text:
\section{Introduction}

Understanding the large-scale behavior of combinatorial objects is
so fundamental to modern combinatorics, that it has become routine and
no longer requires justification.  However, in \emph{algebraic combinatorics},
there are fewer results in this direction, as the objects tend to be have
more structure and thus less approachable.  This paper studies the
asymptotic behavior of the
principal evaluation of Schubert polynomials, partially resolving
an open problem by Stanley~\cite{St}. As the reader shall see,
the results are surprisingly precise.

\smallskip

\subsection*{Main results}
\emph{Schubert polynomials} \hskip.03cm
$\mathfrak{S}_w(x_1,\ldots,x_n) \in \mathbb N[x_1,\ldots,x_n]$, \hskip.03cm $w\in S_n$,
were introduced by Lascoux and Sch\"utzenberger \cite{LSch} to study
Schubert varieties. They have been intensely studied
in the last two decades and remain a central object in algebraic combinatorics.
 The principle evaluation of the Schubert polynomials
can be defined via \emph{Macdonald's identity} \cite[Eq.~6.11]{Mac}:
\begin{equation} \label{eq:macdonald}
\Upsilon_w \, := \, \mathfrak{S}_w(1,\ldots,1) \, = \,
\frac{1}{\ell!} \. \sum_{(a_1,\ldots,a_{\ell}) \in \text{ {\text {\rm sc}  }  R}(w)} \. a_1 \hskip.03cm \cdots \hskip.03cm a_{\ell}\..
\end{equation}
Here $\ell=\ell(w)$ is the \emph{length} of $w$ (the number of inversions, and
\hskip.03cm $\text{ {\text {\rm sc}  }  R}(w)$ \hskip.03cm denotes the set of \emph{reduced words} of $w\in S_n\hskip.03cm$: \hskip.03cm tuples
\hskip.03cm $(a_1,\ldots,a_{\ell})$ \hskip.03cm  such that \hskip.03cm $s_{a_1}\cdots
s_{a_{\ell}}$ \hskip.03cm is a reduced decomposition of $w$ into simple
transpositions $s_i = (i,i+1)$.

Note that $\Upsilon_w$ has a more direct (but less symmetric) combinatorial
interpretation as the number of certain \emph{rc-graphs}
(also called \emph{pipe dreams}), see e.g.~\cite{As}.  In particular,
we have $\Upsilon_w\in \mathbb N$, even though this is not immediately apparent
from~\eqref{eq:macdonald} (cf.~$\S$\ref{ss:finrem-rc}).

Denote by $u(n)$ the largest principal specialization of the Schubert polynomial:
$$
u(n) \, := \, \max_{w \in S_n} \. \Upsilon_w\,.
$$

\begin{conjecture}[Stanley \cite{St}] \label{conj:stan}
There is a limit
$$\lim_{n\to \infty} \,\. \frac{1}{n^2} \, \log u(n)\hskip.03cm.
$$
\end{conjecture}

In addition, Stanley asked whether the permutations $w$ in $S_n$
achieving the maximum \hskip.03cm $\Upsilon_w = u(n)$ \hskip.03cm had a limiting description.
There was some evidence in favor of this (see below), but before we turn
to positive results let us put this conjecture into context.

One can think of $\Upsilon_w$ as a statistical sum of
\emph{weighted random sorting networks} of
the permutation~$w$.  From a combinatorial point of view, this
is a more natural notion, since e.g. $\Upsilon_{w_0}=1$, where
$w_0=(n,n-1,\ldots,1)$ is the permutation with maximal length
\hskip.03cm $\ell(w_0)=\binom{n}{2}$. It is thus natural to expect
$u(n)$ to have nice asymptotic behavior.  In fact, Stanley
gave the first order of asymptotics for~$u(n)$:

\begin{theorem}[Stanley \cite{St}] \label{thm:bound_u(n)}
\begin{equation} \label{eq:bounds-stanley}
\frac{1}{4} \, \leq \, \liminf_{n\to\infty} \. \frac{\log_2 u(n)}{n^2} \, \leq \,
\limsup_{n\to\infty} \. \frac{\log_2 u(n)}{n^2} \, \leq \, \frac{1}{2}\..
\end{equation}
\end{theorem}

Stanley's proof is nonconstructive and based on the
\emph{Cauchy identity} for Schubert polynomials, see~\cite[Prop.~2.4.7]{Man}.
The first constructive lower bound was given by the authors in \cite[$\S$6]{MPP},
where the asymptotics of $\Upsilon_w$ was computed for several families of permutations.
Notably, for a permutation
$$w(b,n-b) \. := \. \bigl(b, \hskip.03cm b-1, \hskip.03cm \ldots\hskip.03cm ,\hskip.03cm 1, \, n, \hskip.03cm n-1, \hskip.03cm \ldots\hskip.03cm ,
\hskip.03cm b+1\bigr) \quad \text{where} \ \ b\hskip.03cm =\hskip.03cm \frac{n}3\.,
$$
we showed that
$$
\frac{1}{n^2} \hskip.03cm \log_2 \Upsilon_{w(b,n-b)} \, \longrightarrow \, C \. \approx \.
0.25162 \quad \text{as} \ \ \, n\to \infty\hskip.03cm.
$$
In fact, it is easy to see that the limit $C$ is the largest limit value
over all ratios $0< b/n<1$.  This also gives a small improvement on the
lower bound in Stanley's theorem.

\emph{Layered permutations} $w(b_k,\ldots,b_1)$ are defined as
\[
w(b_k,b_{k-1},\ldots,b_1) \. := \. \bigl(b_k,b_k-1,\ldots, 1,
b_k+b_{k-1}, b_k+b_{k-1}-1,\ldots, b_k+1,\. \ldots \. , n,\ldots , \hskip.03cm n-b_1+1\bigr),
\]
for integers \hskip.03cm $b_1+\ldots+b_{k-1}+b_k =n$.  They are also called
\emph{Richardson} and \emph{pop-stack sortable permutations} in a different
contexts, see e.g.~\cite[$\S$2.1.4]{Kit} and~\cite{MeS}.
Denote by $\mathcal L_n$ the set of layered permutations $w\in S_n$.

\smallskip

\begin{theorem} \label{thm:main-limit}
Let
$$
v(n) \, := \, \max_{w \in \mathcal L_n} \. \Upsilon_w\hskip.03cm.
$$
Then there is a limit
$$\lim_{n\to \infty} \,\. \frac{1}{n^2} \, \log_2 v(n) \, = \, \frac{ \gamma}{\log 2} \, \approx \, 0.2932362762\hskip.03cm,
$$
where \hskip.03cm $\gamma \approx 0.2032558981$ \hskip.03cm is a universal constant.  Moreover,
the maximum value $v(n)$ is achieved at a layered permutation
$$
w(\,\ldots,\hskip.03cm b_2,\hskip.03cm b_1), \quad \text{where} \quad \ b_i \. \sim\.
\alpha^{i-1}(1-\alpha)\hskip.03cm n \quad \text{as} \ \ \. n\to \infty,
$$
for every fixed~$i$, and where \hskip.03cm $\alpha \approx 0.4331818312$ \hskip.03cm is a universal constant.
\end{theorem}

\smallskip

In other words, the \emph{runs}~$b_i$ form a geometric distribution
in the limit.  See Figure~\ref{fig:limit_shape_richardson} for examples
of the  permutation matrix of such~$w$.  A posteriori this is unsurprising,
since the weights of reduced words are heavily skewed in favor of having
many transpositions at the end.

\begin{figure}[hbt]
\begin{minipage}{.54\textwidth}
  \centering
\includegraphics[height=3.8cm]{richardson1-3-8-18}
\end{minipage}\
\begin{minipage}{.49\textwidth}
  \centering
\includegraphics[height=3.8cm]{richardson-1000}
\end{minipage}
\caption{Shapes of optimal layered permutations
 $w(1,3,8,18)$ and $w(2,4,9,20,46,106,246,567)$, of size $30$ and~$1000$, respectively.}
\label{fig:limit_shape_richardson}
\end{figure}

\smallskip

The story behind the theorem is also quite interesting.   Calculations for
$n\le 10$ reported in~\cite{MeS} and~\cite{St}, prompted Merzon and
Smirnov to make the following conjecture:

\begin{conjecture}[{\cite[Conj.~5.7]{MeS}}] \label{conj:main}
For every~$n$, all permutations $w$ attaining the maximum $u(n)$ are
layered permutations. In particular, $u(n) = v(n)$.
\end{conjecture}

In other words, if the Merzon--Smirnov conjecture holds, our
Theorem proves Stanley's conjecture with the same limit value
and limiting description, as suggested by Stanley
(see~$\S$\ref{ss:finrem-exp} however).  Unconditionally,
Theorem~\ref{thm:main-limit}
improves a the lower bound for the \hskip.03cm $\liminf$ \hskip.03cm in
Theorem~\ref{thm:bound_u(n)} to about~$0.2932$.

\begin{remark}{\rm
We learned about the Merzon--Smirnov
conjecture from Hugh Thomas, who used it to compute $v(n)$
and permutations attaining it up to $n=300$ (see the Appendix).
This data allowed us to make a conjecture on the limit
shape, which we prove in the theorem.
}
\end{remark}

\medskip

\subsection*{Exact constants} The constants $\alpha$
and $\gamma$ in Theorem~\ref{thm:main-limit} are defined
as follows. Consider the function
\begin{equation} \label{eq:defr}
f(x) \, := \, x^2\log x \. - \.\frac12 \. (1-x)^2 \log(1-x)\.
- \. \frac12 \. (1+x)^2\log(1+x) \.  + \. 2\hskip.03cm x\hskip.03cm \log 2\hskip.03cm.
\end{equation}
This function is obtained from a double integral that approximates the
logarithm of the product formula of Proctor \cite{Pr} for the number
of certain plane partitions (Proposition~\ref{p:bdF}). Then $\alpha$ is defined as the solution
other than $x=1$ of the equation
\[
2\hskip.03cm x \hskip.03cm f(x) \. + \. (1-x^2) \hskip.03cm f'(x)\, = \, 0\hskip.03cm,
\]
see Figure~\ref{fig:plots} for plots of $f(x)$ and the equation above.
The constant $\gamma$ is defined as
\[
\gamma \. := \. \frac{f(\alpha)}{1-\alpha^2}\..
\]
One can show that $\alpha$ is transcendental by using Baker's theorem,
see~\cite[$\S$2.1]{Baker}, but this goes beyond the scope of this paper.
It would be interesting to see if existing technology allows to show
that $\gamma$ is also transcendental.

\medskip

\subsection*{Outline of the paper}
 In Section~\ref{sec:background} we give the necessary
background on asymptotics and on the principal evaluation of
Schubert polynomials of layered permutations.
In Section~\ref{sec:proof} we prove Theorem~\ref{thm:main-limit}.
We conclude with final remarks and open problems
in Section~\ref{sec:finrem}.

\bigskip

\section{Background} \label{sec:background}

\subsection{Permutations}
We write permutations of $\{1,2,\ldots,n\}$
as $w=w_1w_2\ldots w_n \in S_n$, where $w_i$ is the
image of~$i$. Given two permutations $u$ in $S_m$ and $v$ in $S_n$ we
denote by $u\times v$ the following permutation of $S_{m+n}$:
\[
u \times v \. := \. u_1\hskip.03cm u_2\hskip.03cm \ldots \hskip.03cm u_m \,  (m+v_1)\hskip.03cm
(m+v_2) \. \ldots \. (m+v_n).
\]
Similarly, denote by \hskip.03cm $1^m \times w$ \hskip.03cm the permutation
$$
1^m \times w \. := \. 1\hskip.03cm 2\hskip.03cm \ldots \hskip.03cm m \, (m+w_1)\hskip.03cm (m+w_2)\.\ldots \. (m+w_n)\hskip.03cm.
$$
Finally, let \hskip.03cm$|b| = b_1+\cdots+b_k$.

\subsection{Product formulas for $\Upsilon_w$ for layered permutations}
In this section we give a product formula for
$\Upsilon_w$ when $w$ is a layered permutation $w(b_k,\ldots,b_1)$.

Let  $w_0$ be the longest permutation
$(p,p-1,\ldots,1)$ and let
$$
F(m,p)\, := \, \Upsilon_{1^m \times w_0}\hskip.03cm.
$$
Fomin--Kirillov~\cite{FK} showed that $F(m,p)$ counts  the number of
plane partitions of shape $(p-1,p-2,\ldots,1)$ with entries at most~$m$.
This number of plane partitions has a product formula given by Proctor~\cite{Pr}.

\begin{theorem}[{\cite{FK,Pr}}] \label{thm:FK}
In the notation above, we have:
$$
F(m,p)
 \, = \, \prod_{1\leq i < j \leq p} \. \frac{2m+i+j-1}{i+j-1}\..
$$
\end{theorem}

\noindent
In notation of~\cite{MPP-asy}, we have:
$$
F(m,p)
 \, = \, \frac{\Lambda(2m+2p)\, \Lambda(2m+1) \,\Phi(p)
 }{\Phi(2m+p) \,\Lambda(2p)\, }\.,
$$
where $\Phi(n):=1!\cdot 2! \cdots (n-1)!$ and $\Lambda(n) := (n-2)!(n-4)!\cdots$

\begin{proposition}\label{prop:red}
For nonnegative integers $b_1,b_2,\ldots,b_k$, let $w(b_k,\ldots,b_1)$
be the associated layered permutation then
\begin{equation} \label{eq:keystep}
\Upsilon_{w(b_k,\ldots,b_1)}  \. = \. \Upsilon_{w(b_k,\ldots,b_2)} \cdot F\bigl(|b| -
b_1,b_1\bigr),
\end{equation}
where \hskip.03cm $|b| = b_1+b_2+\cdots + b_k$.
\end{proposition}

\begin{proof}
The permutation $w(b_k,\ldots,b_1)$ can be written as the product
$w(b_k,\ldots,b_2) \times w_0(b_k)$. By properties of Schubert
polynomials (e.g. see \cite[(4.6)]{Mac} or \cite[Cor. 2.4.6]{Man}) we have that
\[
\mathfrak{S}_{w(b_k,\ldots,b_1)} = \mathfrak{S}_{w(b_k,\ldots,b_2)}
\cdot \mathfrak{S}_{1^{|b|-b_1} \times w_0(b_k)},
\]
and the result follows by doing a principal evaluation.
\end{proof}

\begin{remark} {\rm
Equation~\eqref{eq:keystep} can be turned into a dynamic program to find
layered permutations $w(b_k,\ldots,b_1)$ that achieves $v(n)$, see the
appendix.}
\end{remark}

\bigskip

\section{Asymptotics of the largest $v(n)$} \label{sec:proof}

\subsection{The outline}
We will use \eqref{eq:keystep} inductively to prove the main
result.  Let $p := b_1$ and
$m:=n-p$, so that \hskip.03cm $m= b_2+\ldots+b_k$.
By definition of~$v(n)$, we have that
\[
v(n) \. = \, \max_{b \,:\, |b|=n} \hskip.03cm \Upsilon_{w(b)}\hskip.03cm.
\]
Next, using \eqref{eq:keystep}, $v(n)$ becomes
\begin{equation} \label{eq:defvn}
v(n) \. = \. \max_{1\le p \le n} \hskip.03cm \bigl\{ v(n-p) \hskip.03cm F(n-p,p) \bigr\}.
\end{equation}

We will need very precise estimates on $\log F(m,n-m)$.
Note that the exact asymptotic expansion for the
\emph{Barnes $G$-function}, which can be used to obtain
the asymptotics of $\Phi(\cdot)$ and $\Lambda(\cdot)$,
see e.g.~\cite{AR}.  However, these bounds are insufficient as
we also need sharp bounds for the error terms which hold for
all~$m$ and $n$.  We obtain these in the
next subsection. These estimates are then combined with
Proposition~\ref{prop:red} to prove Theorem~\ref{thm:main-limit}.

\medskip

\subsection{Technical estimates}
Let $f(x)$ be the function  defined in
\eqref{eq:defr}. The next lemma gives bounds on \hskip.03cm $\log
F(m,n-m)$ \hskip.03cm in terms of the function~$f(x)$.

\begin{proposition} \label{p:bdF} For all integers \hskip.03cm $n \ge m \ge 0$, we have:
\[
-2 \hskip.03cm n \. \leq \, \log F(m,n-m) \hskip.03cm - \hskip.03cm n^2 f(m/n) \. \leq \. 0.
\]
\end{proposition}

We split the proof into two lemmas, one for the
upper bound and the other for the lower bound.

\begin{lemma} \label{l:UB}
 For all integers \hskip.03cm $n \ge m \ge 0$, we have:
\[
\log F(m,n-m) - n^2 f(m/n) \leq 0.
\]
\end{lemma}

\begin{proof}
We use the product formula
for $F(m,p)$ in Theorem~\ref{thm:FK}.
\begin{align}
\log F(m,p) &= \sum_{1\leq i<j\leq p} \Bigl( \log(2m+i+j-1) -
  \log(i+j-1) \Bigr) \notag \\
&= \sum_{1\leq i\leq j'\leq p-1} \Bigl( \log(2m+i+j') -
  \log(i+j') \Bigr), \label{eq:sumbound}
\end{align}
where we changed the index to $j'=j-1$. Next, we approximate this sum
using a double integral. Let
\[
g(x,y):= \log(2m+x+y)-\log(x+y).
\]
Notice that the function $g(x,y)$ is
constant along the lines $x+y=k$ for constant $k$. Therefore, we can
shift the terms of the sum in the RHS of \eqref{eq:sumbound} by $(i,j)\mapsto
(i-1/\sqrt{2},j+1/\sqrt{2})$ without changing the sum (see center of
Figure~\ref{fig:triangle})
\begin{equation} \label{eq:sumbound2}
\log F(m,p)  \, = \, \sum_{(i,j) \in S} \hskip.03cm \Bigl( \log(2m+i+j') -
  \log(i+j') \Bigr),
\end{equation}
where \hskip.03cm $S =\bigl\{\mathbb{Z}^2 + (-1/\sqrt{2},1/\sqrt{2})\bigr\} \hskip.03cm \cap \hskip.03cm \bigl\{ (x,y)~:~0\leq x \leq p,
x <  y \leq p\bigr\}$.

\begin{figure}[hbt]
\begin{center}
\includegraphics[scale=0.7]{grid_bounds}
\caption{Illustration of the proof of the upper and lower bounds of
  Proposition~\ref{p:bdF} for $\log F(m,p)$ for $p=5$. The lattice
  points $\bullet$ on the left are the support of the sum $\sum_{i
  \leq j} \. g(i,j)$. This sum remains the same if the support is
shifted by $\bigl(\frac{-1}{\sqrt{2}},\frac{1}{\sqrt{2}}\bigr)$, giving
points ${\footnotesize \textcolor{red}{\Box}}$ in the
middle. The original sum is bounded below by the sum over the support shifted by
$\bigl(\frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}}\bigr)$, giving points ${\footnotesize \Box}$ in the right.}
\label{fig:triangle}
\end{center}
\end{figure}

Next, compute the Hessian \hskip.03cm $ {\text {\rm H}  } $ \hskip.03cm of $g(x,y)$. We have:
\[
 {\text {\rm H}  }  \, = \, C \cdot \begin{bmatrix} 1 & 1 \\ 1 & 1 \end{bmatrix}, \quad \text{where} \quad
C \. = \. \frac{1}{(x+y)^2} \. - \.\frac{1}{(2\hskip.03cm m+x+y)^2} \,\..
\]
Matrix $ {\text {\rm H}  } $ has eigenvalues \hskip.03cm $0$ \hskip.03cm and \hskip.03cm $2\hskip.03cm C$ \hskip.03cm that are nonnegative in
\hskip.03cm $[0,p] \times [0,p]$.
Thus $g(x,y)$ is convex in this region. The modified sum in
\eqref{eq:sumbound2} is the sum of values of $g(x,y)$ over centers of
the unit squares which fit entirely in $R$. By convexity, each such value
of $g(x,y)$ is less than the average value of $g(x,y)$ over its
square. Hence the sum in
\eqref{eq:sumbound2} is bounded above by the double integral,
\begin{align*}
\log F(m,p) \leq \int_{0}^p\int_{y}^p \left(\log(2m+x+y)-\log(x+y)\right)\. dx\hskip.03cm dy.
\end{align*}
Next, we compute this double integral and obtain
\begin{equation} \label{eq:origin_f}
\int_{0}^p\int_{y}^p \hskip.03cm \left(\log(2m+x+y)-\log(x+y)\right)\. dx\hskip.03cm dy \. = \.
(m+p)^2 f(m/(m+p)),
\end{equation}
for $f(x)$ defined in \eqref{eq:defr}. This proves the upper bound.
\end{proof}

\begin{lemma} \label{l:LB}
 For all integers \hskip.03cm $n \ge m \ge 0$, we have:
\[
\log F(m,n-m) - n^2 f(m/n) \. \geq \. -2\hskip.03cm n.
\]
\end{lemma}

\begin{proof}
Since the function $g(x,y)$ is decreasing along
the $x$ direction and $y$ direction then each value $g(i,j)$ in the
sum is bigger than the average value of $g(x,y)$ over the unit square
with center $(i+1/\sqrt{2},j+1/\sqrt{2})$ (see right of
Figure~\ref{fig:triangle}). Hence the original sum in
\eqref{eq:sumbound} is bounded below by the double integral

\begin{equation} \label{eq:keylowerbound}
\log F(m,p) \, = \, \sum_{1\leq i<j\leq p} g(i,j) \geq \int_1^p\int_x^p g(x,y) \. dy\hskip.03cm dx.
\end{equation}
This integral can be written in terms of the original integral,
computed in \eqref{eq:origin_f}, as follows
\begin{align}
 \int_1^p\int_x^p g(x,y) \. dy\hskip.03cm dx \, &  = \, \int_0^p\int_x^p g(x,y) \. dy\hskip.03cm dx
\, - \, \int_0^1\int_x^p g(x,y) \. dy\hskip.03cm dx \notag\\
&= \, (m+p)^2 f(m/(m+p)) \, -  \, \int_0^1\int_x^p g(x,y) \. dy\hskip.03cm dx. \label{eq:pflowerbound_1}
\end{align}
Since the function $g(x,y)$ is decreasing in the $x$ direction then
the double integral in the RHS above is bounded by the following single integral
\begin{equation}
-\int_0^1\int_x^p g(x,y) \. dy\hskip.03cm dx \, \geq \, -\int_0^p g(0,y) \. dy.
\end{equation}  \label{eq:pflowerbound_2}
We evaluate this single integral and use Jensen's inequality to obtain
\begin{align}
- \int_0^p g(0,y) dy \, & = \,
2m\log(2m) \. + \. p\log(p) \. - \. (2m+p)\log(2m+p) \notag \\
&\geq \, (2m+p)\bigl( \log(2m+p) \. - \. \log 2\bigr) \. -
  \. (2m+p)\log(2m+p). \label{eq:pflowerbound_3}
\end{align}
Combining \eqref{eq:keylowerbound},\eqref{eq:pflowerbound_1}, \eqref{eq:pflowerbound_2}, and \eqref{eq:pflowerbound_3} we have
\[
\log F(m,p) \. \geq \. (m+p)^2 f(m/(m+p)) \. + \. (2m+p)\left( \log(2m+p) \.
- \.  \log(2)\right) \. - \. (2m+p)\log(2m+p).
\]
The RHS is greater than or equal to \hskip.03cm $(m+p)^2 f(m/(m+p)) -2(m+p)$,
as desired.
\end{proof}

\medskip

\subsection{Optimizing constants}
Our goal is to show that $\lim_{n\to
  \infty} \log_2 v(n)/n^2$ is a constant. In the previous lemma we gave bounds on the error of approximating
$\log F(m,n-m)$ by $n^2f(x)$ where $x = m/n$ in $[0,1]$. We now find a unique constant
$\gamma$ such that $f(x)+\gamma x^2$ has a unique maximum over $x \in [0,1)$.

\begin{lemma}\label{lemma:max_r}
There exist a unique $\gamma >0$ and $\alpha \in (0,1)$, such that:
\begin{itemize}
\item[(1)] $2\gamma \alpha + f'(\alpha) \hskip.03cm =\hskip.03cm 0$,
\item[(2)] $\gamma \alpha^2 + f(\alpha) \hskip.03cm = \hskip.03cm \gamma$ \hskip.03cm with \hskip.03cm $2\gamma + r''(\alpha) \hskip.03cm \leq \hskip.03cm 0$.
\end{itemize}
And for this $\gamma$, the maximum of \hskip.03cm $f(x) + \gamma x^2$ \hskip.03cm over $x\in [0,1)$ is achieved at
the given $\alpha$, and the value is precisely $\gamma$. That is,
\[
\max_{x\in [0,1)}(f(x) + \gamma x^2) \. = \. f(\alpha) + \gamma \alpha^2 \. = \. \gamma.
\]
\end{lemma}

\begin{proof}
First, it is straightforward to show that $\lim_{x\to 0} f(x)  =
\lim_{x\to 1} f(x) =0$ and that $f(x)>0$ for $x\in(0,1)$ (see plot of
$f(x)$ on the left of Figure~\ref{fig:plots}).

Let $\alpha$ be a solution to the equation $q(x)=0$ where
\begin{align*}
q(x) &:=\,\, f(x) 2x + f'(x)(1-x^2)\\
  &= (1-x)^2\log(1-x) - (1+x)^2\log(1+x) + 2x\log(x) + 2(1+x^2)\log(2).
\end{align*}
This function on the RHS above has one root $\alpha=0.4331818312..$ and the other is $x=1$, as easily seen from the plot, but also can be shown analytically.
Then we set $$\gamma := \frac{f(\alpha)}{1-\alpha^2} = -\frac{f'(\alpha)}{2\alpha},$$ so $\gamma$ and $\alpha$ now satisfy conditions (1) and (2).

\begin{figure}
\includegraphics[width=1.6in]{graph_f.jpg}\quad \includegraphics[width=1.6in]{graph_q.jpg}\quad \includegraphics[width=1.6in]{graph_fgamma.jpg}
\caption{Graphs of the functions $f(x)$, $q(x)$ and $\gamma x^2+f(x)$, on $(0,1)$.}
\label{fig:plots}
\end{figure}

Next, we see that $\gamma = f(\alpha)/(1-\alpha^2) \approx
0.2032558981$. To prove that this is indeed a maximum for $f(x)+\gamma
x^2$, we check that the second derivative,  $d^2(\gamma x^2 +
f(x))/dx^2 =2\gamma + r''(x)<0$ for $x=\alpha$. We have that $r''(x) = \log
(x^2/(1-x^2))$. Since $\alpha \leq 0.45$, we have that $
x^2/(1-x^2) <0.26$ and so $r''(\alpha) <-1.3<-2\gamma $ and so the
value is a local maximum and by condition~(2) it is equal to $\gamma$.
\end{proof}

\medskip

\subsection{Proof of Theorem~\ref{thm:main-limit}}
The theorem follows immediately from the following lemma.

\begin{lemma}\label{l:limit}
For all $n\ge 2$ we have:
\[
\bigl| \log v(n) - \gamma n^2\bigr| \. \leq \. 4 n\hskip.03cm.
\]
Conversely, suppose for a layered permutation $w(b)\in S_n$ we have
\[
\bigl| \log \Upsilon_w - \gamma n^2\bigr| \. \leq \. 4 n\hskip.03cm.
\]
Then $b=(....,b_2,b_1)$, s.t. $b_i \sim (1-\alpha)\alpha^{i-1} n$ for all
fixed $i\ge 1$.
\end{lemma}

\begin{proof}
We proceed by induction to show that \hskip.03cm $|\log v(n) - \gamma n^2| \leq 4 \hskip.03cm n$
\hskip.03cm holds for all $n\ge 2$.  The base cases $n=2$ can be checked directly
(see exact values in the appendix).

We start with \eqref{eq:defvn} and use the induction hypothesis and the upper bound of
Proposition~\ref{p:bdF} to obtain
\begin{align*}
\log v(n) \. &= \. \max_{m < n} \hskip.03cm \bigl(\log v(m) + \log F(m,n-m) \bigr)\\
& \leq \. \max_{m<n} \hskip.03cm \bigl( \gamma m^2 + \log F(m,n-m) +2m \bigr),\\
& \leq  n^2\max_{x\in[0,1)} \bigl(f(x) + \gamma x^2\bigr) \. + \. 2 \hskip.03cm n.
\end{align*}
By Lemma~\ref{lemma:max_r}, the maximum value of
$f(x)+\gamma x^2$ is equal to~$\gamma$. Thus, the above inequality becomes
\[
\log v(n) \. \leq \. \gamma n^2 \hskip.03cm +\hskip.03cm 2\hskip.03cm n.
\]
This maximum is achieved when $x=\alpha$, i.e.\ when $m=n\alpha$ and $p=b_1 = (1-\alpha)n$. By the
definition of~$v(n)$, for this value of~$m$ we have that
\[
\log v(n) \. \geq \. \log v(n\alpha) \hskip.03cm +\hskip.03cm \log F(n\alpha,n-n\alpha).
\]
By the induction hypothesis and the lower bound of
Proposition~\ref{p:bdF}, the above inequality becomes
\begin{align*}
\log v(n) \. & \geq \. \bigl(\gamma n^2\alpha^2 \hskip.03cm - \hskip.03cm 4 \hskip.03cm n\alpha \bigr) \hskip.03cm +\hskip.03cm (n^2 f(\alpha) \hskip.03cm -\hskip.03cm 2\hskip.03cm n) \\
 &= \. \gamma n^2 \hskip.03cm  - \hskip.03cm 2\hskip.03cm (1\hskip.03cm+\hskip.03cm 2\hskip.03cm \alpha)\hskip.03cm n\hskip.03cm \geq \gamma n^2 \hskip.03cm - \hskip.03cm 4\hskip.03cm n.
\end{align*}
Here we again used the fact that \hskip.03cm $f(\alpha) + \gamma \alpha^2 = \gamma$ and that $\alpha \leq 1/2$.
In summary,
$$\bigl|\log v(n) - \gamma n^2 \bigr| \. \leq \. 4 \hskip.03cm n ,
$$
and this bound is attained when \hskip.03cm $b_1 \sim (1-\alpha)n$. Recursively,
we obtain \hskip.03cm $b_i \sim (1-\alpha)\alpha^{i-1}n$ for every fixed $i=2,3,\ldots$.
\end{proof}

\begin{remark}{\rm
Note that the appendix shows rather slow rate of convergence
for \hskip.03cm $h(n) := \frac{1}{n^2} \hskip.03cm \log_2 v(n)$, giving only
$h(300)\approx 0.2904$.  This suggests that \hskip.03cm
$h(n) = \gamma/(\log 2) - 1/n - o(1/n)$, so that the bound in
Lemma~\ref{l:limit} is quite sharp.
}
\end{remark}

\bigskip

\section{Final remarks}\label{sec:finrem}

\subsection{} \label{ss:finrem-limit}
Stanley's Conjecture~\ref{conj:stan} remains open but is very
likely to hold. Denote by
$$
a(n) \. = \. \sum_{w \in S_n} \. \Upsilon_w
$$
the total number of rc-graphs (pipe dreams) of size~$n$.  Since
$$
u(n) \. \le \. a(n) \. \le \. n! \hskip.03cm u(n),
$$
we conclude that it suffices to prove the asymptotics result
for~$a_n$. This suggests connections to counting general tilings
(see e.g.~\cite{AS}), as pipe dreams can be viewed as tilings of
a staircase shape with two types of tiles, but with one global
condition (strains can intersect at most once).  The problem is
especially similar to counting \emph{Knutson-Tao puzzles}
enumerating the \emph{Littlewood--Richardson coefficients},
whose maximal asymptotics was recently studied in~\cite{PPY}.

By analogy with the tilings, one can ask if $u(n)$ satisfies some sort of
super-multiplicativity property.  Formally, let $w\otimes 1^c$ denote
the \emph{Kronecker product permutation} of size $\hskip.03cm c\hskip.03cm n\hskip.03cm$,
whose permutation matrix equals the Kronecker
product of the permutation matrix $P_w$ and the identity~$I_c$
(see~\cite{MPP}).

\begin{conjecture}
For $w\in S_n$, we have \hskip.03cm $\Upsilon_{w \otimes 1^2} \hskip.03cm \geq \hskip.03cm \Upsilon_w^4$.
\end{conjecture}

We verified the conjecture for all $w\in S_n$ where $n\le 5$, but perhaps
more computational evidence would be helpful.

\smallskip

\subsection{} \label{ss:finrem-exp}
Similarly, the Merzon--Smirnov Conjecture~\ref{conj:main} remains open.
In our opinion, the numerical evidence in favor of the conjecture is
insufficient, and it would be interesting to verify it for larger~$n$.
To speedup the computation, perhaps, there are large classes of
permutations $u\in S_n$ which can be proved to be non-maximal, i.e.\
there exists \hskip.03cm $w\in S_n$, s.t. $\Upsilon_u\leq \Upsilon_{w}$.
Such permutations can then be ignored in the exhaustive search.

In fact, Prop.~6.5 in~\cite{MPP} gives explicit
constructions of large families of permutations $w\in S_n$,
for which  $\log \Upsilon_w = \Theta(n)$.  These permutations are
very far from being layered (in the transposition distance),
suggesting that if true, proving Conjecture~\ref{conj:main}
might not be easy.

\smallskip

\subsection{}
In \cite{St}, Stanley also considered the case when $\Upsilon_w$ is
small. It is well known that $\Upsilon_w=1$ if and only if $w$ is
{\em dominant}~\cite{Man}, i.e.\ $132$-avoiding. Stanley conjectured
that $\Upsilon_w=2$ if and only if $w$ has exactly one instance of the
pattern~$132$. This was recently proved by Weigandt~\cite{W}, who also
showed that $\Upsilon_w-1$ is greater than or equal the number of
instances of the pattern $132$ in~$w$.

This suggests the problem of finding permutations where
the number of patterns $132$ is maximal.  In the field of
pattern avoidance, this problem can be rephrased as asking for
permutations $w\in S_n$ with maximal \emph{packing density}
of the pattern $132$, see~\cite[$\S$8.3.1]{Kit}.  The
solution due to Stromquist is extremely well understood,
and has been both refined and generalized,
see~\cite{A+,BSV,HSV}, \cite[$\S$5.1]{Price} and
\cite[\href{https://oeis.org/A061061}{A061061}]{OEIS}.
The maximal packing density is attained at a layered
permutation \hskip.03cm $w(b_1,b_2,\ldots)$, where the runs $b_i$ have a
geometric distribution:
$$
b_i\. \sim \. \rho\hskip.03cm (1-\rho)^{i-1} \hskip.03cm n, \ i=1,2,\ldots \quad \text{where} \quad
\rho \. =  \. \frac{\sqrt{3}-1}{2} \. \approx \.  0.366025
$$

While, of course, $v(n)$ are attained at somewhat different layered
permutations, the similarities to this work are rather striking
and go beyond coincidences.  They are rooted in the recursive nature
of optimal permutations in both cases, which are solutions of
similar (but different!) maximization problems.

\smallskip

\subsection{}\label{ss:finrem-rc}
The bounds for $u(n)$ from Theorem~\ref{thm:bound_u(n)} are obtained
from the Cauchy identity of Schubert polynomials which gives
\begin{equation} \label{eq:CauchySchubert}
\sum_{w_0 = v^{-1}u}\Upsilon_u \Upsilon_v = 2^{\binom{n}{2}}.
\end{equation}
One could then ask for large values of $\Upsilon_w\Upsilon_{w w_0^{-1}}$. Let $u'(n) := \max_{w\in S_n} \{ \Upsilon_w\cdot\Upsilon_{w w_0^{-1}}
\}$. The table below has the values of $u'(n)$ for $n=2,\ldots,9$ and
the permutations $w$ (up to multiplying by $w_0^{-1}$) that achieve
that value $u'(n)$.
\[
\begin{array}{rrc}
\hline
n & u'(n) & w \\ \hline
3 & 2 & 132\\
4 & 6 & 1423\\
5 & 33 & 15243\\
6 & 286 & 162534\\
7 & 4620 & 1736254\\
8 & 162360 &  18527364 \\
9 & 9057090  & 195283746 \\ \hline
\end{array}
\]
Note that for a layered permutation $w(b)$, the permutation $w(b)w_0^{-1}$ is dominant and so $\Upsilon_{w(b) w_0^{-1}}=1$.

There is a combinatorial proof of \eqref{eq:CauchySchubert} by
Bergeron and Billey \cite{BB} involving taking a double {\em $rc$-graph} of
$w_0$ ($2^{\binom{n}{2}}$ many) and reading from each half of it permutations $u$
and $v$ satisfying $w_0 = v^{-1}u$. All such double $rc$-graphs of $w_0$ can be
obtained from an initial double $rc$-graph via
certain local transformations (see \cite[Sec.~4]{BB}). One can use these local
transformations in a Markov chain to obtain a random double $rc$-graph
of $w_0$ and from it read off a permutation~$u$; see
Figure~\ref{fig:random-permdrc}. We conjecture that
the permutation matrix of random permutations~$u$ has
a parabolic frozen region.

The second permutation in Figure~\ref{fig:random-permdrc} is obtained
by running a Markov chain for $5\cdot 10^9$ local moves
on a double $rc$-graph of $v^{-1}u=w_0 \in S_{50}$,
described in~\cite[Sec.~4]{BB}.  Half of the resulting
double $rc$-graph given in Figure~\ref{fig:random-permdrc-app}
is then converted into a permutation $u\in S_{50}$.

\begin{figure}
\begin{center}
\includegraphics{permS9}\qquad
\qquad\includegraphics[scale=0.32]{matrixdrc_graphb.png}
\caption{Permutation matrices  of $195283746$ and of a permutation
$u\in S_{50}$ from the random double $rc$-graph.}
\label{fig:random-permdrc}
\end{center}
\end{figure}

\vskip.7cm

\subsection*{Acknowledgements}
We are grateful to Nantel Bergeron, Sara Billey, Grigory Merzon, Evgeny Smirnov, Richard Stanley
and Damir Yeliussizov for helpful conversations.  We are especially
thankful to Hugh Thomas for sharing the data of layered permutations.
The calculations of $\Upsilon_w$ done in this paper were made using Sage and
its algebraic combinatorics features developed by the Sage-Combinat
community~\cite{sage-combinat}.
The second and third authors were partially supported by the~NSF.

\newpage

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30 for 30 (Television program), George Best.
The Resource 30 for 30 (Television program), George Best.
Context of 30 for 30 (Television program), George Best.
Data Citation of the Collection 30 for 30 (Television program), George Best.


A mayor or full-time commissioner who serves on a municipal, county, or regional board, commission, authority, or development district in an appointed, elected, or ex officio capacity may name a qualified person as his or her designee. The designee will have the same powers as the official. This includes the power to vote except at any meeting the official attends. This law does not apply if there is a provision for such a substitution in a charter, private act, ordinance, or general law. It also does not apply to governor-appointed members of boards, commissions, or authorities. T.C.A. § 6-54-112.


Are you tolerating unwanted behaviour?
Are you aware of what is really driving your behaviour, or the behaviour of your people? I've recently had a number of discussions about how to address the unwanted behaviour of staff as it can be awkward if you don't have solid foundations to stand on.


text:
Chad Opitz at Savage Henry Comedy Club
Chad Opitz is a comic whose hilarious and unique perspectives make him an oft booked staple at Bay Area clubs and showcases. Veering between one-liners, short story jokes, and sometimes even song, Opitz' writing is as well-regarded as his character and performance work.
Chad has been a featured guest on the Doug Loves Movies Podcast and The Benson Interruption. He was a featured performer at the 2016-2019 San Francisco Sketchfests. Chad was the winner of Bay Area legend Jimmy Gunn's "Best Newcomer" award. He is a regular host at Punch Line San Francisco and Sacramento, Cobb's Comedy Club and is a feature act at Rooster T. Feathers Comedy Club and San Jose Improv.
Chad has been featured in several short films and commercials, including Walgreens Red Nose Day to help end child poverty.
He's opened for Michelle Wolf, Melissa Villasenor, David Cross, Scott Thompson, Gad Elmaleh, ISMO, Rob Schneider, Neil Hamburger, Taylor Tomlinson, Tom Green, Bobcat Goldthwait, Brooks Wheelan and many more.
Featuring Geneva Rust-Orta.
Evan Vest opens.
Nando Molina hosts.
Savage Henry Comedy Club | 415 5th Street, Eureka | 845-8864 | savagehenrymagazine.com
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text:
Alcoholism prevention begins early
Apr 22nd, 2015 · by Ashton Brown · Comments:
DOVER — Alcohol is the most commonly used addictive substance in the United States and April is Alcohol Awareness Month, a time to address the issue of alcohol abuse and dependence.
According to the National Council on Alcoholism and Drug Dependence, 17.6 million people, or one in every 12 adults suffer from alcohol abuse or dependence.
According to NCADD, there are four qualities one must possess to be labeled an alcoholic;
•Craving, a strong need, or urge, to drink;
•Loss of control, not being able to stop drinking once drinking has begun;
•Physical dependence, withdrawal symptoms, such as nausea, sweating, shakiness, and anxiety after stopping drinking and;
•Tolerance, the need to drink greater amounts of alcohol to get drunk.
The four issues can then create social problems like unemployment, lost productivity, family problems and violence. The Centers for Disease Control and Prevention reports that excessive long-term drinking can lead to serious health issues as well.
Some health issues associated with heavy alcohol use are dementia, stroke, cardiovascular problems, increased risk for many kinds of cancers including liver, mouth, throat, larynx (voice box) and esophagus, liver disease, depression and anxiety.
One of the keys to reducing the rate of alcoholism is prevention and the Department of Health and Social Services is stepping in with a campaign to prevent underage and binge drinking. The program is an extension of the "Underage? Understand. Don't Drink!" campaign focusing on individuals younger than 25.
Recent studies from the Center for Drug & Alcohol Studies at the University of Delaware report 35 percent of 11th-graders in Delaware reported using alcohol at least once a month in 2013, with 62 percent saying they used it in the past year and 71 percent saying they had used it in their lifetimes.
Among eighth-graders, 14 percent reported at least monthly use of alcohol, with 31 percent saying they used it within the last year and 40 percent in their lifetimes.
According to Alcoholics Anonymous, alcoholics can be anyone regardless of age, race, gender or social class. Individuals can develop alcoholism after drinking any length of time, no matter how they consume alcohol.
Even though anyone can be effected by alcoholism, NCADD research shows that the risk for developing alcoholism runs in families. But a genetic predisposition doesn't mean that the child of an alcoholic parent will become an alcoholic just like how some people develop alcoholism even though no one in their family has a drinking problem.
Although alcoholism is a chronic disease it can be treated through programs that use both counseling and support like AA. The program, founded in 1935 has the goal of helping alcoholics achieve and maintain sobriety.
AA is an organization comprised of individuals who share their experiences with each other to solve their common problem and help others to recover from alcoholism. The only requirement for membership is a desire to stop drinking. There are no dues or other requirements for AA membership.
Members of AA receive counseling and support mainly through meetings where alcoholics share their experiences, how they overcame obstacles and the result the changes have made on their lives.
Other forms of help are also available through state agencies like the Division of Public Health's Help Is Here Delaware which provides information and resources to both alcoholics and their friends and family at helpisherede.com.
Even with counseling and support, alcoholism cannot be cured. Even if an alcoholic has been sober for months or even years, he or she still can suffer a relapse.
AA also reports that finding help truly comes down to the alcoholic themselves; it is not a process friends or family can force someone into.
"The first and most important step in our program is admission by the alcoholic that he or she is powerless over alcohol, and that life has become unmanageable," AA states on its website.
If you realize it's time to seek help with a drinking problem in Kent County, call 736-1567, for New Castle County call 655-5999 and for Sussex, call 856-6452.
Reach staff writer Ashton Brown at abrown@newszap.com. Follow @AshtonReports on Twitter.
Tags:Health care


text:
View source for Canon EXEE
← Canon EXEE
<div class="floatright plainlinks" style="margin:0px 0px 0px 15px";> {{Flickr image | image_source=http://www.flickr.com/photos/14463685@N07/2989249499/in/pool-camerawiki/ | image=http://farm4.static.flickr.com/3024/2989249499_578c4dea80.jpg | image_align=left | image_text=Canon EXEE with a complete set of lenses |image_by= Howard Somerville |image_rights= with permission }} </div> The '''EXEE''' is a 35 mm [[SLR]] camera made by [[Canon]] from 1969 until the early 1970s.<ref name=CCM>[http://global.canon/en/c-museum/product/film75.html Canon Camera Museum] listing for the EXEE.</ref> It was replace by the [[Canon EX Auto]] in 1972. Its most characteristic feature is a rear lens-group (three elements in two groups<ref name=CCM></ref>) fixed on the camera and incorporating the helical focusing mechanism, to which any of a small selection of front groups can be attached by a simple screw fitting. The EXEE offers through-the-lens metering and [[shutter priority|shutter-priority AE]]. It has a focal plane shutter with cloth blinds, travelling horizontally. It offers shutter speeds from 1/8 to 1/500 second plus 'B', and has a delayed-action (self-timer) lever on the front of the body. [[flash sync|X-synchronisation]] for flash is at 1/60 second; there is a [[cold shoe]], and a [[PC socket]] next to the left-hand strap lug. The aperture is set not on the lens, but on a dial around the rewind crank, between f/1.8 and f/16; there are also 'EE' (i.e. auto-exposure) and 'Off' positions. The aperture set is displayed in the viewfinder on a scale with a needle. The available lens front-groups are: * Standard lens: EX50mm f/1.8 * Wide angle: EX35mm f/3.5 (price ¥8000<ref name=CCM></ref> * Portrait: EX95mm f/3.5 (price ¥11000) * Telephoto: EX125mm f/3.5 (price ¥18900) The 125 mm lens was not available until 1972. The fixed rear group must have been something of a constraint of the design of the lenses, but made the accessory lenses cheap relative to lenses incorporating a rear group and focus mechanism in each. For comparison, the Canon Camera Museum gives a price of ¥19500 for the FD35mm f/3.5 (i.e. the old FD mount), introduced in 1973<ref>Listing for the [http://global.canon/en/c-museum/product/fd146.html FD35mm f/3.5] on the [http://global.canon/en/c-museum/ Canon Camera Museum] site.</ref> and ¥27000 for the FD100mm f/2.8, introduced in 1971.<ref>Listing for the [http://global.canon/en/c-museum/product/fd164.html FD100mm f/2.8] on the [http://global.canon/en/c-museum/ Canon Camera Museum] site.</ref> The cost of the telephoto lens was more comparable to a complete lens; the FD135mm f/3.5 cost ¥19900 in 1970.<ref>Listing for the [http://global.canon/en/c-museum/product/fd169.html FD135mm f/3.5] on the [http://global.canon/en/c-museum/ Canon Camera Museum] site.</ref> For metering, it is necessary to set the maximum aperture of the lens front-group being used. This is made possible by having two marks on the film speed dial, one for f/1.8 (i.e. standard lens) and one for f/3.5 (any other lens). The CdS meter reads between EV 4.75 and EV 17 <ref name=CCM></ref>. It requires a 1.3V mercury battery or modern substitute. However, the shutter speeds are timed mechanically, so the camera functions without a battery (without metering). The EXEE has Canon's QL (Quick Load) simplified loading feature, whereby the film leader is simply pulled across the film compartment to a mark, and the back closed, and the uptake mechanism then captures the leader when the advance is wound. Also sold in the US as the Bell & Howell Auto 35/Reflex ==Notes== <references /> ==Links== * [http://www.cameramanuals.org/canon_pdf/canon_ex_ee.pdf Canon EX EE Instruction manual] at Orphan Cameras * [http://www.camera.portraits.srv2.com/canonexee.htm Canon EX EE QL] page at [http://www.camera.portraits.srv2.com Camera Portraits] * [http://www.collection-appareils.fr/x/html/page_standard.php?id_appareil=10508 Canon ExEE QL] at [http://www.collection-appareils.fr/general/html/francais.php Sylvain Halgand's www.collection-appareils.fr] (in French) {{canon}} [[Category: Japanese 35mm SLR]] [[Category: Canon|EXee]] [[Category: C]] [[Category: E|Exee]]
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A team of open-source developers has released software which emulates the PowerPC processor architecture and enables users to run Mac OS and some Unix OSes on PCs powered by Intel x86-architecture processors.
The project, known as PearPC, is not yet stable enough or fast enough, though, to be more than a tool for enthusiasts, the developers have warned.
Using PearPC on a standard PC, they have successfully run Mac OS X 10.3, OpenBSD for PPC, NetBSD for PPC, Darwin for PPC and Mandrake Linux 9.1. PearPC translates PowerPC instructions into x86 instructions, but currently "the client will run about 40 times slower than the host," the developers said.
Main developers Sebastian Biallas and Stefan Weyergraf are looking for extra people to help develop the project, which is now hosted at SourceForge. Another Mac/Windows compatibility project called SoftPear, also under development, will enable Mac OS X applications that have been developed for the PowerPC to be recompiled for x86 CPUs, according to SoftPear's website.
Most of the cross-platform technology that exists involves emulating the Windows PC environment on Apple hardware - the opposite of what PearPC is attempting. Commercial products such as Microsoft's Virtual PC compete with open-source projects like Darwine, designed to let users run the Wine (Wine Is Not an Emulator) environment with Windows applications on Darwin and Mac OS X systems.
The magic of emulation Is there room for MacOS in the corporate world?


text:
"""Utilities functions used in Kytos."""
from datetime import datetime, timezone
from threading import Thread

__all__ = ['listen_to', 'now', 'run_on_thread', 'get_time']

# APP_MSG = "[App %s] %s | ID: %02d | R: %02d | P: %02d | F: %s"

def listen_to(event, *events):
    """Decorate Event Listener methods.

    This decorator was built to be used on NAPPs methods to define which
    type of event the method will handle. With this, we will be able to
    'schedule' the app/method to receive an event when a new event is
    registered on the controller buffers.
    By using the run_on_thread decorator, we also guarantee that the method
    (handler) will be called from inside a new thread, avoiding this method to
    block its caller.

    The decorator will add an attribute to the method called 'events', that
    will be a list of the events that the method will handle.

    The event that will be listened to is always a string, but it can represent
    a regular expression to match against multiple Event Types. All listened
    events are documented in :doc:`/developer/listened_events` section.

    Example of usage:

    .. code-block:: python3

        class MyAppClass(KytosApp):
            @listen_to('kytos/of_core.messages.in')
            def my_handler_of_message_in(self, event):
                # Do stuff here...

            @listen_to('kytos/of_core.messages.out')
            def my_handler_of_message_out(self, event):
                # Do stuff here...

            @listen_to('kytos/of_core.messages.in.ofpt_hello',
                       'kytos/of_core.messages.out.ofpt_hello')
            def my_handler_of_hello_messages(self, event):
                # Do stuff here...

            @listen_to('kytos/of_core.message.*.hello')
            def my_other_handler_of_hello_messages(self, event):
                # Do stuff here...

            @listen_to('kytos/of_core.message.*.hello')
            def my_handler_of_hello_messages(self, event):
                # Do stuff here...

            @listen_to('kytos/of_core.message.*')
            def my_stats_handler_of_any_message(self, event):
                # Do stuff here...
    """
    def decorator(handler):
        """Decorate the handler method.

        Returns:
            A method with an `events` attribute (list of events to be listened)
            and also decorated to run on a new thread.

        """
        @run_on_thread
        def threaded_handler(*args):
            """Decorate the handler to run from a new thread."""
            handler(*args)

        threaded_handler.events = [event]
        threaded_handler.events.extend(events)
        return threaded_handler

    return decorator

def now(tzone=timezone.utc):
    """Return the current datetime (default to UTC).

    Args:
        tzone (datetime.timezone): Specific time zone used in datetime.

    Returns:
        datetime.datetime.now: Date time with specific time zone.

    """
    return datetime.now(tzone)

def run_on_thread(method):
    """Decorate to run the decorated method inside a new thread.

    Args:
        method (function): function used to run as a new thread.

    Returns:
        Decorated method that will run inside a new thread.
        When the decorated method is called, it will not return the created
        thread to the caller.

    """
    def threaded_method(*args):
        """Ensure the handler method runs inside a new thread."""
        thread = Thread(target=method, args=args)

        # Set daemon mode so that we don't have to wait for these threads
        # to finish when exiting Kytos
        thread.daemon = True
        thread.start()
    return threaded_method

def get_time(data=None):
    """Receive a dictionary or a string and return a datatime instance.

    data = {"year": 2006,
            "month": 11,
            "day": 21,
            "hour": 16,
            "minute": 30 ,
            "second": 00}

    or

    data = "21/11/06 16:30:00"

    2018-04-17T17:13:50Z

    Args:
        data (str, dict): python dict or string to be converted to datetime

    Returns:
        datetime: datetime instance.

    """
    if isinstance(data, str):
        date = datetime.strptime(data, "%Y-%m-%dT%H:%M:%S")
    elif isinstance(data, dict):
        date = datetime(**data)
    else:
        return None
    return date.replace(tzinfo=timezone.utc)

redpajama_set_name: RedPajamaGithub


Mr. Lewis has practiced continuously in the Denver and Fort Collins areas for over 50 years handling a wide variety of IP matters. Worked as a Patent Examiner in the U.S. Patent and Trademark Office. Expertise is electronic and electromechanical technology.
My practice includes patent validity and infringement opinions, intellectual property licensing and litigation matters before the Federal Courts.
Representation in Washington, D.C. and in foreign countries and carry on an active domestic and foreign practice including litigation, licensing, and secrecy agreements as relate to all phases of patent, copyright and trademark law.
Received Bachelor of Science degree in Electrical Engineering in 1959 from South Dakota School of Mines and Technology. Received Juris Doctor of Law at the University of Denver after earlier attending George Washington University. Member of the Bar of the State of Colorado, United States Federal Court, District of Colorado. Registered patent attorney with the United States Patent and Trademark Office, Washington, D.C., 20231—July 21, 1965.


This is an extraordinary Fukuro Obi that belonged to a very special Samurai family in Kanazawa. It has been handwoven of pure beige Silk and Gold threads in an intricate background pattern of horizontally flowing lines resembling mystic, hilly, mountainous terrain. Mountains ("Yama") hold a special place in Japanese cultural and religious beliefs, especially in Kanazawa, which sits on the west coast and is separated from the rest of Japan by mountains. Almost 85% of Japan is covered by mountains and, thus, it is understandable that they would figure prominently in the artistic design of local families.
The dramatic black, gray and gold Bamboo ("Take") are superimposed over this backdrop to reinforce an overall feeling of a mountainous landscape. The Bamboo ("Take") is one of the "3 friends of winter" and is considered a good omen. It is considered versatile, graceful and auspicious, and has played a large role in Japan. In addition, the strength and flexibility of Bamboo have taken it far from the nobility's garden into all aspects of everyday life in Japan. The Japanese word for Bamboo, take, is homophonous with words for "warrior" and "bravery" and sounds like the words for "tall" and "hawk." The overall effect of this Obi is one of great beauty, while the narrow gold stripes at the bottom of the pattern denote that a woman of high rank and wealth in Japanese society wore this Obi.
One end of this long, rectangular Obi has been skillfully folded in half and then tied in a bow of typical obi design. A marvelous Japanese Artisan (herself of Samurai lineage) created this artistic representation in order to display year-round the beauty of this wonderful textile, as easily as one would hang a painting. Silk thread has been used on the back to support the tying of this Obi. The Bow is held in place with a matching Silk, hand braided, "Obi-jime," or cord that echoes the color and beauty of the Obi. The Obi-jime is as old as the Obi itself.
This is an extraordinary example of the Fukuro Obi originally intended for both formal and semi formal wear. It has two seams running down each edge of the Obi.
Hand woven of the finest Silk threads in excellent condition.
This is a wonderful way to display an antique Obi year around as an unusual and dramatic wall hanging.


text:
Home › Medical Training › Foundation
London and KSS Foundation Schools
Welcome to the London and KSS Foundation Schools pages; a collaboration between North Central & East London Foundation School, North West London Foundation School and South Thames Foundation School.
The three Schools are managed by a central administrative team based in HEE offices in London but have three distinct indenities which can be explored by clicking on the relevant areas below, along with information relevant across all schools which can be found in the joint school and programme information section.
Covid 19 Response Updates
We wish to thank you for your hard work and understanding during these exceptional times. Our team is working closely with our trusts to ensure that support is available for you, even if circumstances result in major changes to your medical surroundings and situations.
If you find yourself in a worrying situation, please look after yourself first and discuss matters with your supervisor or Foundation Programme Training Director. There are also many other sources of help available in your trusts and more widely, and additional information via the weblink below.
Please keep safe and continue to do a fantastic job.
Dr Keren Davies, FSD NCELFS
Dr Anthea Parry, FSD NWLFS
Professor Jan Welch, FSD STFS
Information relating to HEE's response to Covid-19/Coronavirus can be found on the National Website, please click here for more information.
For all Information regarding the London and KSS Foundation Schools please access the link to the home page of the London and KSS Foundation website by clicking here. This website has detailed information regarding all aspects of the Foundation Programme for North West London, North Central and East London and South Thames Foundation Schools as well as Joint Programme and School Information. Under the blog section of the website are the fortnightly Foundation Bulletins which hold key updates, reminders, event information and useful links.
North West London Foundation School
The North West London Foundation School (NWLFS) is run by Health Education NW London, incorporating Foundation Training Programmes within linked NHS Trusts. The Foundation Programme is a two-year generic training programme designed for medical school graduates. The programme forms the bridge between medical school and core training. It is designed to give Foundation Doctors a range of experience before choosing an area of medicine in which to specialise and delivers an integrated educational programme with defined outcomes.
The Foundation School co-ordinates the allocation processes to Foundation Year 1 and Foundation Year 2 and supports the delivery of Foundation Training and the development of Foundation Doctors.
NWLFS is committed to providing high-quality Foundation Training in all our linked Trusts and works within the General Medical Council Standards for Training for the Foundation Programme. Further information on all aspects of Foundation training can be found on The Foundation Programme website.
For more information about the NWL Foundation School please access the link to the London and KSS Foundation Website.
North Central and East London Foundation School
The North East Thames Foundation School (NETFS) has now merged with the North Central Thames Foundation School (NCTFS) to form the North Central and East London Foundation School (NCELFS) .
It is a foundation school of Health Education North Central and East London (HENCEL) linked to UCL Medical School(UCLMS)and Barts and The London School of Medicine and Dentistry (Barts).
For more information about the NCEL Foundation School please access the link to the London and KSS Foundation Website.
South Thames Foundation School
The South Thames Foundation School was established in 2007 following the merger of the former South East Thames and South West Thames Foundation Schools. It is a collaboration between HE Kent, Surrey and Sussex (HEKSS) and HE South London (HESL); GKT School of Medical Education, King's College, London (KCL), St George's University of London (SGUL) and Brighton and Sussex Medical School (BSMS). HEKSS has day-to-day administrative management and strategic overview of the School, covered by a service level agreement with HESL.
The school manages all F1 and F2 trainees in NHS trusts in the South London and KSS regions (approximately 1700) and is based in two offices in Stewart House and London Bridge. Professor Jan Welch is the Director of the South Thames Foundation School and is based at London Bridge.
Two Associate Directors, Dr Paul Reynolds for Brighton and Dr Mark Cottee for Tooting, provide local leadership. A team of managers and administrators support the director/associate directors.
For more about the ST Foundation School please access the link to the London and KSS Foundation Website.
Joint School and Programme Information
For more information about Joint School and Programme please access the London and KSS Foundation Website.


Appraise the Oppenheimer (2010) and Elliott et al. (1999) articles, summarizing the strengths and weaknesses of each study.
Analyze potential sources of bias in each study, and suggest strategies for minimizing bias.
Suggest possible confounding variables that may have influenced the results of each studyAccording to researchers, the strengths of the Framingham has always been their extensive, well characterized , longitudinal phenotype. This study is on its way to becoming the gold standard for genetic epidemiology of CVD.There study was of cohort design. The strength os this study is that it has been one of the longest running most comprehensive characterized multi-generational studies in the world. In addition, other strength of this study is developmental trends across the life span. Most studies of this type is observational in the sense that they observe the state of the participants without manipulation.
The weakness of the study is that a longitudinal study require an enormous amount of time. As time evolve, the research becomes more and more expensive to run and takes up a huge part of a researchers life.
The issue of bias in research is an important one and demands special attention. It is important to keep bias out of research. One issue relates to the subjective-objective debate in research. For example, "How do we they keep themselves out when researching a topic that has personal significance?" The way to minimize bias in this situation is try to remain as neutral as possible, It involves open end questions that don't steer the participants in a way which might appear to endorse a particular response . It involves modeling the interview after conversation between tow trusting parties or individuals. Nevertheless, it is important not to take or impose my interpretation on the comments out of context in order to make a point about bias in research.


The continued bombardment of violence and killings in Jamaica is very disheartening to a nation, that towards the latter part of last year, had begun to see a reasonable reduction in murders. The problem is that the perpetrators of these heartless activities have really been great statisticians, in their own rights.
These scum, which are few but have significant influence adversely on our Jamaican society, have really sat back and have been analysing the probability of their getting away with their daily atrocities. They seem to have had a mental and thorough calculation of how unlikely it is for them to be brought to justice.
They know that of the thousand crimes or more, they commit each year, a mere handful of them will ever be charged and even worse, a fewer number (a miniscule number) of them will be brought to justice. The latter is due to the fact, it certainly would appear, that some in authority or those having access to incriminating materials (read evidence), are being paid to remove evidence, files, etc, or the overwhelming numbers of witnesses are just too scared to come forward, or just can't do so with the risk of losing out on their regular remittances from these criminal thugs that they use to take care of themselves and children. This is a vicious cycle. One that must be cracked immediately, to change the way the criminals operate.
There needs to be radical changes in the way the powers-that-be conduct their affairs.
Attach the personal information such as work, criminal record, charges and dropped charges, to the licence plate(s) of each registered motor vehicle owner in Jamaica. Accordingly, a data base should be built that can be used by a selected group of officers to track and gather information readily and easily. Any vehicle seen operating without a licence plate, should be immediately deemed illegal and be confiscated for investigations.Simialrly, if a vehicle is checked and its licence plate does not match its registered vehicle, the vehicle should be apprehended and the operator(s) investigated.
All police personnel, from constable to commissioner, should, every six-month period, make a declaration of their personal assets and valuables which exists in or outside of Jamaica.
Jamaican politicians should be subject to the same rules.
The wages declared, through this six-monthly declaration, should be confirmed by an independent and legal body furnished to do so. New legislations may be necessary to effect this, but this should not frustrate this very needed requirement to curtail corruption.
If from (4) it is discovered or uncovered that a police personnel's/politician's assets/expenditure for a given period exhibits discrepancies in relations to official, legal earnings, this should be turned over to the relevant body to be further investigated.
Finally, there needs to be a new zeal and concerted effort to bring to justice those who are accomplice to criminals' wrongdoings. There should be no leniency, irrespective of the level of support, to prosecuting those who abett and aid criminals directly or indirectly in the proliferation of their crimes.
The Witness Protection Programme must not merely come on stream but must be sold effectively to the public so they can be assured that they will not die by the hands of criminals in coming forward to expose criminals and have them brought to justice.
I am somewhat more optimistic than the former Police Commissioner, Mr. Lucius Thomas, for the future, with respect to crime in Jamaica, in the year 2007. I believe that if the foregoing recommendations are adhered to, and Commisioner's office acts on the intelligence it has according to reports in the media, the upcoming elections will be relatively peaceful.


text:
package org.apache.hadoop.yarn.api.records;

import org.apache.hadoop.classification.InterfaceAudience.Public;
import org.apache.hadoop.classification.InterfaceStability.Unstable;
import org.apache.hadoop.yarn.api.protocolrecords.AllocateResponse;

/**
 * Command sent by the Resource Manager to the Application Master in the
 * AllocateResponse
 * @see AllocateResponse
 */
@Public
@Unstable
public enum AMCommand {
  /**
   * Sent by Resource Manager when it is out of sync with the AM and wants the
   * AM get back in sync.
   */
  AM_RESYNC,

  /**
   * Sent by Resource Manager when it wants the AM to shutdown. Eg. when the
   * node is going down for maintenance. The AM should save any state and
   * prepare to be restarted at a later time.
   */
  AM_SHUTDOWN
}


text:
Президентские выборы в Финляндии 2012 года ( ) — общегосударственные выборы Президента Финляндии на период 2012—2018 годов. Действующий президент республики Тарья Халонен пребывала в должности два срока подряд (с 2000 по 2012) и не могла баллотироваться в третий раз.

Первый тур выборов состоялся в воскресенье 22 января 2012 года. Во второй круг, который состоялся 5 февраля, вышли Саули Ниинистё (37 % голосов) и Пекка Хаависто (18,8 %).

Президентом Финляндии избран Саули Ниинистё (62,6 %).

Полномочия президента

Полномочия Президента были сокращены в ходе конституционной реформы 2000 года. В настоящее время президент руководит финской внешней политикой вместе с кабинетом министров. Дела Европейского Союза, однако, не относятся к власти президента, ими ведает премьер-министр. Власть Президента значительно сократилась: президент может распустить парламент, но только по запросу премьер-министра; президент может принять решение не ратифицировать законопроект, но это только возвращает его в парламент, который затем должен одобрить законопроект ещё раз, после чего он становится законом без подписи президента. Власть президента назначать должностных лиц также была сокращена, однако, президент всё ещё назначает всех офицеров, а также судей. Президент является Верховным главнокомандующим вооружённых сил Финляндии. Президент также имеет право на помилование лиц, осуждённых за преступления.

Предвыборная кампания
На предвыборную кампанию Саули Нийнистё коалиционная партия потратила более 0,5 млн евро.

Кандидаты
По закону кандидатом в президенты страны может быть только уроженец Финляндии. Его могут выдвигать либо политическая партия, получившая хотя бы одно место в парламенте на предыдущих выборах, либо группа избирателей числом не менее 20 000 человек.

Все политические партии, представленные в Парламенте Финляндии выдвинули на президентские выборы 2012 года своих кандидатов. В семи партиях кандидатуры были выдвинуты единогласно, а в Социал-демократической партии на выборах победил Пааво Липпонен с 67 % голосов избирателей.

Кандидатам присвоены номера от 2 до 9 которые будут указаны на избирательных бюллетенях.

По отзывам самих кандидатов, они не собираются сотрудничать и создавать коалиции во втором туре голосования.

После окончания выборов, в апреле 2012 года, все кандидаты представили декларации об источниках финансирования своих предвыборных кампаний. Самая дорогая кампания была у Саули Нийнистё, самая дешёвая — у Сари Эссайя.

Опросы общественного мнения
Абсолютным лидером опросов общественного мнения является кандидат в президенты Саули Нийнистё, однако при опросе 5 января 2012 года теле-радиокомпания YLE отмечает, что выросла доля неуверенных избирателей, не знающих, за кого голосовать. Почти каждый третий опрошенный затруднялся называть своего фаворита.

Голосование
Правом голоса на президентских выборах 2012 года обладают 4 402 622 граждан Финляндии (из них 230 422 человека проживают за границей).

10 января 2012 года был последним днём оформления регистрации для домашнего голосования на президентских выборах тех граждан, кто по физическим причинам не в состоянии явиться на избирательный участок.

Первый тур

Предварительное голосование
Предварительное голосование на 903 избирательных пунктах проходило в Финляндии со среды 11 января до 17 января. В первый день предварительного голосования на избирательные участки пришло 5,4 % избирателей (в 2006 — 6,2 %). 13 января (третий день голосования) на проголосовало 4,2 % избирателей, имеющих право голоса (всего за три дня участки посетило 15 % избирателей). На 16 января осуществили своё избирательное право около 25,1 % имеющих право голоса, а на момент закрытия предварительного голосования 17 января проголосовало 32,7 % избирателей (в 2006 — 30,7 %).

За границами Финляндии предварительное голосование для граждан страны проходило с 11 по 14 января. Оно было организовано в 90 странах мира (за рубежом проживают свыше 230 тысяч граждан Финляндии, обладающих правом голоса на президентских выборах) и его посетило рекордное количество избирателей — 47 524 человека (на 50 % больше по сравнению с выборами 2006 года).

Кроме того, в Санкт-Петербурге проголосовало около 300 граждан Финляндии.

Молодёжный альянс учащихся Финляндии провёл среди имеющих право голоса молодых жителей страны голосование, в котором приняло участие 76 417 подростков из 650 учебных заведений, среди которых 63,5 % молодых людей представляли старшую школу, 33 % — среднюю школу и 10 % учащихся — профессионально-технические училища. Их голоса распределились следующим образом:

Результаты первого тура
Первый тур президентских выборов состоялся 22 января 2012 года, в нём приняли участие 3 059 850 избирателей, что составило 72,7 % (в 2006 году — 73,9 %).

Второй тур

Предварительное голосование
Предварительное голосование второго тура проходит по всей Финляндии с 25 по 31 января. Даты предварительного голосования за рубежом — 25-28 января. На 25 января в Финляндии проголосовало 7,4 % избирателей (в 2006 году − 6,7 %). На 26 января проголосовало в общей сложности более 275 тысяч человек, что составило 14,2 % избирателей (в 2006 — 12, 2 %). 27 января проголосовало 20,1 % имеющих право голоса (в 2006 — 17,3 %).

Результаты второго тура
Второй тур президентских выборов состоялся 5 февраля 2012 года, в нём приняли участие 68, 8 % избирателей (в 2006 году — 77,2 %). Наблюдатели отмечали большое количество аннулированных бюллетеней в которых стоял либо прочерк или было пусто (в Оулу таких было аннулировано более 2 тысяч).

По результатам второго тура, президентом Финляндии избран Саули Нийнистё (62,6 %)

По данным социологического опроса, проведённого в марте 2012 года по заказу газеты «Helsingin Sanomat», гомосексуальность Пекка Хаависто стала второй по значимости причиной, по которой третья часть избирателей проголосовала за Саули Нийнистё.

Вступление в должность
Новый президент вступил в должность в первый день месяца, следующего за выборами — 1 марта 2012 года. В 12:00 началась инаугурация, открывшаяся торжественной речью перед парламентом. После этого (около 12:20) начались полномочия нового президента и закончились полномочия предыдущего.

Примечания

Ссылки

2012
22
2012
5
Финляндия
2012 год в Финляндии
2012

redpajama_set_name: RedPajamaWikipedia


Book — xviii, 661 p. : ill. ; 24 cm.
Part 1 Well-being - theory and realization: the commodity basis of well-being-- political morality and the state-- the object of social contracts-- well-being - from theory to measurement-- appendix - political and civil rights indices.
Part 2 Allocation of resources among households - the standard theory: resource allocation mechanisms-- public goods and common property resources-- decentralization and central guidance-- real national income as a measure of general well-being-- uncertainty, insurance and social norms.
Part 3 The household and its setting - extensions of the standard theory: land, labour, savings and credit-- households and credit constraints-- poverty and the environmental resource base-- net national product in a dynamic economy-- food, care and work - the household as an allocation mechanism-- axiomatic bargaining theory-- fertility and resources - the household as a reproductive unit-- strategic complementarities in fertility decisions-- population and savings - normative considerations-- classical utilitarianism in a limited world-- food needs and work capacity-- adaptation to nourishment-- inequality, malnutrition and the disenfranchised-- analysis of allocation mechanisms when nutrition affects productivity-- incentives and development policies. Subject index: agrarian reform-- food subsidies-- employment guarantee schemes and rural infrastructure-- community participation and credit facilities-- health and education-- envoi.
Destitution is the main subject matter of this study. It ranges through moral philosophy and political science to anthropology, welfare economics, economic theory and nutrition science. Dasgupta is concerned with reconciling empirical evidence with theoretical analysis, and with presenting a coherent description of the causes of undernourishment. This volume should be of interest to nutritionists and anthropologists in that it presents undernourishment, differences in calorie needs, and the phenomenon of adaptation to low energy intake - genetic, physiological and behavioural. It also addresses the current debate over methods for estimating the incidence of undernourishment, and is written in a style suitable for readers who are not economists, leaving the formal material to be presented in an appendix. This book is placed in the context of philosophical work on general well-being, and with the aim of stimulating research on policies to remedy the state of destitution. Dasgupta uses, for example, modern analytical political philosophy to define the role of the state in the context of resource-poor economies, and concludes from his empirical evaluation of 40 of the world's poorest countries that there is a striking correlation between a country enjoying greater political and civil liberties and performing better in terms of per capita income, life expectancy and the other measurement standards he outlines. He advocates the existence and recognition of both positive and negative rights, and avoids the tendency of development economics works to concentrate on mortality or growth and ingore the role of these rights.


I've found the perfect autumnal getaway and it's located in the Wye Valley in Wales – Llangoed Hall Hotel. Forget the car, you don't need the hassle of driving. Instead, I'd recommend getting a train with Great Western Railway in First Class travel. Clean, comfy and quiet. Ample legroom, scenic views and complimentary refreshments takes the stress out of a cramped, long drive. Get off at Cardiff and from there a coach will take you the rest of the way.
Llangoed (meaning Holy Meeting Place) looks resplendent upon arrival, the exterior bearing an autumnal feel with its climbing ivy and bucolic surroundings. As wondrous as the exterior and interiors are, one of the biggest draws is the restaurant; recognised as one of the top 100 in Britain by the Sunday Times and number one in Wales. This is thanks to award-winning head chef, Nick Brodie who appeared on the Great British Menu show this year. Most ingredients are either sourced on-site or within close proximity, making it a very British menu. From the rich grouse main to the delicious cheeseboard afterwards, and the eggs, jams and honey you'll find in the morning at breakfast. Take a walk around the little farm round the side of the building to see for yourself.
Indeed, it's all about the walks here. There are several for you to embark on, allowing you to explore the surrounding woodland and reach heights for picture-perfect panoramic views of the Wye Valley.
During your stay, visit Hay-on-Wye – the book capital of the UK, which celebrated its 30th literature and arts festival this year. The quaint town is home to friendly locals and 20+ bookshops; it was once home to more than 50, but everyone's either sadly downloading or shopping online these days for their reading material.
Back at Llangoed, they have their own library of classic literature for you to explore as well as magnificent artwork adorning the walls. Then, at the end of your day, when you drift off to sleep, tell me afterwards if it's not the best bed you've slept on this year. It certainly has been for me.


Commitment: If we have no the size in stock, it takes about 20 days for us to produce the Drainage straight seam welded pipe GB for you if the quantity can be more than 10 tons.
Straight seam steel pipe definition: Refers to the longitudinal and parallel steel pipe of the weld. It is also commonly referred to as a straight seam welded pipe or a straight seam steel pipe. The straight seam steel pipe is made by winding a long strip of certain specifications through a high frequency welding unit and welded by a straight seam.
The production technology of straight seam welded pipe is simple, with high production efficiency, low cost, rapid development. The strength of the spiral welded pipe is generally higher than that of seam welded pipe. It can use a narrow billet to produce the larger diameter welded pipe.
As well as from astm, gb, and din. And whether pipe straight is api, ce, or ul. There are 37,388 pipe straight suppliers, mainly located in Asia. The top supplying country is China (Mainland), which supply 100% of pipe straight respectively. Pipe straight products are most popular in North America, Domestic Market, and Southeast Asia.
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GB/T14291-2006(Welding pipe for mineral fluids). Mainly used to press the wind in the mine, drainage, also include the straight seam welded pipe for release the gas. The representative material is Q235A、B class. GB/T12770-2002(Mechanical structure welded stainless steel pipe).
GB/T14291-1992 (mineral fluid transport welded steel pipe). Mainly used in mine air pressure, drainage, gas drainage shaft with a straight seam welded steel pipe. Its representative material B, Q235A grade steel. GB/T14980-1994 (large diameter welded steel pipe for low pressure fluid delivery).
Straight-seam Welded Steel Pipe, ERW/HFW ( Outer Diameter 21 - 660mm, Wall Thick 2-18mm ) Seamless Steel Pipe ( Outer Diameter 21-1219 mm, Wall Thick 2-100mm ) 1.
GB/T14291-1992 (welded steel pipe for mine fluid conveying). Straight seam welded steel pipe is mainly used for mine forced draught, drainage, wind shaft gas. It is represented by material level Q235A, B grade steel. GB/T14980-1994 (large diameter welded steel pipe for low pressure fluid conveying).
GB / T14291-1992 (Mining fluid transport welding steel pipe). Mainly used for mining pressure air, drainage, gas discharge shaft with straight seam welded steel pipe. Its representative material Q235A, B grade steel. GB / T14980-1994 (Large Diameter Electric Welded Steel Pipe for Low Pressure Fluid Transportation).
Welded steel tubes are divided into straight seam welded pipe and spiral welded pipe.Steel Pipe. Welded steel pipe used in the billet is steel plate or strip, because of its different welding process and divided into furnace welded pipe, welding (resistance welding) pipe and automatic arc welded pipe.
Welded steel pipe used in the blank is steel or strip, because of its different welding process is divided into furnace welded pipe, welding (resistance welding) pipe and automatic arc welding pipe. Because of the different forms of welding into straight seam welded pipe and spiral welded pipe two.
Looking for straight seam pipe factory direct sale? You can buy factory price straight seam pipe from a great list of reliable China straight seam pipe manufacturers, suppliers, traders or plants verified by a third-party inspector. Source with confidence.
Cangzhou Hongyun Steel Pipe Co.,Ltd, Experts in Manufacturing and Exporting seamless steel pipe, welded steel pipe and 8 more Products. A Supplier on Alibaba.
Construction Welded Pipe petroleum,US $ 3,000 - 5,000 / Ton, GB, GB/T 12770-2002, GB/T 12771-2000, GB/T 14291-2006, GB/T 3091-2001, 10Cr9Mo1VNb, Cr-Mo alloy.Source from Shanghai (AXD) Electric Heavy Machinery Co., Ltd. on Alibaba.
Katalor is the professional Chinese Drainage straight seam welded pipe GB supplier .If you need Drainage straight seam welded pipe GB , we can put the Drainage straight seam welded pipe GB order to our steel mill directly or collect these goods from our stock directly if we have enough ex-stock .Besides. if you need any offer or if you want to know the price and any other information about Drainage straight seam welded pipe GB price, please be free to contact us.


Move comes as UN nuclear watchdog says Tehran to further enrich uranium "within days".
Its profits "are available to support the full range of the IRGC's illicit activities, including WMD proliferation and support for terrorism", the department said.
Khatam al-Anbiya was first hit with US sanctions by the administration of George Bush, the former president, in 2007.
Wednesday's penalties apply to Qasemi and Khatam al-Anbiya subsidiaries, the Fater Engineering Institute, the Imensazen Consultant Engineers Institute, the Makin Institute and the Rahab Institute.
Stuart Levey, the US treasury undersecretary for terrorism and financial intelligence, said: "Today's action exposing Khatam al-Anbiya subsidiaries will help firms worldwide avoid business that ultimately benefits the IRGC and its dangerous activities."
The announcement comes as Washington tries to rally international support against Tehran's nuclear programme, seeking fresh sanctionsby the UN Security Council, which has already hit Iran with three sets of sanctions.
Speaking at a White House press briefing on Tuesday, Barack Obama, the US president, said the international community was pursuing "a significant regime of sanctions" against what Washington called Iran's intransigence.
Obama's comments came after Tehran said on Tuesday that it had begun the process of enriching uranium at higher levels, fuelling fears that the process could eventually be used to produce nuclear weapons.
It had been reported in Iranian state media that the process of refining uranium to 20 per cent purity had begun earlier in the week, but Tehran told nuclear inspectors on Wednesday that it had only been making preparations for the higher enrichment.
"We were told that it was expected the facility would begin to produce up to 20 per cent [uranium] within a few days," an internal memo by the UN nuclear watchdog, the International Atomic Energy Agency (IAEA), said.
The IAEA memo indicated that, for now at least, the Iranian operation was modest in scale.
The memo from Yukiya Amano, the IAEA chief, said Iran had recalibrated 164 centrifuges, out of its 8,000 enrichment machines, for higher-scale enrichment at its Natanz plant.
He said Iran notified the IAEA of the plan on Monday and the IAEA quickly asked Iran not to launch it before inspectors could adjust their monitoring procedures, as well as get clarification on the expected duration of the new programme and technical details.
"On Wednesday, when agency inspectors arrived at the pilot plant, they were informed that Iran had begun to feed the low-enriched uranium into one cascade the previous evening for [test] purposes," the memo said.
A cascade is 164 centrifuges hooked up in series that spin and respin uranium gas to the required enrichment level.
The document, relying on onsite reports from IAEA inspectors, also cited Iranian experts at the enrichment site at Natanz as saying that only about 10kg of low enriched uranium out of 1.8 tonnes, had been fed into the cascade for further enrichment.
A nuclear bomb requires uranium of about 90 per cent purity, but nuclear experts say getting to 20 per cent is a big step because low-level enrichment is the most time-consuming and difficult stage of the process.


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Tags: alberta, canada, canmore, hbo, the last of us
CAPITAL FALLING
CAPITAL FALLING As Black Smoke Rises, Order Di...


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By thomasbleach Posted on April 2, 2018 December 28, 2018
ALBUM REVIEW: Kacey Musgraves – Golden Hour
Kacey Musgraves is a force to be reckoned with. Not only is she one of Country music's most talked about singer-songwriters she is also creating quite the buzz in the pop world. She has opened for the likes of Katy Perry, Harry Styles, Lady Antebellum and Little Big Town as well as unsurprisingly sold out her own headlining tours. She's covered all the genre bases and is continuing to grow her arena ready country-pop with a polished fourth studio album. "Golden Hour" is her boldest, strongest and most cohesive record yet. She has truly found her sound and mixed together raw emotion with vulnerability, euphoric hooks and a polished pop production that hears her remaining truthful to her country roots. Album opener "Slow Burn" is a intimate and honest moment that hears her delivering an autobiographical track that reflects on the path she has paved so far in life. The acoustic country production is very simple but perfectly allows the storyline to take lead and welcomes this more emotional approach. "Lonely Weekend" introduces a pop inspired hook that will have you instantly singing along to this heartbreak and confusion track before having her mend your heart on the reflective "Oh, What A World". But it's the romantic "Butterflies" which had me gushing and feeling all giddy. "I didn't know him and I didn't know me. Cloud Nine was always out of reach. Now I remember what it feels like to fly. You give me butterflies". This is one of the songs that are about when she first met her now husband and fell in love after giving up on herself. It's also one of the more traditional country-pop tracks. Following in its footsteps is the sweet "Love Is A Wild Thing" and the empowering "Wonder Woman" but it's her ballads that win a special part of my heart on this record. The traditional ballads "Mother" and "Rainbow" will have you feeling all emotional while "Happy & Sad" gives you a country-pop spin that will have your heart feeling heavy. "Is there a word for the way that I'm feeling tonight? Happy and sad at the same time. You got me smiling with tears in my eyes". The reflective track is heartbreaking and sweet and will have you instantly relating to all those tough feelings. It wouldn't be a country record without some gimmicky tracks and "Velvet Elvis" and "Space Cowboy" deliver those but its "High Horse" that has received the most hype. This disco meets country track is absolutely flawless. It's so shiny and great and will have you dancing and singing along to it's catchy hook. It's the perfect step over the line into the pop world that will open a lot of more doors for her as it's a bonafide bop. The whole record is an impressive collection of raw emotion and polished production where she doesn't sacrifice the country sound she's established but instead hears her growing and evolving as an artist. And she also may have just claimed the best country album of the year title…
You can purchase Kacey Musgraves new album "Golden Hour" from Sanity now; https://www.sanity.com.au/products/2367544/Golden_Hour
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Starting a Group- Wording Ideas for Name?
I won't give too many specific details, but I'm looking to start a Non-Profit in my community to service the mentally ill (of which I am one). The premise is that those who live with mental illness deserve to speak for themselves, so the group would establish grassroots connections, build platforms for people to speak on their own behalf, and organize action among people in the area.
I don't want some stock name like "Council of x" or "The x Group". I want something that seems a bit more, I don't know, progressive? It's all about getting people together to be their own voice, because in policy-making the mentally ill have very little influence. Does anyone have lists or databases or just pitches for different wording that can be used for names?


Roland invites you to attend any or all of the Roland Continuing Education Clinics that are being held in conjunction with LMT's LAB DAY at the Chicago Hyatt on Friday, Feb. 26th and Saturday, Feb. 27th.
Clinics are open to all LMT LAB DAY attendees at no charge and present an opportunity to gain scientific credits.
RSVP is required to save a seat.
Experts from Roland will dissect todays dental laboratory and the day to day needs they have when it comes to CNC machine choices. Learn about Roland's scalable solutions and what important factors should be taken in to consideration when starting or growing your laboratory business.
A light breakfast will be served during this clinic.
Looking Past the ROI, and realizing the hidden benefits of owning and controlling your own manufacturing process with CAD/CAM.
By Dr. Richard Rodriguez C.
Dr. Richard A. Rodriguez C. will cover the use of biomaterials in the treatment of patients with needs of partial or complete restorations. To illustrate each case, he will share CT scans, intraoral scan, restoration CAD design and milled TRINIA bars and Bicon implant systems. Participants will learn about implant strategy utilizing fixed Full Arch Metal-Free TRINIA™ Prosthesis on Bicon SHORT® Implants.
Incorporating CAD/CAM into your lab is a critical step in increasing productivity, and learning how to get the most out of your milled materials is critical. In order to get the highest level of productivity out of your investment, you need to know what materials are optimized for your milling system and when to offer them to your customers. In this interactive lecture you will see how to easily produce the most popular designs being requested in today's dental market. New material options such as VITA Enamic®, which has material properties strikingly similar to natural teeth, as well as other esthetic choices, will be explored. In addition, post milling processing and characterization to fabricate ideal results will be discussed.
Recent advances in dental technology have introduced new restoration fabrication procedures with their use steadily increasing in clinical practice. Advances in computer-aided design/computer-aided manufacturing (CAD/CAM) technology have led to the production of more accurately fitting milled restorations, and more widespread use of a digital workflow for prosthesis fabrication.
The outline of this lecture will include an introduction to the CAD/CAM technology, the different digital workflows in Fixed Prosthodontics and the description of the two major CAM techniques. The use of digital technology in Implant dentistry and the pros/cons of the digital technology will be presented as well. The clinical and laboratory steps of several cases will be presented. The utilization of digital intraoral impressions, lab scanners and different milling machines (including wet mill for glass ceramics and dry milling machine for zirconia) in a University environment will be described. The challenges for the clinicians and the importance of good communication with the lab technician will be discussed as well.
The future of dental technology is firmly rooted in mechanization and automation and there is a major move toward a convergence of interrelated technologies, i.e., the merging of 3D scanned data with 3D radiographs and extraoral facial scans, allowing dentists to create virtual patients with all the metrics required for diagnosis, treatment planning and technology-aided treatment. This lecture will investigate this convergence and show some practical examples of current applications using CAD/CAM technology available today.
Understand Convergence of Imaging Technologies and how it relates to the laboratory technician/ dentist relationship.
Observe Computer Aided Manufacture examples and various types of materials and how they relate.
In the recent digital revolution that has overtaken the Dental Industry, we've seen dozens of different CAD systems emerge that are specifically designed for the design of dental restorations. It's important for lab technicians to recognize the differences in these systems and how these CAD systems can impact the outcome of a local or outsourced manufactured restoration. In this clinic, we will talk about how the CAD can have a huge impact on our ability to properly process files in the CAM software - leading up to a properly manufactured restoration. While we can generally find a work around or manually tweak our manufacturing processes to "override" these shortcomings - it is best to examine both side of the fabrication process to ensure that we are designing and outputting files that are conducive for the manufacturing method we are using. We will also be discussing Open vs Closed CAD systems by examining real-world output samples from these different systems to determine and pinpoint differences between natively open systems and closed systems that offer the option to "open" the output.
Understand how we can properly design restorations for Milling use CAM software.
Understanding commonly misunderstood design parameters and how these impact the CAM.
Tom Hagen has over 20 years experience in the dental industry, with over 12 years CAD/CAM expertise. He is the former owner of Colonial Dental Studio, where we produced over 250 CAD/CAM units per day. Extensive business development experience. Current managing partner and owner of Custom Automated Prosthetics.
Dr. Richard A. Rodriguez C.
Dr. Richard A. Rodriguez C. has been a practicing dental professional for 17 years at a dental practice in Caracas, Venezuela. He is a graduate of Universidad Central de Venezuela and Implant Dentistry Center in Boston, MA. He has lectures on implant placement and restorations and serve as a Clinical Instructor for Bicon Dental Implants.
Dr. Chochlidakis received his D.D.S. from the University of Athens in 2008. In 2010, he joined Eastman Institute for Oral Health Prosthodontics Program. After earning his specialty in Prosthodontics in 2013, he was an Assistant Professor and Co-Director of Clinical Fixed Prosthodontics at Temple University for two years. Earlier this year, Dr. Chochlidakis returned back as a full-time Assistant Professor and Clinic Director in the Prosthodontics Department at University of Rochester.
Jim McGuire has been in the dental field for over 30 years. In 1984, Jim received his Associates of Science Degree in Dental Technology from the Dental Technology Institute in Orange, California and in 1994 became a Certified Dental Technician. Since 2004, Jim has been the Director of Education and Technical Support for VITA North America. Jim has published dental lab implant articles, has frequently lectured, and conducted many hands-on clinical, laboratory implant prosthetic and CAD/CAM courses.
Terence Whitty is one of the most experienced and unique technical instructors and lectures nationally and internationally on a wide variety of dental technology and material science subjects. Terence's specialties include fixed and removable prosthetics, orthodontics, TMD and implantology. He is the owner of Fabdent, a busy Digital Dental Laboratory in Sydney Australia that uses advanced intra and extraoral scanning, Advanced CAD design and data manipulation, Milling, Grinding and 3D printing technologies. Terry has over 60 articles published and these regularly appear in international journals translated into various languages.
President of CIMsystem USA for 2 years – over 6 years of Dental CAD/CAM Support, Training and R&D experience across multiple platforms.
3 lucky winners will each win a GoPro HERO4 Silver!
Must be present to win. Drawing between 7 and 7:15 at the cocktail reception.
As another great year gets underway for Roland and the dental lab community, we'd like to express our appreciation for a growing number of Roland users by hosting a cocktail reception that immediately follows the first day of the show.
Held in the private dining area of the cool and modern, American Craft Restaurant at the Hyatt, the event promises to be an exciting and lively evening with beer, wine, appetizers, and gifts.
This is a closed event and you must be a dealer, partner, or registered Roland user to attend.