text:
\section{Extending the definition of admissibility}

If $G$ is a locally profinite group and $k$ is an algebraically closed field then a $k$-representation of $G$ is a vector space $V$ with a left, $k$-linear $G$-action. Let ${\mathcal M}_{c}(G)$ denote the poset of
pairs $(H, \phi)$ where $H$ is a subgroup of $G$, which is compact open and $\phi : H \longrightarrow k^{*}$ is a continuous character.

A representation $V$ is called smooth (\cite{BH06} p.13) if
\[ V = \bigcup_{K \subset G,  \ K \ {\rm compact, open}} \ V^{K} .\]
$V$ is called admissible (\cite{BH06} p.13) if ${\dim}_{k}( V^{K}) < \infty$ for all compact open subgroups $K$.

Notice that, if $v_{i} \in V^{K_{i}}$ for $i=1,2$ with $K_{i}$ compact open then
a linear combination $a_{1} v_{1} + a_{2} v_{2} \in V^{K_{1} \bigcap K_{2}} $ for $a_{i} \in k$ with
$K_{1} \bigcap K_{2}$ compact open so that
\[ V =  \bigcup_{K \subset G,  \ K \ {\rm compact, open}} \ V^{K}  = {\rm Span}_{K \subset G,  \ K \ {\rm compact, open}} \  V^{K}.  \]

The smooth representations of $G$ form an abelian category.

Define a subspace of $V$, denoted by $V^{(H, \phi)}$, for $(H, \phi) \in {\mathcal M}_{c}(G)$ by
 \[  V^{(H, \phi)} = \{ v \in V \ | \ g \cdot v =  \phi(g)v \ {\rm for \ all} \ g \in H \}   . \]
 Hence $V^{K} = V^{( K,  1)}$ if $1$ denotes the trivial character.

 We shall say that $V$ is ${\mathcal M}_{c}(G)$-smooth\footnote{In \cite{Sn20} I made a childish typographical slip-up, writing $\bigcup$ instead of $\Sigma$ in this definition. Hence this time I have written ${\rm Span}$. In my current time-shortage (\cite{JMOS18} and \cite{XX})  the reader will probably find me making a number of (I hope inconsequential) slip ups.}  if
 \[ V = {\rm Span}_{ (H, \phi) \in {\mathcal M}_{c}(G)} \ V^{(H, \phi)}.\]
 In addition we shall say that $V$ is ${\mathcal M}_{c}(G)$-admissible if
 ${\rm dim}_{k}V^{(H, \phi)} < \infty$ for all  $(H, \phi) \in {\mathcal M}_{c}(G)$.

 \begin{proposition}{$_{}$}
 \label{1.1}
 \begin{em}

 Let $G$ be a locally profinite group and let $k$ be an algebraically closed field. Let $V$ be a $k$-representation of $G$. Suppose that every continuous, $k$-valued character of a compact open subgroup of $G$ has finite image. Then $V$ is
 ${\mathcal M}_{c}(G)$-admissible if and only if it is admissible.
 \end{em}
 \end{proposition}

 Let us begin by recalling, from (\cite{Sn18} Chapter Two \S1), induced and compactly induced smooth representations.

\begin{definition}{Smooth induction}
\label{1.2}
\begin{em}

Let $G$ be a locally profinite group and $H \subseteq G$ a closed subgroup. Thus $H$ is also  locally profinite. Let
\[   \sigma : H \longrightarrow  {\rm Aut}_{k}(W)    \]
be a smooth representation of $H$. Set $X$ equal to the space of functions $f: G \longrightarrow W  $ such that (writing simply $h \cdot w$ for $\sigma(h)(w)$ if $h \in H, w \in W$)

(i) \  $f(hg) = h \cdot f(g)$ for all $h \in H, g \in G$,

(ii)  \  there is a compact open subgroup $K_{f} \subseteq G$ such that $f(gk) = f(g)$ for all $g \in G, k \in K_{f}$.

The (left) action of $G$ on $X$ is given by $(g \cdot f)(x)= f(xg)$ and
\[   \Sigma :  G  \longrightarrow  {\rm Aut}_{k}(X)  \]
gives a smooth representation of $G$.

The representation $\Sigma$ is called the representation of $G$ smoothly induced from $\sigma$ and is usually denoted by $\Sigma = {\rm Ind}_{H}^{G}(\sigma)$.
\end{em}
\end{definition}

\begin{definition}{${\mathcal M}_{c}(G)$-smooth induction}
\label{1.3}
\begin{em}

Let $G$ be a locally profinite group and $H \subseteq G$ a closed subgroup. Let
\[   \sigma : H \longrightarrow  {\rm Aut}_{k}(W)    \]
be an ${\mathcal M}_{c}(H)$-smooth representation of $H$. Set $X$ equal to the space of functions $f: G \longrightarrow W  $ such that (writing simply $h \cdot w$ for $\sigma(h)(w)$ if $h \in H, w \in W$)

(i) \  $f(hg) = h \cdot f(g)$ for all $h \in H, g \in G$,

(ii)  \  Each $f \in X$ may be written as a linear combination of the form $f = \sum_{i=1}^{n} \  a_{i}f_{i}$ where $a_{i} \in k$ and for each $1 \leq i \leq n$
there is $(K_{f_{i}}, \phi_{f_{i}}) \in {\mathcal M}_{c}(G)$ such that
$f_{i}(gk) = \phi_{f_{i} }(k) f_{i} (g)$ for all $g \in G, k \in K_{f_{i}}$.

The (left) action of $G$ on $X$ is given by $(g \cdot f)(x)= f(xg)$ and
\[   \Sigma_{{\mathcal M}_{c}} :  G  \longrightarrow  {\rm Aut}_{k}(X)  \]
gives an ${\mathcal M}_{c}(G)$-smooth representation of $G$.

The representation $\Sigma_{{\mathcal M}_{c}} $ is called the representation of $G$ ${\mathcal M}_{c}$-smoothly induced from $\sigma$ and is will be denoted by $\Sigma_{{\mathcal M}_{c}} = {\rm IND}_{ H}^{G}(\sigma)$.
\end{em}
\end{definition}

We just pause to check the following:
\begin{lemma}{$_{}$}
\label{1.4}
\begin{em}
 If $f \in X$ in Definition \ref{1.3} and $g \in G$ then $g \cdot f \in X$ also.
\end{em}
\end{lemma}

{\bf Proof:}

Suppose that $f \in X$ and $(K_{f_{i}}, \phi_{f_{i}}) \in {\mathcal M}_{c}(G)$ satisfy the second condition of Definition \ref{1.3}. Define $g( (K_{f_{i}}, \phi_{f_{i}}))$ to be the pair consisting of the group $gK_{f_{i}}g^{-1}$ with character
 \[   (g^{-1})^{*}(\phi_{f_{i}}): gK_{f_{i}}g^{-1} \longrightarrow  k^{*} \]
where, for $k \in K_{f_{i}}$,
we set $(g^{-1})^{*}(\phi_{f_{i}})(gkg^{-1}) = \phi_{f_{i}}(k)$. Therefore
\[  \begin{array}{ll}
(g \cdot f_{i})(g'gkg^{-1}) &  = f_{i}(g'gkg^{-1}g) \\
\\
& = f_{i}(g'gk) \\
\\
& = \phi_{f_{i}}(k) f_{i}(g'g) \\
\\
& = (g^{-1})^{*}(\phi_{f_{i}})(gkg^{-1}) f_{i}(g'g) \\
\\
& =  (g^{-1})^{*}(\phi_{f_{i}})(gkg^{-1})   (g \cdot f_{i})(g')  ,
\end{array}   \]
as required. Clearly action by $g \in G$ preserves condition (i) of Definition \ref{1.3} $\Box$

\begin{dummy}{The c-IND variation}
\label{1.5}
\begin{em}

Inside $X$ let $X_{c}$ denote the set of functions which are compactly supported modulo $H$. This means that the image of the support
\[   {\rm supp}(f) = \{ g \in G \ | \  f(g) \not= 0  \}  \]
has compact image in $H \backslash G$. Alternatively  there is a compact subset $C \subseteq G$ such that $  {\rm supp}(f) \subseteq H \cdot C$.

The $\Sigma_{{\mathcal M}_{c}}$-action on $X$ preserves $X_{c}$, since $ {\rm supp}(g \cdot f) =  {\rm supp}(f) g^{-1} \subseteq HCg^{-1}$, and we obtain $X_{c} =  c- {\rm IND}_{H}^{G}(W) $, the compact induction of $W$ from $H$ to $G$ \footnote{I have not yet bothered to check the following:  Note that this condition requires, in Definition \ref{1.3}, at first sight, that $f$ is compactly supported modulo $H$ but not necessarily the individual $f_{i}$'s.}.
\end{em}
\end{dummy}

 \begin{lemma}{$_{}$}
 \label{1.6}
 \begin{em}

 (i) \ If $K$ is an open subgroup of $G$ and $V$ is an  ${\mathcal M}_{c}(G)$-smooth representation then ${\rm Res}_{H}^{G}(V)$ is an  ${\mathcal M}_{c}(H)$-smooth representation.

  (ii) \  If $\chi : G \longrightarrow k^{*}$ is a continuous character and $V$ is an
  ${\mathcal M}_{c}(G)$-admissible representation then $V \otimes_{k} k_{\chi}$ is also an ${\mathcal M}_{c}(G)$-admissible representation. Herre $k_{\chi}$ is $k$ acted upon by $G$ via the character $\chi$.
 \end{em}
 \end{lemma}

 {\bf Proof:}

 (i) \  If $v \in V$ lies in $V^{(J, \phi)}$ for some $J$ compact open in $G$ then $v \in V^{(H \bigcap J, \phi)}$ and $H \bigcap J$ is compact open in $H$. Therefore $V$ is ${\mathcal M}_{c}(H)$-smooth.

 (ii) \ This follows from the relation $(V \otimes_{k} k_{\chi})^{(H, \phi)} = V^{(H, \phi \otimes \chi^{-1})}$.

\begin{remark}{$_{}$}
\label{1.7}
\begin{em}
 Admissibility is not inherited by subgroups. For example, if $H$ is a compact open subgroup of the centre of $G$ and if $V$ has a central character $\underline{\phi}$ then ${\rm Res}_{H}^{G}(V)^{(H, \underline{\phi})} = V$.
\end{em}
\end{remark}
\begin{lemma}{$_{}$}
\label{1.8}
\begin{em}

Let
\[ 0 \longrightarrow V_{1} \longrightarrow V_{2} \longrightarrow V_{3} \longrightarrow 0 \]
be a short exact sequence of $G$-representations.

If $K$ is compact open and $(K , \phi) \in {\mathcal M}_{c}(G)$ then
\[ 0 \longrightarrow V_{1}^{(K , \phi)} \longrightarrow V_{2}^{(K , \phi)} \longrightarrow V_{3}^{(K , \phi)} \longrightarrow 0 \]
is exact.
\end{em}
\end{lemma}

{\bf Proof:}

\[ 0 \longrightarrow V_{1} \otimes_{k} k_{\phi^{-1}} \longrightarrow V_{2} \otimes_{k} k_{\phi^{-1}}  \longrightarrow
V_{3} \otimes_{k} k_{\phi^{-1}}  \longrightarrow 0 \]
is an exact sequence of $K$-representations. Applying $K$-fixed points to this sequence is exact, because $K$ is compact, and the result is the short exact sequence of $k$-vector spaces in the statement of the lemma. $\Box$

\begin{corollary}{$_{}$}
\label{1.9}
\begin{em}

Let
\[ 0 \longrightarrow V_{1} \longrightarrow V_{2} \longrightarrow V_{3} \longrightarrow 0 \]
be a short exact sequence of $G$-representations.

Then $V_{2}$ is
${\mathcal M}_{c}(G)$-admissible if and only if $V_{1}$ and $V_{3}$ are both
\linebreak
${\mathcal M}_{c}(G)$-admissible.
\end{em}
\end{corollary}
\begin{proposition}{$_{}$}
\label{1.10}
\begin{em}

Let $V$ be a smooth representation of $G$. Suppose that $K$ is a compact open subgroups and that
 $(K, \phi) \in {\mathcal M}_{c}(G)$. Then ${\rm dim}(V^{( K, \phi) }) < \infty$.
\end{em}
\end{proposition}
{\bf Proof:}

By (\cite{WCnotes} Proposition 2.1.4 p.20), the restriction of $V$ to $K$ is the direct sum of finite-dimensional irreducible $K$-representations, each appearing with finite multiplicity. If this $K$-representation is $\oplus_{\alpha} \ V_{\alpha}$ then $V^{(K, \phi) } = \oplus_{\alpha, \ V_{\alpha} = k_{\phi}}  \ V_{\alpha}$ which is finite-dimensional. $\Box$

\begin{theorem}{$_{}$}
\label{1.11}
\begin{em}

Let
\[ 0  \longrightarrow  V_{1} \stackrel{i}{\longrightarrow} V_{2} \stackrel{j}{\longrightarrow} V_{3} \longrightarrow 0 \]
be a short exact sequence of $G$-representations. Then
$V_{2}$ is ${\mathcal M}_{c}(G)$-smooth if and only if $V_{1}$ and $V_{3}$ are both ${\mathcal M}_{c}(G)$-smooth.
\end{em}
\end{theorem}

{\bf Proof:}

Assume that $V_{2}$ is ${\mathcal M}_{c}(G)$-smooth. Therefore
\[  V_{2} = {\rm Span}_{ (H, \phi) \in {\mathcal M}_{c}(G)} \ V_{2}^{(H, \phi)}.\]
Since $j( V_{2}^{(H, \phi)} ) \subseteq V_{3}^{(H, \phi)}$ and $j$ is surjective we see that
\[  V_{3} = {\rm Span}_{ (H, \phi) \in {\mathcal M}_{c}(G)} \ V_{3}^{(H, \phi)}.\]

Now suppose that $0 \not= w \in V_{1}$ satisfies $w = u_{1} + u_{2} + \ldots + u_{n}$ with
$u_{i} \in V_{2}^{(H_{i}, \phi_{i})}$ with $(H_{i}, \phi) \in {\mathcal M}_{c}(G)$. We may assume that $H = H_{1} = \ldots = H_{n}$ by taking intersections. We shall proceed by induction on $n$ and start the induction by
Lemma \ref{1.8}. By induction we may assume that $w = u_{1} + u_{2} + \ldots + u_{n}$ with
$u_{i} \in V_{2}^{(H, \phi_{i})}$ with $(H, \phi) \in {\mathcal M}_{c}(G)$ and the $\phi_{i}$'s are pairwise distinct.
We have $j(u_{1} + u_{2} + \ldots + u_{n}) = j(i(w)) = 0$. Choose $g \in G$ such that $\phi_{1}(g) \not= \phi_{2}(g)$. Then
\[  i(g \cdot w) = \phi_{1}(g) u_{1} + \phi_{2}(g) u_{2} + \ldots + \phi_{n}(g) u_{n} \]
so that
\[  i(g \cdot w - \phi_{1}(g) w ) =  (\phi_{2}(g) - \phi_{1}(g) u_{2} + \ldots + (\phi_{n}(g) - \phi_{1}(g) u_{n} . \]
By induction, since
 \[ j(  (\phi_{2}(g) - \phi_{1}(g) u_{2} + \ldots + (\phi_{n}(g) - \phi_{1}(g) u_{n}  ) = 0 ,\]
 we have
 \[  g \cdot w - \phi_{1}(g) w  \in {\rm Span}_{2 \leq s \leq n} \ V_{1}^{(H, \phi_{s})} .\]
 Similarly
  \[  g \cdot w - \phi_{2}(g) w  \in {\rm Span}_{s=1 \ {\rm or} \ 3 \leq s \leq n} \ V_{1}^{(H, \phi_{s})} .\]
 Therefore
 \[  \phi_{2}(g) w - \phi_{1}(g) w  \in  {\rm Span}_{1 \leq s \leq n} \ V_{1}^{(H, \phi_{s})}  \]
 and, since $ \phi_{2}(g)  \not=  \phi_{1}(g)$ we see that
  \[   w  \in  {\rm Span}_{1 \leq s \leq n} \ V_{1}^{(H, \phi_{s})},  \]
  as required. Therefore $V_{1}$ and $V_{3}$ are ${\mathcal M}_{c}(G)$-smooth.

 The converse follows from Lemma \ref{1.8}. $\Box$

 \begin{corollary}{$_{}$}
 \label{1.12}
 \begin{em}

 ${\mathcal M}_{c}(G)$-smooth representations form an abelian category of which ${\mathcal M}_{c}(G)$-admissible representations form an abelian subcategory.
 \end{em}
 \end{corollary}

 \begin{theorem}{$_{}$}
 \label{1.13}
 \begin{em}
  Let $H$ be a closed subgroup of $G$ and let $(\tau, U)$ be an ${\mathcal M}_{c}(H)$-smooth $H$-representation. Then

  (i) \ ${\rm IND}_{H}^{G}(\tau)$ is ${\mathcal M}_{c}(G)$-smooth.

  (ii) \ The map $\Lambda :  {\rm IND}_{H}^{G}(\tau)  \longrightarrow  U$ defined by $\Lambda(f) = f(1)$ is a surjective $H$-map.

  (iii) \ The restriction of $\Lambda$ to any non-zero $G$-subspace of ${\rm IND}_{H}^{G}(\tau)$ is non-trivial.

  (iv) \ If $H \backslash G$ is compact and $(\tau, U)$ is ${\mathcal M}_{c}(H)$-admissible then ${\rm IND}_{H}^{G}(\tau)$ is ${\mathcal M}_{c}(G)$-admissible.

  (v) \ If $(\pi, V)$ is ${\mathcal M}_{c}(G)$-smooth then composition with $\Lambda$ induces an isomorphism of the form
  \[  ( \Lambda \cdot - ) : {\rm Hom}_{G}(V, IND_{H}^{G}(\tau)) \stackrel{\cong}{\longrightarrow }  {\rm Hom}_{H}(V, U).  \]
 \end{em}
 \end{theorem}

 {\bf Proof:}

Part (i) is immediate from the definition.

For part (ii) we observe that $\Lambda( h \cdot f) = f(h) = \tau(h) f(1) = \tau(h)(\Lambda(f))$. Given $u \in U$
choose a compact open subgroups $K_{i}$ of $G$ such that
\linebreak
$(K \bigcap H, \phi_{i}) \in {\mathcal M}_{c}(H)$ and $ u = \sum_{i} \ u_{i}$ with $u_{i} \in U^{(K \bigcap H, \phi_{i})}$. Define $f_{i} \in IND_{H}^{G}(\tau)^{(K \bigcap H, \phi_{i})}$ by
$f_{i}(g) =  \tau(h) u_{i}) $ if $ g=hk, h \in H, k \in K$ and  $f_{i}(g)=0$ otherwise. This is compactly supported modulo $H$ and $\Lambda(f_{i}) = u_{i}$ so $u = \Lambda( \sum_{i} f_{i})$, as required.

For part (iii) suppose that $V$ is a non-trivial $G$-subspace of ${\rm IND}_{H}^{G}(\tau)$ and choose $f \in V$ such that $f(g) \not= 0$ for some $g \in G$. Therefore $g \cdot f \in V$ also and $\Lambda( g \cdot f) = f(g)$.

 For part (iv) suppose that $K$ is a compact open subgroup of $G$ such that $(K, \phi) \in {\mathcal M}_{c}(G)$. Suppose that $X$ is a finite subset of $G$ and that $U_{0}$ is a finite dimensional subspace of $U$. Set
 \[ {\mathcal I}((K, \phi) X, U_{0}) = \{ f  \in IND_{H}^{G}(\tau)^{(K , \phi)} \ | \ f(X) \subseteq U_{0}, \ {\rm supp}(f) \subseteq   H \cdot X \cdot K \} , \]
 which is clearly finite-dimensional.

 Now suppose that $(\tau, U)$ is ${\mathcal M}_{c}(H)$-admissible. Let $(K, \phi) \in {\mathcal M}_{c}(G)$
 and choose a finite set $X$ such that $H \cdot X \cdot K = G$. Let $L = \bigcap_{x \in X} \ xKx^{-1} $ so that $L \bigcap H$ is a compact open subspace of $H$. For each $x \in X$ we have a character $(x^{-1})^{*}(\phi) : xKx^{-1} \bigcap H \longrightarrow k^{*}$
 Take $U_{0} = {\rm Span}_{x \in X} \ U^{(L \bigcap H, (x^{-1})^{*}(\phi))}$ and suppose that $f \in IND_{H}^{G}(\tau)^{(K, \phi)}$. Therefore, if $h \in H, k \in K, x \in X$, then $f(hxk) = \phi(k) \tau(h)(f(x)$. Now suppose that we have any element of $z \in L \bigcap H$ then there is $x \in X$ and $k \in K$ such that $z = xkx^{-1} \in H$.
 Therefore $\tau(xkx^{-1})( f(x)) = f(xkx^{-1}x) = \phi(k) f(x)$ so that $f(x) \in U_{0}$. Therefore
 $IND_{H}^{G}(\tau)^{(K, \phi)} \subseteq  {\mathcal I}((K, \phi) X, U_{0}) $ is finite-dimensional, as required.

 For part (v) define the map in the reverse direction
 \[ \Phi :  {\rm Hom}_{H}(V, U) \longrightarrow    {\rm Hom}_{G}(V, IND_{H}^{G}(\tau)) \]
 by $(\Phi(f)(v))(g) = f(\pi(g)v)$ which is a function of $g \in G$ which on $gk$ satisfies
 $(\Phi(f)(v))(gk) = f(\pi(g)\pi(k)v) = \phi(k)f(\pi(g)\pi(k)v) = \phi(k) (\Phi(f)(v))(g) $ if $v \in V^{(K, \phi)}$ so that the ${\mathcal M}_{c}(G)$-smoothness of $V$ ensures tha $\Phi(f)$ maps $V$ into $IND_{H}^{G}(\tau)$.
 Also composing with $\Lambda$ gives $v \mapsto f(v)$ so that $\Phi \cdot (\Lambda \cdot -) = 1$.
 Also $ (\Lambda \cdot -) \cdot \Phi  = 1$ as in the classical case (\cite{WCnotes} Theorem 2.4.1(e)  p.27).

 \section{Analogue of Jacquet's Theorem for ${\mathcal M}_{c}(G)$-admissibility}

 In this section I shall establish for ${\mathcal M}_{c}(G)$-admissibility results which are analogous to those of
( \cite{AJS79} Chapter III, \S2.3), which is the source of any notation that I forget to elucidate.

 Let $(P,A)$ be a $p$-pair - $P = MN$. Hence $P$ is a parabolic subgroup and $N$ is its unipotent radical and $P=MN$ is its Levi decomposition.

For $\chi : N \longrightarrow k^{*}$ let $V_{\chi}(N)$ be the subspace of $V$ spanned by elements of the form $\pi(n)(v) - \chi(n) v$ as $v \in V$ varies\footnote{When $\chi =1$ \cite{AJS79} writes $V(N)$ sometimes as $V(P)$ but still meaning the subspace of $V$ generated by elements of the form $n \cdot v - v$ with $n \in N, v\in V$. See (\cite{AJS79} p.82).}. The proof of (\cite{AJS79} Lemma 2.2.1 p.82; also a particular case is \cite{DB96} p.461 Proposition 4.4.3)
shows that
\begin{lemma}{$_{}$}
\label{2.1}
\begin{em}
 $v \in V_{\chi}(N)$ if and only if there is a compact open subset $N(v)$ of $N$ such that
 \[   \int_{N(v)}  \chi^{-1}(n)  \pi(n)(v) dn = 0. \]
\end{em}
\end{lemma}

The element $m \in M$ maps $V_{\chi}(N)$ to $V_{(m^{-1})^{*}(\chi)}(N)$ where $(m^{-1})^{*}(\chi)(n) = \chi(m^{-1}nm)$ and $n \in N$ maps $V_{\chi}(N)$ to itself. In the classical case $\chi = 1$ and in that case I shall write $V(N)$ rather than $V_{1}(N)$.

Let $\tau$ be an ${\mathcal M}_{c}(P)$-smooth representation of $P$ which is trivial on $N$ in which $P$ acts on a vector space $U$. Set $\rho = {\rm IND}_{P}^{G}(\tau)$, as in Theorem \ref{1.13}.
Therefore, by Theorem \ref{1.13}(i) $\rho$ is ${\mathcal M}_{c}(G)$-smooth and, since $P \backslash G$ is compact, by Theorem \ref{1.13}(iv) $\rho$ is ${\mathcal M}_{c}(G)$-admissible if $\tau$ is
${\mathcal M}_{c}(P)$-admissible.

Following the method of (\cite{AJS79} Chapter III, \S2.3) we shall prove a series of lemmas in order to establish the following result :

 \begin{theorem}{(Analogue of Jacquet's Theorem)}
\label{2.2}
\begin{em}

Let $X_{0}$ be a non-zero ${\mathcal M}_{c}(G)$-admissible $G$-subrepresentation of ${\rm IND}_{P}^{G}(\tau)$. Then $\Delta(X_{0})$ is a non-zero  ${\mathcal M}_{c}(M)$-admissible $M$-subrepresentation of $U$.
\end{em}
\end{theorem}

Let $(P_{0}, A_{0}) $ is a minimal $p$-pair such that $(P,A) > (P_{0}, A_{0})$ and $\{ K_{j}, 1 \leq j \leq \infty \}$ is a sequence of compact open subsets of $G$ such that

(i)  $\{ K_{j}, 1 \leq j \leq \infty \}$ is a fundamental sequences of neighbourhoods of the identity in $G$,

(ii) Let $(P,A)$ be a $p$-pair of $G$ with Levi decomposition $P=MN$. If $(P,A)$ is standard with respect to $P_{0},A_{0})$ then
$K_{j} = \overline{N}_{j}M_{j}N_{j} = N_{j}M_{j}\overline{N}_{j}$ with $N_{j} = N \bigcap K_{j}, M_{j} = M \bigcap K_{j}, \overline{N}_{j} = \overline{N} \bigcap K_{j}$.

Write $U_{0} = \Delta(X_{0})$ and define, for $1 \leq j \leq \infty$,
\[ \begin{array}{ll}
X_{0}(j, \phi) &  =  X_{0}^{(K_{j}, \phi) }  \\
\\
& = \{ f \in X_{0} \ | \  \rho(k)f = f(- \cdot k) = \phi(k) \cdot f \ {\rm for \ all } \ k \in K_{j} \}  \\
\\
& =  \{ f \in X_{0} \ | \  \phi(k)^{-1} \rho(k)f =  f \ {\rm for \ all } \ k \in K_{j} \}  .
\end{array}   \]
Also
\[  \begin{array}{ll}
U_{0}(j, \phi) & = U_{0}^{(M_{j}, \phi)}   \\
\\
& = \{ u \in U_{0} \ | \  \tau(m) u  = \phi(m)u \ {\rm for \ all } \ m \in M_{j}  \} \\
\\
& =  \{ u \in U_{0} \ | \  \phi(m)^{-1} \tau(m)u  =  u \ {\rm for \ all } \ m \in M_{j}  \}
\end{array} \]

\begin{lemma}{$_{}$}
\label{2.3}
\begin{em}
$\Delta(X_{0}(j, \phi)) \subseteq U_{0}(j, \phi)$.
\end{em}
\end{lemma}

{\bf Proof:}

If $m \in M_{j}$ then $m \in K_{j}$. Now, by (\cite{AJS79} Lemma 2.3.2),  $\tau(m)(f(1)) = f(m) = \phi(m) \Delta(f)$. $\Box$

\begin{lemma}{$_{}$}
\label{2.4}
\begin{em}

For any $j>0$, $\Delta(X_{0}(j, \phi))$ is stable under $\tau$ restricted to $A$.
\end{em}
\end{lemma}

{\bf Proof:}

Since $\Delta(X_{0}(j, \phi))$ is finite-dimensional the set
\[ S = \{a \in A \ | \ \tau(a)\Delta(X_{0}(j, \phi)) \subseteq \Delta(X_{0}(j, \phi))  \}  \]
is a group. Since $A$ is the group generated by $A^{+}(t)$ for any $t>0$, in the notation of (\cite{AJS79} Chapter 0),  it is sufficient to show that there exists $t>0$ such that $a^{-1} \in S$ for all $a \in A^{+}(t)$.

Choose $t$ such that $a \overline{N}_{j}a^{-1} \subseteq \overline{N}_{j}$ ($\overline{N}$ is the opposite of $N$, which is therefore also normalised by $M$) provided that $a \in A^{+}(t)$.

For $a \in A^{+}(t)$ and $f \in X_{0}(j, \phi)$ set
\[ \begin{array}{ll}
f_{(a,j)}  &   =  \int_{K_{j}} \phi(k)^{-1} \rho(ka^{-1}) dk f  \\
\\
 & = \int_{N_{j}} \int_{M_{j}}  \int_{ \overline{N}_{j}   }  \ (\phi(nm  \overline{n})^{-1} \rho(nm \overline{n} a^{-1})\cdot f ) dn dm d\overline{n}  ,
\end{array}  \]
which, assuming normalised measures, $f_{(a,j)} \in X(j, \phi)$ since we have averaged over $K_{j}$.

Notice that $\phi(n) = 1$ for $n \in N_{j}$, if $\Delta(f) \not= 0$, since $\tau(n)$ acts trivially on $U$.

Applying $\Delta$ we obtain, as $a$ centralises with $M_{j}$ (\cite{WCnotes}  p.11),
\[ \begin{array}{ll}
\Delta(f_{a,j}) &  =  f_{a,j}(1) \\
\\
& = \int_{M_{j} }  \int_{\overline{N}_{j} }   \phi(a)  \phi(m \overline{n} a^{-1} )^{-1} \rho(m \overline{n}a^{-1})  dm d\overline{n} f(1) \\
\\
& = \int_{ \overline{N}_{j} }  \phi(a)  d\overline{n}  f(a^{-1} (a\overline{n}a^{-1})) \\
\\
& =  \phi(a) f(a^{-1}) \ {\rm since }  \    a \overline{N}_{j} a^{-1} \subseteq \overline{N}_{j}   \\
\\
& = \phi(a) \tau(a^{-1}) \Delta(f) ,
\end{array} \]
as required. $\Box$

\begin{lemma}{$_{}$}
\label{2.5}
\begin{em}
 $U_{0}(j, \phi) \subseteq \Delta(X_{0}(j, \phi))$.
\end{em}
\end{lemma}

{\bf Proof:}

We must show that, if $u_{0} \in U_{0}(j, \phi)$, then there exists $f_{0} \in X_{0}(j, \phi)$ such that
$\Delta(f_{0}) = u_{0}$.

There exists $j'$ and $\phi_{i} : K_{j'} \longrightarrow k^{*}$ for $1 \leq i \leq N$, with $f_{i} \in X(j', \phi_{i})$ such that $u_{0} = \sum_{i=1}^{N} \ \Delta(f_{i})$.

Suppose that $N$ is minimal integer occurring  in the above type of relation. If $K_{j'} \subseteq K_{j}$ then $M_{j'} \subseteq M_{j}$ and for $m \in M_{j'}$ we have
\[ \begin{array}{ll}
\sum_{i=1}^{N}  \   \phi(m) f_{i}(1) &   =   \phi(m) u_{0} \\
\\
& = \tau(m) u_{0}  \\
\\
 & = \sum_{i=1}^{N} \  ( \rho(m)f_{i})(1)  \\
\\
&  =  \sum_{i=1}^{N} \ f_{i}(m) \\
\\
&  =   \sum_{i=1}^{N} \  \phi_{i}(m) f_{i}(1) . \\
\end{array} \]
Therefore we can eliminate one of the $f_{i}$'s unless each $f_{i} \in X_{0}(j', \phi)$, but such an eliniation would contradict minimality.

If $K_{j} \subset K_{j'}$ a similar minimality argument shows that we may assume $f_{i} \in X_{0}(j', \phi)$ for each $i$, which implies the result in this case.

We continue, assuming at $K_{j'} \subseteq K_{j}$ and that $f_{i} \in X_{0}(j', \phi)$ for each $i$.

Let $\lambda  \in C_{c}(M//M_{j}) $ be the characteristic function of $M_{j}$ multiplied by the reciprocal of the Haar measure of $M_{j}$ (\cite{AJS79} p.30). We have
\[ \begin{array}{ll}
u_{0} & = \int_{M_{j}} \lambda(m) \phi(m)^{-1} \tau(m) dm u_{0} \\
\\
& =  \sum_{i=1}^{N} \  \Delta(\int_{M_{j}} \lambda(m) \phi(m)^{-1}  \rho(m) dm  f_{i}) \\
\\
&  =   \sum_{i=1}^{N} \  \int_{M_{j}} \lambda(m)  \phi(m)^{-1}  f_{i}(m) dm  .
 \end{array}  \]

Assume that $f_{i} \in X_{0}(j', \phi)$ and choose $t > 0$ so that, if $a \in A^{+}(t)$, then
$a \overline{N}_{j} a^{-1} \subseteq \overline{N}_{j'}$. Fix $a \in A^{+}(t)$. Set $\lambda_{a}(m) = \lambda(am)$  for $m \in M$ and $\lambda'_{a}(x) = \lambda_{a}(m)$ if $x = km \in K_{j}M$, $0$ if $x \not\in K_{j}M$. Then $\lambda'_{a} \in C_{c}(K_{j} \backslash G)$, so define $f_{1,i}$ to be the convolution of $\lambda'_{a} $ with
$\phi^{-1} f_{i}$ so that  $f_{1,i} = (\lambda'_{a}) *  \phi^{-1} f_{i}  \in X_{0}(j, \phi)$.

Then
\[ \begin{array}{ll}
((\lambda'_{a}) *  \phi^{-1} f_{i})(1) & = \int_{G}  (\lambda'_{a}(x) \phi(x)^{-1} f(x) dx \\
\\
& = \int_{K_{j}} \phi(xa^{-1})^{-1} f_{i}(xa^{-1} ) dx \\
\\
&  =  \phi(a) \int_{\overline{N}_{j}} \phi(axa^{-1})^{-1} f_{i}(axa^{-1} ) dx \\
\\
& =  \phi(a) \tau(a)  \int_{\overline{N}_{j}}  f_{i}(a \overline{n}a^{-1}) d \overline{n} \\
\\
& = \phi(a) \tau(a)(f_{i}(1))  ,
\end{array} \]
since $a \overline{N}_{j} a^{-1} \subseteq   \overline{N}_{j'}.$
$\Box$

Lemmas \ref{2.3}, \ref{2.4} and \ref{2.5} establish Theorem \ref{2.2}. In particular, combining Theorem \ref{2.2} and
Theorem \ref{1.13}(iv) we obtain the following result.
\begin{corollary}{$_{}$}
\label{2.6}
\begin{em}

 In the notation of \S\S\ref{2.2}-\ref{2.5}, $(\tau, U)$ is ${\mathcal M}_{c}(M)$-admissible if and only if  ${\rm IND}_{H}^{G}(\tau)$ is ${\mathcal M}_{c}(G)$-admissible.
\end{em}
\end{corollary}
\begin{theorem}{$_{}$}
\label{2.7}
\begin{em}
 If $V$ is an ${\mathcal M}_{c}(G)$-admissible representation then $V/V(P) $ is an ${\mathcal M}_{c}(M)$-admissible representation\footnote{Recall that, following the ambiguous notation of \cite{AJS79}, $V(P)$ is also denoted by $V(N)$.}.
\end{em}
\end{theorem}

{\bf Proof:}

By Frobenius reciprocity (see Theorem \ref{1.13}(v)) we have an isomorphism of the form
  \[  ( \Lambda \cdot - ) : {\rm Hom}_{G}(V, IND_{P}^{G}(V/V(P) )) \stackrel{\cong}{\longrightarrow }  {\rm Hom}_{P}(V, V/V(P) ) \]
 and we denote by $T$ the $G$-map on the left which corresponds the the canonical quotient of $P$-representations on the right. Setting $X_{0} = T(V) \subset  IND_{P}^{G}(V/V(P) )$, which is
${\mathcal M}_{c}(G)$-admissible by Corollary \ref{1.9},  implies that $\Delta(X_{0}) = V/V(P)$ is an ${\mathcal M}_{c}(M)$-admissible representation, by Theorem \ref{2.2}. $\Box$

\section{Related remarks and questions}
If $\chi$ is a character of $P$ which is trivial on $M$ then it gives an $M$-fixed character on $N$ and conversely an an $M$-fixed character on $N$ $\chi$ extends to $\chi(mn) = \chi(n)$) on $P$, which is trivial on $M$.

In this case $V/V_{\hat{\chi}}(P)$ of Lemma \ref{2.1} is a $P$-representation\footnote{Similarly, recall that, following \cite{AJS79}, we adopt the ambiguous notation of writing $V_{\hat{\chi}}(P)$ and $V_{\hat{\chi}}(N)$
for the same subspace of $V$.}.

If $\chi: P \longrightarrow k^{*}$ is a continuous character which is trivial on $M$ and $(U, \tau)$ is an ${\mathcal M}_{c}(P)$-admissible representation then so is $U' = U \otimes \chi$. Therefore, by Theorem \ref{1.13}(iv), $X' = {\rm IND}_{P}^{G}(U \otimes \chi)$ is  an ${\mathcal M}_{c}(G)$-admissible representation.

In \cite{Sn18}, \cite{Sn20}, \cite{Sn20b} and \cite{Sn20c} one is often concerned with the subcategory of admissible representations with a fixed central character $\underline{\phi}$ and ${\mathcal M}_{cmc. \underline{\phi}}(G)$-admissibility, where  ${\mathcal M}_{cmc. \underline{\phi}}(G)$ is the poset of pairs $(H, \phi)$ where $Z(G) \subseteq H$ and $\phi$ is a continuous character extending $\underline{\phi}$ and $H$ is compact open modulo the centre. There is an analogue of $  IND_{P}^{G}(-)$ in this setting and presumably the obvious analogue of the classical Jacquet theory.

For the classical definition can one modify the Jacquet proof to show $V$ $G$-admissible implies $V/V_{\chi}(P)$ is $P$-admissible?

If that works then can one try to prove it for ${\mathcal M}_{c}(G)$-admissibility?

A question left in suspense in \cite{Sn20} was the derivation of the general formula for generators of the hyperHecke algebra in term of convolution products. I gave the formula in the case when all characters on compact opens have finite image (as in the classical case). It seems to me that, with a little more expertise with Mahler's theorem (see \cite{AMR00}) my previous proof might be promoted to the general case? Unfortunately, (see  \cite{JMOS18} and \cite{XX}) this may take rather too long, in the absence of access to
``big-hitting Langlands professionals''. This one will have to wait until the unlikely event of my next trip to Toronto, Paris or Princeton.

There is another dangling, incompletely sketched problem, vaguely conjectured in \cite{Sn20b}, concerning the Hopf-like algebra structure of the hyperHecke algebra of general linear groups. An additional discussion of this algebra is skectched in \cite{Sn20c}.


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text:
These Are Fascinating Days.
With A Degree Of Orwellian Nastiness Coming Out.
Animal Farm indeed.
I left the Conservative Party after 2010 over the side lining of members and constituency associations. A constant and unpleasant bullying behaviour seen in two GE campaigns and now this referendum. It was no surprise to hear a BBC reporter refer to the referendum as an election campaign. No doubt privy to the tactical briefings as a "guest" of Downing Street. It would appear Laura Kuenssberg might well have been there, too.
No doubt reserve fall back options for any progress by the leave campaign were also trotted out. Not without a once bullied backbencher noticing, mind you. As for Google, try finding anything about Ipswich and that bullying bunch bussed in, no doubt paid by us, to disrupt Boris's and the leave momentum. That out of the anti-Trump movement employed by the Clinton mobsters from Goldman Sachs. Look how that's turning out!
I suspect the Google bosses realised that. The Downing Street lot too blinkered to understand how their economic Armageddon warnings are backfiring. Long may the idiots cling to ignoring mass migration and overwhelmed public services. Just as they chose to in the GE and are now blindly following a strategy they never once thought would be successful other than damage limitation.
We can only hope that Gove's and Johnson's intellect and honesty will carry the day, with Farage doing the more unpleasant work in the trenches. A better option all round than the rubbish spouted by Mandleson. A guy either deliberately and nastily cunning when mixing up extradition with deportation or very thick. Could be both, of course.
As I titled this post, fascinating. For me there is only one decent side in all this. It's certainly not those using the underhand, EUSSR and Orwellian dictatorial nastiness.
"Democracy" eu style
https://www.youtube.com/watch?v=Tg4goZxXRZk#t=219
So if your MEP doesn't have much of a say in the eu, who does?
http://www.veteranstoday.com/2016/06/08/revolving-door-google-and-eu-govts-cross-hiring-revealed-in-new-report/
RandomAnonymousCrank 9 June 2016 at 07:00
The Pig Molester just isn't trying any more, his sleight of hand abandoned for brazen in your face foul play. The traitor to this country who had to be dragged kicking and screaming to a referenda, the Quisling who fights tooth and nail on the side of a totally non democratic eu has now extended the deadline for voter registration. So that every one can get a chance to vote, to make it more democratic ? Not on your nelly. This referendum has been in the offing for two G/E's past, anyone who isn't registered at this late stage of the game is most likely to be a disinterested political illiterate who will suck up all the remain hogwash or a youngster indoctrinated since birth having known no other and all of a sudden caught up in the hysteria. The Pig Molester knows this and under the cynical flag of giving every one the chance is twisting the rules.
Aha, a few days ago I predicted a last minute "road to Damascus"conversion ploy with Boris, (still hope I'm wrong about it in his case), but it's coming into play with a lessor cats paw, Sarah Wollaston.
http://www.bbc.co.uk/news/uk-politics-eu-referendum-36485464
Yes please let's have a few more Quislings outing themselves.

redpajama_set_name: RedPajamaCommonCrawl


Due to each story corresponding with one another, and the fact that they are so short, I decided it would be best to review all three as one.
These stories of power, politics and pesky poltergeists give you a glimpse into the darker side of the wizarding world, revealing the ruthless roots of Professor Umbridge, the lowdown on the Ministers for Magic and the history of the wizarding prison Azkaban. You will also delve deeper into Horace Slughorn's early years as Potions master at Hogwarts – and his acquaintance with one Tom Marvolo Riddle.
Ok so it's kind of hard to make this an actual review seeing as these books were more of Harry Potter encyclopedias. So there is no real story to review upon. All I can tell you is how they made me feel. Any die hard Potter fan is gonna absolutely adore learning everything there is to know about the Wizarding World! J.K. Rowling inspired all the feels , and her chapter on Remus Lupin had me tearing up all over again. I truly felt like I was being educated on a topic that I sincerely cared about (unlike most my college courses).
The most unique part about the way these books are written is that after each section there is a section titled: "J.K. Rowling's Thoughts." You basically get a glimpse inside of her head as she was brainstorming/writing the Harry Potter books. You discover where her inspiration came from and how she thought up the names of characters. She even talks about ideas that she decided not to go with. If anything, reading these books increased my appreciation of her as an author even more! She did so much research, and put so so much thought into constructing the Harry Potter books; it's absolutely amazing!! Even minor characters (ones I had completely forgotten existed until reading these) were given extensive backgrounds.
Though Rowling does touch on a lot of details I had been wondering about, I can't help but feel that she could still tell us so much more, and give us spin off books on characters (wishful thinking I know). My inner fangirl would love to see a series written on the Marauders! Oh well, I most definitely enjoyed reading these lovely little ebooks, it made my heart happy and made me what to reread all the books now that I have a greater understanding.
I most definitely recommend any Harry Potter fan read these three books! Buy book the series on Amazon here!


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For Dance and the Beauty of Age, Dances For A Variable Population welcomes four choreographers rooted in American Modern Dance and Broadway; Tina Bush (Forces of Nature), Shirley Black Brown Coward (Audelco Award, Black Nativity), Myna Majors (Baba Olatunji Drum and Dancers), and George Faison (Tony award, The Wiz). Dance and the Beauty of Age will also feature 25 seniors from DVP's free Movement Speaks® programs in Harlem which take place at over 6 sites across Upper Manhattan.
In a project of historical, social and technical exploration, Dance and the Beauty of Age celebrates the past performing careers of these artists and the impact these techniques have had on dance history and their lives. Through exploration across dance studios, libraries, senior and recreation centers in Harlem, Dance and the Beauty of Age will bring audiences the unique expression of older adults mixed with the power of older trained professionals.
This one-of-a-kind event will be free to the public. It will provide diverse audiences an opportunity to see movement distilled from the seminal techniques of legendary geniuses, to see the eloquence of the older brain/older body, and to see older artists create.
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Take the A, D, C, B train to 125th St. and walk one block south to Hancock Place. The theatre is between St. Nicholas and Morningside Ave.
ABOUT DANCES FOR A VARIABLE POPULATION Founded in 2005 by Naomi Goldberg Haas, Dances for a Variable Population (DVP) promotes strong and creative movement among people of all ages and abilities with a focus on seniors. The organization's programming includes: a multigenerational performance company that engages community members as participants and audiences; Movement Speaks® and Dances for Seniors, which are free, community-based programs for modest income and culturally underserved older adults, annually serves over 700 seniors; Variable Pop Method Expressive Dance and Fitness classes for adults of all ages, offered year- round; and performance and training opportunities for older professional dancers and choreographers. DVP's site-related performances have been presented in some of New York City's most iconic public spaces, including Times Square, the New York Botanic Garden, Washington Square Park, and the High Line. DVP has also performed at Jacob's Pillow Dance Festival, and internationally in Poland and British Columbia.
The development and performance of Dance and the Beauty of Age has been made possible with funding from the Upper Manhattan Empowerment Zone and administered by the Lower Manhattan Arts Council. UMEZ enhances the economic vitality of all communities in Upper Manhattan through job creation, corporate alliances, strategic investments, and small business assistance. LMCC empowers artists by providing them with networks, resources, and support, to create vibrant, sustainable communities in Manhattan and beyond. The project has also been made possible with support from the New York City Department of Cultural Affairs in partnership with the City Council, Columbia Community Service, the Mertz Gilmore Foundation, the Fan Fox and Leslie R. Samuels Foundation, the West Harlem Development Corporation, and M & T Bank.
Join us for Revival 3 Rehearsals!
Article in The Villager about Movement Speaks!
Photos from Dance and the Beauty of Age!
Ten years ago, Columbia pledged $76 million to local nonprofits. What happens when it runs out?
We love this article from The Uptowner!
Senior Planet Q&A with Naomi!


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text:
Two employees at Jefferson County Sheriff's Office test positive for coronavirus
Ben Tobin
Louisville Courier Journal
LOUISVILLE, Ky. — Two employees from the Jefferson County Sheriff's Office are in self-isolation after testing positive for the coronavirus, Louisville Mayor Greg Fischer announced during a press briefing Tuesday afternoon.
Both employees are in the operations division, according to Jefferson County Sheriff's Office Lt. Col. Carl Yates.
They are both "at home recovering with treatment," Yates said.
One of the employees is a deputy in the EPO/warrants unit who tested positive five or six days ago, while the other employee, a sergeant in the process unit, tested positive over the weekend, according to Yates.
Yates said three other employees in the courts division are in quarantine and that the office is watching to ensure they do not develop COVID-19 symptoms.
Some employees are continuing to work at the sheriff's office in downtown Louisville at the Fiscal Court Building, Yates said.
"We can't shut down everything," Yates told The Courier Journal. "We have a 911 dispatch, so essential workers are still working," he added, saying that the sheriff has not laid off anyone despite the work slowing down.
News:Dayton Jones, whom Matt Bevin pardoned, faces federal child pornography charge
Kentucky coronavirus updates:Louisville has over 400 cases, four new deaths
During his press briefing, Fischer said that 38 of the city's first responders were off today due to the coronavirus. Six employees are in self-isolation after testing positive for COVID-19: Two from the sheriff's office, three Louisville Metro Police officers and one Louisville Department of Metro Corrections officer. Overall, nine first responders have tested positive since the start of the public health crisis, and three have since recovered.
Contact Ben Tobin at bjtobin@gannett.com and 502-582-4181 or follow on Twitter @TobinBen. Support strong local journalism by subscribing today: subscribe.courier-journal.com.


text:
Home / IT / Apple Announces New Mac Pro, 6K Display
Apple Announces New Mac Pro, 6K Display
Gerard Cortez | Wednesday, June 05, 2019
James Martin CNET
Again, this is a computer for audio-video professionals. It looks a lot like the original version of the Mac Pro from over a decade ago that was widely praised. You'll need to spring for a screen to use the Mac Pro.
Check out the stainless steel legs that keep the Mac Pro raised off surfaces. A lattice pattern maximizes airflow and ensures quiet operation. Abandoning the smooth cylinder look of its maligned predecessor, the new Mac Pro looks more like a typical tower full of slots giving users the flexibility they need to fill the machine with up-to-date components as tech improves. Apple says the card can allow you to play back twelve raw 4K video streams simultaneously.
It's been nearly eight years since we saw the release of a new Mac Pro design, and this year's announcement of the third-generation Mac Pro at WWDC 2019 was definitely meant to be exciting. You will be rendered the same experience that you've seen on mobile, where your music catalog will be synced with Apple Music on the Mac.
The Mac Pro 2019 can be configured with a 28-core Intel Xeon processor which has a TDP of 300W and a heavy-duty cooling system. The device is configurable with up to 1.5TB of system memory.
Two MPX modules with dual Radeon Pro Vega II GPUs can be connected to have the power of four in a single workstation. In terms of graphical abilities, the system can be packed with AMD's Radeon Pro Vega 2 or Radeon Pro Vega 2 Duo, and if the latter is doubled, you effectively get four GPUs with a total of 128GB worth of graphics memory. One PCIe slot is reserved for a card featuring two USB-A ports and two Thunderbolt 3 ports. It is called the Pro Display XDR.
And even if the holes don't freak you out, the new Mac Pro just looks kind of off.
The Pro Display XDR is a 32-inch LCD panel with 6016 x 3384 Retina 6k display, featuring more than 20 million pixels. Capping things off, the Pro XDR supports true 10-bit color, good for producing more than a billion colors. The display also features an extra-wide, accurate viewing angle with an anti-reflective coating. The display also features a 1 million to 1 contrast ratio. All told, a Mac Pro using a pair of Radeon Pro Vega II Duo cards can apparently provide some 112.8 TFLOPS/sec of half-precision compute.
The display is VESA-mountable.
The monitors can also be rotated so that they can displayed in portrait as opposed to landscape. It will all be available in the fall. The standard glass configuration will cost $4,999, and the nano-etched model is $5,999.
Cyberpunk 2077 Quest Director Explains the Variety of Paths Available to V
Ubisoft Under Fire for HitRecord Partnership on Watch Dogs: Legion
Unlocked Galaxy S10 Line is $200-$500 Off Right Now
Amazon Prime Day's Best Gaming And Tech Deals
Nintendo Switch Pro Will Not Arrive in 2019
Prime Day Preview: New MacBook Air Just $999
Get your first look at the official Galaxy Note 10 images
Google Admits Humans Are Listening to Assistant Recordings
Latest Windows 10 May 2019 update may cause 0x80070002, 0xc0000005 & 0xc0000001 errors
"Get a refurbished 13" MacBook Pro for $200 off
Google Translate app's camera mode auto-detects languages
Nintendo Reveals $200 Switch Lite Handheld
Samsung Galaxy S10 Snapchat Users receive a Black Bar at the bottom
Purchased Stadia Games Are Playable After Publisher Pulls Support
AMD confirms Radeon 5700 series price cuts two days before launch
Trump's feud with McCain continues, ship kept out of view
John McCain during President Trump's recent visit to Japan - but that it remained in a "normal configuration" during the visit. There is a lot of criticism of how much I speak about my dad, but nine months since he passed, Trump won't let him RIP.
Apple Shutting Down iTunes
Apple takes a cut of sales from apps sold through the store, though that practice is under scrutiny in several legal proceedings. Next Monday at its developer conference, Apple will announce the end of iTunes , according to a Bloomberg report on Friday .
Afghanistan pledge to learn from Australia World Cup drubbing
Australia's Adam Zampa entered this battle of leg-spinners as the underdog ironically against Rashid Khan of Afghanistan . A different David Warner was on show tonight, with him taking the backseat and allowing Finch to express himself.
Yes, Apple just killed iTunes
It launched Apple Music in 2015, but the service has failed to overtake Spotify , and now has around half as many users worldwide. On top of that, the app will contain Apple's original streaming service, Apple TV Plus, once it becomes available this fall.
Pokemon Go-Like Game Dragon Quest Walk Announced, See The First Trailer
Square Enix revealed during a press conference on June 3 a brand new Dragon Quest game for mobiles, Dragon Quest Walk . A Beta Test for Dragon Quest Walk will begin soon in Japan, with 20K players selected, half on Android, half on iOS .
Priyanka Chopra backs Meghan Markle, calls her victim of racism
Trump was made aware of her comments during an interview with The Sun last week and responded: "I didn't know that". Chao has been a celebrity in China since she became the first Chinese-American Cabinet secretary under George W.
Boeing 737 Max 'may not fly until August'
Later on Wednesday, the Boeing CEO also appeared on CBS News, where he publicly apologized to the victims of the 737 MAX crashes. The issue was discovered following an investigation conducted by Boeing and the FAA Certificate Management Office, the FAA said.
Apple Is Finally Killing iTunes After 18 Years
That is expected to be the biggest news from this event but if you were hoping to catch the entire stream, you can do so here . We're also expecting to hear about Apple's plans to make the iPad even more of a replacement for PCs than it has already been.
NBA Draft 2019: Knicks considering trading No. 3 pick
The team is considering trading the third overall selection to the Atlanta Hawks for the No. 8 and No. 10 overall picks, per ESPN. Obviously, the Knicks will want to build around those two and complement them with good, young (and cheap) talent.
Oppo Shows off Under-display Selfie Camera Prototype
That said, in a follow-up post , Shen admitted that this under-screen camera technology is still in its early days. Since then, many Android devices have adopted the notch to house selfie cameras, 3D sensors, and more.
Wildfire situation in Alberta worsens
Meantime, all air quality advisories in the interior - related to the wildfire smoke in Alberta - have now been dropped. Trout Lake, Alta., a community about 300 km northeast of Grand Prairie, came under an evacuation order Friday morning.
Bangladesh start World Cup with South Africa win
Captain Faf du Plessis was the top run-getter with 62 runs as they succumbed to their second consecutive defeat of the tournament. The season will get underway with the Freedom Trophy for the Gandhi-Mandela series against South Africa in September.
Microsoft warns BlueKeep could be as bad as Wannacry
An attacker who successfully exploited this vulnerability could execute arbitrary code on the target system. This new BlueKeep flaw hasn't yet been publicly disclosed, but that doesn't mean there won't be malware.
Actress Priyanka Chopra: Media Criticism of Meghan Markle Rooted in 'Racism'
Ms May extended an invitation to Mr Trump on behalf of the Queen in an Oval Office visit in the first week of his administration. In a new interview with the U.K.'s Sunday Times , she was asked whether she thinks racism plays a role in Markle's treatment.
Mike Pompeo questions whether Jared Kushner's Israeli-Palestinian peace plan can succeed
Kushner ruled out ever running for office himself and said that his father-in-law is "absolutely not" a racist . Trump did not dispute the story, and stood by Pompeo. "I think it probably can", Trump told reporters Sunday.
Facebook, Instagram having connectivity issues for some users
Issues With Uploading, Sending Files Across Platforms Resolved: Facebook
Samsung calls Galaxy Fold 'embarrassing'
Some OnePlus 7 Pro users received a unusual notification today
Tetris is getting a 100-player battle royal game called Tetris Royale
You can now auto-delete your Google's location history and activity data
Huawei Mate 20X 5G Version will Launch Next Month
Vivo demos fastest charger yet, charges 4,000mAh battery in 13 minutes
Grab Your Wand: 'Harry Potter: Wizards Unite' Launches Friday
Firefox Gets Emergency Patch to Stop Zero-Day Attacks
Nintendo makes over Dr. Mario for iOS and Android
Huawei delays launch of Mate X foldable phone after Samsung debacle
Huawei files to trademark mobile OS around the world after U.S. ban
Google Photos File Syncing With Google Drive Ends July 10
Bethesda says its Orion technology improves game streaming


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Search again Opens a new window Visit website Opens a new window Close
Availability Search for Falls Of Moness
Falls Of Moness
The Falls of Moness and the gorge are both visible from a circular walk around the woodland, the Birks of Aberfeldy.
The birks, Scots for birch trees, still cloak the steep slopes of the Moness gorge, along with oak, ash and elm. A narrow, well defined path is overhung by mature trees and rises to a height of 150 m at a bridge directly above the Falls of Moness. From here you can enjoy the roaring white water beneath and, in winter, fine views over the top to Strathtay.
Getting there by railway:- Rail stations at Perth, Birnam (Dunkeld), Pitlochry are the closest. Bus or car hire from there to Aberfeldy. Full details from Aberfeldy Tourist Information Centre.
Getting there by aeroplane:- From Glasgow or Edinburgh airports head north to the city of Perth. Follow the A9 trunk road to Ballinluig and then take the A827 west to Aberfeldy.
Getting there by ferry:- From the port of Rosyth head north to the city of Perth. Follow the A9 trunk road to Ballinluig and then take the A827 west to Aberfeldy.
aberfeldytic@perthshire.co.uk
Aberfeldy,
Perthshire,
PH15 2DD
Accommodation in Perthshire
Things to Do in Perthshire
Overview of Perthshire


Fadi BouKaram was raised in Beirut and claims he never wanted to be a photographer. After a strictly scientific education, degrees in Engineering and Business, and a decade-long corporate career, he realized how much he needed photography, both as a therapeutic tool and as a way to discover oddities within the mundane. In 2013 Fadi was one of the original founders of the OBSERVE collective. It was borne out of a 'common fascination with watching and documenting the diverse humanity that surrounds us.' Three years later, he abandoned the corporate life and became a full-time photographer.


Where can I buy used golf cars or other vehicles?
We offer used golf cars and other vehicles for sale. Please contact our Sales Department or visit our Showroom to see what is available.
Do used golf cars or other used vehicles come with a warranty?
No, used vehicles are sold on an as-is basis. However, the products under the re-manufactured product line come standard with a one year limited warranty. The products under the Remanufactured product line have an optional one year limited Club Car warranty.
How can I tell if my used golf car is a 36 volt, 48 volt or IQ system?
If the charger plus that inserts into your Club Car is rectangular you have a 36 volt vehicle. If your charger plug is round with 3 prongs it is a 48 volt vehicle. A vehicle with our IQ System will also have a round charger plug, but will have a rocker switch for the Forward and Reverse options.
I need a set of golf car batteries. What kind should I buy?
When looking for a golf car battery first determine if you have a 36 volt or 48 volt vehicle. A 36 volt vehicle has six 6 volt batteries and a 48 volt vehicle has six 8 volt batteries or four 12 volt batteries. These are specialized "Deep Cycle Lead Acid" batteries designed for electric vehicle use. DO NOT attempt to use 12 volt automotive batteries.
What is the value of my used vehicle?
This is a common question but one that is impossible to answer accurately sight unseen. As an automobile value depends on age, cosmetic condition and mechanical condition, as well as any options or accessories on the vehicle, the same is true for golf cars. We will be glad to provide you with the value of your used vehicle. Please contact our Sales Department for more information.


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'Maggie May' at Finborough Theatre
Last week we went to see 'Maggie May' at the Finborough Theatre in Earls Court. It's a little performed musical by Lionel Bart (of 'Oliver!' fame) and, by little performed I mean it hasn't been put on professionally for over 50 years, so well done to Finborough for the revival.
I've never seen 'Oliver!' - yes, honestly - but I have seen another little-if-ever performed Lionel Bart musical in the form of 'Twang!' a couple of years ago that really should have been called 'Carry On Robin Hood' so my expectations weren't terribly high for 'Maggie May'. Despite that, I'm pleased to say that my expectations were totally exceeded and, while I can find lots of faults with the musical and with the production, I really enjoyed it.
To set the scene a little, the Finborough Theatre is a small space above a pub in Earls Court. The theatre space is probably slightly less than twice the size of my living room with seating for around 50 people. The stage space is small and there's quite a large cast for this play with lots of very active dancing, legs kicked high and they're oh so close to the people in the front rows - luckily we were in the second row so protected from random feet in the air. There is a lot of energetic dancing for such a small space and occasionally I could feel the floor moving. Nothing wrong with living dangerously in the theatre!
The play is all about Maggie May and Patrick Casey, a prostitute and a docker who grew up together on the Liverpool docks, got separated and then meet again years later and fall in love. It's also about unions and corruption and power but I prefer the love story. I liked Maggie's unapologetic approach to being a prostitute - it's her job, nothing more and noting less and certainly nothing to be ashamed of - which must've been quite startling back in 1964 when it was first performed. I also liked Patrick's approach to loving the woman and ignoring the job despite the dockers all reminding him what she did for money. In that respect it's actually quite progressive for the time.
Of course, the course of true love can't possibly be smooth so there are complications, break-ups, reconciliations and then tragedy. You see, Patrick is a man of principal, no matter how much he wants to distance himself from his father's reputation as a union man and martyr on the docks. But when he finds out the dockers are loading crates of guns heading to South America he can't do it since they're destined to keep the working classes - his brothers and sisters - under control. That's a step too far for him. And... well, you'll have to see the production to find out what happens next.
I liked this production and I liked the play. Our two lead characters change and develop during the play and it's nice to see them recognising changes in themselves, particularly Maggie, the classic whore with a heart of gold. Some of the other characters were more 'stock' (like the docker whose brief must have been 'stay angry and aggressive throughout'). Kara Lily Hayworth was excellent as Maggie, bringing both a tenderness and a hardness to the role with her versatile voice, always righteous and proud, no shame about her job there at all. James Darch was Patrick, the man of principle who knows who he loves and that's enough for him.
The show is sold out for the entire run but you might be able to get return tickets if you're lucky. I'd quite like to see this on a proper stage so here's hoping for a transfer.
Labels: Finborough Theatre, James Darch. Lionel Bart, Kara Lily Hayworth, Maggie May
'Romeo and Juliet' at the Royal Opera House
'Sorolla: Spanish Master of Light' at the National...
'Fiddler on the Roof' at The Playhouse Theatre
'The Renaissance Nude' at the Royal Academy
Bonnard at Tate Modern
'Harry Potter and the Cursed Child' at the Palace ...
'Gently Down The Stream' at the Park Theatre


note: an antique runner with a navy field, brown, terra cotta and wheat with accents of ivory, apricot and cornflower blue. An even pile rug with secured sides and ends. A high quality weave and lustrous wool.


Student Journey by World In Need International, Inc.
by World In Need International, Inc.
Student Journey is designed for young people and is highly interactive.
Every page has additional resources on the website for each page and every page has at least one link to video so the students can see an introduction, a summary, or additional thoughts while using the lessons.
The second section is an effective study of Ephesians 4-6. These lesson are highly effective and spiritual grow young people closer to God and His Word.


In this diverse, gritty survival fantasy, a girl warrior turns against her island clan to find the brother they claim died, uncovering secrets Perfect for fans of Graceling and Snow Like Ashes.In Khya s world, every breath is a battle.On the isolated desert island of Shiara, dying young is inevitable The clan comes before self, and protecting her home means Khya is a warIn this diverse, gritty survival fantasy, a girl warrior turns against her island clan to find the brother they claim died, uncovering secrets Perfect for fans of Graceling and Snow Like Ashes.In Khya s world, every breath is a battle.On the isolated desert island of Shiara, dying young is inevitable The clan comes before self, and protecting her home means Khya is a warrior above all else.But when following the clan and obeying their leaders could cost her brother his life, Khya s home becomes a deadly trap The only person who can help is Tessen, her lifelong rival and the boy who challenges her at every turn The council she hoped to join has betrayed her, and their secrets, hundreds of years deep, reach around a world she s never seen.To save her brother s life and her island home, her only choice is to trust Tessen, turn against her clan, and go on the run a betrayal and a death sentence.
Haven't been reading much of late, but wow! I'm not a fantasy reader really, but honestly, I loved this diverse story and can't wait for the rest of the books in this series to release. Tons of action, adventure, and there's a good reason why so many authors and even Kirkus Reviews have fallen hard for this book. Pick it up today and see for yourself.
I got the chance to read an early version of this book, and it absolutely blew me away! I can't wait for the release date so I can reread it - and so I can have other people to fangirl with!!
I had the chance to read an early copy of this book, and I already can't wait for the sequel. The story is engaging and satisfying with high adventure, subtle yet steamy romance, and beautiful, diverse relationships. Key to this book are the well-developed characters. They give you a glimpse into this world so different from ours by feeling the beats of the story alongside the characters and learning about their society and place in it. Altogether, it's really good read.
I dunno, it was a bit slow and kinda hard to get into.I just couldn't get into it.I hate not finishing books, but I think the one thing that really really threw me off was all the different words. I couldn't keep track of all of them and was literally flipping to the glossary constantly. I made it about a quarter of the way through (a little more than 100 pages) before realizing this book just wasn't for me.


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Baader is a surname of German origin.

People with the surname Baader
 Andreas Baader (1943–1977), militant of the Red Army Faction (Rote Armee Fraktion), also known as the Baader Meinhoff Gang
 Caspar Baader (born 1953), Swiss politician
 Franz Xaver von Baader (1765–1841), German philosopher and theologian
 Johannes Baader (1875–1955), architect, writer and artist associated with Dada
 Joseph von Baader (1763–1835), German railway pioneer
 Louis-Marie Baader (1828–1920), French painter
 Ottilie Baader (1847–1925), German women's right activist and socialist

See also
 Baade (surname)
 Bader
 Badr (disambiguation)

German-language surnames
Occupational surnames

redpajama_set_name: RedPajamaWikipedia


A black silk saree decorated with purple-white kantha embroidered roses. The floral embroidery is arranged in a sloping style along the length of the saree, covering the entire pallav and tapering off at the pleats. The plush silk fabric, gorgeous colours and intricate kantha work make up the charm of this saree. It comes with a running black blouse piece, or you can also pair it with a colourful silk blouse for a vibrant look.


As you're probably aware, Council are deep into the process of reviewing the existing constitution with the aim of amending and updating it to reflect more modern and effective governance practice. To this end, several questions largely around Council structure form and term of office have been raised within recent Compass Point and O-Club newsletters. In an attempt to produce more clarity around the subject and aid you with your understanding of the subject, a few potential examples of what Council could resemble are highlighted within this paper. The discussion below attempts to explain why we need to change the Constitution, point out the differences between the existing Council structure and other potential alternatives and highlights who and what would disappear if a change was brought about.
How do we meet today's best governance practice?
prevailing governance processes are not making the best use of the valuable time and capabilities of volunteer directors or the staff who support them. Consequently, good, well-motivated people cannot perform to their capacity, nor can their organisation benefit from the potential of focused and proactive governance leadership.
While ONZ was not part of this review, the report highlighted many issues which ONZ is facing.
The present Council structure represents a management "hands-on" structure more focused on operational issues rather than providing governance. A more modern form of Council is focused on governance which would see the most suitably skilled candidates elected to sit on Council and address policy and governance issues. The operational side of the sport would be left to be run by the clubs themselves with support of the ONZ staff and committees who can provide technical knowledge and procedures.
Our sport, like others, is evolving and facing increasing challenges around new issues (health and safety, conduct, doping, sports betting) as well as security and terrorism threats when travelling overseas. This requires a good comprehension of policies and how they affect and impose on individuals.
Why change something which is apparently working satisfactorily?
There are some anomalies with the present system which sees Council composed of a President and Vice President elected annually and four Area Representatives (Auckland, Central Districts, Wellington and South Island) with varying terms of office and membership representation.
Taken to an extreme, we could have a situation where the President and VP are elected at the AGM due simply to being in the wrong place at the wrong time and Area Reps who are in the position as nobody else will stand. Just to reassure you – we don't recall anything like this happening in the past and this is certainly not the case with the present Council who work admirably together and provide a wealth of sport and business knowledge to guide and direct our sport – but our structure currently allows for this to occur.
So what alternatives are available for consideration?
The Council would like to move away from the present method of elections and provide for a more democratic process whereby Council members are elected either by members directly or by clubs. We also feel the current President and Vice President roles should be removed and replaced by newly elected Council Members. We do recognise the importance of having a Chair to lead our sport and council, but believe the Chair should be elected by the incoming Council.
There are lots of different models which could be proposed but after much consideration the Council believes the options presented below are representative of current best practice.
Four possible alternatives are shown below.
These diagrams show the positions on Council, who elects them and in the case of the existing Council – who they represent. Two alternatives are significantly different from the current Council in that nominations would be sought for suitable candidates and they would be elected by the membership at large, and two whereby the clubs elect the Council members. As mentioned above, the incoming Council would then elect the Chair.
Options B and B1 go a little further. They recognise that if a particular issue may necessitate certain skills which may not be available within the body of the elected Council, or if there is a perceived geographical imbalance of Council members, the Council could appoint up to 2 additional members.
Options B and B1 also assume the Chair of the new Council will come from the initial six elected Council members, however, this does not preclude an appointed Council member from becoming Chair if their skills sets and qualities are compelling. Also the appointed Council members would not necessarily have to come from within the sport of orienteering so as to offer an alternative viewpoint and wider perspective if required.
While the loss of Area Reps may imply the direct link with ONZ could be lost, the Council believes clubs are now well positioned to manage their own affairs and events, can still utilise the network of neighbouring clubs for event coordination and delivery, as they do so effectively today.
So what do we want from this Discussion Paper?
ONZ is seeking your views around the Council restructure. We are eager to understand clubs or individuals views on how you perceive the existing process works and whether these alternative forms of Council would be better suited to meet your needs and govern our sport. Potential alternative forms of Council have been raised for your consideration and we would particularly appreciate comments relating to these.
We would like to put this to the AGM for their consideration. We are governed by our existing Constitution which requires remits to be tabled 12 weeks prior to the AGM (which this year is before Christmas 2015)! Consequently, we have to have everything completed by this time. To allow for further revisions and consultation, we would like to have your comments back to us by Friday 9 October 2015. Whilst realising that this is a relatively short time frame, clubs and individuals will have further opportunities to provide feedback as changes are made and further consultation is sought.


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Biografia e carriera musicale
Nasce negli Stati Uniti ma quando ha solo 6 anni si trasferisce con la famiglia a Ginevra dove studia lingue e si avvicina alla musica, prendendo lezioni di pianoforte, violino e chitarra. A 10 anni impara a suonare la batteria. A 18 anni abbandona gli studi e si dedica a tempo pieno all'attività di batterista e cantante in un quartetto locale. Registra a Ginevra un demo, Flip Over, che viene acquistato dall'etichetta milanese Harmony, per cui nel 1980 decide di trasferirsi nel capoluogo lombardo.

Nel 1981 lavora come attore di fotoromanzi e partecipa al Festival di Sanremo con Toccami. Il singolo successivo è I Want to Love, che contiene una differente versione di Go Today, il brano in origine inciso come lato B del disco precedente. In questi primi anni di carriera si presenta generalmente in tutte le sue esibizioni in pattini a rotelle e con due ballerine di accompagnamento.

Nel 1982 passa alla casa discografica Full Time, per la quale realizza il 45 giri Dove andiamo e che fu in seguito tradotto in inglese come Talk with Your Body e ristampato su Maxi Single. Nel 1983 esce con Come Back Home e svolge una breve esperienza cinematografica nel lungometraggio Jocks di Riccardo Sesani, un B-movie poi divenuto di culto come uno dei pochi film a descrivere la vita nelle discoteche italiane di quegli anni e che aveva nella colonna sonora il brano Maybe One Day del gruppo riminese The Creatures.

Nel 1984 pubblica il 45 giri Indian Girl/Love Attack e cambia nuovamente etichetta realizzando per la Sensation-Disco Magic il singolo Give It to Me e, sotto lo pseudonimo di "Fax the Fax", anche la cover di Precious Little Diamond, una canzone fortunatissima ed originariamente incisa da Fox the Fox.

Nello stesso anno avviene anche l'incontro con il produttore milanese Roberto Turatti ed il produttore/compositore Miki Chieregato che, per la Baby Records cercavano una nuova voce con cui proseguire nel progetto Den Harrow (che in origine consisteva in una produzione musicale senza un volto ed un personaggio vero e proprio) e così, cantandone i nuovi brani, contribuirà a trasformare lo stesso progetto in uno dei maggiori successi musicali degli anni ottanta in Italia ed in Europa..

La Baby Records lo mette inoltre sotto contratto esclusivo come autore di testi; per loro, nel 1986 compone la hit U.S.S.R. di Eddy Huntington, in cui è anche presente come corista e Dangerous di Alba Parietti, nonché ritorna a cantare nei propri brani come Looking for love (1986), Help Me (1986), Atlantis (1987) e Feeling Okay (1988) firmandosi come Tom Hooker (oppure T. Hooker) od anche con pseudonimi come nel caso "Swiss Boy" (1986) dove si firmò "Lou Sern" (pronuncia fonetica della città di Lucerna) e distribuito in Europa con etichette discografiche differenti..

Nel 1986 partecipa al progetto Fahrenheit 104, band composta anche da Maurizio Vandelli, Jane Hill e Dario Farina, con la quale incide il brano Highway To Freedom, composto da Vince Tempera per la parte musicale e da Michael Kunze per il testo, anch'esso pubblicato come singolo dalla Baby Records<ref>dati ricavati dalla scheda Highway To Freedom sul sito Discogs .</ref>.

Negli anni '90 incide alcuni singoli con lo pseudonimo David Harleyson, ottenendo un buon riscontro commerciale in Thailandia.

Nel 2010 ed in seguito a una polemica avuta su Facebook con Stefano Zandri (negli anni 80 il mimo che prestava il volto al progetto Den Harrow ed in seguito divenuto il detentore dei diritti di quel progetto), rilascia su YouTube una conferenza stampa dove, accompagnato da Michele Chierigato, dimostra di essere lui il cantante di molti dei successi di Den Harrow e chiede a Zandri di non esibirsi più in playback utilizzando la sua (di Tom Hooker) voce.

A partire dal 2011 riprende l'attività musicale al fianco di Chieregato, pubblicando i singoli Future Brain 2011 e Bad Boy 2011, remake dei brani da lui scritti e portati al successo dal progetto Den Harrow negli anni 80, e l'inedito Nobody Loves Me, un suggestivo pezzo pop rock per il quale si firma Tom Hooker & Elastic Band. Nel 2014 lancia con Chieregato il progetto "Tam Harrow", con cui pubblica alcuni singoli e un album, Incredible Idiot, nel 2015. Nel 2017 pubblica il doppio cd Back in Time, 27 brani tra cui il duetto con Linda Jo Rizzo I Want You Tonight.

 Fotografia
A partire dalla fine degli anni 80, con il declino dello stile italo disco, Hooker si allontanò gradualmente dalla scena musicale per curare in modo più professionale il suo hobby della fotografia. Dopo essersi sposato, iniziò una brillante carriera come "visual artist", eseguendo opere fotografiche e di design figurativo. È un apprezzato artista, che espone con successo in gallerie di molti paesi.

Le opere fotografiche di Thomas Barbey rappresentano un mondo surreale. Con immaginazione illimitata e abilità, Barbey combina più immagini, con soggetti anche molto differenti, ottenendo un risultato che si discosta totalmente dalla realtà. Tutto questo con le tecniche fotografiche classiche senza l'utilizzo di post produzione al computer.

 Vita privata

Nato con il cognome di 'Hooker' (letteralmente 'agganciatore' ma traducibile anche come 'adescatore'), dopo il matrimonio prese il cognome di sua madre (Beecher) per evitare di dare il suo nativo alla moglie in quanto 'Hooker' in slang americano può anche significare prostituta; vive con la moglie Suzanne Berquist a Las Vegas.

 Discografia
 Album in studio
1986 - Only One1988 - Bad Reputation1992 - Fighting For Our Love2017 - Back in Time Singoli
1981 - Flip over/We can start it all over again1981 - Toccami/Go today1981 - I want to love/Go today (New version)1982 - Dove andiamo/Try me1982 - Talk with your body/Dove andiamo (Italian version)/Talk with your body (Instrumental)/Try me out1983 - Come back home (Vocal version)/(Radio Version)/(Instrumental version)1984 - Give it to me (Vocal)/Give it to me (Instrumental)'1984 - Indian girl/Love attack1984 - Real men/Football real men (Real men Another mix)1985 - Cry/Don't forget (to buy this record)1985 - Real men (Swedish remix)1986 - Looking for love/Dub Looking for love (Instrumental)1986 - Help me/New Help me1986 - Only one (Slow version)/Only one (Instrumental)1987 - Atlantis/Amnesie Atlantis1988 - Feeling Okay/I'm feeling Okay (Soft version)1988 - No More Heaven1990 - Living in the sunshine/Living in the sunshine (Instrumental)1991 - Sex-O-Phone & Funk Guitar/Pick up the sex (10 Dance mix)/Sex-O-Phone & Funk Guitar (Single version)1992 - Fighting for our love/What about me1994 - Runaway (Extended mix)/Runaway (Club mix)2010 - Change your mind/Change your mind (Ricci remix)/Change your mind (Club mix)2011 - Future Brain 20112011 - Bad Boy 20112011 - No Elevation2011 - My banana2014 - Illusions/Nobody loves me2020 - With Our Love (with Bad Boys Blue and Scarlett)

Collaborazioni varie
2021: A Sailor from the Moon (Remix) - featuring Lord, Begüm Günceler, Mike Blum
2021: In the sign of destiny - featuring Lord, Peter Rafelson
2021: Keep on rolling - featuring Lord

 Filmografia
 Jocks'', regia di Riccardo Sesani (1983)

Note

Collegamenti esterni

Hooker
Fotografi statunitensi


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Ray-Ban RB4258 62321T
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Ray-Ban RB4258 is one of the most popular styles of sunglasses. Oval shape with Full Rim frame makes these glasses look great on everybody. Ray-Ban RB4258 62321T features Shiny opal dark azure frame with Pink flash copper Rx-able lenses are engineered to protect your eyes from harmful UV rays and glare. Material used for the frame provides exceptional reliability and durability. You can wear it by the beach, on the ski slope or behind the wheel of a car; they are durable enough to last for many years. Furthermore, we can make Ray-Ban RB4258 62321T with prescription lenses if you prefer.
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Founded in 1937 by Bausch & Lomb, Ray-Ban is a popular American eyewear brand. With a tradition spanning almost a century, it is best known for its Aviator and Wayfarer sunglasses. The story of the Ray-Ban aviators begins back in the 1920s, when Lieutenant General John MacCready asked Bausch & Lomb to produce a pair of frames especially for the pilots who were susceptible to headaches caused by the glare of the sun. The resulting style was named "Ray-Ban Aviator" and its patent was released in 1937. In 1952, Ray-Ban introduces the Wayfarer. With plastic frames and a timeless, universally-flattering silhouette, the Wayfarers quickly became popular in Hollywood. They were worn by many stars of the time, including James Dean, Kim Novak, Marilyn Monroe, Bob Dylan and even John F. Kennedy. Ray-Ban continued to gain popularity and was featured in movies such as Risky Business (1983), Top Gun (1986) and Men in Black (1997). The brand continued to launch new styles and started to focus on appearing more relevant to the younger generations.
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Having a baby will impact your life in so many ways. The fact of the matter is that it is also an incredible change for your baby. All he has known is the peace and warmth of your womb. Now, he must adapt to this brand new world, which is totally foreign.
Once your baby is delivered, your healthcare provider will remove the fluid from his mouth and nose with a bulb syringe. This will allow your baby to take his first breath. He will then be wiped off with a clean towel to keep him from getting cold. This drying is also a good way of stimulating the baby to give a good cry. If your baby does not cry, do not worry. Some babies will take a bit of time to let out that first cry.
It is important to have contact with your newborn as soon as possible after birth. This contact will enable you to learn about your baby, while allowing him to learn your scent and the sound of your voice. Skin-to-skin contact is significant emotionally as well as physically and is very reassuring for both you and your baby.
When you and your infant are resting skin-to-skin, you will begin to learn about each other on many different levels. For you, the first minutes and hours after birth are a time when you're open emotionally to bond with your baby and begin the new relationship. At the same time, your newborn is ready to accept his new family and his brand new world.
At birth, your newborn will be scored on how he is transitioning to his surroundings outside of the womb. He will be scored on 5 different areas, (as noted below) once at 1 minute after birth and again at 5 minutes. This is the first "test" your baby will have and it is called the Apgar Score.
The Apgar Score was named after Dr. Virginia Apgar who devised this way of assessing a newborn immediately following birth. This was the first consistent method for evaluating the newborn's transition to life outside the womb. The score was presented in 1952 at a scientific meeting, and first published in 1953. This assessment tool is now used throughout the world.
For each area scored your baby will be given a 2, 1, or 0 on each of the above 5 responses. A score of 2 means that your baby has a healthy response to the area scored and a 0 means he is absent of a response. You may hear your nurse say "Apgar Score of 7 for first minute after birth and 9 for 5 minutes after birth." Some scores will be higher, some scores will be lower. This depends on how well your baby is adapting to his new environment. Your infant may need closer observation or his airway cleared. A score of less than 5 usually suggests that your baby may need oxygen, additional monitoring or other special care. This may feel like a scary time, but once the healthcare team works with your baby you may see that score rise. A perfect score is a 10, but most babies score between 7-10. The score will be written as 7/9 meaning the 7 represents 1 minute score and 9 is the 5 minute score.


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Shawn Mendes' "Stitches" Reaches 6x Platinum; "There's Nothing Holdin' Me Back" Now Platinum
The hitmaker just picked up new certifications from the RIAA.
Shawn Mendes on SNL | Will Heath/ NBC
by Brian Cantor Aug 15, 2017, 6:03 pm
As of this week, Shawn Mendes' discography boasts two pop radio number ones: "Stitches" and "There's Nothing Holdin' Me Back."
Both songs received new RIAA certifications on August 14.
"Stitches" improved to 6x platinum in the United States, while "There's Nothing Holdin' Me Back" earned a platinum certification.
The awards confirm 6 million and 1 million US units, respectively. Each unit is equal to 1 paid download or 150 streams.
"Stitches" peaked at #4 on the Billboard Hot 100. "There's Nothing Holdin' Me Back" has thus far reached #6.
shawn mendesstitchesthere's nothing holdin' me back
Sabrina Carpenter's "Thumbs" Earns Gold Certification In United States
Kelsea Ballerini's "Dibs" Earns Platinum Status In The United States


text:
Q: Grouping numbers in a table without using S-column This is bit different than my previous question.
I have a huge tables with 7 to 8 digits.
I need to make a small space between groups of three digits in the numbers.
I have used the package siunitx.
I want to do this without writing \SI in front of all the numbers and without using S-column in my code as my orginal tables are so big.
Also some of the data in my tables, I got a comma in every three digits so I want to replace this comma with a small space as well.
Here is the simplest version of my code:
\begin{tabular}{|l|l|l|}
\hline
x & y & z \\
\hline
9,833.823 & 550,245 & 15004568 \\
\hline
9,458.230 & 81,345.23 & 198000344 \\
\hline
\end{tabular}

A: Your posting seems to contain two separate concerns: (i) some macro-formatting, viz., how to fit a table with many rows and lots of multi-digit numbers into the available text block, and (ii) some micro-formatting, viz., how to group the digits into blocks of three (while disregarding any commas in the input) and how align the numbers on the decimal marker.
For your micro-formatting objectives, by far the best tool around is the siunitx package and its S column type. It's in your best interest to become familiar with its properties, really. If for some reason you do not want to use the S column type, you could proceed by (a) replacing all input commas with \, (thinspace), (b) inserting \, manually wherever needed to achieve grouping in blocks of three, and (c) using lots of \phantom statements to achieve alignment on the decimal markers. (The dcolumn package lets you avoid taking step (c). However, if you don't wish to use the S column type, I can't imagine that you'd want to use the D column type either.)
To achieve your macro-formatting objectives, you could start by reducing the amount of intercolumn whitespace and by switching, locally, to a slightly smaller font size. Omitting all vertical lines -- each such line has width 0.4pt -- is useful both because it economizes on space, i.e., helps with making the table fit inside the available text block, and because the table almost certainly looks better and is more readable without those vertical lines.
The following screenshot shows that both objectives can be pursued simultaneously.

\documentclass{article}
\usepackage{booktabs}  % for good-looking horizontal rules
\usepackage{siunitx}
\sisetup{input-ignore={,},
         input-decimal-markers={.},
         group-minimum-digits=4}

\begin{document}

before:

\smallskip
\begin{tabular}{|l|l|l|}
\hline
x & y & z \\
\hline
9,833.823 & 550,245 & 15004568 \\
\hline
9,458.230 & 81,345.23 & 198000344 \\
\hline
\end{tabular}

\bigskip
after:

\small  % 11% linear reduction in font size
\setlength\tabcolsep{4pt} % default value: 6pt
\small
\begin{tabular}{@{} S[table-format=4.3]
                    S[table-format=6.2]
                    S[table-format=9.0] @{}}
\toprule
{x} & {y} & {z} \\
\midrule
9,833.823 & 550,245 & 15004568 \\
9,458.230 & 81,345.23 & 198000344 \\
\bottomrule
\end{tabular}

\end{document}

redpajama_set_name: RedPajamaStackExchange


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The Deli closes after lunch at 1:30 pm on Friday, June 30th and re-opens at 11:30 am on Tuesday, September 12th.
Please visit the JCCV Food Kiosk at the Saanich Fair on the Labour Day weekend for your favourite pastrami sandwiches, all-beef kosher hot dogs, cheeze blintzes and much, much more.


text:
Cyprus-Switzerland amend taxation treaty in trade boost
Cyprus and Switzerland on Monday signed a protocol amending the Treaty for the avoidance of double taxation in a move both sides said will boost their trade ties while attracting investment.
The Protocol signed by Finance Minister Constantinos Petrides and Swiss Ambassador Pierre-Yves Fux introduces the minimum standards of the OECD's Base Erosion and Profit Shifting (BEPs) as well as provisions concerning benefit entitlement.
The Avoidance of Double Taxation agreement covers taxes on income and on capital related to bilateral agreements.
Upgrading and expanding the network of Double Taxation Conventions is of high economic and political importance as Nicosia aims to further strengthen and attract investments by promoting Cyprus as an international business centre.
Petrides said, "the signing of this protocol emphasises the very good relations in the economic and political sphere between the two jurisdictions".
He looked forward to further advancing and strengthening a mutually beneficial relationship between Cyprus and Switzerland.
"The Republic of Cyprus is confident that an environment that provides certainty also in tax matters is conducive for the promotions of investments, growth and job creation."
Pierre-Yves Fux said signing the protocol was "a little, but important milestone in our relations".
"This treaty is a tool to strengthen the framework for our financial and economic relations and also a tool to create worldwide a safer environment with regard to financial and other transactions.
"I hope that having a very good framework for our trade and commercial relations will be thanks to such a protocol and continue to develop our very good and bilateral relations on all levels, political, tourism, culture, and of course the financial aspect."
Negotiations with Russia
On the negotiations with Russian concerning a request by Moscow to amend the Double Taxation Treaty with Cyprus, Petrides said he expects them to conclude in the coming weeks.
Russia requested a renegotiation of the Double Tax Treaty (DTT) agreement, asking for an increase in the withholding on tax rates on dividend income from 5% or 10% (subject to conditions) to 15%, and on the interest income from 0% to 15%.
"We are in constant communication with the Russian authorities and negotiation are in progress," Petrides said.
"From the outset, we have stated our will to find a mutually agreed solution to the matter."
He said Cyprus has requested "some exemptions and other issues."
"For us, it is very important the position stated by the Russian side that the treaty will not only concern Cyprus but also other jurisdictions must be implemented."
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Moving to, and living in, Boca Raton was the best decision my family and I have made. From my youngest child to my wife, we have all been amazed and delighted at the warmth of the welcome we received and the plethora of activities and events that are available to us; tennis, baseball, parks, the beaches, our lives have definitely changed for the better. But what really surprized us is the sheer amount of goodwill and community activity in Boca Raton, and it's this community spirit that I want to talk about; the face of Boca that may not be immediately visible to commentators and visitors to the city.
Over the weekend, I counted more than one hundred non-profits in Boca covering a range of areas from the environment and the arts to the disabled and the elderly. All of these organizations are dedicated to improving the lives of our 200,000-strong population in our city. Being newcomers, we felt we wanted to give something back to the community that we now live in and enjoy. So, as a family, we have been investigating the possibility of volunteering in the future, and how we might contribute to the Boca community. This has been a difficult task because there are just so many organizations, and we are interested in a variety of sectors. While I would love to list all of the organizations looking for volunteers in the City, I thought I would highlight just a few to give you a flavor of some of the great projects and initiatives underway. For a more comprehensive list of non-profits and charities, visit The Boca Guide http://www.bocaguide.com/volunteer.html and Great Non Profits http://greatnonprofits.org/city/boca-raton/FL.
The Atrium is seeking volunteers to help in their Alzheimer/Dementia Unit. Preferences include: Volunteers who can play an instrument or sing in a group or one-on-one to residents. Volunteers should have some knowledge on Alzheimer's disease and/or related diseases, and volunteers must be positive!
The Tri County Animal Rescue is looking for volunteers to help as cat companions; dog walkers and bathers; front desk; adoption counselors; painters, plumbers and handypersons; fund raising volunteers are needed. Volunteers must 18 years of age or older.
The Gumbo Limbo Environmental Education Center is looking for volunteers with a love of marine animals and who like to meet and talk to new people every day. There are over 20 volunteer positions available at Gumbo Limbo. www.gumbolimbo.org.


text:
When to go China
[China Guide] Public Transport
[How To]: Soundproof Your Life
China City
China Life
Here's Some Adjusted Routes Chinese Airlines are Still Operating
Posted by life-china | May 10, 2020 | Article, Coronavirus, Travel | 0 |
Last week, the Civil Aviation Administration of China (CAAC) announced that China would be drastically cutting passenger flights in an effort to contain a potential 'second wave' of the coronavirus pandemic. As the number of confirmed cases continues to rise outside of China, CAAC ordered Chinese airlines to operate only one route per country, once a week. Three of the 'big four' airlines have announced their adjusted routes via Weibo, which will be in effect until the end of April.
Air China's notice is in effect from March 29 until April 30. International flights from Beijing Capital (PEK) will head to 17 countries across North America, Europe and Asia. Flights originating from Shanghai Pudong (PVG) will have routes to Germany, England, Thailand, Singapore and Japan. Lastly there is one route from Chengdu to Nepal.
China Eastern Airlines' new routes operate from March 29 until May 2. The majority of routes (except for one) will start from Shanghai Pudong (PVG) and fly to countries in Southeast Asia, Asia, Australia, Europe and North America.
The airline's adjusted routes are in effect from March 29 to May 2. Guangzhou Baiyun is the main hub where flights will leave from, and routes will serve 15 countries across Europe, North America, Australia, New Zealand, Southeast Asia and South Asia. Flights to Korea and Japan are only available from Shenyang, Liaoning province.
There are still multiple smaller Chinese airlines flying their own routes, be sure to check on those carrier's official pages, such as Weibo, for more schedules.
READ MORE: 90% of China's Imported COVID-19 Cases are Chinese Nationals
[Cover image via Air China]
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