Meeting the demands of modern lean manufacturing environments requires smaller more flexible machinery. Digitax ST is the first ever drive designed to help machine designers and system integrators meet these challenges; optimized for servo applications requiring high peak torque, dynamic response, ease of use and flexible integration features. Four product variants ensure that the drive's personality perfectly matches your servo applications.
Optimized for centralized control, to operate with motion controllers, motion PLCs and industrial PC based motion systems using a wide range of digital or analogue interface technologies.
Designed for simple standalone positioning applications using an onboard position controller. Fieldbus, Ethernet and IO enable connectivity to other automation components.
This drive offers a stand alone solution for many common indexing and synchronized motion applications. This is achieved using a unique PC programming interface that guides the user through the drive, I/O and motion configuration.
Features a full functionality motion controller, optimized for high performance machine cells requiring drive-to-drive networking and precision synchronization. The motion and communications are configured within a flexible IEC61131-3 software development environment using PLC open function blocks. Fieldbus, Ethernet and I/O connectivity enable interfacing with other automation components and intellectual property protection ensures that your valuable knowledge remains secure.
Our Software makes it easy to access the drives features; it allows you to quickly setup the drive, optimize the tuning, back-up the configuration, program the onboard motion controller and setup communications links.
The Software tools communicate using Ethernet, CTNet, Serial or USB connections. Ethernet allows the software tools to easily use the internet infrastructure allowing Control Techniques drives to be accessed remotely, from virtually anywhere around the world.
Digitax ST - index motion controller is programmed within CTSoft using industry standard Sequential Function Chart (SFC) language. The user can quickly configure a range of motion commands such as homing and various index moves. The focus is on reducing development time and ease of use.
CTScope is a full featured software oscilloscope for viewing and analyzing changing values within the drive. The time base can be set to give high speed capture for tuning or intermittent capture for longer term trends. The interface is based on a traditional oscilloscope, making it familiar to engineers across the globe.
SyPTLite is an easy to use ladder logic program editor, suitable for simple drive applications. SyPTLite is ideal for controlling basic logic and sequencing with Commander SK and Unidrive SP onboard PLC and with SM-Applications Lite option module.
SyPTPro is a full featured automation development environment that can be used for creating solutions to single or multiple drive applications. The programming environment fully supports three industry standard programming languages: Function Block, Ladder and Structured Text. Motion is configured using PLC open function blocks that support a master and slave axis configuration.
SyPTPro is also used to configure CTNet - a high speed drive-to-drive network links together multiple drives, SCADA, operator panels and I/O to form an intelligent networked system.
CTOPCServer is an OPC compliant server that allows PCs to communicate with Control Techniques drives. The server supports communication using Ethernet, CTNet, Serial RS485 and USB. OPC is a standard interface on SCADA packages and is widely supported within Microsoft products.
A wide range of option modules are available to allow you to customize Digitax ST for your application.
Ethernet option module supporting Ethernet/IP and Modbus with built in web server.


text:
Конфлікт всередині каналу розподілу — суперечності, що виникають між учасниками каналу з приводу цілей і функцій кожного учасника, а також коли учасники визначають, хто що має робити і за яку винагороду.

Взаємовідносини між підприємствами, що виконують різні ролі, можуть призводити до різного ступеня співробітництва, конфліктів і конкуренції.

Зрозумілим є бажання виробників та інших продавців, учасників каналу збуту, отримати оплату за товар якомога раніше, а покупців, який би тип посередника вони не представляли, — не оплачувати товар до його фактичного продажу. Конфлікти з цього приводу між учасниками каналів збуту загострюються в умовах нестабільної економічної ситуації.

Конфлікти можуть виникнути як всередині одного каналу розподілу, так і між представниками різних рівнів одного каналу. Наприклад, деякі власники привілеїв фірми незадоволені тим, що деякі їхні партнери не дотримуються рецептури і погано обслуговують відвідувачів, завдаючи цим шкоди репутації товарної марки. Лідер каналу має розробити чіткі правила поведінки, дотримання яких для учасників маркетингової системи є обов'язковим, і вжити заходів щодо найшвидшого розв'язання конфлікту.

Конфлікти у ВМС можуть виникати також між представниками різних рівнів одного каналу. Так, у кінці 70-х років виник конфлікт між "General Motors" та її дилерами через те, що корпорація зробила спробу в примусовому порядку добитися виконання своїх установок щодо технічного обслуговування, ціноутворення і реклами. Слід зазначити, що деякі конфлікти у ВМС неминучі і певною мірою сприяють зміцненню системи управління. У принципі лідер каналу має розробити такі глобальні цілі розвитку, які кожний з учасників міг би підтримати. Вони повинні містити, зокрема, мінімізацію витрат при просуванні товару всередині ВМС, удосконалення інформаційних потоків, що проходять через канал, форми адаптації до потреб споживачів.

Див. також
Торгова війна

Посилання
Конфлікти всередині каналу розподілу
Маркетинг

redpajama_set_name: RedPajamaWikipedia


The Casa do Patrón Museum is an etnographic museum with more than 4,000 pieces collected from all over Galicia. The collection is distributed in three buildings with over 2,000 m2.
The museum houses thirteen theme organized exhibition halls, where the visitor can behold the old Galician schools, the way of life of our ancestors, forgotten trades or a tavern, along with traditional oven and forge. Also in the museum, the visitor will find the implements characterizing all farming and ranching trades and activities from last centuries, living memory of our history.
The museum owns a restaurant located in the environs, specialised in traditional gastronomy and local products.
Activities and workshops prior appointment.


Find It. Control It. You're In Charge.
EditByBSEditor: inSpector text is an Add-In for Microsoft Excel that adds powerful worksheet formula functions for working with text in worksheet cells, including search & replace, and fuzzy matching.
inspector text's search & replace functions are vastly more powerful and useful than the search & replace functions built into Excel (FIND, SEARCH, REPLACE, SUBSTITUTE, LEFT, RIGHT, & mid), yet are easy to use and do not require any special knowledge.
inspector text's powerful, yet easy to use fuzzy matching functions allow you to determine whether or not the text in two cells is Similar.
inspector text also adds worksheet formula functions that evaluate concatenated formulas, that return ordinal indicators for cardinal numbers ("1st" for 1, "2nd" for 2...), that exclude or retrieve lists of characters from text, and that perform Regular Expressions search and replace.
inspector text is an Add-In for Microsoft Excel* that provides powerful worksheet formula functions for working with text in worksheet cells, including search & replace, and fuzzy matching.
inspector text also provides worksheet formula functions that evaluate concatenated formulas, that return ordinal indicators for cardinal numbers, and that perform Regular Expressions search and replace.
inspector text also provides online help from Excel's Tools menu, and utilizes Excel's Insert Function dialog to make using inspector text functions more convenient.
you can free download Inspector Text 2.0 now.
Please be aware that Brothersoft do not supply any crack, patches, serial numbers or keygen for Inspector Text,and please consult directly with program authors for any problem with Inspector Text.


Some quick tips to save money for your rail ticket Zaandam Kogerveld to Villingen-Ham?
The most popular times and dates of departure to travel to Villingen-Ham from Zaandam Kogerveld are almost always more expensive, so try to be flexible if possible.
Our system will always propose you the best fare for your tickets to Villingen-Ham.
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Questions , remarks about your rail trip Zaandam Kogerveld to Villingen-Ham?


text:
Linda Züblin (ur. 21 marca 1986) – szwajcarska lekkoatletka specjalizująca się w wielobojach.

W 2008 roku startowała w igrzyskach olimpijskich w Pekinie gdzie zajęła 30. lokatę w siedmioboju. Startowała w międzynarodowych imprezach juniorskich nie odnosząc jednak sukcesów. Medalistka mistrzostw Szwajcarii oraz była rekordzistka tego kraju w rzucie oszczepem – 53,01 (16 sierpnia 2009, Berlin).

Osiągnięcia

Rekordy życiowe

Przypisy

Linki zewnętrzne

Szwajcarscy olimpijczycy
Szwajcarscy oszczepnicy
Szwajcarscy wieloboiści
Urodzeni w 1986
Uczestnicy Letnich Igrzysk Olimpijskich 2008


text:
United Church of Canada Rejects Atheist Minister's Attempt to Stop Review, Possible Defrocking
By Heather Clark on April 3, 2016 30 Comments
TORONTO — An ordained minister with the United Church of Canada has lost her appeal to stop an official review of her qualifications to be a church leader as she is a professing atheist.
"I don't believe in … the god called God," Gretta Vosper told the Globe and Mail last year. "Using the word gets in the way of sharing what I want to share."
As previously reported, Vosper believes that the Bible is "mythology," and denies that Jesus is the Son of God.
"God, as the source of goodness, and as the way that goodness comes into the world, and as the promise that everything is going to be good in the end, whether in this lifetime or in the afterlife—that God doesn't exist anymore," she states. "We have to recognize that we are only way that good is going to come into this world. We are the definers of what is good. [But] what's good in one community won't be good in another."
Vosper, 57, and who was ordained in 1993, first came out as an atheist in 2001. However, her congregation still supported her until 2008 when she sought to do away with the use of the Lord's Prayer and lost approximately 100 members of her 150-member congregation.
Last year, Vosper wrote an open letter asserting that a belief in God can compel people to commit evil, referencing the Charlie Hebdo massacre in France.
"That didn't go over well," Vosper, who also founded the Canadian Centre for Progressive Christianity, told reporters. "[But] if we are going to continue to use language that suggests we get our moral authority from a supernatural source, any group that says that can trump any humanistic endeavor."
She was soon reported to the United Church of Canada, which launched an investigation into her "effectiveness" as a minister. In May, Nora Sanders, general secretary for the UCC General Council, provided the denomination with standards on which to determine whether Vosper should stay or go.
Attorneys for Vosper filed an appeal of the review, consisting of over 1,600 pages, but on Thursday a denominational committee announced that it had rejected the request.
"After fully and thoroughly considering all submissions by the appellant and respondent, the executive of the judicial committee decided that the appeal did not meet the grounds for an appeal," the one-page decision said in part.
She will now have to face a special committee to give account for her actions and beliefs.
"At the end of the process, [Vosper] will have had a full and fair opportunity to speak directly to the church about her position," David Allen, executive secretary of the Toronto conference, told reporters. "[The] Toronto conference—based on the review process—will have good reasons why she should continue in ministry or good reasons why she should not."
Vosper told reporters that she will be disappointed if she is defrocked.
"I will be really sad that my fitness for ministry is based entirely on whether or not I can affirm an archaic doctrinal statement that describes God in a way that is incomprehensible and no longer has meaning for me or many within the United Church," she told CBC News this week.
"I will feel betrayed by the Church because it has created who I am," she said. "It has been a major force in my life. It has taught me what I know. It has given me the tools to explore. It has demanded that I do that and so I've done that and here we are."
United Church of Canada Rejects Atheist Minister's Attempt to Stop Review, Possible Defrocking added by Heather Clark on April 3, 2016
View all posts by Heather Clark →

redpajama_set_name: RedPajamaCommonCrawl


From left: QPS Deputy Commissioner Steve Gollschewski, Professor Paul Mazerolle - Griffith University Pro Vice Chancellor (Arts, Education & Law), QPS Commissioner Ian Stewart and Deputy Commissioner Peter Martin at the launch of the Social Analytics Lab at Mt Gravatt campus.
Griffith University researchers are analysing more than one million Queensland crimes to forecast where future crime hotspots are likely to occur.
The research is made possible by an Australian-first $1 million research facility – the Social Analytics Lab (SAL), launched by the Minister for Police, Fire and Emergency Services Mark Ryan and Queensland Police Service Commissioner Ian Stewart APM.
The custom-built research facility combines high-performance computing facilities with industry standard security.
It allows sensitive, de-identified administrative data to be stored and studied using advanced analytics to reveal patterns and insights from large complex government agency data.
In one of the first projects to be run in the lab, researchers will use crime data recorded over the past 10 years to identify patterns in burglary and car crime that could inform operational policing.
Predictive policing expert Dr Daniel Birks said burglary and car crime, two types of crime affecting many people, cost the community an estimated $2.5 billion annually.
"Building on recent international studies, our research explores the use of mathematical models that use previous crime patterns to forecast locations and times of future crime risk," he said.
He said research had previously shown that after an initial burglary, the risk of a second burglary increases significantly, not only for the original victim, but also to those who live nearby – with this heightened risk rapidly dissipating over time.
"This could be because offenders or their peers are returning to areas where they were previously successful, or there may be inherent characteristics of an area that make it attractive to offenders in general.
Attending the launch, Queensland Police Commissioner Ian Stewart said the great benefit of the lab was not only researchers having access to the crime data but also other datasets so they can start predicting behaviours.
"We can look at a person who is a career criminal and then work backwards to find out why that person entered into the criminal justice system.
An Australian-first, the SAL joins Griffith research with facilities at the Jill Dando Institute of Crime Science, University College London and the Institute for Canadian Urban Research Studies, Simon Fraser University, Canada.
"This newly forged network of secure facilities provides unprecedented opportunities for collaboration among leading international researchers and practitioners,'' says Associate Professor Michael Townsley, head of the School of Criminology and Criminal Justice.
Queensland Police Service Collaboration: This collaboration between QPS and SAL provides researchers with access to 10 years of crime incident data occurring in Queensland between 2008 and 2017.
Queensland Linkage Project: This project includes linked longitudinal administrative data from six Queensland government departments. These de-identified data include Births, Deaths and Marriages, child safety, youth justice, police, courts, corrections, hospital admissions and mental health.


IP Address Validation product now identifies Tor network users – adding a new layer of fraud protection against invalid or untraceable contacts.
SANTA BARBARA, Calif., October 22, 2013 – Service Objects, the leading provider of real-time contact validation for businesses, announced today the release of a new feature to its DOTS IP Address Validation product – the ability to detect Tor network users.
Using a Tor network, users can direct Internet traffic to conceal their true geographic location. This enables fraudsters to use these networks to conduct malicious and anonymous business transactions, such as placing bogus orders with stolen credit cards, and in turn, create havoc for retailers during the crucial holiday shopping season. Last year, online retailers reported over $3.9 billion in online fraud.
With the updated DOTS IP Address Validation, Service Objects customers can uncover real-time location and network information about the IP address linked to the user, warning them of contacts utilizing Tor and other anonymous proxies. Using this information, companies can make informed decisions about the risks associated with these types of online transactions.
Service Objects uses more than 50 authenticated sources that provide millions of unique IP records, making the service more accurate than any other geolocation offering currently on the market. In addition to its DOTS IP Address Validation service, Service Objects offers businesses a collection of data validation tools that provide a first line of defense against online fraud and bogus contact information.
Founded in 2001, Service Objects is the leading provider of real-time contact validation services. It's validation and location web services allow businesses to identify potentially fraudulent transactions, append additional contact information and process transactions in a more efficient manner. The Company works with major brands like American Express, LendingTree and Amazon; and it has validated over 1.5 billion contacts.


nbeam published 3 years ago in Information Security, Linux, Network Security, Networking, Tunneling.
This was going to be a long article but I decided to cut it short. Use case: You have a Remote Server – You need to securely access some sensitive service or another (let's say a MySQL connection) and don't want to open the port to up to the internet. What's a person to do?


text:
\section{Introduction}
Let $\Omega\subset\R{2m}$ be a bounded domain with smooth boundary. Given a sequence of numbers $\rho_k>0$,
we consider solutions to the mean-field equation of higher order
\begin{equation}\label{eq2}
(-\Delta)^m u_k=\rho_k\frac{e^{2mu_k}}{\int_{\Omega}e^{2mu_k}dx}
\end{equation}
subject to the Dirichlet boundary condition
\begin{equation}\label{dir}
u_k=\partial_\nu u_k=\ldots=\partial_\nu^{m-1}u_k=0\quad \textrm{on }\partial \Omega.
\end{equation}
As shown in Corollary 8 of \cite{mar1}, every $u_k$ is smooth. In this paper we study the limiting behavior of the sequence $(u_k)$. We show that concentration-compactness phenomena together with geometric quantization occur. We particularly emphasize the interesting relationship with the thriving problem of prescribing the $Q$-curvature.

For any $\xi\in\overline \Omega$, let $G_\xi(x)$ denote the Green function of the operator $(-\Delta)^m$ on $\Omega$ with Dirichlet boundary condition (see e.g. \cite{ACL}), i.e
\begin{equation}\label{greenf}
\left\{
\begin{array}{ll}
(-\Delta)^m G_\xi=\delta_\xi&\text{in }\Omega\\
G_\xi=\partial_\nu G_\xi=\ldots=\partial_\nu^{m-1} G_{\xi}=0 & \text{on }\partial\Omega.
\end{array}
\right.
\end{equation}
Also fix any $\alpha\in[0,1)$. We then have
\begin{trm}\label{trm2} Let $u_k$ be a sequence of solutions to \eqref{eq2}, \eqref{dir} and assume that
$$0<\rho_k\leq C.$$ Then one of the following is true:
\begin{itemize}
\item[(i)] Up to a subsequence $u_k\to u_0$ in $C^{2m-1,\alpha}(\overline\Omega)$ for some $u_0\in C^\infty(\overline\Omega)$.
\item[(ii)] Up to a subsequence, $\lim_{k\to\infty}\max_\Omega u_k=\infty$ and there is a positive integer $N$ such that
\begin{equation}\label{quant}
\lim_{k\to\infty}\rho_k=N\Lambda_1,\quad \Lambda_1=(2m-1)!|S^{2m}|.
\end{equation}
Moreover there exists a non-empty finite set $S=\{x^{(1)},\ldots, x^{(N)}\}\subset\Omega$
such that
\begin{equation}\label{green}
u_k\to \Lambda_1\sum_{i=1}^N G_{x^{(i)}}\quad \text{in }C^{2m-1,\alpha}_{\loc}(\overline\Omega\backslash S).
\end{equation}
\end{itemize}
\end{trm}
The mean field equation in dimensions $2$ and $4$ has been object of intensive study in the recent years. We refer e.g. to \cite{NS}, \cite{wei}, \cite{RW} and the references therein. In particular in \cite{RW} the $4$-dimensional analogous of our Theorem \ref{trm2} was proved, and many of the ideas developed there are used in our treatment.

\medskip

The geometric constant $\Lambda_1$ showing up in \eqref{quant} and \eqref{green} is the total $Q$-curvature\footnote{For the definition of $Q$-curvature we refer to \cite{cha}, or to the introduction of \cite{mar1} and the references therein.} of the round $2m$-dimensional sphere. It is worth explaining how this relation with Riemannian geometry arises. It will be shown in Lemma \ref{claim4} below that one can blow up the $u_k$'s at suitably chosen \emph{concentration points}, and get in the limit a solution $u_0$ to the Liouville equation
\begin{equation}\label{liou}
(-\Delta)^m u_0=(2m-1)!e^{2m u_0}\quad\text{in }\R{2m}
\end{equation}
with the bound
\begin{equation}\label{area}
\int_{\R{2m}}e^{2mu_0}dx<\infty.
\end{equation}
Geometrically, if $u_0$ solves \eqref{liou}-\eqref{area}, then the conformal metric $e^{2u_0}g_{\R{2m}}$ on $\R{2m}$ (where $g_{\R{2m}}$ is the Euclidean metric) has constant $Q$-curvature equal to $(2m-1)!$ and finite volume. As shown in \cite{CC}, there are many such conformal metrics on $\R{2m}$, and the crucial step in Lemma \ref{claim4} below is to show that
\begin{equation}\label{eta0}
u_0(x)=:\log\bigg(\frac{2}{1+|x|^2}\bigg).
\end{equation}
The above function has the property that $e^{u_0}g_{\R{2m}}=(\pi^{-1})^*g_{S^{2m}}$, where $g_{S^{2m}}$ is the round metric on $S^{2m}$, and $\pi:S^{2m}\to\R{2m}$ is the stereographic projection. In particular
\begin{equation}\label{vol}
\int_{\R{2m}}e^{2mu_0}dx=|S^{2m}|.
\end{equation}
This is the basic reason why the constant $\Lambda_1$ appears in Theorem \ref{trm2}.
In order to show that \eqref{eta0} holds, we use the classification result of \cite{mar1} and a technique of \cite{RS}, which allows us to rule out all the solutions of \eqref{liou} which are ``non-spherical'', hence whose total $Q$-curvature might be different from $\Lambda_1$.

\medskip

We will further exploit such connections with conformal geometry mainly by referring to Theorem 1 in \cite{mar2}, about the concentration-compactness phenomena for sequences of conformal metrics on $\R{2m}$ with prescribed $Q$-curvature (compare \cite{BM}, \cite{ARS} and \cite{Rob} for $2$ and $4$-dimensional analogous results). We state a simplified version of this theorem in the appendix, since we shall use it several times.

\medskip

The last crucial step in the proof of Theorem \ref{trm2} is the generalization to arbitrary dimension of a clever argument of Robert-Wei \cite{RW} based on a Pohozaev-type identity, which rules out blow-up points at the boundary (see Lemma \ref{claim11}) and allows to sharply estimate the energy concentrating at each blow-up point (see Lemma \ref{claim13})

\medskip

One can also state Theorem \ref{trm2} as an eigenvalue problem, as in \cite{wei}. In this case one replaces the term $\frac{\rho_k}{\int_\Omega e^{2mu_k}}$ by the constant $\lambda_k>0$ in \eqref{eq2}, so we consider the equation
\begin{equation}\label{eq1}
(-\Delta)^m u_k=\lambda_k e^{2mu_k}.
\end{equation}
The assumption $0<\rho_k\leq C$ gets replaced by
\begin{equation}\label{sigmak}
\Sigma_k:=\int_{\Omega}\lambda_k e^{2mu_k}dx\leq C,
\end{equation}
and we keep the boundary condition \eqref{dir}. Then Theorem \ref{trm2} implies that either
\begin{itemize}
\item[(i)] up to a subsequence $u_k\to u_0$ in $C^{2m-1,\alpha}_{\loc}(\overline \Omega)$, or
\item[(ii)] up to a subsequence $\Sigma_k\to N\Lambda_1$ and $(u_k)$ satisfies \eqref{green}, with the same notation of Theorem \ref{trm2}.
\end{itemize}

\medskip

Several times we use standard elliptic estimates. For the interior estimates one can safely rely on \cite{GT} or \cite{GM}. For the estimates up to the boundary, one can refer to \cite{ADN}. Throughout the paper the letter $C$ denotes a large universal constant which does not depend on $k$ and can change from line to line, or even within the same line.

\section{Proof of Theorem \ref{trm2}}

The proof will be organized as follows. We shall see in Corollary \ref{coru}, that if $\sup_{\Omega} u_k\leq C$, then $u_k$ is bounded in $C^{2m-1,\alpha}(\overline\Omega)$ and case (i) of Theorem \ref{trm2} occurs. Therefore, after Corollary \ref{coru} we shall assume that
\begin{equation}\label{ukinfty}
\lim_{k\to\infty}\sup_{\Omega} u_k=\infty,
\end{equation}
and prove that case (ii) of Theorem \ref{trm2} occurs. Let
\begin{equation}\label{alphak}
\alpha_k:=\frac{1}{2m}\log\bigg(\frac{(2m-1)!\int_\Omega e^{2mu_k}dx}{\rho_k}\bigg),\quad \hat u_k:=u_k-\alpha_k.
\end{equation}

\begin{lemma}\label{claim1}
Up to selecting a subsequence, we have $\alpha_k\geq -C$.
\end{lemma}

\begin{proof} Indeed
\begin{equation}\label{eqhat}
(-\Delta)^m\hat u_k= (2m-1)!e^{2m \hat u_k}\quad \textrm{in }\Omega
\end{equation}
and
$$\hat u_k=-\alpha_k,\quad \partial_\nu \hat u_k=\ldots=\partial_\nu^{m-1}\hat u_k=0\quad \textrm{on }\partial\Omega.$$
Moreover
\begin{equation}\label{eq3.2}
\int_{\Omega}e^{2m\hat u_k}dx=\frac{\rho_k}{(2m-1)!}\leq C.
\end{equation}
Using Green's representation formula, we infer
\begin{equation}\label{eq3.3}
\hat u_k(x)=(2m-1)!\int_\Omega G_x(y)e^{2m \hat u_k(y)}dy-\alpha_k.
\end{equation}
Then, integrating \eqref{eq3.3} and using \eqref{eq3.2}, the fact that $\|G_y\|_{L^1(\Omega)}\leq C$, with $C$ independent of $y$, and the symmetry of $G$, i.e. $G_x(y)=G_y(x)$, we get
\begin{equation}\label{eq3.4}
\int_\Omega |\hat u_k+\alpha_k|dx\leq C.
\end{equation}
Now, according to Theorem \ref{main} in the Appendix, we have that one of the following is true:
\begin{itemize}
\item[(i)] $\hat u_k\to \hat u_0$ in $C^{2m-1,\alpha}_{\loc}(\Omega)$ for some function $\hat u_0$.
\item[(ii)] $\hat u_k\to-\infty$ locally uniformly in $\Omega\backslash \Omega_0$, for some closed nowhere dense (possibly empty) set $\Omega_0$ of Hausdorff dimension at most $2m-1$.
\end{itemize}
In both cases the claim of the lemma easily follows from \eqref{eq3.4}.
\end{proof}

\begin{cor}\label{coru} The following facts are equivalent:
\begin{itemize}
\item[(i)] Up to selecting subsequences, $u_k\leq C$.
\item[(ii)] Up to selecting subsequences, $\hat u_k\leq C$.
\item[(iii)] Up to selecting subsequences, $u_k\to u_0$ in $C^{2m-1,\alpha}(\overline\Omega)$ for some smooth function $u_0$.
\end{itemize}
\end{cor}

\begin{proof} (i) $\Rightarrow $ (ii) follows at once from Lemma \ref{claim1}.

\medskip

\noindent (ii) $\Rightarrow$ (iii) follows by elliptic estimates, observing that
$$|(-\Delta)^m u_k|=|(-\Delta)^m \hat u_k|=\big|(2m-1)!e^{2m \hat u_k}\big|\leq C$$
and using \eqref{dir}.

\medskip

\noindent (iii)$\Rightarrow$ (i) is obvious.
\end{proof}

\begin{lemma}\label{claim2} For all $\ell\in\{1,\ldots,2m-1\}$ and for $p\in[1,\tfrac{2m}{\ell})$, there exists $C=C(\ell,p)$ such that
\begin{equation}\label{nablai}
\int_{B_R(x_0)}|\nabla^\ell \hat u_k|^p dx\leq C R^{2m-ip},
\end{equation}
for any $B_R(x_0)\subset\Omega$.
\end{lemma}

\begin{proof}
We prove the claim by duality. Let $\varphi\in C^{\infty}_c(\Omega)$ and $q=\tfrac{p}{p-1}$. Differentiating \eqref{eq3.3}, using Fubini's theorem, the relation $G_x(y)=G_y(x)$ and the estimate (see \cite{DAS})
\begin{equation}\label{DAS}
|\nabla^\ell G_y(x)|\leq \frac{C}{|x-y|^\ell},
\end{equation}
we get
\begin{eqnarray*}
 \int_{B_R(x_0)}|\nabla^\ell\hat u_k|\varphi dx&\leq&C\int_{B_R(x_0)}\left(\int_\Omega\abs{\nabla^\ell G_y(x)}e^{2m \hat u_k
(y)}dy\right)\abs{\varphi(x)}dx\\
&\leq& C\int_\Omega e^{2m \hat u_k(y)}\bigg(\int_{B_R(x_0)}\abs{x-y}^{-\ell}\abs{\varphi(x)}dx\bigg)dy\\
&\leq& C\norm{\varphi}_{L^q(\Omega)}\int_\Omega e^{2m \hat u_k(y)}\bigg(\int_{B_R(x_0)}\frac{dx}{|x-y|^{\ell p}}\bigg)^\frac{1}{p} dy\\
&\leq& C\norm{\varphi}_{L^q(\Omega)} R^{\frac{2m}{p}-\ell},
\end{eqnarray*}
where in the last inequality we used $p<\tfrac{2m}{\ell}$, \eqref{eq3.2}, and the simple estimate
$$\int_{B_R(x_0)}\frac{dx}{|x-y|^{\ell p}}\leq \int_{B_R(y)}\frac{dx}{|x-y|^{\ell p}}\leq CR^{2m-\ell p}.$$
The lemma follows at once.
\end{proof}

\begin{lemma}\label{claim3}
Let $x_k\in\Omega$ be such that
\begin{equation}\label{ukin}
u_k(x_k)=\max_\Omega u_k\to\infty.
\end{equation}
Let $\mu_k:=2e^{-\hat u_k(x_k)}$. Then $\frac{\dist(x_k,\partial\Omega)}{\mu_k}\rightarrow+\infty$.
\end{lemma}

\begin{proof}
Suppose that the conclusion of the lemma is false. Then the rescaled sets
$$\Omega_k:=\tfrac{1}{\mu_k}(\Omega - x_k)$$
converge, up to rotation, to $(-\infty,t_0)\times\R{2m-1}$ for some $t_0\geq 0$. Define
\begin{equation}\label{utilde}
\tilde u_k(x):=\hat u_k(x_k + \mu_k x) +\log(\mu_k),\quad x\in\Omega_k.
\end{equation}
By \eqref{ukin} and Corollary \ref{coru} we have $\mu_k\rightarrow 0$.  Fix $R>0$ such that $B_R(0)\cap\partial\Omega_k\neq\emptyset$, and let $x\in B_R(0)\cap\Omega_k$. Then, for $1\leq \ell\leq 2m-1$, using \eqref{eq3.3} and \eqref{DAS}, we get
\begin{eqnarray*}
 \abs{\nabla^\ell\tilde u_k(x)}
&\leq & C   \mu_k^\ell\int_\Omega|\nabla^\ell G_{x_k + \mu_kx}(y)|e^{2m\hat u_k(y)}dy\\
&\leq& C\mu_k^\ell\bigg(\int_{\Omega\setminus B_{2R\mu_k}(x_k)}\frac{1}{\abs{x_k + \mu_k x - y}^\ell}e^{2m\hat u_k(y)}dy\\
&&+\int_{B_{2R\mu_k}(x_k)}\frac{1}{|x_k + \mu_k x - y|^\ell}e^{2m\hat u_k(y)}dy\bigg)\\
&\leq& CR^{-\ell}\int_\Omega e^{2m\hat u_k}dy+ C\mu_k^{\ell-2m}\int_{B_{2R\mu_k}(x_k)}\frac{dy}{\abs{x_k + \mu_k x - y}^\ell}\\
&\leq& C(R),
\end{eqnarray*}
where we used that for $y\in \Omega\setminus B_{2R\mu_k}(x_k)$ and $x\in B_R(0)\cap \Omega_k$ we have $R\mu_k\leq \abs{x_k + \mu_k x - y}$ and, for any $y\in \Omega$ we have $e^{2m\hat u_k(y)}\leq 2^{2m}\mu_k^{-2m}$. This implies
$$|\tilde u_k(x)-\tilde u_k(0)|\leq C(R)|x|\quad \textrm{for }|x|\leq R.$$
Choosing $x\in B_R(0)\cap \partial \Omega_k$ we get $|u_k(x_k)|=\abs{\hat u_k(x_k)+\alpha_k}\leq C(R)$, contradicting \eqref{ukin}.
\end{proof}

\begin{rmk}\label{claim3bis}
In the choice of the scales $\mu_k$ we are free to some extent. Our particular choice is made in order to give a cleaner form to the blow-up limit described in Lemma \ref{claim4} and to make the connection with the problem of prescribing the $Q$-curvature more transparent.
\end{rmk}

From now on we shall assume that \eqref{ukinfty} holds.

\begin{lemma}\label{claim4}
Let $\tilde u_k$ be defined as in \eqref{utilde}. Then, up to selecting a subsequence, we have
\begin{equation}\label{eqclaim4} \lim_{k\rightarrow +\infty}\tilde u_k(x)=\log\bigg(\frac{2}{1+\abs{x}^2}\bigg)\quad \textrm{in }C^{2m-1,\alpha}_{\loc}(\R{2m}).
\end{equation}
\end{lemma}

\begin{proof} We give the proof in two steps.

\medskip

\noindent\emph{Step 1.}
We first claim that up to a subsequence, $\tilde u_k\to \tilde u_0$ in $C^{2m-1,\alpha}_{\loc}(\R{2m})$, for some smooth function $\tilde u_0$ satisfying
\begin{equation}\label{u0}
(-\Delta)^m\tilde u_0=(2m-1)!e^{2m\tilde u_0}.
\end{equation}
Let us first assume $m>1$. We apply Theorem \ref{main} on $\R{2m}$ to the sequence $(\tilde u_k)$, where it is understood that one has to invade $\R{2m}$ with bounded sets and extract a diagonal subsequence in order to get the local convergence on all of $\R{2m}$. Since $\tilde u_k\leq \log 2$, we have $S_1=\emptyset$, in the notation of Theorem \ref{main}. Then one of the following is true:

\begin{itemize}
\item[(i)] $\tilde u_k\to \tilde u_0$ in $C^{2m-1,\alpha}_{\loc}(\R{2m})$ for some function $\tilde u_0\in C^{2m-1,\alpha}_{\loc}(\R{2m})$, or
\item[(ii-a)] $\tilde u_k\to -\infty$ locally uniformly in $\R{2m}$ (case $S_0=\emptyset$), or
\item[(ii-b)] there exists a closed nowhere dense set $S_0\neq \emptyset$ of Hausdorff dimension at most $2m-1$ and numbers $\beta_k\to\infty$ such that
$$\frac{\tilde u_k}{\beta_k}\to\varphi\textrm{ in }C^{2m-1,\alpha}_{\loc}(\R{2m}\backslash S_0),$$
where
\begin{equation}\label{eq71}
\Delta^m\varphi\equiv 0,\quad \varphi\leq 0,\quad \varphi\not\equiv 0 \textrm{ on }\R{2m},\quad \varphi\equiv 0\textrm{ on }S_0.
\end{equation}
\end{itemize}
Since $\tilde u_k(0)=\log 2$, (ii-a) can be ruled out. Assume now that (ii-b) occurs. From Liouville's theorem and \eqref{eq71}, we get $\Delta\varphi\not\equiv 0$, hence for some $R>0$ we have
$\int_{B_R(0)}|\Delta\varphi|dx>0$ and
\begin{equation}\label{72}
\lim_{k\to \infty}\int_{B_R}|\Delta \tilde u_k|dx=\lim_{k\to\infty}\beta_k\int_{B_R(0)}|\Delta\varphi|dx=+\infty.
\end{equation}
By \eqref{nablai}, and using the change of variables $y=x_k+\mu_k x$, we get, for $1\leq j\leq m-1$,
\begin{eqnarray}
\int_{B_R(0)}|\Delta^j \tilde u_k|dx&=& \mu_k^{-2m+2j}\int_{B_{R\mu_k}(x_k)} |\Delta^j \hat u_k|dy
  \nonumber\\
&\leq&C \mu_k^{-2m+2j}(R\mu_k)^{2m-2j}\leq C R^{2m-2j},\label{deltaj}
\end{eqnarray}
which contradicts \eqref{72} for $j=1$ and any fixed $R>0$. Hence (i) occurs. Clearly $\tilde u_0$ satisfies \eqref{u0} and our claim is proved.

For the case $m=1$, we infer from Theorem 3 in \cite{BM} that either case (i) or (ii-a) above occur, and case (ii-a) is ruled out as above.

\medskip

\noindent\emph{Step 2.} We now want to prove that $\tilde u_0=\log\frac{2}{1+|x|^2}$. From Fatou's lemma and \eqref{eq3.2} we infer
\begin{eqnarray*}
\int_{\R{2m}}e^{2m\tilde u_0}dx&=&\lim_{R\to\infty}\int_{B_R(0)}e^{2m\tilde u_0}dx \leq \lim_{R\to\infty}\liminf_{k\to\infty}\int_{B_R(0)}e^{2m\tilde u_k}dx\\
&=&\lim_{R\to\infty}\liminf_{k\to\infty}\int_{B_{R\mu_k}(x_k)}e^{2m\hat u_k}dx \leq\int_{\Omega}e^{2m\hat u_k}dx\leq C.
\end{eqnarray*}
If $m=1$, then our claim follows directly from \cite{CL}. Assume now $m>1$.  From Theorem 2 in \cite{mar1} we get that either
\begin{equation}\label{eqstsol}
\tilde u_0=\log\frac{2\lambda}{1+\lambda^2\abs{x-x_0}^2}
\end{equation}
for some $\lambda>0$ and $x_0\in\R{2m}$, or there exists $j\in\{1,\ldots,m-1\}$ such that
\begin{equation}\label{deltau}
 \Delta^j\tilde u_0(x)\rightarrow a\text{ as }\abs x\rightarrow +\infty,
\end{equation}
for some constant $a<0$. On the other hand, \eqref{deltau}
implies that for every $R>0$ large enough there is $k(R)\in\mathbb{N}$ such that
$$\int_{B_R(0)}|\Delta^j \tilde u_k|dx\geq \frac{|a|}{2}|B_R(0)|\geq \frac{R^{2m}}{C},\quad \text{for }k\geq k(R).$$
This contradicts \eqref{deltaj} in the limit as $R\to 0$, whence \eqref{eqstsol} has to hold.
Since $\tilde u_k(0)=\max_{\Omega_k}\tilde u_k=\log 2$, the same facts hold for $\tilde u_0$. Therefore $x_0=0$ and $\lambda=1$ in \eqref{eqstsol}. This proves our second claim, hence the lemma.
\end{proof}

\begin{lemma}\label{hp} There are $N>0$ converging sequences $x_{k,i}\to x^{(i)}$, $1\leq i\leq N$,  with $\lim_{k\to\infty}u_k(x_{k,i})=\infty$ such that, setting
\begin{equation}\label{ki2}
\tilde u_{k,i}(x):=\hat u_k(x_{k,i}+\mu_{k,i}x)+\log\mu_{k,i},\quad
\mu_{k,i}:=2e^{-\hat u_k(x_{k,i})},\\
\end{equation}
we have
\begin{enumerate}
 \item[($A_1$)] $\lim_{k\to\infty}\frac{\abs{x_{k,i} - x_{k,j}}}{\mu_{k,i}} +\infty$ for $1\leq i\neq j\leq N$,
 \item[($A_2$)] $\lim_{k\to \infty}\frac{\dist(x_{k,i},\partial\Omega)}{\mu_{k,i}}=+\infty$, for $1\leq i\leq N$
 \item[($A_3$)] $\tilde u_{k,i}\rightarrow \eta_0$ in $C^{2m-1,\alpha}_{\loc}(\R{2m})$, for $1\leq i\leq N$, where $\eta_0(x)=\log\Big(\frac{2}{1+\abs{x}^2}\Big)$.
\item[($A_4$)] For $1\leq i\leq N$
\begin{equation}\label{energiai}
\lim_{R\to\infty}\lim_{k\to\infty}\int_{B_{R\mu_{k,i}}(x_{k,i})}e^{2m\hat u_k}dx=|S^{2m}|.
\end{equation}
\item[($A_5$)] $\inf_{1\leq i\leq N}|x-x^{(i)}|^{2m} e^{2m\hat u_k(x)}\leq C$ for every $x\in \Omega$.
\end{enumerate}
\end{lemma}

\begin{proof} We proceed inductively.

\medskip

\noindent\emph{Step 1.}
For $N=1$, choose $x_{k,1}$ such that $u_k(x_{k,1})=\sup_\Omega u_k$. Then Lemma \ref{claim3} and Lemma \ref{claim4} imply that $(x_{k,1})$ satisfies $(A_2)$ and $(A_3)$. Moreover $(A_1)$ is empty and $(A_4)$ follows at once from $(A_3)$ \eqref{vol}. If also $(A_5)$ is satisfied, we are done. Otherwise we construct a new sequence, as in the inductive step below.

\medskip

\noindent\emph{Step 2.} Assume that $\ell$ sequences $\{(x_{k,i})\to x^{(i)}:1\leq i\leq \ell$\}, have been constructed so that they satisfy $(A_1)$, $(A_2)$, $(A_3)$ and $(A_4)$, but not $(A_5)$.
Set
$$w_k(x):=\inf_{1\leq i\leq \ell}|x-x_{k,i}|^{2m}e^{2m\hat u_k(x)},$$
so that $\lim_{k\to\infty}\sup_\Omega w_k=\infty$, and choose $y_k\in\Omega$ such that $w_k(y_k)=\sup_{\Omega}w_k$.
Then $y_k\to y$ up to a subsequence. Also set
\begin{equation}\label{eqclaim5}
\gamma_k=2e^{-\hat u_k(y_k)},\qquad v_k(x)=\hat u_k(y_k+\gamma_k x)+\log \gamma_k.
\end{equation}
We claim that $(A_1)$, $(A_2)$, $(A_3)$ and $(A_4)$ hold for the $\ell+1$ sequences
$$\{(x_{k,i})\to x^{(i)}:1\leq i\leq \ell+1\},$$
if we set
$$
\left\{
\begin{array}{l}
x_{k,\ell+1}:=y_k\\
x^{(\ell+1)}:=y\\
\tilde u_{k,\ell+1}:=v_k\\
\mu_{k,\ell+1}:=\gamma_k
\end{array}
\right.
$$
Since $w_k(y_k)\rightarrow +\infty$ we get
$$\lim_{k\to\infty}\frac{|y_k-x_{k,i}|}{\gamma_k}\geq \lim_{k\to\infty}\frac{w_k(y_k)^\frac{1}{2m}}{2}=+\infty\quad\text{for } 1\leq i\leq \ell.$$
We claim that we also have
$$\lim_{k\to\infty}\frac{\abs{y_k-x_{k,i}}}{\mu_{k,i}}=+\infty\quad \text{for }1\leq i\leq \ell.$$ Indeed, setting $\theta_{k,i}:=\frac{y_k-x_{k,i}}{\mu_{k,i}}$, we have
$$
 \abs{y_k-x_{k,i}}^{2m}e^{2m\hat u_k(y_k)}=\abs{\theta_{k,i}}^{2m}\exp(2m[\hat u_k(x_{k,i} +\mu_{k,i}\theta_{k,i})+\log\mu_{k,i}]).
$$
If our claim were false, then the right-hand side would be bounded thanks to $(A_3)$, but then we would have
$w_k(y_k)\leq C,$
against our assumption. This proves $(A_1)$.
Fix now $\varepsilon, R>0$. Since $\max w_k$ is attained at $y_k$, and using \eqref{eqclaim5}, we have
\begin{equation}
 e^{2mv_k(x)}\leq 2^{2m}\frac{\inf_{1\leq i\leq \ell}|y_k-x_{k,i}|^{2m}}{\inf_{1\leq i\leq \ell}|y_k+\gamma_k x-x_{k,i}|^{2m}}.
\end{equation}
Choose $k(\varepsilon,R)$ such that $\abs{y_k - x_{k,i}}\geq\frac{R}{\varepsilon}\gamma_k$ for $k\geq k(\varepsilon,R)$ and $1\leq i\leq \ell$. Then
$$\frac{\abs{y_k-x_{k,i}}}{\abs{y_k-x_{k,i} +\gamma_k x}}\leq \frac{1}{1-\varepsilon}\quad  \text{for } x\in B_R(x), \;k\geq k(\varepsilon,R),\;1\leq i\leq \ell,$$
hence
$$e^{2mv_k(x)}\leq \frac{2^{2m}}{(1-\varepsilon)^{2m}} \quad \text{for }x\in B_R(0),\; k\geq k(\varepsilon,R).$$
With this information, we can apply the proofs of Lemma \ref{claim3} and Lemma \ref{claim4} to get $(A_2)$ and $(A_3)$ for $i=\ell+1$. Finally, $(A_4)$ follows from $(A_3)$.

\medskip

\noindent\emph{Step 3.} The procedure has to stop, i.e. $(A_5)$ has to be satisfied after a finite number of inductive steps. Indeed at the $\ell$-th steps we get
\begin{eqnarray*}
\lim_{k\to\infty}\int_\Omega e^{2m\hat u_k}dx&\geq&\lim_{R\to\infty}\lim_{k\to\infty}\sum_{i=1}^\ell\int_{B_{R\mu_{k,i}}(x_{k,i})}e^{2m\hat u_k(y)}dy\\
&=&\lim_{R\to\infty}\lim_{k\to\infty} \sum_{i=1}^\ell\int_{B_{R}(0)}e^{2m\tilde u_{k,i}(y)}dy\\
&=&\ell\int_{\R{2m}}e^{2m \eta_0}dx=\ell|S^{2m}|,
\end{eqnarray*}
which, together with \eqref{eq3.2}, gives an upper bound for $\ell$. Setting $N$ to be the $\ell$ at which our inductive procedure stops, we conclude.
\end{proof}

From now on, the $N$ converging sequences
$$\{x_{k,i}\to x^{(i)}:1\leq i\leq N\} $$ produced with Lemma \ref{hp} will be fixed and we shall set
\begin{equation}\label{S}
S:=\{x^{(i)}:1\leq i\leq N\}.
\end{equation}

\begin{lemma}\label{claim7}
For $\ell\in\{1,\ldots,2m-1\}$ there exists $C>0$ such that
\begin{equation}
\inf_{1\leq i\leq \ell}|x-x_{k,i}|^\ell\abs{\nabla^\ell\hat u_k(x)}\leq C,\text{ for }x\in\Omega.
\end{equation}
\end{lemma}

\begin{proof}
As already noticed, we can use \eqref{eq3.3}, \eqref{DAS} and the symmetry of $G$ to get
\begin{equation}\label{int0}
|\nabla^\ell\hat u_k(x)|\leq C\int_\Omega \frac{e^{2m\hat u_k(y)}}{|x-y|^\ell}dy.
\end{equation}
Let $\Omega_{k,i}:=\{x\in\Omega:\;\dist(x,\{x_{k,1},\ldots,x_{k,N}\})=\abs{x-x_{k,i}}\}$, fix $x\in \Omega_{k,i}$, and write
\begin{equation}\label{int}
\int_{\Omega_{k,i}}\frac{e^{2m\hat u_k(y)}}{\abs{x-y}^\ell}dy=\int_{\Omega_{k,i}\cap B_{k,i}}\frac{e^{2m\hat u_k(y)}}{\abs{x-y}^\ell}dy
+ \int_{\Omega_{k,i}\setminus B_{k,i}}\frac{e^{2m\hat u_k(y)}}{\abs{x-y}^\ell}dy,
\end{equation}
where $B_{k,i}:=B_{\frac{|x-x_{k,i}|}{2}}(x_{k,i})$. By Property $(A_5)$ we get
\begin{eqnarray}
e^{2m\hat u_k(y)}&\leq& C\abs{y-x_{k,i}}^{-2m} \quad \text{for }y\in\Omega_{k,i}\setminus B_{k,i}\label{*1}\\
|x-y|&\geq&\frac{1}{2}\abs{x-x_{k,i}}\quad \text{for }y\in\Omega_{k,i}\cap B_{k,i}.\label{*2}
\end{eqnarray}
Then, using \eqref{eq3.2} and \eqref{*1}, we get
\begin{equation}\label{int2}
\int_{\Omega_{k,i}\cap B_{k,i}}\frac{e^{2m\hat u_k(y)}}{\abs{x-y}^\ell}dy\leq \frac{C}{|x-x_{k,i}|^{\ell}}.
\end{equation}
As for the last integral in \eqref{int}, we write $\Omega_{k,i}\setminus B_{k,i}=\Omega_{k,i}^{(1)}\cup \Omega_{k,i}^{(2)}$, where
$$\Omega_{k,i}^{(1)}=(\Omega_{k,i}\backslash B_{k,i})\cap B_{2|x-x_{k,i}|}(x),\quad \Omega_{k,i}^{(2)}=(\Omega_{k,i}\backslash B_{k,i})\backslash B_{2|x-x_{k,i}|}(x).$$
Then straightforward computations and \eqref{*2} imply
\begin{eqnarray*}
\int_{\Omega_{k,i}\backslash B_{k,i}}\frac{e^{2m\hat u_k(y)}dy}{|x-y|^\ell}&\leq&C\int_{\Omega^{(1)}_{k,i}}\frac{dy}{|y-x_{k,i}|^{2m}|x-y|^\ell}\\
&&+C\int_{\Omega^{(2)}_{k,i}}\frac{dy}{|y-x_{k,i}|^{2m}|x-y|^\ell}\\
&\leq&\frac{C}{|x-x_{k,i}|^{2m}}\int_{\Omega_{k,i}^{(1)}}\frac{dy}{|x-y|^\ell}+C\int_{\Omega_{k,i}^{(2)}}\frac{dy}{|y-x_{k,i}|^{2m+\ell}}\\
&\leq&\frac{C}{|x-x_{k,i}|^\ell}.
\end{eqnarray*}
Summing up with \eqref{int0}, \eqref{int} and \eqref{int2}, the proof is complete.
\end{proof}

\begin{lemma}\label{claim10} Up to a subsequence, we have
$$\lim_{k\to\infty}\alpha_k=+\infty.$$
\end{lemma}

\begin{proof} We argue by contradiction. Suppose $\lim_{k\to\infty}\alpha_k=\alpha_0\in\R{}$.

\medskip

\noindent\emph{Step 1.} We claim that $S\subset\partial\Omega$, where $S$ is as in \eqref{S}, and there is a function $u_0\in C^{2m-1,\alpha}(\overline \Omega)$ such that
$$u_k \to u_0\quad \text{in } C^{2m-1,\alpha}_{\loc}(\overline \Omega\backslash S).$$ Moreover $u_0$ satisfies
\begin{equation}\label{u02}
\left\{\begin{array}{ll}
(-\Delta)^mu_0=(2m-1)!e^{-2m\alpha_0}e^{2mu_0}\text{ in }\Omega\\
u_0=\partial_\nu u_0=\ldots=\partial^{m-1}_{\nu}u_0=0\text{ in }\partial\Omega
\end{array}\right.
\end{equation}
Indeed \eqref{eq3.4} and the assumption that $\alpha_k\to \alpha_0$ imply that
\begin{equation}\label{stimaL1}
\norm{\hat u_k}_{L^1(\Omega)}\leq C.
\end{equation}
Since $\hat u_k$ satisfies \eqref{eqhat} and \eqref{eq3.2}, we can apply Theorem \ref{main} from the appendix. This implies that one of the following is true
\begin{itemize}
\item[(i)] Up to a subsequence, $\hat u_k\to \hat u_0$ in $C^{2m-1,\alpha}_{\loc}(\Omega)$.
\item[(ii)] Up to a subsequence $\hat u_k\to -\infty$ locally uniformly in $\Omega\backslash\Omega_0$ for a set $\Omega_0$ of Hausdorff dimension at most $2m-1$.
\end{itemize}
Clearly case (ii) contradicts \eqref{stimaL1}, hence case (i) occurs and $S\subset\partial\Omega$. Using the boundary condition, Lemma \ref{claim7}, and elliptic estimates, we actually infer that $\hat u_k\to \hat u_0$ in $C^{2m-1,\alpha}_{\loc}(\overline \Omega\backslash S)$. Then clearly $u_k\to u_0:=\hat u_0+\alpha_0$ in $C^{2m-1,\alpha}_{\loc}(\overline \Omega\backslash S)$ and $u_0$ satisfies \eqref{u02}.

We finally want to prove that $u_0$ is continuous in $\overline\Omega$, hence smooth.
In the limit as $k\to \infty$, Lemma \ref{claim7} implies
$$\inf_{1\leq i\leq N}|x-x^{(i)}||\nabla u_0(x)|\leq C \quad \text{for } x\in \Omega\setminus S.$$
Fix $x^{(i)}\in S$ and $\delta>0$ such that
$$|x-x^{(i)}|\abs{\nabla u_0(x)}\leq C \quad \text{for } x\in \Omega\cap B_\delta(x^{(i)})\setminus \{x^{(i)}\}.$$
Then there is a constant $C>0$ such that
$$|u(x)-u(y)|\leq C\quad \text{for }x,y\in\Omega\cap B_\delta(x^{(i)})\setminus \{x^{(i)}\},\;|x-x^{(i)}|=|y-x^{(i)}|. $$
By taking $y\in\partial\Omega$ and using \eqref{dir}, we obtain that $u$ is bounded near $x^{(i)}$. Then \eqref{u02} and elliptic regularity imply that $u_0\in C^\infty(\overline\Omega)$.

\medskip

\noindent\emph{Step 2.} If $S=\emptyset$, then Step 1 yields $u_k\to u_0$ in $C^{2m-1,\alpha}_{\loc}(\overline \Omega)$, which contradicts the assumption $\sup_\Omega u_k\to+\infty$. If instead there exists $x_0\in S\subset\partial\Omega$ and take $\delta>0$ such that $S\cap B_\delta(x_0)=\{x_0\}$.
Set for $0< r\leq\delta$
\begin{equation}\label{rhokr}
 \rho_{k,r}=\frac
{\int_{\partial\Omega\cap B_r(x_0)}
(x-x_0)\cdot\nu(x)|\Delta^\frac{m}{2} u_k|^2}
{\int_{\partial\Omega\cap B_r(x_0)}
\nu(x_0)\cdot\nu(x)|\Delta^\frac{m}{2}u_k|^2},
\end{equation}
where for $m$ odd we put $\Delta^\frac{m}{2} u_k:=\nabla \Delta^\frac{m-1}{2}u_k\in\R{2m}$ (compare \eqref{nablam} below), $\nu(x)$ denotes the exterior normal to $\partial\Omega$ at $x$, and we assume that the denominator in \eqref{rhokr} does not vanish, otherwise we simply set $\rho_{k,r}=r$. Set also
\begin{equation}\label{ykr}
y_{k,r}:= x_0+\rho_{k,r}\nu(x_0).
\end{equation}
Up to taking $\delta$ even smaller, we may assume that
\begin{equation}\label{1/2}
\frac{1}{2}\leq\nu(x_0)\cdot\nu(x)\leq 1 \quad \text{for } x\in\partial \Omega\cap \overline B_r(x_0),\;r\leq\delta,
\end{equation}
hence $|\rho_{k,r}|\leq 2r.$
Applying Lemma \ref{poho} to $u_k$ on the domain $\Omega':=\Omega\cap B_r(x_0)$, with
$$Q=(2m-1)!e^{-2m\alpha_k},\quad y=y_{k,r},$$
and by the property $(A_4)$, we get
\begin{eqnarray}
\Lambda_1&\leq&\lim_{k\to\infty}(2m-1)!\int_{\Omega'}e^{2m\hat u_k}dx\nonumber\\
&=&\lim_{k\to\infty}\frac{(2m-1)!}{2m}\int_{\partial \Omega'}(x-y_{k,r})\cdot\nu_{\Omega'} e^{2m \hat u_k}d\sigma\label{s3m}\\
&&-\lim_{k\to\infty}\frac{1}{2}\int_{\partial \Omega'}(x-y_{k,r})\cdot\nu_{\Omega'} |\Delta^\frac{m}{2} u_k|^2d\sigma  +\lim_{k\to\infty}\int_{\partial \Omega'}f_kd\sigma,\nonumber
\end{eqnarray}
where $f_k$ is defined on $\partial\Omega'$ by
\begin{equation}\label{eqfk}
f_k(x)=\sum_{j=0}^{m-1}(-1)^{m+j+1}\nu_{\Omega'}\cdot\Big(\Delta^\frac{j}{2}((x-y_{k,r})\cdot \nabla u_k(x))\Delta^\frac{2m-1-j}{2}u_k(x)\Big).
\end{equation}
Now write $f_k=f_k^{(1)}+f_k^{(2)}$, where
\begin{equation}\label{f22k}
 f_k^{(2)}(x)=\left\{\begin{array}{ll}
                      \nu_{\Omega'}\cdot\Delta^\frac{m}{2}u_k(x)\, (x-y_{k,r})\cdot \Delta^\frac{m}{2}u_k(x)&\text{ if }m\text{ is odd}\\
                      D^2\Delta^\frac{m-2}{2}u_k(x)(\nu_{\Omega'},x-y_{k,r})\,\Delta^\frac{m}{2}u_k(x)&\text{ if }m\text{ is even,}
                     \end{array}\right.
\end{equation}
where we use the notation $D^2\varphi(x)(\xi,\zeta):=\frac{\partial^2 \varphi(x)}{\partial x^i\partial x^j}\xi^i\zeta^j.$
Using \eqref{form1} below, one can see that
\begin{eqnarray*}
f_k^{(1)}(x)&=&\sum_{j=0}^{m-2}(-1)^{m+j+1}\nu_{\Omega'}\cdot\Big(\Delta^\frac{j}{2}((x-y_{k,r})\cdot \nabla u_k(x))\Delta^\frac{2m-1-j}{2}u_k(x)\Big)\\
&&+\;g_k(x),\\
g_k(x)&=&\left\{\begin{array}{ll}
                 (m-1)\nu_{\Omega'}(x)\cdot \Delta^\frac{m}{2}u_k(x)\,\Delta^\frac{m-1}{2}u_k(x)&\text{ if }m\text{ is odd}\\
                 (m-1)\nu_{\Omega'}(x)\cdot \Delta^\frac{m-1}{2}u_k(x)\,\Delta^\frac{m}{2}u_k(x)&\text{ if }m\text{ is even.}
                \end{array}\right.
\end{eqnarray*}
Notice that \eqref{dir} implies that $\nabla^\ell u_k=0$ on $\partial\Omega$ for $0\leq \ell\leq m-1$.
Since each monomial of $f_k^{(1)}$ contains a factor of the form $\partial^\gamma u_k$ for some multi-index $\gamma$ with $|\gamma|\leq m-1$,
we get
$$\int_{\partial\Omega\cap B_r(x_0)}f_k^{(1)}d\sigma=0.$$
We now claim that
\begin{multline}\label{fk22}
\int_{\partial \Omega\cap B_r(x_0)}\bigg[-\frac{1}{2}(x-y_{k,r})\cdot\nu_{\Omega} |\Delta^\frac{m}{2} u_k|^2+f_k^{(2)}\bigg]d\sigma\\
=\frac{1}{2}\int_{\partial \Omega\cap B_r(x_0)}(x-y_{k,r})\cdot\nu_{\Omega} |\Delta^\frac{m}{2} u_k|^2d\sigma.
\end{multline}
It $m$ is odd, $\Delta^\frac{m-1}{2}u_k\equiv 0$ on $\partial \Omega$ implies that $\Delta^\frac{m}{2} u_k(x)\perp \partial\Omega$ for $x\in\partial \Omega$, whence
$$f_k^{(2)}(x)=\nu_{\Omega'}\cdot \Delta^\frac{m}{2}u_k\,(x-y_{k,r})\cdot \Delta^\frac{m}{2}u_k=\nu_{\Omega'}\cdot (x-y_{k,r})|\Delta^\frac{m}{2}u_k|^2, \quad x\in\partial\Omega.$$
Then \eqref{fk22} follows.
When $m$ is even, we also have
\begin{equation}\label{nuk}
f_k^{(2)}(x)=\nu_{\Omega'}\cdot (x-y_{k,r})|\Delta^\frac{m}{2}u_k|^2\quad \text{on }\partial \Omega.
\end{equation}
To see that, write $U_k:=\Delta^\frac{m-2}{2}u_k$. Then $U_k\equiv 0$ and $\nabla U_k\equiv0$ on $\partial \Omega$, hence
$$D^2 U_k(x)=\nu^i_{\Omega}\nu^j_{\Omega} \Delta U_k,$$
\eqref{nuk} is proven and \eqref{fk22} follows.

\medskip

Now, the second integral in \eqref{fk22} must be zero by \eqref{rhokr} and \eqref{ykr}, if the denominator in \eqref{rhokr} does not vanish. If it vanishes, observe that, by \eqref{1/2}
$$
\nu(x_0)\cdot \nu(x) |\Delta^\frac{m}{2}u_k|^2\geq \frac{1}{2}|\Delta^\frac{m}{2}u_k|^2,
$$
therefore we obtain $\Delta^\frac{m}{2}u_k=0$ on $\partial\Omega\cap B_r(x_0)$, and also in this case the integrals in \eqref{fk22} vanish.

\medskip

By \eqref{dir} and Lemma \ref{claim1}, we also have
$$\bigg|\frac{(2m-1)!}{2m}\int_{\partial \Omega\cap B_r(x_0)}(x-y_{k,r})\cdot \nu_{\Omega'}e^{2m\hat u_k}  \bigg|\leq C\int_{\partial \Omega\cap B_r(x_0)} r e^{-2m\alpha_k}\leq Cr^{2m}.$$
All the other terms on the right-hand side of \eqref{s3m}, namely the integrals over $\Omega\cap\partial B_r(x_0)$, are bounded by $C r^{2m-1}$ for $0<r\leq\delta$ and $k\geq k(r)$ large enough. Indeed, by Step 1 we have
$$\lim_{k\to\infty} \sup_{\partial B_r(x_0)\cap \Omega }|\nabla^\ell u_k-\nabla^\ell u_0|=0, \quad |\nabla^\ell u_0|\leq C,\quad 0\leq \ell\leq 2m-1.$$
Therefore, taking the limit as $k\to 0$ first and $r\to 0$ then, we infer
$$\Lambda_1\leq Cr^{2m-1}.$$
This gives a contradiction as $r\to 0$, hence completing the proof in the case when $m$ is odd.

\end{proof}

\begin{lemma}\label{claim9}
Up to selecting a subsequence,
\begin{equation}\label{menoinf}
\hat u_k\rightarrow-\infty \quad\text{locally uniformly on }\overline \Omega\setminus S,
\end{equation}
where $S$ is as in \eqref{S}. Moreover
\begin{equation}\label{limuk}
 \lim_{k\rightarrow +\infty}u_k=\sum_{i=1}^N\beta_i G_{x^{(i)}}\text{ in }C^{2m-1,\alpha}_{\loc}(\bar\Omega\setminus S),
\end{equation}
with
\begin{equation}\label{beta}
\beta_i:=(2m-1)!\lim_{\delta\rightarrow 0}\lim_{k\rightarrow\infty}\int_{B_{\delta}(x^{(i)})\cap\Omega}e^{2m\hat u_k}dy,
\end{equation}
and $\beta_i \geq \Lambda_1$, for $1\leq i\leq N$.
\end{lemma}

\begin{proof} \emph{Step 1.} We claim that $\hat u_k\to-\infty$ locally uniformly on $\overline\Omega\backslash S$. Indeed take $\delta>0$ such that $\Omega_\delta:=\Omega\setminus\cup_{i=1}^N\overline B_\delta(x_i)$ is connected and $\partial \Omega_\delta\cap\partial\Omega\neq\emptyset$. Lemma \ref{claim7} implies that $\hat u_k$ is Lipschitz on $\Omega_\delta$, and we also have $\hat u_k=-\alpha_k$ on $\partial\Omega_\delta\cap\partial\Omega$, hence
\begin{equation}\label{ukbdd}
|u_k|=|\hat u_k +\alpha_k|\leq C_\delta \textrm{ in }\overline\Omega_\delta.
\end{equation}
Since $\alpha_k\to+\infty$, we have $\hat u_k\to-\infty$ uniformly on $\overline \Omega_\delta$, hence the claim is proved.

\medskip

\noindent\emph{Step 2.}
By \eqref{dir} and Lemma \ref{claim7}, the $u_k$'s are bounded in $C^0_{\loc}(\overline\Omega\setminus S)$. Since
$$(-\Delta)^m u_k=(2m-1)!e^{-2m\alpha_k}e^{2mu_k},$$
where the right-hand side is bounded $C^0_{\loc}(\overline\Omega\backslash S)$,
by elliptic regularity we have that, up to a subsequence,
$$u_k\to \psi \quad \text{in } C^{2m-1,\alpha}_{\loc}(\overline\Omega\backslash S),$$ for some $\psi\in C^{2m-1,\alpha}_{\loc}(\overline\Omega\setminus S)$. Up to taking $\delta>0$ smaller, we may assume that $\overline{B_{\delta}(x^{(i)})}\cap \overline{B_{\delta}(x^{(j)})}=\emptyset$ for $i\neq j$. Since $\hat u_k\rightarrow -\infty$ uniformly on the compact $\overline\Omega_{\delta}$, we have by \eqref{eq3.3}
\begin{eqnarray}
\lim_{k\rightarrow\infty}u_k(x)&=& (2m-1)!\lim_{k\rightarrow\infty}\int_\Omega G_x(y)e^{2m\hat u_k(y)}dy\nonumber\\
&=& (2m-1)!\lim_{k\rightarrow\infty}\sum_{i=1}^N\int_{B_{\delta}(x^{(i)})\cap\Omega}G_x(y)e^{2m\hat u_k(y)} dy.\label{green2}
\end{eqnarray}
Now we want an explicit expression for $\psi$. Fix $x\in \overline \Omega\backslash S$. We observe that $G(x,\cdot)$ is smooth away from $x$; in particular it is continuous on $B_{\delta}(x^{(i)})$ for all $i$ (up to decreasing $\delta$). By \eqref{eq3.2}, up to a subsequence we have
$$e^{2m\hat u_k}(y)dy\rightharpoonup \nu\quad \text{in }\overline\Omega$$
weakly in the sense of measures, for some positive Radon measure $\nu$.
On the other hand, since \eqref{menoinf} implies that the support of $\nu$ is contained in $S$, we get
$$\nu=\sum_{i=i}^N\beta_i\delta_{x^{(i)}},$$
for some constants $\beta_i\geq 0$.
Then \eqref{green2} implies
$$
\lim_{k\rightarrow\infty} u_k(x)=\sum_{i=1}^N\beta_i G_{x^{(i)}}(x)\quad\forall x\in\Omega\setminus S,
$$
where $\beta_i$ is as in \eqref{beta}.
Now we fix a point $x^{(i)}\in S$ and we set $\mu_{k,i}$ and $x_{k,i}$ as in Lemma \ref{claim4}. By ($A_4$)
$$\lim_{k\rightarrow \infty}\int_{B_{\delta}(x^{(i)})\cap\Omega}e^{2m\hat u_k(x)}dx\geq\lim_{R\to\infty}\lim_{k\rightarrow \infty}\int_{B_{R\mu_k}(x_{k,i})}e^{2m\hat u_k(x)}dx=|S^{2m}|.
$$
Taking the limit as $\delta\to 0$ we get $\beta_i\geq \Lambda_1$, as claimed.
\end{proof}

\begin{lemma}\label{claim11}
For any $x_0\in\partial\Omega$ we have
\begin{equation}\label{r0}
 \lim_{r\rightarrow 0}\lim_{k\rightarrow+\infty}\int_{B_r(x_0)\cap\Omega}e^{2m\hat u_k}dx=0.
\end{equation}
In particular $S\cap\partial\Omega=\emptyset$.
\end{lemma}

\begin{proof}
Fix $x_0\in\partial\Omega$. If $x_0\not\in S$, then \eqref{r0} follows at once from Lemma \ref{claim9}. Then we can assume $x_0=x^{(j)}\in \partial\Omega\cap S$ for some $1\leq j\leq N$, and proceed by contradiction. Take $\delta>0$ such that $S\cap B_{\delta}(x_0)=\{x_0\}$. Let $\nu:\partial\Omega\rightarrow S^{2m-1}$ be the outward pointing normal to $\partial\Omega$. Set $\rho_{k,r}$ and $y_{k,r}$ as in \eqref{rhokr} and \eqref{ykr}.
Take $r>0$ so small that
$$\frac{1}{2}\leq\nu(x_0)\cdot\nu(x)\leq 1 \quad \text{for } x\in\partial\Omega\cap\overline B_r(x_0),$$
so that $|\rho_{k,r}|\leq 2r$.
Applying Lemma \ref{poho} to $u_k$ on the domain $\Omega':=\Omega\cap B_r(x_0)$, with
$$Q=(2m-1)!e^{-2m\alpha_k},\quad y=y_{k,r},$$
we obtain
\begin{eqnarray*}\label{int12}
(2m-1)!\int_{\Omega'}e^{2m\hat u_k}dx&=&\frac{(2m-1)!}{2m}\int_{\partial \Omega'}(x-y_{k,r})\cdot\nu_{\Omega'} e^{2m \hat u_k}d\sigma\\
&&+\int_{\partial \Omega'}\bigg[-\frac{1}{2}(x-y_{k,r})\cdot\nu_{\Omega'} |\Delta^\frac{m}{2} u_k|^2+f_k^{(2)}(x)\bigg]d\sigma  \\
&&+\int_{\partial \Omega'}f_k^{(1)}(x)d\sigma,\nonumber
\end{eqnarray*}
where
$f_k(x)=f_k^{(1)}+f_k^{(2)}$, with the same notations as in \eqref{eqfk}, \eqref{f22k}.
Since each monomial of $f_k^{(1)}$ contains a factor of the form $\partial^\gamma u_k$ with $|\gamma|\leq m-1$,
we get
$$\int_{\partial\Omega\cap B_r(x_0)}f_k^{(1)}d\sigma=0.$$
Again we have that \eqref{fk22} holds and the corresponding integral vanishes, thanks to our choice of $\rho_{k,r}$ and $y_{k,r}$. This takes care of the integral on $\partial\Omega\cap B_r(x_0)$.

Since $G_{x_0}\equiv 0$, and the derivatives of $G_{x^{(i)}}$ are bounded in $\overline{B_r(x_0)}$ for $x^{(i)}\neq x_0$, \eqref{limuk} implies
$$
\lim_{k\rightarrow+\infty}\int_{\Omega\cap\partial B_r(x_0)}f_k^{(1)} d\sigma\leq Cr^{2m-1},
$$
and
$$\lim_{k\to\infty}\int_{\Omega\cap \partial B_r(x_0)}\bigg[-\frac{1}{2}(x-y_{k,r})\cdot\nu|\Delta^\frac{m}{2} u_k|^2+f_k^{(2)}\bigg]d\sigma\leq Cr^{2m}.$$
As for the first term on the right-hand side of \eqref{int12}, \eqref{dir} and Lemma \ref{dir} imply
$$
\int_{\partial\Omega'}(x-y_{k,r})\cdot\nu_{\Omega'}e^{-2m\alpha_k}e^{2mu_k}d\sigma\leq Cr^{2m}.
$$
Summing up all the contributions and letting $r\rightarrow 0$ we get \eqref{r0}.
\end{proof}

\begin{lemma}\label{claim13}
In \eqref{limuk} and \eqref{beta} we have $\beta_i=\Lambda_1$ for all $1\leq i\leq N$.
\end{lemma}

\begin{proof}
Since $S\cap\partial\Omega=\emptyset$, there exists $\delta>0$ such that $B_{\delta}(x^{(i)})\subset\Omega$, and $S\cap B_{\delta}(x^{(i)})=\{x^{(i)}\}$ for all $1\leq i\leq N$. Fix $i$ with $1\leq i\leq N$ and suppose, up to a translation, that $x^{(i)}=0$. Recall that
$$
\beta_i=(2m-1)!\lim_{\delta\rightarrow 0}\lim_{k\rightarrow \infty}\int_{B_{\delta}(0)}e^{2m\hat u_k}dx.
$$
By the Pohozaev identity of Lemma \ref{poho}, applied to $u_k$ on the domain $B_\delta:=B_{\delta}(0)$ with $y=0$ and $Q=(2m-1)!e^{-2m\alpha_k}$, we get
\begin{equation}\label{eqpoh}
(2m-1)!\int_{B_{\delta}}e^{2m\hat u_k}dx=I_\delta(u_k)+II_\delta(u_k)+III_\delta(u_k),
\end{equation}
where
\begin{eqnarray*}
 I_\delta(u_k)&=&\frac{\delta(2m-1)!}{2m}\int_{\partial B_{\delta}} e^{2m\hat u_k}d\sigma\\
II_\delta(u_k)&=&-\frac{\delta}{2}\int_{\partial B_{\delta}}|\Delta^\frac{m}{2} u_k|^2 d\sigma\\
III_\delta(u_k)&=&\sum_{j=0}^{m-1}(-1)^{m+j+1}\int_{\partial B_\delta}\nu\cdot\left(\Delta^\frac{j}{2}\left(x\cdot \nabla u_k\right)\Delta^\frac{2m-1-j}{2}u_k \right)d\sigma
\end{eqnarray*}
From Lemma \ref{claim9} we infer
\begin{eqnarray*}
\lim_{k\rightarrow\infty}II_\delta(u_k)&=&II_\delta(\beta_i G_0)=\beta_i^2II_\delta(G_0)\\
\lim_{k\rightarrow\infty}III_\delta(u_k)&=&III_\delta(\beta_i G_0)=\beta_i^2III_\delta(G_0).
\end{eqnarray*}
Since the functions $e^{2m\hat u_k}\to 0$ in $C^0(\partial B_\delta)$, we have
$$
\lim_{k\rightarrow\infty}I_\delta(u_k)=0.
$$
The Green function $G_0$ can be decomposed in the sum of a fundamental solution for the operator $(-\Delta)^m$ on $\R{2m}$ and a so-called regular part $R$, which is smooth:
Let us write
$$G_0=g+R\quad \text{in }\overline\Omega$$
where
$$g(x):=\frac{1}{\gamma_{2m}}\log\frac{1}{|x|},\quad \gamma_{2m}:=\frac{\Lambda_1}{2}$$
satisfies $(-\Delta)^m g=\delta_0$ (see e.g. Proposition 22 in \cite{mar1}),
and $R:=G_0-g\in C^\infty(\overline\Omega)$.
Since
\begin{equation}\label{R}
|\nabla^j R|\leq C,\quad |\nabla^j g|\leq \frac{C}{\delta^j}\quad \text{on }\partial B_\delta,
\end{equation}
we get
$$ II_\delta(R+g)-II_\delta(g)\leq C \delta \int_{\partial B_{\delta}}C\left(|\Delta^\frac{m}{2} g| +C\right)d\sigma\leq C \delta^m.$$
For the terms in $III_\delta(R+g)$, \eqref{R} implies
\begin{eqnarray*}
III_\delta^{(j)}(g+R)&:=& \int_{\partial B_\delta}\nu\cdot\left(\Delta^\frac{j}{2}\left(x\cdot \nabla (R+g)\right)\Delta^\frac{2m-1-j}{2}(R+g)\right)d\sigma\\
&=&\int_{\partial B_\delta}\nu\cdot\left(\Delta^\frac{j}{2}\left(x\cdot \nabla g\right)\Delta^\frac{2m-1-j}{2}g\right)d\sigma\\
&&+\int_{\partial B_\delta}\nu\cdot\left(\Delta^\frac{j}{2}\left(x\cdot \nabla R\right)\Delta^\frac{2m-1-j}{2}g\right)d\sigma\\
&&+\int_{\partial B_\delta}\nu\cdot\left(\Delta^\frac{j}{2}\left(x\cdot \nabla g\right)\Delta^\frac{2m-1-j}{2}R\right)d\sigma\\
&&+\int_{\partial B_\delta}\nu\cdot\left(\Delta^\frac{j}{2}\left(x\cdot \nabla R\right)\Delta^\frac{2m-1-j}{2}R\right)d\sigma\\
&=&III_\delta^{(j)}(g)+O(\delta)\quad \text{as }\delta\to 0,
\end{eqnarray*}
where $|O(\delta)|\leq C\delta$ as $\delta\to 0$.
Summing up all what we proved until now, we obtain

$$\beta_i=\beta_i^2\lim_{\delta\rightarrow 0}\lim_{k\to\infty}\big[I_\delta(u_k)+II_\delta(u_k)+III_\delta(u_k)\big]=\beta_i^2 \lim_{\delta\to 0}\big[II_\delta(g)+III_\delta(g)\big].$$
On the other hand, since $II_\delta(g)$ and $III_\delta(g)$ do not depend on $\delta$, it is enough to compute

\begin{equation}\label{eqg}
\beta_i=II_\delta(g)+III_\delta(g)
\end{equation}
for an arbitrary $\delta>0$.
Using the formula
$$\gamma_{2m}\Delta^k g=(-1)^k(2k-2)!!\frac{(2m-2)!!}{(2m-2k-2)!!}r^{-2k},$$
we find
$$
II_\delta(g)=-\frac{\delta}{2}\int_{\partial B_\delta}\left[\frac{(2m-2)!!}{\gamma_{2m}}r^{-m}\right]^2d\sigma=-|S^{2m-1}|\frac{[(2m-2)!!]^2}{2\gamma_{2m}^2}.
$$
Observing that
\begin{eqnarray*}
\Delta^k(x\cdot \nabla g)&=&2k\Delta^kg+r\partial_r\Delta^k g=0,\\
\partial_r(x\cdot\nabla g)&=&-r^{-1} - x\cdot\nabla(r^{-1})=0,\\
x\cdot\nabla g&=&r\partial_rg=-\frac{1}{\gamma_{2m}},\\
\gamma_{2m}\partial_r\Delta^k g&=&(-1)^{k+1}(2k)!!\frac{(2m-2)!!}{(2m-2k-2)!!}r^{-2k-1} \\
\end{eqnarray*}
we see that $III_\delta^{(j)}(g)=0$ for $1\leq j\leq m-1$, and
\begin{eqnarray*}
III_\delta(g)&=&III_\delta^{(0)}(g)=(-1)^{m+1}\int_{\partial B_\delta}(x\cdot \nabla g)\partial_r\Delta^{m-1}gd\sigma\\
&=&|S^{2m-1}|\frac{[(2m-2)!!]^2}{\gamma_{2m}^2}.
\end{eqnarray*}
From \eqref{eqg} we get
$$
\frac{1}{\beta_i}=|S^{2m-1}|\frac{[(2m-2)!!]^2}{2\gamma_{2m}^2}=\frac{1}{(2m-1)!|S^{2m}|},
$$
whence $\beta_i=\Lambda_1$.
\end{proof}

\medskip

\noindent\emph{Proof of Theorem \ref{trm2}.} By Corollary \ref{coru}, it suffices to prove that, under the assumption \eqref{ukinfty}, case (ii) of the theorem occurs. This follows at once putting together Lemmas \ref{hp}, \ref{claim9}, \ref{claim11} and \ref{claim13}.
\phantom{ }\hfill$\square$

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text:
Q: How to parse html tag from response of responsebody in retrofit My code is as shown below:
   private void testInfo() {
        if (InternetConnection.checkConnection(LogInActivity.this)) {
            Observable<ResponseBody> results = RetroClient.getApiService()
                    .testInfo("Basic NTcyODQ4MDc0NzEzNTIwOToxMjhiNTNkMS1iMTc2LTQxOTEtYWJmYS1hN2RhYjIzYmFjMzk=", "application/x-www-form-urlencoded",
                            "John Q. Test", "Visa", "4747474747474747", 12, 25, 999, "123 A. Street",
                            "Orem", "UT", "84058", "USA", "4355824", "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");
//            showProgressBar();
            results.subscribeOn(Schedulers.io()).observeOn(AndroidSchedulers.mainThread())
                    .subscribe(new Subscriber<ResponseBody>() {
                        @Override
                        public void onCompleted() {
                            unsubscribe();
                        }

                        @Override
                        public void onError(Throwable e) {
//                            hideProgressBar();
                            Toast.makeText(LogInActivity.this, e.getMessage(), Toast.LENGTH_LONG).show();
                        }

                        @Override
                        public void onNext(ResponseBody response) {
                            Log.d(TAG, "onNext: " + response.string());
                        }
                    });
        } else {
            Toast.makeText(LogInActivity.this, R.string.string_internet_connection_warning, Toast.LENGTH_LONG).show();

        }
    }

Now for this, I get the following as my response:
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">

<title>

</title>

    <form method="post" action="./spr.aspx" id="form1">
<input type="hidden" name="__VIEWSTATE" id="__VIEWSTATE" value="" />

<input type="hidden" name="__EVENTVALIDATION" id="__EVENTVALIDATION" value="k2sKy+QLc68jCgZVuadfy2ONS4SO3c0" />

        Processing, please wait...

    Please wait, your transaction is processing. Please don't hit back or stop.

    <input name="ResponseCipher" type="hidden" id="ResponseCipher" value="6s31abi0RZUSAw3Iwk0db9irVWKTi2+UtpSVTUE7DKlhWqLd1WBlQ==" /></form>

Here, what I want is , I want to access value of input with id ResponseCipher. What should I do to achieve that?

A: Jsoup is a library lets you parse numerous HTML tags/attributes off String.
Just parse your desire input Id and you should access the value as well.
Take a look at the following sources.

*

*Parsing HTML in Android with Jsoup

*Parsing input element using JSoup

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text:
Home » Articles » New Crittall steel window meets tough specification Over 46129 entries
Wednesday, 31st January 2018
New Crittall steel window meets tough specification
Latest advancements in high performance Crittall steel window design have been successfully combined with traditional aesthetics to meet the exacting standards demanded by one of the United States' major Ivy League universities.
Both client and architect called for neo-Gothic style fenestration to blend with the design of classrooms, student accommodation, offices, libraries and dining halls for the new college buildings.
A variety of bespoke window shapes was required, some with curved tops, others with Gothic-style heads and trefoils, but all had to satisfy tough thermal and acoustic requirements.
Crittall turned to its Berkeley range which was modified with the addition of triple glazing comprising an exterior true leaded glass panel separated via a vented cavity to an interior insulating glass unit.
An exterior putty-effect sloping glazing detail was used to replicate old putty-glazed windows, but using an interior glazing bead for ease of servicing.
The slim sightlines that are a hallmark of Crittall steel windows perfectly matched the characteristic appearance of traditional, single pane, putty glazed fenestration.
Traditional welded steel bullet style hinges, hardware patterns and back plates were incorporated but offering modern functionality and safety.
The bespoke Berkeley windows were hot dipped galvanized and polyester powder coated so as to achieve durability combined with low maintenance. The system also had a matching-profile variance offering a 45-minute UL fully-accredited and tested fire rating for particular parts of the building.
This specially designed windows contributed to the building meeting the Gold certification standard of the Leadership in Energy and Environmental Design (LEED) rating system devised by the United States Green Building Council. This was also achieved thanks to the combination of strong, slim steel profiles and the advanced glazing specification that combined to afford high solar gains.
Other features specific to the technically challenging contract included the client's requirement that the system could be "bench-glazed" off-site and brought to the building ready for fast-track installation. Window clips were pre-installed in the window perimeters to make this possible.
The Berkeley windows also needed to provide specific perimeter detailing to ensure correct watertightness marrying together the custom window profile with period stone exterior facade detailing and the demands of new-build insulation. This new detailing was designed specifically for the job and tested in a mock-up exterior wall on-site prior to the installation proper.
Says Crittall Managing Director Stuart Judge ,
"We were given the competitive challenge to develop a new product, designed in collaboration with the architects and contractors – to meet stringent performance and technical criteria, coupled with aesthetic stipulations and engineered to ensure fast track installation on these significant builds. This has been achieved."
www.crittall-windows.co.uk
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Crittall Windows


text:
WBUR News
Listen Live: Fresh Air
Supreme Court Rejects Mass. Drug Evidence Policy
This article is more than 11 years old.
The U.S. Supreme Court ruled against the state of Massachusetts on Thursday in a case that could have significant implications for how drug cases are prosecuted.
In a 5-4 ruling, the court found that defendants have a constitutional right to cross-examine drug lab analysts.
"What the Supreme Court is saying in this ruling is prosecutors can no longer rely on a certificate from a lab that a particular substance was drugs," said David Frank, a reporter with Mass Lawyers Weekly who has written about the case.
The case represents a victory for Luis Melendez-Diaz, who was convicted for cocaine trafficking based partly on drug lab evidence, and who had appealed the verdict of several lower courts.
Attorney General Martha Coakley, who had argued the case before the Supreme Court, said she was disappointed in the ruling.
"We will now be taking chemists who were doing analysis out of the lab to wait, sometimes hours, sometimes days, in district court," Coakley said. "They can't be doing work if they're traveling all over the commonwealth. So it is a huge burden."
Justice Antonin Scalia wrote for the narrow majority, arguing that Massachusetts' drug evidence policy was unconstitutional based on Melendez-Diaz's right to "confront" the evidence of his accusers.
This program aired on June 25, 2009. The audio for this program is not available.


text:
Der Okres Kežmarok (deutsch Bezirk Käsmark) ist eine Verwaltungseinheit im Osten der Slowakei mit  Einwohnern () und einer Fläche von 629,9 km².

Historisch gesehen liegt der Bezirk fast vollständig im ehemaligen Komitat Zips, ein kleiner Teil in den Leutschauer Bergen (Levočské vrchy) am Fluss Torysa gehört zum ehemaligen Komitat Sáros (siehe auch Liste der historischen Komitate Ungarns).

Städte
Kežmarok (Käsmark)
Spišská Belá (Zipser Bela)
Spišská Stará Ves (Altendorf)

Gemeinden

Das Bezirksamt ist in Kežmarok, eine Zweigstelle in Spišská Stará Ves.

Der Militärbezirk Javorina ist zum 1. Januar 2011 aufgelöst worden und das Gebiet wird auf die benachbarten Gemeinden aufgeteilt.

Kultur

Weblinks

Kezmarok


The government of Prime Minister Alexis Tsipras got a vote of confidence in parliament on Wednesday evening, with the support of 151 deputies, out of a total of 300. His victory clears major obstacle for Greece's approval of a deal to end Macedonia name dispute.
The prime minister initiated the motion after the resignation of Panos Kammenos, leader of Independent Greeks (ANEL), the junior member of the ruling coalition. Kammenos, who served as National Defence minister, resigned over the Prespes Agreement.
A total of 148 deputies voted down the motion, and one deputy of main opposition New Democracy (Giorgos Kassapidis) was absent for health reasons.
"Today the Parliament gave a confidence vote to stability; a confidence vote for the effort to recover internationally the credibility of our country", Prime Minister Tsipras said followed the result of the roll call.
Prime Minister Alexis Tsipras accused main opposition leader Kyriakos Mitsotakis of "theatricality" and of "shouting without substantive arguments," during the debate in parliament over a vote of confidence on Wednesday evening.
"I called for this debate and the process of a vote of confidence in full understanding of the historicity of the times, and mainly with a complete sense of my duty toward parliament, the Greek people, and democracy," Tsipras said.
"I have taken the risk of asking for clear solutions," he said.
The prime minister also charged Mitsotakis of demanding a vote of confidence and then not having the courage to table a motion of censure. "Now that I have dared (table a motion for confidence), you have an issue with it again," Tsipras said, and called on each deputy to assume their patriotic and national duty.
Addressing himself to parties of the opposition, said, "You commit an injustice to yourselves with the criticism you exercise," and said that his government needs to complete the critical issues ahead and requires the full confidence of parliament's majority to reach the end of his full term in October 2019.
During his address – the last speech before the roll-call vote – Tsipras said that FYROM's note verbale informing Greece that it had completed the terms of the Prespes Agreement just reached Athens, and told Mitsotakis there will be plenty of time to discuss it. He also challenged him to a TV channel of his choice.
"So what do we have here, Mr. Mitsotakis? The full and complete deconstruction of the excuses you discovered in order to hide from the historical obligation allotted to you and your party," Tsipras concluded.
Potami leader said he will not give the government a vote of confidence, in his address in parliament on Wednesday evening.
He also called on parties to agree they will not allow deputies leaving the party under which they gained a seat in parliament to switch to other parliamentary groups.


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Q: Freeglut, OpenGL and memory I've started practicing OpenGL with Glew and Freeglut.
I have a question about my application and was wondering if anyone ran into the same problem (if it is one)?
When I initially execute my application, the memory used is around 22,000 KB. After minimizing my window and maximizing it again, it only takes 2,900-3,300 KB of memory and continues to do so even after minimizing and maximizing the window again as well as performing mouse and keyboard input while the window has the focus.
I'm wondering why this is so? I don't know too much about FreeGlut and I'm wondering if anyone else has noticed this behavior when minimizing/maximizing the window with FreeGlut. Or maybe this is an OS-specific thing?
Sorry for not mentioning it before, but I'm using Windows XP SP3 and I'm setting up the OpenGL context with the following lines of code:
glutInit(&argc, argv);
glutInitContextVersion(3, 3);
glutInitDisplayMode(GLUT_RGBA | GLUT_DOUBLE | GLUT_DEPTH);
glutInitWindowPosition(30, 30);
glutInitWindowSize(1000, 562);
glutCreateWindow("Testing");

glewExperimental = GL_TRUE;
glewInit();

A: This is highly OS dependent and also depends on how you measure memory usage, but I can give you a little bit of insight into why this might be happening on Microsoft Windows. Microsoft has the following to say about user-mode memory usage in an application that uses a WDDM-based driver:

Existing games and other graphics applications frequently allocate virtual memory for a copy of the video memory resources that the application uses. The application uses this copy to restore the display quickly if the contents of video memory are lost. For example, the application uses this copy if the user presses ALT+TAB or if the user puts the computer in standby. Typically, the DirectX run time manages the copy on behalf of the application when the application creates a managed resource. However, an application can also manage the copy itself. The virtual memory that the copy uses is directly proportional to the video memory resources that the application allocates.

Now, while Microsoft describes this a DirectX problem it actually applies to OpenGL too. Behind the scenes OpenGL usually deals with "device lost" events completely transparently (this is not a part of OpenGL itself, but of the window system -- WGL in this case). Although you can actually receive these events in your software in OpenGL 4.x using one of the robustness extensions you usually want to pretend like they do not exist. In any case, I suspect that this is what is to blame.
Your memory consumption will vary wildly depending on how you measure your application's memory consumption, whether it's simply a count of the number of virtual memory pages allocated (virtual size), or actual resident pages (working/resident set). On Windows, if you look in the task manager at memory consumption that is usually a measure of working set. Working set is a very vague concept, and usually refers to the number of pages that were "recently" referenced; it can grow/shrink depending on when it is sampled irrespective of how much memory is actually resident at that exact instant. I would chalk this up to normal driver behavior, and realize that this memory is probably not going to affect anything seriously.
If you're running on a modern desktop 64-bit platform (x86-64) you actually have a 48-bit hardware address space (256 TiB) and the OS will give you a fraction of this (8 TiB on Windows) for individual user-mode processes, so 22,000 KiB is completely insignificant (if you actually compiled your software as 64-bit).


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Whether you are a SuccessFactors user or not - we can help you get to the next level of expertise with your human capital technology to maximize performance from your workforce. If you already use SuccessFactors - we can help you optimize your current solutions to make sure you are getting the most out of your investment.
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text:
in: Unknown year release, Universal films, Sequels,
Based on books
Based on comics
Fanon
Galaxion 2 was a planned sequel to the 1999 Universal animated film Galaxion, which in turn is based on the comic series of the same name by Canadian artist Tara Tallan.
The plot is currently unknown.
The first film was a box office failure.
Universal lost the rights to the original Galaxion comic series.
The sequel was permanently cancelled and the first film remains as a stand-alone.
3 The Lego Batman Movie 2


Whether you are the founder, a volunteer or a donor that is hands off, if you are going to be the representative to pitch the group for funding your nominated non-profit; you will need to know what they do and how they do it.
In just 5 minutes you need to be able to tell what the non-profit does, what impact you make on the Mat-Su community and specifically what the non-profit will do with the money that is donated by this group of women.
The women sitting the the room are committed to the 100 Plus Women Who Care because of the SIMPLICITY, the quick decisiveness and the camaraderie of seeing all of the great work in the Mat-Su community… Use the time to make a huge impact. Even if your non-profit isn't chosen as the benefactor for the night, you have had the audience of change makers in our Mat-Su community…use this time wisely.
Practice your elevator speech. You need to be able to tell the story of the work your organization does in less than 1 minute. People get easily lost by long drawn out explanations. Write down what your non-profit does, how they do it and who benefits. Then wrap that around a few sentences and Voila! You have got your pitch.
Where will the money go! The people in the room are ready to make a wise choice about where they donate. Those that struggle to define where the folks hard earned money will go once they write that check will find they struggle to get those checks written at all. We are not talking about detailed financial statements here, what we are talking about is a strong description of what the funds will be supporting. It could be general operating budget to help grow a new local organization, it could be for materials to distribute as a part of the programs work. Taking the time to find out where the money will go pays off in the long run and will give you the confidence to stand up and make your pitch to the group. If you don't explain in your allotted time to give your pitch, they will ask in the Q & A, you will still have to have an answer .
Be prepared or say "No thanks, I'll do it next time" if you aren't ready to speak, and INSPIRE YOUR AUDIENCE WITH YOUR CAUSE!
Remember that you must be a member of 100+ Women Who Care in order to make a presentation at a meeting.
To join 100 Plus Women Who Care Mat-Su Chapter, complete an online Membership form or print this form and bring it to the next meeting. To nominate a charity for consideration, complete a Nomination Form and email it to: 100pluswwcmatsu@gmail.com at least two days before the next meeting. You must be at the meeting to put your name in the hat to be eligible to be drawn as one of the three selected members to speak about the organization you would like to promote.


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text:
Hillcrest's Chastine signs with Shelton State
Edwin Stanton @edwinstantonu2
Kyle Chastine is quite familiar with Shelton State.
The Hillcrest left-handed pitcher has attended baseball camps directed by Buccaneers head coach Bobby Sprowl for several years.
He will be seeing a lot more of Sprowl next year. Chastine signed with Shelton State last week.
"I've know coach Sprowl my whole life," Chastine said.
Last season Chastine helped the Patriots earn a spot in the Class 6A semifinals with a 6-3 record, 2.22 ERA and 88 strikeouts. He wants to be a leader for the 2020 season and get the Patriots back to the semis and beyond.
"You want to be one of the top pitchers in the state and make all-state and everything, and have a chance to win the state championship, and just do everything you can to help the team out," Chastine said.
"We are going to have to work harder this year to get back there. We do have a lot of talent coming up that can help us."
Chastine gave up just 20 earned runs in 63 innings last season with just 31 walks.
"Kyle's an electric lefty for us," Hillcrest coach Mark Garner said. "He's one of, if not the hardest workers on the team. He's changed his body over the last couple of years and changed his attitude and he's worked himself into the position where he is now.
"This year Kyle is going to be our guy. He has more responsibility but he has more of an opportunity to be a leader on our team. He can play left field for us, play first base and hit in the middle of our lineup. He will be one of our key players.
Reach Edwin Stanton at 205-722-0226, edwin.stanton@tuscaloosanews.com or via Twitter, @edwinstantonu2


A 32-bp deletion in CCR5 (CCR5 Delta 32) confers to PBMC resistance to HIV-1 isolates that use CCR5 as a coreceptor. To study this mutation in T cell development, we have screened 571 human thymus tissues for the mutation. We identified 72 thymuses (12.6%) that were heterozygous and 2 (0.35%) that were homozygous for the CCR5 Delta 32 mutation. We found that thymocyte development was normal in both CCR5 Delta 32 heterozygous and homozygous thymuses. In 3% of thymuses we identified a functional polymorphism of CD45RA, in which cortical and medullary thymocytes failed to down-regulate the 200- and 220-kDa CD45RA isoforms during T cell development. Moreover, we found an association of this CD45 functional polymorphism in thymuses with the CCR5 Delta 32 mutation (p = 0.00258). In vitro HIV-1 infection assays with CCR5-using primary isolates demonstrated that thymocytes with the heterozygous CCR5 Delta 32 mutation produced less p24 than did CCR5 wild-type thymocytes. However, the functional CD45RA polymorphism did not alter the susceptibility of thymocytes to HIV-1 infection. Taken together, these data demonstrate association of the CCR5 Delta 32 mutation with a polymorphism in an as yet unknown gene that is responsible for the ability to down-regulate the expression of high m.w. CD45RA isoforms. Although the presence of the CCR5 Delta 32 mutation down-regulates HIV-1 infection of thymocytes, the functional CD45RA polymorphism does not alter the susceptibility of thymocytes to HIV-1 infection in vitro.