text:
\section{Introduction}

Let $(X,g)$ be a Riemannian manifold isometric to $\RR^n$ outside a compact set.  Let $\Lap$ denote the (non-negative) Laplace-Beltrami operator
$$
\Lap=\frac 1{\sqrt{g}} D_i g^{ij} \sqrt{g} D_j,
$$
where $D_i = -\imath \pa_{x_i}.$  The \emph{resolvent}
$$
(\Lap-\lambda^2)^{-1}
$$
is a priori defined as a family of bounded operators $L^2(X)\to
L^2(X),$ as $\lambda$ runs over the upper half-space $\Im \lambda>0.$
When the manifold is precisely $\RR^n$ we can write down the Schwartz
kernel of the resolvent by Fourier methods;
for instance in $\RR^3$ the Schwartz kernel is
$$\frac{e^{i\lambda\smallabs{x-y}}}{4 \pi \smallabs{x-y}}.$$  We thus see
explicitly that this kernel analytically continues to be an
entire function of $\lambda \in \CC.$ It has the modest defect of exponential
growth at infinity, which is remedied if we consider it as a map
$L^2_c(\RR^3)\to L^2_{\text{loc}}(\RR^3).$ The same holds true on $\RR^n$ for all
odd $n.$

Putting geometry back into the picture, we may regard $X$ as a
perturbation of Euclidean space, and an easy application of analytic
Fredholm theory (see, e.g., \cite{Sjostrand-Zworski1} in a much more general
setting) shows that in general, for $n$ odd, $(\Lap-\lambda^2)^{-1}$
continues as a \emph{meromorphic} family of operators $L^2_c(X)\to
L^2_{\text{loc}}(X),$ for all $\lambda \in \CC.$ The poles of this family of
operators are known as the \emph{resonances} of the Laplacian.  We may
equally well think of them as the poles of the \emph{cutoff resolvent
  family}
$$
\chi (\Lap-\lambda^2) \chi: L^2(X)\to L^2(X)
$$
with $\chi \in \CcI(X),$ and we will adopt this point of view in what
follows.  (For a survey of some recent developments in the theory of
resonances complementary to the discussion here, we refer the reader
to \cite{Zworski:Notices}.)

We note that while the new results described in this paper fit (more
or less) in the geometric context described above, much of the history
of the subject is closely tied to the problem where $X$ is replaced by
an exterior domain of a smoothly bounded subset of $\RR^n$ (the
``obstacle problem'') equipped with, say, Dirichlet boundary
conditions.  As the obstacle problem has considerable similarities to that
considered here, we will cite results on the obstacle problem as
motivation without further comment.

We now recall two different estimates in the theory of evolution
equations that follow from an ``appropriate'' understanding of the
resolvent continued to the real axis and beyond.

\subsection{Energy decay for the wave equation}
Let $U(t) ={\sin t \sqrt\Lap}/{\sqrt\Lap}$ be (part of the) wave
propagator.  Then we may write $U(t)$ as a contour integral around the
spectrum of the Laplacian, which is in this situation simply
continuous spectrum along the positive real axis.  Thus, letting
$\Gamma$ denote the contour shown in Figure~\ref{figure:contour}, we
have
\begin{equation}\label{wavecontour}
\begin{aligned}
\chi U(t)\chi &= \frac{1}{2\pi \imath}\int_\Gamma \chi (\mu-\Delta)^{-1}\chi \frac{\sin
t\sqrt{\mu}}{\sqrt\mu}\, d\mu\\
&=-\frac{1}{\pi \imath}\big(\int_{\RR+\imath 0} \chi R(\lambda)\chi
e^{\imath t\lambda} \,
d\lambda+\int_{\RR+\imath 0} \chi R(\lambda)\chi e^{-\imath t\lambda} \, d\lambda\big)
\end{aligned}
\end{equation}

\begin{figure}
\centering
\def1.9in{1in}
\includesvg{gamma}
\label{figure:contour}
\caption{The contour of integration in \eqref{wavecontour}.}
\end{figure}
Here we have made the change of variables $\mu=\lambda^2$ and pushed
the contour within $\epsilon$ of the real axis for any $\ep>0$ (hence
the contour is written $\RR+\imath 0$).

Now suppose we are interested in the local large-$t$ asymptotics of a
solution to the wave equation, i.e., of $\chi U(t) f$ for $f$
compactly supported, or equivalently to $\chi U(t) \chi g$ for any $g
\in L^2(X);$ here $\chi$ is again a compactly supported cutoff
function.  For $t \gg 0,$ can can always slide the contour of
integration in the first integral on the last line of
\eqref{wavecontour} upward to $\RR+\imath \nu$ ($\nu>0$) and we get exponential
decay, $O(e^{-\nu t})$ for this term.  The second integral, however,
is trickier, as we would wish to slide this contour \emph{downward}
below the real axis, where we only know that the resolvent is
meromorphic.

In order to deal with this second term, let us now suppose we have:
\begin{enumerate}
\item $\chi (\Lap-(\mu+\imath \nu)^2)^{-1}\chi$ analytic for $-\nu_0 \leq \nu\leq 0.$
\item $\displaystyle\norm{\chi (\Lap-(\mu+\imath \nu)^2)^{-1}\chi}_{L^2}
  \lesssim \ang{\mu}^N$ in this strip.\footnote{Here and henceforth,
    $f\lesssim g$ means $f \leq C g$ for some constant $C.$}
\end{enumerate}

\begin{figure}
\centering
\def1.9in{1.5in}
\includesvg{resfree}
\caption{A resonance-free strip.}
\end{figure}

If these conditions hold, then we can shift the second contour, at the cost of some powers of $\mu$ or,
equivalently, powers of $\Lap$ and for $K$ sufficiently large get the bound $O(e^{-\nu t})$ for
any $\nu<\nu_0$ for the
smoothed wave operator $\chi \ang{\Lap}^{-K} U(t)\chi.$ Thus we
obtain \emph{exponential decay of local energy} (potentially with derivative loss).

We further remark that in flat space, $N=-1$ in the second condition
and we in fact have no derivative loss in the estimates: whenever
$(D_t^2 -\Lap)u=0$ and $u$ has compactly supported Cauchy data,
$$
\norm{\chi u_t}^2 + \norm{\chi \nabla u}^2\leq C e^{-\nu t} \big(\norm{u_t(0)}^2 + \norm{\nabla u(0)}^2\big)
$$
(where the constant may depend on the size of the support).

\subsection{Local smoothing for the Schr\"odinger equation}

We now consider a second application, which only involves the cut-off
resolvent estimate on the real axis.  This application is to the initial value problem for the time-dependent Schr\"odinger equation:
\begin{equation}\label{scheqn}
\begin{aligned}
\big(\imath^{-1} \frac{\pa}{\pa t}+ \Lap) u&=0,\
u|_{t=0}=u_0.
\end{aligned}
\end{equation}
The estimate on the cut-off resolvent that holds on the real axis in Euclidean space,
\begin{equation}\label{eucres}
\norm{\chi R(\mu)\chi}_{L^2} \lesssim \ang{\mu}^{-1},
\end{equation}
implies the following property of $u:$
$$
\int_0^1 \norm{\chi u}_{H^{1/2}}^2\, dt \lesssim \norm{u_0}_{L^2}^2.
$$
In other words, we have the following mapping property of the propagator:
$$
e^{-\imath t\Lap}: L^2\to L^2([0,1]; H^{1/2}_\text{loc} (X))
$$
(see Constantin-Saut \cite{CS}, Sj\"olin \cite{sjolin}, Vega
\cite{Vega}, Kato-Yajima \cite{Kato-Yajima}, Yajima \cite{Yajima2}).
A proof that \eqref{eucres} gives this estimate proceeds via a standard ``$T T^*$'' estimate which reduces to proving the corresponding estimate on the inhomogeneous equation:
$$
\big(\imath^{-1} \frac{\pa}{\pa t}+ \Lap) v=\chi f,\ u|_{t=0}=0 \Longrightarrow \norm{\chi u}_{L^2_t H^{1/2}_x} \lesssim \norm{\chi f}_{L^2_t H^{-1/2}_x}.
$$
This inhomogeneous estimate, in turn, follows from Fourier transform and \eqref{eucres}.

\subsection{Semi-classical rescaling, and estimates in non-trapping geometries}

Having established that cut-off resolvent estimates on and below the
real axis are of key importance in the study of the wave and
Schr\"odinger equations, we now pursue the question of when they hold
in non-Euclidean geometries.  To begin, we note that both the validity
of the estimate \eqref{eucres} and also of the existence of a
pole-free strip with polynomial resolvent bounds are
\emph{high-frequency} questions: they manifestly hold in any compact
range of $\Re \lambda,$ hence they hinge only on the
asymptotics of the resolvent as $\Re \lambda \to +\infty.$
Consequently, we now introduce a \emph{semi-classical rescaling} of
the problem: we set
$$
\lambda^2=\frac{z}{h^2}
$$
and study the operator family
$$
P_h(z) \equiv h^2 \Lap-z
$$
and its inverse
$$
R_h (z) \equiv (h^2 \Lap-z)^{-1}.
$$
We now note that
the existence of a resonance
free strip in $\lambda$ is equivalent to pole-free region in $z$
for $\chi R_h(z)\chi$ of form
$$
[1-\delta,1+\delta] + i [-\nu_0 h, 0],
$$
and the desired polynomial growth estimate in $\Re \lambda$ becomes a polynomial estimate in $h^{-1}.$
Likewise the free resolvent estimate on the real axis \eqref{eucres} rescales to:
$$
\norm{\chi R_h(z) \chi} \lesssim h^{-1},\quad z \in [1-\delta,1+\delta].
$$

In order to explain a broad setting in which these estimates
generalize, we now introduce the notion of \emph{trapped set.}
Let $\mathsf{H}_p$ denote the Hamilton vector field of
$p=\sigma_h(P),$ i.e., the generator of geodesic flow in the cosphere
bundle. Then the trapped set $K$ is defined by
$$
\rho \in K \Longleftrightarrow \exp(t\mathsf{H}_p)
 \text{ remains in a compact set for all }  t.
$$
We say the metric is \emph{non-trapping} if $K=\emptyset.$

The following is the classical result on estimates for non-trapping metrics:
\begin{proposition}
If the metric is nontrapping then there is a resonance free region of the form
$$
[1-\delta,1+\delta] +\imath [-\nu_0 h\smallabs{\log h}, 0]
$$
and the free
resolvent estimate holds: $$\norm{\chi R_h(z) \chi} \lesssim h^{-1},\ z \in [1-\delta,1+\delta].$$
\end{proposition}
Indeed, a somewhat stronger statement holds on the distribution of
resonances: for $h$ small, the region $[1-\delta,1+\delta] +\imath [-\nu h\smallabs{\log h}, 0]$
contains only finitely many resonances, for \emph{any} value of $\nu.$

These estimates have a lengthy history in both the obstacle case and
the metric setting considered here.  The deduction of exponential
energy decay from the eventual smoothness of solutions to the wave
equation with compactly supported data (a very weak form of Huygens'
Principle) follows from work of Lax-Phillips \cite{Lax-Phillips1} and Vainberg
\cite{Vainberg:Exterior,Vainberg:Asymptotic}.  (For further references
on the propagation of singularities arguments leading to these
estimates in the obstacle case, we refer the reader to
\cite{Tang-Zworski1}; in the metric case dealt with here, it simply
follows from H\"ormander's theorem on propagation of singularities for
operators of real principal type \cite{MR48:9458}.)

The estimate on the real axis is sharp: Ralston
\cite{Ralston:Localized} showed (in the obstacle setting) that the
estimate on the real axis can \emph{only} hold if the trapped set is
empty.  Indeed, if there is \emph{stable} trapping, e.g.\ a closed
elliptic geodesic, then it is known that the resolvent grows
on $\RR,$ with resonances approaching the real axis, as $\Re \lambda \to
 +\infty$ (see e.g., \cite{Stefanov-Vodev1,Stefanov-Vodev2}, \cite{Tang-Zworski2},
\cite{Stefanov:Quasimodes}). The minimal size
of the resonance free strip was established by Burq \cite{Burq1}, who
showed that there must always be a region of the form $\Im
\lambda>-Ce^{-\ep\smallabs{\lambda}}$ free of poles of
$(\Lap-\lambda^2)$ and consequently there is energy decay for the wave
equation at the rate $\log(2+t)^{-k}$ if we accept loss of $k$
derivatives.

\section{Resolvent estimates in the presence of mild trapping}

\subsection{Normally hyperbolic trapping}
What, then, if there are trapped orbits, i.e., $K \neq \emptyset,$ but
the trapping is at least \emph{unstable}?  The classical example of Ikawa sheds
considerable light on this problem: in the case of the exterior
problem for two strictly convex obstacles, there is a unique trapped
orbit consisting of the single orbit bouncing back and forth between
them; this orbit is highly unstable, and Ikawa was able to show that
in this case there is a strip $\Im z \geq -\nu_0 h$ that is free of
resonances, and indeed to derive asymptotics for the locations of the
resonances.  A refinement of Tang-Zworski \cite{Tang-Zworski1} and Burq
\cite{MR2066943} shows that while the non-trapping estimate cannot
hold on the real axis, we still have:
$$
R_h(\lambda) \lesssim \frac{\smallabs{\log h}}{h}, \quad \lambda \in [1-\delta,1+\delta].
$$
In other words, we lose only a factor of $\abs{\log h}$ relative to
the non-trapping estimate.  This implies, among other things, that the
local smoothing estimate for the Schr\"odinger propagator only barely
fails: for any $\ep>0,$
$$
e^{-\imath t\Lap}: L^2 \to L^2([0,1]; H_{\text{loc}}^{1/2-\ep}).
$$
In the boundary-less case, the analogous situation in
which we have a single unstable hyperbolic orbit (e.g., the unique closed
geodesic on the surface of revolution shown in
Figure~\ref{figure:revolution} below)
was analyzed by
Christianson \cite{Christianson1}.  More generally, the author and
Zworski \cite{Wunsch-Zworski:normhyp} have recently studied the situation of \emph{normally
  hyperbolic trapping}, in which there is a whole manifold of unstable
trapped orbits.  We now describe these results.

One motivation for considering this geometric set-up comes from the
\emph{Kerr black hole.}  This is a family of Lorentzian metrics which
solve the Einstein equations and describe rotating black holes.  The
trapped set of null-geodesics (known as the ``photon sphere'' in the
special, spherically symmetric, case of the Schwarzschild metric) has the dynamical structure
described below, and thus the results of \cite{Wunsch-Zworski:normhyp}
address the obstructions to decay posed by the trapped rays.
Considerable geometric and analytic difficulties are present in the
study of wave decay on Kerr backgrounds that are not addressed by
\cite{Wunsch-Zworski:normhyp} however; see, e.g.
\cite{Tataru2},
\cite{Tataru-Tohaneanu1} \cite{DSS1}, \cite{Dafermos-Rodnianski3},
\cite{Andersson-Blue1}, \cite{FSKY,FSKY:erratum} for results along these
lines and for further references.
  In the
related setting of Kerr-de-Sitter black hole metrics\footnote{These
  metrics describe rotating black holes in a universe with positive
  cosmological constant.} and their perturbations, some of the
obstructions to decay posed by the asymptotically Euclidean end of the
de Sitter space are not present.  In the case of
slowly-rotating\footnote{Slowly rotating means that the angular
  momentum parameter in the metric, usually denoted $a,$ is taken to
  be small.}
Kerr-de-Sitter metrics,
Dyatlov \cite{Dyatlov:KdS1,Dyatlov:KdS2} used the results from
\cite{Wunsch-Zworski:normhyp} presented
below to show that wave equation solutions decay exponentially to a
constant value; Vasy \cite{Vasy:KdS} was able to extend such
decay estimates to a wide class of perturbations of Kerr-de-Sitter
space, again using the results of \cite{Wunsch-Zworski:normhyp} to cope
with the trapped set.

The dynamical hypotheses employed in \cite{Wunsch-Zworski:normhyp} are as follows.
For simplicity of exposition here we stick to the geometric set-up
described above, where we consider the operator $h^2\Lap$ on the
manifold $(X,g)$
with $g$
Euclidean outside a compact set.
Let $\varphi^t$ denote the corresponding geodesic flow.
Let
$r$ denote the distance function to a fixed point in $X$ and locally
define the backward/forward trapped sets by:
$$
\Gamma_{\pm}=\{\rho: \lim_{t \to \mp\infty} r(\varphi^t(\rho)) \neq \infty\}.
$$
The the \emph{trapped set} is simply
$$
K=\Gamma_+\cap \Gamma_-.
$$

We make dynamical assumptions as follows:
\begin{enumerate}
\item \label{gammas}$\Gamma_\pm$ are codimension-one
smooth
manifolds intersecting transversely at $K.$ (It
is not difficult to verify that $\Gamma_\pm$ must then be coisotropic and
$K$ symplectic.)

\item \label{normflow} The flow is hyperbolic in the normal directions
to $K$ within the energy surface: letting the superscript $1$
denote the intersection of the set in question with the unit cosphere
bundle (e.g., $K^1=K\cap S^*X$) then there exist subbundles $E^\pm$ of
$T_{K^1} \Gamma_\pm^1$ (the ``unstable/stable subspaces'') such that
$$
T_{K^1} \Gamma_\pm^1=T K^1 \oplus E^\pm,
$$
where $$d\varphi^t:E^\pm \to E^\pm$$ and
there exists $\theta>0$ such that on $K^1,$
\begin{equation}
\label{eq:normh}
\| {d\varphi^t(v)} \|  \leq C e^{-\theta | t | } \| {v} \| \
\text{for all } v \in E^{\mp},\ \pm t \geq 0.
\end{equation}
\end{enumerate}

These assumptions can be verified directly
(see \cite{Wunsch-Zworski:normhyp}) for the trapped set of a
slowly rotating Kerr black hole\footnote{See also \cite{Vasy:KdS} for
  analogous discussion of the Kerr-de-Sitter metric.} (i.e.\ when the
angular momentum parameter $a$ is small---see
\cite{Wunsch-Zworski:normhyp} for the explicit form of the metric) but
they are not stable under perturbations, hence do not obviously apply
to perturbations of Kerr metrics.  However, the bicharacteristic flow
for the Kerr metric in fact satisfies a more
stringent (and well-studied) hypothesis that \emph{is} stable under
perturbation, and that implies the dynamical hypotheses above.  In
particular, the standard dynamical notion of \emph{$r$-normal
  hyperbolicity} implies items \eqref{gammas} and \eqref{normflow},
and \emph{is} stable under perturbations, modulo possible loss of
derivatives.  This hypothesis says, roughly speaking, that along $K$
the tangent space of the normal bundle to $K$ splits into subbundles
$E^\pm$ which are exponentially expanded/contracted by the flow, while
the expansion/contraction of directions along $TK$ is much milder by
comparison (e.g., polynomial in the case of the Kerr metric).  It is
then a profound theorem of Fenichel \cite{Fenichel:Persistence} and
Hirsch-Pugh-Shub \cite{Hirsch-Pugh-Shub1} that there exist
stable/unstable manifolds $\Gamma_\pm$ tangent to $E^\pm$ and
satisfying the dynamical hypotheses above, and moreover that these
stronger hypotheses are structurally stable.\footnote{Albeit in
  general, perturbing results in loss of differentiability of the
  manifolds $\Gamma_\pm$ and $K;$ however for any desired
  \emph{finite} degree of differentiability, shrinking the
  perturbation preserves that degree of smoothness, which suffices for
  our purposes.}

Our main result on the resolvent for normally hyperbolic trapping is
as follows:
\begin{theorem}{(Wunsch-Zworski \cite{Wunsch-Zworski:normhyp})}\label{theorem:normhyp}
Under the normal hyperbolicity hypotheses described above, there
exist $\delta, \nu_0>0$ such that $(h^2\Lap-z)^{-1}$ is
meromorphic in the region
$$
[1-\delta,1+\delta] +\imath [-\nu_0 h, 0]
$$
and the following polynomial resolvent estimates on the hold: on the
real axis, we have $$\norm{\chi R_h(\lambda) \chi} \lesssim
\frac{\smallabs{\log h}} h,\ \lambda \in [1-\delta,1+\delta],$$ while
  below the axis there exists $k>0$ such that
$$\norm{\chi R_h(z) \chi} \lesssim
h^{-k},\ z\in [1-\delta,1+\delta] +\imath [-\nu_0 h, 0].$$
\end{theorem}

In the case when the operator has real analytic coefficients
a more precise resonance free region was obtained by
G\'erard-Sj\"ostrand \cite{Gerard-Sjostrand:Lyapunov}, albeit without the polynomial bound
on the resolvent that makes contour deformation (with loss of
derivatives) feasible to obtain exponential energy decay for solutions
to the wave equation.  A similar estimate on the optimal width of the
resonance free strip in the setting considered here, and with much reduced
smoothness assumptions on the stable/unstable manifolds $\Gamma_\pm,$ has been
recently announced by Nonnenmacher-Zworski \cite{Zworski:Private}.

Estimates like Theorem~\ref{theorem:normhyp} have also been proved in
the case when $K$ is \emph{fractal} rather than a smooth manifold:
provided the set is sufficiently filamentary, in a manner measured by
a \emph{topological pressure} condition, an estimate of the same form
was previously proved by Nonnenmacher-Zworski
\cite{Nonnenmacher-Zworski1}; in \cite{N-Z:Semiclassical} these
authors also obtain more precise resolvent bounds below the real axis.
(See also Christianson \cite{Christianson:Cutoff} and Datchev \cite{Datchev:Local} for
applications to Schr\"odinger local smoothing in the presence of
various assumptions on the ends of $X$.)

\subsection{Degenerate hyperbolic trapping}

Since stable trapping, for instance by elliptic closed geodesics, generates
exponentially growing resolvent estimates, while unstable trapping
with hyperbolic dynamics
leads only to a loss of $\smallabs{\log h}$ on the real axis, the
reader might wonder whether there are situations in which a nontrivial
polynomial loss occurs.  This phenomenon was demonstrated by the
author and Hans Christianson \cite{Christianson-Wunsch1} in the following
situation:
We consider the manifold $X = \RR_x \times \RR_\theta / 2 \pi
\ZZ$, equipped with a metric of the form
\[
ds^2 = d x^2 + (1 + x^{2m})^{1/m} d \theta^2,
\]
Here the trapped set is again the closed orbit where $x=0.$  If $m=1,$
this is again the classic case of a single trapped hyperbolic orbit,
but if $m$ is an integer greater than $1$ the hyperbolicity
\emph{degenerates} with the stable and unstable manifold no longer
intersecting transversely.  Christianson and the author showed the
following:
\begin{theorem}{(Christianson-Wunsch \cite{Christianson-Wunsch1})}
For $m$ an integer at least $2,$
$$
\norm{\chi R_h(\lambda)\chi}\lesssim h^{-2m/(m+1)},\quad \lambda \in [1-\delta,1+\delta]
$$
and this estimate is sharp.
\end{theorem}
Consequently, the optimal local smoothing estimate in this situation entails a
nontrivial loss of derivatives:
$$
e^{-\imath t\Lap}: L^2 \to L^2([0,1]; H_{\text{loc}}^{1/(m+1)}),
$$
and we may obtain a polynomial rather than exponential rate of energy decay for the wave
equation.

\subsection{Trapping by cone points}

While metrics with trapped rays always have losses in resolvent
estimates on the real axis and in Schr\"odinger local smoothing (see
Doi \cite{Doi1} and Burq-Bony-Ramond \cite{B-B-R} as well as Ralston
\cite{Ralston:Localized} in the obstacle case), we now present a
situation involving wave propagation on singular manifolds in which a
weaker form of ``diffractive'' trapping results in (almost) no loss whatsoever.
This is the setting of \emph{manifolds with cone points.}

In joint work with Dean Baskin, the author considers a manifold $X$ of
dimension $n$ with conic singularities that is isometric to $\RR^n$
outside a compact set.  Here a manifold with conic singularities means
a manifold $X$ with compact boundary $Y=\pa X$ equipped with a metric
that can be brought to the form
$$
g=dx^2 + x^2 h
$$
in a neighborhood of $Y,$ with $h$ a smooth tensor restricting to
give a metric on $Y.$  The metric thus degenerates at the
boundary, and each boundary component becomes a cone
point.

In considering trapping, we must now distinguish two kinds of geodesic
on $X.$  Following Melrose-Wunsch \cite{Melrose-Wunsch1},  we let a
\emph{diffractive geodesic} denote a geodesic that can enter and leave
a cone point (i.e., a single boundary component) along \emph{any} pair
of geodesics.  By contrast, a \emph{geometric geodesic} is one that is
restricted to enter and leave a single cone point along a pair of
geodesics that are connected by a
geodesic of length $\pi$ inside $Y$ (with respect to the metric $h\rvert_{Y}$).  In \cite{Melrose-Wunsch1},
the geometric geodesics are shown to be exact those that are (locally)
approximable by ordinary geodesics in $X^\circ.$

We impose geometric hypotheses
that \begin{enumerate}
\item The flow
along geometric geodesics is non-trapping.
\item
No three cone points are collinear along a geometric geodesic.
\item
No two cone points are conjugate to one another.
\end{enumerate}
(The last condition can be most easily interpreted as saying that the geodesic
flowouts from two different cone points intersect transversely.)

Then the following estimate on the resolvent holds:
\begin{theorem}{(Baskin-Wunsch \cite{BW1})}\label{theorem:conedecay}
For $\chi \in \CcI(X),$ there exist $\delta, \nu_0>0$ such that the cut-off resolvent
$$
\chi (h^2\Lap-z)^{-1}\chi
$$
can be analytically continued from $\Im z >0$ to the region
$$
z\in [1-\delta,1+\delta]+\imath [-\nu_0 h \smallabs{\log h}, 0]
$$
and for some $C,T>0$ enjoys the estimate
$$
\norm{\chi (h^2\Lap-z)^{-1}\chi}_{L^2\to L^2} \leq \frac{C}{h} e^{T \smallabs{\Im z}/h}
$$
in this region.
\end{theorem}
This implies that the trapping of waves induced by diffraction among
cone points has only a very weak effect on the decay of solutions to
the wave equation on such a manifold: in particular, solutions to the
wave equation on $\RR\times X$ enjoy exponential local energy decay.
Likewise, the resolvent estimate on the real axis (which is the same
as would be obtained with \emph{no} trapped rays) implies that the
Schr\"odinger propagator $e^{-\imath t\Lap}$ enjoys the local smoothing
estimate with no loss, mapping $L^2\to L^2([0,1]_t; H^{1/2}_{\text{loc}}(X)).$

The theorem is proved by first establishing a result on weak escape of
singularities for solutions to the wave equation.  We recall that in
odd dimensional Euclidean space, Huygens' Principle tells us that any
solution to the wave equation with compactly supported Cauchy data is
eventually zero in any fixed compact set $F$; in a non-trapping
perturbation of Euclidean space (of any dimension), the solution does
not in general vanish after long time but instead, by propagation of
singularities, is eventually in $\CI(F).$ In the conic situation, by
contrast, we expect that singularities may persist forever in a
compact set, diffracting back and forth among the cone points, but it
turns out that they become milder and milder as time passes:
\begin{theorem}{(Baskin-Wunsch \cite{BW1})}\label{theorem:conesmoothing}
For any
$r$ there exists $T_r$ such that for $\abs{t}>T_r,$ for all $s,$
$$
\chi \cos t\sqrt{\Lap}\chi: \mathcal{D}_s\to \mathcal{D}_{s+r}.
$$
\end{theorem}
\noindent (Here $\mathcal{D}_s$ is the domain of $\Lap^{s/2}$ and agrees with
$H^s$ away from the cone points.)  One can then deduce
Theorem~\ref{theorem:conedecay} from
Theorem~\ref{theorem:conesmoothing} by adapting an argument of
Vainberg \cite{Vainberg:Asymptotic} that employs the Fourier transform
of the outgoing singular parts of the solution as an initial
parametrix for the resolvent, solving away the resulting errors by
using the free wave operator (for which the resolvent estimate
assuredly holds).

One especially interesting and elementary setting in which our result
on resonance-free regions applies is that of exterior domains to
polygons in $\RR^2.$  We can \emph{double} such domains by gluing
together two copies along their boundary to obtain a manifold with
cone points; solving the wave equation with Dirichlet/Neumann boundary
conditions is equivalent to working with odd/even solutions on the
doubled manifold.  Provided the domain is
nontrapping in the sense that billiard trajectories missing the cone
points escape to infinity, we can thus show that there is a
logarithmic region free of resonances for the obstacle problem with
either boundary condition.\footnote{There is some mild technical
  complication from the fact that the manifold has two Euclidean ends,
  rather than just one as in our hypotheses, but the same strategy of
  proof applies.}

We remark that the size of the resonance free region in
Theorem~\ref{theorem:conesmoothing} is probably sharp: in the related
situation of the exterior problem in $\RR^2$ outside two strictly
convex analytic obstacles, one having a corner, Burq \cite{Burq:Coin}
has shown that resonance poles for $(\Lap-\lambda^2)^{-1}$ lie
(asymptotically) along curves of the form $\Im \lambda=C\abs{\Re \lambda} +D.$
The poles are thus at distance $O(h
\smallabs{\log h})$ from the real axis after semiclassical rescaling.  (We also refer the reader to
Zworski \cite{Zworski4} where analogous logarithmic strings of poles are
shown to arise from finite order singularities of a one-dimensional
potential, thus substantiating heuristics from
Regge \cite{Regge:Analytic}.)  Consequently, the only loss in this setting of
``diffractive trapping'' relative to the non-trapping case is that we
expect that some region of the form $z\in [1-\delta,1+\delta]+\imath [-\nu_0 h \smallabs{\log h}, 0]$
probably contains infinitely many resonances in the former case, while
this is not so in the latter.

\section{From resolvent estimates to damped waves}

We now turn to a problem related to, but crucially distinct from, that
of resolvent estimates and decay for solutions to the wave equation:
we now consider the \emph{damped wave equation} on a \emph{compact,} connected
Riemannian manifold $X.$  We fix a nonnegative ``damping function''
$a(x) \in \CI$ and consider the initial value problem:\footnote{Recall
  that the Laplacian employed here is the \emph{positive} operator $\Lap=d^*d.$}
\begin{equation}
\label{eq:dwe}
\bigg\{ \begin{array}{l}
\left( \partial_t^2 + \Delta_g +
a(x) \partial_t \right) u(x,t) = 0, \\
u(x,0) = u_0\in H^1(X), \quad \partial_t u(x,0) = u_1\in H^0(X).
\end{array}
\end{equation}
It is well known \cite{MR94b:93067}, \cite{MR97i:58173} that if $a>0$
somewhere, then any solution tends to zero as $t\to +\infty.$  Moreover
Lebeau has shown (see \cite{MR97i:58173}) that the energy of the waves,
$$
E(u,t)=\frac{1}{2}\int_X \big( | \partial_t u |^2 + | \nabla u |^2
\big) dx
$$
decays at a logarithmic rate provided the data lie in a space with
higher regularity than the energy space; this is of course analogous
to the results discussed above for energy decay of solutions to the wave equation
on noncompact manifolds in the presence of trapping.

To understand decay rates for the damped wave equation in further
detail, we make a semiclassical reduction: Fourier transforming, it
turns out that we can replace the damped wave operator by an operator
of the form
\begin{equation}\label{damped}
h^2\Lap + \imath h \sqrt{z} a-z;
\end{equation}
exponential energy decay then
follows from the existence of a pole-free region of the form
\begin{equation}\label{polefreeregion} z\in [1-\delta,1+\delta]+\imath
  [-\nu_0 h,0]\end{equation} together with polynomial
bounds for the inverse of this non-self-adjoint operator; smaller
regions of analyticity yield sub-exponential decay rates.  In
the results discussed here, the $z$ dependence of the middle term in \eqref{damped} will
be treatable as a perturbation in the operator above, and we study the family
\begin{equation}\label{dampingresolvent}
(h^2\Lap + \imath h a-z)^{-1}
\end{equation}
which is at least formally quite similar to the resolvent studied in
previous sections.

Now in analogy with the trapped set in noncompact problems, we introduce the \emph{undamped set}
\begin{equation}
\mathcal{N}=\{\rho\in S^*X: \forall t\in\RR, a\circ e^{t\mathsf{H}_p}(\rho)=0 \}
\end{equation}
consisting of points that do not encounter the interior of the damping region under
the forward- or backward-bicharacteristic flow.  If $\mathcal{N}=\emptyset$ we
are said to be in the situation of \emph{geometric control.}
Classic results of Rauch-Taylor \cite{RaTa75}, Bardos-Lebeau-Rauch
\cite{MR94b:93067} and Lebeau \cite{MR97i:58173} show that in the setting of geometric control, we
do have a pole-free region of the form \eqref{polefreeregion} and
exponential decay of energy.  By contrast, if $\mathcal{N}\neq
\emptyset,$ it is known that exponential decay cannot hold without
derivative losses.  The situation is thus closely analogous to that
described above for resolvent estimates, leading one to wonder if
there is a link between the resolvent estimates for a noncompact
manifold $\widetilde{X}$ with trapped set $K$ and estimates for
\eqref{dampingresolvent} on a compact manifold $X$ with undamped set $\mathcal{N}
\equiv K,$ as long as the two manifolds are isometric in a
neighborhood of the undamped/trapped set.  In joint work with Hans
Christianson, Emmanuel Schenck, and Andr\'as Vasy, the author has
proved that this is so: provided one has polynomial resolvent bounds
on the real axis,
one can ``glue'' these bounds to obtain the exact same estimate for
the damped resolvent family \eqref{dampingresolvent}.  While our
motivation comes from gluing on non-compact ends, the following
theorem is in fact phrased in terms of the resolvent for the problem with
``complex absorbing potential'' $\imath a$ replacing the damping
coefficient $\imath h a;$ such a potential has the effect of
annihilating semiclassical wavefront set along (forward)
bicharacteristics passing through it.  Estimates with non-compact ends
and with complex absorbing potential are known to be
equivalent in a wide variety of geometric settings by a recent gluing
theorem of Datchev-Vasy \cite{Datchev-Vasy:Gluing}.  Phrasing the
resolvent estimate in this way allows us to stay within the setting of
compact manifolds, however:
\begin{theorem}{(Christianson-Schenck-Vasy-Wunsch \cite{CSVW})}
\label{theorem:damping}
Assume  that for some $\delta \in (0,1)$
fixed and $k \in \ZZ$, there is a function $1 \leq \alpha(h) = O( h^{-k})$ such that
\[
\| (h^2\Delta_g +\imath a-z)^{-1} \|_{L^2 \to L^2} \leq \frac{\alpha(h)}{h},
\]
for $z \in [1-\delta, 1+
\delta]$.  Then there exist $C, \nu_0>0$ such that
\[
\| (h^2\Delta_g+\imath ha -z )^{-1} \|_{L^2 \to L^2} \leq C \frac{\alpha(h)}{h},
\]
for $z \in [1-\delta,1+\delta] + \imath [-\nu_0 h/\alpha(h) , 0 ]$.
\end{theorem}

\begin{figure}
\centering
\def1.9in{2in}
\includesvg{dampedpeanut}
\caption{The compact manifold $X$ with damping.}
\end{figure}
\begin{figure}
\centering
\def1.9in{1.9in}
\includesvg{noncompact}
\caption{The noncompact manifold $\widetilde{X}.$}
\label{figure:revolution}
\end{figure}
An essential new ingredient in the proof is a recently obtained
estimate of Datchev-Vasy \cite{Datchev-Vasy:Trapped} which improves
the microlocal resolvent estimates available at points which are
backwards- or forwards-trapped relative to those which are trapped
along both directions of the flow.

Theorem~\ref{theorem:damping} has applications in all the examples
discussed above (normally hyperbolic
trapping, fractal hyperbolic trapping, degenerate hyperbolic trapping)
giving various subexponential decay rates for solutions to the damped
wave equation in these settings; we refer the reader to \cite{CSVW}
for further details, including the explicit decay rates thus
obtained.  It is at least sometimes \emph{sharp}, e.g.\ in the case of
a surface of rotation with $\mathcal{N}$ given by an single undamped
hyperbolic orbit, according to work of Burq-Christianson
\cite{Burq-Christianson:Peanut}.

redpajama_set_name: RedPajamaArXiv


Wages & salaries for Computer programmers in Decatur, IL ?
The BLS estimates that in Decatur, IL there were around 70 employed in the field of Computer programmers.
Computer programmers in Decatur, IL earned 22% less than average for Computer programmers in the United States.
Computer programmers in Decatur, IL earned 56% more than the average worker in Decatur, IL.
Computer programmers in Decatur, IL earned 23% more than the average worker in Illinois.
Computer programmers in Decatur, IL earned 38% more than the average worker in the United States.


text:
Exploring New Ways to Engage the Community
Venues and Staff Tapped in Creative Ways During the Pandemic
by Mark Wallace
In the midst of dealing with the cancellations of Broadway shows and other events due to the pandemic, Blumenthal Performing Arts has worked hard to keep hope alive. Finding alternative spaces for events through strategic partnerships is just one part of it. Blumenthal and its employees have also refocused within, finding creative ways to tap its own venues and staff during these difficult times.
Blumenthal Front of House Manager Tommy Cantrell had been conducting tours of the theaters based on availability, but now that the theaters are empty, it was decided to make them more of a regular thing to bring in a little revenue during the downtime. Tour groups have been kept small because of COVID-19 restrictions. Guests were appreciative of the tours.
Tommy Cantrell
"I did have a few say that they will never complain about the ticket price again after they heard what all goes into the producing a Broadway tour," said Cantrell. One guest said: "Thank you for providing this opportunity. We loved having a tour guide that has been with the Blumenthal for 20 years."
Another said: "Great way to bring show goers and newbies back to the theaters. Tommy went above and beyond."
For a taste of the backstage tours, IT Director Robert Schoneman walks us through the Booth Playhouse decked out for the holidays.
When the backstage tours cranked up in late fall, it was the perfect time to include ghost tours in the theaters as well. Several staff members took turns conducting those tours, telling of eerie encounters in the Blumenthal buildings.
Staff also played a big part in an outdoor, socially distanced touring show that came to Charlotte called Art Heist Experience. The interactive event required participants to move in loose groups from site to site uptown to get different clues from an actual unsolved art heist.
Above are some of the different characters and locations for Art Heist Experience.
Blumenthal Season Marketing Manager Kitty Janvrin took on the role of production coordinator. "I worked with the directors and the production company to essentially build the Charlotte production using the script and past productions as a base," she said. She also coordinated local casting and rehearsals, scouted locations for the clue stations, worked on costuming and props for the characters, worked with tech and front of house on health and safety protocols and enforcement, and served as the "on-the-ground director" and stage manager once the show started.
Booth Playhouse is decorated for the holidays for groups to rent out and view their favorite holiday movies.
During the holiday season, Booth Playhouse was converted into a private movie theater for groups to rent and view their favorite holiday movies. The tech department brought in lighting and sofas and Tommy Cantrell decorated Christmas trees and helped guide the overall decorating of the theater.
Blumenthal's education department kept things alive in the organization with programs that engaged students and teachers in the performing arts.
Andie Maloney
"Our goal is to create programs that meet the needs of our community," said Blumenthal Vice President of Education Andie Maloney. "This year in particular has created rapidly changing needs, and we have stayed nimble to respond."
For instance, when the beloved Blumey Awards ceremony in May had to be canceled because of COVID-19, the education department quickly shifted gears and worked with PBS Charlotte to create a special televised program that honored the hard work and dedication of former and current high school musical theater students and teachers. It was presented in partnership with Wells Fargo and PBS Charlotte.
Since restrictions are still in place, most schools are not able to produce shows. This year's Blumey Awards program has been restructured so that individual school musical productions are not required. Instead, students from participating schools will use an audition model that can take place in-person or virtually. This year's ceremony will be a celebration, featuring students from each participating school in musical numbers, either with a live or virtual audience.
Teen Actor's Lab takes place at Spirit Square.
This past fall, Blumenthal's education department started a weekly Teen Actor's Lab at Spirit Square for middle and high school students of all skill levels. The program ran three days a week from September through November, with each day consisting of supervised study hall to complete schoolwork, and then hands-on theater workshops.
"The Teen Lab filled a gap in theater training and safe in-person peer interactions for teens while school was fully remote," said Maloney.
Diving even deeper into musical theater training, Broadway Bootcamps were set up to give eighth through 12th graders intense and in-person one-day masterclasses in acting, voice and dance from working Broadway actors and industry pros. One was held in October and one in December.
Students participate in Blumenthal's Broadway Bootcamp.
Maloney says more of the "bootcamps" are to come, so stay tuned.
For younger students, Blumenthal usually conducts the Junior Theater Celebration at Knight Theater with in-person workshops, giving elementary and middle school students a chance to perform on a real stage. This year's Junior Theater Celebration will move to a digital platform the last week in March.
To support educators with resources and development opportunities, the education department initiated an Arts Educator Network. The four-hour workshop covered rehearsing and presenting a musical online.
"The timing of the program launch happened to come when educators most needed to share resources and connect while adapting to the pandemic," Maloney said. "We hope the launch of this program has helped them feel valued and appreciated while they work so hard to keep the arts thriving and accessible for their students."
Teachers participate virtually in the Art Educator Network.
Also, at the request of the Rock Hill district arts coordinator, Blumenthal will be developing a full-day workshop to support the professional growth of creative industry teachers and programs in the Rock Hill School District.
Maloney said the Arts Educator Network program is here to stay. "We look forward to a day when we can gather in person to network and celebrate, including attending performances together."
Late last year, Blumenthal also hosted some industry panels. One titled "Young, Gifted and Black: Bringing the Young Black Artist Center Stage" was streamed live from the McGlohon Theater stage.
"The Young, Gifted and Black panel discussion was a step in the journey to increase diversity in theater; uplifting talent that is underrepresented to ensure our youth hear and see role-models that look like them, or don't look like them for that matter," Maloney said.
"Thank you for all you do, both for arts education here in Charlotte, and especially thank you for last night," said Casey Starkey at Central Academy of Technology and Arts after viewing the program. "It was honestly the most encouraging event and something I can't even begin to describe how it impacted my heart and the hearts of my kids!"
The other panel was "Home for the Holidays" featuring three Charlotte natives who are in the Broadway industry – actor and teacher Tyler McKenzie, producer Thomas Laub, and stage manager Ryan Gardner. They discussed their paths in the industry, what it was like working in professional theater during the holidays, and life while theaters are dark. Maloney wants to do more of these type panels this year.
Open Mic continued on, as well, but outside instead of inside the McGlohon Theater. In October and November, a stage was set up on the landing at the back entrance of Spirit Square, and socially distanced mask-wearing watchers gathered on the square at Spirit Square.
"Artists have not stopped during the pandemic and the need for art – to entertain, to express, to commune – is as essential as ever," Maloney said. "I am excited for the renaissance on the horizon that will feature an explosion of beautiful and powerful works of art uniting, celebrating and challenging people from all backgrounds to experience, explore and share together." ◼
On the next page, see videos of some of what Blumenthal has had to offer during the pandemic, and messages of hope.
Still-standing Historical Spaces
Blumenthal in Videos

redpajama_set_name: RedPajamaCommonCrawl


text:
Evaluación y diagnóstico de las dificultades de atención: TDAH-5
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Skiing, snowboarding, tobogganing and parapenting to name but a few wintersports are activities with a higher than average injury rate, with stats suggesting that the majority of injuries are from the popular pastimes of downhill skiing and snowboarding.
User error is the root cause of most injuries, with is isolated falls from going too fast, or tackling a terrain that is beyond the skills set of the person in question being the main cause. Collisions are responsible for 10% of injuries, as are lift related incidents, and finally 5% of injuries are due to equipment failure.
Warm Up – it is easier to injure a cold muscle than a warmed up one. Do some stretching before hand and ease yourself into those difficult slopes or more challenging manoeuvres.
Familiarise yourself with your surroundings – go out in good visibility so you can see where rocks, trees and treacherous patches may be, that way avoiding them will be a lot easier and less likely to result in injury.
Stay alert! – Tiredness can lead to lack of concentration and reduced reaction time as well as poor decision making. Rest well and avoid alcohol before taking to the slopes.
If you are heading off on holiday, get in touch for a quote. We can tailor your policy to meet your needs whatever activities you decide to do!
This entry was posted in Ski Insurance, Travel Advice, Travel Insurance on January 17, 2013 by worldwideinsure.


text:
News On Medical
Your Medical News Source
Health, Fitness & Food
Apple will disrupt the health sector as the iPhone did wireless, former CEO John Sculley says
Apple CEO Tim Cook's vision for health-care services has gotten a stamp of approval from a past chief of the tech giant. John Sculley, who helmed the company from 1983 to 1993, told CNBC on Thursday that Cook is "absolutely onto something" with his plans to inject Apple into the health-care space and that "it
January 11, 2019 by admin 0 Comments
Health-care stocks are a way to ride this market comeback, Charles Schwab chief strategist says
Investors should lean on defensive stocks such as the health-care sector as Wall Street starts the year off positive, Charles Schwab chief strategist Liz Ann Sonders told CNBC on Wednesday. She said the S&P 500's 3 percent rally thus far in 2019 is "pretty decent" but said the odds of it being long-term are "relatively
Investors get dose of government shutdown as FDA chief delivers keynote via video call, loses audio
Attendees at the annual J.P. Morgan Healthcare Conference, the industry's largest annual event, unexpectedly got a taste of the government shutdown Tuesday. Food and Drug Administration Commissioner Scott Gottlieb's keynote address was delivered via video conference from a meeting room in Washington, D.C. to thousands of investment bankers and health-care executives, and his audio cut
January 9, 2019 by admin 0 Comments
GlaxoSmithKline CEO Emma Walmsley gets 'radical' about reshaping portfolio
After announcing two major deals in December, GlaxoSmithKline CEO Emma Walmsley is optimistic about her efforts to transform Britain's largest drugmaker. "I think we have tremendous opportunities to improve both operating performance and to get radical about reshaping our portfolio," Walmsley told CNBC's Jim Cramer on "Squawk Alley" on Monday. Walmsley took the helm of
Americans are sicker and dying younger, despite the billions pouring into digital health
Silicon Valley has spent years promising to disrupt the $3.5 trillion health-care industry. In 2018, venture investors — from the Bay Area, Boston and elsewhere — poured billions of dollars into the sector, funding start-ups that aim to bring down the costs of care while improving quality and access to the right providers. Some of
Digital health market is frothy, but it doesn't look like a bubble
Since my company, Rock Health, began researching and tracking funding into the digital health space in 2011, we've reported steady growth nearly every year. 2018 was no different, with a massive $7.9 billion in venture filling start-ups' coffers. But the signals we're seeing — large, late-stage rounds at high valuations and shorter periods between early
Ocean Cleanup device breaks down, well before ridding Pacific of plastics
An ambitious project to clean up a vast tide of ocean pollution has been sidelined. The project's 2,000-foot-long screen — which was already failing to capture plastic while stationed more than 1,000 miles off the coast of California — broke apart just before New Year's under the constant wind and waves of the Pacific Ocean.
Breast pump start-up Naya Health shuts down after failing to raise money
Naya Health, the maker of a $1,000 breast pump that was supposed to be "revolutionary," has shut its doors after the company was unable to find an investor or buyer. The start-up emailed its users on Wednesday about the decision and took down its website. The email was forwarded to CNBC. "We are sorry to
The best-performing sector last year could be the top bet for 2019, technician says
Health-care stocks did not just survive a volatile 2018. They thrived. The S&P 500 sector ended the year up 4 percent, the only positive area of the market, while components of the XLV health-care ETF such as Eli Lilly, Merck and Pfizer ended with double-digit gains. The party might not be over yet, the sector
Judge clears the way for appeal of ruling against US health law
A federal judge in Texas who recently declared the Affordable Care Act unconstitutional has stayed his ruling to allow for appeals. That means "Obamacare" remains in effect while litigation continues. In a ruling issued Sunday, Judge Reed O'Connor in Fort Worth wrote that he stands by his earlier conclusion that the entire law is invalidated
Orlando clinic develops virtual reality to treat PTSD in veterans
An Orlando clinic is using a $3 million grant from the U.S. Department of Defense to develop virtual reality (VR) technology for treating post-traumatic stress disorder (PTSD) in veterans and emergency services workers. The University of Florida's RESTORES clinic has been testing VR therapy, which uses the tech to expose veterans to the scenes and
December 31, 2018 by admin 0 Comments
The $35 billion race to cure a liver disease that affects 30 million Americans
At the Mayo Clinic in Jacksonville, Florida, the liver transplant group is busy handling an onslaught of patients who have come from all over the country in hopes of a chance at life. For many, a liver transplant is their last hope, after being diagnosed with a deadly disease sweeping the nation at epic proportions.
FDA weighs legalizing interstate sales of cannabis-based CBD in food and drinks
The Food and Drug Administration is looking for "pathways" to legalize the sale of CBD oil and other cannabis-based compounds in food and beverages in a move that could remove one of the last remaining legal hurdles for companies hoping to sell such products across state lines. FDA Commissioner Scott Gottlieb outlined steps the agency
Doctors are asking Silicon Valley engineers to spend more time in the hospital before building apps
As an emergency room physician, Richard Zane often considers how software can help him their patients. The problem is that engineers and doctors are from different planets. Zane, who's also the chief innovation officer at UCHealth in Colorado, said that most engineers he's met have never seen the inner workings of a hospital and don't
Amazon gets into health insurance — and more 2019 health-tech predictions
2018 was an important year for the booming health-technology sector. Start-ups in the space got record levels of funding from venture capitalists, and M&A activity finally picked up in the second half of the year. Also this past year, technology companies like Apple and Amazon explored opportunities to target their products to the medical sector,
FDA warns some antibiotics can cause fatal heart damage
Certain antibiotics can cause painful and sometimes fatal damage to the body's main artery, the Food and Drug Administration said Thursday. Fluoroquinolone antibiotics might raise the risk of an aortic dissection, and people who are already at risk should be cautious about taking those antibiotics, the FDA said. "A U.S. Food and Drug Administration (FDA)
Altria looks to a future beyond cigarettes but investors aren't cheering its $15 billion bet
It's getting harder to be a cigarette company. Altria knows that. Altria shelled out $14.6 billion to take large stakes in companies outside its traditional hold in cigarettes over the past two weeks — a 45 percent share of cannabis company Cronos and 35 percent stake in e-cigarette maker Juul. The latter, which valued Juul
As obesity rates in America soar, new weight loss drugs are in the offing that offer hope
The average American is getting shorter and fatter, and on the verge of matching the medical definition for obesity, according to a report this week from the Centers for Disease Control. The six new drugs to treat obesity set to release in the U.S. by 2026 can't come soon enough. These weight-loss drugs could improve
Facebook, Snapchat and TikTok have a massive underage problem — here's why it matters
Rates of adolescent depression and suicide are on the rise, and many parents and psychologists alike are linking this trend to the prevalence of smartphones and social media. According to a report by Influence Central, the average kid gets their first smartphone at age 10.3, and opens their first social media account by age 11.4.
I tried the keto diet that's sweeping Silicon Valley with help from a gadget that tracks progress
Ketogenic dieting has become a favorite pastime of Silicon Valley techies who want to hack their bodies to improve energy levels and performance. The regimen involves eating foods that are high in fat and some protein, while keeping carbohydrates to a minimum. The goal of ketogenic diets is to get body to a state calld
Health Secretary Azar tells Trump U.S. Capitol attack was assault on democracy that tarnishes legacy
Moderna looks to test Covid-19 booster shots a year after initial vaccination
Dr. Fauci warns Covid variant found in South Africa could pose threat to antibody drugs
Wall Street analysts are cautiously optimistic on J&J's 'one-dose' Covid vaccine
Israel's massive vaccine drive isn't keeping up with new cases — especially among younger victims
Covid killing nearly 3,000 in U.S. every day as CDC warns of 'surge event' from Capitol riots
White House Covid task force warns of possible new 'USA variant' driving spread
Texas health officials identify state's first case of new Covid strain found in UK
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How do you give new life to an old company? Bring new vision to a place that lost its own? And how do you bring your team -- and your new audience! -- along for the change? Those are the challenges Neil Vogel faced when taking over the old internet giant About.com and transforming it into a thriving company called Dotdash.


text:
BSD/OS (früher BSD/386) ist ein kommerzielles Unix-Betriebssystem des Unternehmens Berkeley Software Design (BSDI) und stammt aus der BSD-UNIX-Familie. Die Entwicklung wurde 2003 eingestellt. BSD/OS wurde vor allem im Bereich von Internet-Serversystemen eingesetzt und zuletzt von der Firma Wind River Systems weiterentwickelt und vertrieben.

Geschichte

BSD/386
1991 verließ eine Gruppe von BSD-Entwicklern die Universität Berkeley und gründete das Unternehmen Berkeley Software Design (BSDI), um ein kommerzielles Unix-Betriebssystem für i386-Prozessoren zu entwickeln. Basierend auf 4.3BSD Net/2 entstand das Betriebssystem BSD/386. Die erste öffentliche Version 0.3.1 wurde im April 1992 freigegeben.

Kurz nach der Veröffentlichung der Version 1.0 verließ der Entwickler Bill Jolitz im März 1993 die Gruppe, um das freie Unix-Betriebssystem 386BSD zu entwickeln, welches später zu einer wichtigen Grundlage für die freien BSD-Derivate FreeBSD und NetBSD wurde.

Gegenüber den Konkurrenzprodukten zeichnete sich BSD/386 vor allem durch niedrige Lizenzgebühren für den Quelltext aus.

BSD/OS
Nach einem Rechtsstreit mit den Unix System Laboratories (USL) um die Rechte an Unix entwickelte BSDI die Version 2.0 ihres Betriebssystems auf der Basis von 4.4BSD-Lite, womit es keine USL-basierenden Quelltexte mehr enthielt. Zudem wurde das System in BSD/OS umbenannt, um sich in der weiteren Entwicklung nicht auf die i386-Architektur zu beschränken und im Januar 1995 als BSD/OS 2.0 veröffentlicht. Einer der wichtigsten Einsatzbereiche war der Internet-Server-Bereich.

Obwohl sich BSD/OS durch eine weit entwickelte SMP-Unterstützung und den kommerziellen Support von den damaligen freien BSD-Derivaten absetzte, bekam es von diesen zunehmende Konkurrenz. Auch die fehlende Zertifizierung durch die Open Group führte dazu, dass gegen Ende der 1990er Jahre die Verkaufszahlen immer weiter zurückgingen.

Durch eine Fusion von BSDI mit Walnut Creek CDROM, dem damals größten Distributor von FreeBSD und der Linux-Distribution Slackware, im März 2000 erweiterte sich das Angebot von BSDI. Im April 2001 übernahm die Firma Wind River Systems schließlich die Rechte an BSD/OS sowie den FreeBSD-Vertrieb von BSDI und sicherte ihrerseits zu, die Entwicklung von FreeBSD zu fördern. Am 13. Dezember 2003 wurde die Weiterentwicklung und gegen Ende 2004 der Support von BSD/OS durch Wind River Systems eingestellt.

Siehe auch
 Vergleich von BSD-Betriebssystemen

Einzelnachweise

BSD-Betriebssystem
Proprietäre Software
BSDOS
Historische Software

redpajama_set_name: RedPajamaWikipedia


To many people, travelling is like a hobby as many at the same time get caught up travelling to adventure in new places and visit people in new parts of the globe. At times many people get caught up in situations like lack of money during the journey. This is the absolute moment when one can use some wee charms to make a little cash that can save his or her neck to overcome the circumstances, furthermore, being able to actually make some cash during travel can help you pay for your travel expenses and other anticipated occurrences that may feature in your way.
You shouldn't be in the habit of thinking of application of a job during travelling when it's mentioned that there are ways and means one can use to make money during a travel. It's totally a different kettle of fish. The major part of this is creativity. When you're creative then you've have successfully gone through a bigger percentage of it. Take a moment and think of or trying your luck at a poker.
You can launch especially in casinos that are mostly visited by tourists. Once you have got some little cash in your pockets then minting it into multiples is not all difficult.
Try your hand into this if you feel to have got the guts and out of blue you can come out with of it with a broad face.
Having a travel blog is of great help when it comes to this situation.
Blog where you can advertise all your travel experiences. If you blog your real experiences and precisely put in your real stories then you're sure to get many readers who'll love it. Take advantage of this and see yourself making some good cash out of it.
There are so many types of online jobs that you can do even when on a travel.
If you can write articles, transcript, or even do some simple data entry then you're on a sure way of making money.
Register to any of the many websites that offer these jobs as part time and see yourself hired. You can do it and it's not difficult.
It is not a mandatory that you have to be an amateur photographer or waiting for what you call a perfect' time to take the photos, do it and take a lot of them.
Sell them online. There are so many sites online that can help you sell those photos hence stay loose and indulge into the operation.
Some of your photos might really be relevant to what a group or a company would be in need of hence they can purchase them and give you some good dollars. It works and it's not a fiction or a fallacy.
If you're certain you have got some useful information or unique knowledge about something, then it's again your opportunity to write an EBook.
It can look very hectic at the first moments but if you're determined then you have made for yourself a perpetual source of income.
You can sell monthly or annual updates to your EBook and make a tremendous lot of money.
Excellent work, several truly good suggestions! I appreciate you crafting this posting and the rest of your web-site is terrific!


The Queen Elizabeth II ship is set to finally open as a floating hotel in Dubai.
A "soft opening" will take place on April 18 before a "grand launch" in October.
Visitors will be welcomed on board the Cunard ship almost a decade after it completed its final voyage from Southampton to the Middle East in November 2008.
After being bought by a Dubai government-owned company for $100 million (£70 million), the vessel was expected to be quickly reinvented into a hotel - but the global financial crisis delayed the project.
The ship has undergone a £70 million transformation.
Its owners say that it has now been "thoughtfully restored to her former glory" after 2.7 million man-hours of work.
The 13-deck hotel is docked permanently at Port Rashid and features an interactive museum on the QE2's history.
Guests staying in the smallest rooms will have just 17 square metres of floor space while those in the royal suites will enjoy 76 square metres including a private veranda, conservatory and dining room.
The maiden voyage took place in 1969 from Southampton to New York and since then it has crossed the Atlantic more than 800 times and carried more than 2.5 million passengers.
It was even used during the Falklands War as a means of transporting soldiers.
The ship took its maiden voyage in 1969.


Fight monsters, solve puzzles, help commoners, and find treasure! Join this adventure as Ben, the Dungeon Master, guides you on a magical journey in this classic fantasy role-playing game.
Please bring a pencil and notepad. Sign up for only one group. Group A will be doing the same journey as Group B.


Description: The hike begins at the base parking lot and gradually ascends to an elevation of 1594 feet (486 meters). The hiking trail is well marked and except for a few spots is a moderate climb. The trail is a frequent favorite for local hikers. On a daily basis hundreds of people make the climb to enjoy the 360 degree panoramic views of the county of San Diego. The mountain is a part of the protected area known as Mission Trails City Park. All of its native plant life and animal life are protected, including the local species of rattlesnake, which is rarely seen but does exist.
Activity: Hike to the summit and back. Option B: Enjoy a picnic at nearby Lake Murray.


Do you think you know everything about push advertising? Have you tried them all and didn't see the results? Our wonderful Clickadu team headed by Demian is ready to present you a new advertising format - push-up. Nothing to do with women's bra, just mobile native ad format that makes money! Go ahead and read it.
RichPush launched a new feature recently — SmartCPC. It buys clicks lower when possible, lowers average CPC and saves your budget to buy much more clicks. A couple of our advertisers shared their results using this feature at RichPush, so let's see how it worked out for them.
If you are looking for new sources for campaigns we strongly suggest you try DatsPush. To prove you they worth we have a case study that shows that results can be quite impressive. Check them out!
One of our best partners ClickDealer decided to step up the game and created their own SmartLink for dating traffic. Go ahead and be the first to use it!


text:
/**
 */
package org_eclipse_smarthome_schemas_thing_description_v1__0Simplified.util;

import org.eclipse.emf.common.notify.Adapter;
import org.eclipse.emf.common.notify.Notifier;

import org.eclipse.emf.common.notify.impl.AdapterFactoryImpl;

import org.eclipse.emf.ecore.EObject;

import org_eclipse_smarthome_schemas_thing_description_v1__0Simplified.*;

/**
 *
 * The Adapter Factory for the model.
 * It provides an adapter createXXX method for each class of the model.
 *
 * @see org_eclipse_smarthome_schemas_thing_description_v1__0Simplified.org_eclipse_smarthome_schemas_thing_description_v1__0SimplifiedPackage
 * @generated
 */
public class org_eclipse_smarthome_schemas_thing_description_v1__0SimplifiedAdapterFactory extends AdapterFactoryImpl {
	/**
	 * The cached model package.
	 *
	 *
	 * @generated
	 */
	protected static org_eclipse_smarthome_schemas_thing_description_v1__0SimplifiedPackage modelPackage;

	/**
	 * Creates an instance of the adapter factory.
	 *
	 *
	 * @generated
	 */
	public org_eclipse_smarthome_schemas_thing_description_v1__0SimplifiedAdapterFactory() {
		if (modelPackage == null) {
			modelPackage = org_eclipse_smarthome_schemas_thing_description_v1__0SimplifiedPackage.eINSTANCE;
		}
	}

	/**
	 * Returns whether this factory is applicable for the type of the object.
	 *
	 * This implementation returns true if the object is either the model's package or is an instance object of the model.
	 *
	 * @return whether this factory is applicable for the type of the object.
	 * @generated
	 */
	@Override
	public boolean isFactoryForType(Object object) {
		if (object == modelPackage) {
			return true;
		}
		if (object instanceof EObject) {
			return ((EObject)object).eClass().getEPackage() == modelPackage;
		}
		return false;
	}

	/**
	 * The switch that delegates to the createXXX methods.
	 *
	 *
	 * @generated
	 */
	protected org_eclipse_smarthome_schemas_thing_description_v1__0SimplifiedSwitch<Adapter> modelSwitch =
		new org_eclipse_smarthome_schemas_thing_description_v1__0SimplifiedSwitch<Adapter>() {
			@Override
			public Adapter caseBridgeType(BridgeType object) {
				return createBridgeTypeAdapter();
			}
			@Override
			public Adapter caseBridgeTypeRef(BridgeTypeRef object) {
				return createBridgeTypeRefAdapter();
			}
			@Override
			public Adapter caseChannel(Channel object) {
				return createChannelAdapter();
			}
			@Override
			public Adapter caseChannelGroup(ChannelGroup object) {
				return createChannelGroupAdapter();
			}
			@Override
			public Adapter caseChannelGroups(ChannelGroups object) {
				return createChannelGroupsAdapter();
			}
			@Override
			public Adapter caseChannelGroupType(ChannelGroupType object) {
				return createChannelGroupTypeAdapter();
			}
			@Override
			public Adapter caseChannels(Channels object) {
				return createChannelsAdapter();
			}
			@Override
			public Adapter caseChannelType(ChannelType object) {
				return createChannelTypeAdapter();
			}
			@Override
			public Adapter caseConfigDescription(ConfigDescription object) {
				return createConfigDescriptionAdapter();
			}
			@Override
			public Adapter caseConfigDescriptionRef(ConfigDescriptionRef object) {
				return createConfigDescriptionRefAdapter();
			}
			@Override
			public Adapter caseConfigDescriptionsType(ConfigDescriptionsType object) {
				return createConfigDescriptionsTypeAdapter();
			}
			@Override
			public Adapter caseCriteriaType(CriteriaType object) {
				return createCriteriaTypeAdapter();
			}
			@Override
			public Adapter caseEvent(Event object) {
				return createEventAdapter();
			}
			@Override
			public Adapter caseFilterType(FilterType object) {
				return createFilterTypeAdapter();
			}
			@Override
			public Adapter caseOption(Option object) {
				return createOptionAdapter();
			}
			@Override
			public Adapter caseOptions(Options object) {
				return createOptionsAdapter();
			}
			@Override
			public Adapter caseOptionsType(OptionsType object) {
				return createOptionsTypeAdapter();
			}
			@Override
			public Adapter caseOptionType(OptionType object) {
				return createOptionTypeAdapter();
			}
			@Override
			public Adapter caseParameter(Parameter object) {
				return createParameterAdapter();
			}
			@Override
			public Adapter caseParameterGroup(ParameterGroup object) {
				return createParameterGroupAdapter();
			}
			@Override
			public Adapter caseProperties(Properties object) {
				return createPropertiesAdapter();
			}
			@Override
			public Adapter caseProperty(Property object) {
				return createPropertyAdapter();
			}
			@Override
			public Adapter caseState(State object) {
				return createStateAdapter();
			}
			@Override
			public Adapter caseSupportedBridgeTypeRefs(SupportedBridgeTypeRefs object) {
				return createSupportedBridgeTypeRefsAdapter();
			}
			@Override
			public Adapter caseTags(Tags object) {
				return createTagsAdapter();
			}
			@Override
			public Adapter caseThingDescriptionsType(ThingDescriptionsType object) {
				return createThingDescriptionsTypeAdapter();
			}
			@Override
			public Adapter caseThingType(ThingType object) {
				return createThingTypeAdapter();
			}
			@Override
			public Adapter defaultCase(EObject object) {
				return createEObjectAdapter();
			}
		};

	/**
	 * Creates an adapter for the target.
	 *
	 *
	 * @param target the object to adapt.
	 * @return the adapter for the target.
	 * @generated
	 */
	@Override
	public Adapter createAdapter(Notifier target) {
		return modelSwitch.doSwitch((EObject)target);
	}

	/**
	 * Creates a new adapter for an object of class '{@link org_eclipse_smarthome_schemas_thing_description_v1__0Simplified.BridgeType Bridge Type}'.
	 *
	 * This default implementation returns null so that we can easily ignore cases;
	 * it's useful to ignore a case when inheritance will catch all the cases anyway.
	 *
	 * @return the new adapter.
	 * @see org_eclipse_smarthome_schemas_thing_description_v1__0Simplified.BridgeType
	 * @generated
	 */
	public Adapter createBridgeTypeAdapter() {
		return null;
	}

	/**
	 * Creates a new adapter for an object of class '{@link org_eclipse_smarthome_schemas_thing_description_v1__0Simplified.BridgeTypeRef Bridge Type Ref}'.
	 *
	 * This default implementation returns null so that we can easily ignore cases;
	 * it's useful to ignore a case when inheritance will catch all the cases anyway.
	 *
	 * @return the new adapter.
	 * @see org_eclipse_smarthome_schemas_thing_description_v1__0Simplified.BridgeTypeRef
	 * @generated
	 */
	public Adapter createBridgeTypeRefAdapter() {
		return null;
	}

	/**
	 * Creates a new adapter for an object of class '{@link org_eclipse_smarthome_schemas_thing_description_v1__0Simplified.Channel Channel}'.
	 *
	 * This default implementation returns null so that we can easily ignore cases;
	 * it's useful to ignore a case when inheritance will catch all the cases anyway.
	 *
	 * @return the new adapter.
	 * @see org_eclipse_smarthome_schemas_thing_description_v1__0Simplified.Channel
	 * @generated
	 */
	public Adapter createChannelAdapter() {
		return null;
	}

	/**
	 * Creates a new adapter for an object of class '{@link org_eclipse_smarthome_schemas_thing_description_v1__0Simplified.ChannelGroup Channel Group}'.
	 *
	 * This default implementation returns null so that we can easily ignore cases;
	 * it's useful to ignore a case when inheritance will catch all the cases anyway.
	 *
	 * @return the new adapter.
	 * @see org_eclipse_smarthome_schemas_thing_description_v1__0Simplified.ChannelGroup
	 * @generated
	 */
	public Adapter createChannelGroupAdapter() {
		return null;
	}

	/**
	 * Creates a new adapter for an object of class '{@link org_eclipse_smarthome_schemas_thing_description_v1__0Simplified.ChannelGroups Channel Groups}'.
	 *
	 * This default implementation returns null so that we can easily ignore cases;
	 * it's useful to ignore a case when inheritance will catch all the cases anyway.
	 *
	 * @return the new adapter.
	 * @see org_eclipse_smarthome_schemas_thing_description_v1__0Simplified.ChannelGroups
	 * @generated
	 */
	public Adapter createChannelGroupsAdapter() {
		return null;
	}

	/**
	 * Creates a new adapter for an object of class '{@link org_eclipse_smarthome_schemas_thing_description_v1__0Simplified.ChannelGroupType Channel Group Type}'.
	 *
	 * This default implementation returns null so that we can easily ignore cases;
	 * it's useful to ignore a case when inheritance will catch all the cases anyway.
	 *
	 * @return the new adapter.
	 * @see org_eclipse_smarthome_schemas_thing_description_v1__0Simplified.ChannelGroupType
	 * @generated
	 */
	public Adapter createChannelGroupTypeAdapter() {
		return null;
	}

	/**
	 * Creates a new adapter for an object of class '{@link org_eclipse_smarthome_schemas_thing_description_v1__0Simplified.Channels Channels}'.
	 *
	 * This default implementation returns null so that we can easily ignore cases;
	 * it's useful to ignore a case when inheritance will catch all the cases anyway.
	 *
	 * @return the new adapter.
	 * @see org_eclipse_smarthome_schemas_thing_description_v1__0Simplified.Channels
	 * @generated
	 */
	public Adapter createChannelsAdapter() {
		return null;
	}

	/**
	 * Creates a new adapter for an object of class '{@link org_eclipse_smarthome_schemas_thing_description_v1__0Simplified.ChannelType Channel Type}'.
	 *
	 * This default implementation returns null so that we can easily ignore cases;
	 * it's useful to ignore a case when inheritance will catch all the cases anyway.
	 *
	 * @return the new adapter.
	 * @see org_eclipse_smarthome_schemas_thing_description_v1__0Simplified.ChannelType
	 * @generated
	 */
	public Adapter createChannelTypeAdapter() {
		return null;
	}

	/**
	 * Creates a new adapter for an object of class '{@link org_eclipse_smarthome_schemas_thing_description_v1__0Simplified.ConfigDescription Config Description}'.
	 *
	 * This default implementation returns null so that we can easily ignore cases;
	 * it's useful to ignore a case when inheritance will catch all the cases anyway.
	 *
	 * @return the new adapter.
	 * @see org_eclipse_smarthome_schemas_thing_description_v1__0Simplified.ConfigDescription
	 * @generated
	 */
	public Adapter createConfigDescriptionAdapter() {
		return null;
	}

	/**
	 * Creates a new adapter for an object of class '{@link org_eclipse_smarthome_schemas_thing_description_v1__0Simplified.ConfigDescriptionRef Config Description Ref}'.
	 *
	 * This default implementation returns null so that we can easily ignore cases;
	 * it's useful to ignore a case when inheritance will catch all the cases anyway.
	 *
	 * @return the new adapter.
	 * @see org_eclipse_smarthome_schemas_thing_description_v1__0Simplified.ConfigDescriptionRef
	 * @generated
	 */
	public Adapter createConfigDescriptionRefAdapter() {
		return null;
	}

	/**
	 * Creates a new adapter for an object of class '{@link org_eclipse_smarthome_schemas_thing_description_v1__0Simplified.ConfigDescriptionsType Config Descriptions Type}'.
	 *
	 * This default implementation returns null so that we can easily ignore cases;
	 * it's useful to ignore a case when inheritance will catch all the cases anyway.
	 *
	 * @return the new adapter.
	 * @see org_eclipse_smarthome_schemas_thing_description_v1__0Simplified.ConfigDescriptionsType
	 * @generated
	 */
	public Adapter createConfigDescriptionsTypeAdapter() {
		return null;
	}

	/**
	 * Creates a new adapter for an object of class '{@link org_eclipse_smarthome_schemas_thing_description_v1__0Simplified.CriteriaType Criteria Type}'.
	 *
	 * This default implementation returns null so that we can easily ignore cases;
	 * it's useful to ignore a case when inheritance will catch all the cases anyway.
	 *
	 * @return the new adapter.
	 * @see org_eclipse_smarthome_schemas_thing_description_v1__0Simplified.CriteriaType
	 * @generated
	 */
	public Adapter createCriteriaTypeAdapter() {
		return null;
	}

	/**
	 * Creates a new adapter for an object of class '{@link org_eclipse_smarthome_schemas_thing_description_v1__0Simplified.Event Event}'.
	 *
	 * This default implementation returns null so that we can easily ignore cases;
	 * it's useful to ignore a case when inheritance will catch all the cases anyway.
	 *
	 * @return the new adapter.
	 * @see org_eclipse_smarthome_schemas_thing_description_v1__0Simplified.Event
	 * @generated
	 */
	public Adapter createEventAdapter() {
		return null;
	}

	/**
	 * Creates a new adapter for an object of class '{@link org_eclipse_smarthome_schemas_thing_description_v1__0Simplified.FilterType Filter Type}'.
	 *
	 * This default implementation returns null so that we can easily ignore cases;
	 * it's useful to ignore a case when inheritance will catch all the cases anyway.
	 *
	 * @return the new adapter.
	 * @see org_eclipse_smarthome_schemas_thing_description_v1__0Simplified.FilterType
	 * @generated
	 */
	public Adapter createFilterTypeAdapter() {
		return null;
	}

	/**
	 * Creates a new adapter for an object of class '{@link org_eclipse_smarthome_schemas_thing_description_v1__0Simplified.Option Option}'.
	 *
	 * This default implementation returns null so that we can easily ignore cases;
	 * it's useful to ignore a case when inheritance will catch all the cases anyway.
	 *
	 * @return the new adapter.
	 * @see org_eclipse_smarthome_schemas_thing_description_v1__0Simplified.Option
	 * @generated
	 */
	public Adapter createOptionAdapter() {
		return null;
	}

	/**
	 * Creates a new adapter for an object of class '{@link org_eclipse_smarthome_schemas_thing_description_v1__0Simplified.Options Options}'.
	 *
	 * This default implementation returns null so that we can easily ignore cases;
	 * it's useful to ignore a case when inheritance will catch all the cases anyway.
	 *
	 * @return the new adapter.
	 * @see org_eclipse_smarthome_schemas_thing_description_v1__0Simplified.Options
	 * @generated
	 */
	public Adapter createOptionsAdapter() {
		return null;
	}

	/**
	 * Creates a new adapter for an object of class '{@link org_eclipse_smarthome_schemas_thing_description_v1__0Simplified.OptionsType Options Type}'.
	 *
	 * This default implementation returns null so that we can easily ignore cases;
	 * it's useful to ignore a case when inheritance will catch all the cases anyway.
	 *
	 * @return the new adapter.
	 * @see org_eclipse_smarthome_schemas_thing_description_v1__0Simplified.OptionsType
	 * @generated
	 */
	public Adapter createOptionsTypeAdapter() {
		return null;
	}

	/**
	 * Creates a new adapter for an object of class '{@link org_eclipse_smarthome_schemas_thing_description_v1__0Simplified.OptionType Option Type}'.
	 *
	 * This default implementation returns null so that we can easily ignore cases;
	 * it's useful to ignore a case when inheritance will catch all the cases anyway.
	 *
	 * @return the new adapter.
	 * @see org_eclipse_smarthome_schemas_thing_description_v1__0Simplified.OptionType
	 * @generated
	 */
	public Adapter createOptionTypeAdapter() {
		return null;
	}

	/**
	 * Creates a new adapter for an object of class '{@link org_eclipse_smarthome_schemas_thing_description_v1__0Simplified.Parameter Parameter}'.
	 *
	 * This default implementation returns null so that we can easily ignore cases;
	 * it's useful to ignore a case when inheritance will catch all the cases anyway.
	 *
	 * @return the new adapter.
	 * @see org_eclipse_smarthome_schemas_thing_description_v1__0Simplified.Parameter
	 * @generated
	 */
	public Adapter createParameterAdapter() {
		return null;
	}

	/**
	 * Creates a new adapter for an object of class '{@link org_eclipse_smarthome_schemas_thing_description_v1__0Simplified.ParameterGroup Parameter Group}'.
	 *
	 * This default implementation returns null so that we can easily ignore cases;
	 * it's useful to ignore a case when inheritance will catch all the cases anyway.
	 *
	 * @return the new adapter.
	 * @see org_eclipse_smarthome_schemas_thing_description_v1__0Simplified.ParameterGroup
	 * @generated
	 */
	public Adapter createParameterGroupAdapter() {
		return null;
	}

	/**
	 * Creates a new adapter for an object of class '{@link org_eclipse_smarthome_schemas_thing_description_v1__0Simplified.Properties Properties}'.
	 *
	 * This default implementation returns null so that we can easily ignore cases;
	 * it's useful to ignore a case when inheritance will catch all the cases anyway.
	 *
	 * @return the new adapter.
	 * @see org_eclipse_smarthome_schemas_thing_description_v1__0Simplified.Properties
	 * @generated
	 */
	public Adapter createPropertiesAdapter() {
		return null;
	}

	/**
	 * Creates a new adapter for an object of class '{@link org_eclipse_smarthome_schemas_thing_description_v1__0Simplified.Property Property}'.
	 *
	 * This default implementation returns null so that we can easily ignore cases;
	 * it's useful to ignore a case when inheritance will catch all the cases anyway.
	 *
	 * @return the new adapter.
	 * @see org_eclipse_smarthome_schemas_thing_description_v1__0Simplified.Property
	 * @generated
	 */
	public Adapter createPropertyAdapter() {
		return null;
	}

	/**
	 * Creates a new adapter for an object of class '{@link org_eclipse_smarthome_schemas_thing_description_v1__0Simplified.State State}'.
	 *
	 * This default implementation returns null so that we can easily ignore cases;
	 * it's useful to ignore a case when inheritance will catch all the cases anyway.
	 *
	 * @return the new adapter.
	 * @see org_eclipse_smarthome_schemas_thing_description_v1__0Simplified.State
	 * @generated
	 */
	public Adapter createStateAdapter() {
		return null;
	}

	/**
	 * Creates a new adapter for an object of class '{@link org_eclipse_smarthome_schemas_thing_description_v1__0Simplified.SupportedBridgeTypeRefs Supported Bridge Type Refs}'.
	 *
	 * This default implementation returns null so that we can easily ignore cases;
	 * it's useful to ignore a case when inheritance will catch all the cases anyway.
	 *
	 * @return the new adapter.
	 * @see org_eclipse_smarthome_schemas_thing_description_v1__0Simplified.SupportedBridgeTypeRefs
	 * @generated
	 */
	public Adapter createSupportedBridgeTypeRefsAdapter() {
		return null;
	}

	/**
	 * Creates a new adapter for an object of class '{@link org_eclipse_smarthome_schemas_thing_description_v1__0Simplified.Tags Tags}'.
	 *
	 * This default implementation returns null so that we can easily ignore cases;
	 * it's useful to ignore a case when inheritance will catch all the cases anyway.
	 *
	 * @return the new adapter.
	 * @see org_eclipse_smarthome_schemas_thing_description_v1__0Simplified.Tags
	 * @generated
	 */
	public Adapter createTagsAdapter() {
		return null;
	}

	/**
	 * Creates a new adapter for an object of class '{@link org_eclipse_smarthome_schemas_thing_description_v1__0Simplified.ThingDescriptionsType Thing Descriptions Type}'.
	 *
	 * This default implementation returns null so that we can easily ignore cases;
	 * it's useful to ignore a case when inheritance will catch all the cases anyway.
	 *
	 * @return the new adapter.
	 * @see org_eclipse_smarthome_schemas_thing_description_v1__0Simplified.ThingDescriptionsType
	 * @generated
	 */
	public Adapter createThingDescriptionsTypeAdapter() {
		return null;
	}

	/**
	 * Creates a new adapter for an object of class '{@link org_eclipse_smarthome_schemas_thing_description_v1__0Simplified.ThingType Thing Type}'.
	 *
	 * This default implementation returns null so that we can easily ignore cases;
	 * it's useful to ignore a case when inheritance will catch all the cases anyway.
	 *
	 * @return the new adapter.
	 * @see org_eclipse_smarthome_schemas_thing_description_v1__0Simplified.ThingType
	 * @generated
	 */
	public Adapter createThingTypeAdapter() {
		return null;
	}

	/**
	 * Creates a new adapter for the default case.
	 *
	 * This default implementation returns null.
	 *
	 * @return the new adapter.
	 * @generated
	 */
	public Adapter createEObjectAdapter() {
		return null;
	}

} //org_eclipse_smarthome_schemas_thing_description_v1__0SimplifiedAdapterFactory

redpajama_set_name: RedPajamaGithub


This chain is 1.25" Wide, with 49 links, and 1 blue link. If you have a 246 and the chain has 3 blue links, use part HV072.
Replace if chain is stretched or has kinks. A new chain will run quieter then one damaged or stretched.


thepete.com: The blonde woman behind me clearly needs to take the #RadioCityMusicHall #NewYorkSpringSpectacular more seriously!! I'm ready to transmute into my #Rockettes-fan configuration!!
The blonde woman behind me clearly needs to take the #RadioCityMusicHall #NewYorkSpringSpectacular more seriously!! I'm ready to transmute into my #Rockettes-fan configuration!!


If you've ever wanted to sit around the kitchen table with Blanche, Dorothy, Sophia and Rose, here's your chance. Funko has released a limited edition "Golden Girls" cereal. It's available for a limited time at Target.
The cereal comes with a collectible "Golden Girls" toy.
On social media, some are questioning why the cereal is blue, instead of the an obvious golden color and why it doesn't taste like cheesecake. Maybe the blue color is a reference to "blue hairs," a slang for elderly women?
Fans are also expressing frustration that the cereal can be hard to find. So if you find it, be sure to tell us in the comments so we can get some, too. Thank you for being a friend.


Harry Styles wouldn't be too shocked if Taylor Swift's next hit was about their breakup.
The One Direction star revealed that he fully expects Swift to use their relationship, which lasted from late 2012 to Janurary 2013, as material for a new song.
"It would be hypocritical for me to say she couldn't do it because everybody writes songs based on personal experience," the 19-year-old singer said. "I can't say I'd have dated someone less famous to avoid it."
But the British heartthrob didn't want to be permanently put on her bad side, so he added, "at least she's a great songwriter!"
The "22" singer recently told Rolling Stone that "the floodgates just opened the last couple weeks" while writing lyrics to her next album. Hopefully Styles would react to the 23-year-old entertainer's new songs a bit more maturely than John Mayer.


text:
Polydesmus zonkovi är en mångfotingart som beskrevs av Karl Wilhelm Verhoeff 1937. Polydesmus zonkovi ingår i släktet Polydesmus och familjen plattdubbelfotingar. Inga underarter finns listade i Catalogue of Life.

Källor

Plattdubbelfotingar
zonkovi


text:
Q: How to load more than 1 module asynchronously in web pack 2? I am trying to split code and async load modules on demand in webpack2. I am able to load one module using
require.ensure([], function(require) {
            var obj1 = require("./module1");
})
However, I am unable to load 2 modules say in this case module1 and module2. I could create module12 comprising module1 and module2, but would be great to know if there is a way to load more than 1 module through web pack.

A: Why can you not just do this?—
require.ensure([], function(require) {
  var obj1 = require("./module1");
  var obj2 = require("./module2");
})

redpajama_set_name: RedPajamaStackExchange


Dhanush as an actor is recognised all over India. Now his films are also watched and rewatched in the most native way possible. Yes, Aadukalam's Telugu version is releasing today in Andhra / Telangana titled as 'Pandem Kollu'.
Recently, his latest film VIP was also released in its Telugu dubbed version as Raghuvaran B. Tech on Jan 1, 2015. This film was well-received amidst the Telugu audience and became a hit.
This multifaceted actor is looked upon for his acting abilities across states. He has two most-awaited films coming up in Feb. Shamitabh, also starring Amitabh Bachchan and Akshara Haasan, directed by Balki is set to release on Feb 6th. Another film in his line is Anegan co-starring Karthik, Amyra Dastur and Aishwarya Devan, directed by KV Anand and set to hit the screens on Feb 13th.
It is indeed going to be back to back treats for all Dhanush fans spread across the country.
People looking for online information on Aadukalam Telugu version, Anegan, Dhanush, Pandem Kollu, Shamitabh will find this news story useful.


The research study is concentrated an audit as an aids to accountability in public service. The project research commences with an introduction and over view of the history of audit in Nigeria. Sequel to this effect, data were collected from primary and secondary sources, primary sources involves the design and distribution of questionnaires to 106 respondents of the ministry of finance and economic departments and Enugu State Audit. The secondary source extensively reviewed the opinion of some scholars who had earlier drawn written conclusions that are related to the project topic. Data collected were analysed and tested using percentage and formulated hypotheses.
The main findings were based on the analysis and subsequent test, which showed that auditing is a strong tool for accountability in the public service. Poor and irregular payment of staff salaries and remuneration has caused diversion of public fund to private purposes. Moreover, management skill has not improved operational standard in the state service.
Based on the findings, the researcher made possible recommendations to correct the negative conception of an audit and to appraise audit standard in the state public service.
This project research is therefore, beneficial to both the students, lecturers, politician, public and private sectors.
2.7 Statutory positions, powers and functions of an auditing general of the state.
The question on how to increase efficiency and positive result in audit work in public sector is a perennial problem in Nigeria, and one that is increasing warning the generality of the people of this country. The response has been to upgrade the quality of audit staff ad powers conferred on audit institutions in the public sector. There is also the for training of audit staff in modern techniques of auditing to enhance effectiveness and result oriented rather than restricting them to the traditional methods of trick and turnover which is inadequate and outdated.
Public sector auditing is conferred towards ensuring the proper and efficient use of public funds, development of sound financial management, the orderly executive administrative activities and the communication of information to the public through the publication of objective reports. These are necessary for the stability and development of the nation. There is a need to map out the machineries and method of carrying out a research functions effectively as to achieve a desired result.
In the past, the emphasis of an audit was on the traditional approach which ha been mainly the compliance audit to ensure that all books and records comply with the laid down procedures and regulation. But in the modern time, there is the need for a shift of emphasis to modern concept of effectiveness and efficiency.
Based on these individual views of auditing and its functions, the researcher took a keen inherent to rest empirically auditing as an aid to accountability with a particular reference to Enugu State Ministry of Finance and economic development.
The increase incidence of fraud and misappropriation of public fund and property by the accounting officers and chief executives in the public sector/ service passes a question as to whether auditing plays any role towards ensuring proper accountability in the public service especially the state government and particularly the ministry of finance and economic development.
Auditing is to control, deter and find out any fraud or misappropriation of public fund or property by officers entrusted with such duties.
It is because of this onerous task that the Enugu state audit department was established to appraise the work of those entrusted with responsibility of accountability.
Commission, authorities, agencies, including all persons and bodies established by a law of the House of Assembly of the state.
Inspite of all these provisions and safeguards, there is always an increased rate of fraud and misappropriation of public funds and parties by those entrusted with their safeguards. In view of the foregoing, this study is aimed at appraising the functions of the Enugu state audit department, problem affecting its efficiencies performance, and suggested solutions to enhance its effectiveness.
The researcher aims to examine the major cause of fraud or misappropriation of public funds in the state public service and offer useful suggestions to arrest the ugly situation. This study will also be of immense important for it will appraise the performance of the Enugu state audit department and assess the extent it has been able to achieve its objectives. The researcher will in addition offer valuable solutions on how to achieve accountability in the state public service.
The origin of audit department is as old as Nigeria. The present Enugu state audit department had its root from the colonial administrations. During colonial administration, there was one audit in the federation known as the colonial audit. The colonial masters have their representatives in Nigeria. These representatives were responsible and report to the Queen of England. The country was divided into four Regions as follows: Northern Region, Southern Region, Eastern Region and Western Region. Each of the regions had its own audit department but reports under the control of the colonial administration. This gives rise to regional audits.
Section 61 (1) of the Eastern Nigeria 1958, constitution states, and "There shall be a director of audit for the region whose office shall be an office in the public services of the region. In 1976 there was a further creation of states in the country and it was then that Anambra state and Imo states was created from the former Eastern central state. In 1992, the old Anambra state was further divided into Anambra state and the present Enugu state. Following this, each state now has her own audit department with a director of Audit or Auditor general of the state. The state was empowered by section 25 (2) of the 1999 constitution of the Federal Republic of Nigeria and section 4 (2) of chapter 13 of the audit law to have its audit department. The internal audit department in the ministry of Finance and economic development is being leaded by the state auditor-general.