text:
\section{Introduction}
Contraction of Lie algebras first appeared in the work of Segal \cite{Segal51} and  {I}n\"{o}n\"{u} and Wigner \cite{Inonu-Wigner53}. Over the years, many applications to mathematical physics where found e.g., see \cite{Saletan61,PhysRevA.6.2211,MR1275599,MR720801,BI,MR3687831} and references therein. Several years ago, the authors, together with  their collaborators, introduced the notion of \textit{strong contraction} for representations of Lie algebras \cite{Subag12}. This involves a new setup for contraction  of representations which utilize  representations that are realized on certain  spaces of functions.  Many contractions, and most notably {I}n\"{o}n\"{u}-Wigner contractions, are being preformed with respect to a subgroup (or sub-Lie-algebra). Here, we shall focus on  the  contraction of   $\mathfrak{gl}_n(\mathbb{R})$ with respect to the Lie algebra $\mathfrak{m}_n$ consisting of all   $n\times n$ real matrices having their last row  equal to zero.
This is the Lie algebra of the mirabolic  group $M_n$, consisting of all invertible $n\times n$ matrices having their last row given by   $(0,0,...,0,1)$.
The Lie algebra  obtained via this contraction is the semidirect product  $\mathbb{R}^{n}\rtimes \mathfrak{m}_n$. It is the Lie algebra of  $\mathbb{R}^{n}\rtimes {M}_n$. The mirabolic group $M_n$  has the following remarkable property: any  unitary irreducible representation of $GL_n(\mathbb{R})$ restricted to $M_n$  remains irreducible. This is known as the \textit{Kirillov conjecture}, proven in the $\mathfrak{p}$-adic case in \cite{MR748505} and for real groups in \cite{MR1999922}. An important feature of the irreducible representations of $GL_n(\mathbb{R})$ is the existence of their Kirillov model which is  a   realization on a certain space  of functions on $GL_{n-1}(\mathbb{R})$ \cite{MR0139691}. The Kirillov model  arises in various contexts in automorphic representation theory  and representation theory of finite groups of Lie type, e.g., see\cite{MR2154720,MR1063847}. Recently, an explicit formulas for the space of $K$-finite vector in the  Kirillov model of $GL_2(\mathbb{R})$ was found \cite{MR3055523}. This  was used  in \cite{Subag12} to obtain the skew-Hermitian irreducible  representations of the Poincar\'e Lie algebra $\mathfrak{iso}(1,1)$ as  strong contractions of representations of $\mathfrak{sl}_2(\mathbb{R})$.

The first purpose of this paper is  to demonstrate how the Kirillov conjecture  and the Kirillov   model are useful for strong contractions in the context of  contraction of $\mathfrak{gl}_n(\mathbb{R})$ with respect to $\mathfrak{m}_n$.  In particular we shall use the Kirillov conjecture to prove the following result.\\

\noindent \textbf{Theorem 1.}
\textit{Let  $\pi:GL_n(\mathbb{R})\longrightarrow \mathcal{U}(\mathcal{H})$ be a unitary irreducible representation, realized on a Hilbert space of functions $\mathcal{H}$. Let $\pi_0:\mathbb{R}^{n}\rtimes {M}_n\longrightarrow \mathcal{U}(\mathcal{H})$  be the unitary irreducible representation given by the restriction of $\pi$ to $M_n$ extended  trivially to  $\mathbb{R}^{n}\rtimes {M}_n$. Let $d\pi$ and $d\pi_0$,  be the representations of  Lie algebras  associated with  $\pi$  and $\pi_0$ (respectively) on the space of smooth vectors of $\mathcal{H}$.
Then the constant family of representations  $\{d\pi_{\epsilon}=d\pi \}_{\epsilon\in \mathbb{R}^*}$
  strongly contract to  $d\pi_{0}$.
}\\

 The second purpose  is to obtain the full unitary dual of   $\mathbb{R}^{2}\rtimes M_2$ as a strong contraction. More precisely we prove the following result.\\

\noindent \textbf{Theorem 2.}
\textit{For any unitary irreducible representation $\pi_0$  of $\mathbb{R}^{2}\rtimes M_2$ the following hold.
\begin{enumerate}
\item There is  a realization of $\pi_0$ on  a Hilbert space of functions  $\mathcal{H}$.
\item There is a dense $(\mathbb{R}^{2}\rtimes \mathfrak{m}_2)$-invariant subspace $\mathcal{H}^{\infty}$ of $\mathcal{H}$.
\item There is a family  of representations $\{d\pi_{\epsilon}:\mathfrak{g}_2\longrightarrow \operatorname{End}(\mathcal{H}^{\infty}) \}_{\epsilon\in \mathbb{R}\neq 0}$,   or a sequence of representations $\{d\pi_{\epsilon_n}:\mathfrak{gl}_2(\mathbb{R})\longrightarrow \operatorname{End}(\mathcal{H}^{\infty}) \}_{n\in \mathbb{N}}$
that  strongly contracts to  $d\pi_{0}:\mathbb{R}^{2}\rtimes \mathfrak{m}_2\longrightarrow \operatorname{End}(\mathcal{H}^{\infty})$.
\end{enumerate}}

\section{Contractions}
In this section we  introduce  notations and review some generalities on {I}n\"{o}n\"{u}-Wigner contraction \cite{Inonu-Wigner53}. We  spell out an {I}n\"{o}n\"{u}-Wigner contraction \cite{Inonu-Wigner53} of $\mathfrak{gl}_n(\mathbb{R})$ with respect to the Lie algebra of the mirabolic group $M_n$. Then we recall the notion  of  strong contraction of  representations of Lie algebras.
\subsection{Contraction of Lie algebras}\label{sec}
Given a real Lie algebra $\mathfrak{g}=(V,[\_,\_])$ (with $V$ the underlying vector space ,and $[\_,\_]$ the Lie brackets of $\mathfrak{g}$) and a decomposition  $V=\mathfrak{k}\oplus \mathfrak{s}$ with $\mathfrak{k}$  being a subalgebra and $\mathfrak{p}$ a vector space complement to $\mathfrak{k}$, there is a corresponding   {I}n\"{o}n\"{u}-Wigner contraction; For every nonzero $\epsilon \in \mathbb{R}$ we have a linear invertible map $t_{\epsilon}:V\longrightarrow V$ given by $t_{\epsilon}(X_{\mathfrak{k}}+X_{\mathfrak{s}})=X_{\mathfrak{k}}+\epsilon X_{\mathfrak{s}}$,  for  $X_{\mathfrak{k}}\in \mathfrak{k}$ and  $X_{\mathfrak{s}}\in \mathfrak{s}$. For  $X,Y\in V$, the formula  $[X,Y]_{\epsilon}:=t_{\epsilon}^{-1}[t_{\epsilon}(X),t_{\epsilon}(Y)]$ defines  Lie brackets on $V$. We denote the  corresponding Lie algebra by  $\mathfrak{g}_{\epsilon}=(V,[\_,\_]_{\epsilon})$.
Moreover, for every $X,Y\in V$,
\[ [X,Y]_{0}:=\lim_{\epsilon \longrightarrow 0}t_{\epsilon}^{-1}[t_{\epsilon}(X),t_{\epsilon}(Y)] \]
converges and defines Lie brackets on $V$. The obtained Lie algebra $\mathfrak{g}_{0}=(V,[\_,\_]_{0})$ is called the contraction of $\mathfrak{g}=\mathfrak{g}_{1}$. The Lie algebra $\mathfrak{g}_0$ is a semidirect product of $\mathfrak{k}$ and the  abelian ideal $\mathfrak{s}$.   This contraction is  denoted by $\mathfrak{g} \stackrel{t_{\epsilon}}{\rightarrow}\mathfrak{g}_0$.

\subsection{The case of $\mathfrak{m}_n\subset \mathfrak{gl}_n(\mathbb{R})$ }
Consider the Lie algebra of $n\times n$ real matrices, $\mathfrak{gl}_n(\mathbb{R})$. We denote its underlying vector space by $V_n$, and we shall use the standard basis $\{e_{i,j} | 1 \leq i,j \leq n\}$ of $V_n$ to define a subalgebra  and a vector space complement. As the subalgebra $\mathfrak{k}$  we take $\mathfrak{m}_n=\operatorname{span}_{\mathbb{R}}\{e_{i,j}| 1\leq i\leq n-1, 1\leq j \leq n \}$ and choose the complement $
\mathfrak{s}_n:=\operatorname{span}_{\mathbb{R}}\{e_{nj}| 1\leq j \leq n \}$.
For $\epsilon \neq 0$, the corresponding contraction maps $t_{\epsilon}:V_n\longrightarrow V_n$ are given by
\begin{eqnarray}\nonumber
&& t_{\epsilon}(e_{ij})=\begin{cases}
e_{ij} & , i\neq n\\
\epsilon e_{ij}  &, i=n.
  \end{cases}
\end{eqnarray}
For every $\epsilon \in \mathbb{R}$, the Lie brackets $[\_,\_]_{\epsilon}$ on $V_n$ are  explicitly given by
\begin{eqnarray}\nonumbe
&&[e_{ij},e_{kl}]_{\epsilon}=\begin{cases}
[e_{ij},e_{kl}]=\delta_{jk}e_{il}-\delta_{li}e_{kj} &, i\neq n, j\neq n \\
[e_{ij},e_{kl}]=\delta_{jk}e_{il}-\epsilon \delta_{li}e_{kj} &, i=n, j\neq n\\
[e_{ij},e_{kl}]=\epsilon\delta_{jk}e_{il}- \delta_{li}e_{kj} &, i\neq n, j= n\\
\epsilon[e_{ij},e_{kl}]=\epsilon(\delta_{jk}e_{il}-\delta_{li}e_{kj}) &, i=k=n.
\end{cases}
\end{eqnarray}
The group $\mathbb{R}^{n}\rtimes M_n$ with product given by
\[(v,A)(u,B)=(v+(A^{-1})^Tu,AB) \]
for $(v,A),(u,B) \in \mathbb{R}^{n}\times M_n$,  is a Lie group containing $M_n$ as a subgroup and having $(\mathfrak{gl}_n(\mathbb{R}))_0$ as its Lie algebra.

\subsection{Strong contractions}
Below we recall the definition of \textit{strong contraction} in the special case of a common underlying inner product space of functions, for all representations that take part in the contraction procedure. This will be enough for the purposes of this paper. For the general definition see \cite{MR3687831}.

Keeping the previous notation, suppose that $t_{\epsilon}:V\longrightarrow V$ is a family  of linear invertible  maps  that realizes a contraction from $\mathfrak{g}=\mathfrak{g}_{1}=(V,[\_\_,\_\_]_1)$ to  $\mathfrak{g}_{0}=(V,[\_\_,\_\_]_0)$. Let $X$ be a topological space, and $\mu$ a posItive Borel measure on $X$.  Let $W$ be a subspace  of $L^2(X,d\mu)$.  Let  $\pi_{0}:\mathfrak{g}_0\longrightarrow \operatorname{End}(W)$ be a representation of  $\mathfrak{g}_0$ and   for every $\epsilon \neq 0 $,  $\pi_{\epsilon}:\mathfrak{g}\longrightarrow \operatorname{End}(W)$ a representation  of $\mathfrak{g}$.
The representation $\pi_0$ is a \textit{strong contraction} of the family $\{\pi_{\epsilon} \}_{\epsilon \neq 0}$ if the following hold.
\begin{enumerate}
\item For every $f\in W$, every $Y \in V$  and every $x\in X$,
\[\lim_{\epsilon\rightarrow 0}\left( \pi_{\epsilon}(t_{\epsilon}Y)f\right) (x)=\left( \pi_{0}(Y)f\right) (x).\]
\item  For every $f\in W$ and every $Y \in V$,
\[\lim_{\epsilon\rightarrow 0}\|\left( \pi_{\epsilon}(t_{\epsilon}Y)f\right)- \left( \pi_{0}(Y)f\right) \|=0.\]
\end{enumerate}
Similarly, a  sequence of representations  $\pi_{n}:\mathfrak{g}\longrightarrow \operatorname{End}(W)$ strongly contract to  $\pi_{0}:\mathfrak{g}_0\longrightarrow \operatorname{End}(W)$ if theres is a sequence of real numbers $\epsilon_n$ converging to zero such that
\begin{enumerate}
\item For every $f\in W$, every $Y \in V$  and every $x\in X$,
\[\lim_{n \rightarrow \infty}\left( \pi_{n}(t_{\epsilon_n}Y)f\right) (x)=\left( \pi_{0}(Y)f\right) (x).\]
\item  For every $f\in W$ and every $Y \in V$,
\[\lim_{n\rightarrow \infty}\|\left( \pi_{n}(t_{\epsilon_n}Y)f\right)- \left( \pi_{0}(Y)f\right) \|=0.\]
\end{enumerate}

\section{Strong contraction of constant families of unitary irreducible representations of $GL_n(\mathbb{R})$ }
This section deals with strong contractions of constant families of unitary irreducible representations of $GL_n(\mathbb{R})$. We shall start our discussion proving a simple lemma which is applicable in  more general context.

Let  $\mathfrak{g} \stackrel{t_{\epsilon}}{\rightarrow}\mathfrak{g}_0$ be a contraction of Lie algebras  with respect to a decomposition  $V=\mathfrak{k}\oplus \mathfrak{s}$ as above (recall that $V$ is the underlying vector space of $\mathfrak{g}$). Let $G$ and $G_0$ be Lie groups with Lie algebras $\mathfrak{g}$ and $\mathfrak{g}_0$ respectively, and $K$ a common subgroup of $G$ and $G_0$ with Lie algebra $\mathfrak{k}$. Further assume that $G_0=K\ltimes S$ with $S$ an abelian vector group having  $\mathfrak{s}$ as its Lie algebra.
With any  unitary  representation $\pi$ of $G$ on a Hilbert space $\mathcal{H}$ we can associate a unitary representation $\pi|_{K}$ of $K$ on  $\mathcal{H}$, simply by restriction.   With $\pi|_{K}$ we associate a unique  unitary  representation $\pi_0$ of  $G_0$ on $\mathcal{H}$ such that    $\pi_0|_{K}=\pi|_{K}$ and $\pi_0(s)$ is the identity operator for any $s\in S$.    In this section  we let $\mathcal{H}^{\infty}$ be the space of  $G$-smooth vectors in $\mathcal{H}$. It is known to be dense (e.g., see \cite[Thm. 3.15]{Knapp}) and via differentiation it carries representations $d\pi$ and $d\pi_0$ of  $\mathfrak{g}$ and  $\mathfrak{g}_0$, respectively.

\begin{lemma}\label{lem1}
Let  $\pi:G\longrightarrow \mathcal{U}(\mathcal{H})$ be a unitary irreducible representation, realized on a Hilbert space of functions $\mathcal{H}$.
Then  the constant family of representations  $\{d\pi_{\epsilon}:\mathfrak{g}\longrightarrow \operatorname{End}(\mathcal{H}^{\infty}) \}_{\epsilon\in \mathbb{R}\neq 0}$
with $d\pi_{\epsilon}=d\pi$,  strongly contracts to  $d\pi_{0}:\mathfrak{g}_0\longrightarrow \operatorname{End}(\mathcal{H}^{\infty})$.
\end{lemma}
The proof  is elementary and is  included just for completeness.
\begin{proof}
We can assume that $\mathcal{H}$ is a subspace of $L^2(X)$ for some measurable space $X$ with a positive Borel measure $\mu$. For every $Y\in \mathfrak{k}$, every  function $f\in \mathcal{H}$  and every $x\in X$, we have
\begin{eqnarray}\nonumber
&&\lim_{\epsilon\rightarrow 0}\left( d\pi_{\epsilon}(t_{\epsilon}Y)f\right) (x)=\left( d\pi(Y)f\right) (x)=\left( d\pi_0(Y)f\right) (x),\\ \nonumber
&&\lim_{\epsilon\rightarrow 0}\|\left( d\pi_{\epsilon}(t_{\epsilon}Y)f\right)- \left( d\pi_{0}(Y)f\right) \|=0.
\end{eqnarray}
For every $Y\in \mathfrak{s}$, every  function $f\in \mathcal{H}$  and every $x\in X$, we have
\begin{eqnarray}\nonumber
&&\lim_{\epsilon\rightarrow 0}\left( d\pi_{\epsilon}(t_{\epsilon}Y)f\right) (x)=\lim_{\epsilon\rightarrow 0}\epsilon\left( d\pi(Y)f\right) (x)=0=\left( d\pi_0(Y)f\right) (x),\\ \nonumber
&&\lim_{\epsilon\rightarrow 0}\|\left( d\pi_{\epsilon}(t_{\epsilon}Y)f\right)- \left( d\pi_{0}(Y)f\right) \|=\lim_{\epsilon\rightarrow 0}\|\left( \epsilon d\pi(Y)f\right)-0 \|=\lim_{\epsilon\rightarrow 0}|\epsilon| \|\left(  d\pi(Y)f\right) \|=0.
\end{eqnarray}
\end{proof}

We keep the above notation and let $G=GL_n(R)$, $K=M_n$ and  $S=\mathbb{R}^n$. Then the Kirillov conjecture implies that $\pi|_{M_n}$ (and hence also  $\pi_0$) is unitary irreducible for any unitary irreducible $\pi$. In general, that is for other groups,  $\pi_0$ is typically reducible.  Lemma \ref{lem1} implies the following result for the above mentioned contraction with respect to the mirabolic subgroup.

\begin{theorem}\label{th1}
Let  $\pi:GL_n(\mathbb{R})\longrightarrow \mathcal{U}(\mathcal{H})$ be a unitary irreducible representation, realized on a Hilbert space of functions $\mathcal{H}$.
Then $\pi_0$ is unitary irreducible and  the constant family of representations  $\{d\pi_{\epsilon}:\mathfrak{gl}_n(\mathbb{R})\longrightarrow \operatorname{End}(\mathcal{H}^{\infty}) \}_{\epsilon\in \mathbb{R}\neq 0}$
with $d\pi_{\epsilon}=d\pi$,  strongly contracts to  $d\pi_{0}:\mathbb{R}^{n}\rtimes \mathfrak{m}_n\longrightarrow \operatorname{End}(\mathcal{H}^{\infty})$.
\end{theorem}

\section{The unitary dual of  $\mathbb{R}^{2}\rtimes M_2$}\label{s4}
In this section, using the Mackey machine \cite{MR0031489,MR0044536,MR0396826}, we describe the unitary dual of $\mathbb{R}^{2}\rtimes M_2$. We shall explicitly write the associated representation of $\mathfrak{g}_0=\mathbb{R}^{2}\rtimes \mathfrak{m}_2$ on a corresponding dense subspace of the space of  smooth vectors. These realizations are  used in section \ref{Chap4}.

The character group $\widehat{\mathbb{R}^{2}}$ consists of all
functions of the form  \begin{eqnarray} \nonumber
&&\chi_{u}:\mathbb{R}^2\longrightarrow \mathbb{C} \\ \nonumber
&& \chi_{u}\left(v\right)=e^{i\langle u,v\rangle} ,
\end{eqnarray}
with $u,v\in \mathbb{R}^2$. The mirabolic group  $M_2$ acts on $\widehat{\mathbb{R}^{2}}$ by $A\cdot \chi_{u}=\chi_{Au}$. Unitary irreducible representations of $\mathbb{R}^{2}\rtimes M_2$ are parameterized by an orbit of some $\chi_{u}$ in  $\widehat{\mathbb{R}^{2}}$  and a unitary irreducible representation of the stabilizer of $\chi_{u}$. Below we give an exhaustive list of these representations up to equivalence. \begin{enumerate}
\item \textbf{The orbit of the  trivial character $\chi_{(0,0)}$}. In this case we obtain unitary irreducible representations that are trivial on $\mathbb{R}^2$. Such a representation is given by  a unitary irreducible representation of $M_2$. Explicitly,  we have exactly the following cases.
\begin{enumerate}
	\item For  $\lambda \in \mathbb{R}$ and $\sigma\in \{0,1\}$, the representation $\eta_{(0,0)}^{\lambda,\sigma}:	M_2\longrightarrow GL(\mathbb{C})\cong \mathbb{C}^*$   given by \[\eta_{(0,0)}^{\lambda,\sigma}\left(\begin{matrix}
a& b   \\
0 &  1   \end{matrix}\right) =\operatorname{sgn}(a)^{\sigma}|a|^{i\lambda}\mathbb{I}.\]
The associated representation $d\eta_{(0,0)}^{\lambda,\sigma}$ of $\mathfrak{g}_0$ on $\mathbb{C}$ is given by
\begin{eqnarray}\nonumber
&& e_{11}\longmapsto i\lambda,\hspace{2mm} e_{12} \longmapsto 0,\hspace{2mm} e_{21}\longmapsto 0, \hspace{2mm} e_{22} \longmapsto 0.
\end{eqnarray}
	\item The   representation $\eta_{(0,0)}:M_2 \longrightarrow \mathcal{U}(L^2(\mathbb{R^*},\frac{dx}{|x|}))$  given by
	\[\left(\eta_{(0,0)}\left(\begin{matrix}
a& b   \\
0 &  1   \end{matrix}\right) f\right)(x)=e^{ibx} f(a x).\]
The associated representation $d\eta_{(0,0)}$ of $\mathfrak{g}_0$ on $ C^{\infty}_c(\mathbb{R^*},\frac{dx}{|x|})$, the inner product  space of smooth compactly supported functions in $L^2(\mathbb{R^*},\frac{dx}{|x|})$, is given by
\begin{eqnarray}\nonumber
&& e_{11}\longmapsto x\partial_x,\hspace{2mm} e_{12} \longmapsto i  x,\hspace{2mm} e_{21}\longmapsto 0, \hspace{2mm} e_{22} \longmapsto 0.
\end{eqnarray}
\end{enumerate}
\item  \textbf{The orbit of the   character $ \chi_{(1,0)} $.}  For $\lambda\in \mathbb{R}$, the  representation $\eta_{(1,0)}^{\lambda}$  on $L^2(\mathbb{R}^*,\frac{dx}{|x|})$  given by
\[\left({\eta}^{\lambda}_{(1,0)}  \left( \left(\begin{matrix}
v_1   \\
v_2    \end{matrix}\right),\left(\begin{matrix}
a& b   \\
0 &  1    \end{matrix}\right) \right)f \right)(x)=e^{iv_1x^{-1}}e^{i  \lambda b x} f( x a ).\]
The associated representation $d\pi_{(1,0)}^{\lambda}$ of $\mathfrak{g}_0$ on $ C^{\infty}_c(\mathbb{R^*},\frac{dx}{|x|})$, is given by
\begin{eqnarray}\nonumber
&& e_{11}\longmapsto x\partial_x,\hspace{2mm} e_{12} \longmapsto i \lambda x,\hspace{2mm} e_{21}\longmapsto \frac{i}{x}, \hspace{2mm} e_{22} \longmapsto 0.
\end{eqnarray}

\item  \textbf{The orbit of the   character $ \chi_{(0,\beta)}$, with $\beta\neq 0$.} For $\lambda\in \mathbb{R}$ and $\sigma\in \{0,1\}$, the representation $\eta^{\lambda,\sigma}_{(0,\beta)}$   on
$L^2\left(\mathbb{R},dx\right)$  given by
\[\left(\eta^{\lambda,\sigma}_{(0,\beta)} \left( \left(\begin{matrix}
v_1   \\
v_2   \end{matrix}\right),\left(\begin{matrix}
a& b   \\
0 &  1    \end{matrix}\right) f\right)\right)(x)=e^{i\beta(-xv_1+v_2)}\operatorname{sgn}(a)^{\sigma}|a|^{i\lambda-1/2} f\left( \frac{b+x}{a}\right).\]
The associated representation $d{\eta}_{(0,\beta)}^{\lambda, \sigma}$ of $\mathfrak{g}_0$ on $ C^{\infty}_c(\mathbb{R},dx)$,  the inner product  space of smooth compactly supported functions in $L^2(\mathbb{R},dx)$,    is given by
\begin{eqnarray}\nonumber
&& e_{11}\longmapsto   i\lambda -\frac{1}{2} - x\partial_x,\hspace{2mm} e_{12} \longmapsto \partial_x,\hspace{2mm} e_{21}\longmapsto -i \beta x, \hspace{2mm} e_{22} \longmapsto i\beta.
\end{eqnarray}
\end{enumerate}

We summarize the above discussion in a Lemma.

\begin{lemma}\label{lem2}
The list below contains exactly one representative from  each equivalence class of  unitary irreducible representations of $\mathbb{R}^{2}\rtimes M_2$:
\begin{enumerate}
\item $\{\eta_{(0,0)}^{\lambda,\sigma}| \lambda \in \mathbb{R}, \sigma\in \{0,1\}\}\cup \{ \eta_{(0,0)}\}$,
\item $\{\eta_{(1,0)}^{\lambda}| \lambda \in \mathbb{R}\}$,
\item $\{\eta^{\lambda,\sigma}_{(0,\beta)} | \beta\in \mathbb{R}^*, \lambda \in \mathbb{R}, \sigma\in \{0,1\}\}$.
\end{enumerate}
\end{lemma}

\section{The unitary dual of  $\mathbb{R}^{2}\rtimes M_2$   as strong contraction}\label{Chap4}
In this section for any unitary irreducible representation of $\mathbb{R}^{2}\rtimes M_2$, in one of  the explicit realizations that are  given in Section \ref{s4},
 we build a corresponding strong contraction and, by doing so, proving Theorem \ref{th2}. We shall organize our calculations according to the orbits of $M_2$ on $\widehat{\mathbb{R}^2}$.
\subsection{The orbit of the  trivial character $\chi_{0}$ }
For every $\mu \in \mathbb{R}$, we let $\pi_{\mu}$ be the unitary one dimensional representation of $GL_2(\mathbb{R})$ given by
\[ A\longmapsto |\det A|^{i\mu}. \]
The corresponding representation $d\pi_{\mu}$ of $\mathfrak{gl}_2(\mathbb{R})$ is given by
\begin{eqnarray}\nonumber
&& e_{11}\longmapsto i\mu,\hspace{2mm} e_{12} \longmapsto 0,\hspace{2mm} e_{21}\longmapsto 0, \hspace{2mm} e_{22} \longmapsto i\mu.
\end{eqnarray}

\begin{proposition}\label{p1}
For every $\lambda\in \mathbb{R}$ and $\sigma\in \{0,1\}$,  the representation  $d\eta_{(0,0)}^{\lambda,\sigma}:\mathbb{R}^{2}\rtimes \mathfrak{m}_2 \longrightarrow \operatorname{End}(\mathbb{C})$ is a strong contraction of the (constant) family $\{ d\pi_{\lambda}:\mathfrak{gl}_2(\mathbb{R}) \longrightarrow \operatorname{End}(\mathbb{C})\}_{\epsilon \neq 0 }$.
\end{proposition}
  We first remark that in this case we can  think of the one dimensional vector space $\mathbb{C}$ as the space of square integrable functions on the trivial measurable space consisting of one point only.
\begin{proof}
In this case, since the underlying vector space is one dimensional  pointwise convergence implies norm convergence. Indeed,
\begin{eqnarray}\nonumber
&& \lim_{\epsilon \longrightarrow 0 } d\pi_{\lambda}:(t_{\epsilon}(e_{11})) =  i\lambda= d\eta_{(0,0)}^{\lambda,\sigma}(e_{11}),  \\ \nonumber
&& \lim_{\epsilon \longrightarrow 0 } d\pi_{\lambda}:(t_{\epsilon}(e_{12})) =0= d\eta_{(0,0)}^{\lambda,\sigma}(e_{12}),  \\ \nonumber
&& \lim_{\epsilon \longrightarrow 0 } d\pi_{\lambda}:(t_{\epsilon}(e_{21})) =0= d\eta_{(0,0)}^{\lambda,\sigma}(e_{21}),  \\ \nonumber
&& \lim_{\epsilon \longrightarrow 0 } d\pi_{\lambda}:(t_{\epsilon}(e_{22})) = \lim_{\epsilon \longrightarrow 0 } \epsilon  i\lambda=0= d\eta_{(0,0)}^{\lambda,\sigma}(e_{22}).
\end{eqnarray}
\end{proof}

\begin{proposition}
There is a unitary irreducible representation $\pi$  of $GL_2(\mathbb{R})$ on   a Hilbert space of functions  $\mathcal{H}$ and a dense $\mathfrak{gl}_2(\mathbb{R})$-invariant subspace  $\mathcal{H}^{\infty}$ of  $\mathcal{H}$,  such that the (constant) family of representations  $\{ d\pi:\mathfrak{gl}_2(\mathbb{R}) \longrightarrow \operatorname{End}(\mathcal{H}^{\infty})\}_{\epsilon \neq 0 }$ strongly contract to a representation isomorphic to $d\eta_{(0,0)}:\mathbb{R}^{2}\rtimes \mathfrak{m}_2 \longrightarrow \operatorname{End}(C^{\infty}(\mathbb{R^*},\frac{dx}{|x|}))$.
\end{proposition}
\begin{proof}
We can take for $\pi$ any unitary irreducible infinite-dimensional representation of $GL_2(\mathbb{R})$ realized on a Hilbert space of functions. For example, we can take a unitary irreducible principal series with $\mathcal{H}$  a Hilbert space of functions on $GL_2(\mathbb{R})$. Theorem \ref{th1} guarantees that $\pi_0$ is unitary irreducible and  the constant family of representations  $\{d\pi_{\epsilon}:\mathfrak{g}_2\longrightarrow \operatorname{End}(\mathcal{H}^{\infty}) \}_{\epsilon\in \mathbb{R}\neq 0}$
with $d\pi_{\epsilon}=d\pi$,  strongly contracts to  $d\pi_{0}:\mathbb{R}^{2}\rtimes \mathfrak{m}_2\longrightarrow \operatorname{End}(\mathcal{H}^{\infty})$. The representation $\pi_0|_{M_2}$ of $M_2$ is unitary irreducible and infinite-dimensional. Up to equivalence there is exactly one such representation. Since $\mathbb{R}^2\rtimes 1$ acts trivially via   $\pi_0$ then   $\pi_0$ must be equivalent to $\eta_{(0,0)}$.  Hence $d\pi_0$ is equivalent to $d\eta_{(0,0)}$.
\end{proof}

\subsection{The orbit of the   character $ \chi_{(1,0)} $.}
For every integer $n>1$  there is a discrete series representation  $D^{n}$ of $GL_2(\mathbb{C})$ in which the scalar matrices act trivially.  In the  Kirillov model on $L^2(\mathbb{R}^*,\frac{dx}{|x|})$ the corresponding representation of $\mathfrak{gl}_2(\mathbb{R})$  on   $C^{\infty}_c(\mathbb{R^*},\frac{dx}{|x|})$ is given by
\begin{eqnarray}\nonumber
&& e_{11}\longmapsto x\partial_x, \hspace{1mm}e_{12}\longmapsto i x, \hspace{1mm} e_{21} \longmapsto -i\frac{n^2-1}{4x} +ix\partial_{xx},\hspace{1mm} e_{22}\longmapsto -x\partial_x.
\end{eqnarray}
For more details, see \cite{MR3055523}.
For $ 0 \neq q\in \mathbb{R}$ we  twist the above mentioned representation via conjugation by the diagonal matrix $\operatorname{diag}(q,1)$  to obtain the isomorphic representation $d{D^{n,q}}$ given by
\begin{eqnarray}\nonumber
&& e_{11}\longmapsto x\partial_x, \hspace{1mm}e_{12}\longmapsto iq x, \hspace{1mm} e_{21} \longmapsto -i\frac{n^2-1}{4q x} +i\frac{x}{q}\partial_{xx},\hspace{1mm} e_{22}\longmapsto  -x\partial_x.
\end{eqnarray}

\begin{proposition}\label{pro3}
For any  $0\neq \lambda\in \mathbb{R}$   the representation $d\eta_{(1,0)}^{\lambda}:\mathbb{R}^{2}\rtimes \mathfrak{m}_2\longrightarrow \operatorname{End}( C^{\infty}_c(\mathbb{R^*},\frac{dx}{|x|}))$ is a strong contraction of the sequence  $\{ d{D^{n,\lambda}}:\mathfrak{gl}_2(\mathbb{R}) \longrightarrow \operatorname{End}( C^{\infty}_c(\mathbb{R^*},\frac{dx}{|x|}))\}_{n\in \mathbb{N}  }$.
\end{proposition}
\begin{proof}
We shall use the sequence  $\epsilon_n=-\frac{4\lambda}{n^2 }$. For pointwise convergence observe that for every $f\in C^{\infty}_c(\mathbb{R^*})$ and $x\in \mathbb{R}$,
\begin{eqnarray}\nonumber
&& \lim_{n\longrightarrow \infty } \left(d{D^{n,\lambda}}(t_{\epsilon_n}(e_{11}))f\right)(x) =  \lim_{n\longrightarrow \infty } \left(x\partial_x\right)f(x)= x\partial_xf(x)=\left(d\eta_{(1,0)}^{\lambda}(e_{11})f\right)(x),\\ \nonumber
&& \lim_{n\longrightarrow \infty } \left(d{D^{n,\lambda}}(t_{\epsilon_n}(e_{12}))f\right)(x) =  i \lambda xf(x)=\left(d\eta_{(1,0)}^{\lambda}(e_{12})f\right)(x),\\ \nonumber
&& \lim_{n\longrightarrow \infty } \left(d{D^{n,\lambda}}(t_{\epsilon_n}(e_{21}))f\right)(x) =\lim_{n\longrightarrow \infty }  -\frac{4\lambda}{n^2 \lambda} \left( -i\frac{n^2-1}{4x} +ix\partial_{xx}\right)f(x)= \\ \nonumber
&& ix^{-1}f(x)=\left(d\eta_{(1,0)}^{\lambda}(e_{21})f\right)(x),\\ \nonumber
&& \lim_{n\longrightarrow \infty } \left(d{D^{n,\lambda}}(t_{\epsilon_n}(e_{22}))f\right)(x) =   \lim_{n\longrightarrow \infty } -\frac{4\lambda}{n^2 }   \left(-x\partial_x\right)f(x)=0= \left(d\eta_{(1,0)}^{\lambda}(e_{22})f\right)(x).
\end{eqnarray}
Norm convergence  follows from Lebesgue dominated convergence theorem.
\end{proof}

\begin{proposition}
The representation $d\eta_{(1,0)}^{0}:\mathbb{R}^{2}\rtimes \mathfrak{m}_2\longrightarrow \operatorname{End}( C^{\infty}_c(\mathbb{R^*},\frac{dx}{|x|}))$ is a strong contraction of the sequence  $\{ d{D^{n,1/n}}:\mathfrak{gl}_2(\mathbb{R}) \longrightarrow \operatorname{End}( C^{\infty}_c(\mathbb{R^*},\frac{dx}{|x|}))\}_{\epsilon \neq 0 }$.
\end{proposition}
Using $\epsilon_n=-\frac{4}{n^3}$ the proof is similar to that of Proposition \ref{pro3}.

\subsection{The orbit of the   character $\chi_{(0,\beta)}$ with  $0\neq \beta \in \mathbb{R} $.}

In the non-compact picture, the unitary  principal series of $SL_2(\mathbb{R})$  are realized on $L^2(\mathbb{R},dx)$  via
\[\left(\mathcal{P}^{\sigma,\nu} \left(\begin{matrix}
a& b   \\
c &  d    \end{matrix}\right) f\right)(x)=\operatorname{sgn}(-b x+d)^{\sigma}|-b x+d|^{-1-i\nu}f\left( \frac{ax-c}{-bx+d}\right),\]
here $\sigma\in \{0,1\}$ and $\nu\in \mathbb{R}$. See e.g., \cite[p. 36]{Knapp}.  We twist this representation by precompose $\mathcal{P}^{\sigma,\nu}$ with inverse transpose. Explicitly,  the new action is  $\widetilde{\mathcal{P}}^{\sigma,\nu}$  given by
\[\left(\widetilde{\mathcal{P}}^{\sigma,\nu} \left(\begin{matrix}
a& b   \\
c &  d    \end{matrix}\right) f\right)(x)=\operatorname{sgn}(c x+a)^{\sigma}|c x+a|^{-1-i\nu}f\left( \frac{dx+b}{cx+a}\right).\]
 For every $\mu\in \mathbb{R}$, we  extend $\widetilde{\mathcal{P}}^{\sigma,\nu}$ to a unitary irreducible representation $\widetilde{\mathcal{P}}^{\sigma,\nu,\mu}$ of  $GL_2(\mathbb{R})$,  by
 \[\left(\widetilde{\mathcal{P}}^{\sigma,\nu,\mu} \left(\begin{matrix}
a& b   \\
c &  d    \end{matrix}\right) f\right)(x)=|ad-bc|^{1/2+i\mu}\operatorname{sgn}(c x+a)^{\sigma}|c x+a|^{-1-i\nu}f\left( \frac{dx+b}{cx+a}\right).\]

 The corresponding  representation  $d\widetilde{\mathcal{P}}^{\sigma,\nu,\mu} $ of $\mathfrak{gl}_2(\mathbb{R})$ on $C^{\infty}_c(\mathbb{R})$ is given by
\begin{eqnarray}\nonumber
&& e_{11}\longmapsto  i\mu-\frac{1}{2}-i\nu -x\partial_x,\hspace{1mm} e_{12}\longmapsto \partial_x, \\ \nonumber
&& e_{21} \longmapsto  -(1+i\nu)x -x^2\partial_{x}, \hspace{1mm}
 e_{22}\longmapsto    \frac{1}{2}+i\mu +x\partial_x.
\end{eqnarray}

 \begin{proposition}\label{p5}
For $\lambda\in \mathbb{R}$ and $\sigma\in \{0,1\}$, the representation $d\pi^{\lambda,\sigma}_u:\mathbb{R}^{2}\rtimes \mathfrak{m}_2\longrightarrow \operatorname{End}( C^{\infty}_c(\mathbb{R}))$
 is a strong contraction of the family $\{ d\widetilde{\mathcal{P}}^{\sigma,\beta/\epsilon,\lambda+\beta/\epsilon}:\mathfrak{gl}_2(\mathbb{R}) \longrightarrow \operatorname{End}( C^{\infty}_c(\mathbb{R}))\}_{\epsilon \neq 0 }$.
\end{proposition}

\begin{proof} For pointwise convergence observe that for every $f\in C^{\infty}_c(\mathbb{R^*})$ and $x\in \mathbb{R}$,
\begin{eqnarray}\nonumber
&& \lim_{\epsilon \longrightarrow 0 } \left(d\widetilde{\mathcal{P}}^{\sigma,\beta/\epsilon,\lambda+\beta/\epsilon}(t_{\epsilon}(e_{11}))f\right)(x) =   \lim_{\epsilon \longrightarrow 0 }\left(i(\lambda+\frac{\beta}{\epsilon})-\frac{1}{2}-i\frac{\beta}{\epsilon} -x\partial_x \right)f(x)=\\ \nonumber
&&  \hspace{1cm} \left(i\lambda -\frac{1}{2} - x\partial_x\right)f(x)= \left(d\pi^{\lambda,\sigma}_u(e_{11})f\right)(x),  \\ \nonumber
&& \lim_{\epsilon \longrightarrow 0 } \left(d\widetilde{\mathcal{P}}^{\sigma,\beta/\epsilon,\lambda+\beta/\epsilon}(t_{\epsilon}(e_{12})) f\right)(x)=\partial_xf(x)= \left(d\pi^{\lambda,\sigma}_u(e_{12})f\right)(x),  \\ \nonumber
&&  \lim_{\epsilon \longrightarrow 0 } \left(d\widetilde{\mathcal{P}}^{\sigma,\beta/\epsilon,\lambda+\beta/\epsilon}(t_{\epsilon}(e_{21}))f\right)(x) = \lim_{\epsilon \longrightarrow 0 }\epsilon\left( -(1+i\frac{\beta}{\epsilon})x -x^2\partial_{x}\right)f(x) =\\ \nonumber
&& \hspace{1cm}-i\beta xf(x)=   \left(d\pi^{\lambda,\sigma}_u(e_{21})f\right)(x),  \\ \nonumber
&& \lim_{\epsilon \longrightarrow 0 }  \left(d\widetilde{\mathcal{P}}^{\sigma,\beta/\epsilon,\lambda+\beta/\epsilon}(t_{\epsilon}(e_{22}))f\right)(x) = \lim_{\epsilon \longrightarrow 0 } \epsilon \left(  \frac{1}{2}+ i(\lambda+\frac{\beta}{\epsilon})+x\partial_x\right)f(x)
= \\ \nonumber
&&\hspace{1cm}i\beta f(x)= \left(d\pi^{\lambda,\sigma}_u(e_{22})f\right)(x).
\end{eqnarray}
Norm convergence  follows from the following lemma which easily  proved using  Lebesgue dominated convergence theorem.
\begin{lemma}
For every  $\epsilon \in \mathbb{R}$, let $D_{\epsilon}$ be a smooth  differential operator  on $C^{\infty}_c(\mathbb{R})$. Explicitly, $D_{\epsilon}=\sum_{i=0}^nd_{i,\epsilon}(x)\partial_x^i$
for some smooth functions $d_{i,\epsilon}(x)\in C^{\infty}(\mathbb{R})$.  If for every $i\in \{1,2,,,n\}$,  and every $x\in \mathbb{R}$,   $\epsilon \longmapsto d_{i,\epsilon}(x)$  is a continuous  function (of $\epsilon$) then  for every $f\in   C^{\infty}_c(\mathbb{R})$,
\[ \lim_{\epsilon \longrightarrow 0}\int_{\mathbb{R}}|D_{\epsilon}(f)(x)|^2dx=\int_{\mathbb{R}}|D_{0}(f)(x)|^2dx.\]
\end{lemma}
\end{proof}

Combining Lemma \ref{lem2} and Propositions \ref{p1}-\ref{p5} we obtaine the  following result.
\begin{theorem}\label{th2}
For any unitary irreducible representation $\pi_0$  of $\mathbb{R}^{2}\rtimes M_2$ the following hold.
\begin{enumerate}
\item There is  a realization of $\pi_0$ on  a Hilbert space of functions  $\mathcal{H}$.
\item There is a dense $(\mathbb{R}^{2}\rtimes \mathfrak{m}_2)$-invariant subspace $\mathcal{H}^{\infty}$ of $\mathcal{H}$.
\item There is a family  (or a sequence) of representations $\{d\pi_{\epsilon}:\mathfrak{gl}_2(\mathbb{R})\longrightarrow \operatorname{End}(\mathcal{H}^{\infty}) \}_{\epsilon\in \mathbb{R}\neq 0}$
that  strongly contract to  $d\pi_{0}:\mathbb{R}^{2}\rtimes \mathfrak{m}_2\longrightarrow \operatorname{End}(\mathcal{H}^{\infty})$.
\end{enumerate}
\end{theorem}

\section*{References}
\bibliographystyle{vancouver}

redpajama_set_name: RedPajamaArXiv


text:
Q: getCurrentSession gives No Session Bound to Context, openSession does not I'm trying to integrate Spring 3.1 with Hibernate 4.1.4, but I am having problems when getting my session from a generic DAO.
The problem is, if I use getCurrentSession() I get a NullPointerException and Hibernate says No session is bound to the context, yet if I use openSession everything seems to be working. Somehow I feel I should be using getCurrentSession, but can't find the origin of the problem.
I've searched this over the internet but none of the solutions worked for me.
Here's my genericDAO code:
public class GenericDaoHibernateImpl<E, PK extends Serializable> implements GenericDao<E, PK> {

    private Class<E> entityClass;

    protected GenericDataBaseExceptionHandler exceptionHandler;

    private SessionFactory sessionFactory;

    @SuppressWarnings("unchecked")
    public GenericDaoHibernateImpl() {
        this.entityClass = (Class<E>) ((ParameterizedType) getClass().
            getGenericSuperclass()).getActualTypeArguments()[0];
    }

    public void setExceptionHandler(GenericDataBaseExceptionHandler exceptionHandler) {
        this.exceptionHandler = exceptionHandler;
    }

    public void setSessionFactory(SessionFactory sessionFactory) {
        this.sessionFactory = sessionFactory;
    }

    protected Session getSession() {
        if (sessionFactory.getCurrentSession() == null)
            throw new IllegalStateException("Session has not been set on DAO before usage");
        return sessionFactory.getCurrentSession(); //This crashes
//      return sessionFactory.openSession(); //This does not
    }

    public Class<E> getEntityClass() {
        return entityClass;
    }

    public void persist(E entity) throws GenericDataBaseException {
        try {
            getSession().persist(entity);
        } catch (Throwable t) {
            Collection<Object> args = new ArrayList<Object>();
            args.add(entity);
            throw exceptionHandler.handle(t, "persist", args);
        }
    }
    (...)

}

And my spring config file:
    <context:annotation-config />
<bean id="dataSource" class="com.mchange.v2.c3p0.ComboPooledDataSource"
        destroy-method="close">
        <property name="driverClass">
            <value>com.mysql.jdbc.Driver</value>
        </property>
        <property name="jdbcUrl">
            <value>jdbc:mysql://localhost/forestool</value>
        </property>
        <property name="user">
            <value>forestool</value>
        </property>
        <property name="password">
            <value>forestool</value>
        </property>
    </bean>

    <!-- Declaración de la factoría de sesiones hibernate con los mappings necesarios -->
    <bean id="sessionFactory" class="org.springframework.orm.hibernate4.LocalSessionFactoryBean">
        <property name="dataSource">
            <ref bean="dataSource"/>
        </property>
        <property name="mappingLocations">
            <list>
                <value>classpath*:/hbm/*.hbm.xml</value>
            </list>
        </property>
        <property name="hibernateProperties">
            <ref bean="hibernateProperties"/>
        </property>
    </bean>

    <bean id="transactionManager" class="org.springframework.orm.hibernate4.HibernateTransactionManager">
     <property name="sessionFactory">
         <ref bean="sessionFactory"/>
     </property>
    </bean>
<bean id="hibernateProperties" class="java.util.Properties">
    <constructor-arg index="0">
        <props>
            <prop key="hibernate.dialect">org.hibernate.dialect.MySQLInnoDBDialect</prop>
        </props>
    </constructor-arg>
</bean>

Exception:
org.hibernate.HibernateException: No Session found for current thread
    at org.springframework.orm.hibernate4.SpringSessionContext.currentSession(SpringSessionContext.java:97)
    at org.hibernate.internal.SessionFactoryImpl.getCurrentSession(SessionFactoryImpl.java:1041)
    at es.fsc.core.dao.impl.GenericDaoHibernateImpl.getSession(GenericDaoHibernateImpl.java:83)
    at es.fsc.core.dao.impl.GenericDaoHibernateImpl.findAll(GenericDaoHibernateImpl.java:244)
    at es.fsc.dao.explotacion.impl.ExplotacionDaoImpl.getExplotacionesAbiertas(ExplotacionDaoImpl.java:21)
    at es.fsc.service.explotacion.impl.ExplotacionServiceImpl.getExplotacionesAbiertas(ExplotacionServiceImpl.java:22)
    at sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)
    at sun.reflect.NativeMethodAccessorImpl.invoke(Unknown Source)
    at sun.reflect.DelegatingMethodAccessorImpl.invoke(Unknown Source)
    at java.lang.reflect.Method.invoke(Unknown Source)
    at org.springframework.aop.support.AopUtils.invokeJoinpointUsingReflection(AopUtils.java:318)
    at org.springframework.aop.framework.JdkDynamicAopProxy.invoke(JdkDynamicAopProxy.java:196)
    at $Proxy5.getExplotacionesAbiertas(Unknown Source)
    at es.fsc.app.FscApp.runApp(FscApp.java:58)
    at es.fsc.app.App.run(App.java:65)
    at es.fsc.main.Main.main(Main.java:20)
Exception in thread "main" java.lang.NullPointerException
    at es.fsc.core.dao.impl.GenericDaoHibernateImpl.findAll(GenericDaoHibernateImpl.java:253)
    at es.fsc.dao.explotacion.impl.ExplotacionDaoImpl.getExplotacionesAbiertas(ExplotacionDaoImpl.java:21)
    at es.fsc.service.explotacion.impl.ExplotacionServiceImpl.getExplotacionesAbiertas(ExplotacionServiceImpl.java:22)
    at sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)
    at sun.reflect.NativeMethodAccessorImpl.invoke(Unknown Source)
    at sun.reflect.DelegatingMethodAccessorImpl.invoke(Unknown Source)
    at java.lang.reflect.Method.invoke(Unknown Source)
    at org.springframework.aop.support.AopUtils.invokeJoinpointUsingReflection(AopUtils.java:318)
    at org.springframework.aop.framework.JdkDynamicAopProxy.invoke(JdkDynamicAopProxy.java:196)
    at $Proxy5.getExplotacionesAbiertas(Unknown Source)
    at es.fsc.app.FscApp.runApp(FscApp.java:58)
    at es.fsc.app.App.run(App.java:65)
    at es.fsc.main.Main.main(Main.java:20)

A: I don't see anything in this configuration that would actually open a Hibernate session for you, or control when that is done.
If you are new to Spring, you might just want to configure an OpenSessionInViewFilter in your web.xml to have a Session open and bound to each request automatically.

redpajama_set_name: RedPajamaStackExchange


You can bring that certified master chef skills out with this Family-size 1. 2 cuft capacity microwave. This oven offers Panasonic patented "Inverter" Technology that offers linear cooking the prevents overcooking on the edges and surfaces and gives juicer and tender food every time. The NN-SN643S offers a 1. 2 cubic foot capacity, 1200 watts of high cooking power, while its 12-Menu Category one-touch sensor cook/reheat calculates cooking times automatically, making cooking a variety of food easier than ever. Other highlights include a Tactile Membrane keypad and 5-Buttons for easy programming, Inverter Turbo Defrost technology, 10 Power Levels, Popcorn Key, Keep Warm mode, Delay start, Timer, Quick Minute, 13 1/2″ Turntable and More/Less Control. The countertop microwave oven measures 20 11/16″ L x 15 13/16″ W x 12 1/4″ H and weighs 25. 5 lbs. Stainless Steel face with a silver wrap finish. Optional Panasonic Stainless Steel Wall Installation Trim Kits available in 27″ (NN-TK621SS). PLEASE NOTE : Upper-left corner of door has a small indentation to allow door to open smoothly One-Touch Genius Sensor Cook and Reheat for automatic cooking settings and even Keep Warm feature PLEASE NOTE : Upper-left corner of door has a small indentation to allow door to open smoothly.


Images exclusives du tournage hors-normes de Free Solo !
Watch the Oscar-winning documentary feature #FreeSolo, playing across select cinemas across India starting April 12th.
Do peoples even watch climber?
not sure how he can climb with such big balls..
Any other athletic accolade just seems pale in comparison.
Alex most definitely has balls of steel.
Absolutely incredible. This is a feat beyond my own comprehension to big extent. Right now as I'm watching 'The dawn wall' where Tommy Caldwell climbs el cap during several DAYS and still that is after years of practice, planning and attempting routes.. And this guy free climbs it in mere hours. With meticulous, repetitive practice of course.. but it's still just unreal. Can't imagine the feeling of being on that wall, seeing expert climbers practice their way up el cap with ropes and falling, falling falling and retrying over and over. The smallest mistake, grab the notch on the rock just an 8th of an inch and it's over. Unbelievable.
Oh god its massive....one needs to develop his character, discipline, meditation, diet and..and last but not least grow fire in his heart to succeed. Gods blessings sure a part in this venture.
Just watched "Free Solo" on DVD. This stunning Academy Award winning documentary about Alex Honnold's free solo climb 3000 feet up El Capitan is absolutely amazing, gripping and awe-inspiring. His unflinching determination, grit and courage to overcome all fear is amazing and inspirational! No fear.
The impossible is made in our heads,nothing is impossible!
Funny, but interesting thought here. I would like to see something like this, with this attitude, both about the potential negatives of this dangerous interest, and also the understanding part, of exploring. When it comes to the exploring of your own mind, with drugs. And I would never want to see that climbing like this would be illegal. Nor do I want to see experimenting with drugs to be that, as well!
I once climbed my sofa.
To much drama, not enough climbing. More time spent watching him in his bunk, working on a refrigerator, driving his van, tying his shoes, staring up the nostrils of everyone, than the actual climbing.
*************************** i am definitely watching this.
I can do that. Here, hold my beer.
Alex мужик! На это просто смотреть страшно , не говоря о восхождении!
Does anybody know the background music??
This guy does the impossible and lives in a van and they call Lionel Messi a genius and give him tens of millions for putting a ball between 3 metals bars. What a twisted world!
Michael Jordan, LeBron James, Lionel Messi.... Alex is so far beyond all them, it is not even close. Anyone who doubts this has not seen the movie yet.
This gives me anxiety just watching the trailer.
If I train for several months I think I can watch this.
Yay they are finally making an Uncharted movie!
got around to watching this a couple days ago on hulu plus. it is one of the most amazing things i have ever seen. my palms were sweating the entire film. This guy is insane.
A strong spirited person and a very touching documentary!!!
So Alex gives his phone a cover protective casing but gives little thought on his safety to do this daredevil attempt?
securedigit I know that you're joking around, but he gives tons of thought to his safety and to risk mitigation.
he shouldn't be able to do this with such heavy balls. very impressive!
How did he climb that mountain with those two boulders hanging between his legs.
The most exceptional physical and mental feat I've ever witnessed.
Alex is one of the most amazing humans to walk this planet... this is straight up legendary!
I literally held my breath the whole ending of the movie! The Ultimate rush!
That woman punched a sizeable hole in this docu. She was so out of place and unnecessary. I'm a bit sorry to say this, but she 100% looks to be one of those women who piggyback a great man's achievements, knowingly, pre-meditated while adding nothing expect for a slight negative drag. Very telling that she was the one who had to leave for the climb to happen.
I watched this last night. It's way more then about climbing. I feel kind of bad for Alex. He seems very emotionally detached from people . Being told he could always do more and losing his father very young. I think he has a very good heart and just wants to climb and be left alone. He looks at death with a callous thought. I hope you find peace Alex, keep doing what makes you happy. In the film he also said he never knew how to hug and love. Climb on brother and stay safe !!!
Free soloing is stupid. I hope he falls.
Am I the only who didn't like Sanni right off the bat and had that feeling she is bad news for Alex? After all, she's a groupie with a hidden agenda.
I feel alive eating peanut butter and jelly sandwiches.
Doesn't seem like a clever idea to me.
Knowing you could die with a simple slip to me is plain carelessness. Especially when you have a kid and a partner constantly worrying about you it isn't worth it.
Adam Ondra is so far best on El Cap!! Champion!
Sua mente ti leva onde você quiser.... Alex é a prova disso.
IDK...I found it disapointing and way over hyped most of it was the back story on his life and interviews with him and his relationship with his girlfriend and once you take away the actual feat of free soloing El cap you realize he really isnt that intresting and kinda seems like a total d-bag.
This isn't a movie about climbing without a rope. It's about showing the world how big your 🏈 ⚽ 🏀 are.
men this was faking incredible !!!!! Amazing..
The brave do not live forever, but the cautious do not live at all.
I watched the movie and just bought the DVD. I will put it somewhere where I can always see it and when I get angry or annoyed with any on my day to day small problems/issue I will look at it.
Who wants to climb Trump's wall ??
His poor girlfriend seems simple but nice and certainly beautiful. And she has ZERO clue that this guy will NEVER commit emotionally to anything but those cliff faces.
"Free Solo" binds us together as human species and shows what we, as individuals, are capable of, as apposed to the collective "politically correct" Marxist hive mind. Deservedly so, this documentary won the Oscar. Much respect and congratualations to Alex and his film crew.
What's the name of this music?
This is no humble-brag. Watching Oscar winner "Free Solo" tonight (finally!) about Alex Honnold's insane "no ropes, mom!" climbing of Yosemite's El Capitan—a 3,300-foot slab of granite—reminded me of how I almost never made it past 2003. It was on the Cullin Hills, a range of craggy rock located on the Isle of Skye in Scotland, where as a cocky and somewhat naive amateur I free-solo climbed by myself (scrambling without protection) and nearly lost my footing and fell to my death. Lesson: Leave it to the pros. Alex's near 4-hour climb is the most impressive human achievement I've heard about, let alone witness on a large theater screen.
Could a climber explain how difficult this is? I need a comparison of this to another sport or endeavor. Sorry, I don't climb, and those professional climbers didn't really explain well in the documentary.
The route is fairly difficult, in that you'd need to be a pretty good climber to be able to do the moves successfully. The part that makes this such a big deal is that usually, people would climb with a rope to protect them if they fall, but a free solo is when you climb without a rope. So if he slipped or fell he'd die.
I got to see this on the big screen last night and it changed my life. My brother and I were sitting at the bottom of the theatre and it made the experience even better. Watch this on the big screen if you can.


Each year we dedicate a special time to honour citizens who volunteer their time and talents to worthy causes across our country, region and the local community. We want to acknowledge the incredible efforts of volunteers across Halton and say THANK YOU. National Volunteer Week is when we can all take time to recognize volunteers and celebrate the power of volunteerism in our community. Our theme for National Volunteer Week 2018 is Celebrating the Value of Volunteering – Building CONFIDENCE, CONNECTIONS, and COMMUNITY.
Volunteer Halton is privileged to witness like-minded individuals and groups who identify the need and move into action. Volunteers are everyday individuals who answer the call for change. Many come together as strangers, connect through a cause, and end up with lasting friendships. Volunteer Halton recognizes the wonderful volunteers who come from different backgrounds and experiences from all ages to be the roots of strong communities. ~~~ Ann Coburn – Director, Volunteer Halton.
Volunteers reach out beyond themselves, to engage in kindness and caring for others. People from all walks of life engage in volunteerism for a variety of reasons some of which are: to tackle the issues of poverty, the environment, homelessness, to promote social inclusion, and most importantly, to be the voice and hands of compassion and hope.
Canadians have a rich history of volunteering and community involvement. The work of the volunteer is an essential work. National Volunteer Week pays tribute to the millions of Canadian volunteers who donate their time and energy.
National Volunteer Week is the biggest celebration of volunteers and voluntarism Canada has and Volunteer Canada is taking the lead on the celebrations every year. National Volunteer Week campaigns were developed to help organizations and individuals from coast to coast to coast deliver their own volunteer week celebrations.


The 2010 global atheists convention was in Melbourne last week. It could well turn out to be the best thing for theism that happens this year.
For someone who has made a career out of telling everyone how much more tolerant the world would be if only religion were obliterated from the human psyche, Dawkins manages to appear remarkably intolerant towards anyone who disagrees with him... the arch-hater of religious intolerance himself behaves with the zeal of a religious fundamentalist and, despite excoriating religion for stifling debate, does this in spades.
[W]hy do leading atheists, so sure of their superior morality, feel licensed to be meaner than leading Christians? Is this what morally superior people do when God has gone? In that case, bring God back.
They dug a pit in my path - but they have fallen into it themselves.
Note that Andrew Bolt only wants the moral, communitarian, this-worldly benefits of belief in a God. He doesn't necessarily want to trust Jesus Christ as his Lord and Saviour. He's not interested in being saved from God's wrath at the last day.
But, I think we should rejoice in the fair-mindedness and clear-headedness of these commentators. Perhaps honesty really is the best policy. Maybe the truth will eventually win out.


Critically acclaimed, publicly revered and yet to have performed in its native Auckland. Against all odds, one of NZ theatre's most innovative productions arrives at The Civic as 360 enchants audiences from January 13th.
Travelling back through the memories of a prodigal son, 360 tracks the series of events that led to his final departure; his memories paint a vivid portrait of a family who are funny, exquisitely melancholic and charmingly clown-like. Expect the unexpected as two worlds collide when the son opens the same door he closed behind him years before.
Created by Chapman Tripp award winners, Carl Bland, the late Peta Rutter and Ben Crowder, 360 is filled with larger-than-life characters and surreal situations, as the intimate audience sits on the vaunted stage of The Civic Theatre, enclosed in a proverbial bullring as fireworks, song, dance, a life-sized seal and the rest of the action unfolds around them.
With a capacity of only 80 per show the audience is literally at the heart of action; seated on swivel chairs they are surrounded by the huge circular stage. As you spin and swivel to follow the turn of events on stage it is near impossible not to be drawn into the constant surprises of theatre magic courtesy of some of the country's most experienced designers working at the very top of their game.
Where its 2011 season never came to fruition, the yearning for this Auckland show will finally be satisfied after a four year wait, as the cast of seven take to the roulette-wheel like stage for this long awaited Auckland premiere.
With a strictly limited capacity, this show will sell out – so book now!


text:
Home > List of families > Fabaceae subfamily Mimosoideae > Entada > mossambicensis
Entada mossambicensis Torre
We have few details about this taxon; if you can provide any information, photos or reliable records, please contact one of the site authors. Email addresses are given on the home page.
Images: None on this site.
Detailed records: Display species records QDS maps by: Google Maps Point records by Google Maps
Species details: Click on each item to see an explanation of that item (Note: opens a new window)
Derivation of specific name:
Altitude range:
Flowering time:
Worldwide distribution:
Mozambique distribution: N
Growth form(s):
Endemic status: Endemic
Red data list status:
Insects associated with this species:
Spot characters: Display spot characters for this species
Literature:
Brenan, J.P.M. (1970). Mimosoideae Flora Zambesiaca 3(1) Page 23.
Burrows, J.E., Burrows, S.M., Lötter, M.C. & Schmidt, E. (2018). Trees and Shrubs Mozambique Publishing Print Matters (Pty), Cape Town. Page 213. (Includes a picture).
Other sources of information about Entada mossambicensis:
African Plants: A Photo Guide (Senckenberg): Entada mossambicensis
Biodiversity Explorer (Biodiversity of southern Africa): Entada mossambicensis
BHL (Biodiversity Heritage Library): Entada mossambicensis
EOL (Encyclopedia of Life): Entada mossambicensis
ePIC (electronic Plant Information Center): Entada mossambicensis
Flora Zambesiaca web site: Entada mossambicensis
GBIF (Global Biodiversity Information Facility): Entada mossambicensis
Google: Web - Images - Scholar
GRIN (Germplasm Resources Information Network): Entada mossambicensis
IPNI (International Plant Names Index): Entada mossambicensis
JSTOR Plant Science: Entada mossambicensis
Kew Herbarium catalogue: Entada mossambicensis
Mansfeld World Database of Agricultural and Horticultural Crops: Entada mossambicensis
The Plant List (version 1.1): Entada mossambicensis
Tropicos: Entada mossambicensis
Hyde, M.A., Wursten, B.T., Ballings, P. & Coates Palgrave, M. (2019). Flora of Mozambique: Species information: Entada mossambicensis.
https://www.mozambiqueflora.com/speciesdata/species.php?species_id=167780, retrieved 20 July 2019

redpajama_set_name: RedPajamaCommonCrawl


text:
How universities are levelling up opportunity
The Government has set a clear ambition to level up opportunity and investment across the regions of the UK and unleash the country's full potential. We share that ambition.
Russell Group universities strive to serve the whole of the UK as educators, leaders in research and innovation, as business incubators and as the gateway to people and ideas from around the world. In turn, our institutions have become anchors for growth and investment in their local, regional and national communities and are helping to transform many of our major cities through the high-value jobs, businesses and overseas investment they attract.
19 of the 24 Russell Group universities are located outside of London, based in cities in every nation and region of the UK. Together, they generate around £87 billion for the UK economy every year through their research, teaching, exports, local buying power and other activities – but we want to do even more.
Investing in place-based economic growth, in fundamental research, in key strategic science-based missions and in the talent pipeline for future high-level skills will create jobs, help realise the levelling-up ambition and boost our knowledge economy as we work to overcome Covid-19.
Read the full briefing which covers how Russell Group universities are playing their part in levelling up opportunity and investment across the regions and nations of the UK:
Levelling up across the country
Robot uses machine learning to harvest lettuce
Engineers have trained a 'Vegbot' to recognise and harvest iceberg lettuce, using computer technology.
Improving access to maternity care in developing countries
Of the thousands of maternal deaths worldwide each year, 99% occur in the developing world. This shocking marker of global inequality puts improving maternal health and reducing maternal mortality high on global policy agendas. Research into social, economic and structural barriers to maternity care carried out at King's College London, has led to improvements in the delivery and design of maternal care worldwide.


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In today's Sun: they don't call them Cons for nothing
Truly shocking – and unnecessary.
If senior people within the Conservative Party of Canada conspired to rig the May 2011 election – and, increasingly, it looks like they did – what are the consequences?
For Stephen Harper's party, the penalties could be very, very significant. They range from fines and jail time, to deregistration of Harper's party and liquidation of its assets.
A recap: as has been well-documented in the media, Conservatives used automated pre-recorded "robocalls" to contact voters in ridings across the country to provide them with false and misleading information about polling stations. Other voters were called late at night and, they say, harassed and intimidated.
Conservative Socialist says:
If the accusations are true, then of course there has to be consequences.
Should the election be overturned? As you said in your article, the Conservatives would have won the damn thing anyway. You can't punish a whole swath of the electorate by denying them political representation even if the bastards they voted for acted like bastards. I suppose that where the robocalls had the most effect would be in close ridings where Conservatives eked out a narrow victory. Should those MPs be forced to resign and the runner-ups be sworn in? Or a re-do in those ridings for by-elections?
Call me cynical, but there has always been corruption and dirty underhanded tactics in politics. The history of electoral politics is rife with vote rigging, ballot stuffing and tossing out votes.
Eventually the public will tire of the Conservatives and it's scandals and the bums will be voted out in the next election. De-registering the Conservative party would just cause a new registered conservative party (by another name) and the centre-right vote will coalesce with them.
Let there be tamper-proof electronic voting whose counting mechanisms are fair and transparent (while also preserving the anonymous ballot).
Big Daddy says:
I see the Conservatives are drawing some kind of equivalency between Vikileak (a nasty but not illegal act) and trying to rig an election (a crime punishable by 5 years in jail) I think they are grasping at straws
Kingsley says they could also be facing charges under Canada's Criminal Code:
"The people who were making those calls, if they knew what they were doing, in my view, this could also constitute an infraction to the statute," says Kingsley. "If you're hired by somebody to say you're somebody else and you know that, then you're really asking for trouble."
This violation, however, is not found in the Canada Elections Act. Instead, Section 403 of the Criminal Code finds individuals who fraudulently personate others "(a) with intent to gain advantage for themselves or another person" or "(c) with intent to cause disadvantage to the person being personated or another person" guilty of identity fraud. On an indictment, the convicted faces up to 10 years in prison.
http://www.ottawacitizen.com/news/Allegations+unprecedented+elections+chief+says/6218981/story.html#ixzz1nfkhg9vv
MississaugaLibPeter says:
In the heart of HarperLand …
http://www.calgaryherald.com/news/This%2BZimbabwe/6219844/story.html
… The Calgary Herald makes me proud to have worked there for many years!
patrick deberg says:
I find it astounding that the troops that have spent 10 years in Afghanistan fighting for democracy have to come home to a government that purports to love these ideals above anything else then launches a full out war on democracy itself. And to see the CPC in the house hide and deflect from the truth. At least where they stand on true democracy is now in plain sight. Any true conservative in good conscience can not stand behind this Miscarriage of Justice that seems to spread wider and wider each day. This action is anti Canadian. If you love this country do not support this treason.
I thought Chantal had an interesting perspective today:
http://www.thestar.com/news/canada/politics/article/1137648–hebert-robo-call-accusations-raise-uncomfortable-questions
Cath says:
Good column WK! All this does is add another reason and another party for the public to lose trust in our electoral system…..like we needed another reason.
I think Hebert's column a good piece today too.
We need a full Public Inquiry!
And in the meantime no legislation should be passed.
Nadine Lumley says:
best. week. of. my. life.
Uber lick-spittle and Harper Bum Boy Dean Del Mastro announces that Papa Doc Harper's Con-Con Macoutes are going to go after the misguided Adam Carroll in Committee for the Viki-leaks.
Del Mastro is quoted as saying: "This is just the latest in a long history of shady Liberal practices that harm our democracy. These nasty, dirty Internet tricks were deeply personal and fall short of the standard of behaviour that Canadians have come to expect,"
As stupid as Carroll was to engage in this low-brow stuff, he didn't publish anything that was not a matter of public record.
We have become a banana republic if this nonsense prevails!


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Supporting our Mission
The Board of Trustees is volunteer based and supports the work of KIPP MA by providing mission-based leadership and strategic and fiduciary governance.
Board Agenda & Meeting Minutes
Amanda Seider
Amanda joined the KIPP MA Board in 2011. She is currently the Massachusetts Executive Director at OneGoal, a national organization that works to close the college degree divide between students from low-income communities and their peers from high-income areas. Amanda began her career as a Teach For America corps member in Atlanta, where she was a fourth grade teacher. She is a native of Dorchester, and a graduate of Boston Public Schools. She holds an AB from Harvard College, and a Master's Degree in anthropology from Emory University.
Close Bio
Matt Fates
Matt has worked with KIPP MA for a number of years on various projects and committees, but this is his first term on the Board of Directors. Matt is a General Partner at Ascent Venture Partners in Boston, a leading early stage technology venture capital firm. Over the past 15 years at Ascent, Matt has focused on investments in emerging tech fields such as data analytics, business SaaS and security. Prior to Ascent, Matt worked at Norwest Venture Partners, where he worked on enterprise technology venture investments and at Alex Brown & Sons, a leading technology investment bank, where he helped execute both IPO and M&A transactions. Matt was a double major in computer science and economics at Yale University where he was also captain of the rugby team. He later earned an MBA from the Tuck School of Business at Dartmouth (Tuck Scholar). Matt was also an Overseer at the Boston Museum of Science and an advisor to the Sarah Greenwood School in Dorchester.
Nikki Barnes, Ex-Officio
Nikki is the Executive Director of KIPP Massachusetts. Nikki joined the KIPP MA Team and Family in 2013 as a 6th grade humanities teacher at KIPP Academy Boston Middle School. Nikki has spent her professional career teaching in and advocating for public schools. She has over 20 years of classroom experience in elementary, middle and high school.
After serving as the Dean of Students at KIPP Academy Boston in 2014, she became the School Leader in 2015. Under her leadership, KIPP Academy Boston experienced some of the highest student growth in the state of Massachusetts, including three grade levels performing among the top ten schools in the KIPP Network with the highest reading growth on the Measure of Academic Progress (MAP) assessment
Nikki's accomplishments as a teacher include being the first Black classroom teacher to earn National Board Certification in the state of Virginia. She was also one of two teachers chosen to represent the state of Virginia at the National Teacher Forum in 2000 held in Washington, DC. She also has nearly 10 years of experience working in educational non-profit organizations focusing on teacher quality issues and minority community outreach including overseeing a multi-million dollar partnership with The Tom Joyner Foundation to increase the number of fully licensed teachers of color in high minority, high poverty districts.
Nikki is a graduate of Virginia Polytechnic University (1991) and Virginia Commonwealth University (2003) where her graduate research around Teacher Leadership led to the creation of the VCU Center for Teacher Leadership.
Nikki is the proud mother of her two children: Adrianna and Jordan, both of whom are teachers at KIPP Boston.
Tom Beecher
Tom is the President of Kate Farms, a medical nutrition company that offers plant-based formulas designed for improved tolerance with organic ingredients and without dairy, soy, gluten, corn or nuts. Prior to Kate Farms, he was the CEO of Cartera Commerce, a venture-backed, Boston-based loyalty marketing company. Prior to Cartera, Tom was CFO and later CEO at Imagitas and a consultant at Bain & Co. He attended Dartmouth College and Harvard Business School. Tom is married and has two children.
Doug Borchard
Doug joined the KIPP MA Board in 2014, where he Chairs the Compensation Committee and serves on the Teaching and Learning Committee. Doug is a Managing Partner and Chief Operating Officer at New Profit. In addition to managing New Profit's finances and internal operations, Doug has worked closely with several of New Profit's portfolio organizations, including Achievement First, iMentor, KIPP, Year Up, and currently serves on the boards of Leading Educators, New Classrooms, and UnboundEd. Prior to joining New Profit, he worked as a program and logistics officer with Save the Children, where he was part of a team that started up field operations in the Sudan, and created and managed a multi-million dollar relief and development operation. Doug has served on the boards of a number of growing organizations, including Venturcom, iMarket, and Computers for Youth. He graduated from Princeton with a BS in engineering, and received his MBA from the Stanford Business School, where he was an Arjay Miller Scholar.
Ivelisse Gonzalez
Ive is a Human Resources professional with over 20 years of successfully developing and delivering Human Resources programs to include talent acquisition, diversity and inclusion, employee relations, talent management, federal and state regulatory compliance in various industries. Ive joined Eastern Bank, the largest and oldest mutual bank in the country, in 2004. She currently holds the position of Vice President, Talent Acquisition and Inclusion Director and is responsible for identifying and addressing strategic HR issues that impact business performance to include implementing and managing talent acquisition strategies, diversity and inclusion programs and partnership opportunities with diverse, civic, professional and nonprofit organizations. Proudly born and raised in Lynn, MA, Ive is committed to the community serving on several boards including Family and Children's Services of Greater Lynn, Lynn Business Education Foundation, La Vida, Inc., the Lynn Area Chamber of Commerce, as well as serving as a Mentor with Raw Arts Works. Ive is passionate about giving kids and young adults the opportunity to learn and thrive. Ive holds a Bachelor's degree in Sociology with a minor in Business Administration from Merrimack College and a Masters degree in Management Communications from Emerson College. Additionally, she is an alumna of three leadership programs for high potential professionals, The Emerging Leaders Program at UMASS Boston, The Partnership, Inc., and Conexión. She is also a graduate of the INROADS program.
Michael Kendall
Michael is currently serving his fifth year on the KIPP MA Board. In his five years on the board, Michael has seen KIPP MA grow from one middle school serving nearly 320 students in Lynn, MA, to two districts in Lynn and Boston, MA serving nearly 1,900 students in grades K-12. He is a partner in Goodwin Procter LLP's Private Equity and Technology Companies Group, and focuses his corporate finance and securities practice on private equity and venture capital transactions, mergers and acquisitions, public securities offerings and representing emerging growth companies. He advises a variety of companies in industries including software, information technology, telecommunications, information services, biotechnology, healthcare, financial services, and retail. Michael is listed in Chambers USA: America's Leading Lawyers for Business, The Best Lawyers in America, Boston's Best Lawyers, and has been recognized as a Massachusetts "Super Lawyer." Michael is a graduate of Boston University School of Law and Boston University Graduate School of Management.
Paul Ketterer
Board Treasurer
Paul is responsible for investment origination and asset management for AEW's series of Opportunity Real Estate Funds. He leads the firm's hospitality group with responsibility for investment origination and asset management for all hotel investments in North America and has been involved in transactions with all of the major hotel brands. Additionally, Paul is also responsible for office, retail, residential and industrial acquisitions in the greater Boston, MA., Chicago, Il., and Washington, D.C. regions. Since joining AEW in 2004, he has been involved in over $1.5 billion dollars of equity and debt related real estate transactions. Additionally, Paul currently manages a portfolio of investments with a gross value of approximately $750 million. During his tenure at AEW, Paul has been involved in acquisitions, dispositions, financing, capital restructurings, development and asset management for a wide variety of commercial real estate product types across North America. Prior to beginning his commercial real estate career, Paul was a professional musician and a teacher at, and director of Harvard University affiliated Child Care Centers. He is a member of the Urban Land Institute (ULI) and is a graduate of Tufts University (B.A.) and Boston University School of Management (MBA). Paul lives in Winchester with his wife and two sons. He continues to be an active musician and coaches multiple youth sports.
Shenkiat Lim
Shenkiat (Shen) is the Vice President for People Strategy at City Year, an organization that provides additional support to students in high-needs communities to ensure they reach the 10th grade on track and on time. Prior to joining City Year, Shen was Vice President for Staff Support & Administration at Teach For America where he led the team responsible for human assets strategy, compensation, benefits, and HRIS. Other professional experiences include product development at Fidelity Investments and HR consulting with the Hay Group (now Korn Ferry). Shen's journey in social justice began as a Teach For America corps member, when he spent two years teaching fifth grade social studies in rural Mississippi. Since that time, Shen has been committed to supporting the work of organizations like KIPP that seek to ensure that all kids have the opportunities they deserve. Shen is on the board of the The Collective-Massachusetts (Teach For America's association for alumni of color) and plays violin with the Longwood Symphony Orchestra. He is a graduate of Harvard University and received his MBA from the MIT Sloan School of Management.
Stephanie Pierre-Louis
Stephanie Oliveras is a Senior Vice President, Senior Relationship Manager for Bank of America Merrill Lynch's Healthcare, Education & Not for Profit Group (HENP). Stephanie is responsible for leading commercial banking teams that deliver financial and treasury solutions to clients located in New England.
Stephanie joined Bank of America in 2006 and spent twelve years in Community Development Banking, a division of Commercial Real Estate Banking. Stephanie leveraged a deep understanding of the real estate industry to effectively structure financing packages for affordable multifamily, senior, mixed-use and supportive housing projects. Most recently, she led the effort to expand the charter school lending platform nationally. She brought an interesting perspective to the role having worked in the Bank's NYC, LA, Washington D.C. and Boston markets.
Stephanie is passionate about serving charter schools that focus on closing the achievement gap. She serves as a Board of Ambassador member for Brooke Charter School and Excel Academy. She also serves on the finance committee for KIPP MA. She is an avid traveler, enjoys volunteering for homeless organizations and is a financial literacy advocate/volunteer.
Shellina Semexant
Shellina Semexant is a devoted wife, mother of three children, educator, and advocate for social justice. She holds a BA from Lesley College and an MBA in Special Education from Grand Canyon University. She has been a resident of the City of Boston for over three decades. Shellina has been part of the KIPP Boston community for over six years, and is the President of KIPP Boston Parent Council. Shellina is the co-founder of KIPP Academy Boston's Families and KIPPsters Together (FAKT) Parent Engagement Team. She is the Program Coordinator for Boston Schools Finder, a non-profit organization that helps "families in choosing a school that is the right fit for their families". Shellina also serves as a Parent Leader for Union Capital Boston where they believe in "transforming social capital into opportunities by rewarding communities' engagement". Shellina's mission is to engage families in the discussion of education, equity, and equality around Boston by closing the gap of engagement between families and schools.


The Maldives is hot and sunny all year, with average temperatures of between 23ºC / 74ºF and 31ºC / 88 ºF, making it an ideal year-round destination for some fun in the sun. There are, however, better times of the year to travel to the Maldives, as some months see higher rainfall and winds than others. The island nation enjoys the best weather between November and April with full days of sunshine, warm air and sea temperatures, and very little rainfall. The monsoon season runs between May and October, peaking around June, with the northern atolls seeing the highest rainfall between May and November, and the southern atolls between November and March.
The dry season in the Maldives typically runs from around mid-December through early May, but these tend to change each year. The Northeast Monsoon season, which is most prevalent in the northern atolls, actually occurs between November and March, but due to being the dry season, it rarely amounts to anything more than a quick downpour or shower, a couple times a week. The rainy season in the Maldives runs from early May through mid-December, with the Southwest Monsoon season (in the southern atolls) officially being in July and August.
Typical of the tropics, when it rains in the Maldives, it pours down heavily for a short time and then clears up just as quickly. Even during the dry season, it is not unusual to have a brief, torrential downpour in the afternoon, followed by a beautifully clear and balmy evening. During the rainy season, it tends to rain more at night, so days are sunny and bright with just a few interspersed clouds and some light rainfall. It's rare to have more than a few cloudy days per week with sunny days in between.
It is relatively humid all year round in the Maldives with a typically muggy tropical feel, which takes a few days to become acclimatized to. The temperature, however, rarely peaks much above the averages, so even the high humidity is never unbearable like it can be in Mediterranean Europe during the hottest summer months.
Being an archipelagic island nation strung through a vast portion of the Indian Ocean, steady winds cross through the Maldives throughout the year, bringing cool breezes to the islands. During the Southern Hemisphere winter, which lasts from March until October, the North-East and South-West monsoons bring off-shore winds that create beautiful, peaking surfing waves for those who are there to surf.
Here is a month-by-month guide to the weather in the Maldives and the best times to visit.
The Maldives' weather in January sees hot, sunny days with low humidity and plenty of sunshine. There might be a slight chance of some rain, but this tends to occur in the afternoons and passes over quickly. The ocean is clear and warm with excellent visibility and is perfect for snorkeling and scuba-diving.
February is probably one of the best months to visit the Maldives. It's the nation's driest month, with less than 70 mm of monthly rainfall, around 10 hours of sunshine every day, and balmy temperatures of 30°C / 86°F plus. Visibility is excellent for snorkeling and scuba-diving.
March in the Maldives sees temperatures rising to an average of 30°C / 88°F which are great for long, lazy days on the beach, sunbathing, snorkeling and swimming. There might be a few possible short bursts of rain, which offer relief from the steaming temperatures, and visibility is excellent for snorkeling and scuba-diving. March is also the beginning of the surfing season in the Maldives, which brings beautiful waves and last until October. During this 'surfing season,' the biggest waves are most likely to occur between June and August, caused by storms in the Roaring Forties bringing big swells to the archipelago.
This is another gorgeously hot month in the Maldives with temperatures reaching into the mid-30s / 80s. April is officially the end of the dry season, and frequent showers begin to occur around the middle of the month. The air also becomes more humid, however, visibility for snorkeling and scuba-diving is excellent.
May is officially the beginning of the wet season with hot, muggy days, average temperatures of 31°C / 88°F, and a high risk of heavy rainfall and storms during the day. Due to the heavy rainfall and higher levels of plankton in the water, visibility for snorkeling and scuba-diving is slightly reduced, but still enjoyable. Be aware that if there are thunderstorms in the area, it's not a good idea to be in the water, so head down to the beach for some water-based activities. May also sees the start of the holy month of Ramadan (known as Ramazan in the Maldives), bringing some restrictions to local islands.
While June has a high chance of rainfall and reduced visibility due to the plankton in the water, this is a fantastic time to dive with manta rays and whale sharks that come to feed on the vast amounts of plankton in the water. This month sees many of the resorts offering special deals where visitors can enjoy the plethora of non-beach and water-based amenities that they have to offer. The holy month of Ramadan (Ramazan) continues into June.
The Maldives' weather in July is hot and humid, with short heavy downpours. This is a particularly good time of the year for surfers with the largest waves stemming from the storms in the Roaring Forties bringing big swells to the archipelago. Swell is amazingly consistent during this time of the year, with the average wave measuring two to eight-foot in height. It is also still a great time to dive with manta rays and whale sharks that come to feed on the enormous amounts of plankton in the water. The 26th July is the Maldivian Independence Day and sees parades and public celebrations on most of the resort islands.
August is hot, humid and wet, with an average of seven hours of sunshine each day and short heavy downpours throughout the day. Visibility is slightly reduced due to the plankton in the water, but many of the resorts offer enticing deals, making it a favorite time to visit.
September in the Maldives is one of the wettest months with average maximum temperatures of 30°C / 86°F and around seven hours of sunshine each day. Due to the heavy rainfall and higher levels of plankton in the water, visibility for snorkeling and scuba-diving is slightly reduced, but still enjoyable with excellent chances of seeing manta rays and whale sharks.
October is the Maldives' wettest month, with high humidity and full days of rain. This is the last month of the Maldives' surfing season, with the South-West monsoons, which occur between May and October, providing outstanding surfing the Northern and Central Atolls. Due to the heavy rainfall and higher levels of plankton in the water, visibility for snorkeling and scuba-diving is slightly reduced, but still, a great time to dive with manta rays and whale sharks.
November in the Maldives is the end of the wet season with short showers in the afternoons and otherwise bright, sunny days. Temperatures average around 30°C / 86°F, and the visibility of the water begins to clear of the plankton, making for good scuba-diving and snorkeling.
The climate in December is primarily hot and dry with showers around the middle of the month. This time of year is ideal for a mid-winter escape and some sun. Christmas and New Year are particularly popular and may include minimum stays at some resorts.


text:
Carroll comments on Sarkisian hiring
By Rich Hammond | rhammond@scng.com | Orange County Register
Pete Carroll commented on USC's hiring of Steve Sarkisian today, as well as Ed Orgeron's resignation. Sarkisian and Orgeron both worked under Carroll as assistant coaches at USC. Thanks to the Register's Michael Lev for passing along these quotes from Seattle…
CARROLL: "I'm thrilled for him. This is a lifelong dream for him. As a kid who grew up in Southern California, there's no coach they could have hired that understands L.A. better and what that's all about. That's my opinion. He has a tremendous sense for the area and the schools and the coaches and the traditions and all of that. That's why it was such a big deal for him to get that opportunity. He had a great time here at Washington. He loved it. He did a great job with them. But it's just a chance to go home and do it at a great university. There's a number of guys who could have gotten the job and done a great job with it. I think Sark will do an extraordinary job.
"I'd like to say this too: Eddie Orgeron did an incredible job. I thought it was one of the most incredible illustrations of leadership and direction and amazing ability to turn something like that. I'm so impressed with what he did. It's unfortunate that he doesn't get the job. But there's only one spot there. I'm sure he's going to do something great too."
Rich Hammond | Reporter
Rich Hammond was a high school senior when the Rams left town in 1995, and now he's their beat writer for the Southern California News Group. A native of L.A., Rich broke in at the Daily Breeze as a college freshman and also has covered USC, the Kings, the Lakers and the Dodgers. He still loves sports and telling stories. Don't take the sarcastic tweets too seriously.
rhammond@scng.com
Follow Rich Hammond	@Rich_Hammond


text:
VIRAL VIDEO: Woman cooking in Newport News gets into crabby, steamy situation
Virginia Simmons of Newport News decided she'd steam her own crabs for the first time. She recorded her efforts and the fight she had with her crabs.
Published: 7:37 PM EDT July 25, 2018
NEWPORT NEWS, Va. (WVEC) — All she wanted to do was steam crabs for the first time. Unfortunately, for a Newport News woman, the crabs had a different agenda.
Virginia Simmons learned the hard way how not to steam crabs on Saturday. She shared a hysterically fantastic video, that has over 6.7 million views, of her journey to cook some crabs. She explained that her brother convinced her to steam the crabs, even though she has only boiled them her whole life.
Simmons' gets into a 'pinch' when she tried to empty the bag of crabs into a steam pot. Several crabs escape, and it's complete chaos trying to get them back into the pot. One crab even ends up on her floor and fights her tongs to try and escape.
Several minutes of the viral video is Simmons' trying to get all the crabs back into the pot.
At the end of the video, when all the crabs are in the pot, she toasts to the crabs' memory and says "let the steaming begin."
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► Make it easy to keep up to date with more stories like this. Download the 13News Now App.


TheatreWorks, New Milford: Leave it to Ken Ludwig to write a farce with a title that leads one to believe that the comedy is going to feature two actresses. Well, it doesn't. The thing is that the leading ladies in this show are actually male actors pretending to be women. Right from the naming of this farce, Ludwig doesn't miss an opportunity for wit. The men are Shakespearean actors. They take their work seriously and are crushed when their Scenes From Shakespeare bottoms out at a Moose Lodge event. That their last names are Clark and Gable is another example of Ludwig not missing an opportunity for fun with words.
Mind you, this play is not as funny or clever as Ludgwig's Lend Me a Tenor, but it is funny enough to keep an audience well entertained.
The production is polished thanks to the skills of Michael Bolinski. If this director's name sounds familiar, it's because he has directed top notch productions at just about all of the area's local theaters from Goshen and Thomaston, to The Gary, The Olivia and many others as well. He never shies away from a challenge, whether it's directing Waiting for Godot or Steel Magnolias. This time he takes on a farce that requires a great deal from the two leading men. It becomes obvious very quickly that this comedy has similarities to Some Like It Hot, which featured Tony Curtis and Jack Lemmon playing women in order to get work as musicians. Ludwig has his two men parading as a wealthy old woman's lost nieces, but both men, just like the men in the movie, end up falling in love with female characters.
If the two men convince the dying aunt that they are her nieces, then they can inherit millions of dollars. Considering that they are penniless, they give it their all. Enter Meg, played with an extra dose of charm to win over the audience by Carey Van Hollen. Meg is engaged to be married to the Rev. Duncan Woolery played with just the right amount of arrogance and insensitivity by Daniel Basiletti. Duncan doesn't want to go to see Clark and Gable in a Shakespeare production at the Moose Lodge, which Meg has been so looking forward to.
Hal Chernoff and Rob Pawlikowski deliver fine performances dressed as women, but they really shine when they play their Shakespearean roles with great comedic panache. Ron Dukenski as the doctor who keeps thinking erroneously that Aunty is dead also does a good job as do Mary Wilson, Edwin Arce II, and Victoria Calamito.
Susan Aziz's costumes contribute significantly to the comedy with her outrageous Shakespearean renderings of Cleopatra and Hamlet. Judy Tringali's set is simply superb with a central staircase and plenty of doors that get use throughout this farce.


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text:
package com.intellij.usages;

import com.intellij.navigation.NavigationItem;
import com.intellij.psi.PsiNamedElement;
import consulo.ui.image.Image;

import javax.annotation.Nonnull;

/**
 * @author Maxim.Mossienko
 */
public class PsiNamedElementUsageGroupBase<T extends PsiNamedElement & NavigationItem> extends PsiElementUsageGroupBase<T> {

  public PsiNamedElementUsageGroupBase(@Nonnull T element, Image icon) {
    super(element, icon);
  }

  public PsiNamedElementUsageGroupBase(@Nonnull T element) {
    super(element);
  }
}

redpajama_set_name: RedPajamaGithub


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Individuals in the Redlands area have plenty of reasons to store their furniture. For some, they need a short-term storage unit while they're between permanent homes. Others may have antique furniture they cannot bear to part with but may not fit in their current home. Still some may be saving furniture for a child who will be off to college or his own place in a few years. Rather than shoving these important pieces of furniture into a corner and covering them with a sheet, individuals should consider finding a safe, climate controlled, and accessible storage unit.
Self-storage units, like Vines Storage, offer clients a great solution in housing belongings hey can't keep at home, but still want to preserve. At Vines Storage the units are climate controlled and safe from environmental elements like weather, debris, and outdoor critters. Whether you need a rental solution for several weeks or several years, a small space for a few belongings, or a larger space for a houseful of gear, the staff at Vines Storage want to help you find the right solution.
Here, we provide tips for how to keep your furniture safe and protected while they're in storage.
Store the items clean. If there are spots or stains on your favorite couch, have it professionally cleaned before storing it. Even if there are no visible stains it's a good idea to give it a final wipe down as an added layer of protection. After cleaning, be sure to let the furniture dry completely before storing it so that those areas do not become discolored.
Take items apart. Items like tables, dressers, and couches often transport and store better when they are taken apart. Remove the legs, drawers, and cushions from these items, but be sure to keep them placed, or even wrapped, with the larger item to ensure pieces don't get lost.
Cover the items. Most people know to use bubble wrap or newspaper on fragile items like dishes and glassware, but mirrors, large pictures, and legs from chairs and tables should also be wrapped with cloths, sheets, or blankets. This protects the furniture from dirt and debris while allowing the air to circulate.
Consider layout. When placing items in your storage unit, give some thought to location. As a general rule of thumb, you'll want to keep space between your items so air can flow and items will be protected from damage; however, lightweight items can be placed on top of heavier items.
For more information about storing your furniture, visit Vines Storage today.


text:
Bengaluru unlikely to host Premier Badminton League matches
Bengaluru is unlikely to host Premier Badminton League (PBL) matches, due to the unavailability of the Sree Kanteerava Indoor Stadium.
Ashwin Achal
BENGALURU 09 January, 2020 14:14 IST
The PBL commences on January 20 in Chennai, before moving to Lucknow on January 25. - Nagara Gopal
Bengaluru is unlikely to host Premier Badminton League (PBL) matches, due to the unavailability of the Sree Kanteerava Indoor Stadium. Hyderabad has emerged as the frontrunner in the search for a replacement venue.
In the original schedule, Bengaluru was set to host two league stage matches, followed by the semifinals and the final (February 5 to 9). "Bengaluru is unlikely to host matches this season. We are looking to shift the matches to Hyderabad," Atul Pande, Managing Director, Sportzlive, the official license holder of PBL told Sportstar on Thursday.
SCHEDULE| Premier Badminton League: Fifth edition to start on Jan 20
PBL organisers are disappointed that government authorities did not grant permission to use the Sree Kanteerava Indoor Stadium. The Mini Olympics, a multi-sports event organised by the Karnataka Olympic Association is scheduled to be held at the stadium in the same week.
"The league commences in just about 10 days, so we cannot wait for much longer. It is a pity because the people of Bengaluru have been denied the chance to see big stars like P.V. Sindhu and Tai Tzu in action," Pande said.
The PBL commences on January 20 in Chennai, before moving to Lucknow on January 25. The Hyderabad leg starts on January 29, and if the city is chosen as the replacement venue, the league will stay on there until its conclusion.
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