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text:
\section{Statement of the results.}\label{s1}

Our purpose in this paper is to answer the following issues when $A$ is a  bounded  operator in
 $L^2 (\R^n)$:

 1. Under what condition,  the Weyl symbol of  $A$ is a bounded continuous function on $\R^{2n}$ ?

 2. Under what condition,   $A$ is the anti-Wick quantization of a bounded continuous function on $\R^{2n}$ ?

 3. Can one express the Weyl and anti-Wick symbols with a  Campbell-Hausdorff type formula ?

These questions are also mentioned in  \cite{K-R}. A positive answer to the first two questions (a sufficient condition) is given by Theorem \ref{t1}  for the Weyl symbol and by Theorem \ref{t3}
for the anti-Wick symbol. Concerning Question 3, an answer is given combining  Theorem \ref{t1} or Theorem \ref{t3}  with Theorem  \ref{transfo-beals}. For instance, one gets (\ref{AWCH})
in the case of  the anti-Wick quantization.

Let us emphasize that it is also our aim to provide conditions and formulas for the two symbols where the dimension is not explicitly written down using Gaussian measures. Thus, the dimension can tends to infinity and more importantly, one can expect to consider the infinite dimension setting for theses purposes in a further work.

In the article \cite{HS-RD}, H\"ubner and Spohn have introduced the so-called scattering identification operator (unbounded operator) and considered the wave operator in the context of the infinite dimension, concerning some physical model. With L. Jager, we have proved in
 \cite{A-J-N} that the first operator (scattering identification) can also be defined with the anti-Wick quantization. That is, this operator is defined by an integral formula and it would be interesting to know if the second operator (wave) shares that property. One may expect that the present work, adjusted to the infinite dimension case, could  give an answer to that question.

We begin by recalling the two quantizations under consideration here. See, $e.g.$,
 Berezin \cite{FAB},  Combescure and Robert \cite{C-R}, Folland \cite{F}, H\"ormander \cite{HO},
 Lerner \cite{Ler}, Unterberger \cite{U}\cite{Unt-OH}, $\dots$ for these purposes.

One can define the Weyl symbol of a continuous operator $A$ from  ${\cal S}(\R^n)$
to ${\cal S}'(\R^n)$ as an element of  ${\cal S}'(\R^{2n})$. More precisely, denoting by $K_A(x , y)$ the distributional kernel
of $A$ (belonging to ${\cal S}'(\R^{2n}))$,
the  Weyl symbol of $A$ is defined by:
\begin{equation}\label{noyau-symbole}  F(x , \xi) =   \int _{\R^n} e^{ - i v\cdot \xi} K_A ( x + v/2,  x - v/2)
dv \end{equation}
where the above integral is actually a Fourier transform in sense of tempered distributions.

The second kind of quantization under consideration in this paper is the anti-Wick one, which involves  coherent states.
These states are a standard family of functions  $\Psi_X$ indexed by $X = (x , \xi)\in \R^{2n}$ defined by:

 $$ \Psi _{x , \xi} (u) =  \pi ^{-n/4} e^{ - \frac {1} {2} |u-x|^2
 + i u \cdot \xi -  \frac {i} {2} x \cdot \xi}. $$

One has:

 \begin{equation}\label{PSEC}  < \Psi_X , \Psi_Z >
 = e^{ -  \frac {|X- Z|^2} {4} + \frac {i} {2}
\sigma (X , Z) } \end{equation}
where  $\sigma $ is the symplectic form, $\sigma ( (x , \xi), (y, \eta)) = y \cdot \xi - x \cdot \eta$.
For any function $G$,  bounded and continuous on  $\R^{2n}$, one defines
 the anti-Wick operator $Op^{AW}(G)$ associated with the function $G$, as the unique operator satisfying for all $f$ and $g$ in $L^2(\R^n)$:

 \begin{equation}\label{def-AW}  <Op^{AW}(G) f , g> = (2\pi )^{-n} \int _{\R^{2n}} G(Z)
 < f, \Psi_Z> < \Psi _Z , g> dZ. \end{equation}

Before developing Question 3 with Campbell Hausdorff type formulas and iterated commutators, we present answers to the first two questions addressed above, in the spirit of the characterization of A. Unterberger \cite{U}.

\begin{theo}\label{t1}
Let $A$ be a bounded operator in $L^2(\R^n)$ and assume that:

 \begin{equation}\label{hyp-Weyl}   \sup _{X\in \R^{2n}}  \pi ^{-n} \int _{\R^{2n} }
 \left |\frac {   <  A \Psi_{X+Z}  , \Psi_{X-Z}  >} {  <   \Psi_{X+Z}  , \Psi_{X-Z}  >} \right |
 e^{ - |Z|^2} dZ <  \infty. \end{equation}

 Then, the Weyl symbol $F$ of $A$ is a bounded continuous function on $\R^{2n}$  given by the formula:

\begin{equation}\label{symbole-weyl}  F(X) =  \pi ^{-n}  \int _{\R^{2n}}
\frac {   <  A \Psi_{X+Z}  , \Psi_{X-Z}  >} {  <   \Psi_{X+Z}  , \Psi_{X-Z}  >}
  e^{ -|Z|^2}  dZ. \end{equation}

\end{theo}

We underline that hypothesis (\ref{hyp-Weyl}) and equality (\ref{symbole-weyl}) are uniform with respect to the dimension since these expressions only use the variance $1/2$  Gaussian measure which also exists in infinite dimension. For a reader interested only in the finite dimensional case, one can check that, using (\ref{PSEC}),
the hypothesis  (\ref{hyp-Weyl}) can also be written as:
$$  \sup _{X\in \R^{2n}} \int _{\R^{2n} }
 |< A \Psi_{X+Z} ,  \Psi_{X-Z}>| dZ <  \infty $$
and (\ref{symbole-weyl}) can also be expressed as:
$$ F(X)  =  \pi ^{-n}  \int _{\R^{2n}}  <  A \Psi_{X+Z}  , \Psi_{X-Z}  > e^{i \sigma (X , Z) }
dZ.$$

Next we turn to conditions ensuring the existence of a bounded continuous symbol with the anti-Wick quantization for a given bounded operator.

Firstly, we give a necessary condition.

 \begin{theo}\label{t2}  If $A= Op^{AW}(G)$ with  $G$ bounded and continuous on $\R^{2n}$ then:

 \begin{equation}\label{CN}  |<  A \Psi_X  , \Psi_{Y}  > | \leq \Vert G \Vert _{\infty } e^{ - \frac {1} {8}
| X -  Y |^2 }.\end{equation}

 \end{theo}

In particular, the following estimate holds,

 $$   | < A \Psi_{X+Y}   , \Psi_{X -Y}  >| \leq \Vert G \Vert _{\infty }
 e^{ - \frac {1} {2} |  Y |^2 }$$
for all $X$ and $Y$ in $\R^{2n}$, when $A= Op^{AW}(G)$ where  $G$ is bounded and continuous on $\R^{2n}$.

Secondly, we provide a sufficient condition, together with an integral expression for a possible anti-Wick symbol.

 \begin{theo}\label{t3} Suppose that  $A$ is a bounded operator in $L^2 (\R^n)$ satisfying:

 \begin{equation}\label{CSAW}  \sup  _{X\in \R^{2n}} (2\pi )^{-n} \int _{\R^{2n}}
  \left |\frac {   <  A \Psi_{X+Z}  , \Psi_{X-Z}  >} {  <   \Psi_{X+Z}  , \Psi_{X-Z}  >} \right |
 e^{ - \frac {|Z|^2} {2} } dZ < \infty. \end{equation}

 Then, there exists a bounded continuous function $G$ on $\R^{2n}$ such that
 $A = Op^{AW} (G)$.  This function is given by:

   \begin{equation}\label{formule-symb-AW}
   G(X) =  (2\pi )^{-n}  \int _{\R^{2n}}
   \frac {   <  A \Psi_{X+Z}  , \Psi_{X-Z}  >} {  <   \Psi_{X+Z}  , \Psi_{X-Z}  >}
    \ e^{- \frac {1} {2} |  Z |^2 } dZ.\end{equation}

\end{theo}

Note that condition (\ref{CSAW}) can also be written as:

 $$ \sup  _{X\in \R^{2n}} (2\pi )^{-n} \int _{\R^{2n}}
   | < A \Psi_{X+Z}   , \Psi_{X -Z}  >|\   e^{  \frac {1} {2} |  Z |^2 }
   dZ < \infty$$
and equality (\ref{formule-symb-AW}) is also:
$$  G(X) =  (2\pi )^{-n}  \int _{\R^{2n}}
    < A \Psi_{X+Z}   , \Psi_{X -Z}  > e^{ i\sigma (X , Z)}
   \ e^{  \frac {1} {2} |  Z |^2 } dZ. $$

We now give answers to Question 3 in the spirit of Beals characterization \cite{Bea}.

We first note that the function appearing in  (\ref{symbole-weyl})  and (\ref{formule-symb-AW})
can also be written with an expression comparable to the  Campbell-Hausdorff formula.  To this end, we denote by $ \Phi_S(Z)$ the differential operator:
\begin{equation}\label{PhiS}  \Phi_S(Z) = \sum _{j = 1}^n \left ( z_j u_j + \zeta_j \frac {1} {i}
\frac {\partial } {\partial u_j}\right ) \end{equation}
for all $Z = (z , \zeta)\in \R^{2n}$.
\begin{theo}\label{transfo-beals} For all $X$ and $Z$ in $\R^{2n}$, we have the following equality:
\begin{equation}\label{it-comm}  \frac {   <  A \Psi_{X+Z}  , \Psi_{X-Z}  >} {  <   \Psi_{X+Z}  , \Psi_{X-Z}  >}
= \Big < e^{- \Phi_S(Z) }  A e^{\Phi_S(Z) }   \Psi_{X},
 \Psi_{X}   \Big > . \end{equation}

\end{theo}

One notices that the operator  $e^{\Phi_S(Z) }$  is unbounded in $L^2(\R^n)$. Nevertheless, its action on coherent states is well defined. It is  given by:
\begin{equation}\label{segal-EC}  e^{\Phi_S(Z) } \Psi_X = e^{ \frac{1} {2} |Z|^2 + Z \cdot X -  \frac{i} {2} \sigma (Z, X)}
     \Psi_{X+Z}.\end{equation}
One observes that (\ref{it-comm}) only uses iterated commutations according to the Campbell Hausdorff formula.
One has in  the sense of formal series:
$$ e^{-\Phi_S(Z) }  A e^{\Phi_S(Z) }   = \sum _{m= 0}^{\infty }  \frac{(-1)^m } {m!}
   \big ( {\rm ad}\, \Phi_S(Z) \big ) ^m A. $$
Inserting this equality in  (\ref{symbole-weyl})  and in (\ref{formule-symb-AW}), one then obtains an expression for the Weyl and anti-Wick symbol  of $A$ with an integral using only iterated commutations.
To be specific, for the possible anti-Wick symbol $G$ of an operator $A$, if the integral is absolutely converging, one has
\begin{equation}\label{AWCH}   G(X) =  (2\pi )^{-n}  \int _{\R^{2n}}
\Big < e^{- \Phi_S(Z) }  A e^{\Phi_S(Z) }   \Psi_{X},
 \Psi_{X}   \Big >  \ e^{  - \frac {1} {2} |  Z |^2 } dZ. \end{equation}

One can also give a result (see below) specific to the finite dimension, close to the Beals characterization theorem \cite{Bea}.
 Denote by $V_1,\dots,V_n$ the canonical basis of
$\R^n$ and set  $a(V_j) = x_j + \partial _{x_j}$. For all multi-indexes
$\alpha$ and any bounded operator $A$ from ${\cal S}(\R^n)$
to ${\cal S}'(\R^n)$, set $({\rm ad} \,a(V)) ^{\alpha} A =
{\rm ad}\,  a(V_1)^{\alpha _1} \dots {\rm ad}\,  a(V_n)^{\alpha _n}A$.

\begin{prop}\label{beals}  For any operator $A$ from ${\cal S}(\R^n)$
to ${\cal S}'(\R^n)$ with iterated commutators
$({\rm ad}\, a(V)) ^{\alpha} A$ bounded
in $L^2 (\R^n)$ when $|\alpha | \leq 2n+1$, one has:
\begin{equation}\label{norme-beals}    \int _{\R^{2n}}
  |<  A \Psi_{X+Z}  , \Psi_{X-Z}  >|  dZ \leq C_n
  \sum _{ |\alpha | \leq 2n+1 } \Vert ({\rm ad}\, a(V)) ^{\alpha} A \Vert \end{equation}
where the constant  $C_n$ depends on the dimension  $n$ but not on the operator $A$.

\end{prop}
We then recover in particular a well known result of  R. Beals \cite{Bea}
for the Weyl symbol $F$ of an operator $A$:
$$ \sup _{X\in \R^{2n}} |F(X)| \leq C_n  \sum _{ |\alpha | \leq 2n+1 }
\Vert ({\rm ad}\,  a(V)) ^{\alpha} A \Vert. $$
We also mention that there is a result of  C. Rondeaux \cite{R} where above, the supremum bound is replaced by the $L^1$ norm and the operator norm is replaced by the trace class norm.

Theorem  \ref{t1} and  Theorem \ref{t3} rely on a inversion result for the heat operator (Theorem \ref{t-2-1}) that is proved in Section \ref{s2}. On the basis of this result (Theorem \ref{t-2-1}),  Theorems
\ref{t1} and  \ref{t3}  are proved in Sections  \ref{s3} and  \ref{s4}.
 Equality (\ref{segal-EC}),   Theorem \ref{transfo-beals}
and Proposition \ref{beals} are proved in Section \ref{s5}.

 \section{Inversion of the heat operator.}\label{s2}

For each $\lambda >0$,  the heat operator $H _{\lambda }$ is defined for all bounded continuous function $F$ on $\R^{2n}$ by:
$$ (H _{\lambda } F) (z , \zeta) =   (2 \pi \lambda ) ^{-n}  \int _{\R^{2n}} F(x, \xi )
e^{ -  \frac {1} {2 \lambda } \big (  (x-  z)^2 +  (\xi  - \zeta )^2 \big )  } dx d\xi
\hskip 2cm (z , \zeta ) \in \C^{2n} $$
where  $z^2  = z_1 ^2 + \cdots + z_n ^2$ for all $z = ( z_1 , \cdots z_n)\in\C^n$.
This function is holomorphic on $\C^{2n}$.

The purpose of Theorem \ref{t-2-1} is to prove that the image of the operator $H _{\lambda }$
contains some specific space playing a role in the following sections. We also use another function $ S _{\lambda } F$
on $\C^{2n}$ defined by:
\begin{equation}\label{rotat}  (S _{\lambda } F) (z , \zeta) =  (H _{\lambda } F) (i \zeta, -iz ).\end{equation}
That is:
\begin{equation}\label{S-lambda-1} (S _{\lambda } F) (z , \zeta) =   (2 \pi \lambda ) ^{-n}  \int _{\R^{2n}} F(x, \xi )
e^{ -  \frac {1} {2 \lambda } \big (  (x - i \zeta)^2 +  (\xi  + i z)^2 \big )  } dx d\xi
\hskip 2cm (z , \zeta ) \in \R^{2n}.  \end{equation}

\begin{theo}\label{t-2-1}   Let $\Phi$  be a holomorphic function on  $\C^{2n}$. Set $\lambda >0$ and suppose that:
\begin{equation}\label{S-lambda-2} \sup _{(x , \xi) \in \R^{2n}  } (2\pi \lambda ) ^{-n} \int _{\R^{2n}}
|\Phi ( x + i \xi + z + i \zeta ,   x - i \xi - z + i \zeta ) | e^{- \frac {|z|^2 + |\zeta |^2  } {2\lambda }} dz d\zeta  < \infty. \end{equation}
Define the function $F$ on  $\R^{2n}$  by:
\begin{equation}\label{S-lambda-3} F(x , \xi) =  (2\pi \lambda ) ^{-n} \int _{\R^{2n}}
\Phi ( x + i \xi + z + i \zeta ,   x - i \xi - z + i \zeta )  e^{- \frac {|z|^2 + |\zeta |^2  } {2\lambda }} dz d\zeta.
\end{equation}

 Then,  $F$ is a bounded continuous function on $\R^{2n}$ satisfying:

 \begin{equation}\label{H-lambda} (H_{\lambda } F ) (z , \zeta ) = \Phi ( z + i \zeta  ,
  z - i \zeta ) \hskip 2cm (z , \zeta ) \in \C^{2n} \end{equation}

 \begin{equation}\label{S-lambda-4} (S_{\lambda } F ) (z , \zeta ) = \Phi ( z + i \zeta  ,
 - z + i \zeta ) \hskip 2cm (z , \zeta ) \in \C^{2n}. \end{equation}

 \end{theo}

 {\it Proof.} The fact that $F$ is well defined, bounded and continuous, is a direct consequence of hypothesis (\ref{S-lambda-2}).
 For all $(x , \xi)\in\R^{2n}$,  let $\Psi_{(x , \xi)} $ be the holomorphic function on $\C^{2n}$ defined by:

 $$ \Psi _{(x , \xi)}  (Z_1 , Z_2) =  \Phi  (Z_1 , Z_2) e^{   \frac {1} {2 \lambda }
 \big ( Z_1 Z_2 + x^2 + \xi^2 - x ( Z_1 + Z_2) + i \xi ( Z_1 - Z_2) \big ) }.$$

 Set $\varphi$  the mapping from $\R^{2n}$ to $\C^{2n}$ defined by
 $\varphi (s, t) = ( s+i t, -s + i t)$.
Equality  (\ref{S-lambda-3}) can then be written as:

 $$ F(x , \xi) =  (2\pi \lambda ) ^{-n}  \int_{\R^{2n}}
   \Psi _{(x , \xi)}  \big (  ( x+ i \xi , x - i \xi) + \varphi (s, t) \big )
 ds dt. $$

 We then apply Lemma \ref{DSS} below with $n$ replaced by
 $2n$, $E = \{ (x + i \xi, x - i \xi), \ (x , \xi) \in \R^{2n} \}$, together with the above functions  $\varphi$ and $\Psi =  \Psi _{(x , \xi)}$. According to hypothesis (\ref{S-lambda-2}), for all compact sets $K$
 of $\R^{2n}$, with $(x, \xi)$ being fixed:

 $$ \sup _{(y, \eta)\in K}  \int _{\R^{2n}}
|\Psi _{(x , \xi)} \big ( (y+ i \eta ,   y - i \eta) + \varphi (s , t) \big ) | ds dt < \infty.$$
 Consequently, hypothesis  (\ref{hyp-lemm})  of Lemma \ref{DSS} is satisfied.
 According to that Lemma, one has:

 $$ F(x , \xi) =  (2\pi \lambda ) ^{-n}  \int _{\R^{2n}}
 \Psi _{(x , \xi)}   \big ( \varphi (s, t) \big )
 ds dt.$$

 This equality can be written as:

 $$ F(x , \xi) =   (2\pi \lambda ) ^{-n} \int _{\R^{2n}}
 \Phi ( z + i \zeta ,   - z + i \zeta )
 e^{ -  \frac {1} {2 \lambda } \big (  (z - i \xi)^2 +  (\zeta   + i x)^2 \big )  }
 dz d\zeta.  $$

Set:

 $$ G(z, \zeta) =   \Phi ( z + i \zeta ,   - z + i \zeta )
 e^{- \frac {|z|^2 + |\zeta |^2  } {2\lambda }}
 \hskip 2cm
 H(x , \xi) = F( \xi, -x)\  e^{- \frac {|x|^2 + |\xi |^2  } {2\lambda }}.  $$
Hypothesis (\ref{S-lambda-2}) with  $(x , \xi)= (0, 0)$ shows that the function $G$ belongs to $L^1(\R^{2n})$.
The above equality reads as:
$$  H(x , \xi) = ( 2\pi \lambda ) ^{-n} \int _{\R^{2n}} G(z, \zeta)
e^{- \frac {i} {\lambda }  ( x\cdot z + \xi \cdot \zeta)} dz d \zeta.$$
Thus, $H$ is the Fourier transform depending on the parameter
$\lambda$ of $G$. Since $F$ is bounded and continuous then $H\in L^1(\R^ {2n})$.
Hence,
$$  G(x , \xi) = ( 2\pi \lambda ) ^{-n} \int _{\R^{2n}} H(z, \zeta)
e^{ \frac {i} {\lambda }  ( x\cdot z + \xi \cdot \zeta)} dz d \zeta.$$
This equality is equivalent to  (\ref{S-lambda-4}) for real  $(z , \zeta)$.
Equality (\ref{S-lambda-4}) then follows for $(z , \zeta)\in \C^{2n}$ using the holomorphic properties of the two hand sides. Equality (\ref{H-lambda}) then holds according to (\ref{rotat}).  \fpr

The Lemma below would be in the particular case of the dimension one, the result for changing integration contours with holomorphic functions when these integration contours are parallel lines.

\begin{lemm}\label{DSS}  Set $E$ a $n-$dimensional real subspace of $\C^n$.
Let $\varphi $ be a linear map from $\R^n$ to $\C^n$ satisfying
 ${\rm det } \varphi ' \not=0$. Assume that $E \oplus {\rm Im} \varphi = \C^n$.
Set $\Psi$ a holomorphic function on $\C^n$.
Suppose that, for any compact set $K$ of $E$:
\begin{equation}\label{hyp-lemm}  \sup _{a\in K} \int _{\R^n} | \Psi (a + \varphi (t ))|  d t < \infty.  \end{equation}
Set:
$$ I(a) = \int _{\R^n} \Psi (a + \varphi (t )) d t $$
for any $a\in E$ where $dt $ is the  Lebesgue measure on $\R^n$. Then $I$ is independent of  $a\in E$.

\end{lemm}

{\it Proof of the Lemma.} For all $R>0$, set:
$$ K_R = \{ t \in \R^n , \ \ |t_j| \leq R , \ \ \ \ 1 \leq j \leq n \}.$$
Set $\partial K_R$ the boundary of $K_R$ with the canonical measure $d \mu_R$.
For all $k\leq n$, we have:
$$ \left | \int _{K_R }  \frac { \partial } {\partial t_k} \Psi (a + \varphi (t )) dt
\right  |  \leq \int _{\partial K_R } |\Psi (a + \varphi (t )) | d \mu_R(t).  $$
Since $\Psi$ is holomorphic:
$$ \left | \sum _{j= 1}^n  \frac { \partial \varphi_j  } {\partial t_k}
  \int _{K_R}  (\partial _j \Psi) (a + \varphi (t )) dt \right  |
  \leq \int _{\partial K_R } |\Psi (a + \varphi (t )) | d \mu_R(t).   $$

As the determinant of the matrix $ \frac { \partial \varphi_j  } {\partial t_k} $
is non vanishing, one gets for all  $j \leq n$:

  $$ \left |   \int _{K_R}  (\partial _j \Psi) (a + \varphi (t )) dt  \right  |
   \leq C \int _{\partial K_R } |\Psi (a + \varphi (t )) | d \mu_R(t)  $$

with $C>0$. Using that  $\Psi$ is holomorphic, there exists another constant $C>0$ such that,  for all $Z\in \C^n$:

  \begin{equation}\label{moyenne} |\Psi (Z)| \leq C \int _{B(Z, 1)} |\Psi (W)| dW. \end{equation}

 Consequently, with another constant  $C$ and another $\rho >0$:

  $$ \int _{\partial K_R } |\Psi (a + \varphi (t )) | d \mu_R(t)
  \leq C \int _{B_E(a, \rho) \times F ( \partial \Gamma _R , \rho) }
  |\Psi (a'  + \varphi (t )) | \  d\mu_E (a') dt $$

  where $B_E(a, \rho) $ is the ball of $E$  centered at $a$ with radius $\rho$, $\mu_E$ is the canonical measure on $E$ and  $F ( \partial \Gamma _R , \rho)$
  is the set of all points in  $\R^n$ whose distance to $\partial \Gamma _R $
  is smaller than $\rho$. One then deduces that, for all  $a$ and $b$ in $E$, for any $R>0$:

  $$  \left | \int _{K_R}  \big (  \Psi (a + \varphi (t )) - \Psi (b + \varphi (t ))
  \big ) dt   \right  |  \leq  C  \int _{F_E([a, b], \rho) \times F ( \partial \Gamma _R , \rho) }
  |\Psi (a'  + \varphi (t )) | \  d\mu_E (a') dt   $$

  where $F_E([a, b], \rho)$ is the set of all points in  $E$ whose distance to the interval
  $[a, b]$ is smaller than $\rho$.
  The right hand side tends to zero (the constants $C$ and $\rho$ are independent of $R$) as $R$ goes to infinity.
 One then concludes that
  $I(a) = I(b)$ which proves the Lemma.
  \fpr

Let us also mention another property of the operator $S_{\lambda}$. Denote by  $M_{\lambda}$ the following multiplication operator:
$$ (M_{\lambda}F) (x , \xi) = e^{-  \frac {1} {2 \lambda } ( |x|^2 +  |\xi |^2) }
F(x , \xi). $$
One then sees that $M_{\lambda}\ S_{\lambda} F = T_{\lambda}\ M_{\lambda} F$ where:
$$  (T_{\lambda}F) (z , \zeta) = ( 2\pi \lambda ) ^{-n} \int _{\R^{2n}}
F(x , \xi) \  e^{  \frac {i} { \lambda } ( z \cdot \xi - x \cdot \zeta ) }
dx d\xi.$$
One notes that $T_{\lambda}$ is an isometry from $L^2(\R^{2n} )$ into itself,
whose square is the identity operator. It is the symplectic Fourier transform with parameter (see \cite{C-R}). Hence,  $S_{\lambda}$ is an isometry from
$E = \{ F , M_{\lambda}F\in L^2(\R^{2n} ) \} $ into itself, whose square is the identity. These properties are not further used in this work.

 \section{Weyl symbol.}\label{s3}

It is knwon (\cite{F}, page 139)  that, for any bounded operator $A$ from  ${\cal S}(\R^n)$ to ${\cal S}'(\R^n)$,
there exists an homomorphic function   $B(A)$ on $\C^{2n}$  such that, for all  $X = (x , \xi)$ and $Y = (y , \eta)$  identified with elements of $\C^n$:
\begin{equation}\label{bisymbole}  \frac {   <  A \Psi_X  , \Psi_{Y}  >} {  <   \Psi_X  , \Psi_{Y}  >} =
B(A) ( x+ i \xi, y - i \eta). \end{equation}
Set $A$ a bounded operator in
$L^2(\R^n)$ satisfying (\ref{hyp-Weyl}).  Assumption (\ref{hyp-Weyl}) then reads as:

 $$  \sup _{X\in \R^{2n}}  \pi ^{-n} \int _{\R^{2n} }
 \left | B(A) ( X+Z , \overline X - \overline Z ) \right |
 e^{ - |Z|^2} dZ <  \infty. $$

That is, the function  $\Phi = B(A)$ satisfies the assumption of Theorem
 \ref{t-2-1} with $\lambda = 1/2$. According to that Theorem, the function $F$ defined by  (\ref{S-lambda-3}), that is to say by (\ref{symbole-weyl}) when $\lambda = 1/2$ and $\Phi = B(A)$, is continuous and bounded on  $\R^{2n}$ and verifies (\ref{S-lambda-4}) with $\lambda = 1/2$.
Namely:

 \begin{equation}\label{egal-bisymb-1}  (S_{1/2}F) (Z) =   B( A) (Z , - \overline Z).    \end{equation}

Inverting the  transform in
 (\ref{noyau-symbole}), one associates with   $F$ some tempered distribution on
 $\R^{2n}$ which is the kernel $K_{A'} $ of some operator $A'$, bounded from ${\cal S}(\R^n)$
to ${\cal S}'(\R^n)$,  whose Weyl symbol is $F$.
In view of the Lemma below, one has for all $Z\in\C^n$:

 \begin{equation}\label{egal-bisymb-2}  B( A') (Z , - \overline Z) = (S_{1/2}F) (Z).   \end{equation}

We recall Proposition 1.69 in \cite{F}.  If  $G$ is a holomorphic function on  $\C^n \times \C^n$
and if  $G (Z, - \overline Z)=0$ for all $Z\in\C^n$ then  $G$ is entirely vanishing.
Indeed, all the  $\partial ^{\alpha }G$ are vanishing at the origin by iteration.
Thus, from (\ref{egal-bisymb-1}) and (\ref{egal-bisymb-2}),
      $ B( A - A')$ is identically zero. Then,
 $ < (A-A')\Psi_X , \Psi_Y >= 0$ for all $X$ and $Y$ in $\R^{2n}$ proving that
 $A-A'= 0$. Therefore $F$ is the Weyl symbol of  $A$.

 \begin{lemm} Set $F$ a bounded continuous function on  $\R^{2n}$. Let
 $A' $ be the bounded operator from    ${\cal S}(\R^n)$ to ${\cal S}'(\R^n)$
  with  $F$ as Weyl symbol.  Then, (\ref{egal-bisymb-2}) holds where
  $S_{1/2}$  is defined in (\ref{S-lambda-1}).

  \end{lemm}

 {\it Proof of the Lemma.}  In view of (\ref{noyau-symbole}),  the operator $A'$, bounded from  ${\cal S}(\R^n)$ to ${\cal S}'(\R^n)$)
 with a Weyl symbol equal to  $F$, satisfies for all  $X$ and $Y$ in $\R^{2n}$:

 \begin{equation}\label{Weyl-A} < A' \Psi_X  , \Psi_Y  >  =
  \pi ^{-n}  \int _{\R^{2n}} F(Z) <\Sigma _Z \Psi_X  , \Psi_Y  >  dZ \end{equation}

 where $ \Sigma _Z$ for each $Z = (z, \zeta)\in\R^{2n}$ is the operator acting in
 $L^2(\R^n)$ defined by:

 $$ \Sigma _Z f (u) = e^{2i ( x - z)\cdot \zeta} f ( 2z - x)
 \hskip 2cm    f\in L^2(\R^n). $$

 In particular:

 $$ \Sigma _Z \Psi_X = e^{i \sigma (X , Z)} \Psi_{ 2Z - X} $$

 and therefore, using (\ref{PSEC}):

 \begin{equation}\label{Weyl-B}  < \Sigma _Z \Psi_X  ,\Psi_{-X} >
 = e^{2 i \sigma (X , Z)-  |Z|^2 }.  \end{equation}

One deduces from  (\ref{bisymbole}), (\ref{PSEC}), (\ref{Weyl-A}), (\ref{Weyl-B}),
and (\ref{S-lambda-1}):

 \begin{align*}
 B(A') (Z , - \overline X )  &=  \frac {   <  A' \Psi_X  , \Psi_{-X}  >} {  <   \Psi_X  , \Psi_{-X}  >}  \\
 &=  e^{ |X|^2} <A'  \Psi_X ,  \Psi_{-X} > \\

&=  \pi ^{-n} e^{ |X|^2}   \int _{\R^{2n}} F(Z) <\Sigma _Z \Psi_X  , \Psi_{-X}   >  dZ  \\

 &= \pi ^{-n}  \int _{\R^{2n}} F(Z)  e^{ |X|^2 + 2 i \sigma (X , Z)-  |Z|^2 }  dZ    = S_{1/2} F (X)

 \end{align*}
which proves the Lemma. \fpr

  \section{Anti-Wick symbol.}\label{s4}

{\it Proof of Theorem \ref{t2}. } If $A = Op^{AW}(G)$ then, according to (\ref{def-AW}):
$$ <  A \Psi_X  , \Psi_{Y}  > = (2\pi )^{-n}  \int _{\R^{2n}}  G(Z)
 < \Psi_X , \Psi_Z> < \Psi _Z , \Psi_{Y} > dZ. $$
Using (\ref{PSEC}):
\begin{equation}\label{egalite}   < A \Psi_X  , \Psi_{Y}  >  = (2\pi )^{-n}  \int _{\R^{2n}}  G(Z)
e^{ - \frac {1} {4} \big ( |X - Z|^2 + |Y - Z|^2 \big ) + \frac {i} {2}
\sigma (X - Y , Z)       }dZ.\end{equation}
From the parallelogram identity:
$$ | < A \Psi_X  , \Psi_{Y}  >| \leq (2\pi )^{-n}  \int _{\R^{2n}}  |G(Z)|
e^{ - \frac {1} {2} \left  | Z - \frac {X+Y} {2} \right  |^2 - \frac {1} {8}|X-Y|^2 } dZ.$$
One then obtains (\ref{CN}).\fpr

{\it Proof of Theorem \ref{t3}. } Set   a bounded operator $A$ in
$L^2(\R^n)$ satisfying (\ref{CSAW}). That is, the function $B(A)$ defined by (\ref{bisymbole}) satisfies the assumption of Theorem  \ref{t-2-1} with $\lambda = 1$. According to that Theorem, the function $G$ defined by
 (\ref{S-lambda-3}) with $\lambda = 1$ and $\Phi = B(A)$, or equivalently by
  (\ref{formule-symb-AW}),  is bounded and continuous on $\R^{2n}$ and satisfies (\ref{S-lambda-4})
with $\lambda = 1$. In other words:

 $$ (S_{1}G) (Z)  =  B(A) (Z , - \overline Z).$$

One can define an operator $A' = Op^{AW} (G)$ bounded in $L^2(\R^n)$ with the function $G$ since $G$ is bounded and continuous.
In view of the Lemma below, one has
$ B(A - A')(Z , - \overline Z) = 0$, for all $Z\in\C^n$. One finishes the proof similarly to the one of Theorem  \ref{t1}. \fpr

  \begin{lemm} Let  $G$ be a bounded continuous function on $\R^{2n}$ and set
 $A' =  Op^{AW} (G) $ (bounded operator in $L^2(\R^n)$).
Then:
\begin{equation}\label{BSAW} B(A') (Z , - \overline Z) = (S_{1}G) (Z). \end{equation}

 \end{lemm}

 {\it Proof of the Lemma.} From (\ref{egalite}) with $A$ replaced by $A'$,
one has, for any  $X\in\C^n$:

 $$   < A' \Psi_X  , \Psi_{-X}  >  = (2\pi )^{-n}  \int _{\R^{2n}}  G(Z)
e^{ - \frac {1} {4} \big ( |X - Z|^2 + |X +  Z|^2 \big ) +  i
\sigma (X , Z)       } dZ. $$
From  (\ref{bisymbole}), (\ref{PSEC}) and (\ref{S-lambda-1}) with $\lambda = 1$,
one then obtains (\ref{BSAW}). \fpr

 \section{Iterated commutators.}\label{s5}

{\it Proof of (\ref{segal-EC}).}  We first note that  $\Psi_0 (u) =  \pi ^{-n/4} e^{ - \frac {1} {2} |u|^2}$,
and that, as $\Phi_S(X)$
is the operator defined in (\ref{PhiS}), we have:
$$ e^{\Phi_S(X) }  \Psi_0 =  e^{ \frac{1} {2} |X|^2 }  \Psi_X $$
and:
$$  e^{\Phi_S(Z) }   e^{\Phi_S(X) }  = e^{ - \frac{i} {2} \sigma (Z, X) }   e^{\Phi_S(Z+ X ) }.   $$
Thus, one gets (\ref{segal-EC}). \fpr

{\it Proof of Theorem \ref{transfo-beals}.}  From (\ref{segal-EC}):
 $$ \Big < e^{- \Phi_S(Z) }  A e^{\Phi_S(Z) }   \Psi_{X},
 \Psi_{X}   \Big > =  e^{  |Z|^2 - i\sigma (Z, X)    }  <  A \Psi_{X+Z } ,\Psi_{X-Z } >. $$
With equality (\ref{PSEC}):
$$  <   \Psi_{X+Z } ,\Psi_{X-Z } >  =  e^{ - |Z|^2 + i\sigma (Z, X)    }. $$
These two equalities prove Theorem \ref{transfo-beals}. \fpr

{\it Proof of Proposition \ref{beals}.} One has $\Psi_X = W_X \Psi_0$
with
\begin{equation}\label{WX}  (W_X f) (u) = f(u - x)  e^{  i u \cdot \xi -  \frac {i} {2} x \cdot \xi}.  \end{equation}
Thus:
\begin{equation}\label{prod-scal}  <  A \Psi_{X+Z}  , \Psi_{X-Z}  > = < W_{Z-X} A  W_{Z+X} \Psi_0 , \Psi_0>.\end{equation}
Denote by $V_1, \dots, V_n$ the canonical basis of $\R^n$. Set $a(V_j) = u_j + \partial _{u_j}$
and $a^{\star} (V_j) = u_j - \partial _{u_j}$. One checks that:
$$ [ a(V_j) , W_{x , \xi}  ]   = (x_j + i \xi_j) W_{x , \xi} .  $$
For all $X = (x , \xi)$, set $\varphi_j (X) = x_j + i \xi_j$.
Let  $A$ be a bounded operator in  $L^2(\R^n)$ such that, the right hand side of (\ref{norme-beals}) is well defined.
Since $a(V_j) \Psi_0 = 0$:
 \begin{align*} <  W_{Z-X} A W_{Z+X} \Psi_0 , a^{\star} (V_j) \Psi_0 >
&= < [ a(V_j) , W_{Z - X}  ] A W_{Z+X} \Psi_0 , \Psi_0 >  \\
&\ + < W_{Z-X} [ a(V_j) , A]W_{Z+ X}  \Psi_0 , \Psi_0 > \\
&\ +<  W_{Z-X} A [ a(V_j) , W_{Z + X}  ] \Psi_0 , \Psi_0 > \\%-----
& = 2 \varphi _j (Z)  <  W_{Z-X} A W_{Z+X} \Psi_0 ,\Psi_0 > +
< W_{Z-X} [ a(V_j) , A]W_{Z+ X}  \Psi_0 , \Psi_0 > .
 \end{align*}
By iteration and using (\ref{prod-scal}),  one gets, for all multi-indices $\alpha$:
$$ \varphi (Z) ^{\alpha } <  A \Psi_{X+Z}  , \Psi_{X-Z}  > = \sum _{\beta + \gamma = \alpha }
c _{\alpha, \beta, \gamma } <  W_{Z-X} ({\rm ad}\, a(V) ) ^{\beta} A W_{Z+X} \Psi_0 , (a^{\star} (V))^{\gamma}  \Psi_0 >.  $$
One  set above $ \varphi (Z) ^{\alpha } = \prod \varphi _j (Z) ^{\alpha _j} $
and similarly for $ (a^{\star} (V))^{\gamma}$. Thus, there exists $C_n$ such that:
$$  |<  A \Psi_{X+Z}  , \Psi_{X-Z}  >| \  \sum _{ |\alpha | \leq 2n+1 } |\varphi (Z) ^{\alpha } |
\leq C_n  \sum _{ |\beta | \leq 2n+1 }\Vert ({\rm ad} \ a(V)) ^{\beta} A \Vert.$$
One then gets  (\ref{norme-beals}) since the inverse of the left hand side belongs to $L^1(\R^{2n})$.
\fpr

redpajama_set_name: RedPajamaArXiv


At the age of six or so, I was riding in the car with my mother when I got my first lesson in the difficulty of referring to a human female. I had said something about "a woman," and my mother intervened. "Lady," she corrected. I was surprised. I hadn't intended to use a rude word. Well, Mom, fifty years on, and it's still no clearer.
As a society, we can't seem to figure out what to call female people. We swing from girls, gals, and chicks, to women, ladies, and a whole host of nasty terms. None seem quite right. They all seem loaded with innuendo in contrast to the simple word for a male human, "man," or its friendly cousin, "guy." Let's break it down.
In her blog post, "Call Me Woman," University of Cambridge professor Deborah Cameron has designed a quiz to unpack the subtleties of "woman" versus "lady." How would you fill in these blanks?
She was a perfect ______ about it.
The flowers were arranged by the _____ of the congregation.
Esther thought of her grandmother as a strong and capable ______.
Some _____ reported that they experienced multiple orgasms.
In Victorian times, it was common for _____ to die in childbirth.
A _____ was raped in the city centre last night.
For those reasons, and because we seem endlessly conflicted about women, "lady" lost favor with feminists, and "woman" gained in political correctness. As Cameron has pointed out however, "woman" carries a sexual connotation which some people consider impolite (like my mother). Those speakers may hesitate to use the term in a professional setting, particularly in greeting. So, you are unlikely to hear someone say, "Well, hello, women!" I can imagine someone's discomfort in saying, "The women in the office are planning a surprise party," and expect they would try to rephrase it. American speakers tend to avoid labeling young women as "women," and would hesitate to refer to "high school women." They are in the unenviable position of trying to figure out what to call a female somebody between 16 and 25, a conundrum highlighted by a query posted on stackexchange.com who was looking for a term that didn't imply gender bias. Several responders wrote that "woman" was a term for a person older than 25 and probably married. One wrote, "Unfortunately, there isn't an age-neutral word for 'guy' that you can use for women." Most recommended that the writer go with "girl." Which brings us to the "girl" problem.
If "lady" has lost favor, "girl" has really lost it with the police of political correctness. Because it's also a term for a female child, using it to refer to a grown woman is considered insulting, in some circles. It's widely used by women to refer to themselves, as in "Girls' Night Out," or "It's just us girls tonight." And the term "girlfriend" is very popular even when people object to "boyfriend" as being demeaning.
Men sometimes reach for this term because they've been told "girls" is out, and they can't bring themselves to say "women" because it sounds inappropriate. Women also often use this casual term to refer to themselves. A women's group in my town is called "Good Ole Gals" which emphasizes its down-to-earth and unpretentious nature. You'll hear women say, "Come sit with us gals," or "The gals are getting together after work." Substituting "women" in those phrases alters the tone, but "gals" presents its own problems. It's not used everywhere in the U.S. and has a southern feel which many might not be comfortable with. It's used more by older women which implies that the "gals" are old girls, which some may find degrading in two ways; they're labeled as both old and as diminutive.
As a side note, I'm very surprised at how many cashiers refer to me as "miss," "Did you find everything you were looking today, miss?" I don't mind because I'm not like that, but I would have thought I'm too old to be a "miss." Not to them apparently. "Ma'am," the shortened form of "madam," is standard usage in the military, but seems not to be in common usage, at least in California. It's true that some men dislike being called "sir," the "ma-am" male counterpart because it makes them feel old.
So, it's a mess. One responder on stackexchange.com wrote, "This is a real problem in English, and even native speakers have trouble with it." It's hard to find a word that doesn't trigger some sort of reaction. I sometimes wonder if it's because at our core we are conflicted about women. We can't decide if they're more like Madonna or more like Mary Magdalene, and our words slide across that spectrum unleashing innuendo and implied judgment.
Jennifer: enjoyed this article! Thought provoking and as you as note, current as 50 years ago. I had a similar exchange in my high school years with some family friends having said, 'I hope you women are doing well!' To which one of them said, 'Well, I hope we all are ladies!' I walked away confused yet 'Got it,' what she was trying to say.
So much innuendo, right? Thanks for your comment.


text:
Hopedale, Bellingham get nearly $3M for intersection fixes
Alison Bosma abosma@wickedlocal.com @AlisonBosma
A pair of local communities will see a slice of more than $72 million in 2019 MassWorks award money.
Bellingham and Hopedale were two of 35 communities to get the funding, with official award ceremonies held throughout the region earlier this month.
Hopedale picked up $1 million to revamp the intersection at Rte. 16 and Hopedale Street, while Bellingham secured $1.8 million for improvements to the Rte. 140 and Rte. 126 intersection and surrounding area.
Both towns will see updated traffic lights. Hopedale's intersection, which officials said was important to upgrade because of its proximity to Milford Regional Medical Center and frequent congestion, will get new turning lanes. The Bellingham project will see widened lanes, as well as updated sidewalks.
Bellingham's intersection of Rte. 140 and Rte. 126 is also its downtown, with Town Hall and the town common within walking distance. The project to update the area will "reconstruct" the town center, Selectman Daniel Spencer said, at the formal award presentation last week, as well as improve traffic flow.
The project will also provide access to two planned developments in downtown Bellingham. Those are a 350,000-square-foot commercial warehouse and distribution facility, as well as a mixed-use commercial and housing development, expected to include 152 residential units.
It's not yet clear if the latter will be apartments, condominiums or houses.
"When I was a selectman, my number one objective was to stop talking about overhauling the intersection and execute the plan," former Bellingham Selectman and current state Rep. Michael Soter said in a press release from the state. "As state representative, I eagerly advocated for and secured over $1.8 million to bring this plan to fruition. It has been a pleasure working with the Baker/Polito administration to bring this much-needed funding into the 8th Worcester District."
This was Hopedale's third attempt at the grant.
Interim Town Administrator Robert Reed said the town expects to put the project out to bid in the spring. The intersection is expected to be complete by June 2021.
"The Town of Hopedale is excited about the Route 16/Hopedale Street Improvement project and grateful to the state for providing the funding. This project addresses numerous safety, traffic and pedestrian issues and is highly important from both local and regional perspectives," Hopedale Select Board Chairman Brian Keyes said in a state press release. "We look forward to working with the state to bring this timely project to a successful completion."
The project's total cost will be available once companies send in their estimates, along with more defined timelines. Reed said he hopes to have the plan up on the town's website for residents.
Alison Bosma can be reached at 508-634-7582 or abosma@wickedlocal.com. Find her on Twitter at @AlisonBosma.
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The product provides market, customer, competitive and product understanding, enabling better and faster business decisions, helping to increase competitiveness, raise profitability and facilitate development of new ideas and innovations.


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SpinVox and Mutare application voicemail-to-text respond eliminates 'message mild dread' for Nortel enterprise clients.
getting rid of the time-consuming want for americans to pick heed to and transcribe equitable voicemail, Mutare EVM with SpinVox Speech-to-text takes the spoken content of a Nortel CallPilot voicemail, converts it to textual content and promises the message with customized Caller identification (name, electronic mail and call number) and not obligatory audio attachment to up to 5 e-mail bills or any wise cell, PDA or mobile phone.
A joint evolution with the aid of SpinVox and Mutare application, Mutare EVM with SpinVox Speech-to-textual content, moreover referred to as visible Voice, is an software applied in firms as a server-based utility solution, it merges voice and facts into one unified messaging journey and is usurp with any email equipment or internet-enabled machine. It allows for company clients to system voicemail as much as 4 times faster as they could now prioritize, ahead, file, reproduction and delete transformed voicemail messages with the identical ease and console of e-mail, enhancing individual productivity, consumer responsiveness, and workgroup collaboration.
• cell employees can now access and browse each and every messages from a smart mobile, laptop computing device, or any internet-enabled equipment, any place, any time.• commercial enterprise users can discreetly scan via and browse voicemail messages whereas in conferences, strident areas, whereas on other calls, or in any circumstance the region being attentive to the message is complicated or inappropriate. Voicemail in readable e-mail form can now live forwarded to an administrative lieutenant or group member for quick response.• client keeping specialists now believe the potential to arrange voicemails similar to emails to give more desirable customer provider and response.• listening to impaired laborers can read voice messages without further suffuse of propietary gadget (Mutare EVM supports american citizens With Disabilities Act (ADA) compliance).
The EVM capability is now supported with the Nortel CallPilot Unified Messaging portfolio and comprises Mutare software's EVM gateway and SpinVox Speech-to-text messaging carrier. each and every transmitted messages are processed via an conclusion-to-end protection system for both audio and text codecs, with encryption utilized from the voice mail domain through each and every ranges of the conversion procedure.
Mutare EVM with SpinVox Speech-to-textual content has been established interoperable with Nortel CallPilot 5.0 as a section of the Nortel select Product program and is accessible automatically in the U.S. and Canada. Supported languages include English, French, German, Italian, Portuguese and Spanish.
getting rid of the time-drinking want for americans to hearken to and transcribe ordinary voicemail, Mutare EVM with SpinVox Speech-to-text takes the spoken content of a Nortel CallPilot voicemail, converts it to text and supplies the message with customized Caller id (identify, electronic mail and compose contact with quantity) and non-compulsory audio attachment to up to 5 e-mail money owed or any smart phone, PDA or cellular telephone.
A joint pile by means of SpinVox and Mutare application, Mutare EVM with SpinVox Speech-to-textual content, moreover known as visual Voice, is an utility carried out in businesses as a server-based mostly application solution, it merges voice and facts into one unified messaging event and is suitable with any e mail gadget or internet-enabled gadget. It makes it practicable for traffic clients to process voicemail up to four instances quicker as they could now prioritize, ahead, file, replica and delete converted voicemail messages with the same ease and convenience of email, improving particular person productiveness, client responsiveness, and workgroup collaboration.
• mobile laborers can now access and read each and every messages from a wise mobile, computer computer, or any information superhighway-enabled machine, anywhere, any time.• enterprise clients can discreetly scan via and skim voicemail messages while in meetings, strident areas, while on different calls, or in any situation the region taking note of the message is complicated or inappropriate. Voicemail in readable email form can now live forwarded to an administrative lieutenant or group member for brief response.• client keeping authorities now believe the skill to organize voicemails just dote emails to give more desirable consumer service and response.• hearing impaired workers can examine voice messages devoid of extra cost of propietary machine (Mutare EVM supports american citizens With Disabilities Act (ADA) compliance).
The EVM potential is now supported with the Nortel CallPilot Unified Messaging portfolio and comprises Mutare application's EVM gateway and SpinVox Speech-to-text messaging provider. each and every transmitted messages are processed via an end-to-end protection device for each audio and textual content formats, with encryption applied from the voice mail container through each and every ranges of the conversion technique.
Mutare EVM with SpinVox Speech-to-textual content has been established interoperable with Nortel CallPilot 5.0 as section of the Nortel elect Product program and is accessible immediately within the U.S. and Canada. Supported languages consist of English, French, German, Italian, Portuguese and Spanish.
SpinVox capabilities can live found directly on www.spinvox.com and through leading carriers and thru new media, Unified Communications and other provider suppliers globally.
at the heart of SpinVox is its floor-breaking Voice Message Conversion gadget™ (VMCS), which works by route of combining state-of-the-art speech technologies with a live-discovering language process to guarantee nice of conversion. SpinVox VMCS primarily uses speech applied sciences to transfigure speech into text but, if it is now not able to finished the conversion, it may well quiz a human agent for aid to ensure that the message is precisely transformed and actively learns from the process itself. This has resulted in VMCS at the moment having a corpus of over two billion words and phrases.
SpinVox is now reside with Alltel, SaskTel, Rogers wireless, TELUS, Telstra, Vodacom South Africa, Vodafone Spain, Movistar Chile, Movistar Argentina, Movistar Ecuador, Movistar Guatemala, Movistar Mexico, Movistar Panama, Movistar Colombia, Skype and Livejournal. To grow the voice-to-text market further, SpinVox introduced the launch of its API programme at the nascence of 2009, enabling developers to register at http://create.spinvox.com/. considering the fact that then, 750 builders believe develop into SpinVox API program individuals and reside functions enabled by SpinVox, corresponding to Ipadio, 0800TXTMUM and QuickVoice professional believe been launched. SpinVox API is attainable in English, Spanish, German, French, Italian and Portuguese.
during this limpid option explore at various they evaluated the latest unified messaging applications from IP telephony providers Avaya, Cisco, Nortel and Siemens Communications. A subsequent examine is deliberate of stand-on my own and third-celebration unified messaging choices.
In measure installations, the unified messaging equipment is a application add-on to a PBX gadget that works with it to give effective, consolidated, "fingers-free" entry to voice mail and e mail by means of any telephone gadget, observed anyplace. In most circumstances, the unified messaging device handles the voice mail directly from the PBX and provides the processing quintessential to combine the voice mail and email by route of a LAN connection to the electronic mail server.
during this limpid option verify they evaluated the newest unified messaging packages from IP telephony vendors Avaya, Cisco, Nortel and Siemens Communications . A subsequent check is planned of stand-by myself and third-celebration unified messaging choices.
Siemens placed second, with its primary strengths being incredible administrative access to the unified messaging environment, a very agreeable net interface to unified e-mail and voice mail, and tailorable voice awareness alternatives.
Nortel's strengths covered broad language assist and tailorable voice awareness. Architecturally its unified messaging most efficient works with Nortel PBXs. Nortel's TTS readout (what you hear as the unified messaging gadget is analyzing your e-mail to you) changed into negative, comparatively speakme, and a proprietary voice mail-encoding layout complicates matters by using requiring that a Nortel-particular participant live sequel in on your desktop to play the message.
We found that, for the four products they tested, an estimated eighty% of the e mail/in-box-primarily based unified messaging points and person interface are without rigor the same. The real action lies in new unified messaging interfaces, which promise more straightforward entry and improved person productiveness. Their verify concentrated on each and every supported interfaces, including the classical e mail in-box-based mostly entry, web-primarily based interfaces and the subsequent generation of cellphone person interface (TUI). Their test went past commonplace TUI critiques in that they attempted to accomplish each and every of it by route of voice interplay, the region the user may maneuver in the course of the unified messaging device totally "palms free" - ideally by means of a limpid "herbal-language" circulate, the region the equipment would read out e-mails precisely and in the applicable language.
In prevalent, the Outlook Inbox offers the highest plane of performance for unified messaging across the items proven. additionally, the internet Outlook interface, which is not supported by means of each and every the vendors, allows quick entry from anywhere, each time. youngsters, this net-enabled view offers a lot less direct access to the messaging environment.
Avaya's Modular Messaging gadget (MMS) contains the entire aspects they sought apart from voice cognizance, which comes from the Unified Communications headquarters (UCC).
Avaya gives what they believe the gold measure net interface, similar in many respects to Microsoft's Outlook net entry. it is cleanly and simple to compose utilize of, and is a attainable alternative to processing voice mail and electronic mail by route of the Outlook in-container. A miniature but noteworthy shortcoming is that there is not any direct interaction with phone dialing. You cannot directly district a recrudesce cellphone call to, say, a voice mail source from the Outlook interface; you exigency to travel to an associated mobilephone and dial a code to region a recrudesce call. They found that Cisco and Siemens believe been similarly confined.
Avaya's voice recognition - in keeping with nuance eight.5, a third-birthday party speech-attention software engine from nuance Communications - is astounding when it comes to the herbal-language stream of the interface. The equipment is developed around some 40 fastened phrases. It is not simply extensible or person trainable, but they found it adequate for general-aim, speaker-unbiased entry to the complete purview of voice mail and e-mail functions. a pleasant contact is that the consumer can assure "support" at any point and fetch valuable and practical assistance on the route to proceed.
Avaya's TTS - in accordance with Speechify 2.1.3, a 3rd-birthday celebration TTS utility engine from Scansoft - moreover did the most efficient job supplying TTS, and performed best ratings in 4 out of seven test messages. a flawless ranking skill each word in the message became as it should live recognized and spoken. And the suitable overseas language became applied immediately in each and every situations, based on an analysis of the text in the physique of the e mail message. Avaya's common TTS equipment includes eleven alien languages, nine of which can moreover live energetic at a time.
within the Avaya configuration, voice mail messages believe been saved on the change server. Voice mail could alternately believe been stored on an Avaya Linux-based voice mail server, which may moreover live deployed redundantly. it's additionally feasible to believe the Avaya server again up the change server, so voice mails are nonetheless authorized and saved if the alternate server is unavailable.
Configuration-smart, Avaya's package works with many third-birthday celebration PBXs, including these from Cisco, Mitel, Siemens and NEC. moreover, Avaya says its unified messaging device will connect with Nortel, Cisco and Siemens PBXs by the utilize of Q.Sig over a T-1 through this summer. Avaya's MMS and UCC relate one after the other to the underlying PBX, but many connectivity alternate options are supported, ranging from analog trunks to T-1s with PRI signaling to the extra advanced Q.Sig interface.
there's respectable flexibility when it comes to voice mail vocoding settings, together with G.711 and Microsoft's GSM 6.10. Scalability is ample. up to sixty nine concurrent unified messaging periods, assisting a number of hundred or thousand users, are supported per Avaya server, and the system can expand to as much as 10 servers. Avaya does not tender an built-in fax server feature with its unified messaging kit.
Siemens can withhold voice mail on its HiPath Xpressions server or directly on the user's trade electronic mail server. With the Siemens software running on windows 2003 servers (counseled; windows 2000 moreover supported), redundancy will moreover live finished by means of Microsoft's server clustering.
Like Avaya, Siemens presents a pleasant internet interface for entry to each and every unified messages. besides the fact that children, Avaya's became a tad less difficult to maneuver. Siemens' Outlook interface offered a bit extra flexibility than the others in some respects. for example, Siemens lets the person deposit voice mails into either of two Outlook folders, and then hold full access, including via voice consciousness, to messages in either folder. With the other packages, full access become generally supported to voice mails in precisely one folder.
despite the fact, as with Avaya, the person cannot launch telephone calls without detain from the Outlook interface. Siemens says this can live achieved by route of a divorce desktop telephony integration software it offers, referred to as SimplyPhone.
Siemens' voice-focus ingredient they established turned into silent in late beta. it's scheduled to live introduced to a protection free up of Siemens' unified messaging package this summer. The third-birthday celebration speech-cognizance utility engine, SpeechWorks edition three from SpeechWorks overseas, requires its personal server. They concept the voice recognition become certainly well accomplished. an extensive vocabulary of terms is supported and, with tips from Siemens technical support, the vocabulary can live prolonged.
whereas Siemens moreover gets its TTS capabilities from Speechify, it only makes utilize of version three.02. The shortcoming with this prior version is that handiest German and English are supported, one at a time, set device-large. The unified messaging package cannot immediately commemorate and apply different languages in response to the text body of e-mails. Siemens says language support may live improved in the next release.
The HiPath Xpressions kit runs over 14 different companies' PBXs, including many European corporations (Ericsson, Alcatel, Philips and Ascom). Connectivity is ISDN PRI in just about each and every instances. Scalability of Siemens' equipment is configuration dependent. With adequate home windows server resources, as much as 255 concurrent ports are supported. although, there will moreover live only a unique voice mail message shop.
Cisco's cohesion commercial enterprise unified messaging equipment receives its power from its voice awareness and high-availability features delivered as divorce add-ons.
Voice awareness is delivered by means of Cisco's personal lieutenant utility - driven additionally by route of Scansoft's nuance engine, which requires its personal server. The very own lieutenant voice-recognition features were neatly built-in - however assist simplest voice mail entry. Cisco doesn't support voice-recognition access to e mail, and cannot bring the same fingers-free maneuvering through e mail and selective playout by means of TTS that competitors can. The harmony kit moreover comprises Scansoft's RealSpeak TTS software engine, which performed pretty much as well as Avaya's TTS, but did not achieve any flawless ratings in their check e-mail messages.
Cisco does not tender an internet interface to unified voice mail and e-mail.
despite these aggressive shortcomings, Cisco deserves consciousness for a brace of trait interface touches. One is the Outlook embedded player: handiest Cisco provided single-button playback of voice mail attachments without detain from the Outlook interface. The others required a brace of steps to determine, choose, open and playback a specific voice mail message. additionally, Cisco did some trait engineering so so you might hasten up the playback of a lengthy voice mail while the content remains perfectly comprehensible. Nortel additionally presents a "pace-up alternative" from the Outlook player, however the playback best isn't pretty much as agreeable as Cisco's. (word that this is not quickly-ahead, which skims over content, and which each and every of the companies that they tested help. in case you quickly ahead, you typically don't hear anything as you movement throughout the message, if you occur to "speed-up" you hear the message - most efficient quicker.) also, the entire providers steer some manner of "velocity-up" by means of the audio, or TUI, entry to voice mail.
Cisco gets immoderate marks for configuration and structure, thanks in vast section to its high-availability and survivability alternatives. One, referred to as solidarity Message Repository, provides voice mail backup to the alternate message keep. another is a disaster-recuperation application utility, called dirt, that comes free with harmony.
Cisco's scalability is achieved by route of clustering of dissimilar servers. commonly, the per-server concurrent-port means is according to the energy of the servers you sprint it on. Cisco says that as much as 7,500 users (seats) can live serviced by a unique solidarity server. Cisco presents the broadest latitude of settings on the topic of voice vocoders, in terms of space for storing and bandwidth consumption.
Cisco moreover gets high marks for its comfy voice mail help. If a voice mail is marked at ease in Cisco's union device, it best can live played from a device mobilephone, and not by means of the Outlook participant. also, relaxed voice mail cannot live copied or forwarded.
Cisco additionally presents an add-on fax server but at $25,000, it is just too costly for each and every however the biggest, fax-intensive agencies.
despite those barriers, they frequently laud the Nortel equipment. for instance, best Nortel lets clients at once vicinity telephone calls from the unified Outlook interface. The person can select a concurrent voice mail, hit the one-touch withhold in mind, and the mobile device will automatically vicinity a call to the voice mail supply, connecting to whatever thing mobilephone gadget the user has linked to his computer.
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A joint evolution by SpinVox and Mutare Software, Mutare EVM with SpinVox Speech-to-Text, moreover known as Visual Voice, is an application implemented in Enterprises as a server-based software solution, it merges voice and data into one unified messaging flavor and is compatible with any email system or Internet-enabled device. It enables traffic users to process voicemail up to four times faster as they can now prioritize, forward, file, copy and delete converted voicemail messages with the same ease and convenience of email, improving individual productivity, customer responsiveness, and workgroup collaboration.
• Mobile workers can now access and read each and every messages from a Smart phone, laptop computer, or any Internet-enabled device, anywhere, any time.• Enterprise users can discreetly scan through and read voicemail messages while in meetings, strident areas, while on other calls, or in any situation where listening to the message is difficult or inappropriate. Voicemail in readable email form can now live forwarded to an administrative lieutenant or team member for quick response.• Customer keeping professionals now believe the capability to organize voicemails just dote emails to provide better customer service and response.• Hearing impaired workers can read voice messages without additional cost of propietary equipment (Mutare EVM supports Americans With Disabilities Act (ADA) compliance).
The EVM capability is now supported with the Nortel CallPilot Unified Messaging portfolio and includes Mutare Software's EVM gateway and SpinVox Speech-to-Text messaging service. each and every transmitted messages are processed through an end-to-end security system for both audio and text formats, with encryption applied from the voice mail box through each and every stages of the conversion process.
About SpinVoxSpinVox® is the world's largest privately-held speech technology company, providing the only voice to text messaging services which are used daily by millions of people and whose user basis has grown over twenty-fold in the terminal 12 months.
Implemented as a carrier-class hosted network feature, SpinVox has proven it can easily create value from everyday user behavior using voice and deliver rapid and smooth implementation of low input, sustained high reward services.
At the heart of SpinVox is its ground-breaking Voice Message Conversion System™ (VMCS), which works by combining state-of-the-art speech technologies with a live-learning language process to assure trait of conversion. SpinVox VMCS primarily uses speech technologies to transfigure speech into text but, if it is not able to complete the conversion, it can quiz a human agent for wait on to ensure that the message is accurately converted and actively learns from the process itself. This has resulted in VMCS currently having a corpus of over two billion words and phrases.
SpinVox is now live with Alltel, SaskTel, Rogers Wireless, TELUS, Telstra, Vodacom South Africa, Vodafone Spain, Movistar Chile, Movistar Argentina, Movistar Ecuador, Movistar Guatemala, Movistar Mexico, Movistar Panama, Movistar Colombia, Skype and Livejournal. To grow the voice-to-text marketplace further, SpinVox announced the launch of its API programme at the nascence of 2009, enabling developers to register at http://create.spinvox.com/. Since then, 750 developers believe become SpinVox API program members and live services enabled by SpinVox, such as Ipadio, 0800TXTMUM and QuickVoice Pro believe been launched. SpinVox API is available in English, Spanish, German, French, Italian and Portuguese.
ATLANTA, June 8, 1999 — Today at SUPERCOMM '99, Microsoft Corp. President Steve Ballmer announced Microsoft's vision for unified messaging, providing knowledge workers with any-time, anywhere access via any phone or other device to a unique inbox containing e-mail, voicemail, fax and page messages. The announcement demonstrated Microsoft's substantial efforts to provide the leading platform for unified messaging based on the Microsoft® Windows NT® and Windows® 2000 operating systems, Microsoft Exchange Server and Windows CE. More than 50 companies, including industry leaders Lucent Technologies Inc., Nortel Networks Corp. and energetic Voice Corp., are actively developing and delivering unified messaging solutions on the Microsoft platform, directly benefiting customers through increased productivity, enhanced manageability and lower total cost of ownership. Today's announcement highlighted the unified messaging features of the next release of Exchange Server, including a high-performance Web Store and support for the Voice Profile for Internet Messaging (VPIM) standard, as well as Windows 2000 and Windows CE features.
The digital dashboard enables knowledge workers to manage their e-mail, voicemail, fax and page messages with the same interface they utilize to search the Web or an intranet, and access corporate data and applications.
The Web Store is the basis of the next-generation unified messaging platform and will tender knowledge workers one region to store and manage each and every their information, including documents, e-mail and voicemail messages, and Web pages.
Mobility and wireless access are increasingly famous to knowledge workers, enabling them to access their unified inbox with wireless phones and devices, with messages delivered in a format optimized for the situation, person and device.
Intelligent interface research will transform the route people utilize computers, bringing technology innovation such as natural language processing to the next generation of unified messaging.
Just as Exchange Server has emerged as the leading platform for unified messaging, Microsoft Windows operating system products believe become the leading platform for open, unified communications. Windows NT Server includes support for telephony services, remote access, routing and virtual private networking. Microsoft is advancing the platform with Windows 2000, which will include quality-of-service enhancements, the energetic Directory TM directory service and the Microsoft Management Console for integrated e-mail, voicemail and network system management. Microsoft's unified messaging strategy encompasses wireless access and the full purview of devices powered by the Windows CE operating system, intelligently linking these devices both online and wirelessly to Exchange Server e-mail and voicemail. This extends the power of the PC to mobile professionals and knowledge workers regardless of location or device used.
Microsoft supports both commonly used architectures for unified messaging, the integrated model where divorce servers are merged at the client, and the Exchange Server-based unified model that combines each and every voice and data management on one server with a unique point of directory and administration.
Founded in 1975, Microsoft (Nasdaq"MSFT") is the worldwide leader in software for personal computers. The company offers a wide purview of products and services for traffic and personal use, each designed with the mission of making it easier and more enjoyable for people to pick handicap of the full power of personal computing every day.
In this limpid election Test they evaluated the latest unified messaging packages from IP telephony vendors Avaya, Cisco, Nortel and Siemens Communications. A subsequent test is planned of stand-alone and third-party unified messaging offerings.
In this limpid election Test they evaluated the latest unified messaging packages from IP telephony vendors Avaya, Cisco, Nortel and Siemens Communications . A subsequent test is planned of stand-alone and third-party unified messaging offerings.
Siemens placed second, with its major strengths being exceptional administrative access to the unified messaging environment, a very agreeable Web interface to unified e-mail and voice mail, and tailorable voice recognition options.
Nortel's strengths included broad language support and tailorable voice recognition. Architecturally its unified messaging only works with Nortel PBXs. Nortel's TTS readout (what you hear as the unified messaging system is reading your e-mail to you) was poor, comparatively speaking, and a proprietary voice mail-encoding format complicates matters by requiring that a Nortel-specific player live installed on your laptop to play the message.
We found that, for the four products they tested, an estimated 80% of the e-mail/in-box-based unified messaging features and user interface are effectively the same. The real action lies in new unified messaging interfaces, which promise simpler access and greater user productivity. Their test focused on each and every supported interfaces, including the classical e-mail in-box-based access, Web-based interfaces and the next generation of telephone user interface (TUI). Their test went beyond typical TUI evaluations in that they attempted to accomplish it each and every by voice interaction, where the user could maneuver through the unified messaging system entirely "hands free" - ideally via a cleanly "natural-language" flow, where the system would read out e-mails accurately and in the usurp language.
In general, the Outlook Inbox provides the highest plane of functionality for unified messaging across the products tested. Additionally, the Web Outlook interface, which is not supported by each and every the vendors, enables quick access from anywhere, anytime. However, this Web-enabled view provides much less direct access to the messaging environment.
Avaya's Modular Messaging System (MMS) includes each and every the features they sought except voice recognition, which comes from the Unified Communications headquarters (UCC).
Avaya provides what they deem the best Web interface, similar in many respects to Microsoft's Outlook Web Access. It is cleanly and smooth to use, and is a viable alternative to processing voice mail and e-mail via the Outlook in-box. A miniature but noteworthy shortcoming is that there is no direct interaction with telephone dialing. You can't directly region a recrudesce phone call to, say, a voice mail source from the Outlook interface; you must travel to an associated phone and dial a code to region a recrudesce call. They found that Cisco and Siemens were similarly limited.
Avaya's voice recognition - based on nuance 8.5, a third-party speech-recognition software engine from nuance Communications - is superb in terms of the natural-language tide of the interface. The system is built around some 40 fixed phrases. It is not readily extensible or user trainable, but they found it adequate for general-purpose, speaker-independent access to the full purview of voice mail and e-mail functions. A nice handle is that the user can assure "help" at any point and fetch useful and practical guidance on how to proceed.
Avaya's TTS - based on Speechify 2.1.3, a third-party TTS software engine from Scansoft - moreover did the best job delivering TTS, and achieved flawless scores in four out of seven test messages. A flawless score means every word in the message was correctly identified and spoken. And the amend alien language was applied automatically in each and every cases, based on an analysis of the text in the body of the e-mail message. Avaya's measure TTS package includes 11 alien languages, nine of which can live energetic at a time.
In the Avaya configuration, voice mail messages were stored on the Exchange server. Voice mail could alternately believe been stored on an Avaya Linux-based voice mail server, which can live deployed redundantly. It's moreover practicable to believe the Avaya server back up the Exchange server, so voice mails are silent accepted and saved if the Exchange server is unavailable.
There is agreeable flexibility in terms of voice mail vocoding settings, including G.711 and Microsoft's GSM 6.10. Scalability is adequate. Up to 69 concurrent unified messaging sessions, supporting several hundred or thousand users, are supported per Avaya server, and the system can expand to up to 10 servers. Avaya does not tender an integrated fax server feature with its unified messaging package.
Siemens can store voice mail on its HiPath Xpressions server or directly on the user's Exchange e-mail server. With the Siemens software running on Windows 2003 servers (recommended; Windows 2000 moreover supported), redundancy can live achieved via Microsoft's server clustering.
Like Avaya, Siemens offers a nice Web interface for access to each and every unified messages. However, Avaya's was a tad easier to maneuver. Siemens' Outlook interface offered a minute more flexibility than the others in some respects. For example, Siemens lets the user deposit voice mails into either of two Outlook folders, and then retain full access, including via voice recognition, to messages in either folder. With the other packages, full access was generally supported to voice mails in just one folder.
However, as with Avaya, the user cannot launch phone calls directly from the Outlook interface. Siemens says this can live accomplished via a divorce computer telephony integration application it offers, called SimplyPhone.
Siemens' voice-recognition component they tested was silent in late beta. It is scheduled to live added to a maintenance release of Siemens' unified messaging package this summer. The third-party speech-recognition software engine, SpeechWorks Version 3 from SpeechWorks International, requires its own server. They thought the voice recognition was particularly well done. An extensive vocabulary of terms is supported and, with assistance from Siemens technical support, the vocabulary can live extended.
While Siemens moreover gets its TTS capabilities from Speechify, it only uses Version 3.02. The shortcoming with this earlier version is that only German and English are supported, one at a time, set system-wide. The unified messaging package cannot automatically detect and apply different languages based on the text body of e-mails. Siemens says language support will live expanded in the next release.
The HiPath Xpressions package runs over 14 other vendors' PBXs, including many European companies (Ericsson, Alcatel, Philips and Ascom). Connectivity is ISDN PRI in almost each and every cases. Scalability of Siemens' package is configuration dependent. With enough Windows server resources, up to 255 concurrent ports are supported. However, there can live only a unique voice mail message store.
Cisco's union Enterprise unified messaging package gets its power from its voice recognition and high-availability features delivered as divorce components.
Voice recognition is delivered via Cisco's Personal lieutenant software - driven moreover by Scansoft's nuance engine, which requires its own server. The Personal lieutenant voice-recognition functions were well integrated - but support only voice mail access. Cisco does not support voice-recognition access to e-mail, and cannot deliver the same hands-free maneuvering through e-mail and selective playout via TTS that competitors can. The union package moreover includes Scansoft's RealSpeak TTS software engine, which performed nearly as well as Avaya's TTS, but did not achieve any flawless scores in their test e-mail messages.
Cisco does not tender a Web interface to unified voice mail and e-mail.
Despite these competitive shortcomings, Cisco deserves recognition for a brace of nice interface touches. One is the Outlook embedded player: Only Cisco offered single-button playback of voice mail attachments directly from the Outlook interface. The others required a brace of steps to identify, select, open and playback a selected voice mail message. Also, Cisco did some nice engineering so that you can accelerate the playback of a lengthy voice mail while the content remains perfectly understandable. Nortel moreover offers a "speed-up option" from the Outlook player, but the playback trait isn't nearly as agreeable as Cisco's. (Note that this is not fast-forward, which skims over content, and which each and every of the vendors that they tested support. When you swiftly forward, you typically don't hear anything as you stir through the message, when you "speed-up" you hear the message - only faster.) Also, each and every of the vendors support some manner of "speed-up" via the audio, or TUI, access to voice mail.
Cisco gets high marks for configuration and architecture, thanks in great section to its high-availability and survivability options. One, called union Message Repository, provides voice mail backup to the Exchange message store. Another is a disaster-recovery software utility, called DIRT, that comes free with Unity.
Adding to its configuration appeal is that Cisco's union package runs with 17 other vendors' PBXs. The linkages are quite diverse, and include a specialized Cisco gateway that converts Session Initiation Protocol call control on the Cisco side to and from the protocol of the other PBX.
Cisco's scalability is achieved via clustering of multiple servers. Generally, the per-server concurrent-port capacity is based on the power of the servers you sprint it on. Cisco says that up to 7,500 users (seats) can live serviced by a unique union server. Cisco offers the broadest purview of settings with regards to voice vocoders, in terms of storage space and bandwidth consumption.
Cisco moreover gets high marks for its secure voice mail support. If a voice mail is marked secure in Cisco's union system, it only can live played from a system phone, and not via the Outlook player. Also, secure voice mail can't live copied or forwarded.
Cisco moreover offers an add-on fax server but at $25,000, it is too expensive for each and every but the largest, fax-intensive companies.
Nortel's CallPilot unified messaging package is useful and rich, but it only works with Nortel phone systems, which is a major disadvantage. That, and the fact that only Nortel employs a proprietary voice mail-encoding scheme - so voice mail has to live played out via Nortel's player application, are two reasons they rated the CallPilot package below equitable in the configuration and architecture category.
Despite those limitations, they generally laud the Nortel package. For example, only Nortel lets users directly region phone calls from the unified Outlook interface. The user can select a recent voice mail, hit the one-touch recall, and the phone system will automatically region a call to the voice mail source, connecting to whatever phone device the user has associated with his laptop.


Once you're familiar with the Game Plan, utilize these tools and resources to join the #HalfTimeChallenge. You'll find free images on the main Resources page.
Tell others about this initiative. Email your friends, family, co-workers … anyone within your network! But, what do you say? Here's a quick template to use. Just copy, paste and send.
You can invite a Coalition member to share at your event. Interested? Email the Coalition to request a speaker.
We've separated sample statistics and quotes into two categories based on twitter's 140-character limit. This is the list that fits Twitter. Sources are offered with most, but not included in the 140-character limit for tweets. Remember to include hashtags!
USA kids are NOT for Sale! Congress, please take the #HTchallenge & join the fight to end #humantrafficking!
Take the #HTchallenge today by telling someone these HT victim warning signs! http://www.polarisproject.org/human-trafficking/recognizing-the-signs.
Visit njhumantrafficking.org 2learn how 2B part of Today's #Halftime Challenge!
Trafficking isn't about smuggling; it's about exploitation! #EndTrafficking & join our #HTchallenge by talking about trafficking 2day!
Don't want the #HTchallenge to end? To request a trainer or speaker about Human Trafficking, contact:training@polarisproject.org.
The following quotes exceed twitter's 140-character limit, but are informative and perfect for other social media outlets like facebook, G+ and instagram. Again — don't forget the hashtags!


UM Shore Medical Center at Chestertown provides inpatient acute care, 24-hour emergency care, same-day surgical services and outpatient care.
UM Shore Medical Center at Dorchester is a medical/surgical community hospital with 24-hour emergency services and in/outpatient services that include gynecological, orthopedic, acute rehabilitation, behavioral health and critical care.
UM Shore Medical Center at Easton provides care for acute inpatient rehabilitation and offers services such as lab testing, cardiology and pulmonary care, imaging and neurology in Caroline, Dorchester, Queen Anne's, Talbot and Kent counties.
UM Shore Emergency Center at Queenstown is open 24 hours a day for patients with acute illnesses, injuries and trauma. The Emergency Center offers full diagnostic imaging and laboratory services.
UM Shore Medical Pavilion at Queenstown, located next to UM Shore Emergency Center on Shoreway Drive, is home to a wide array of medical services.


text:
San Adrián de Valdueza es una localidad del municipio de Ponferrada, situado en El Bierzo, en la provincia de León, (España).

El pueblo había sido abandonado en 1974, junto con otros pueblos del entorno, pero San Adrián de Valdueza ya no continúa deshabitado.

Situación

Se encuentra en un pequeño valle, que comunica mediante un camino de tierra con Villanueva de Valdueza, donde conecta con la carretera procedente Ponferrada.

Es un entorno conocido por sus rutas de montaña, dentro del espacio cultural e histórico de la Tebaida leonesa.

Localidades de Valdueza
Localidades de Ponferrada
Localidades de la Quintería de Montes

redpajama_set_name: RedPajamaWikipedia


whenever I go on a geocaching/Waymarking trip, I sometimes see crosses, boards, monuments and cemeteries of past epidemics like the epidemic of bubonic plague in the Medieval. I looked through our categories and couldn't found a appropriate category.
What dou you think about this topic? Is it a potential category for us?
If it is a real memorial and not just a marker then they can go to Disaster Memorials. I have found several memorials for victims of yellow fever, typhus or smallpox in this category.


Northern Indiana is a regional hub for semi trucks carrying freight out of Chicago to the coasts and throughout the nation. Every day, thousands of truckers rely on I-80, I-90 and Highway 20 to move their trailers through the Michiana region.
Truck drivers and truck company owners are heavily regulated by the Federal Motor Carrier Safety Act. When a motor vehicle accident involves a commercial truck, the investigation usually begins with determining whether the driver and truck company were in compliance with the law.
If you were injured or have lost a loved one in a truck accident on a road or highway in northern Indiana, call the office of Jay Lauer, Attorney at Law, in South Bend. Personal injury litigation attorney Jay Lauer has been helping victims of truck accidents recover full and fair compensation for medical care and financial damages for more than 25 years. Truck accident injury and wrongful death claims in Indiana can become very complex. Truck companies often protect themselves from serious financial liability by withholding critical evidence or pushing hard to settle with the injured party as early as possible. Before you talk to an insurance adjuster or a representative from the trucking firm, make sure you know your rights.
Just Passing Through The Area?
If you are not a local resident of the Michiana region and were injured in a truck accident while passing through northern Indiana, Mr. Lauer can handle your personal injury claim locally. He will take care of all details concerning gathering records and reports, investigating the cause of the accident and determining the full extent of the compensation you may be entitled to.
Call to schedule a free consultation and case evaluation. If you retain us as your legal counsel, we will cover the upfront costs of investigating, preparing and settling your case. You remain in control of the final decision about accepting a negotiated settlement or taking your case to trial.
From offices in South Bend, Indiana, litigation lawyer Jay Lauer provides legal advice and representation for clients throughout the Michiana region. Call toll free (574) 208-6267 or contact our office by email to arrange a consultation with South Bend truck accident attorney Jay Lauer today.