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text:
\section{Introduction}\label{sec:intro}
Interest in the Painlev\'e equations has grown since they were recognised as universal models in mathematical physics, in fields such as random matrix theory \cite{Deift2007, For2003, TW1994}, quantum gravity \cite{Gross1990a}, quantum field theory \cite{CTW1981}, nonlinear optics \cite{GJ1989}, general relativity \cite{Mac1983} and statistical mechanics \cite{Levi1992}. Critical solutions of interest in such applications were first identified through asymptotic analysis \cite{WMTB76,MTW77} (see also \cite{FIKN2006}), usually as the independent variable approaches a fixed singular point at infinity. However, the asymptotic analysis of the Painlev\'e equations remains incomplete in the literature, particularly for the third, fourth and fifth Painlev\'e equations in the complex plane. In this paper, we provide new results describing generic leading order behaviours of these equations.

To make the asymptotic analysis more explicit, we write the first five Painlev\'e equations in the following form (known as Boutroux form for $\text{P$_{\text{I}}$}-\text{P$_{\text{II}}$}$ \cite{Bout13})
\begin{align}
\text{P$_{\text{I}}$}: u_{zz}&=6u^2-1-\,\frac{u_z}{z}+\frac{4u}{25 z^2},\label{p1u}\\
\text{P$_{\text{II}}$}: u_{zz}&=2u^3-u-\,\frac{\alpha+u_z}{z}+\frac{u}{9 z^2},\label{p2u}\\
\text{P$_{\text{III}}$}:  u_{zz}&=\frac{u_z^2}{u} +\frac \delta u +\gamma\, u^3 + \frac{\alpha\, u^2+\beta}{z} - \frac{u_z}z,\label{p3u}\\
\text{P$_{\text{IV}}$}:  u_{zz}&=\frac{u_z^2}{2\,u}+2\,u+4\,u^2+\frac{3}{2}u^3-\frac{\alpha\,u}{z}-\frac{u_z}{z}+\frac{\beta}{4\,z^2\,u}+\frac{u}{8\, z^2},\label{p4u}
\\
\text{P$_{\text{V}}$}:  u_{zz}&=\left(\frac{1}{2u}+\frac{1}{u-1}\right)u_z^2-\frac {u_z}{z} +\frac{(u-1)^2}{z^2}\left(\alpha\, u+\frac{\beta}{u}\right)+\gamma\frac u z+\delta\, u\frac{u+1}{u-1}.\label{p5u}
\end{align}
Note that $\text{P$_{\text{III}}$}$ and $\text{P$_{\text{V}}$}$ are in the original form \cite{G09}, and $\text{P$_{\text{IV}}$}$ is a transformed version of its conventional form. (See Appendix \ref{A} for the transformations required for $\text{P$_{\text{I}}$}$, $\text{P$_{\text{II}}$}$ and $\text{P$_{\text{IV}}$}$.)

In the limit $|z|\to\infty$, the above equations become autonomous and these limiting equations have first integrals. This observation leads us to the following definitions of slowly varying quantities that play a crucial role in our analysis of $\text{P$_{\text{I}}$}-\text{P$_{\text{V}}$}$:
\begin{subequations}\label{eq:Ham}
\begin{align}
E_{\rm I}:=&\frac12\left(u_z^2-4u^3+2u\right),\\
E_{\rm II}:=&\frac12\left(u_z^2-u^4+u^2\right),\\
E_{\rm III}:=&\frac{1}{2\,u^2}\left(u_z^2-\gamma u^4+\delta\right),\label{eq:HamIII}\\
E_{\rm IV}:=&\frac{1}{2\,u}\left(u_z^2-u^4-4\,u^3-4\,u^2\right),\\
E_{\rm V}:=&\frac{1}{2\,u\,(u-1)^2}\left(u_z^2+2\,\delta\,u^2\right).
\end{align}
\end{subequations}
Note that these may be considered as Hamiltonians and are conjugate to the Hamiltonians in the literature \cite{O80}. We rewrite equations \eqref{eq:Ham} as
\begin{equation}\label{e:uprimeJ}
u_z^2=:P_{\rm J}(u; E_{\rm J}),
\end{equation}
for $\rm J=\rm I,\ldots \rm V$, and define the corresponding functionals $\omega^{(\rm J)}_k$, $\tilde{\om}^{(\rm J)}_k$ by
\begin{eqnarray}\label{periodints}
\omega^{(\rm J)}_k&=&\oint_{C_k} \frac{du}{\mathpalette\DHLhksqrt{P_{\rm J}(u; E_{\rm J})}}=\frac{d}{dE_{\rm J}}\tilde{\om}^{(\rm J)}_k,
\end{eqnarray}
on a universal covering space for $u\in\mathbb C$, where $C_k$, $k=1, 2$ are independent closed contours enclosing a pair of roots of $P_{\rm J}$. The leading-order behaviour of each equation $\text{P$_{\text{J}}$}$ is given by an elliptic function with periods given by $\{\omega^{(\rm J)}_1, \omega^{(\rm J)}_2\}$.

For each $J=\rm I, \dots, V$, the Picard-Fuchs equations for these elliptic integrals take the following form:
\begin{eqnarray}\label{pfeq}
\frac{d^2\tilde{\om}^{(\rm J)}_k}{dE_{\rm J}^2}=F_{\rm J}(E_{\rm J})\tilde{\om}^{(\rm J)}_k,
\end{eqnarray}
where $k=1,2$. The expressions for the coefficients $F_{\rm J}(E_{\rm J})$ are given in Theorem \ref{thm} below (see section \ref{s:main}).

Such behaviours were first considered by Boutroux \cite{Bout13, Bout14}. For $\text{P$_{\text{I}}$}$ and $\text{P$_{\text{II}}$}$, Joshi and Kruskal \cite{JoshiThesis, JK1988,JK1992} analysed leading-order elliptic-function behaviours in the limit $|z|\to\infty$ for $z\in\mathbb C$ by developing a complex averaging method to obtain the modulation of such behaviours as the angle of approach to infinity changes. We obtain such modulations for the first time for $\text{P$_{\text{III}}$}$, $\text{P$_{\text{IV}}$}$ and $\text{P$_{\text{V}}$}$ in this paper.

The prevailing method of asymptotic study for the $\text{Painlev\'e }$ equations in the literature relies on the Riemann-Hilbert or isomonodromy approach applied to linear equations associated with the $\text{Painlev\'e }$ equations \cite{FIKN2006}. A review of the application of the isomonodromy method for elliptic-function-type behaviours of ${\rm P}_{\rm I}$ and ${\rm P}_{\rm II}$ can be found in \cite{Kitaev94}. Such studies were motivated by the need to find connections between asymptotic behaviours that hold along certain distinguished directions in the complex plane. In the Boutroux form for ${\rm P}_{\rm J}$ given above, these directions are given by semi-axes lying along the real and imaginary directions for $z\in\mathbb C$. To the best of our knowledge, the Riemann-Hilbert approach has not been used to find the modulation of elliptic-function-type behaviours in the interior of sectors bounded by such rays, i.e., quadrants in $z\in\mathbb C$.
In the present paper, we focus on the problem in the interior of quadrants and deduce new results for the third, fourth and fifth Painlev\'e equations.

Our main result is given by Theorem \ref{thm} (see Section \ref{s:main} below). For each ${\rm J}={\rm III}$, $\rm IV$, $\rm V$, we find that the slow modulation of $E_{\rm J}$ is given to leading order by complete elliptic integrals associated to the leading-order elliptic function. It is surprising to find that the equation for the modulation of $E_{\rm J}$, i.e., Equation \eqref{eq:modulation}, turns out to be identical for $\text{P$_{\text{I}}$}$ to $\text{P$_{\text{V}}$}$; see Theorem \ref{thm} below. This unexpected result suggests that the \text{Painlev\'e } equations share a fundamental asymptotic property, which has not been observed before.

\subsection{Main result}\label{s:main}
 In this section, we state our main result, namely Theorem \ref{thm}. We start with some preliminary notation to describe initial value problems and and remarks to clarify the hypotheses of the theorem.

For each $\rm J=\rm I,\ldots, \rm V$, suppose $0<\epsilon<1$ and $a, \,p\in\mathbb C$ are given numbers such that $|p|>\epsilon$ and for $\rm J={\rm III},\, {\rm IV},\, \rm V$, $\epsilon<|a|$, while for $\rm J=\rm V$, $\epsilon<|a-1|$.

\begin{definition}\label{def11}
Assume that $\Phi$ lies in an annulus given by $\mathcal D_\epsilon=\{|z|>1/\epsilon\}$. For each ${\rm P}_{\rm J}$, define initial values
\[
u(\Phi)=a, \; u'(\Phi)=p,
\]
where $a\neq 0$ for $\text{P$_{\text{III}}$}$ and $\text{P$_{\text{IV}}$}$, and $a\neq 0$ or $1$ for $\text{P$_{\text{V}}$}$.  Define the set of numbers $\Phi$, $a$, $p$ satisfying the above conditions to be {\em admissible}.
\end{definition}

\begin{rem}
Note that standard theorems applied to admissible initial data give a unique solution $u(z)$ in a domain containing $\Phi$ in the interior of $\mathcal D_\epsilon$. By the well known fact that solutions are meromorphic in domains of the universal covering space not containing the fixed singularities of ${\rm P}_{\rm J}$, the domain of existence of $u$ can be extended to a large bounded disk punctured at its movable poles  (see, in particular, the description of \lq\lq cheese-like\rq\rq\ regions in \cite{JK1994}).
\end{rem}
\begin{rem}
Each admissible $a$ and $p$ gives a value of $E_{\rm J}$ at $\Phi$. For each $\rm J$, we can apply the inverse function theorem to the respective Equation \eqref{eq:Ham} in a neighbourhood of $\Phi$, to get two new values of $z$ at which $u$ takes on the value $a$. This result is related to the fact that \eqref{eq:Ham} defines an elliptic curve for each $\rm J$, with $E_{\rm J}$ providing the modulus of the leading-order elliptic function behaviour. To see that these new points can be reached by analytic continuation of $u$, we apply similar arguments to those given in \cite{JK1994}. The separation between each of these points and $\Phi$ is approximately equal to a period of the leading order behaviour $\omega_i$, $i=1,2$, defined above by Equation \eqref{periodints}. These results are proved in Theorem \ref{thm} below.
Let these new points be given by $\Phi+\Omega_i$,  $i=1,2$. Each $\Omega_i$ is approximated by .
\end{rem}
We are now in a position to state our main result.
\begin{thm}\label{thm}
Given $0<\epsilon<1$,  let $\Phi$, $a$, $p$ be admissible numbers and assume $u(z)$ is a solution of ${\rm P}_{\rm J}$ satisfying $u(\Phi)=a, u'(\Phi)=p$. Define $E_{\rm J}$ for each respective $\rm J=\rm I,\ldots, \rm V$ by Equations \eqref{eq:Ham}. Then for sufficiently large $\Phi$ there exist $\Omega_i$ such that
\begin{equation}\label{eq:modulation}
E_{\rm J}(\Phi+\Omega_i^{(\rm J)})-E_{\rm J}(\Phi)=-\frac{\tilde{\om}_i^{(\rm J)}}{\Phi}+\frac{\omega_i^{(\rm J)}\tilde{\om}_i^{(\rm J)}}{\Phi^2}+\mathcal{O}\left(\frac{1}{\Phi^3}\right),
\end{equation}
where $i=1,2$. Moreover, $E_{\rm J}$ is bounded along a ray going to infinity with a fixed angle. The corresponding elliptic integrals $\tilde{\om}_i^{(\rm J)}$ satisfy a second order Picard-Fuchs differential equation $\tilde{\om}_i^{(\rm J)}{''}=F_{\rm J}(E)\tilde{\om}_i^{(\rm J)}$, where primes denote differentiation with respect to $E$. The coefficients $F_{\rm J}$ are given by
\begin{eqnarray*}
F_{\rm I}(E)&=&-\frac{15}{4}\frac{1}{(27E^2-2)},\\
F_{\rm II}(E)&=&-\frac32\frac{1}{E\left(8E-1\right)},\\
F_{\rm III}(E)&=&-\frac14\frac{1}{(E^2+\delta\gamma)},\\
F_{\rm IV}(E)&=&-\frac{6}{E\left(27 E-16\right)},\\
F_{\rm V}(E)&=&-\frac{1}{E\left(4E+\delta\right)}.
\end{eqnarray*}
Furthermore, the distances to the next repeated initial value in the directions of the two local periods are given by
\begin{equation}
\Omega_i^{(\rm J)}=\omega_i^{(\rm J)}-\frac{1}{\Phi}\frac{\tilde{\om}_i^{(\rm J)}\omega^{(\rm J)}_{i} {'}}{2}-\frac{\omega^{(\rm J)}_{i} {'}}{\Phi}G_{\rm J}( u(\Phi))+\mathcal{O}(1/\Phi^2),
\end{equation}

where $'=\frac{d}{dE_{\rm J}}$, and
\begin{align*}
G_{\rm I}(u(z))&=-\frac{4}{15\,u_z}(6u^4 - 9u^2 - 6Eu+2),\\
G_{\rm II}(u(z))&=\alpha\, u-\frac{u^5-2u^3+(1-2E)u}{3u_z},\\
G_{\rm III}(u(z))&=\frac{\alpha\,u^2-\beta}{u}-\frac{\gamma u^4+\delta}{uu_z},\\
G_{\rm IV}(u(z))&=-\alpha\,u-\frac{3u^4+ 18u^3 + 32u^2 + (16-3E)u}{6u_z},\\
G_{\rm V}(u(z))&=-\frac{\gamma}{2}\frac{u+1}{u-1}+\delta\frac{u(u+1)}{u_z(u-1)}.
\end{align*}
\end{thm}
In the remainder of the paper, we provide a proof of this theorem for each of ${\rm P}_{\rm J}$, $\rm J={\rm III}, {\rm IV}, {\rm V}$.

\subsection{Background}
We use standard notation for asymptotic relations in a limit (see \cite{BO1999} for further details). The method of averaging \cite{SVM2007} is used to describe the modulation of the leading-order asymptotic behaviours approaching infinity, which involve (doubly) periodic functions. In this approach, we describe the solution's behaviour by separating it into two parts, where the first leading-order averaged solution is periodic over a long time scale, while the remaining smaller part of the solution fluctuates on a short time scale.  Typically, the method of averaging is applied after introducing a small parameter. In this paper, the small parameter is understood to be given locally by the size of $1/|z|<\epsilon$.

We note that the method of multiple-scales could also have been used in this context. An extension of the classical multiple-scales method was developed in \cite{JoshiThesis, JK1988} to study the global asymptotic behaviour of generic solutions of $\text{P$_{\text{I}}$}$ and $\text{P$_{\text{II}}$}$. However, there is a technical requirement for the periods of the leading-order solution to be fixed before multiple-scales is applied. This requirement leads to a non-conformal mapping of the complex plane, which means that the equation and its solutions needed to be embedded in a framework of non-analytic functions. For simplicity, to avoid these technicalities, we focus here on the method of averaging to obtain our results.

\subsection{Outline of the paper}
The remainder of the paper gives results for each of $\text{P$_{\text{III}}$}$, $\text{P$_{\text{IV}}$}$, $\text{P$_{\text{V}}$}$. Section \ref{sec:p3} and Appendix \ref{B} provide a detailed calculation and necessary arguments for the proof of Theorem \ref{thm} for $\text{P$_{\text{III}}$}$. In Section \ref{sec:p4}, we present an outline of the proof for $\text{P$_{\text{IV}}$}$, while that for $\text{P$_{\text{V}}$}$ is presented in Section \ref{sec:p5}. The paper ends with a conclusion and discussion of the main results in Section 5.

\section{The third \text{Painlev\'e } equation}\label{sec:p3}
In this section we give the proof of Theorem \ref{thm} for $\text{P$_{\text{III}}$}$, i.e. Equation \eqref{p3u}. In particular, we carry out the averaging method for the Hamiltonian $E_{\rm III}$, find the Picard-Fuchs equations for the related elliptic integrals, and deduce the asymptotic expansion of $\Omega_i^{\rm (III)}$. For simplicity, we drop the label $\rm J=III$ in this section.

We first make use of a transformation $u=e^{v}$ so that when we do an expansion the first-derivative term is removed from the leading order equation, see Appendix \ref{A2} for derivation. This transformation is defined on the universal covering space $U$ defined by $\exp: U\to C\backslash\{0\}$. One can do this transformation at the step of calculating $E(\Phi+\Omega_i)-E(\Phi)$, however we rather apply this transformation at the beginning of the analysis to make consistency manifest. Equation \eqref{p3u} becomes
\begin{equation}\label{p3inv}
v_{zz}=\gamma e^{2v} + \delta e^{-2v} -\frac{v_z}{z}+\frac{\alpha e^v+\beta e^{-v}}{z}.
\end{equation}
Integrating equation \eqref{p3inv} once leads to
\begin{equation}\label{vteq}
v_z^2=\gamma e^{2v}-\delta e^{-2v}+2E,
\end{equation}
where $E$  is the same as in \eqref{eq:HamIII} (after transformation). We take the initial conditions $v(\Phi)=\ln a:=b$ and $v'(\Phi)=\frac pa:=q\neq 0$, where $a$ and $p$ are {\em admissible}, and $|\Phi|\gg1$. We decompose the solution into two parts: $v= V+\hat{v}$, where $\hat{v}\ll V$ as $|z|\to\infty$. Substituting into \eqref{vteq}, the equation decouples into
\begin{subequations}\label{p3v}
\begin{align}
 V''&=\gamma e^{2 V}+\delta e^{-2 V}\label{p3vcpp},\\
\hat{v}''&=\gamma e^{2 V}\sum_{n=1}^{\infty}\frac{(2\hat{v})^n}{n!}+\frac{\delta}{e^{2 V}}\sum_{n=1}^{\infty} \frac{(-2\hat{v})^n}{n!} -\frac{ V'+\hat{v}'}{z}+\frac{\alpha e^{ V+\hat{v}}+\beta e^{- V-\hat{v}}}{z},\label{p3vhpp}\\
&=2\hat{v}(\gamma e^{2 V}-\delta e^{-2 V})-\frac{ V'}{z}+\frac{\alpha e^{ V}+\beta e^{- V}}{z}\nonumber\\
&\hspace{2cm}+2\hat{v}^2(\gamma e^{2 V}+\delta e^{-2 V})-\frac{\hat{v}'}{z}+\hat{v}\frac{\alpha e^{ V}-\beta e^{- V}}{z}+\mathcal{O}(z^{-3}).\nonumber
\end{align}
\end{subequations}
and the initial values become
\begin{equation*}
 V(\Phi)=b, \; V'(\Phi)=q,\;\hat{v}(\Phi)=0,\; \hat{v}'(\Phi)=0.
\end{equation*}
Equation \eqref{p3vcpp} tells us that $V=\mathcal{O}(1)$, and $V$ and $V''$ have the same order. A dominant balance analysis on each leading order term in \eqref{p3vhpp} tells us that $\hat{v}=\mathcal{O}(1/z)$; $\hat{v}$, $\hat{v}'$ and $\hat{v}''$ are of the same order, moreover $V$ and $V'$ are also of the same order. After integrating equation \eqref{p3vcpp} once, we define two integrals (analytically continued),
\begin{eqnarray}
\tilde{\om}_i&=&\oint_{\Gamma_i}\mathpalette\DHLhksqrt{\gamma e^{2 v}+2E - \delta e^{-2 v}}\,d v, \text{ and}\label{omtinv}\\
\omega_i&=&\oint_{\Gamma_i}\frac{1}{\mathpalette\DHLhksqrt{\gamma e^{2 v}+2E - \delta e^{-2 v} } } \,d v,\label{ominv}
\end{eqnarray}
where $i=1,2$. These are elliptic integrals when expressed in $u$. The linearly independent contours to be taken are depicted in Fig 1.
\begin{figure}[h!]\label{contourp3}
\begin{tikzpicture}[scale=0.5]
\draw[->] (-5,0)--(6,0) node[right]{};
\draw[->] (-4,-5)--(-4,5) node[above]{};
\draw[fill] (3,1) circle [radius=0.05];
\draw[fill] (-3,-1) circle [radius=0.05];
\draw[fill] (-2,2.5) circle [radius=0.05];
\draw[fill] (2,-2.5) circle [radius=0.05];
\draw[thick, decoration={markings, mark=at position 0.125 with {\arrow[line width=1.4pt]{>}}}, postaction={decorate}] (2.2,-0.2) ellipse (20mm and 35mm);
\node at (4,4) {$\Gamma_1$};
\draw[thick, decoration={markings, mark=at position 0.125 with {\arrow[line width=1.4pt]{>}}}, postaction={decorate}] (0.4,2) ellipse (42mm and 18mm);
\node at (4.9,-1) {$\Gamma_2$};
\end{tikzpicture}
\caption{The contour choice for $\omega$ and $\tilde{\om}$ integrals.}
\end{figure}
\subsection{Averaging of the Hamiltonian}
In this subsection the averaging of $E_{\rm III}$ defined by $\Delta E:=E(\Phi+\Omega_i)-E(\Phi)$, $i=1,2$, is  calculated, where
\begin{equation*}
E=\frac12\left(v_z^2-\gamma e^{2v}+\delta e^{2v}\right),
\end{equation*}
and the subscript $i$ will be dropped hereafter for convenience. Our task is therefore to evaluate
\begin{equation}\label{p3ave}
E(\Phi+\Omega)-E(\Phi)=\frac 1 2 \left(v_z^2(\Phi+\Omega)-v_z^2(\Phi)\right).
\end{equation}
In order to find $v_z(\Phi+\Omega)$, we first use a Taylor expansion on $v(z)$ around $\Phi+\omega$. We remark here that we expect $\Omega$ is close to $\omega$. Setting $z=\Phi+\Omega$ and substituting $v= V+\hat{v}$, we obtain
\begin{equation*}
v(\Phi+\Omega)=\left. \left(V+\hat{v}+(\Omega-\omega)( V'+\hat{v}')+\frac{(\Omega-\omega)^2}{2}( V''+\hat{v}'')\right)\right|_{z=\Phi+\omega}+\mathcal{O}((\Omega-\omega)^3).
\end{equation*}
where $'=\frac{d}{d\,z}$. We solve this equation for $\Omega-\omega$ to find
\begin{equation}\label{p3Om}
\Omega-\omega=\left.\left(-\frac{\hat{v}}{ V'}+\frac{\hat{v}\vh'}{( V')^2}-\frac{ V''\hat{v}^2}{2( V')^3}\right)\right|_{z=\Phi+\omega}+\mathcal{O}((\Omega-\omega)^3),
\end{equation}
which shows that $\Omega-\omega$ is of order $\hat{v}$, therefore is of order $\frac1z$. Using \eqref{p3Om} and performing the analogous expansion on $v_z$, we obtain
\begin{eqnarray*}
v_z^2(\Phi+\Omega)&=&\left.\left(( V')^2+2( V'\hat{v}'- V''\hat{v})+(\hat{v}')^2-2\hat{v}\vh''+\frac{ V'''\hat{v}^2}{ V'}\right)\right|_{z=\Phi+\omega}+\mathcal{O}(z^{-3}),
\end{eqnarray*}
where $ V'''=2 V'(\gamma e^{2 V}-\delta e^{-2 V})$. Therefore the expression \eqref{p3ave} becomes
\begin{eqnarray}
&&E(\Phi+\Omega)-E(\Phi)\label{E31}\\
&=&\hspace{-1mm}\left.\left(( V'\hat{v}'- V''\hat{v})+\frac 1 2 (\hat{v}')^2-\hat{v}\vh''+(\gamma e^{2 V}-\delta e^{-2 V})\hat{v}^2\right)\right|_{z=\Phi+\omega}+\mathcal{O}(z^{-3}).\nonumber
\end{eqnarray}
The goal is to rewrite \eqref{E31} such that the leading order depends only on $V$ and its derivatives. Notice that $\hat{v}$ and $\hat{v}'$ vanish at $z=\Phi$, hence we can rewrite \eqref{E31} as
\begin{equation}\label{dE}
\Delta E=\left[\frac{\alpha e^{ V}-\beta e^{- V}}{z}\right]_{\Phi}^{\Phi+\omega}+\int_\Phi^{\Phi+\omega}-\frac{( V')^2}{z}-\frac{ V'\hat{v}'- V''\hat{v}}{z}+\frac{\alpha e^{ V}-\beta e^{- V}}{z^2}+\mathcal{O}(z^{-3})\,dz.
\end{equation}
Now, using \eqref{p3v}, we find
\begin{equation*}
\frac{ V'\hat{v}'- V''\hat{v}}{z}=\frac{\alpha e^{ V}-\beta e^{- V}}{z^2}-\frac{\alpha e^{ V(\Phi)}-\beta e^{- V(\Phi)}}{\Phi\, z}+\frac 1 z\int_{\Phi}^{z}-\frac{( V')^2}{z}\,dz +\mathcal{O}(1/z^3).
\end{equation*}
Using this, we obtain
\begin{eqnarray*}
\Delta E\nonumber&=&\left[\frac{\alpha e^{ V}-\beta e^{- V}}{z}+\frac{\alpha e^{ V(\Phi)}-\beta e^{- V(\Phi)}}{\Phi}\ln z \right]_{\Phi}^{\Phi+\omega}\nonumber\\
&&\hspace{15mm}+\int_\Phi^{\Phi+\omega}-\frac{( V')^2}{z}+\frac 1 z\int_{\Phi}^{z}\frac{( V')^2}{z}\,dz +\mathcal{O}(1/z^3)\,dz.
\end{eqnarray*}
Note that the expansion of $\frac1z$ around $\Phi$ is:
\begin{equation*}
\frac 1 z=\frac{1}{\Phi+z-\Phi}=\sum_{n=0}^{\infty}\frac{[-(z-\Phi)]^{n+1}}{\Phi^n}=\frac 1 \Phi-\frac{z-\Phi}{\Phi^2}+\frac{(z-\Phi)^2}{\Phi^3}+\mathcal{O}(1/\Phi^4),
\end{equation*}
together they yield the result
\begin{eqnarray}
\hspace{-15mm}E(\Phi+\Omega)-E(\Phi)\nonumber&=&-\frac{\tilde{\om}}{\Phi}+\frac{\omega\,\tilde{\om}}{\Phi^2}+\mathcal{O}(1/\Phi^3),\label{p3E}
\end{eqnarray}
using integration by parts. This shows that the Hamiltonian varies slowly and only depends on the initial point $\Phi$.
\subsection{The Picard-Fuchs equation for the elliptic integral $\tilde{\om}$}
In this subsection the Picard-Fuchs equation for $\tilde{\om}$ is derived, leaving some of the detail to Appendix \ref{B}. Consider the indefinite incomplete elliptic integral
\begin{eqnarray*}
\tilde{\phi}(z)&:=&\int_{ v(\Phi)}^{ v(z)}\mathpalette\DHLhksqrt{\gamma e^{2 v}+2E-\delta e^{-2 v}}d v, \\
\phi(z)&:=&\int_{ v(\Phi)}^{ v(z)}\frac{1}{\mathpalette\DHLhksqrt{\gamma e^{2 v}+2E-\delta e^{-2 v}}}d v.
\end{eqnarray*}
Note that $\tilde{\om}=\tilde{\phi}(\Phi+\omega)$ and $\omega=\phi(\Phi+\omega)$.  Integrating $\tilde{\phi}$ by parts yields the alternative form  (see Appendix \ref{B}):
\begin{equation}\label{phiteq}
\tilde{\phi}= v_z(z)- v_z(\Phi)+2E\tilde{\phi}'-2\delta\Psi
\end{equation}
where $'=\frac{d}{dE}$, and
\begin{eqnarray*}
\Psi&:=&\int_{ v(\Phi)}^{ v(z)}\frac{1}{e^{ v}\mathpalette\DHLhksqrt{\gamma e^{4 v}+ 2E e^{2 v}-\delta}} d v,
\end{eqnarray*}
and a further computation will show that (see Appendix \ref{B})
\begin{eqnarray*}
\Psi=\frac{1}{e^{2 v(\Phi)} v_z(\Phi)}-\frac{1}{e^{2 v(z)}v_z(z)}+ 2\gamma \tilde{\phi}''+2 E \Psi'.
\end{eqnarray*}
Eliminating $\Psi$ and its derivatives from \eqref{phiteq} and its derivative in $E$ leads to the following second-order differential equation satisfied by $\tilde{\phi}$:
\begin{equation} \label{pfphip3}
4(E^2+\delta\gamma)\tilde{\phi}''+\tilde{\phi}- \left.\frac{\gamma e^{2 v}+\delta e^{-2 v}}{ v_z}\right|_{ v(\Phi)}^{ v(z)}=0.
\end{equation}
In the special case that $\tilde{\phi}(\Phi+\omega)=\tilde{\om}$, the Picard-Fuchs equation satisfied by $\tilde{\om}$ is obtained:
 \begin{equation*}
4(E^2+\delta\gamma) \tilde{\om}''+\tilde{\om}=0.
\end{equation*}
We note that the singularities of the above equation occur where the elliptic function $ U$ becomes degenerate.

 \subsection{The expansion of distance $\Omega$ to the next repeated value}
Equation \eqref{p3Om} can be understood as an expansion of $\Omega$ in $v$ in which the leading order term is simply $\omega$. The expression $\hat{v}/ V_z$ is evaluated in Appendix \ref{B}. The distances to the next repeated value of the initial value in $u$ for $\text{P$_{\text{III}}$}$ have the expansion
\begin{eqnarray*}
\Omega&=&\omega-\frac{\tilde{\om}\omega'}{2\Phi}-\frac{1}{\Phi}\left[\frac{\alpha u^2(\Phi)-\beta}{ u(\Phi)}-\frac{\gamma u^4(\Phi)+\delta}{ u(\Phi) u_z(\Phi)}\right]+\mathcal{O}(1/\Phi^2).\label{Omexpp3}
\end{eqnarray*}
This concludes our calculation for $\text{P$_{\text{III}}$}$.

 \subsection{Boundedness of $E$}\label{bound}
In this section we show that $E_{III}$ is bounded along a ray with fixed angle. We expect that the governing equation for $E$ are the same as $\text{P$_{\text{I}}$}$ and $\text{P$_{\text{II}}$}$ to leading order since $E_{\rm I}-E_{\rm V}$ possess the same behaviour to leading order. $E(z)$, which may not be analytic in $z$ because its derivative is path dependent, see \cite{JoshiThesis}, have the following `Taylor' expansion around $\Phi$ using Wirtinger derivative,
\begin{eqnarray*}
E(z)&=& E+(z-\Phi)E_z+(\overline{z}-\bar{\Phi})E_{\overline{z}}\\
&&\hspace{-5mm}+\frac12\left[(z-\Phi)^2E_{zz}+(z-\Phi)(\overline{z}-\overline{\Phi})E_{z\overline{z}}+(\overline{z}-\overline{\Phi})^2E_{\overline{z}\zb}\right]+\cdots
\end{eqnarray*}
evaluating at $(\Phi+\Omega_j,\overline{\Phi}+\overline{\Om}_j)$ gives us
\begin{eqnarray}
E(\Phi+\Omega_j)&=& E(\Phi)+\Omega_j E_z+\overline{\Om}_j E_{\overline{z}}+\frac12\left[\Omega_j^2 E_{zz}+\Omega_j \overline{\Om}_j E_{z\overline{z}}+\overline{\Om}_j ^2E_{\overline{z}\zb}\right]+\mathcal{O}\left(\frac{1}{z^2}\right).\nonumber
\end{eqnarray}
After expanding $\Omega$ by using \eqref{Omexpp3}, this becomes
\begin{eqnarray}
E(\Phi+\Omega_j)- E(\Phi)&=&\omega_j E_z+\overline{\omega}_j E_{\overline{z}}+\frac12\left[\omega_j^2 E_{zz}+\omega_j \overline{\omega}_j E_{z\overline{z}}+\overline{\omega}_j ^2E_{\overline{z}\zb}\right]+\mathcal{O}\left(\frac{1}{z^2}\right)\nonumber\\
&=&-\frac{\tilde{\om}}{\Phi}+\frac{\omega\,\tilde{\om}}{\Phi^2}+\mathcal{O}(\frac{1}{\Phi^3})\nonumber\\
\Rightarrow&&\omega_j E_z+\overline{\omega}_j E_{\overline{z}}=-\frac{\tilde{\om}_j}{z}+\mathcal{O}(\frac{1}{z^2})\label{Ediff}.
\end{eqnarray}
Converting \eqref{Ediff} to polar coordinates $z=r e^{i\theta}$, then applying $t=\ln r$ gives us
\begin{equation}
E_t=\frac{e^{-2i\theta} \kappa-Y}{Y_E}+\mathcal{O}(e^{-t}).
\end{equation}
where
\begin{eqnarray*}
\kappa&:=&\tilde{\om}_1\omega_2-\omega_1\tilde{\om}_2,\\
Y&:=&\tilde{\om}_1\overline{\omega}_2-\overline{\omega}_1\tilde{\om}_2,\\
Y_E&:=&\omega_1\overline{\omega}_2-\overline{\omega}_1\omega_2.
\end{eqnarray*}
Using results from Appendix \ref{C}, we obtain
\begin{eqnarray*}
E_t=-2E+2\frac{e^{-2i\theta}|E|+E}{\ln\left(\frac{8|E|}{|\mu|^{1/2}}\right)}+\mathcal{O}\left(\frac1E,\frac{1}{E\ln|E|}\right)
\end{eqnarray*}
where $\mu=-\gamma\delta$. This proves that $E$ is bounded on a path to infinity at any fixed angle.
\section{The fourth \text{Painlev\'e } equation}\label{sec:p4}
In this section we briefly repeat the analysis described in Section \ref{sec:p3}  for the fourth {\text{Painlev\'e }} equation \eqref{p4u}. The designation $J=\rm IV$ and the subscript $i$ will be dropped for convenience. Starting with the transformation $u=\frac14 v^2$, equation \eqref{p4u} is converted to
\begin{equation}
v_{zz}=\frac{3}{64} v^5+\frac{v^3}{2}+v-\frac{v_z}{z}-\frac{\alpha v}{2z}+\frac{2\beta}{z^2 v^3}+\frac{v}{16z^2},\label{transp4}
\end{equation}
which does not have a first derivative term in the leading order. This equation has the corresponding Hamiltonian,
\begin{equation}
E_{\rm IV}=\frac12\left(v_z^2-\frac{v^6}{64}-\frac{v^4}{4}-v^2\right).
\end{equation}
The initial conditions are now $v(\Phi)=b$ and $v'(\Phi)=q\neq0$ where $|\Phi|\gg1$. The decomposition $v=V+\hat{v}$, where $\hat{v}\ll V$, decouples equation \eqref{transp4} into:
\begin{eqnarray}
 V_{zz}&=&\frac 3 {64} V^5+\frac12 V^3+ V\label{p4vceq},\\
\hat{v}_{zz}&=&\hat{v}\left(\frac{15}{64} V^4+\frac32 V^2+1\right)-\frac{2 V_z+\alpha  V}{2z}\nonumber\\
&&+\hat{v}^2\left(\frac{15}{32} V^3+\frac32 V\right)-\frac{2\hat{v}_z+\alpha \hat{v}}{2z}+\frac{ V}{16z^2}+\frac{2\beta}{z^2 V^3}\nonumber+\mathcal{O}(1/z^3),\nonumber
\end{eqnarray}
and the initial conditions become
\begin{equation*}
V(\Phi)=a,\;V'(\Phi)=q,\; \hat{v}(\Phi)=0,\;\hat{v}'(\Phi)=0.
\end{equation*}
By using the same argument as before we find that $ V=\mathcal{O}(1)$ and $\hat{v}=\mathcal{O}(1/z)$; $\hat{v}$, $\hat{v}'$ and $\hat{v}''$ are of the same order; and $V$, $V'$ and $V''$ are of the same order.
The change in the Hamiltonian is
\begin{eqnarray*}
&&E(\Phi+\Omega)-E(\Phi)\\
&=&\left. \left(V'\hat{v}'- V''\hat{v}+\frac12(\hat{v}')^2 - \hat{v}\vh'' +\frac12\left(\frac{15}{64} V^4+\frac32 V^2+1\right)\hat{v}^2\right)\right|_{z={\Phi+\omega}}+ \mathcal{O}(z^{-3})\nonumber\\
&=&-\frac{\tilde{\om}}{\Phi}+\frac{\omega\tilde{\om}}{\Phi^2}+\mathcal{O}(\Phi^{-3})
\end{eqnarray*}
As before, two incomplete elliptic integrals $\phi$ and $\tilde{\phi}$ are defined from \eqref{p4vceq}, and  from using \eqref{periodints},
\begin{eqnarray*}
\phi(z)&=&\int_{ v(\Phi)}^{ v(z)}\frac{d v}{\mathpalette\DHLhksqrt{\frac{ v^6}{64}+\frac{ v^4}{4}+ v^2+2E}},\\
\tilde{\phi}(z)&=&\int_{ v(\Phi)}^{ v(z)}\mathpalette\DHLhksqrt{\frac{ v^6}{64}+\frac{ v^4}{4}+ v^2+2E} d v.
\end{eqnarray*}
The integral $\tilde{\phi}$ can be expressed as
\begin{equation*}
\tilde{\phi}=\frac14  v v_z|_{ v(\Phi)}^{ v(z)}+\frac{3}{2}E\tilde{\phi}'+\frac1{16}\Psi,
\end{equation*}
where $'=\frac{d}{dE}$, and
\begin{eqnarray*}
\Psi&:=&\int_{ v(\Phi)}^{ v(z)}\frac{v^4+8v^2}{\mathpalette\DHLhksqrt{\frac{ v^6}{64}+\frac{ v^4}{4}+ v^2+2E_0}}d v,\\
&=&\left.\frac{(\frac{1}{2} v^5+\frac{20}{3} v^3)}{ v_z}\right|_{ v(\Phi)}^{ v(z)}-\frac{128}{3}\tilde{\phi}'-\left(\frac{16}{3}-3E\right)\Psi'-\frac{256E}{3}\tilde{\phi}''.
\end{eqnarray*}
Together we have
\begin{equation*}
\left(\frac92 E-\frac83\right)E\tilde{\phi}''+\tilde{\phi}-\left[\frac{ v v_z}{4}+\frac{3 v^5 + 40 v^3+8(16-9 E)v}{ 96v_z}\right]_{ v(\Phi)}^{ v(z)}=0.
\end{equation*}
At $\tilde{\phi}(\Phi+\omega)=\tilde{\om}$, we have the Picard-Fuchs equation for $\tilde{\om}$
\begin{equation*}
\left(\frac92 E-\frac83\right)E\,\tilde{\om}''+\tilde{\om}=0.
\end{equation*}
The distance to the next repeated initial value is:
\begin{align}
\Omega(\Phi)&=\omega-\frac{\tilde{\om}\omega'}{2\Phi}+\frac{\omega'}{\Phi}\Bigl(\frac{3 v^7(\Phi) + 72 v^5(\Phi) + 512 v^3(\Phi) + 64(16-3E) v(\Phi)}{768 v_z(\Phi)}\label{Om4v}\\
&\phantom{=\omega-\frac{\tilde{\om}\omega'}{2\Phi}+\frac{\omega'}{\Phi}\Bigl(}
\ +\frac{\alpha v^2(\Phi)}{4} \Bigr)+\mathcal{O}\left(\frac{1}{\Phi^2}\right).\nonumber
\end{align}
After transforming equation \eqref{Om4v} back to the variable $u$, we have the result stated in Theorem \ref{thm}. Following the argument from Section \ref{bound} and using results from Appendix \ref{C} give us
\begin{equation}
E_t=-\frac32 i E+\frac{3a_1}{2a_0}e^{-2i\theta}|E|^{2/3}+\frac{3 a_1^2E^{2/3}}{2a_0^2\overline{E}^{1/3}}+\mathcal{O}(1),
\end{equation}
which shows that $E$ is bounded along a ray going to infinity.
\section{The fifth \text{Painlev\'e } equation}\label{sec:p5}
As in the previous section, we briefly repeat the analysis for equation \eqref{p5u}, with the understanding that $\rm J=\rm V$ and $i$ will remain unspecified. The transformation $u = \left(\frac{e^v+1}{e^v-1}\right)^2$ eliminates the first derivative terms in the leading order part of $\text{P$_{\text{V}}$}$, obtaining
\begin{equation}
v_{zz}=-\frac{\delta}{8e^{2v}}\left(e^{4v}-1\right)-\frac{\gamma(e^{2 v}-1)}{4 e^v z}-\frac{v_z}{z}-\frac{4 e^{v} \left[\alpha(e^v+1)^4+\beta (e^v-1)^4\right]}{z^2 \left(e^{2v}-1\right)^3}.\label{pvbbdep}
\end{equation}
The Hamiltonian of $\text{P$_{\text{V}}$}$ transforms into the following form
\begin{equation}
E=\frac12\left(v_z^2+\frac{\delta}8 (e^{2v}+e^{-2v})-\frac{\delta}{4}\right),
\end{equation}
the term $\frac{\delta}{4}$ is added for consistency with the $u$-equation. The initial conditions are taken to be $v(\Phi)=b$ and $v'(\Phi)=q\neq0$ where $|\Phi| \gg1$. Analogously we use the decomposition $v=V+\hat{v}$, where $\hat{v}\ll V$ as $|z|\to\infty$, the equation \eqref{pvbbdep} and the initial conditions decouple into
\begin{eqnarray*}
 V_{zz}&=&-\frac{\delta}{8}(e^{2 V}-e^{-2 V}),\label{p5vcpp}\\
\hat{v}_{zz}&=&-\frac{\delta}{4} (e^{2 V}-e^{-2 V}) \hat{v}-\frac{\gamma}{4z}(e^{ V}-e^{- V})-\frac{ V'}{z}-\frac{\delta}{4}(e^{2 V}-e^{-2 V})\hat{v}^2\nonumber\\
&&-\frac{\gamma e^{ V}}{4z}\hat{v}(e^{ V}+e^{- V})-\frac{\hat{v}'}{z}-\frac{4 \left[\alpha  (e^{ V}+1)^4+\beta (e^{ V}-1)^4\right]}{z^2}+\mathcal{O}(1/z^3),\nonumber
 \end{eqnarray*}
and
\begin{equation*}
 V(\Phi)=a,\;V'(\Phi)=q,\;\hat{v}(\Phi)=0,\;\hat{v}'(\Phi)=0.
\end{equation*}
By using another dominant balance analysis we find that $ V=\mathcal{O}(1)$ and $\hat{v}=\mathcal{O}(1/z)$; $\hat{v}$, $\hat{v}'$ and $\hat{v}''$ are of the same order; and $V$, $V'$ and $V''$ are of the same order. The evolution of the Hamiltonian $E$ is
\begin{eqnarray*}
&&E(\Phi+\Omega)-E(\Phi)\\
&=&\left. \left(V'\hat{v}'- V''\hat{v}+\frac12(\hat{v}')^2-\hat{v}\vh''-\frac{\hat{v}^2\delta}{8}(e^{2 V}+e^{-2 V})\right)\right|_{z=\Phi+\omega}+\mathcal{O}(z^{-3})\\
&=&-\frac{\tilde{\om}}{\Phi}+\frac{\omega\tilde{\om}}{\Phi^2}+\mathcal{O}(\Phi^{-3}).
\end{eqnarray*}
The following integrals are defined corresponding to the analytically continued elliptic integrals for $v$ using \eqref{periodints}:
\begin{eqnarray*}
\phi(z)&=&\int_{ v(\Phi)}^{ v(z)}\frac{1}{\mathpalette\DHLhksqrt{-\frac{\delta}{8}(e^{2 v}+e^{-2 v})+2E+\frac{\delta}{4}}}\,d v,\\
\tilde{\phi}(z)&=&\int_{ v(\Phi)}^{ v(z)}\mathpalette\DHLhksqrt{-\frac{\delta}{8}(e^{2 v}+e^{-2 v})+2E+\frac{\delta}{4}}d v.\\
\end{eqnarray*}
The differential equations for $\tilde{\phi}$ is,
\begin{equation*}
\left(4E^2-\frac{\delta^2}{16}\right)\tilde{\phi}''+\tilde{\phi}+\left.\frac{\delta}{8}\frac{e^{2 v}-e^{-2 v}}{ v_z}\right|_{ v(\Phi)}^{ v(z)}=0,
\end{equation*}
and at $\tilde{\phi}(\Phi+\omega)=\tilde{\om}$, the above equation becomes
\begin{equation*}
\left(4E^2-\frac{\delta^2}{16}\right)\tilde{\om}''+\tilde{\om}=0.
\end{equation*}
The exact distance to the next repeated value of $u(\Phi)$ of the fifth \text{Painlev\'e } equation takes the form
\begin{eqnarray*}
\Omega(\Phi)&=&\omega-\frac{\tilde{\om}\omega'}{2\Phi}-\frac{\omega'}{\Phi}\left[-\frac{\gamma}{4}(e^{ v(\Phi)}+e^{- v(\Phi)})+\frac{\delta}{8}\frac{e^{-2 v(\Phi)}-e^{2 v(\Phi)}}{ v_z(\Phi)}\right]+\mathcal{O}(1/\Phi^2).
\end{eqnarray*}
Once again, transforming the above expression back to the variable $u$ yields the result stated in Theorem \ref{thm}. Following the same argument from Section \ref{bound} and Appendix \ref{C} gives us
\begin{equation}
E_t=-2E+2\frac{E+|E|e^{-2i\theta}}{\ln\left(\frac{64|E|}{|\delta|}\right)}+\mathcal{O}(1),
\end{equation}
which shows that $E$ is bounded along a ray going to infinity.

\section{Conclusion}
In this paper we showed how to describe the leading-order asymptotic behaviours of the Painlev\'e equations $\text{P$_{\text{I}}$}-\text{P$_{\text{V}}$}$ as the independent variable in each equation becomes large. The resulting behaviours are given by elliptic functions to leading-order in the complex plane. Each elliptic function has a modulus which is related to the Hamiltonian of the respective equation. Our main result shows how the Hamiltonian is bounded, and changes locally as the independent variable moves over a domain given by the local period parallelogram. The Picard-Fuchs equation was derived for each case, and used to estimate intervals between repeated values of the solution. The results expressing the change of each Hamiltonian are remarkably similar for all the equations, despite their differences in form.

The similarity of our results for $\text{P$_{\text{I}}$}-\text{P$_{\text{V}}$}$ suggest a deep connection to the geometry of their initial-value space \cite{O79}. Another open question concerns the discrete Painlev\'e equations which share a similar geometry of initial-value spaces. In the collection of all known discrete Painlev\'e equations only a few cases have been studied asymptotically, by different approaches.

Another intriguing question arises for the case of $\text{P$_{\text{VI}}$}$. Known asymptotic results for $\text{P$_{\text{VI}}$}$ do not appear to involve elliptic functions. On the other hand, our results suggest that some connection to elliptic functions should appear, because $\text{P$_{\text{VI}}$}$ has a coalescence limit to $\text{P$_{\text{V}}$}$. What these behaviours are for $\text{P$_{\text{VI}}$}$ remains an open question.

redpajama_set_name: RedPajamaArXiv


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LARRY LAGE
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Direct measurement of ecosystem evapotranspiration by the eddy covariance method and simulation modeling were employed to quantify the growing season (May–October) evapotranspiration (ET) of eight forest ecosystems representing a management gradient in dominant forest types and age classes in the Upper Great Lakes Region from 2002 to 2003. We measured net exchange of water vapor fluxes in a 63-year-old mature hardwood(MHW) stand, a 60-year-old mature red pine (MRP) stand, a 3-year-old young hardwood (YHW) stand, a 17-year-old intermediate hardwood (IHW) stand, a young red pine (YRP age 8) stand, an intermediate red pine (IRP age 21) stand, and two pine barren ecosystems burned 12 years (PB1) and 2 years (PB2) ago. Field data suggested that there were no significant differences in growing season (June–September) ET/precipitation ratio among all ecosystems in 2002. However, PB2 had significantly lower ET/precipitation than those of other ecosystems in 2003. The ratios were much higher for all ecosystems, up to 0.90 for IHW, during the peak summer months (June–July). PB2 was the lowest (0.64) during that period. Stand leaf area index alone did not explain ecosystem ET at the landscape scale. Seasonal ET values measured by the eddy covariance method were significantly lower than those simulated with a process-based hydrologic model, MIKE SHE. Our integration approach combined with field measurements and simulation modeling proved to be useful in providing a full picture of the effects of forest cover type change on landscape scale water balance at multiple temporal scales. The ET procedure used in the MIKE SHE model needs improvement to fully account for the effects of vapor pressure deficit on tree transpiration. Seasonal distributions of ET coincided with precipitation in the growing season, when fluxes estimated by both field and models were the highest. The simulation model suggests that removal of conifer forests in the study region may reduce ET immediately by 113–30 mm/year or about 20%, but our field data suggests that ET can recover within 8–25 years from re-growth of hardwood forests.


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text:
import { DirectiveLocationEnum } from "../type/directives";

/*
query IntrospectionQuery {
    __schema {
    queryType { name }
    mutationType { name }
    subscriptionType { name }
    types {
        ...FullType
    }
    directives {
        name
        description
        locations
        args {
        ...InputValue
        }
    }
    }
}

fragment FullType on __Type {
    kind
    name
    description
    fields(includeDeprecated: true) {
    name
    description
    args {
        ...InputValue
    }
    type {
        ...TypeRef
    }
    isDeprecated
    deprecationReason
    }
    inputFields {
    ...InputValue
    }
    interfaces {
    ...TypeRef
    }
    enumValues(includeDeprecated: true) {
    name
    description
    isDeprecated
    deprecationReason
    }
    possibleTypes {
    ...TypeRef
    }
}

fragment InputValue on __InputValue {
    name
    description
    type { ...TypeRef }
    defaultValue
}

fragment TypeRef on __Type {
    kind
    name
    ofType {
    kind
    name
    ofType {
        kind
        name
        ofType {
        kind
        name
        ofType {
            kind
            name
            ofType {
            kind
            name
            ofType {
                kind
                name
                ofType {
                kind
                name
                }
            }
            }
        }
        }
    }
    }
}
*/
export const introspectionQuery: string;

export interface IntrospectionQuery {
    __schema: IntrospectionSchema;
}

export interface IntrospectionSchema {
    queryType: IntrospectionNamedTypeRef;
    mutationType?: IntrospectionNamedTypeRef;
    subscriptionType?: IntrospectionNamedTypeRef;
    types: IntrospectionType[];
    directives: IntrospectionDirective[];
}

export type IntrospectionType =
    | IntrospectionScalarType
    | IntrospectionObjectType
    | IntrospectionInterfaceType
    | IntrospectionUnionType
    | IntrospectionEnumType
    | IntrospectionInputObjectType;

export interface IntrospectionScalarType {
    kind: "SCALAR";
    name: string;
    description?: string;
}

export interface IntrospectionObjectType {
    kind: "OBJECT";
    name: string;
    description?: string;
    fields: IntrospectionField[];
    interfaces: IntrospectionNamedTypeRef[];
}

export interface IntrospectionInterfaceType {
    kind: "INTERFACE";
    name: string;
    description?: string;
    fields: IntrospectionField[];
    possibleTypes: IntrospectionNamedTypeRef[];
}

export interface IntrospectionUnionType {
    kind: "UNION";
    name: string;
    description?: string;
    possibleTypes: IntrospectionNamedTypeRef[];
}

export interface IntrospectionEnumType {
    kind: "ENUM";
    name: string;
    description?: string;
    enumValues: IntrospectionEnumValue[];
}

export interface IntrospectionInputObjectType {
    kind: "INPUT_OBJECT";
    name: string;
    description?: string;
    inputFields: IntrospectionInputValue[];
}

export type IntrospectionTypeRef = IntrospectionNamedTypeRef | IntrospectionListTypeRef | IntrospectionNonNullTypeRef;

export interface IntrospectionNamedTypeRef {
    kind: string;
    name: string;
}

export interface IntrospectionListTypeRef {
    kind: "LIST";
    ofType?: IntrospectionTypeRef;
}

export interface IntrospectionNonNullTypeRef {
    kind: "NON_NULL";
    ofType?: IntrospectionTypeRef;
}

export interface IntrospectionField {
    name: string;
    description?: string;
    args: IntrospectionInputValue[];
    type: IntrospectionTypeRef;
    isDeprecated: boolean;
    deprecationReason?: string;
}

export interface IntrospectionInputValue {
    name: string;
    description?: string;
    type: IntrospectionTypeRef;
    defaultValue?: string;
}

export interface IntrospectionEnumValue {
    name: string;
    description?: string;
    isDeprecated: boolean;
    deprecationReason?: string;
}

export interface IntrospectionDirective {
    name: string;
    description?: string;
    locations: DirectiveLocationEnum[];
    args: IntrospectionInputValue[];
}

redpajama_set_name: RedPajamaGithub


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Турніри з хокею із шайбою на зимових Олімпійських іграх 2006, що пройшли у Турині з 11 по 26 лютого на льодових аренах «Пала Альпитур» та «Торіно Еспозіціоні». 12 чоловічих і 8 жіночих команд розіграли два комплекти нагород в чоловічому та жіночому турнірах відповідно.

Медальний залік

Медалісти

Джерела

 Зимові Олімпійські ігри 2006

Хокей на зимових Олімпійських іграх 2006

redpajama_set_name: RedPajamaWikipedia


Because of the costs and inconvenience incurred when changing damaged or blocked membranes in large filtration plants, much care should be taken. In any case it is recommended to do pilot studies before using a large membrane plant. Such studies should include the membrane cleaning aspects as well as any changes that might be necessary to give excellent results. Today's membrane technology is in most of all cases able to produce clean and healthy water independent of the feed quality. To make the processes beneficial to the user, the membrane manufacturer, the plant supplier and the producer of detergents these all have to work together from the very beginning of new projects.


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UMass ARCH: Karrie Jacobs, The Perfect $100,000 House Then and Now: the Distance between Architectural Fantasy and Reality
Home > Events > UMass ARCH: Karrie Jacobs, The Perfect $100,000 House Then and Now: the Distance between Architectural Fantasy and Reality
October 8, 2015 March 28, 2016 by Comment Closed
October 6, 2015 @ 5:30 pm – 6:30 pm
Integrative Learning Center
Room S211, North Pleasant Street, Amherst, MA
What happens when someone who has spent much of their life critiquing architecture and design builds a house, when the author of The Perfect $100,000 House confronts imperfect reality? What is the distance between the shelter-book fantasy of home building and what actually transpires on site? Are decades of ruminating about architecture useful in day-to-day dealings with an architect and a contractor?
Karrie Jacobs is a professional observer of the unnatural landscape. She currently writes for Architect Magazine and Curbed.com and is a faculty member at the School of Visual Arts' MA program in Design Research. She was the founding editor-in-chief of Dwell and the founding executive editor of Benetton's Colors.


I was recently looking into methods that I would be in a position to attempt to much better contend with the competitors. My small business had fallen behind in recent many years to some of the bigger and much better funded competitors. I took a lot of the duty for that, and I wanted to make sure that I was the 1 who worked to fix the issue. I determined that it would be a fantastic idea to see what I could do in the realm of electronic marketing. I had listened to plenty about this, and I felt that there must be something to it. If it was helping out these other companies so a lot, then it could certainly do some miracles for mine.
I really came up with the business name prior to I arrived up with the company design. About a yr in the past, one of my buddies pointed out how nicely-linked I am and I stated, "Yeah, that's what I do. I'm connectual." I purchased the domain title later that evening.
If you only have a weblog or Fb web page, opportunity are you're lacking out. Individuals appear to web sites to learn about a company. A great web site puts a stake in the floor, showing what you're about, your value, choices, solutions, and differentiators. It can be used to capture prospects, accept order, provide updates or distribute info.
Google agency believes that as the webpages of a web site raises and show a strong web presence so will the page rank improve as well. With the improvement in the page rank, the divisions in scale will perk up as well and hence 1 will succeed to market their website for Digital Marketing Singapore. Many times addition of pages can fall the tool bar point. It can occur in this way if the page is already ranked reduce but addition of new links can rank it slightly higher. There are chances that the web page will in the end end up just below the subsequent division.
As I have currently said, I have many desires that I intent to make a reality. One of them is making it big in the Lookup Engine Optimization industry. I idolize Andreas Roell because of that. By the way, he is the co-founder, CEO and President of Geary Team.
Why am I asking you to select ClickBank? Simple, the commissions they give outweigh the petty commissions you get from PPC, pay per lead and other affiliate networks. When you're just starting out with your blogspot account, you'll require all the revenue you can get from your initial couple of visitors.
It is not at all unusual – in fact it's fairly common – to see the start and quit of the company publication happen time and time once more. A couple of problems make it out, but soon sufficient everyday company priorities merely get in the way. Hmmmm.should I call that consumer back, or create this post?
A Digital Marketing business also provides mobile application services. With mobiles ruling the life of the individuals creating mobile applications is a extremely good company and foolproof one too. The cellular app developers make all kinds of applications for blackberry, android or even I phone. Because cellular apps assist the consumer in its daily actions and since it is free the popularity of such app is immense. It is higher time for all the businesses to enter the Digital Advertising market and make their presence felt online. So if you are preparing to get into this field then do it now rather than later on and regret.


Though she's not at a loss for nieces and nephews, Khloé Kardashian faced some troubling news on Keeping Up With the Kardashians while visiting a fertility specialist, and now fears she may not be able to get pregnant.
MORE: Khloé Kardashian's Extreme Weight Loss to Blame for Latest Instagram Fail!
But as the exam went on, the doctor informed Khloé that she appears to be less fertile than he had initially expected.
Clearly the news came as a shock to the Strong Looks Better Naked author.
As Life & Style previously reported, Khlo wants multiple children with NBA boyfriend Tristan Thompson, so we hope that everything works out for her.
Scroll through the gallery below to see Khloé and Tristan's cutest moments!
The duo shared a smooch on New Year's Eve.
"Merry Christmas & Happy Holidays from me and mines, to you and yours," the pro basketball player captioned this shot with his lady love.
Halloween saw the couple dress up as Storm and Black Panther.
The pair confirmed their relationship in September during a trip to Miami.
The reality star and her athlete beau shared a slow dance before ringing in 2017.
"Him," Khlo simply captioned this pic of the duo in matching camouflage.
Couples that wear coordinating bling together, stay together?
The blonde beauty recently confessed that she and Tristan "use the 'L' word."


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ADHD: Fact or Fiction? Monday, September 15th @ Orinda Library
August 16, 2014 / angela / Events
Are we in the midst of a medical crisis, or is something else going on? Leading experts STEPHEN HINSHAW, PhD, and RICHARD SCHEFFLER, PhD, tackle the tough questions on everybody's minds and provide fact-based answers based on their research on the social, economic, and medical impact of ADHD on our society.
Past Events: 6/5/2014 @Commonwealth Club, San Francisco
May 3, 2014 / angela / Events
"The ADHD Explosion: Myths, Medication, Money, and Today's Push for Performance" Join us at Commonwealth at 6pm in the Gold Room to learn the impact ADHD diagnoses have on children today. ADHD diagnosis is soaring, but is it a real psychiatric disorder — or a social construction used to label kids or adults who don't fit […]
6/1/14 @ Book Passage in Marin
March 20, 2014 / angela / Events
Attention-deficit/hyperactivity disorder (ADHD) is one of the most controversial and misunderstood medical conditions today. With skyrocketing rates of diagnosis and medication treatment, it has generated a firestorm of controversy.
Come learn about this emerging challenge directly from co-author of "The ADHD Explosion", Richard Scheffler, and receive a signed copy with purchase.
4/13/14 Barnes & Noble, Corte Madera
March 7, 2014 / angela / Events
In honor of "Opening the World", a Community Service & Travel Program for At-Risk Young Adults, authors Stephen Hinshaw and Nell Berstein will discuss their books addressing emerging challenges for American youth. Co-author Stephen Hinshaw will discuss his new book, " The ADHD Explosion". Details can be found on the flier.
3/10/14 Children's Health: Research and Policy @UCB
March 5, 2014 / Ari / Events
"The ADHD Explosion: Clinical Realities and Policy Implications" Book Talk, Hosted by The Center for Child and Youth Policy at UC Berkeley Steve Hinshaw & Richard Scheffler Monday, March 10 4:30 p.m. All presentations will be at the Men's Faculty Club, UC Berkeley Berkeley, CA 94720 (map) (510) 540-5678 Other events in this series: "Using Predictive […]
4/16/14 @ Education Psychology Library, UC Berkeley
February 4, 2014 / angela / Events
The ADHD Explosion: Myths, Medication, Money, and Today's Push for Performance. By Stephen P. Hinshaw and Richard M. Scheffler Thursday, April 17th, 2014 4-5:15 pm Education Psychology Library Tolman Hall, UC Berkeley (Map) Free and open to all. Dr. Hinshaw is Professor of Psychology at UC Berkeley. This is one in a series […]
2/27/14 Richard Scheffler @ UCLA School of Public Health
February 2, 2014 / Ari / Events
UCLA Talk – Richard M. Scheffler February 27th School of Public Health ADHD Explosion
2/14/14 Stephen Hinshaw @ Teaching Self-Aware Minds
Stephen Hinshaw will give a talk on Feb 14 at: Teaching Self-Aware Minds: Using Brain Science to Boost Social and Emotional Skills February 13-15, 2014 At the Fairmont San Francisco Hotel in San Francisco, CA
This powerful, fact-packed survey is complex, thought-provoking, and urgent.


Maharshi, Superstar Mahesh Babu's upcoming movie, is the talk of Tollywood now! Despite the election and IPL fevers gripping our country, there are very few cinema stars who can rise above all this din and make a statement with their movies' news! One such star is Mahesh Babu and he put up an Instagram post that comes as an exciting gift for all his fans. The first single from Maharshi - 'Choti Choti Baatein' was released on 29 March and came in for a lot of acclaim. Following this, the second single - 'Nuvve Samastham' was released last week and it became an instant rage amongst the Prince's fans. Now, he has announced the release date and time of the preview of his next song - 'Everest Anchuna'!
On Wednesday, Mahesh Babu revealed through a post on his Instagram page that the #EverestAnchuna song preview will happen on 19 April at 4:05 pm. It looks like this Friday just can't come soon enough for Mahesh Babu's fans! Maharshi is an action drama directed by Vamsi Paidipally and produced by Dil Raju, C Ashwini Dutt and the Potluri family under their Sri Venkateswara Creations, Vyjayanthi Movies and PVP Cinema banners! This movie stars Pooja Hegde as the female lead with Allari Naresh, Meenakshi Dixit, Jagapathi Babu, Sai Kumar and Rajendra Prasad in important roles! The star cast is quite huge with a number of other top actors like Naveen Chandra, Nassar, Kota Srinivasa Rao, Posani Krishna Murali, Rao Ramesh, Naresh, Vennela Kishore and Brahmaji also touted to be a part of it!
nextAsuran: GV Prakash starts recording two more songs for the Dhanush starrer!


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Moores dismisses Proteas link as 'paper speculation'
Cape Town - Former England coach Peter Moores has dismissed reports linking him with the role of the new Proteas team director, saying the rumours are "paper speculation".
The Proteas sacked head coach Ottis Gibson and his entire coaching staff after the Cricket World Cup with Cricket South Africa (CSA) restructuring the management of the national side.
Enoch Nkwe was appointed as Proteas team director on an interim basis for the upcoming tour to India with a permanent successor for Gibson is set to be announced ahead of England's tour to South Africa in November.
Moores had two stints as England mentor, from 2007-2009 and then again in 2014 until 2015, and is now coaching county side Nottinghamshire where his contract expires at the end of the season.
He has, however, squashed talks of taking on the Proteas job, saying he will discuss his future with Nottinghamshire in due course.
"With South Africa, it's paper speculation Moores told Nottinghamshire Live.
"You can't help that as a coach. Post-World Cup there's movement because it's the end of an international cycle. There's nothing in it from my end. I'm focusing on the job here...
"I've not looked any further than enjoying working for Notts," said Moores.
Corrie van Zyl is currently in the role of acting director of cricket within Cricket South Africa and has the responsibility of appointing a full-time team director for the Proteas.
Get a daily dose of Africa Leader news through our daily email, its complimentary and keeps you fully up to date with world and business news as well.
Publish news of your business, community or sports group, personnel appointments, major event and more by submitting a news release to Africa Leader.
Partly Cloudy / Windy in Cape Town
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Practice Relating to Rule 65. Perfidy
Section D. Simulation of surrender
Canada's LOAC Manual (1999) states: "The following are examples of perfidy if a hostile act is committed while: … feigning … to surrender."
Canada, The Law of Armed Conflict at the Operational and Tactical Level, Office of the Judge Advocate General, 1999, p. 6-2, § 9(a) (land warfare) and p. 7-2, § 17(a) (air warfare); see also p. 8-11, § 81(b) (naval warfare).
The manual also considers that "feigning surrender of an aircraft and then firing on an unsuspecting adversary after such surrender was accepted" constitutes perfidy in air warfare.
Canada, The Law of Armed Conflict at the Operational and Tactical Level, Office of the Judge Advocate General, 1999, p. 7-2, § 18(b).
The manual further identifies as a grave breach of the 1977 Additional Protocol I and a war crime the "perfidious use of … protective signs recognized by the Geneva Conventions or [the 1977 Additional Protocol] I".
Canada, The Law of Armed Conflict at the Operational and Tactical Level, Office of the Judge Advocate General, 1999, p. 16-2, § 8(a) and p. 16-3, § 16(f).
Canada's LOAC Manual (2001) states in its chapters on land warfare and air warfare: "The following are examples of perfidy if a hostile act is committed while: a. feigning an intent … to surrender".
Canada, The Law of Armed Conflict at the Operational and Tactical Levels, Office of the Judge Advocate General, 13 August 2001, §§ 603.2.a (land warfare) and 706.2.a (air warfare).
In its chapter on air warfare, the manual further states that it is an example of perfidy in air warfare "if a hostile act is committed while … b. feigning surrender of an aircraft and then firing on an unsuspecting adversary after such surrender was accepted".
Canada, The Law of Armed Conflict at the Operational and Tactical Levels, Office of the Judge Advocate General, 13 August 2001, § 706.3.b.
In its chapter on naval warfare, the manual states: "The following are examples of perfidy if a hostile act is committed while: … b. feigning distress or surrender (e.g., by sending a distress signal or by the crew taking to the life rafts)".
In its chapter on "War crimes, individual criminal liability and command responsibility", the manual identifies as a grave breach of Additional Protocol I and a war crime the "perfidious use of … protective signs recognized by the Geneva Conventions or [the 1977 Additional Protocol] I".
Canada, The Law of Armed Conflict at the Operational and Tactical Levels, Office of the Judge Advocate General, 13 August 2001, § 1608.2.f.
IV. National Legislation
Canada's Geneva Conventions Act (1985), as amended in 2007, provides: "Every person who, whether within or outside Canada, commits a grave breach [of the 1977 Additional Protocol I] … is guilty of an indictable offence."
Canada, Geneva Conventions Act, 1985, as amended in 2007, Section 3(1).
Canada's Crimes against Humanity and War Crimes Act (2000) provides that the war crimes defined in Article 8(2) of the 1998 ICC Statute are "crimes according to customary international law" and, as such, indictable offences under the Act.
Canada, Crimes against Humanity and War Crimes Act, 2000, Section 4(1) and (4).
V. National Case-law
In 2013, in the Sapkota case, Canada's Federal Court dismissed a request for review of a decision denying refugee protection to the applicant on grounds of complicity in crimes against humanity in Nepal between 1991 and 2009. While reviewing the submissions of the respondent, Canada's Minister of Citizenship and Immigration, the Court stated: "The Respondent notes that the Rome Statute of the International Criminal Court … is endorsed in Canada as a source of customary law."
Canada, Federal Court, Sapkota case, Reasons for Judgment and Judgment, 15 July 2013, § 28.
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except that no amount shall be paid to any State on account of amounts expended from amounts paid to the State under section 458 or to carry out an agreement which it has entered into pursuant to section 463. In determining the total amounts expended by any State during a quarter, for purposes of this subsection, there shall be excluded an amount equal to the total of any fees collected or other income resulting from services provided under the plan approved under this part.
(C) 66 percent for fiscal year 1990 and each fiscal year thereafter.
(3)(A) The Secretary shall pay to each State, for each quarter in fiscal years 1996 and 1997, 90 percent of so much of the State expenditures described in paragraph (1)(B) as the Secretary finds are for a system meeting the requirements specified in section 454(16) (as in effect on September 30, 1995) but limited to the amount approved for States in the advance planning documents of such States submitted on or before September 30, 1995.
(B)(i) The Secretary shall pay to each State or system described in clause (iii), for each quarter in fiscal years 1996 through 2001, the percentage specified in clause (ii) of so much of the State or system expenditures described in paragraph (1)(B) as the Secretary finds are for a system meeting the requirements of sections 454(16) and 454A.
(ii) The percentage specified in this clause is 80 percent.
(iii) For purposes of clause (i), a system described in this clause is a system that has been approved by the Secretary to receive enhanced funding pursuant to the Family Support Act of 1988 (Public Law 100-485; 102 Stat. 2343) for the purpose of developing a system that meets the requirements of sections 454(16) (as in effect on and after September 30, 1995) and 454A, including systems that have received funding for such purpose pursuant to a waiver under section 1115(a).
(II) the State has submitted to the Secretary a corrective compliance plan that describes how, by when, and at what cost the State will achieve such compliance, which has been approved by the Secretary, then the Secretary shall not disapprove the State plan under section 454, and the Secretary shall reduce the amount otherwise payable to the State under paragraph (1)(A) of this subsection for the fiscal year by the penalty amount.
(ii) All failures of a State during a fiscal year to comply with any of the requirements referred to in the same subparagraph of section 454(24) shall be considered a single failure of the State to comply with that subparagraph during the fiscal year for purposes of this paragraph.
(V) 30 percent of the penalty base, in the case of the fifth or any subsequent such fiscal year.
(ii) The term "penalty base" means, with respect to a failure of a State to comply with a subparagraph of section 454(24) during a fiscal year, the amount otherwise payable to the State under paragraph (1)(A) of this subsection for the preceding fiscal year.
(III) the State has not failed such a review.
(ii) If a State with respect to which a reduction is made under this paragraph for a fiscal year with respect to a failure to comply with a subparagraph of section 454(24) achieves compliance with such subparagraph by the beginning of the succeeding fiscal year, the Secretary shall increase the amount otherwise payable to the State under paragraph (1)(A) of this subsection for the succeeding fiscal year by an amount equal to 90 percent of the reduction for the fiscal year.
(iii) The Secretary shall reduce the amount of any reduction that, in the absence of this clause, would be required to be made under this paragraph by reason of the failure of a State to achieve compliance with section 454(24)(B) during the fiscal year, by an amount equal to 20 percent of the amount of the otherwise required reduction, for each State performance measure described in section 458(b)(4) with respect to which the applicable percentage under section 458(b)(6) for the fiscal year is 100 percent, if the Secretary has made the determination described in section 458(b)(5)(B) with respect to the State for the fiscal year.
then the Secretary shall not disapprove the State plan under section 454, and the Secretary shall reduce the amount otherwise payable to the State under paragraph (1)(A) of this subsection for the fiscal year by the penalty amount.
(ii) All failures of a State during a fiscal year to comply with any of the requirements of section 454B shall be considered a single failure of the State to comply with subparagraphs (A) and (B)(i) of section 454(27) during the fiscal year for purposes of this paragraph.
(V) 30 percent of the penalty base, in the case of the 5th or any subsequent such fiscal year.
(ii) The term "penalty base" means, with respect to a failure of a State to comply with subparagraphs (A) and (B)(i) of section 454(27) during a fiscal year, the amount otherwise payable to the State under paragraph (1)(A) of this subsection for the preceding fiscal year.
(C)(i) The Secretary shall waive all penalties imposed against a State under this paragraph for any failure of the State to comply with subparagraphs (A) and (B)(i) of section 454(27) if the Secretary determines that, before April 1, 2000, the State has achieved such compliance.
(ii) If a State with respect to which a reduction is required to be made under this paragraph with respect to a failure to comply with subparagraphs (A) and (B)(i) of section 454(27) achieves such compliance on or after April 1, 2000, and on or before September 30, 2000, then the penalty amount applicable to the State shall be 1 percent of the penalty base with respect to the failure involved.
(D) The Secretary may not impose a penalty under this paragraph against a State for a fiscal year for which the amount otherwise payable to the State under paragraph (1)(A) of this subsection is reduced under paragraph (4) of this subsection for failure to comply with section 454(24)(A).
(b)(1) Prior to the beginning of each quarter, the Secretary shall estimate the amount to which a State will be entitled under subsection (a) for such quarter, such estimates to be based on (A) a report filed by the State containing its estimate of the total sum to be expended in such quarter in accordance with the provisions of such subsection, and stating the amount appropriated or made available by the State and its political subdivisions for such expenditures in such quarter, and if such amount is less than the State's proportionate share of the total sum of such estimated expenditures, the source or sources from which the difference is expected to be derived, and (B) such other investigation as the Secretary may find necessary.
(2) Subject to subsection (d), the Secretary shall then pay, in such installments as he may determine, to the State the amount so estimated, reduced or increased to the extent of any overpayment or underpayment which the Secretary determines was made under this section to such State for any prior quarter and with respect to which adjustment has not already been made under this subsection.
(3) Upon the making of any estimate by the Secretary under this subsection, any appropriations available for payments under this section shall be deemed obligated.
(d) Notwithstanding any other provision of law, no amount shall be paid to any State under this section for any quarter, prior to the close of such quarter, unless for the period consisting of all prior quarters for which payment is authorized to be made to such State under subsection (a), there shall have been submitted by the State to the Secretary, with respect to each quarter in such period (other than the last two quarters in such period), a full and complete report (in such form and manner and containing such information as the Secretary shall prescribe or require) as to the amount of child support collected and disbursed and all expenditures with respect to which payment is authorized under subsection (a).
(e)(1) In order to encourage and promote the development and use of more effective methods of enforcing support obligations under this part in cases where either the children on whose behalf the support is sought or their noncustodial parents do not reside in the State where such cases are filed, the Secretary is authorized to make grants, in such amounts and on such terms and conditions as the Secretary determines to be appropriate, to States which propose to undertake new or innovative methods of support collection in such cases and which will use the proceeds of such grants to carry out special projects designed to demonstrate and test such methods.
(2) A grant under this subsection shall be made only upon a finding by the Secretary that the project involved is likely to be of significant assistance in carrying out the purpose of this subsection; and with respect to such project the Secretary may waive any of the requirements of this part which would otherwise be applicable, to such extent and for such period as the Secretary determines is necessary or desirable in order to enable the State to carry out the project.
(3) At the time of its application for a grant under this subsection the State shall submit to the Secretary a statement describing in reasonable detail the project for which the proceeds of the grant are to be used, and the State shall from time to time thereafter submit to the Secretary such reports with respect to the project as the Secretary may specify.
(4) Amounts expended by a State in carrying out a special project assisted under this section shall be considered, for purposes of section 458(b) (as amended by section 5(a) of the Child Support Enforcement Amendments of 1984), to have been expended for the operation of the State's plan approved under section 454.
(5) There is authorized to be appropriated the sum of $7,000,000 for fiscal year 1985, $12,000,000 for fiscal year 1986, and $15,000,000 for each fiscal year thereafter, to be used by the Secretary in making grants under this subsection.
(f) The Secretary may make direct payments under this part to an Indian tribe or tribal organization that demonstrates to the satisfaction of the Secretary that it has the capacity to operate a child support enforcement program meeting the objectives of this part, including establishment of paternity, establishment, modification, and enforcement of support orders, and location of absent parents. The Secretary shall promulgate regulations establishing the requirements which must be met by an Indian tribe or tribal organization to be eligible for a grant under this subsection.
 See Vol. II, P.L. 99-177, Title II, "Balanced Budget and Emergency Deficit Control Act of 1985", §256 [as amended by P.L. 100-119], with respect to treatment of child enforcement program; and §257(11), with respect to references to §401(c)(2) of the "Congressional Budget Act of 1974".
 P.L. 97-248, §174(b); 96 Stat. 403.
 P.L. 98-378, §5; 98 Stat.1305.


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Q: webforms all children performing async postback even when updatemode set to conditional I have an update panel with UpdateMode set to conditional, and childrenastriggers set to false, but all the controls in the panel are performing async postbacks...
   <asp:ScriptManager ID="ScriptManager1" runat="server" />

    <asp:UpdateProgress ID="pnlUpdateProgress" DisplayAfter="1" runat="server">
        <ProgressTemplate>
            Update in progress...
        </ProgressTemplate>
    </asp:UpdateProgress>
    <asp:UpdatePanel runat="server" ID="pnlUpdate" UpdateMode="Conditional" ChildrenAsTriggers="false">
    <Triggers>
        <asp:AsyncPostBackTrigger ControlID="btnDoNothing" EventName="Click" />
    </Triggers>
    <ContentTemplate>

        <asp:Button runat="server" ID="btnDoNothing" Text="Do nothing" OnClick="Unnamed_Click" />
        <asp:Button runat="server" ID="btnSync" Text="Sync" OnClick="btnSync_Click" />

                        Description

                    <asp:Literal runat="server" ID="litList" />

    <asp:Literal runat="server" ID="litDebugText" />

    <asp:HiddenField runat="server" ID="txtEditID" />

        <asp:Literal ID="litEditList" runat="server">

        </asp:Literal>

            Your Product: <asp:Literal runat="server" ID="litEditProductName" />

    </ContentTemplate>
</asp:UpdatePanel>

Here both btnSync and btnDoNoting are performing async postbacks, where I would expect only btnDoNothing to post back async, btnSync should perform a full postback

A: AsyncPostBackTrigger only sets controls that are outside of the panel.

Controls on the page outside of an update panel can refresh an UpdatePanel control by defining them as triggers. Triggers are defined by using the AsyncPostBackTrigger element.

Controls that postback will always postback. I think the ChildrenAsTriggers="false" won't stop the postbacks - it will just stop the content from updating.

A: As @wazz stated in their answer, this is normal behavior in an update panel. To make a full back you need to make a "PostBackTrigger" as documented in the answer to this question.
<asp:UpdatePanel ID="UpdatePanel1" UpdateMode="Conditional" runat="server">
  <ContentTemplate>
      ...
  </ContentTemplate>
  <Triggers>
      <asp:PostBackTrigger ControlID="myFullPostBackControlID" />
  </Triggers>
</asp:UpdatePanel>

redpajama_set_name: RedPajamaStackExchange


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Favorite Songs By Favorite Artists (Series Two) #22: KISS
March 15, 2021 / J. Eric Smith
Note: For an index of all articles in this second "Favorite Songs" series, click here. For a summary of all artists covered in the original series, click here.
Who They Are: While KISS are not quite at Neil Diamond, David Bowie, Elvis Presley, or Fleetwood Mac levels of cultural, critical, and commercial ubiquity, they have sold upwards of 80 million albums since their formation in 1972, and their stage make-up is pretty much instantly recognizable to anyone with a passing awareness of the American world around them over the past half-century. So I'm guessing that if you are culturally attuned enough to read my website, then you know who Gene Simmons, Paul Stanley, Ace Frehley and Peter Criss are (and what they look like in their stage regalia, if not what they sound like), even if you're not enough of a metal nerd to be fluent in the latter day incarnations of the group, where Stanley and Simmons have long reigned as the sole permanent members. I, on the other hand, am well-versed in the both the group's heyday releases and those issued in their after-years, so you can thank me for listening to many of those records so that you don't have to. Community service is always important, here at mine blog.
When I First Heard Them: Some time in the mid-'70s when they were emerging as cultural juggernauts. I was trying to think whether I had seen them or heard them first, and I can't recall any explicit, particular moment on either front. I do know, though, that in the late '70s, after my parents had a born-again religious awakening, that KISS somehow came to stand as the exemplars of everything bad and evil and wicked about modern pop culture, with church leaders declaring that the band's name stood for "Knights in Satan's Service," which was nonsense, but worked well from the pulpit, apparently. I smile to remember a time when I was in high school, and my parents said they needed to talk to me about something after dinner one night. "Uh oh," thought I, trying to quickly get in order whatever story I needed to defuse or deny whatever malfeasance I was about to be accused of. But, instead, I heard a terrible tale about my friend, Andy, whose parents had (as good Christian parents do) rooted around in his bedroom, finding something awful in his underwear drawer: a copy of Gene Simmons' solo album from 1978. Gasp!! I was interrogated at length on what I knew about this depravity, and how I felt about it. I was, legitimately, ignorant of what Andy kept with his tighty-whities, and was actually a bit surprised that he was into KISS, since he'd not shared such a secret with me. It made me like him more. I did not directly admit to the fact that I actually liked KISS in that conversation, since there was nothing to be gained by doing so. Headphones were, to my mind at the time, invented for the sole purpose of hiding what I was listening to from my parents, and that was fine by me. I saw KISS live in 1979 (I'm not sure where I told my parents I was going to be that night, but it certainly wasn't the truth), and it was a wonderful, memorable show, with explosions and lasers and blood and boobs (being flashed from the audience) and almost all of the other things that make teenage boys function and tick. It was among the stupidest shows I ever saw (well, until I saw KISS again in 1996), but also among the best. And what's more rock and roll than that, really?
Why I Love Them: Parents hated KISS in the '70s, as noted above, which made kids of my age and acquaintance love them all the more. They were utterly ubiquitous and extremely prolific in the latter half of the '70s, so if you didn't like their latest album, you only had to wait a few months to see if the next one rocked better for you. The imagery and the personalities were a big part of the story, of course, but none of that would have worked without some really good, really memorable music, which KISS delivered by the bucket-load at the peak of their powers. There's a lot of dross in their catalog, for sure, but the high points are true pinnacles, catchy, memorable, and totally fine for shouting along with in concert, or while driving, or around the house when nobody else is there to hear your Gene imitation. While Stanley and Simmons were and remain the primary songwriters and singers, Frehley and Criss also wrote, and also sang, and also anchored a pair of the group's most successful commercial moments, with "Beth" (by Criss) as an unexpected breakthrough pop ballad hit, and "New York Groove" (from Frehley's edition of the four solo albums issued simultaneously in 1978) standing a fine fist-pumping anthem and singalong, a perfect embodiment of its time and place. As noted above, I saw KISS again in 1996 during the reunion (and re-masking) tour of the original quartet, and it was even bigger, and louder, and stupider than the '79 show I caught. I reviewed it for the local newsweekly at the time, and also did a standalone piece explaining why you should care about such a KISS reunion tour. Both of those articles, which more deeply explain the "why I love them" factor, are available at this link.
#10. "War Machine" from Creatures of the Night (1982)
#9. "I Was Made For Lovin' You" from Dynasty (1979)
#8. "New York Groove" from Ace Frehley (1978)
#7. "Black Diamond" from Kiss (1974)
#6. "Detroit Rock City" from Destroyer (1976)
#5. "Calling Doctor Love" from Rock and Roll Over (1976)
#4. "Goin' Blind" from Hotter Than Hell (1974)
#3. "Shout It Out Loud" from Destroyer (1976)
#2. "Rock And Roll All Night" from Dressed to Kill (1975)
#1. "Cold Gin" from Kiss (1974)
Favorite Songs By Favorite Bands, Music
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5 thoughts on "Favorite Songs By Favorite Artists (Series Two) #22: KISS"
Ah, KISS — my first concert! Although I saw them in the less-celebrated late '80s, sans makeup. And I didn't even go to see them; I was there (with my country-loving parents and younger sister!) for opening act Anthrax (about whom my dad quipped – "What's this band's name? Amtrax? Makes sense, because they sound like a trainwreck."). But I digress …
KISS was a stupidly good time with FIRE! and LASERS! and BLOOD! and GLOW IN THE DARK DRUMSTICKS DURING THE DRUM SOLO! that, by show's end, even my dad had to concede they put on a heck of a show and a good time was had by all.
That show is what got me digging into the back catalog for gems like "Calling Dr. Love" (Ace's best solo) and "Shock Me" (their best song, IMO) – as you noted, there are a fair number of duds in the catalog, but plenty of gems to be found. And who can forget Paul Stanley's sparkling stage banter?
Great stories!! "Shock Me" would have been next on the list had I done a Top 11 instead of a Top 10 . . . I considered swapping it in for "War Machine," but my sense of completism made me feel like I needed to have at least ONE song from the post-original four era!!!
Fair enough … and "War Machine" is a good choice from that period. Although, Paul's ridiculous rallying cry of "It ain't a crime/to be good to yourself/Wooooo!" from "Lick it Up" makes it a strong contender to these ears. (And let's not forget what is arguably Gene's best post-70s vocal on "I Love it Loud".)
Jeff Claus
Confession: I am not a KISS fan.
I could say it's because they were overproduced to the point of adsurdity, but I do like the Ramones, and they did an album with Phil Spector of all people.
I could say that I don't like the fact that they were crude just for the sake of being crude, but I loved The Tubes back in the day, and Fee Waybill gave no ground to anyone when it came to being tasteless. (And I still regret not seeing them during their Mondo Bondage tour.)
And after all that, I can't think of a song that better wrapped up the ethos of teenage guys in the 1970's than Rock And Roll All Night.
To Gene and the boys, make your platform heels never wobble, and may your makeup never run, no matter how hot the lights are. Rock on!
I think it helps that I lived on Long Island from '76 to '80, at the peak of their commercial heyday. The locals counted them "as one ours," so there was pretty blind enthusiasm for them among everybody I hung out with, and that was contagious. See also Good Rats: https://jericsmith.com/2009/11/04/in-praise-of-good-rats-2/
Except at church, of course. Them Satanic Knights occupied a lot of preacherly head space, even there, even then . . .


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There are a series of intangibles that can be just as important in interior-design as colour, luminosity and shape. Often, the most potent first impression and subsequent memory of a space can be its smell. This scent collection evokes historical memories of British life, of travelling and trading across the globe and returning to the gritty smells of modern international London. London captures the smell of red brick and London parks with crocuses and nettles, and the salty smell of the Thames at Dagenham. Tom Dixon candles are made in the UK from 50% natural ingredients (50% natural soy, 50% paraffin wax) and contain 10% fragrance - a much higher level compared to the standard 1-3%, meaning the scent is stronger and will last longer.
Dimensions: H920 x W950x D950 mm
Scent: Top Notes: Black Pepper.
Middle Notes: Oud Wood and Vetiver.
Base: Cedar Wood and Patchouli.
Burn Time: 70 Hrs
Material: Container: Copper
Lid: Solid Morwad marble
Brand: Tom Dixon
Collection: Scent eclectic
About Tom Dixon
Tom is a restless innovator who works mainly in lighting, accessories and furniture. From back in the early eighties welding salvaged steel into radical furniture, he has constantly reinvented himself through a series of different design lives – working with luxury Italian goods with Cappellini, as Creative Director at Habitat and Artek, creating plastics company Eurolounge and finally instigating his own eponymous brand in 2002 rethinking the product designer's relationship with industry.
15 years on, Tom Dixon is now a widely celebrated global force in interior design with hubs in New York, Hong Kong, London, Los Angeles and Tokyo. His 600 products range from lighting to furniture, from tableware through to fragrance and are distributed in over 65 countries; they are instantly recognisable for their sculptural qualities and engineered materiality.


Subscription Video-on-Demand (SVoD) is an entertainment programming model where users pay a monthly fee in exchange for instant access to a streaming library consisting of movies, TV shows, and other media content. Since around 2006, companies like Netflix, Hulu, and Amazon have taken advantage of this new system of media consumption and used the technology to grow their brands into some of the biggest names in the entertainment industry. The demand for their services is only expected to increase from here, with worldwide digital video revenue expected to grow in the coming years and SVoD accounting for a larger percentage each year. Additionally, the number of SVoD users worldwide is expected to skyrocket from around 283 million in 2018 to 411 million in 2022. Younger generations are the ones driving demand the most, with 18-24 year olds spending an average of 39 minutes per day using some sort of SVoD service.
As the market has matured, SVoD providers have quickly realized the importance of adding their own original programming to their content library. In 2017 alone, Amazon produced 56 original content titles, amounting to 285 hours of original content. In the same year, Netflix produced 300 original titles, and a total of around 1257 hours of original content. However, the race to create and distribute more original shows does not seem to be rooted in a 'quantity over quality' mentality – despite the obvious competition in the industry. With programs such as Stranger Things (Netflix), The Handmaid's Tale (Hulu), and The Marvelous Mrs. Maisel (Amazon), these companies are showing that they aren't satisfied with simply generating more content for their viewers; they want recognition for their efforts. At the 2018 edition of the Primetime Emmy Awards, Netflix collected 23 awards, tying for the most of any network.
In addition to the wealth of high quality original content, these SVoD services also provide subscribers with access to ever-growing libraries of movies and acquired TV network series. Considering the massive amount of content being provided at the touch of a button, one of the most important factors for the success of SVoD is surely its price point. With many options available for less than 15 dollars per month, it is clear why people are beginning to leave their cable subscription behind. Netflix and Hulu have the highest 'value for money' ratings of any video entertainment platform, making it easy to understand why SVoD is seeing so much success.
As consumers continue to 'cut cords', traditional forms of media access such as cable and satellite will find it harder and harder to compete with the growing influence of SVoD. Bolstered by both the strength of the technology itself and the success of the individual companies competing in the market, the SVoD industry appears to be set for years of continued success.
Topic: Home video market in the U.S.


FireDaemon wtlext is a header-only C++ library built in the spirit of ATL (Active Template Library) and WTL (Windows Template Library), providing functionality not found in WTL. This library is incorporated into various FireDaemon software products.
The code inherits WTL's Microsoft Public License (MS_PL) which encourages both commercial and non-commercial use.


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ABOUT SOUTHEND
BID MEMBER'S AREA
visiT southend
Visit Southend is hugely popular and the website is the number one information website for Southend, which receives up to 80,000 visits a month. We also manage the associated social media channels, which have amassed in excess of 40,000 followers.
To complement our online presence, we design and produce a number of printed maps guides, including a visitor guide, accommodation guide, food, and nightlife guides. These guides are available to download here, and are also distributed nationwide by the Visitor Information Centre.
Homelessness Campaign
We're working alongside Essex Police, Southend-on-Sea Borough Council, StreetLink, and support services in providing a website and marketing campaign that aims to educate the public with regards to rough sleepers and street begging.
This supports our ongoing work across the town centre and seafront to encourage engagement with the appropriate services.
ANTI-LITTER
We launched a promotional film that was published across both Southend BID and Visit Southend websites and social media channels to encourage the responsible disposal of rubbish.
The video was supported by a well-received marketing campaign, which included posters featuring BID businesses and members of the public alongside positive messages to dispose of litter correctly.
Heavily focused on our fun and interactive anti-litter initiatives installed across the BID area, our intention was also to remind visitors to not simply discard of litter on the floor but use our Ballot, Gumdrop and 'talking' bins instead.
Streetscape improvements
As part of our plans to make Southend town centre more appealing, we fund and manages a range of streetscape improvements.
These include the bright lamp column banners, High Street bunting, hanging baskets and floral planters, street cleaning, vacant unit artwork, and repainting and upkeep of litter bins.
safety &
Safety and security has been voted by Southend BID businesses as one of the most important of its deliverables, we manage a team of four full-time Street Rangers and the Keeping Together wristband scheme.
We also host a bi-monthly Southend Retail Against Crime (SRAC), promote DISC, the crime database and Townlink radio system and work continually alongside the police, CCTV and other services.
In 2018, we upgraded the Christmas lighting scheme for the town centre, the first update since 2005.
The new gold and silver lights trailed across the High Street, which glittering angels adorning each lamp column, and the response from the public and BID businesses has been fantastic.
The new additions didn't stop there, we also invested in the biggest Christmas tree Southend has ever seen, 46ft tall, which was equally festive in the new gold and silver lighting scheme.
Copyright © Southend BID 2019. All Rights Reserved.
Company number: 8346559, registered in England.
Registered address: 7 Nelson Street, Southend on Sea, Essex SS1 1EH