov{\sigma}$ is isomorphic to a representation of the form $$\ov{\sigma}'=\bmat \tr \sigma \circ \tau$. Note that for semisimple $\sigma$ and fields $A$ this is equivalent to $\sigma^{\vee} \cong \sigma(3-2k)$.

\[reprsd\] The functor assigning to an object $A \in
\textup{LCN}(E)$ the set of strict equivalence classes of $\tau$-self-dual short crystalline (at $p$), minimal deformations to $\GL_{4}(A)$ is representable by the quotient of $R'$ by the ideal generated by $\{\tr (\sigma')^{\rm univ}(g)-\tr (\sigma')^{\rm univ}(\tau(g)) \mid g \in G_{\Sigma} \}$. We will denote this quotient by $R$ and will write $\sigma^{\rm univ}$ for the corresponding universal deformation.

We write $R^{\rm red}$ for the quotient of $R$ by its nilradical and $\sigma^{\rm red}$ for the corresponding (universal) deformation, i.e., the composite of $\sigma^{\rm univ}$ with $R\twoheadrightarrow R^{\rm red}$.

Lattice {#Lattice}
=======

\[centralizer\] Let $E$ be a finite extension of $\bfQ_p$ with valuation ring $\Oo$, uniformizer $\varpi$ and $\bfF=\Oo/\varpi\Oo$.


Tot}(R^{\rm red})),$$ where $A^?_{i,j}$ are fractional ideals of $R^{\rm red}$ (and $A^{\sigma}_{i,j}$ are ideals of $R^{\rm red}$) that satisfy $$A^?_{i,j}A^?_{j,i} \subset A^?_{i,k}, \quad A^?_{i,i} = R^{\rm red}, \quad A^?_{i,j}A^?_{j,i} \subset \fm_{R^{\rm red}}.$$

-   The data $\mE$ can be adapted so that the $R^{\rm red}$-algebra map $\varphi': {\rm GMA}(\mA^{\sigma}) \twoheadrightarrow {\rm GMA}(\mA^T)$ induced from $\varphi$ has the property that $\varphi'(\mA^{\sigma}_{i,j})=\mA^T_{i,j}$.

The statements (i), (ii) for $?=T$ and (i) for $?=\sigma$ are a direct consequence of Theorem 1.4.4 in [@BellaicheChenevierbook]. To show that we can also obtain (ii) for $?=\sigma$ we argue as in [@BergerKlosin13], Proposition 2.8 which uses Lemma 1.3.7 of [@BellaicheChenevierbook]. Finally, we proceed as in the proof of Lemma 2.5 in [@BergerKlosin13] to show that $\mE$ can be adapted to satisfy (iii).

\[adaptness11\] The data $\mE=\{e_i, \psi_i\mid i[@BergerKlosin13], section 6.1 for discussion of this assumption as well as section \[Examples\] in the current paper). This implies that the set of strict equivalence classes of short crystalline, minimal deformations of $\rho$ to $\GL_2(\Oo)$ with determinant equal to $\epsilon^{2k-3}$ contains a single element. We will write $\tilde{\rho}$ for a fixed representative of this strict equivalence class.

Consider short crystalline, semi-abelian $\ov{\sigma} : G_{\Sigma} \to \GL_4(\bfF)$ of the form $$\ov{\sigma}=\bmat \chi^{k-2} & a & b\\ & \rho & c \\ && \chi^{k-1}\emat$$ with $a,c$ giving rise to non-zero elements of $H^1_{f}(\bfQ, \rho(1-k))$ (cf. Corollary \[splitting at ell\]).

We assume in this section that $$\dim_{\bfF}H^1_f(\bfQ, \rho(1-k)) =1.$$ For $A$ an object of ${\rm LCN}(E)$ we will call a matrix $M\in \GL_4(A)$ upper-triangular if $$M=\bmat *&*&*&*\\ 0&*&*&*\\ 0&*&*&*\\ 0&0&0&*\emat.$$ We will say


that a homomorphism $\sigma': G_{\Sigma} \to \GL_4(A)$ is upper-triangular if for all $g \in G_{\Sigma}$, the matrix $\sigma'(g) \in \GL_4(A)$ is upper-triangular. Finally, we say that a deformation $\sigma : G_{\Sigma} \to \GL_4(A)$ of $\ov{\sigma}$ is upper-triangular if there exists a member $\sigma'$ of the strict equivalence class of $\sigma$ which is upper-triangular.

\[5\] Every short crystalline minimal deformation $\sigma$ of $\ov{\sigma}$ to $\GL_4(A)$ such that $\tr \sigma = T_1 + T_2 +T_3$ with $T_1, T_2, T_3$ pseudocharacters such that $T_1 \equiv \chi^{k-2}$, $T_2 \equiv \tr \rho$, $T_3 \equiv \chi^{k-1}$ mod $\fm_A$ is upper-triangular.

This is Theorem 1.1 in [@Brown08]. Note that the Artinian assumption in [@Brown08] is unnecessary. See also remarks to Theorem 1 in [@Urban99].

\[diag pieces\] Consider an upper-triangular deformation of $\ov{\sigma}$ to $\GL_4(\bfF[X]/X^2)$. Then every upper-triangular member\in {\rm LCN}(E)$. Then $I \supset I'_R$ if and only if $(\sigma')^{\rm univ}$ mod $I$ is an upper-triangular deformation of $\ov{\sigma}$ to $\GL_4(R'/I)$.

The proof of Corollary 7.8 in [@BergerKlosin13] carries over to three Jordan-Hölder factors with the application of Theorem 7.7 in [@BergerKlosin13] replaced by an application of Lemma \[5\] above.

The rest of the proof of Corollary \[structure map\] is the same as the proof of Proposition 7.10 in [@BergerKlosin13] with the application of Corollary 7.8 in [@BergerKlosin13] now replaced with an application of Lemma \[conj to upper\].

\[Lvalue bound\] Let $\tilde{\rho}$ be a representative of the unique deformation of $\rho$ to characteristic zero. Suppose that $\#H^1_{f}(\bfQ, \tilde{\rho}(1-k)\otimes E/\Oo) \leq \#\Oo/L\Oo$ for some $L \in \Oo$. Then $\# R^{\rm red}/I^{\rm tot}\leq \#\Oo/L\Oo$.

Again by Lemma 7.11 of [@BergerKlosin13] it is


Bloch-Kato Selmer group has order 3, but we were not able to confirm this. However, this abelian surface has been proved to be paramodular by Brumer et al. using the Faltings-Serre method, but a proof has not yet appeared in print.

When the conjectured congruence is with the Saito-Kurokawa lift of a modular form with non-rational Fourier coefficients it is sometimes possible to check that $R_{\ov{\rho}_f}$ is a discrete valuation ring. This is the case for the examples of conductor $N=349, 353$ and $389$ on the list in [@PoorYuen15]. These surfaces have rational $p$-torsion for $p=13, 11$ and $5$, respectively. We have, however, not tried to check the Selmer group assumptions for these cases.

Another example we want to highlight is that of conductor $N=997$, where there exists an abelianis longer.

2.  Using the longer vector in $\JRMJ_{6,5}^{+,-}$, we have sufficiently many Fourier coefficients to apply $T_2$, obtaining a shorter expansion of $T_2h^{+,-}$ modulo $5$. But this vector is sufficiently long to identify in $\JRMJ_{6,5}^{+,-}$, again giving us a long enough expansion to apply $T_2$ again, and so on.

This technique shows that $T_2^ih^{+,-}$ for $i=0,1,\dotsc,124$ are linearly independent modulo $5$, and so $\dim_{\Ffive}{{{{{\mathcal S}}_{4}({{\rm K}(731)})}}}^{+,-}[6]_5\ge125$. Similarly, bootstrapping with $h^{-,+}$ gives $\dim_{\Ffive}{{{{{\mathcal S}}_{4}({{\rm K}(731)})}}}^{-,+}[6]_5\ge124$. Thus altogether we have shown that $\dim_{\Ffive}{{{{{\mathcal S}}_{4}({{\rm K}(731)})}}}^{-}[6]_5\ge125+124=249$, and we may select a basis modulo $5$ of a $249$-dimensional subspace of ${{{{{\mathcal S}}_{4}({{\rm K}(731)})}}}^{-}_5$. So, because $719+249=968$, altogether we have reductions modulo $5$ of linearly independent elements that span a codimension $4$ subspace of ${{{{{\mathcal S}}_{4}({{\rm K}(731)})}}}$. This is comfortably beyond the needed codimension $\dim{{\rm J}_{2,731}^{\rm cusp}}-1=17$.

Determining ${{{{{\mathcal S}}_{2}({{\rm K}(731)})}}}^-$
--------------------------------------------------------

The $H_4(N,2,1)^-$


look at drug and marijuana users.

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[quote name='theyarecomingforyou' timestamp='1355762032' post='595398372']
Sounds like a well-adjusted individual. I definitely can't see any issue with people like that being allowed to own firearms.
[/quote]

And yet his mother/relatives could and this would happen all over again...deductive engine. But Hypothetical Datalog is powerful enough to even apply the same technique to model assumptions in SQL queries, with the (non-standard) clause [[`ASSUME`]{}]{}. This clause enables both positive and negative assumptions on data, as shown in Section \[assume\], which are useful for modelling “what-if” scenarios. Finally, we present the deductive system DES at work with examples of [[`WITH`]{}]{} and [[`ASSUME`]{}]{} queries in Section \[examples\]. Our approach is also useful for connecting with external relational database systems which cannot process these clauses. DES then behaves as a front-end capable of processing either novel or unsupported features in such systems.

The SQL [WITH]{} Clause {#with}
=======================

Typically, complex SQL queries are broken-down for applying the [*divide-and-conquer*]{} principle as well as for enhancing readability and maintenance. Introducing intermediate views with [CREATE VIEW]{}


translated to Hypothetical Datalog, because each $R_i$ can represent each temporary view definition, as will be shown in the next section.

Translating SQL into Datalog {#translating}
============================

We consider standard SQL as found in many textbooks (e.g., [@Silberschatz6th]), but also allowing `FROM`-less statements, i.e., providing a single-row output constructed with the comma-separated expressions after the `SELECT` keyword (Oracle, for instance, resorts to feed the row from the `dual` table to express the same feature). Here, we define a function [[`SQL_to_DL`]{}]{} that takes a relation name and an SQL statement as input and returns a multiset of Datalog rules providing the same meaning as the SQL relation for a corresponding predicate with the same name as the relation. The following (incomplete) definition for this function includes only a couple of the basicpressure sensor or a combination of an accelerator and force sensing resistor. The accuracy of these elements is affected by the environment around the sensor during use. For example, variations in atmospheric pressure or temperature may change the reference values needed to compare when the shoe is in use or not in use. In another example, the sensor is said to measure a physical metric that changes as the shoe wears out which requires that the sensor change correspondingly with the shoe. These disadvantages require a robust and complex analysis of the starting and ending state of the sensor throughout the shoe use and, in some cases, foreknowledge of the wear rate of the shoe.
Another disadvantage of the prior art is the inability to distinguish a non-destructive compression


from a destructive compression. Although the art describes methods to make this comparison, such as the physical displacement of the sensor or the amount of acceleration above the minimal level, this analysis becomes more complicated as the shoe wears which will change the reference point, requiring a robust and complex analysis of the starting and ending state of the sensor. Other methods require foreknowledge of the user's weight, stance-to-foot swing phase and other values specific to the shoe construction.
Another disadvantage of the prior art is the requirement that the output of the information of the invention be transmitted outside the shoe or by removing the invention from the shoe and connected it to a terminal. In another art, the information is actively communicated to the user through aart is the requirement that the device is constructed out of reusable materials which increases the cost of the device by the use of durable components that can be used again. Although this may be advantageous for some applications, the maintenance and reliability of such a reused device is an added burden to the user. For example, although the razor blade may be resharpened after it has reached its initial end of life, the complexity of sharpening it and the understanding of how many more sharpenings it should receive is more cumbersome than users are willing to tolerate and therefore they simply discard the used razor.
Accordingly, there is a need for a low cost device that measures the destructive compressions of the shoe in such a manner that


that “history will not look kindly upon this panel. … It will be remembered, like the House Un-American Activities Committee and McCarthy hearings for its excesses and abuses of power.” Or, if Trump and the GOP succeed in their planned attempt to gut Planned Parenthood’s federal funding, history will record the panel as a wildly effective propaganda machine.Stephen Teles’s writing about the American “kludgeocracy” that does everything in about the least efficient way possible.

Geoff, I’m not so comfortable with such broad statements about why the Constitution was written and what it intended given the plurality of opinions about its significance and meaning from the day its ink dried, though I’d agree that most people in a far less connected 18th century world would have been prone to think locally rather than nationally, to varying degrees. Regardless, I suppose I just have less confidence that, given the interconnectedness of today’s world, a system that empowered states and localities would lead to anything but more bureaucratic and jurisdictional complexity; I’m still not convinced that a top-down approach isn’t more conducive to less government overall. But since neither


most powerful back-to-back championship squads in CFL history. With the likes of Doug Flutie, Mike “Pinball” Clemons, Robert Drummond and Mike O’Shea on his roster, Matthews guided the Boatmen to a combined record 39-15 in three seasons, capturing the ’96 and ’97 championships.

“We are so saddened by the passing of our legendary coach Don Matthews,” said Michael Copeland, President and CEO of the Argonauts. “Twenty years ago, Don led the Argos to back-to-back Grey Cup championships. We were hopeful he could join us later this year when we honour those Grey Cup teams. But on that day, and every day thereafter, he will always be in our hearts. On behalf of our entire organization and our fans, we send our deepest condolences to the Matthews family, and histhe casing while the 2500-pound weight of the casing hammer pushes the casing in the newly drilled hole.

As new casing is welded on, the ground can be checked to see where the static water table is. When hard formations are encountered and the casing won’t follow, then the air-operated casing hammer is fired to drive the casing ahead. In clean sand aquifers, when there is enough depth in the water table to meet codes and water volume requirements, the drill rods are pulled and a screen is set. In gravel aquifers, water will start gushing out from the air compressor and the well is developed out. With this well drilling method, we can see every inch of ground we drill through and cannot "miss" any water. Through our


Spine and Back Health

Natural Fusion

10/27/2010

Question:

I had a herniation removed from lumbar 4/5. I developed MRSA in the disc that they removed the hernitation from. The MRSA has removed all the cartilage and the two discs are now bone on bone. I am being told that the disc may naturaly fuse togeather on it`s own. Is this possible?

Answer:

Hello, thank you for your question. It turns out that cartilage is a very effective barrier to bone growth or bone fusion. If you take away the cartilage (i.e. disc) between two vertebrae, it's actually pretty common for them to just fuse together. I've seen patients who fused all by themselves a while after having a disc infection, so it's definitely possible. I hope you heal up and get better. Good luck.

Pleaseand police told USA Today they believe he was was not targeted, but instead was hit by errant gunfire.

"It infuriates me that we have a good kid doing what we all expect him to do, and he's a victim of something like this," Police Superintendent Eddie Johnson told reporters. "This is why we have to have common sense gun legislation in this country. Not just this city, this state, but in this country, to stop things like this from happening."

Story continues

Don't miss: Melania Trump’s Popularity Soars Amid Reports of the President's Alleged Affairs

Compared to 2017, Chicago saw a 22.3 percent reduction in murders and a 26.5 percent decrease in shooting incidents from January 1 through the end of April, according to data collected by the city and the


Abandoned Coral. These colors look really great together! I did the smooshing technique where you put some ink down on your craft mat, spritz with water and 'smoosh' your watercolor cardstock into the ink. I usually do it in two colors and use the heat gun for a few seconds. You may or may not need to dab with a paper towel. Then I'll dab it in another color or two and use heat gun again for a few seconds. It's totally up to you because it will turn out different each time you do it so you just have to judge it for yourself to see when it looks right to you. I love it when there is a little bit of white left. I took thepresent inventors have realized that a space diversity system can be implemented in a wireless hub of a transmission system to reduce the disadvantages mentioned above and improve the performance of a wireless system. The present invention provides an optimized analysis of statistically independent diverse signals that increases the robustness and performance of a wireless hub.
The present invention is embodied as a method of space diversity for broadband wireless access, comprising the steps of, receiving spatially diverse signals, separately demodulating each of the spatially diverse signals, selecting a most correct of the demodulated signals, and forwarding the selected demodulated signal for further processing.
The present invention includes a space diversity device for a wireless hub, comprising, PHY layer equipment, including, a set of at least two antennas for receiving


frontier is.

I think this reflects a deeper set of issues. For example, I think that the natural sciences are much more comfortable (and not just more able — because I think the social sciences are roughly equally able) to declare victory and move on. Yet, very often in the social sciences, we don’t do that. We don’t allow ourselves to say, “You know, we have pretty much sorted this topic out.” There are still important topics — just like anatomy is an important topic – people obviously still need to learn anatomy, and we need people that work in, and teach, anatomy — but we really don’t need a lot of research into gross anatomy anymore. We need to identify where the interesting anatomical research is – forto the environment. What is the impact of the environment on human activity? What is the impact of human activity on the environment? Could any of this have an evolutionary basis? What are attitudes toward preservation of the environment, and to what extent is the environment seen as a commons? How do attitudes and behaviour with respect to the environment spread in social networks? And so forth.

Or another example might be new methodological approaches in the social sciences. There are at least three very radical changes in the social sciences that I think are in the offing that we should embrace.

First, a biological hurricane is approaching the social sciences. Discoveries in physiology, neuroscience, and genetics are going to push up against the social sciences, and we social scientists


discoveries have had tremendous impact on human welfare. But in the 21st century, the social sciences offer equal promise – I would even say more promise – for improving human welfare because so many of our problems arise from human behaviours. A deeper understanding of behaviour and the development of intervention strategies would be very valuable – for example, with new ideas regarding institutional arrangements, nudges of different sorts, or even social network interventions. For example, in some of our own work, we’ve done experiments involving thousands or even millions of people, showing that we can get groups to be more healthy, more cooperative, and more civic-minded, by exploiting an understanding of both face-to-face and online social networks. These diverse sorts of interventions offer promise for improving humanwhy should we fund that?” And they might ask, can you instead tell us something about the stem cell biology of insulin-producing cells?

I think the social sciences have to keep moving. We have to identify where the frontier is and put manpower where that frontier is. And we have to identify the ways in which discoveries there can be translated. It’s a tall order, but I am certain that we are capable of it.

Professor Christakis, Professor Patrick Dunleavy, Dr Amanda Goodall, Professor Andrew Oswald will be discussing this topic further on Tuesday 21st October, 2014 at the LSE for the event Do We Need to Shake Up the Social Sciences? Follow the debate on Twitter at #LSEsocialsciences.

Note: This article gives the views of the author, and not the


/* Copyright (C) 2011  Jan Källman
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 * version 2.1 of the License, or (at your option) any later version.

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 * but WITHOUT ANY WARRANTY; without even the implied warranty of
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insights.

In the 1960s, psychiatrist Claudio Naranjo found that it helped people get along in group therapy settings, to trust and empathize with each other. Around the same time, the drug even began to be used in couples therapy for this reason. A psychiatrist named Rick Ingrasci treated 100 patients with MDMA, about a third of them couples. He wrote that “what [MDMA] does is actually remove the fear of being real, of being authentic with yourself and with other people.”

“You basically couldn’t design a molecule that is better for therapy than MDMA," psychiatrist Julie Holland told The Guardian this past April. And yet, in 1985, the drug was labeled as a Schedule 1 drug, despite protestation from many clinicians—essentially halting research on its therapeutic applications.

The first time Greg


---
abstract: 'We determine for which known finite simple groups $G$ and which primes $p$ the $p$-fusion system of $G$ is simple. This means first collecting together the results that were already known (and correcting two errors made in an earlier study of this question), and then handling the remaining cases. At the same time, we develop some new tools to use when determining $O^{p''}(\calf)$ for arbitrary saturated fusion systems.'
address:
- 'Université Sorbonne Paris Nord, LAGA, UMR 7539 du CNRS, 99, Av. J.-B. Clément, 93430 Villetaneuse, France.'
- 'Departament de Matemàtiques, Universitat Autònoma de Barcelona, E–08193 Bellaterra, Spain'
author:
- Bob Oliver
- Albert Ruiz
title: Simplicity of fusion systems of finite simple groups
---

[^1]

[^2]

For a prime $p$ and a finite group $G$, the *fusion system* of $G$ over a Sylow $p$-subgroup $S$ of $G$ isthat the analogy for a group $G$ is “subgroups of $G$ that contain $O^{p'}(G)$”, not arbitrary subgroups of index prime to $p$ in $G$. For example, the fusion system of $S$ is not, in general, of index prime to $p$ in an arbitrary fusion system $\calf$ over $S$.

\[d:p’-index\] 2 Let $\calf$ be a saturated fusion system over a finite $p$-group $S$.

[@AKO Theorem I.7.7.d] Let $O^{p'}_*(\calf)\subseteq\calf$ be the fusion subsystem (not necessarily saturated) generated by the groups $O^{p'}({\Aut_{\calf}}(P))$ for all $P\le S$, and set $$\begin{aligned}
    {\Aut_{\calf}}^0(S) &= {{\bigl\langle}\alpha\in{\Aut_{\calf}}(S) \,\big|\,
    \alpha|_P\in \Hom_{O^{p'}_*(\calf)}(P,S),
    ~\textup{some $P\in\calf^c$} {\bigr\rangle}} \\
    {\Gamma_{p'}(\calf)} &= {\Aut_{\calf}}(S)/{\Aut_{\calf}}^0(S).
    \end{aligned}$$

A fusion subsystem $\cale\le\calf$ has *index prime to $p$* in $\calf$ if $\cale$


of index prime to $p$ are summarized as follows.

\[p:thetaF\] 2 The following hold for each saturated fusion system $\calf$ over a finite $p$-group $S$.

There is a unique multiplicative map $\theta_\calf{\colon}\Mor(\calf^c)\too{\Gamma_{p'}(\calf)}$ whose restriction to ${\Aut_{\calf}}(S)$ is the natural surjection. Also, $\theta_\calf$ is strongly multiplicative, and is universal in the following sense: if $\Gamma$ is a group and $\theta{\colon}\Mor(\calf^c)\too\Gamma$ is strongly multiplicative, then there is a unique homomorphism $f{\colon}{\Gamma_{p'}(\calf)}\too\Gamma$ such that $\theta=f{\mathchoice
    {\mathbin{\scriptstyle\oldcirc}}{\mathbin{\scriptstyle\oldcirc}}
    {\mathbin{\scriptscriptstyle\oldcirc}}
    {\mathbin{\scriptscriptstyle\oldcirc}}}\theta_\calf$.

There is a bijection $$\bigl\{ \textup{subgroups of ${\Gamma_{p'}(\calf)}$} \bigr\}
    {\overset{\cong}{{\;{\count255=0 \loop \relbar\mathrel{\mkern-6mu}    \advance\count255 by1\ifnum\count255<5\repeat\rightarrow}\;}}}
    \left\{ \parbox{50mm}{\rm saturated fusion subsystems $\cale\le\calf$
    of index prime to $p$} \right\}$$ that sends $H\le{\Gamma_{p'}(\calf)}$ to the fusioncertain full subcategories are also universal among *strongly* multiplicative maps.

\[p:pi1(Fcr)\] Let $\calf$ be a saturated fusion system over a finite $p$-group $S$, let $\scrp\subseteq\calf^c$ be a family of subgroups closed under $\calf$-conjugacy and containing $\calf^{cr}$, and let $\calf^\scrp\subseteq\calf^c$ be the full subcategory with object set $\scrp$. Then $$\theta_\calf^{\scrp} = \theta_\calf|_{\Mor(\calf^{\scrp})}
    {\colon}\Mor(\calf^{\scrp}) {\overset{}{{\;{\count255=0 \loop \relbar\mathrel{\mkern-6mu}    \advance\count255 by1\ifnum\count255<5\repeat\rightarrow}\;}}} {\Gamma_{p'}(\calf)}$$ is universal among all strongly multiplicative maps $\Mor(\calf^{\scrp})\too\Gamma$.

Let $\theta{\colon}\Mor(\calf^{\scrp})\too\Gamma$ be the universal strongly multiplicative map, and let $f{\colon}\Gamma\too{\Gamma_{p'}(\calf)}$ be such that $f{\mathchoice
    {\mathbin{\scriptstyle\oldcirc}}{\mathbin{\scriptstyle\oldcirc}}
    {\mathbin{\scriptscriptstyle\oldcirc}}
    {\mathbin{\scriptscriptstyle\oldcirc}}}\theta=\theta_\calf^{\scrp}$. In particular, $\theta(O^{p'}({\Aut_{\calf}}(P)))=1$ for all $P\in\scrp$ and $\Gamma={{\langle}\theta(\Mor(\calf^{\scrp})){\rangle}}$. Also, $f$ is onto since $\theta_\calf^\scrp$ is onto.

Set $\cale={{\langle}\theta^{-1}(1){\rangle}}$: the smallest fusion system over $S$ containing all morphisms in $\theta^{-1}(1)$. Thus $\cale\supseteq


few cases.

\[d:hyp(F)\] Let $\calf$ be a saturated fusion system over a finite $p$-group $S$.

The *hyperfocal subgroup* of $\calf$ is defined as follows: $$\hyp(\calf) = {{\bigl\langle} g^{-1}\alpha(g) \,\big|\, g\in P\le S, ~
    \alpha\in O^p({\Aut_{\calf}}(P)) {\bigr\rangle}}.$$

A fusion subsystem $\cale\le\calf$ over $T\le S$ has *$p$-power index* in $\calf$ if $T\ge\hyp(\calf)$, and for all $P\le T$, $\Aut_\cale(P)\ge O^p({\Aut_{\calf}}(P))$.

By [@BCGLO2 Theorem 4.3] or [@AKO Theorem I.7.4], for each saturated fusion system $\calf$ over $S$ and each $T\le S$ containing $\hyp(\calf)$, there is a unique saturated fusion subsystem $\calf_T$ over $T$ of $p$-power index in $\calf$, and $\calf_T={{\langle}\Inn(S),O^p({\Aut_{\calf}}(P))\,|\,P\le T{\rangle}}$ by the second reference.

\[l:Op’Op<Op’\] 2 Let $\cale\le\calf$ be saturated fusion systems over finite $p$-groups $T\le S$, where $\cale$ has $p$-power index in $\calf$ and $T$ is normal in $S$. Then $O^{p'}(\cale)\leand lies in $\Inn(S)$. So $f_1$ is injective, and ${\Gamma_{p'}(\calf)}$ is isomorphic to a subquotient of ${\Gamma_{p'}(\cale)}$.

The next lemma is useful when comparing subsystems of index prime to $p$ in a simple group with those in its quasisimple coverings.

\[mod-Z(F)\] 2 Let $\calf$ be a saturated fusion system over a finite $p$-group $S$. Then for each central subgroup $Z\le Z(\calf)$, we have $O^{p'}(\calf/Z)=O^{p'}(\calf)/Z$ and ${\Gamma_{p'}(\calf/Z)}\cong{\Gamma_{p'}(\calf)}$. Thus if $\calf=\calf_S(G)$ for a finite group $G$, then for $Z\le Z(G)$, we have ${\Gamma_{p'}(\calf_{SZ/Z}(G/Z))}\cong{\Gamma_{p'}(\calf)}$.

Assume $P\in\calf^{cr}$, and consider the subgroup $\Delta=\{\alpha\in{\Aut_{\calf}}(P)\,|\,[\alpha,P]\le Z\}$. All elements of ${\Aut_{\calf}}(P)$ restrict to the identity on $Z$, so $\Delta{\trianglelefteq}{\Aut_{\calf}}(P)$, and each $\alpha\in\Delta$ induces the identity on $Z$ and on $S/Z$ and hence has $p$-power order [@Gorenstein Corollary 5.3.3]. Thus $\Delta\le
O_p({\Aut_{\calf}}(P))=\Inn(P)$ since $P$ is $\calf$-radical. So if $gZ\in
C_{S/Z}(P/Z)$,


hence $$|{\Gamma_{p'}(\calf)}| \le \bigl| {\Aut_{\calf}}(A) :
    O^{p'}({\Aut_{\calf}}(A))\cdot\Aut_{O^{p'}(\cale)}(A) \bigr|.$$ In particular, $O^{p'}(\calf)=\calf$ if ${\Aut_{\calf}}(A)=O^{p'}({\Aut_{\calf}}(A))\cdot\Aut_{O^{p'}(\cale)}(A)$.

Since $O^{p'}(\cale)\le O^{p'}(\calf)$, we have $\Aut_{O^{p'}(\cale)}(A) \le \Aut_{O^{p'}(\calf)}(A) =
\Ker({\theta_{\calf}^{(A)}})$ by Lemma \[theta-F-A\](a). The other claims now follow from the surjectivity of ${\theta_{\calf}^{(A)}}$ and since $p\nmid|{\Gamma_{p'}(\calf)}|$.

If $A$ is an *abelian* subgroup that is $\calf$-centric and weakly closed, then we can say more. The next lemma will be our main tool for getting lower bounds on $|{\Gamma_{p'}(\calf)}|$ when it is nontrivial.

\[p:p’-index\] 4 Let $\calf$ be a saturated fusion system over the $p$-group $S$, and let $A{\trianglelefteq}S$ be an abelian subgroup which is $\calf$-centric and weakly closed in $\calf$. Set $$X = \{ t\in A \,|\, t^\calf\subseteq A \},$$ and assume $X\cap Z(S)\ne\{1\}$. Choose $1\ne Z\le{{\langle}X\cap Z(S){\rangle}}$, set $\cale=C_\calf(Z)$ and $\cale_0=O^{p'}(\cale)$, and let $N_0\le     \vphantom{\chi}}}(A)=A={\protect{\overset{{\mskip1mu\leaders\hrule height0.4pt\hfill\mskip1mu}}{\varphi}
      \vphantom{\varphi}}}(A)$ since $A$ is weakly closed. Then ${\protect{\overset{{\mskip1mu\leaders\hrule height0.4pt\hfill\mskip1mu}}{\chi}
      \vphantom{\chi}}}^{-1}{\protect{\overset{{\mskip1mu\leaders\hrule height0.4pt\hfill\mskip1mu}}{\varphi}
      \vphantom{\varphi}}}|_A\in{\Aut_{\calf}}(A)$, and $({\protect{\overset{{\mskip1mu\leaders\hrule height0.4pt\hfill\mskip1mu}}{\chi}
      \vphantom{\chi}}}^{-1}{\protect{\overset{{\mskip1mu\leaders\hrule height0.4pt\hfill\mskip1mu}}{\varphi}
      \vphantom{\varphi}}})|_P=\chi^{-1}(\chi\varphi)=\varphi$.

Let $\theta_0:\Aut_{\calf}(A)\too{\Aut_{\calf}}(A)/N$ be the natural map. We first extend $\theta_0$ to a strongly multiplicative map defined on $\Mor(\calf^c)$ (see Definition \[d:multiplicative\]).

Fix $\varphi\in\Mor_{\calf}(P,Q)$, where $P,Q\in\calf^c$. In particular, $P,Q\ge Z(S)\ge Z$, and $\varphi(Z)\subseteq\varphi(X\cap Z(S))\subseteq A$ by definition of $X$. By , $\varphi|_Z$ is the restriction of some automorphism $\alpha\in{\Aut_{\calf}}(A)$. If $\alpha'\in{\Aut_{\calf}}(A)$ is another automorphism for which $\alpha'|_Z=\varphi|_Z$, then $\alpha^{-1}\alpha'\in C_{{\Aut_{\calf}}(A)}(Z)\le N$, and so we can define $\theta(\varphi)=\theta_0(\alpha)=\theta_0(\alpha')$. We thus have a well defined map of sets $\theta{\colon}\Mor(\calf^c)\too{\Aut_{\calf}}(A)/N$, and $\theta|_{{\Aut_{\calf}}(A)}=\theta_0$. Clearly, $\theta$


the cases where $G\in\Lie(q)$ for $q\ne p$, using Lemmas \[l:Op’F=F:1\], and \[l:Op’F=F:2\], and \[p:p’-index\]. We first look at the case $p=2$.

\[p:2’-index\] Let $G$ be a finite simple group of Lie type in odd characteristic, fix $S\in{\textup{Syl}_{2}(G)}$, and set $\calf=\calf_S(G)$. Assume $S\nnsg\calf$. Then $O^{2'}(\calf)=\calf$, and $\calf$ is simple.

We will prove that $O^{p'}(\calf)=\calf$. Once we know this, then since no proper nontrivial subgroup of $S$ is strongly closed with respect to $G$ by [@FF Theorem 1.1], it follows by Lemma \[l:no.str.cl.\] that $\calf$ is simple.

By [@BMO2 Proposition 6.2], we can assume that $G$ satisfies Case (III.1) of [@BMO2 Hypotheses 5.1]. Hence $G\cong{\mathbb{G}}(q)$ for $q\equiv1$ (mod $4$) (i.e., a Chevalley group), or $G\cong{}^2{\mathbb{G}}(q)$ for ${\mathbb{G}}=A_n$, $D_n$, or $E_6$ and $q\equiv1$ (mod $4$). So by [@BMO2 Lemma 5.3], there is a centricformulas for the orders of these groups, $$\begin{aligned}
    v_p\bigl(|\GL_{n+1}(q):\GL_{n}(q)|\bigr) &= v_p(q^{n+1}-1) \\
    v_p\bigl(|\GL_{2n}(q):\Sp_{2n}(q)|\bigr) &=
    \textstyle\sum_{i=1}^nv_p(q^{2i-1}-1) \\
    v_p\bigl(|\GL_{2n+1}(q):\SO_{2n+1}(q)|\bigr) &=
    \textstyle\sum_{i=1}^{n+1}v_p(q^{2i-1}-1) \\
    v_p\bigl(|\GL_{2n}(q):\GO_{2n}^{\varepsilon}(q)|\bigr) &=
    v_p(q^n+{\varepsilon})\cdot\textstyle\sum_{i=1}^{n}v_p(q^{2i-1}-1) \\
    v_p\bigl(|\SO_{2n}^{\varepsilon}(q):\SO_{2n-1}(q)|\bigr) &= v_p(q^n-{\varepsilon})
    \end{aligned}$$ (see, e.g., [@Taylor pp. 19, 70, 141]).

\[equiv-simp-2\] Fix an odd prime $p$ and a prime power $q$ such that $p\nmid q$. Let $q^\vee$ be a prime power such that $q^\vee\equiv-q$ (mod $p$) and $v_p((q^\vee)^{p-1}-1)=v_p(q^{p-1}-1)$. Then

$\PSU_n(q)\sim_p \PSL_n(q^\vee)$ for all $n$;

$\varOmega_{2n}^{\varepsilon}(q) \sim_p \varOmega_{2n}^{(-1)^n{\varepsilon}}(q^\vee)$ for all ${\varepsilon}\in\{\pm1\}$ and all $n$;

$E_6(q) \sim_p {\def\test{E}\def\tst{G}\ifx\test\tst{{}^{2}E_{6}}
\else{{}^{2}\!E_{6}}\fi}(q^\vee)\sim_p F_4(q^\vee)$; and

${\mathbb{G}}(q) \sim_p {\mathbb{G}}(q^\vee)$ when ${\mathbb{G}}=\varOmega_{2n+1}$ or $\Sp_{2n}$ for $n\ge2$, or ${\mathbb{G}}=G_2$, $F_4$, $E_7$, or $E_8$.

These are


symplectic, or orthogonal.

**Case 1:** Assume $q\equiv\pm1$ (mod $p$). If $G=\PSL_n(q)$ and $q\equiv1$ (mod $p$), then $O^{p'}(\calf)=\calf$ by Proposition \[p:p’-ind-1\](a). If $G=\PSL_n(q)$ and $q\equiv-1$ (mod $p$), so that $\ord_p(q)=2$, then set $k=[n/2]$. We have $$G \sim_p \GL_n(q) \sim_p \GL_{2k}(q) \sim_p \GO_{2k}^{\varepsilon}(q)$$ for ${\varepsilon}=(-1)^k$ by Lemma \[equiv-simp-1\](a,d). Also, $O^{p'}(\calf)$ has index $2$ in $\calf$ by Proposition \[p:p’-ind-1\](a,d), and it is realized by the simple group ${\textit{P}\varOmega}_{2n}^{\varepsilon}(q)$ by Table \[tbl:m-mu-theta\] and Lemma \[theta-F-A\](c).

If $G$ is one of the groups $\PSp_{2n}(q)$ or $\varOmega_{2n+1}(q)$ for $q\equiv\pm1$ (mod $p$), or ${\textit{P}\varOmega}_{2n}^{\varepsilon}(q)$ for $q\equiv\pm1$ and $q^n\not\equiv{\varepsilon}$ (mod $p$), then a similar argument shows that $O^{p'}(\calf)$ has index $2$ in $\calf$ and is realizable by a simple orthogonal group. If $G={\textit{P}\varOmega}_{2n}^{\varepsilon}(q)$ where $q\equiv\pm1$ and $q^n\equiv{\varepsilon}$ (mod $p$), then $O^{p'}(\calf)=\calf$ by Proposition \[p:p’-ind-1\](c).

Thus $O^{p'}(\calf)$ is realizable (and& G(m,1,\kappa) & G\sim_p\PGO_{2n'}^{\varepsilon}(q) &
    {\textit{P}\varOmega}_{2n'}^{\varepsilon}(q) & \PGO_{2n'}^{\varepsilon}(q){{\langle}\psi_{q_0}{\rangle}}
    \end{array}$$

Thus in all three cases, G(m,m,) = \_[O\^[p’]{}()]{}(A) \_(A) G(m,1,) = \_[G\_1]{}(A), \[e:G<Aut<G\] where the second inequality follows from . Hence \_(A)G(m,1,) = G(m,r,) \[e:G(m,r,k)\] If $r>2$, then $\cale$ is exotic by Lemma \[l:exotic\], and $\cale\ngeq\calf_0$ since $\Aut_{\calf_0}(A)=G(m,\gcd(m,2),\kappa)$.

Now assume $r\le2$, and hence that $\Aut_\cale(A)\ge\Aut_{\calf_0}(A)$. By , there is $H\le G_1$ such that $G_0{\trianglelefteq}H$ and $\Aut_H(A)=\Aut_\cale(A)$. Since $O^{p'}(\calf_S(H))=O^{p'}(\calf_0)=O^{p'}(\cale)$, we have $\cale\cong\calf_S(H)$ by Lemma \[Op’F1=Op’F2\].

We claim that this is, in fact, an equality (and hence that $\cale\ge\calf_0$). Set $\Gamma=\Aut_{O^{p'}(\calf)}(A)=G(m,m,\kappa)$ and $\Gamma_0=O_{p'}(\Gamma)\cong(C_m)^{\kappa-1}$ for short. The five-term exact sequence for the cohomology of $\Gamma$ as an extension of $\Gamma_0$ by $\Gamma/\Gamma_0$ (see [@Benson2 p. 110]) restricts to an exact sequence 0 3 H\^1(;A) 3 \[e:H1=0\] in


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D. Benson, Representations and cohomology II: cohomology of groups and modules, Cambridge Univ. Press (1991)

C. Broto, N. Castellana, J. Grodal, R. Levi, & B. Oliver, Subgroup families controlling $p$-local finite groups, Proc. London Math. Soc. 91 (2005), 325–354

C. Broto, N. Castellana, J. Grodal, R. Levi, & B. Oliver, Extensions of $p$-local finite groups, Trans. Amer. Math. Soc. 359 (2007), 3791–3858

C. Broto, & J. M[ø]{}ller, Chevalley p-local finite groups.of 3, 6, 12, 24 or 36 μg/kg in 10 minutes, followed by 24-hour continuous infusions at rates of 0.05, 0.1, 0.2, 0.4 and 0.6 μg/kg/min, dose-dependent increases of cardiac output and stroke volume together with a rapid decreases of pulmonary capillary wedge pressure and right atrial pressure were measured. Slight heart rate increases and reductions in mean blood pressure were also seen. Calculated peripheral vascular resistance was linearly reduced with increasing doses. Protocol defined dose limiting events were tachycardia \>20% and systolic blood pressure \<90 mmHg, mainly in patients receiving higher doses of 0.4 and 0.6 μg/kg/min. Headaches and nausea also occurred in some cases. Based on this study infusion rates of 0.05 to 0.2 μg/kg/min were recommended to achieve favorable hemodynamic effects with good tolerance.

Clinical trials


occurred under dobutamine than under levosimendan,[@b4-dddt-3-073] p \< 0.023, while hypotension was observed in 9 patients under levosimendan compared to 4 under dobutamine (p = 0.252). Thus, there was an overall advantage of levosimendan in this trial.

The second randomized clinical trial (RUSSLAN) compared levosimendan, infused for 6 hours in 4 different doses, with placebo in 504 patients with clinical and radiological signs of left ventricular failure following an acute myocardial infarction.[@b28-dddt-3-073] The primary aim was to test the tolerability of levosimendan with the end-points hypotension and myocardial ischemia. Secondary end-points included all cause mortality and worsening HF. At doses of 0.1 to 0.2 μg/kg/min levosimendan did not increase the incidence of hypotension or ischemia and reduced the combined risk of death and worsening HF during the first 24patients for 24 hours; the average dose of dobutamine was 6 μg/kg/min. Patients were hospitalized at intensive care units but not invasively monitored. Also in this trial iv diuretics and concomitant vasodilators were allowed. The primary end-point was survival at 180 days. At the end of follow up there were 173 deaths (26%) in the levosimendan group as compared to 185 (28%) on placebo (p = 0.4). However, a subgroup analysis at 31 days showed a survival advantage of levosimendan in patients with a prior history of heart failure. Also plasma BNP levels decreased significantly more at 24 hours and at 3 to 5 days after levosimendan than after dobutamine. The rates of serious adverse events were not different in the two treatments groups, but there were more


           .withA("some String")
            .withB("some String")
            .withKeyValue(new KeyValue("A", "B"))
            .withKeyValue(new KeyValue("C", "D"))
            .build();

Obviously using this over the static varargs method in your question is largely a stylistic choice

High efficiency filters are used for capturing, removing and/or eliminating hazardous bacteria, viruses and other undesirable matter from fluids, and more particularly from the flow of gases such as air, oxygen and the like in environments in which the purity of the gases is critically sensitive and must not contain contaminants or other forms of pollutants.


Extreme crustal oxygen isotope signatures preserved in coesite in diamond.
The anomalously high and low oxygen isotope values observed in eclogite xenoliths from the upper mantle beneath cratons have been interpreted as indicating that the parent rock of the eclogites experienced alteration on the ancient sea floor. Recognition of this genetic lineage has provided the foundation for a model of the evolution of the continents whereby imbricated slabs of oceanic lithosphere underpin and promote stabilization of early cratons. Early crustal growth is thought to have been enhanced by the addition of slab-derived magmas, leaving an eclogite residuum in the upper mantle beneath the cratons. But the oxygen isotope anomalies observed in eclogite xenoliths are small relative to those in altered ocean-floor basalt and intermediate-stage subduction-zone eclogites, and this haswere convicted of murdering the teens during two separate trials. Stoltzfus and Martinolich both received life sentences in separate state prisons. On March 28, 2010, Leroy Stoltzfus died at the Select Specialty Hospital at Conemaugh Memorial Medical Center in Johnstown. Stoltzfus was 61 and had served 40 years in prison. Officials said that he had been hospitalized for a lengthy period prior to his death and died from natural causes. Robert Martinolich is still serving his life sentence at the State Correctional Institution - Laurel Highlands in Somerset, PA. He is 63 years old

Robert Martinolich, left, and Leroy S. Stoltzfus Jr., right, being escorted to their preliminary arraignment by police officers. They were eventually convicted of the murder of Glenn Eckert and Marilyn Sheckler. This picture was published


Q:

Passing C# value type by reference to avoid boxing

One way to avoid boxing in C# is to pass the value type by reference.  I have read that a generic method can also be used to avoid boxing.  Although writing a generic method solely for the purpose of avoiding boxing seems to be a little extreme - if the type will always be the same.
My question is - if writing code for the best performance and to avoid boxing, is it reasonable to pass all value types (like an int) by reference - even though the method in question is only working on the object and not creating it?  Are there any drawbacks to this?

A:

The best way to avoid boxing of value types is: just usethe barn. The man he saw at the still was later identified to him as the appellant.
Agent Brewer called to Hamner and told him that they had arrested the appellant, who, when Hamner next saw him, was in custody and wore the same clothing that the man he saw at the still had worn.
A deputy sheriff related (after testifying as to the requisite predicate of voluntariness) that after his arrest Oden told the officers:
"I carried the sugar down there. If you hadn't caught me this time you wouldn't have caught me and I just carried it for another fellow because *382 the water was up and he would have so far to go around. * * * You could make this light on me and let me pay


it off."
Appellant, in his brief, argues three points: (1) that the verdict was (a) coerced and (b) a compromise; (2) that, inasmuch as the forms of verdict suggested by the trial judge did not include any form as to count 1, there was error in receiving the verdict of the jury which expressly found Oden guilty under count 1 and not guilty under count 2; and (3) the refusal of requested written charge 35 was error.
We have considered the record as to what is alleged to constitute the coercion. It would seem that the court finished charging the jury about noon and instructed the jurors to go to lunch and return at 1:30. The record is silent until an entry of 5:15 p. m. in which we findhe hasn't sold it already?" "Not that I'm complaining." "I've had some filthy times in this state." "Don't screw this up, all right?" "Because that's our only lead on this guy." "Be thankful I haven't killed you." "Oh, yeah?" "What are you, Eliot Ness now?" "Were you upset because I screwed you?" "Don't act like you haven't done that to 10 times as many people." "All right, we're just crooks that got caught, Lincoln." "This guy, this isn't gonna work." "Why don't we all just focus on who's got Scylla?" "What do you say?" "Hey, Scofield." " Where am I?" " He's awake." "I said where am I?" "It's a house in the woods, 60 miles from anywhere." "Swept clean of weapons so you don't need to worry


works for us." "Your mother is alive." "Had to come in to look for a fight." " Hey, we don't open till 3." " Sorry, I'm just looking for someone." "I haven't got the guy's name." "Called here yesterday about three times." "New Yorker, dark hair, bits of gray." "You know where I can find him?" "Yeah, can't help you, sorry." "You sure?" "You need to check your ears, he said we don't know who you're talking about." " Is that right?" " Yeah, that's right." "Well, what about blondie?" "You got about two seconds..." " How about it?" " I don't know his name." " How about it?" " I don't know his name." "He works..." "This girl works here, he dates her." "Then you'll take me" The hell you been?" " Figuring this whole thing out." "I know who it is, the buyer." "Lawrence Wilcott." "He's been working for the Company for 10 years." " How did you figure that out?" " I still have friends on the inside." "Been putting together a profile, narrowing down candidates." "Wilcott got on a plane in Bogotá and flew to the Bahamas yesterday and got on a boat." "The guy who took Scylla, we pulled his image off security tape." "Company's running a recognition match." "Gonna take all day." "Do you know where he is now?" "With Wilcott, we need to go now." "Because better yet, I know where Wilcott's staying." "Okay, we need to move before Scylla does." "Let's go." "Let's go." " Come on."


take notice. Lord Taverne, a former financial secretary to the Treasury, accused the Home Office of presiding over “a national scandal, every bit as outrageous as the treatment of the Windrush immigrants”.

In a meeting of the same home affairs select committee, the Labour MP Naz Shah told the home secretary, Sajid Javid, that the use of 322(5) “smacks of the Windrush scandal”.

The government scrambled to limit the damage. Javid promised a review but increasing numbers of MPs were discovering they had constituents fighting paragraph 322(5) rulings. The Scottish National party MP Alison Thewliss, having found she represented at least five highly skilled migrants in such circumstances, called a debate in Westminster Hall on the issue.

Engineer deemed security threat over tax error gets visa in Home Office U-turn Readthe Xbox and ranging in price from $49-$59.

But there are other “M” games for non-shooter types like The Elder Scrolls V: Skyrim, a role-play game allowing players to create their own characters, customizing look and abilities and then adventuring to towns, cities and dungeons to combat and conquer. Skyrim is an Xbox and Playstation 3 game costing between $49 and $59.

Assassin’s Creed: Revelations is the final in a four-game series offering adult game-play in a free roaming adventure that sets the stage for a new saga. It’s immersive, epic play following a complex storyline. It’s available for Xbox and Playstation 3 and costs around $59. This game is also being released for the PC on Dec. 31.

There’s no shortage of new video games this holiday season. Determine the


away from the curtain, triumphant in their victory, without understanding that the reversal spell had switched the directions of the world! North became south, east became west...and the wrong direction became the right.

Switch

And wouldn't you know it, once the frames are separated, Stile remains in Phaze, while Blue's soul occupies an android in Proton (I'm not even going to go into the storyline about the original Blue Adept's soul...I told you this book was complicated). Stile gets to remain with his love, the Lady Blue, after all!How is this possible, you ask? By the very reversal spell that determined the match of Phazite Ball. It sent Stile and Blue to the opposite worlds they were expecting, because it's like, a reversal spell. Whether this sends everyone else tosatisfied, for example, when a police car was 100 feet behind a motorist on an otherwise-deserted road. But the court said it doesn’t apply to a driver who’s turning right on the opposite side of the street from the only other car in the vicinity, which wasn’t turning anywhere.

“Because the evidence is undisputed the officer was not and could not have been affected by the turn and there were no other motorists on the road, no violation occurred,” the court said in a 3-0 ruling. And because the stop was illegal, so was the search, and both defendants can withdraw their guilty pleas, the court said.

Deputy Attorney General Scott Taylor said his office hasn’t decided whether to appeal the ruling. Carmona’s lawyer, Jay Moller, said Carmona has already


different repeating patterns of colors (i.e., three primary colors and black) permitting the formation of multicolor images on the record medium. The images are formed by energizing the appropriate thermal elements as the desired color inks are moved into registration with the elements.
This system, however, has several practical problems. First, due to the use of a mosaic color pattern, circuitry for activating a particular color is very complicated and costly since synchronization is needed, based upon the position of a particular mosaic in two directions for achieving accurate registration. Second, such mosaics are difficult and costly to manufacture. In fact, if high resolution is desired the mosaic color dot spacing must be decreased which increases manufacturing difficulties and cost. Further, the higher resolution desired complicates the synchronization problemsBehrstock, Hagen, and Sisto [@BHS2 Question D]. As a byproduct of Theorem \[mainGraphProducts\], we extend the results of [@ABD] to show that clean containers are not only preserved by taking free and direct products, but also by graph products.

\[mainGraphProducts\] Let $\Gamma$ be a finite simplicial graph, $\mathcal{G}=\{G_v\}_{v\in V}$ be a family of hierarchically hyperbolic groups with the intersection property and clean containers. Then the graph product $\Gamma\mathcal{G}$ is a hierarchically hyperbolic group with the intersection property and clean containers.

*Clean containers* (see Remark \[container\_remark\]), a notion introduced originally by Abbott, Behrstock, and Durham [@ABD], is a technical condition that in the mapping class group setting translates into the following: if $V\subseteq S$ is a subsurface of the surface $S$, then $V$ and $S\setminus V$ are disjoint, and *any* subsurface


disjoint from $V$ is contained into $S\setminus V$. On the other hand, the intersection property is a condition that we introduce, and in the mapping class group setting means that, given two subsurfaces $V,U\subseteq S$, the subsurface $V\cap U$ is the biggest subsurface of $S$ that is contained in both $V$ and $U$. The intersection property gives to the index set $\mathfrak{S}$ the structure of a lattice. At this point, it is instructive to notice that both $V\cap U$ and $S\setminus V$ could be *non-connected* subsurfaces of $S$, and indeed the hierarchically hyperbolic structure with clean containers and the intersection property of a mapping class group $\mathcal{M}\mathcal{C}\mathcal{G}(S)$ is obtained considering all, possibly non-connected, subsurfaces of $S$.

Both properties are satisfied in all known examples of hierarchically hyperbolic spaces, in the sense $\phi$ is coarsely lipschitz;

2.  $\phi$ is a quasi-isometric embedding;

3.  the maps $\mathfrak{g}_{\phi(\mathcal{X})}\colon{\textbf F}_{\phi(S)}\to\phi(\mathcal{X})$ and $\mathfrak{g}_{{\textbf F}_{\phi(S)}}\colon\phi(\mathcal{X})\to\textbf{F}_{\phi(S)}$ are quasi-inverses of each other, and in particular quasi isometries;

4.  the subspace $\phi(\mathcal{X})\subseteq \mathcal{X}'$, endowed with the subspace metric, admits a hierarchically hyperbolic structure obtained from the one of $\mathcal{X}$ by composition with the map $\phi$ (and its induced maps at the level of hyperbolic spaces);

5.  $\pi_{W}(\phi(\mathcal{X}))$ is uniformly bounded for every $W\in\mathfrak{S}'\setminus\phi(\mathfrak{S})$.

Organisation of the paper {#organisation-of-the-paper .unnumbered}
-------------------------

The paper is organized as follows. In Section \[SectionHH\] we fix the notation, and recall all the necessary definitions and facts concerning hierarchically hyperbolic spaces and groups. In Section \[section3\] we introduce the notions of *intersection property*, of $\varepsilon$-*support*, and of *concreteness* of a hierarchically hyperbolic space (see Definition \[intersectionproperty\_definition\], Definition \[supports\],


and Definition \[concreteness\]). As already mentioned, we conjecture that all hierarchically hyperbolic spaces satisfy the intersection property. On the other hand, concreteness is a technical condition that will play a pivotal role in the proofs of Theorem \[winning\_theorem\] and of Theorem \[mainT\]. In Proposition \[concreteness\_making\] we prove that, without loss of generality, any hierarchically hyperbolic space with the intersection property can be assumed to be concrete (and this is why concreteness does not appear as an hypothesis in Theorem \[mainT\]).

In Section \[Section4\] we prove Theorem \[thmB\] of the Introduction, which is then used in the proofs of Theorem \[winning\_theorem\] and Lemma \[consequence\_winning\_theorem\]. These results will be applied repeatedly in Section \[Section5\], which is devoted to the proof of Theorem \[mainT\]. In Subsection \[trees\_with\_decorations\] we introduce a trick, which we call the *decoration* of a tree of hierarchicallythe hyperbolic spaces $\mathcal{C}W\in\mathfrak{S}$. Moreover, there exists $K$ so that all $W\in\mathfrak{S}$, the coarse map $\pi_{W}$ is $(K,K)$-coarsely lipschitz and $\pi_W(\mathcal{X})$[^1] is $K$-quasiconvex in $\mathcal{C}W$.

2.  [**(Nesting)**]{} The index set $\mathfrak{S}$ is equipped with a partial order $\sqsubseteq$ called *nesting*, and either $\mathfrak{S}$ is empty or it contains a unique $\sqsubseteq$-maximal element. When $V\sqsubseteq W$, $V$ is nested into $W$. For each $W\in\mathfrak{S}$, $W\sqsubseteq W$, and with $\mathfrak{S}_W$ we denote the set of all $V\in\mathfrak{S}$ that are nested in $W$. For all $V,W\in\mathfrak{S}$ such that $V\sqsubsetneq W$ there is a subset $\rho_W^V\subseteq \mathcal{C}W$ with diameter at most $\xi$, and a map $\rho_V^W\colon \mathcal{C}W\to 2^{\mathcal{C}V}$.

3.  \[A3\] [**(Orthogonality)**]{} The set $\mathfrak{S}$ has a symmetric and antireflexive relation $\perp$ called *orthogonality*. Whenever $V\sqsubseteq W$ and $W\perp U$, then $V\perp U$


be assumed to be uniformly coarsely surjective. Without loss of generality, we will always assume this.

\[hierarchical\_quasiconvexity\] Let $(\mathcal{X},\mathfrak{S})$ be a hierarchically hyperbolic space. A subspace $\mathcal{Y}\subseteq \mathcal{X}$ is $k$-*hierarchically quasiconvex*, for some function $k\colon [0,+\infty)\to[0,+\infty)$, if:

1.  for all $U\in\mathfrak{S}$ the image $\pi_U(\mathcal{Y})$ is a $k(0)$-quasiconvex subspace of the hyperbolic space $\mathcal{C}U$;

2.  for all $\kappa\geqslant 0$, if $x\in\mathcal{X}$ is such that $d_U(\pi_U(x),\pi_U(\mathcal{Y}))\leqslant \kappa$ for all $U\in\mathfrak{S}$, then $d_{\mathcal{X}}(x,\mathcal{Y})\leqslant k(\kappa)$.

\[remark:hierarchical\_quasiconvexity\] It is extremely important to stress that, in [@BHS2], a hieromorphism $\phi\colon (\mathcal{X},\mathfrak{S})\to(\mathcal{X}',\mathfrak{S}')$ is called quasiconvex if $\phi(\mathcal{X})$ is a $k$-hierarchically quasiconvex subspace of $\mathcal{X}'$ - in the sense of Definition \[hierarchical\_quasiconvexity\] - *and* $\phi$ is already a quasi-isometric embedding (compare [@BHS2 Definition 8.1]).

In this work, by $k$-hierarchically quasiconvex hieromorphism we just mean a hieromorphism whose image is aimmediate consequence of it:

Let $M$ be a closed $3$-manifold that does not have a $Sol$ or $Nil$ component in its prime decomposition. Then $\pi_1(M)$ is a hierarchically hyperbolic space with the intersection property and clean containers.

The fact that $\pi_1(M)$ is a hierarchically hyperbolic space is proved in [@BHS2 Theorem 10.1], and it has clean containers by [@ABD Proposition 3.5]. Hierarchical hyperbolicity is proved, for closed non-geometric *irreducible* $3$-manifolds, by constructing a tree of hierarchically hyperbolic spaces where supports are uniformly bounded (therefore, by [@BHS2 Lemma 8.20], comparison maps are uniform quasi isometries), and where vertex spaces are direct products ${\mathbb R}_v\times \Sigma_v$. Here, ${\mathbb R}_v$ is a copy of the real line, and $\Sigma_v$ is the universal cover of a hyperbolic surface with totally geodesic boundary, whose hierarchically


into $T_{[V]}\cap T_{[W]}$.

By definition of nesting, we have that $[U]\perp [V]$ and $[U]\perp [W]$, and therefore, by Lemma \[clean\_containers\_use\], we have that $[U]\perp \bigl([V]\vee[W]\bigr)=[V\vee W]$, that is $[U]\sqsubseteq T_{[V\vee W]}=T_{[V]}\cap T_{[W]}$.

If $T_{[V]}\cap T_{[W]}=\emptyset$, then there is no element $S\in\mathfrak{S}_2$ that is nested in both $T_{[V]}$ and $T_{[W]}$. The wedge between these two elements of the index set is $$\label{equation_intersection_final}
\begin{aligned}
T_{[V]}\wedge T_{[W]}&=\bigvee \bigl\{[U]\mid [U]\sqsubseteq T_{[V]}\text{ and } [U]\sqsubseteq T_{[W]}\bigr\}\\
&=[{\text{cont}}_{\perp}{V_v}]\wedge[{\text{cont}}_{\perp}{W_w}]
\end{aligned}$$ Notice that any $[U]$ as in Equation will be supported on the geodesic $\sigma$ connecting $T_{[V]}$ to $T_{[W]}$.

[**(Orthogonality)**]{} We first prove that if $T_{[V]}\sqsubseteq T_{[W]}$ and $T_{[W]}\perp [U]$, then $ T_{[V]}\perp [U]$. As $[U]\perp T_{[W]}$, we have that $T_{[W]}\subseteq T_{[U]}$. Therefore $T_{[V]}\subseteq T_{[U]}$, that is $[U]\perp T_{[V]}$. The analogous case of three equivalence classes satisfying the relations $[V]\sqsubseteq [W]$ and $[W]\perpin $\widehat T$ connecting $x$ to $\rho_{T_{[W]}}^{[V]}$ passes through the set $T_{[W]}\setminus T_{[V]}$. In this case, we have that $\pi_{[V]}(x)=\pi_{[V]}\bigl(\pi_{T_{[W]}}(x)\bigr)$ is equal to $\rho_{[V]}^{T_{[W]}}\bigl(\pi_{T_{[W]}}(x)\bigr)$. Therefore the consistency inequality is satisfied also in this case.

[**(Finite complexity)**]{} It is enough to show finite complexity in $\mathfrak{S}_1$ and $\mathfrak{S}_2$ independently.

Finite complexity in $\mathfrak{S}_1$ follows from [@BHS2 Lemma 8.11]. For $\mathfrak{S}_2$, notice that any chain of proper nestings $$T_{[U_1]}\sqsupsetneq T_{[U_2]}\sqsupsetneq \dots \sqsupsetneq T_{[U_n]}$$ induces the corresponding chain of proper nestings $[U_1]\sqsubsetneq [U_2]\sqsubsetneq\ldots\sqsubsetneq[U_n]$ in $\mathfrak{S}_1$, by Corollary \[reverse\_nesting\_blue\].

As only equivalence classes are allowed to be nested into an intersection of supports, and not vice versa, finite complexity is proved.

In particular, it follows that the complexity of $\bigl(\mathcal{X}(\mathcal{T}),\mathfrak{S}\bigr)$ is twice the complexity of $\mathfrak{S}_1$ plus one, and the complexity of $\mathfrak{S}_1$ is $\max_v\chi_v +1$,


would imply that $X_j\cap\sigma$ is contained in either $(X_{k_1}\cup X_{k_s})\cap\sigma$ or $(X_{k_r}\cup X_{k_s})\cap\sigma$. As a consequence we obtain that $X_{k_s}\cap\sigma\subseteq X_j\cap\sigma$, which is a contradiction, since $X_{k_s}$ is maximal with respect to nesting.

From here we can conclude that $\lvert Y_{max}\rvert\leq d_{T_{[W]}}(\pi_{T_{[W]}}(x),\pi_{T_{[W]}}(x'))$. Indeed, given any $\sqsubseteq$-maximal element $X_i\in Y_{max}$ and its cone point $v_i$, the following dichotomy holds: either $v_i$ is a vertex in the geodesic path $\widehat{\sigma}$, or not. In the latter case, it must be that $\widehat \sigma$ contains either one or two edges of the support $X_i$. Therefore, the bound is proved.

Therefore, if $d_{T_{[U]}}(\pi_{T_{[U]}}(x),\pi_{T_{[U]}}(x'))>4$ for some $T_{[U]}\in\mathfrak{S}_{T_{[W]}}\setminus\{T_{[W]}\}$, that is $T_{[U]}\in Y$, then $T_{[U]}\sqsubseteq X$ for some $\sqsubseteq$-maximal element $X$ of the set $Y$.

We now address the case when $X$ is an equivalence classes $X=[V]\in\mathfrak{S}_{T_{[W]}}$. By definition,K$, that $d_{S}\bigl(\pi_{S}(x),\pi_{S}(y) \bigr)\leqslant K$ for all $S\in \mathfrak{S}_2$, and that $d_{[V]}\bigl(\pi_{[V]}(x),\pi_{[V]}(y) \bigr)\leqslant K$ for all $[V]\in\mathfrak{S}_1$.

Suppose that the distance in $\widehat T$ from $\pi_{\widehat T}(x)$ to $\pi_{\widehat T}(y)$ is realized by a path only consisting of vertices of $T\subseteq \widehat T$, and let $$v_0=\pi_T(x),v_1,\dots,v_{k-1},\pi_T(y)=v_k,$$ be these vertices, where $k\leqslant K$. In particular, no four consecutive vertices can belong to the same support tree, because this would produced a shorter path in $\widehat T$ joining $x$ to $y$.

We have that $d_{\mathcal{X}}(x,y)\leqslant\sum_{i=0}^kd_{\mathcal{X}_{v_i}}\bigl(\mathfrak{g}_{v_i}(x),\mathfrak{g}_{v_i}(y)\bigr)+k$. Moreover, for all $i=0,\dots, k$ we have that the distance $d_{\mathcal{X}_{v_i}}\bigl(\mathfrak{g}_{v_i}(x),\mathfrak{g}_{v_i}(y)\bigr)$ is uniformly bounded. Indeed, if this is not the case, by Uniqueness in the hierarchically hyperbolic space $(\mathcal{X}_{v_i},\mathfrak{S}_{v_i})$, there exists $V\in\mathfrak{S}_{v_i}$ such that $d_V\bigl(\pi_V(\mathfrak{g}_{v_i}(x)),\pi_V(\mathfrak{g}_{v_i}(y))\bigr)$ is not bounded. By [@BHS2 Lemma 8.18] and Theorem \[thmB\], we have


Let $G_e$ be the edge group, and let $\phi_v(G_e)$ and $\phi_w(G_e)$ be its (hierarchically quasiconvex) images into the vertex groups. By [@Sp1 Theorem 1], the subgroup $\phi_v(G_e)$ induces a hierarchically hyperbolic structure $\mathfrak{S}^0$ on $G_v$, given by cosets of certain quasiconvex subgroups (up to finite Hausdorff distance). To obtain a full hieromorphisms $\phi_v$, we are forced to induce on the edge group $G_e$ the hierarchical structure $\mathfrak{S}^0_{\phi_v(G_e)}$. On the other hand, $\mathfrak{S}^0_{\phi_v(G_e)}$ induces on the other vertex group $G_w$ a new hierarchical structure $\mathfrak{S}^1$, and to make the hieromorphism $\phi_w$ full, we need to enrich the structure of the edge group $G_e$ with all the (possibly new) cosets that appear in $\mathfrak{S}^1_{\phi_w(G_e)}$, and so on.

If this process stabilizes after a finite number of times, then the groups canEquation .

Any element of $\mathfrak{S}_1$ is an equivalence class $[V]$, equipped with a favourite representative $V_w$ in the Bass-Serre tree $T$ for which $\mathcal{C}[V]=\mathcal{C}V_w$. On the other, any element of $\mathfrak{S}_2$ is a support tree $T_{[V]}$, and the metric space $\mathcal{C}T_{[V]}$ is the tree $T_{[V]}$ in which all properly contained support trees $T_{[W]}$ are coned-off.

For each $[V]\in\mathfrak{S}_1$, the projection $\pi_{[V]}$, as defined in Equation and Equation , is $$\pi_{[V]}(x)=\begin{cases}
\mathfrak{c}_w\circ\pi_{V_w}(x),&\quad \forall x\in \mathcal{X}_v,\ v\in T_{[V]};\\
\mathfrak{c}_{e^+}\circ\pi_{V_{e^+}}(\phi_{e^+}(\mathcal{X}_e)),&\quad
\forall x\in \mathcal{X}_v,\ v\notin T_{[V]},
\end{cases}$$ where $e=e(v)$ is the last edge in the geodesic connecting $v$ to $T_{[V]}$ such that $e^+\in T_{[V]}$, and the maps $\mathfrak{c}_w$ and $\mathfrak{c}_{e^+}$ denote the appropriate comparison maps to the favorite representative of $[V]$.

Let $x\in\mathcal{X}_v\subseteq\mathcal{X}$ and let $T_{[V]}\in\mathfrak{S}_2$. Then, $\pi_{T_{[V]}}(x)$ is defined as the composition of the closest point projection


hierarchically hyperbolic group. Therefore, the consistent tuple $\vec{c}$ admits a realization point $z\in G_{\Gamma\setminus\{v\}}$, and thus we obtain that $\pi_{[V]}(z)\asymp b_{[V]}$ for every $[V]\in\mathfrak{S}_1$. Furthermore, since $\pi_{T_{[V]}}(G_{\Gamma\setminus\{v\}})$ is a point, we also have that $\pi_{T_{[V]}}(z)=b_{T_{[V]}}=\pi_{T_{[V]}}(G_{\Gamma\setminus\{v\}})$ for every $T_{[V]}\in\mathfrak{S}_2$. That is, the second condition of hierarchical quasiconvexity is proved, and the inclusion $G_{\Gamma\setminus\{v\}}\hookrightarrow G_{\Gamma}$ is a hierarchically quasiconvex hieromorphism.

Moreover, for each $V\in\mathfrak{S}_{\Gamma\setminus\{v\}}$ the map $\mathcal{C}V\to\mathcal{C}[V]$ is an isometry. Note that, if an element $[V]\sqsubseteq i^{\lozenge}(U)=[U]$, where $U\in\mathfrak{S}_{\Gamma\setminus\{v\}}$, then $T_{[U]}\subseteq T_{[V]}$. By assumption $\alpha\in T_{[U]}$, and therefore $\alpha\in T_{[V]}$ and there exists $V\in\mathfrak{S}_{\Gamma\setminus\{v\}}$ such that $i^{\lozenge}(V)=[V]$.

Thus, we proved that all induction hypotheses are satisfied by the inclusion $G_{\Gamma\setminus\{v\}}\hookrightarrow G$, that is that the embedding is a full, hierarchically quasiconvex hieromorphism, which induces isometries at the level of hyperbolic spaces.

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Apart from DJ Iyce moving from hospital to the other to educate people about the awareness of heart attack, there will be a concert which will feature musicians such as Kwabena Kwabena, Bisa Kdei, Reggie Rockstone to create the awareness.
According to DJ Iyce, not many people are aware of the causes of heart attack which is killing most people in Ghana now.
“Come first week IN September my team and I togetherLuke indicated that this rule of Jesus would be over the whole house of Jacob (καὶ βασιλεύσει ἐπὶ τὸν οἶκον Ἰακὼβ) forever (εἰς τοὺς αἰῶνας). No longer would it just be Judah or Judea, but all the tribes of Israel, or the sons of Jacob, would be reunited. This sounds like a political and religious unification of Israel. However, there would be no end to his kingdom (καὶ τῆς βασιλείας αὐτοῦ οὐκ ἔσται τέλος), since this was not a temporary rule, but an eternal one. The house of Israel would be united under Jesus forever. It did not exactly work out that way.


studied in a condition without task relevance as well as in a task-relevant condition. ADDH children showed smaller P3 amplitudes and (marginally) smaller MMN to auditory deviant stimuli, irrespective of task relevance, so smaller P3s in ADDH children are due to stimulus deviancy per se. In the visual modality the P3 effect failed to reach significance. Because the smaller P3s were also found in a condition not requiring task-related motivation, recent motivational interpretations of differences with normal children are not supported. ADDH children also showed smaller P1 amplitudes than normal children to all stimuli except visual novels. The ERP differences were unrelated to performance, since both groups performed equally well.
Ditch the GPS - lelf
https://www.washingtonpost.com/opinions/ditch-the-gps-its-ruining-your-brain/2019/06/05/29a3170e-87af-11e9-98c1-e945ae5db8fb_story.html
======
dmytroi
I'm learning how to fly, and tell you what, cognitive overload is real. At
first students have a hard time to coupe with stick/pedals, airspeed indicator
and looking around for positioning / avoiding other planes. Having a "moving
map" that tells you in which airspace you are exactly and where you're going -
priceless. Simply because beginner students don't have cognitive capability to
comprehend everything at a same time. And as experience grows, cognitive load
required decreases, so people have easier time to read paper maps as they
progress. That being said, in emergency fewer things to worry - the better. If
primary instruments fail (airspeed / attitude / etc), one doesn't have mental
capability to deal with instrument failures AND deal with paper maps at a same
time.

This is directly transferable to road


is any good at all), listening to the radio (assuming they don't
read well written full length books on the radio) is not.

~~~
TillE
Radio dramas have been extremely popular in many places since forever. So have
"books on tape". It's utterly bizarre to make these kinds of accusations.

~~~
jacquesm
What's bizarre about it? Driving is a full-time occupation, not a part-time
occupation. If you have to do it do it responsibly.

In complex situations listening to audiobooks is a dangerous affair, in simple
situations it may improve attention but simple situations can turn complex in
a hurry in a moving vehicle.

[https://www.ncbi.nlm.nih.gov/pubmed/29223795](https://www.ncbi.nlm.nih.gov/pubmed/29223795)

------
thdrdt
I never use a GPS because I just look on the map, remember where my
destination is, and drive to it.

But even before GPS there were a lot of people who could not navigate. For
those people it isI’m going to do it in C or python C-Types, I may as well tell people about it though. The example is in the download. We could also use this type of an approach to examine and fuzz particular APIs with Python C-Types.

So, if we’re targeting an undocumented API that is exported with a descriptive name, we need to breakpoint on the interesting inter-modular call. Then we let the code run. When we hit the breakpoint, we can examine the stack and register state. This should let us get an idea of how to prototype the function. Another interesting use for examining things in a debugger would be if you wanted to…I don’t know…add a certificate to the local store like you would with certmgr.exe. Think SSL man-in-the-middle


Court of Appeals erred. We are of opinion that the Commission's suspension order of December 27, 1989 should be reinstated.
When interpreting Code § 65.1-43, or any other statute, we follow the settled rule that the construction accorded a statute by public officials charged with its administration is entitled to be given weight by the courts. Peyton v. Williams, 206 Va. 595, 600, 145 S.E.2d 147, 151 (1965). Indeed, the Court of Appeals has said that the Commission's construction of the Workers' Compensation Act should be given "great" weight. Graham v. Peoples Life Ins. Co., 7 Va.App. 61, 68, 372 S.E.2d 161, 165 (1988).
As we understand the Commission's approach, once the employee's net third-party recovery is determined, the employee will be entitled to payment of no further compensation ormedical expenses subsequent to the date fixed in the suspension order until the employee can establish that further benefit entitlements exceed the net amount received by the employee from the third-party recovery. As we read the suspension order in this case ("if and when this net is used toward compensation benefit"), the Commission has not foreclosed the payment of attorney's fees in increments as medical expenses and compensation benefits accrue during the suspension period. The Commission's method foreshadowed and is consistent with Bower, and does not eliminate use of the Hunter approach, adopted by the Court of Appeals.
Criticizing incremental administration of the payment of attorney's fees as "pay-as-you-go" and "litigate-as-you-go," the employer contends that if compensation entitlement must be determined periodically, rather than at the end of the


the midsummer festival, Kekri, a celebration of harvest and the ancestors, and Joulu, the midwinter festival.

Some Finnish Neopagans visit sacred forests, where wooden god-images or sacred stones can sometimes be found. Some celebrate the circling of the year at certain dates, for example by burning bonfires, dancing, sacrificing, or making other kinds of rituals. One ritual, which is also an authentic practice of the ancestors, is to drink a toast for the thunder god Ukko at the midsummer festival (Finnish: Ukon juhla).

See also

 Estonian mythology
 Kalevala

Uralic religions
 Estonian Neopaganism
 Mari Neopaganism
 Mordvin Neopaganism
 Udmurt Vos

Chuvash religion
 Vattisen Yaly

Baltic religions
 Dievturi
 Romuva
 Druwi

Slavic religions
 Rodnovery

Notes

Resources
 Ala-Huissi, Jaana: Maauskoisilla on jääkauden kalenteri. Helsingin Sanomat, 20.3.2010. Sanoma News.
 Arola, Iiro: "Ni sit mä tajusin, et on muitakin kuin minä” – Suomenuskoistenplurality of application servers for invoking the plurality of component service instances, wherein the plurality of component service instances are associated to the composite service instance, and sending a first service report comprising an information about the composite service instance to a service supervision system, wherein this information enables the service supervision system to identify reports about the component service instances as being associated to the composite service instance. The service supervision system may be used for charging and billing the user for the composite service(s) provided. For instance for an offline charging, the service composition node might generate a so-called Charge Data Record (CDR) that is transferred to the service supervision system. The CDR might contain the ID of the composite service instance and the IDs of


studied integer-based flaws, but this is the first work to consider those introduced solely from the migration to 64-bit. Another thing to add to the ever-growing worry list!

Where do integer related vulnerabilities come from?

Many software vulnerabilities are rooted in subtleties of correctly processing integers, in particular, if these integers determine the size of memory buffers or locations in memory. Leveraging these flaws, an attacker can trigger buffer overflows, write to selected memory locations, or even execute arbitrary code.

In standard C there are 5 different integer base types: char , short , int , long , and long long , and these come in both signed and unsigned variations. Unsigned types hold only positive numbers, and thus can store larger positive numbers than their signed counterparts which can storesignedness issues, for example using a signed variable of type int to specify the amount of memory to copy with memcpy . Dormant integer overflows – e.g loops using variables of size_t that increment or decrement an (unsigned) int in their loop body. Dormant signedness issues, e.g. calls to strlen that do not take a string literal, and assign the return value to an (unsigned) int . Unexpected behaviour of library functions, e.g. calls to snprintf that make use of the return value.


the data program operation, difference in the program speed between the memory cells connected to the selected word line is increased, and the repeated number of the program and verify operations is increased. Thus, there is a problem that the program speed is reduced. In the NAND type flash memory, there exists difference in the program time of about 2 order between the memory cells within the selected word line. In a conventional mode in which program pulses of the same pulse voltage values and the same pulse time widths are simply repeatedly applied, it is required that the number of the program and verify be performed about by 100 times. In this case, time taken to switch the voltage of the program operation and the verify readmay be one
in ten. It's for sure not as low as the data from the surveys show.
Probably somewhere in between but until we get the population to understand
what LD is and what it is not and we get the population
to understand that people with LD just learn differently and the
perceived stigma associated with self-disclosure is removed, we will
probably get low figures in surveys.


An example of previously know N-time cyclic filters is shown in a block diagram in FIG. 2. In the figure, numbers 1 through 4 indicate unit delay elements providing a unit delay D each, which are connected in series; 5 is an input adder; 6 is an output adder; 7 through 14 are multipliers for weighing the unit delay elements 1 through 4 by coefficients a.sub.1, a.sub.2, a.sub.N-1, a.sub.N, b.sub.1, b.sub.2, b.sub.N-1 and b.sub.N, respectively, the multiplier 7 being connected between an output of the unit delay element 1 and the input adder 5, the multiplier 11 being connected between the output of the unit delay element 1 and the output adder 6, the multiplier 8 being connected between an output of the unit delay element 2 and/*
 * Copyright (C) 2010 The Android Open Source Project
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 *      http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */

package com.replica.replicaisland;

/**
 * Provides an interface for controlling a sprite with animations.  Manages a list of animations
 * and provides a drawable


equations are considered and more details can be found. For brevity, when we mention that, say, $a$ is uniformly continuous in $x$, we mean uniformity with respect to $\alpha,
\beta,x$. The Lipschitz or Hölder continuity also presume that the corresponding constants are independent of $\alpha,\beta$.

In 1989 Ishii [@Is_89] proved the existence of viscosity solutions for possibly degenerate equations with Lipschitz continuous $a$ and $b$ and uniformly continuous $c$ and $f$ with respect to $x$ under the condition that for a constant $\delta>0$ $$\label{4.3.1}
c^{\alpha\beta}\geq\delta.$$

In the same year 1989 Trudinger [@Tr_89] (see Corollary 3.4 there, also see [@Tr_88]) proved the existence (for uniformly nondegenerate case) dropping and reducing the Lipschitz continuity of $a$ to the $1/2-\varepsilon$-Hölder continuity and assuming that $b,c,f$ are uniformly continuous with respect to $x$. In [@Tr_89] the)$ are continuous with respect to $\beta\in B$ for each $(\alpha, x)$ and continuous with respect to $\alpha\in A$ uniformly with respect to $\beta\in B$ for each $x$, and $$\|g\|_{ C^{1,1}({\mathbb{R}}^{d})}\leq K_{0},$$

\(ii) For any $x \in{\mathbb{R}}^{d}$ and $(\alpha,\beta )\in A\times B $ $$\|a^{\alpha\beta}( x )\|,|b^{\alpha\beta}( x )|,
|c^{\alpha\beta}( x )|,|f^{\alpha\beta}( x )|
\leq K_{0},$$ where for a matrix $\sigma$ we denote $\|\sigma\|^{2}
={\text{\rm tr}\,}\sigma\sigma^{*}$,

\(iii) For any $(\alpha,\beta )\in A\times B $ and $x,y\in{\mathbb{R}}^{d}$ we have $$\|a^{\alpha\beta}( x )-a^{\alpha\beta}( y )\|
\leq K_{0}|x-y|^{\gamma},$$ $$|u^{\alpha\beta}( x )-u^{\alpha\beta}( y )|
\leq K_{0}\omega(|x-y|),$$ where $u=b,c,f$, and $\omega$ is a fixed continuous increasing function on $[0,\infty)$ such that $\omega(0)=0$,

\(iv) For all values of arguments $a^{\alpha\beta}\in{\mathbb{S}}_{\delta}$.

\[remark 4.5.1\] It is convenient to assume that $$|x-y|^{\chi}\leq\omega(|x-y|),$$ whenever $|x-y|\leq1$. Clearly this assumption does not restrict generality.

We will be dealing with equation


boundary condition $u=v=g$ on $\partial G$ has a unique solution in the class $C^{1,1}_{loc}(G)
\cap C(\bar G)$.

By $u_{K}$ and $v_{K}$ we denote the solutions of and , respectively. These are the central objects of our investigation. Here is a simple property they possess.

\[lemma 4.1.1\] There exists a constant $N$, depending only on $d,\delta$, $K_{0}$, and $G$, such that in $G$ $$|u_{K}-g|+|v_{K}-g|\leq N\rho,\quad
|u_{K} |+|v_{K} |\leq N,$$ where $\rho(x)={{\rm dist}\,}(x,G^{c})$.

This result for $u_{K}$ follows from the fact that $|\max(F[0],-K)|\leq|F[0]|$, $g\in C^{1,1}$, $G\in C^{2}$, and $u_{K}$ satisfies a linear equation $$a_{ij}D_{ij}u_{K}+b_{i}D_{i}u_{K}-cu_{K}+f=0,$$ where $(a_{ij})\in{\mathbb{S}}_{\hat \delta}$, $|(b_{i})|\leq K_{1}$, $K_{1}\geq c\geq 0$, and $|f|\leq K_{0}$. The case of $v_{K}$ is quite similar.

To characterize some smoothness properties of $u_{K}$ and $v_{K}$ introduce $C^{1+\chi}(G)$ as the space of continuously differentiable functions in $G$ with finite norm givensecond-order derivatives of $W$ is nonpositive at $(\bar x,\bar y)$, which yields (ii).

By taking $\eta=0$ in and using the fact that $|D^{2}\bar u^{(\varepsilon)}|\leq N M
\varepsilon^{\chi-1}$ we see that $$D^{2}\bar u(\bar x)\leq 2\nu K+NM
\varepsilon^{\chi-1}.$$ Furthermore $$D_{ij} u=\psi D_{ij} \bar u+(D_{i}\psi)D_{j}\bar u
+(D_{i}\bar u)D_{j}\psi+(D_{ij}\psi)\bar u,$$ which implies that $$D^{2}  u(\bar x)\leq N(\nu K+ M
\varepsilon^{\chi-1}),\quad P[u](\bar x)
\leq N_{1}(\nu K+ M
\varepsilon^{\chi-1} ).$$ We now choose and fix $\nu$ such that $$\label{3.28.2}
N_{1}\nu\leq1/4,\quad   .$$ As is easy to see $M\varepsilon^{\chi-1}\leq \nu K$ for $K$ satisfying with an appropriate $N $. Then we have $P[u](\bar x)\leq   K/2<K$, which implies that $F[u](\bar x)\geq0$. We have just proved .

Moreover, not only $M\varepsilon^{\chi-1}\leq \nu K$ for $K$ satisfying , but also $NM\varepsilon^{\chi-1}\leq \nu K$, where $N$ is taken from , if we increase $N$