text:
\section{Introduction}

In \cites{crass,mst, mst2}, G. Tomassini and the authors initiated the study of the geometry of weakly complete spaces; the question had been raised by G. Tomassini and the second author in \cite{ST}, where they also defined the minimal kernel of a weakly complete space, an essential tool in the investigations presented in \cites{mst, mst2}.

In that first attempt, complex surfaces which admit a real-analytic plurisubharmonic exhaustion function were considered; in \cite{M}, the first author considered, inside such surfaces, open domains with an exhaustion which could be, \emph{a priori}, only smooth and proved that they actually admit a real-analytic exhaustion.

This paper aims to study the case of an open domain, inside a complex surface with a global real-analytic exhaustion, which admits only a continuous plurisubharmonic exhaustion function, thus generalizing the results of \cite{M} to the continuous case.

We obtain the following result.
\begin{teorema}\label{teo_main}Let $X$ be a complex surface which admits a real-analytic plurisubharmonic exhaustion function and consider a domain $D\subseteq X$ which admits a continuous plurisubharmonic exhaustion function. Then, one of the following holds true:
\begin{enumerate}
\item $D$ is a modification of a Stein space of dimension $2$
\item $X$ and $D$ are proper over open Riemann surfaces
\item $X$ and $D$ are of Grauert type.
\end{enumerate}\end{teorema}

Such an exploration is also useful as a small step towards the general problem of understanding the geometry of a weakly complete surface, with no assumptions on the regularity of the exhaustion.

\medskip

Our work is organized as follows.

In Section 2 we gather some preliminary results which are essentially well known in the smooth case and whose extension to the continuous case relies, for the most part, on the approximation results of Richberg (see \cite{rich}); Section 3 studies the connections between compact sets with the local maximum property and the (complex) analytic structure of the minimal kernel.
Finally, Section 4 contains the proof of our main result, together with some easy, but interesting, consequences.

\section{Preliminary results}

Let $M$ be a complex manifold.

An upper semicontinuous function $\phi:M\to\R$ is called \emph{strongly} plurisubharmonic at $p\in M$ if it is plurisubharmonic at $p\in M$ and stays so under small $\Ci^2$ perturbations; if this happens at every point $p\in U$ for some open set $U$, we call $\phi$ a strongly plurisubharmonic function on $U$.

Suppose $M$ is endowed with a continuous plurisubharmonic exhaustion function, i.e. $M$ is weakly complete; for every such function $\phi:M\to\R$, let $Z_\phi$ be the set of points $p\in M$ at which $\phi$ is \emph{not} strongly plurisubharmonic. We define the \emph{continuous minimal kernel} of $M$ as
$$\Sigma_M=\bigcap_{\phi}Z_\phi$$
where the intersection is taken over all the continuous plurisubharmonic exhaustion functions $\phi:M\to\R$. This is the same construction described in \cite{ST} for $\Ci^k$ functions, $k\geq 2$; we do not emphasize the use of continuous functions in the symbol $\Sigma_M$, as opposed to $\Ci^2$ o $\Ci^\infty$ or real-analytic functions, because in the present paper we only deal with the continuous case and, for the same reason, we will refer to it simply as the minimal kernel.

A continuous plurisubharmonic exhaustion function $\phi:M\to\R$ is called \emph{minimal} (for $\Sigma_M$) if $Z_\phi=\Sigma_M$; it can be showed that, if $M$ is weakly complete, a continuous minimal function always exists.

\medskip

Now, we present the generalization to the continuous case of the following well-known result: if a manifold admits a smooth exhaustion function which is strongly plurisubharmonic outside of a compact set, then it is a modification of a Stein space of the same dimension.

The proof is essentially a suitable application of Richberg approximation theorem (see \cite{rich}); the result itself is surely known, but we were not able to find an appropriate reference.

\begin{lemma}\label{lmm_richberg}Let $M$ be a complex manifold and $\phi:M\to\R$ a continuous plurisubharmonic exhaustion function. Assume that $\phi(\Sigma_M)$ does not contain any half-line $(a,+\infty)$, with $a\in\R$. Then $M$ is a modification of a Stein space.
\end{lemma}
\begin{proof}Let $\psi$ be a (continuous) minimal function on $M$.

Since $\phi(\Sigma_M)$ does not contain any half-line, there is an increasing sequence $\{c_n\}_{n\in\N}$ of real numbers such that $c_n\to+\infty$  and $\phi(\Sigma_M)\not\ni c_n$ for every $n\in\N$. Set $c_{-1}=-\infty$ and
$$F_n=\Sigma_M\cap\{c_{n-1}<\phi<c_n\}\;.$$
The sets $F_n$ are compact and pairwise disjoint and their union is $\Sigma_M$; we define
$$c'_n=\min_{F_n}\phi\qquad c''_n=\max_{F_n}\phi\;.$$
We have $c'_n<c_n<c''_{n+1}$, so
$$c'_0\leq c''_0<c'_1\leq c''_1<\ldots\leq c''_{n-1}<c'_n\leq c''_{n}<c'_{n+1}\leq \ldots$$
and $\phi(F_n)\subseteq [c'_n, c''_n]$.

Consider $U_n=\{c''_{n}<\phi<c'_{n+1}\}$, for a fixed $n$, and the function $\phi_t=\phi+t\psi$, where $t>0$ is chosen such that
$$t\max_{\overline{U}_n}|\psi|<\frac{c'_{n+1}-c''_{n}}{8}=\delta\;.$$
The function $\phi_t$ is strongly plurisubharmonic on $U_n$, because $\psi$ is minimal and $\Sigma_M$ does not intersect $U_n$; moreover, if $c''_n+2\delta<c<c'_{n+1}-2\delta$, then
$$\{\phi_t=c\}\subset \{|c-\phi|=t|\psi|\}\subseteq\{|c-\phi|<\delta\}\subseteq\{c-\delta<\phi<c+\delta\}\subset U_n$$
which implies that the level set $\{\phi_t=c\}$ is compact in $U_n$.

Set $V_n=\{c''_n+2\delta<\phi_t<c'_{n+1}-2\delta\}$ and apply Richberg's approximation result \cite{rich}*{Satz 4.3} to $\phi_t\vert_{V_n}$, which is strongly plurisubharmonic, in order to obtain a $\Ci^\infty$ function $\psi_n:V_n\to\R$ such that $\psi_n$ is strictly plurisubharmonic on $V_n$ and
\begin{equation}\label{eq_stimarich}
0\leq \psi_n(x)-\phi_t(x)\leq \frac{1}{2}\min\{\phi_t(x)-c''_n-2\delta, c'_{n+1}-2\delta-\phi_t(x)\}\;.\end{equation}

By Sard's theorem, there is $d_n\in (c''_{n}+2\delta, c'_{n+1}-2\delta)$ such that the level $\{\psi_n=d_n\}$ is regular; by \eqref{eq_stimarich}, such a level is compact. Therefore, the domain
$$\Omega_n=\{x\in M\ :\ \phi_t(x)<c''_n+2\delta\}\cup\{x\in V_n\ :\ \psi_n(x)<d_n\}$$
is relatively compact in $M$ and, for $0<\eta<d_n-c''_n-2\delta$, the function
$$\rho_n(x)=\left\{\begin{array}{ll}\phi_t(x)&x\in M\setminus (\Omega_n\cup V_n)\\\max\{c''_n+2\delta+\eta, \psi_n(x)\}&x\in V_n\\c''_n+2\delta+\eta&x\in\Omega_n\setminus V_n\end{array}\right.$$
is continuous and plurisubharmonic on $M$,smooth and strictly plurisubharmonic on a neighborhood of $b\Omega_n$. By \cite{grau1}*{Theorem 1}, $\Omega_n$ is holomorphically convex and, given the existence of $\rho$, a modification of a Stein space.

We note that $\Omega_n$ is strictly contained in $\{\phi<c'_{n+1}\}$ and $\Omega_{n+1}$ contains $\{\phi<c''_{n+1}\}$, so, as $c''_{n+1}\geq c'_{n+1}$, we have that $\Omega_n\Subset\Omega_{n+1}$.

Therefore $\Omega_1\Subset\Omega_2\Subset\ldots\Subset\Omega_n\Subset\ldots$ is an increasing family of relatively compact domains which are all modifications of Stein spaces and all have smooth stricly pseudoconvex boundary.

Let us show that $\Omega_j$ is Runge in $\Omega_{j+1}$, for every $j$; to such aim, we will use some well known facts about Remmert reduction, which we collected in \cite{Fuffa}, as we were not able to find a concise reference.

Let $\pi_j:\Omega_j\to Y_j$ be the Remmert reduction of $X_j$; let $R$ be the relation on $\Omega_j$ such that $x_1Rx_2$ if and only if there exists a compact connected complex subvariety of $\Omega_j$ which contains both $x_1$ and $x_2$, then $Y_j=X_j/R$. Therefore, $\pi_j^{-1}(y)$ is a compact complex subvariety of $\Omega_j$  for every $y\in Y_j$, so, $\rho_{j-1}$ is constant on $\pi^{-1}_j(y)$ for all $y\in Y_j$. This grants us the existence of a continuous function $\psi_j:Y_j\to \R$ such that $\psi_j\circ \pi=\rho_{j-1}$.

Set
$$S_j=\{y\in Y_j\ :\ \dim\pi^{-1}_j(y)>0\}\;,$$
then $\pi_j$ is a biholomorphism from $X_j\setminus \pi_j^{-1}(S_j)$ to $Y_j\setminus S_j$, therefore $\psi_j$ is plurisubharmonic on $Y_j\setminus S_j$ and, being continuous, is bounded around every point of $S_j$. By \cite{GraRem}*{Satz 3}, $\psi_j\vert_{Y_j\setminus S_j}$ extends uniquely to a plurisubharmonic function $\tilde{\psi}_j:Y_j\to\R$; let $y\in S_j$ and let $S_y=\pi_j^{-1}(y)$. We know that $\rho_{j-1}$ and $\tilde{\psi}_j\circ\pi_j$ are both constant on $S_y$; let $j:\Delta\to M$ be a complex disc intersecting $S_y$ at a single regular point $p\in S_y$, such that $j(0)=p$. The functions $\rho_{j-1}\circ j$ and $\tilde{\psi}_j\circ\pi_j\circ j$ are both subharmonic on $\Delta$ and coincide in $\Delta\setminus\{0\}$, but then
$$\tilde{\psi}_j\circ\pi_j\circ j(0)=\limsup_{\zeta\to 0} \tilde{\psi}_j\circ\pi_j\circ j(\zeta)=\limsup_{\zeta\to 0}\rho_{j-1}\circ j(\zeta)=\rho_{j-1}\circ j(0)\;.$$
So $\rho_{j-1}(p)=\tilde{\psi}_j\circ\pi_{j}(p)$, therefore $\tilde{\psi}_j(y)=\psi_j(y)$, thus proving that $\psi_j$ is (continous and) plurisubharmonic on $Y_j$.

In conclusion, by \cite{Nar}*{Corollary 1, Section 4}, the set
$$\{y\in Y_j\ :\ \psi_j(y)<d_{j-1}\}$$
is Runge in $Y_j$. By \cite{KK}*{Lemma 63.4}, this implies that $X_{j-1}$ is Runge in $X_j$.

\medskip

Finally, as $M$ is an increasing union of holomorphically convex domains, each one Runge in the next one, we conclude that $M$ is itself holomorphically convex. Let $\pi:M\to Y$ be the Remmert reduction of $M$; as $\psi$ is strongly plurisubharmonic on $M\setminus\Sigma_M$, we conclude that $\pi:M\setminus\Sigma M\to \pi(M\setminus\Sigma_M)$ is biholomorphism, therefore $Y$ and $M$ have the same dimension and $Y$ is an irreducible (because $M$ is a manifold) Stein space, so $M$ is a modification of a Stein space.

It is now easy to show that
$$S=\{y\in Y\ :\ \dim \pi^{-1}(y)>0\}$$
is a discrete set in $Y$, which implies that $M$ is the modification of $Y$ along a collection of at most countably many points.\end{proof}

As an obvious consequence, we have the following.

\begin{corol}Let $M$ be a complex manifold, with $\phi:M\to\R$ a continuous plurisubharmonic exhaustion, which is strongly plurisubharmonic outside a compact set. Then $M$ is a modification of a Stein space.\end{corol}

\begin{rem}
In the situation of Lemma \ref{lmm_richberg}, the Remmert reduction of $M$ has the same dimension of $M$, i.e. there exists a proper holomorphic function $f:M\to N$, where $N$ is a Stein space of the same dimension of $M$; moreover there exists a locally finite collection $\{E_j\}_{j\in \N}$ of compact complex subspaces of $N$, pairwise disjoint, such that, setting $E=\bigcup_j E_j$, the restriction of $f$ to $M\setminus E$ is a biholomorphism and $f(E)$ is a discrete set of points in $N$. It is easy to show that $\Sigma_M=E$.
\end{rem}

As a general principle, if we have an exhaustion which is strongly plurisubharmonic outside a compact set which is, in some sense, ``special'' for plurisubharmonic functions, then such a compact set has to belong to the minimal kernel; we see an easy instance of this idea in the following statement.

\begin{corol}\label{cor_modstein}Assume $M$ admits a continuous plurisubharmonic exhaustion function which is strictly plurisubhamonic outside $\bigcup_n C_n$, where $\{C_n\}$ is a sequence of compact complex curves. Then $\Sigma_M=\bigcup_n C_n$ and $M$ is a modification of a Stein space.\end{corol}
\begin{proof}By definition, $\Sigma_M\subseteq \bigcup_n C_n$. Moreover, given a minimal function $\alpha:M\to\R$, we see that $\alpha\vert_{C_n}\equiv c_n\in\R$, so $\Sigma_M=\bigcup_n C_n$; therefore, $\alpha(\Sigma_M)$ is a countable set in $\R$ and the previous lemma applies.\end{proof}

\section{Minimal kernel and local maximum sets}

The general principle stated before Corollary \ref{cor_modstein} applies also to compact sets with the local maximum property, as it is shown in the next lemma.
The rest of this section studies the interplay between local maximum sets and the analytic structure of the minimal kernel that was studied in \cite{mst}.

\begin{lemma}\label{lmm_complete}Let $K$ be a compact set in $M$ with the local maximum property and suppose there exists $\phi:M\to\R$ continuous plurisubharmonic exhaustion which is strongly plurisubharmonic on $X\setminus K$. Then $K$ is contained in the union of finitely many compact complex subspaces of $M$.\end{lemma}
\begin{proof}Obviously, $\Sigma_M\subseteq K$. By Lemma \ref{lmm_richberg} and the Remark following it, we have a proper holomorphic surjection $f:M\to N$, where $N$ is a Stein space and $f(\Sigma_M)$ is a discrete set; however, as $\Sigma_M$ is compact in this case, $f(\Sigma_M)$ will be a finite number of points. Therefore, $\Sing N$ consists of finitely many points and we can embedd properly $N$ into some $\C^n$ by some holomorphic map $j:N\to \C^n$. The set $S=j(f(\Sigma_M))$ is obviously complete pluripolar in $\C^n$, so we have a plurisubharmonic function $u:\C^n\to\R\cup\{-\infty\}$ such that $u^{-1}(-\infty)=S$; by considering $\rho=u\circ j\circ f$, we show that $\Sigma_M$ is complete pluripolar in $M$. We can suppose that $\rho$ is smooth and strongly plurisubharmonic outside $\Sigma_M$.

Now, suppose that $K\not\subseteq \Sigma_M$ and let $m=\max_{K}\rho$; then $m>-\infty$. Take $z_0\in K$ such that $m=\rho(z_0)$ and consider a small ball $B$ around $z_0$ such that $B\cap\Sigma_M=\emptyset$ and a function $\chi\in\Ci^\infty_0(B)$ such that
$$\chi\geq 0,\quad \chi(z_0)=1,\quad \chi(x)<1\textrm{ if }x\in B\setminus\{z_0\}\;.$$
For sufficiently small $\epsilon>0$, the function $\rho_\epsilon=\rho+\epsilon\chi$ is plurisubharmonic in $B$ and its restriction to $B\cap K$ has a strict maximum in $z_0\in K$, which contradicts the characterization of local maximum sets given in \cite{Sl2}*{Prop. 2.3(iv)}. As this is impossible, we conclude that $K=\Sigma_M$.\end{proof}

In \cite{mst}, we describe the structure of the minimal kernel of a complex surface which admits a real-analytic plurisubharmonic exhaustion; we find two types of compact sets with some analytic structure: compact complex curves and compact Levi-flat hypersurfaces with dense complex leaves. Both are ``minimal'' among compact sets with local maximum property, in a sense which we make more precise in what follows.

The next proposition is obvious.

\begin{propos}\label{prp_ovvia}Let $C$ be a complex compact irreducible curve in a complex manifold $M$. Then $C$ does not contain any proper compact local maximum set.\end{propos}

More generally, the presence of a Levi foliation prescribes the behaviour of local maximum sets.

\begin{lemma}Let $M$ be a complex manifold of (complex) dimension $2$ and $S\subset M$ a compact regular real-analytic Levi-flat hypersurface (i.e. of real dimension $3$). Let $K$ be a compact local maximum set in $S$, then $K$ is a union of leaves of the Levi foliation.\end{lemma}
\begin{proof}We start by proving a local version.
\begin{center}\parbox{0.9\textwidth}{\it Let $L$ be a leaf of the Levi foliation. Then for every $p\in L$ there exists a neighborhood $B_p$ such that  every connected component of $L\cap B_p$ is either contained in $K$ or disjoint from $K$.}
\end{center}
Since $S$ is regular and real analytic, there are holomorphic coordinates $(z,w)$ in some neighborhood $V$ of $p$ such that $p$ has coordinates $(0,0)$; we define $B_p=\{(z,w)\ :\ |z|^2+|w|^2< 1\}$, then $S\cap B_p\subseteq \{\Im w=0\}$. The foliation of $S$ in $\{\Im w=0\}\cap\{|z|^2+|w|^2< 1\}$ are the discs $\{\Re w=\mathrm{const}\}\cap\{\Im w=0\}\cap\{|z|^2+|w|^2< 1\}$.

If the local version is false in $B_p$, then $K$ intersects the disc
$$\{\Re w=t_0\}\cap\{\Im w=0\}\cap\{|z|^2+|w|^2<1\}$$
but does not contain it. The set $K_0=K\cap B_p\cap\{\Re w=t_0, \Im w=0\}$ is  a proper relatively closed subset of a complex disc, so it must have a peak point in the disc. That is, there are a complex number $z_0$ and a polynomial $f(z)$ such that  $f(z_0)=1$ and $|f(z)|<1$ if $(z,t_0)\in K_0$ and $z\neq z_0$.Let now
$$\psi(z,w)=|f(z)|-\Re[(w-t_0)^2]\;.$$
Then $\psi$ is a plurisubharmonic function on $B_p$ such that $\psi<1$ on $K_0\setminus\{(z_0,t_0)\}$ and $\psi(z_0,t_0)=1$; this contradicts the local maximum property of $K$, thus proving the local version.

\medskip

Let us now turn our attention to the original statement. Let $L$ be a leaf which intersects $K$; we will denote by $L_{\mathrm{st}}$ the leaf $L$ with the topology induced by the inclusion in $S$ and by $L_{\mathrm{cov}}$ the leaf $L$ with the topology whose open sets are the connected components of the intersection of $L$ with any open set of $S$.

The identity map $id_L:L_{\mathrm{cov}}\to L_{\mathrm{st}}$ is continuous, so $K\cap L$ is a relatively closed subset of both; the local version implies that $K\cap L$ is relatively open in $L_{\mathrm{cov}}$; as $L$ is connected with respect to both topologies, $K\cap L=L$, i.e. $L\subseteq K$.
\end{proof}

As a consequence, we finally obtain the analogue of Proposition \ref{prp_ovvia} for compact Levi-flat hypersurfaces with dense leaves.

\begin{corol}\label{cor_denso}If $M$ is a Grauert type surface and $\chi$ is the pluriharmonic function given by \cite{mst}*{Main Theorem}, then $S=\chi^{-1}(d)$, where $d$ is a regular value, does not contain any proper compact local maximum set.\end{corol}
\begin{proof} By the previous lemma, a local maximum set in $S$ would contain a leaf of the Levi foliation, but every leaf is dense in $S$ (see \cite{mst}*{Corollary 3.8}), so every local maximum set contained in $S$ coincides with $S$.\end{proof}

\section{Subdomains of a weakly complete space}

We now prove Theorem \ref{teo_main}.

\medskip

Let $X$ be a complex surface which admits a real-analytic plurisubharmonic exhaustion function and $D\subseteq X$ a domain which admits a $\Ci^0$ plurisubharmonic exhaustion function.

According to \cite{mst}*{Main Theorem}, there are three possibilities:
\begin{enumerate}
\item $X$ is a modification of a Stein space
\item $X$ is proper over an open Riemann surface
\item $X$ is of Grauert type.\end{enumerate}

The first case is the easiest.

\begin{propos} If $X$ is a modification of a Stein space, then $D$ is a modification of a Stein space as well.\end{propos}
\begin{proof} We have that $\Sigma_D\subseteq\Sigma_X$, so $\Sigma_D$ is contained in a union of compact complex curves. By Proposition \ref{prp_ovvia}, $\Sigma_D$ is the union of some irreducible components of these curves, which are then contained in $D$. By Corollary \ref{cor_modstein}, $D$ is a modification of a Stein space.\end{proof}

In the other two cases, we have a set $T\subset\R^n$ and a real-analytic proper map $F:X\to T$ with pluri(sub)harmonic components; for the Grauert type surface it is obvious, with $n=1$ and $F=\chi$ (up to passing to a double cover of $X$), where $\chi$ is the pluriharmonic function given by \cite{mst}*{Main Theorem} (on $X$ or on a double cover of $X$). In the remaining case, let $\pi:X\to R$ be the proper surjective holomorphic map, where $R$ is an open Riemann surface; we embedd properly $R$ in $\C^3$ by $g:R\to\C^3$, then $F=g\circ \pi$ is a proper map from $X$ to $\R^n$, $n=6$, with pluriharmonic components.

We set $V=F(D)$ and we note that in both cases the set of singular values is a discrete set $\{t_j\}_{j\in\N}$. We recall a result from \cite{M}.

\begin{propos}If there is $t_0\in V$ such that $F^{-1}(t_0)\subset D$, then $D=F^{-1}(V)$, hence $F:D\to V$ is proper and $D$ is of the same type as $X$.\end{propos}

To conclude, we just need to prove the following.

\begin{lemma} If for all $t\in V$, $F^{-1}(t)\not\subset D$, then $D$ is a modification of a Stein space.\end{lemma}
\begin{proof}Let $\phi$ be a minimal continuous function for $\Sigma_D$; consider $t_0\in V$ such that $\Sigma_D\cap F^{-1}(t_0)\neq\emptyset$. For $p$ in this intersection, let
$$K=\{F=t_0\}\cap\{\phi=\phi(p)\}\cap\Sigma_D\;.$$
We claim that $K$ is a compact set with the local maximum property; indeed, as $\phi$ and the components of $F$ are plurisubharmonic functions, we can apply \cite{Sl3}*{Lemma 4.8}, which proves that $K$ is a local maximum set. Compactness is obvious.

Either by Proposition \ref{prp_ovvia} or Corollary \ref{cor_denso}, if $t_0$ is a regular value, then $K=F^{-1}(t_0)$, which is impossible; then, $\Sigma_D\cap\{F^{-1}(t)\}\neq \emptyset$ if and only if $t$ is a singular value. Therefore,
$$\Sigma_D\subseteq \bigcup_{j\in\N}F^{-1}(t_j)\;.$$
For $j\in\N$, let
$$K_j=\Sigma_D\cap\{F=t_j\}$$
and note that
$$K_j=\bigcup_{c\in \phi(K_j)}\Sigma_D\cap\{F=t_j\}\cap\{\phi=c\}\;.$$
The sets on the right were shown to be local maximum sets, so their union $K_j$, being closed, also enjoys the local maximum property (see \cite{Sl2}*{Proposition 3.5(b)}).

Fix $j\in N$, let $B$ be a small ball around $t_j$ in $V\subset\R^n$ such that, for $m\neq j$, $t_m\not\in B$ and define $D_j=D\cap F^{-1}(B)$. Consider $v:B\to\R$ a convex exhaustion, then $\rho=\phi+v\circ F$ is a continuous plurisubharmonic exhaustion for $D_j$, which is strongly plurisubharmonic outside $K_j$ (as $\phi$ is minimal for $\Sigma_D$ and $D_j\cap\Sigma_D=K_j$).

By Lemma \ref{lmm_complete}, $K_j$ is contained in the union of finitely many compact curves; therefore $\Sigma_D\subseteq \bigcup K_j$ is contained in the union of at most countably many compact curves. By Corollary \ref{cor_modstein}, $D$ is a modification of a Stein space.
\end{proof}

This concludes the proof of our main result.

\medskip

There are two easy consequences, which are nonetheless worth mentioning.

The first consequence is that, in the situation we study, the minimal kernel does not depend on the regularity of the functions we consider.

\begin{corol}\label{cor_reg_ker}Let $X$ be a complex surface which admits a real-analytic plurisubharmonic exhaustion function and consider a domain $D\subseteq X$ which admits a continuous plurisubharmonic exhaustion function. Then the minimal kernels of $D$ with respect to continuous function and with respect to real-analytic functions are the same set.\end{corol}

The second consequence can be formulated as a regularization result: if we know that a continuous exhaustion exists, we can produce a real-analytic exhaustion.

\begin{corol}\label{cor_reg_exh}Let $X$ be a complex surface which admits a real-analytic plurisubharmonic exhaustion function and consider a domain $D\subseteq X$; if $D$ admits a continuous plurisubharmonic exhaustion function, then it admits a real-analytic plurisubharmonic exhaustion function, which is strongly plurisubharmonic outside the minimal kernel.\end{corol}

Finally, by Corollary \ref{cor_reg_ker}, a minimal continuous exhaustion and a minimal real-analytic exhaustion are strongly plurisubharmonic on the same open set.

It is also worth noting that the results presented imply that we can generalize Corollary 3.1 in \cite{M} to the case of domains with a continuous exhaustion, thus implying an analogue of Main Theorem in \cite{mie} and Theorem 1.1 in \cite{LY} for such domains in a Hopf surface.

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    }
\bib{crass}{article}{
author={Mongodi, Samuele},
   author={Slodkowski, Zbigniew},
   author={Tomassini, Giuseppe},
title = {On weakly complete surfaces},
journal = {Comptes Rendus Mathematique},
volume = {353},
number = {11},
pages = {969 -- 972},
year = {2015},
note = {},
issn = {1631-073X},
doi = {10.1016/j.crma.2015.08.009},

}

  \bib{mst}{article}{
     author = {Mongodi, Samuele},
     author = {Slodkowski, Zbigniew},
		author = {Tomassini, Giuseppe},
      title = {Weakly complete compex surfaces},
    journal = {Indiana Univ. Math. J.},
     volume = {67},
       year = {2018},
     number = {2},
      pages = {899 \ndash 935},
}

	\bib{mst2}{article}{
author = {Mongodi, Samuele},
     author = {Slodkowski, Zbigniew},
		author = {Tomassini, Giuseppe},
title = {Some properties of Grauert type surfaces},
journal = {International Journal of Mathematics},
volume = {28},
number = {08},
pages = {1750063},
year = {2017},
doi = {10.1142/S0129167X1750063X},}

\bib{Nar}{article}{
   author={Narasimhan, Raghavan},
   title={The Levi problem for complex spaces. II},
   journal={Math. Ann.},
   volume={146},
   date={1962},
   pages={195--216},
   issn={0025-5831},
   review={\MR{0182747}},
   doi={10.1007/BF01470950},
}

\bib{rich}{article}{
   author={Richberg, Rolf},
   title={Stetige streng pseudokonvexe Funktionen},
   language={German},
   journal={Math. Ann.},
   volume={175},
   date={1968},
   pages={257--286},
   issn={0025-5831},
   review={\MR{0222334}},
   doi={10.1007/BF02063212},
}
 \bib{Sl2}{article}{
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   title={Local maximum property and $q$-plurisubharmonic functions in
   uniform algebras},
   journal={J. Math. Anal. Appl.},
   volume={115},
   date={1986},
   number={1},
   pages={105--130},
   issn={0022-247X},

   doi={10.1016/0022-247X(86)90027-2},
}
\bib{Sl3}{article}{
	author={Slodkowski, Zbigniew},
	title={Pseudoconcave decompositions in complex manifolds},
	journal={Hopkins-Maryland Complex Geometry Seminar proceedings volume of the AMS Contemporary Mathematics series},
	note={to appear},
	}
\bib{ST}{article}{
    author={Slodkowski, Zibgniew},
   author={Tomassini, Giuseppe},
   title={Minimal kernels of weakly complete spaces},
   journal={J. Funct. Anal.},
   volume={210},
   date={2004},
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}

  \end{biblist}
\end{bibdiv}

\end{document}

redpajama_set_name: RedPajamaArXiv


text:
"Mayhap happiness or haplessness is mere happenstance?"
Posted by megan hicks in fairy tales
Csenge Zalka, fairy tale lobby, fairy tales, mary grace ketner, megan hicks, national storytelling network, storytelling, Vasilisa
Walter Crane's Aladdin and the missus, several years into their "happily ever after" phase. Teamwork! Together they vanquished the wicked magician. (Did you forget that the story says the action took place in China?)
Sagacia gave her friend the squint-eye.
"Thinking deep thoughts again?" she queried.
"Trying to," Simplia admitted. "But when you're a Simpleton, the path to deep thinking is a slippery slope." She sat down on the chesterfield and poured herself another cup of tea. "I'm pondering Happily in Hapsburg's question concerning those newly weds who came to the end of their fairy tale with a glib statement about living happily ever after."
Murzik, who was obviously eavesdropping, gave an eyeroll that commicated an unequivocal, "Bo-ring."
Ring! Ring! Ring!
"That sounds like bicycle bells." Simplia ran to the door. "That was bicycle bells. Tarkabarka and Flossie Squashblossom are coming up the walk!"
Sagacia got up to put to put the kettle on for more tea.
As soon as they were seated and a plate of cookies was set out, Flossie cut right to the chase.
"I adore this month's question to Vasilisa the Wise. You hear so much about family dysfunction in fairy tales… and to be fair, you wouldn't have a story if some sort of problem didn't rear its ugly head, but SO MUCH dysfunction gets tedious and predictable."
"Still," said Simplia, "too much 'function' in a fairy tale family, and you just have another version of The Brady Bunch."
"True. I guess that's why the story of Aladdin is one of my all-time favorites. That story puts the 'fun' in family dysfunction and 'function' alike."
"That's right!" Sagacia agreed.
Tarkabarka was too busy dunking her windmill cookies to do much besides nod in enthusiastic agreement.
"Really?" asked Simplia.
"Really," Flossie asseverated. "But you have to stay with the story past the time when boy gets girl. When you read the second part of the story, you see just how strong was the bond between Aladdin and his wife. See, he starts the story as a wastrel, a nebish, a hormone-driven no-goodnik. But he is clever, and he keeps his wits about him. So when fortune deals him a stroke of luck, he shows us that he is eminently teachable. He shares his wealth, he behaves deferentially toward the sultan; over the years, he becomes a wise leader, a loving husband, and an able statesman. And that only takes you two thirds of the way through the story."
Sagacia was familiar with this story. "That's right!" she said. "And by the actual end of the story, he and his wife are no long young lovers. They are a seasoned couple."
Flossie nodded and said, "Bingo!"
Now Tarkabarka was ready to make her contribution.
"Anait! And her husband Vachagan. A story from the Caucasus. She was a master artisan but not of royal birth, and she shocked everybody by refusing to marry Prince Vachagan, who was smitten by her brilliance as much as by her beauty. She said she'd never enter into a marriage with a man who couldn't, if he had to, support his family by the work of his hands."
"But he was a prince," said Simplia. "He would never have to ply a trade."
"That's what he said. But she insisted, and he was really, really in love. So he learned how to weave. Might have cost him some macho points among his peers, but he was really, really in love. The marriage took place. The happy couple assumed the throne, and several years into 'happily ever after,' Vachagan found that knowing a trade not only came in handy, it saved his life and his kingdom."
Flossie said under her breath, "Another teachable man. I think teachable people must live happier ever after than the ones who think they're already smart enough."
"Well," Sagacia said, "that gives us two more post-honeymoon success stories to share with Happily in Hapsburg. I wonder what else is out there."
Flossie looked at her watch and said, "I need to be on my way right now, but there is another story — a rip snorter — I'd love to tell you about. When I pass this way again."
"Deal!" said Simplia.
"Lovely!" said Sagacia.
"Mmmph!" said Tarkabarka, around another tea-dunked windmill cookie.
About megan hicks
The best parts of my life happen when I pull magic from thin air. That happens with the spoken word. The written word. Reclaiming trash in the material world. It's about recognition. Re-cognition. Learning fresh the truth I've always known. Seeing new potential as a result of a change in context. It's alchemy.
View all posts by megan hicks »

redpajama_set_name: RedPajamaCommonCrawl


Home School Day: Farmhouse Afire!Thursday, June 20 : 01:00 PM - 03:00 PMHome School Day: Farmhouse Afire!
In New Jersey, the hunting of deer is permitted from September to February.
The MCPC establishes a hunting schedule each year based on the dates permitted under New Jersey Division of Fish and Wildlife regulations.
The MCPC usually prepares its hunting schedule during the summer. The schedule is then reviewed at a MCPC public meeting.
The schedule is posted online each year.
Since the list of parks included in the program is subject to change each year, it is important to check the schedule each year.
By State law, no hunting is permitted at MCPC facilities on Sundays.
Parks and trails will be closed to the public on dates when hunting with firearms is scheduled.
Firearm hunts occur over 10-12 days in November through February.
Park closure dates are always scheduled during weekdays to minimize inconvenience to non-hunting park patrons.
Unless otherwise specified, parks and trails remain open on dates when bow hunting is scheduled.
Park patrons must remain on trails when visiting a park. Hunters are required to maintain a sufficient distance from trails to minimize any negative encounters.
Parks have signs posted in parking areas and major trail heads that specify the type of hunting scheduled and any park closure dates.
Residents that live adjacent to a County park are advised to check the website or call the MCPC to verify whether hunting is scheduled for that park.
Since signs are only posted on official MCPC blazed trails, individuals that access the parks using non-designated paths may not see sign postings.
All hunters are provided with a hunt map for the park in which they are registered.
Hunt maps indicate which areas of the park hunters can access to hunt deer.
Hunters are required to maintain a distance of 450 feet from occupied buildings and school playgrounds when in possession of a loaded firearm or nocked arrow. This area is referred to as a "safety zone" and is taken into account on the hunt maps.
Hunt maps are subject to updates each year.
Hunting on unscheduled dates, the entering of safety zones and other unlawful behavior is not tolerated by the MCPC. Observations of inappropriate activity should be reported to the Morris County Park Police, as they are occurring: (973) 326-7654.


One of Mass Effect's most notable themes is the journey and change that everyone undergoes throughout the duration of the series. Liara T'Soni is a prime example of someone that experiences great personal change over the course of the three games.
When we first meet Liara on Therum, she is a young and curious scientist engrossed in the mysteries of the Protheans, an ancient and highly intelligent race that once inhabited the galaxy. Though her previous expeditions had been primarily uneventful, her trip to Therum lands her in a rather precarious standoff between herself and several of Saren's troops. After barricading herself behind an energy field within the underground structures on the planet, Liara accidentally traps herself in a second field. Help, however, is not far away, as the arrival of Commander Shepard yields relief for Liara from both the Prothean technology and Saren's ruthless troops.
Liara is quickly drawn into the odyssey of the Reapers when she learns that Shepard came into contact with a Prothean beacon. Liara's initial meld with Shepard in an attempt to decipher the bizarre images from the beacon shifts her focus to the conflict with Saren, and on a larger scale, the impending war with the Reapers. Shepard serves as the catalyst for this new step in Liara's journey, providing her with a rich reserve of new data that she cannot ignore. By connecting with the beacon, Shepard unknowingly became a port to one of the greatest sources of Prothean knowledge that Liara has ever had access to.
Liara's formidable intelligence is clear early on, though she is also presented as a socially naïve damsel that requires rescuing by others. Despite her shortcomings and lack of familiarity with Shepard and their crew, Liara displays compassion towards them throughout their mission to stop Saren. Even after the death of her mother Matriarch Benezia, Liara continues to help Shepard and does not allow her personal loss to derail the mission.
Months after Saren's defeat and shortly after the destruction of the Normandy, Liara embarks on her own personal quest for information regarding Commander Shepard. Inspired by her loyalty to Shepard and deep concern for her friend, she relentlessly pursues leads on the whereabouts of Shepard's body. This ultimately leads her to the mysterious Shadow Broker, a clandestine information broker that makes a business out of the galaxy's most dangerous secrets. In the process of retrieving Shepard's body, Liara is forced to leave behind another friend in order to escape, but she vows to return and save him from the grips of the Broker.
As the result of a deal with Cerberus, Liara is unable to see or to speak to Shepard for two years while the Commander is rebuilt. During those two years, her hatred of the Shadow Broker sprouts a vein of ruthlessness in her. Though she comes across as hardened, it makes her particularly effective as an information broker on the planet Illium. Her position there allows her to gain leads on both the Shadow Broker, which fuel her plans to eventually enact revenge.
Another of Liara's greatest developments occurs in her pursuit of the Shadow Broker. After an attempted assassination attempt, she hunts down the Spectre Tela Vasir, who was secretly working for the Shadow Broker. Liara does not back down from the Spectre, instead she tracks them down and takes Vasir out, ending any threat that the Spectre posed to her. Liara no longer shies away from threats to her person or to her goals, instead she tackles them head on and resolves them with deadly force, if necessary.
At the climax of her long feud with the Shadow Broker, Liara and Shepard take him down and rescue her friend Feron. In the aftermath, Liara makes the decision to take up the role of the new Shadow Broker, both at a personal sacrifice and effort to aid Shepard in their conflict with the Collectors and Reapers. The decision is not only a reflection of Liara's change and growth as an individual, but also her devotion to Shepard.
At the start of the Reaper War, Liara is stationed on Mars to work on the Prothean archives. When Shepard and the Normandy arrive, the base is overrun with Cerberus troops that are seeking information about an ancient Prothean weapon. They try to capture Liara, but she takes out the troopers pursuing her as Shepard looks on. This time, Liara did not need Shepard to save her; she saved herself. We also learn that Liara made a bold move to protect her assets as the Shadow Broker from the hands of Cerberus. When the Illusive Man went looking for the Shadow Broker's ship in the Hagalaz system, Liara destroyed it to prevent Cerberus from acquiring it and its resources. She doesn't allow the Illusive Man the opportunity to gain access to her knowledge and connections, and without hesitation she cuts off his only route to the Shadow Broker's network.
During the war, Liara witnesses the overwhelming capture of her home planet Thessia by Reaper forces. In her grief, Shepard reminds her that she can still help and make a difference to the remaining asari in the galaxy. Liara immediately begins efforts to help the refugees that have escaped the planet. She is also a major contributor in the construction of the Crucible, an ancient weapon designed for destroying the Reapers. In uncovering the blueprints and offering resources to the Alliance for its construction, Liara aids the galaxy in building a potential resolution to the threat of the Reapers.
Over the course of the Mass Effect trilogy, Liara transforms into a determined and ruthless individual with a great drive to help not only her friends, but also the galaxy. She learns to not only save herself from present threats, but also to enable safeguards to protect herself from future dangers. In situations where a tough call must be made, she doesn't shy away from the difficult choices that must be made. Liara is no longer a quiet scientist that reserves herself to solitary dig sites; she is a major player in the galaxy that aids in shifting the course of events, and aiding Commander Shepard in their quest to stop the Reapers.


According to Reuters, Iranian Foreign Minister Mohammad Javad Zarif mocked U.S. President Donald Trump on Friday over the collapse of a summit on North Korean denuclearization.
Zarif vowed that Washington would not get a better Iran nuclear deal than the one it exited last year.
Zarif returned to his job after Iranian President Hassan Rouhani rejected his resignation earlier this week.
29, 2015, FILE PHOTO PHOTO GALLERY FEB.


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Yellow Punch-Out Aleph Bet Letters, Ideal for Bulletin Boards, Class Projects, Displays, Announcements and much more... The Alef is 2.75" tall, all other letters are proprtional. Available in 8 colors on varnished card stock" 90 Letters (quantity of each letter according to statistical use).
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text:
Home Music Bands Listen to this! Belfast based Blues Rockers MASK unleash debut single!
Rock Reviews
Listen to this! Belfast based Blues Rockers MASK unleash debut single!
Paul Scott-Bates
Living miles apart from each other whilst juggling parental duties, MASK are a band who reflect what it means to be a rock band in the real world. Deliberately avoiding studio trickery, auto-tune and generic fakery, they are genuine friends delivering their tracks in a couple of takes with vintage equipment with the sole purpose of entertaining their audience. If this clashes with the preconception of the modern rock band, then this is only the beginning of their boundary-breaking, with their highly anticipated live appearance giving all proceeds to charity.
MASK are led by H (guitar/vocals) who is based in Belfast, along with childhood friends Daz (bass) and Craig (guitar/vocals), the band are spread across Northern Ireland, England and Scotland – in fact, with well over 1100 miles between their locations, it would be far easier to have given up years ago. MASK are the antithesis of your typical rock stars – they describe themselves as unapologetically uncool; they're all working dads; they're releasing their first album twelve years after starting out, only creating their best material at a time where life is throwing everything in their paths to make it all but impossible.
Despite all this, MASK have succeeded in creating a unity and an energy which many more established bands can only dream of. Their time playing together is precious and the furious energy produced when they meet is tangible on their tracks. Coupled with their use of vintage 60's and 70's equipment, MASK are bringing truth and passion back to rock music, proving that though life can often threaten to get in the way, the ability to create real music is always there.
Following on from "The Truth", their debut EP released in 2017, "The Famous" is a marauding beast of an album. Abandoning plans for vast orchestras and gospel choirs, the decision was made to go back to basics, allowing the tracks to develop naturally rather than to produce something contrived or generic. With lyrics which range from profound to acerbically comic, MASK are the antidote to rock by numbers and will release Celebrity, the first single from the album, on August 31st.
The MASK website is here: masktheband.com. They an be followed on Twitter as @MaskTheBand1 and Liked on Facebook.
All words via Paul Scott-Bates. More of Paul's writing on Louder Than War can be found at his author's archive. Paul's website is hiapop and you can follow him on Twitter as @hiapop, and on Facebook here.
The Famous
Previous articleS.F. Sorrow – The First Concept Album Of Its Kind … Two of the Pretty Things talk to Nathan Whittle
Next articleWatch This! London Trio Black Surf Premiere Sun Kissed Latest Single Open Fire
https://www.hiapop.com
Born and bred in Lancashire, currently residing in the Rossendale Valley. Father, Husband, Blogger, Home-Brewer, Poet, Chicken-Keeper, Tweeter, Socialist - @hiapop. Keen to be green. Childhood ambitions to be a pop-star thwarted due to being unable to sing. Instead, began listening to music of every type. Everything deserves one listen, but, not necessarily a second. Only (ex-Community) DJ to ever play Nat 'King'Cole followed by Nine Inch Nails, and, eat Fish and Chips live on air. http://www.hiapop.com


The Irish Childhood Bereavement Network (ICBN) will host the first Irish conference on childhood bereavement on October 4th in Dublin Castle.
The conference addresses creation of frameworks of support for those supporting a bereaved child and will focus on social media, voluntary group support and traumatic loss. A personal reflection will be shared by Irish Times journalist Roisin Ingle, who lost her own father when she was aged eight.
The conference costs €48 for ICBN members, €58 for an early bird ticket and €68 full price. It will take place from 9:30am- 4pm and includes a light lunch.


Kennesaw, GA - June 28, 2011 – On Saturday, June 18th LearningRx Kennesaw was a platinum sponsor of The Golden Soldiers Big Day Out at the Acworth Sports Complex. Close to 600 people attended the second annual free event which provided fun and excitement for children with special needs and their families.
BIG DAY OUT was held at the Acworth Sports Complex adjacent to the Horizon special needs field. The parking lot was filled with carnival games, inflatables, music, jugglers, a vendor walk, and a surprise visit from Freddie the Falcon and the Atlanta Falcon's Cheerleaders.
For many of the attendees, it can be a challenge to find venues and events geared only for children who may have a variety of disabilities. The free and fun events put on by The Golden Soldiers are making it easier for those who care for a special needs child or adult.
Founder and CEO Lindsey Turner's vision of putting into practice the "Golden Rule" has turned into a passion for helping families. "To have a parent come up to me and tell me that this was the first place they went where their child was treated with kindness, patience and understanding by all who attended is the ultimate compliment to me" said Turner. "Our vision is to reach more and more kids each year and to continue to bring joy and amusement to the special needs community ".
The Golden Soldiers, along with community partner LearningRx sponsors sensory friendly movies throughout the year at the NCG cinemas in Acworth. Movies without trailers, the lights turned on and the volume down low have been a huge success. Once again it is all tied into Turner's vision of doing all that he can to help kids with special needs just be kids and treating others the way he would like to be treated.


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text:
Rob O'Byrne
Home » Business thoughts » Virtual Assistants: The 'Secret Sauce' that Saves Time and Makes Money
Virtual Assistants: The 'Secret Sauce' that Saves Time and Makes Money
Posted on November 6, 2019 in Business thoughts, Career Tips
Entrepreneur and consultant, Rob O'Byrne, says he can no longer keep to himself the 'secret sauce' that has helped him drastically cut back his working hours, and boost his business income. At this public seminar, he will reveal the colossal differences a virtual assistant can make to your business.
Seriously! Virtual Assistants Can Win You More Time and Money
So you are a small business owner, an entrepreneur? How many hours do you work a week? How many hours on your business, how many hours in your business?
Rob O'Byrne says that nine years ago he was putting in 80—100 hours a week, "absolutely killing" himself trying to do all the tasks in his business.
"I think this is a very common thing for small business owners and entrepreneurs, but it doesn't need to be like that."
Rob found a "secret sauce" about eight years ago that allowed him to cut back his working commitments from eighty-plus hours a week to around 50, and which also allows him to take three months' holiday a year —all while actively directing his six—count them—six, businesses.
Learn Rob's Secret at a Free Seminar in Sydney on November 26
"The secret sauce for me has been tapping into really expert resources overseas at a much, much lower cost than here in my home country."
During his three-hour, More Time More Money seminar, Rob will share valuable information that he wishes he could have learned at a seminar eight years ago. His insights will include:
Where your time goes, and what you SHOULD be focusing on
What virtual assistants are, and what they are not
How to go about finding and hiring Vas
How to communicate with a virtual assistant
How to pay offshore virtual assistants
How your VA can actually boost your sales
What things you could outsource to grow your business
Understanding cultural issues
How to get started with outsourcing
The costs involved in outsourcing
Admin outsourcing
"I will take you step by step through the process so that you will know by the end of the seminar whether a virtual assistant is going to help you get your time back, and where you can find them."
Why has Rob called the event "More Time, More Money"?
Because, he says, that is what all small business owners and entrepreneurs want. They work too many hours and don't seem to get the rewards.
"This secret sauce that I am sharing with you will give you that time, and give you that extra income in the business."
Importantly, says Rob, outsourcing has helped him to develop more businesses, and employ more people locally in Australia.
The Team at Virtual Done Well
At the seminar, Rob will reveal details about his team of virtual assistants—the ones who allow him to take his foot off the pedal and hand over to his "co-drivers" from time to time.
They are a dynamic group based in the Philippines, operating as Virtual Done Well (VDW) and comprising researchers, telemarketers, social media managers, graphic and digital designers, and website design and management professionals.
A Two-Way Flow
While the team has become essential to his business, Rob also regards VDW as a "social enterprise" that he funds.
He has recently realised that trying to keep VDW a secret to avoid attention from his competitors is contrary to the group's promotional and marketing mission, and its ability to grow as a business.
It is more important, he says, to share his secrets and promote VDW's excellent service—and in the process help small business owners and entrepreneurs free up their time, and maximise their business-related energies.
"I will share all the mistakes that I have made so that you don't have to make them as well. I have seen so many small business owners and entrepreneurs really struggling and they just don't realise how easy it is to tap into this kind of support."
Special Guest Star—Sally Illingworth
Sally is a strategic business advisor and communications strategist, specialising in digital influence. She is highly successful in social media in growing businesses and will be sharing tips on this subject at the seminar.
As one of Australia's leading LinkedIn media personalities, Sally boasts more than 700 profile views per day. She is clearly a popular leader in her field!
Why Would You Not be There?
"It's going to be a fantastic event. And it's free! You would be nuts not to come along."
Rob adds that the seminar would be especially suitable if you are a small business owner in professional services, consulting, coaching, online business, training, or education.
"Heck, in fact any small business!"
There are limited places and these are going fast. Don't lose out. Book for Rob's free More Time More Money seminar NOW!
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January 29, 2023 | Stars Disappear Before Our Eyes: Startling Analysis From Globe at Night
Astronomers Discover Mysterious Blue Ring Nebula, See the Fate of Binary Stars
TOPICS:AstronomyAstrophysicsPopularPrinceton University
By Princeton University November 21, 2020
A team of scientists including Princeton's Guðmundur Stefánsson investigated the mysterious Blue Ring Nebula, composed of expanding hydrogen gas (blue) expanding from a central star, which is the remnant core of a stellar merger. Red filaments are shockwave filaments from the merging event. Credit: NASA/JPL-Caltech/M. Seibert (Carnegie Institution for Science)/K. Hoadley (Caltech)/GALEX Team
Scientists have discovered a rare object called the Blue Ring Nebula, a ring of hydrogen gas with a star at its center. The properties of this system suggest it is the remnant of two stars meeting their ultimate demise: an inward orbital dance that resulted in the two stars merging. The result offers a new window into the fate of many tightly orbiting binary star systems.
In 2004, scientists with NASA's Galaxy Evolution Explorer spotted an object unlike any they'd seen in our Milky Way Galaxy: a large, faint blob of gas that seemed to have a star at its center. In the ultraviolet wavelengths used by the satellite, the blob appeared blue — though it doesn't actually emit light visible to the human eye — and careful observations identified two thick rings within it, so the team nicknamed it the Blue Ring Nebula. Over the next 16 years, they studied it with multiple Earth- and space-based telescopes, but the more they learned about it, the more mysterious it seemed.
A team of scientists including Princeton University's Guðmundur Stefánsson, the Henry Norris Russell Postdoctoral Fellow in astrophysical sciences, combined ground-based observations with detailed theoretical modeling to investigate the object's properties. The paper describing their findings appears in the November 19, 2020, issue of Nature.
"We were in the middle of observing one night, with a new spectrograph that we had recently built, when we received a message from our colleagues about a peculiar object composed of a nebulous gas expanding rapidly away from a central star," said Stefánsson. "How did it form? What are the properties of the central star? We were immediately excited to help solve the mystery!"
Most stars in the Milky Way are in binary systems — pairs of stars orbiting each other. If they are close enough together, such systems can meet their demise in a stellar merging event: As stars evolve, they expand, and if they are close enough together, one of the stars can engulf its orbiting companion, causing the companion to spiral inward until the two stars collide. As the companion loses its orbital energy, it can eject material away at high speeds.
Could that explain the mysterious Blue Ring Nebula?
Further evidence in support of this hypothesis came from observations with two different spectrographs on large telescopes on the ground: the HIRES optical spectrograph on the 10-meter Keck Telescope on top of Maunakea in Hawaii, and the near-infrared Habitable-zone Planet Finder on the 10-meter Hobby-Eberly Telescope at McDonald Observatory in Texas, a new near-infrared spectrograph that Stefánsson helped design, build and commission to detect planets around nearby stars.
The Blue Ring Nebula consists of two expanding cones of debris. The base of one cone is moving toward Earth. Both bases are outlined in magenta, revealing shockwaves created as the debris races through space. Blue represents material behind the shockwave and is visible only where the cones overlap. Credit: NASA/JPL-Caltech/R. Hurt
"The spectroscopic observations were key in allowing us to understand the object further, from which we see that the central star is inflated, and we see signatures of accretion likely from a surrounding disk of debris," Stefánsson said.
"Indeed, the spectroscopic data coupled with theoretical modeling shows that the Blue Ring Nebula is consistent with the picture of a merging binary star system, suggesting that the inwards spiraling companion was likely a low-mass star," said Keri Hoadley, a postdoctoral fellow at Caltech and lead author of the paper.
Although the relics of a few such binary merging events have been observed before, all such objects have been enshrouded by opaque dust and clouds, obstructing the view of the properties of the central stellar remnant. The Blue Ring Nebula is the only object allowing an unobstructed view of the central stellar remnant, offering a clear window into its properties and yielding clues about the merging process.
"The Blue Ring Nebula is rare," said Hoadley. "As such, it is really exciting that we were able to find it, and we are excited about the possibility of finding more such objects in the future. If so, that would allow us to gain further insights into the remnants of stellar mergers and the processes that govern them."
Read Perplexing 16-Year-Old Cosmic Mystery Solved, Revealing Stellar Missing Link for more on this study.
Reference: "A blue ring nebula from a stellar merger several thousand years ago" by Keri Hoadley, D. Christopher Martin, Brian D. Metzger, Mark Seibert, Andrew McWilliam, Ken J. Shen, James D. Neill, Gudmundur Stefansson, Andrew Monson and Bradley E. Schaefer, 18 November 2020, Nature.
Perplexing 16-Year-Old Cosmic Mystery Solved, Revealing Stellar Missing Link
Hubble Captures Unprecedented Fading of Stingray Nebula – "This Is Very, Very Dramatic, and Very Weird"
New Hubble Data Helps Reveal Ring Nebula's True Form
Sixteen Incredible Images for Spitzer's Sweet 16
MIT Astronomers Discover Mysterious "Black Widow" Binary System
Hubble Reveals Surviving Companion Star in Aftermath of Titanic Supernova Explosion
NASA's Webb Space Telescope Captures a Cosmic Tarantula
Astronomers Build Incredible 3D Visualization of Exploded Star Using NASA's Great Observatories [Video]
1 Comment on "Astronomers Discover Mysterious Blue Ring Nebula, See the Fate of Binary Stars"
kamir bouchareb st | November 22, 2020 at 2:22 am | Reply
nice topic
Stars Disappear Before Our Eyes: Startling Analysis From Globe at Night


text:
Q: JAXB fails to load file having name containing URL encoded characters I have a file whose path looks like this /home/jwayne/test/55-0388%25car.xml. I try to unmarshall the XML back to an object using JAXB as follows.
File file = new File("/home/jwayne/test/55-0388%25car.xml");
JAXBContext context = JAXBContext.newInstance(Rectangle.class);
Unmarshaller unmarshaller = context.createUnmarshaller();
Rectangle rectangle = (Rectangle) unmarshaller.unmarshal(file);

However, I get a FileNotFoundException (FNFE) with the stacktrace as follows.

[java.io.FileNotFoundException: /home/jwayne/test/55-0388%car.xml (No such file or directory)]
    at com.sun.xml.internal.bind.v2.runtime.unmarshaller.UnmarshallerImpl.unmarshal0(UnmarshallerImpl.java:246)
    at com.sun.xml.internal.bind.v2.runtime.unmarshaller.UnmarshallerImpl.unmarshal(UnmarshallerImpl.java:214)
    at javax.xml.bind.helpers.AbstractUnmarshallerImpl.unmarshal(AbstractUnmarshallerImpl.java:157)
    at javax.xml.bind.helpers.AbstractUnmarshallerImpl.unmarshal(AbstractUnmarshallerImpl.java:162)
    at javax.xml.bind.helpers.AbstractUnmarshallerImpl.unmarshal(AbstractUnmarshallerImpl.java:171)
    at javax.xml.bind.helpers.AbstractUnmarshallerImpl.unmarshal(AbstractUnmarshallerImpl.java:189)
...

Note that somehow (as suggested by the stacktrace), the unmarshaller has modified the file name from 55-0388%25car.xml to 55-0388%car.xml.
Stepping through the code, however, the problem is actually pretty deep: sun.net.www.protocol.file.Handler has a method openConnection that does the following.
File var4 = new File(ParseUtil.decode(var1.getPath()));

That sun.net.www.ParseUtil.decode method actually transforms the file path.
Any idea on how to quickly fix this problem (besides renaming the file)? (Note I am using JDK v1.8.0_191).

A: The root cause of your problem is that there is a % that is used to URL encode special characters. For % it is %25.
What JAXB does internally is that it decodes %25 to plain % and thus the file cannot be found.
Quick (and dirty) solution is to do some string replacing, like:
String fileName = "/home/jwayne/test/55-0388%25car.xml":
fileName = fileName.replace("%25", "%2525");
File file = new File(fileName);

This applies whenever there is %25 in a file name. But I guess this happens to any URL encoded characters. So if there are any other special characters you need some handling for each or some clever regexp solution.
Update:
to get around this JAXB behaviour provide it with InputStream instead of File. So like:
FileInputStream fis = new FileInputStream(fileName);
Rectangle r2 = (Rectangle) unmarshaller.unmarshal(fis);

Then there is no means for JAXB to alter any URI / filename.

redpajama_set_name: RedPajamaStackExchange


The Langley School Board finally filled the empty trustee position Tuesday night when it swore in by-election winner Cecelia Reekie as the seventh trustee. But despite finally playing with a full set, the board decided not to choose a chair or vice-chair in a move the Langley Teachers' Association says shows a lack of strong leadership.
The board, which has been on a rotating chair schedule since former chair Joan Bech resigned from the board in October, voted five-to-two to keep the rotating chair schedule until after the November school board elections.
"The board believed that this particular time, given the length of the term and the fact that it has worked well for us to have a rotating chair, we chose to keep it," says Trustee Alison McVeigh.
Susan Fonseca, president of the Langley Teacher's Association (LTA), says she was surprised by the decision and feels it goes against the board's duty to provide leadership for the school community.
"I am not aware of any other district where they have that kind of a process set up, and I'm very concerned that there won't be anybody seen as providing leadership in our district. I just wrote a letter to the rotating board chair for January, and who responds to it?" Fonseca told The Tyee.
"And we have no vice chair right now. There is no recognized public focus person for our board, and I think that gives too much control to senior management."
McVeigh denies senior district management has any sway over the board's decisions and says the chair's only duties are to speak on behalf of the board when necessary, and chair the board meetings.
The board also decided to reinstate oral question period at the end of its meetings after public outcry over a decision in October that all questions to the board must be written down and given to the assistant superintendent to read allowed. McVeigh says the board had preferred the written system, but agreed to return to oral questions provided certain guidelines were followed.
"That the questions are directed to the board chair, that questions must pertain to the business of the board, they can't be commentary, they must not be directed at individual trustees, they must not pertain to personnel issues or contractual issues," she says.
Katie Hyslop reports on education for the Tyee Solutions Society, and is a freelance reporter for a number of other outlets including The Tyee.


text:
Q: My application (java) isn't displayed in the window I set for it I created a java application in eclipse using processing (processing.org) supposed to be displayed in this windownot displayed at the right place, but as you can see it's doesn't work.
I already tried the way to compile the app using proclipsing : http://www.instructables.com/id/Proclipsing-Using-the-Eclipse-IDE-for-Processing-p/, but it's doesn't work and I don't want to use this way.
So that's my code :
package HelloProcessing;

import java.awt.*;
import javax.swing.*;
import processing.core.*;

public class main
{

    public static void main(String args[])
    {
        PApplet.main(new String[] {"--present", "HelloProcessing.HelloProcessing"});
        JFrame frame = new JFrame("HelloProcessing");
        frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
        JLabel emptyLabel = new JLabel("");
        emptyLabel.setPreferredSize(new Dimension(HelloProcessing.xs, HelloProcessing.ys));
        frame.getContentPane().add(emptyLabel, BorderLayout.CENTER);
        frame.pack();
        frame.setVisible(true);
    }
}

package HelloProcessing;

import processing.core.*;

public class HelloProcessing extends PApplet
{
    /*
     * public static void main(String args[])
     * {
     * PApplet.main(new String[] {"--present", "HelloProcessing.HelloProcessing"});
     * }
     */

    float rb = 255;
    float gb = 255;
    float bb = 255;
    static int xs = 500;
    static int ys = 500;

    float xe = 150;
    float ye = 150;
    float we = 100;
    float he = 100;

    float re = 255;
    float ge = 0;
    float be = 0;

    float xr = 250;
    float yr = 250;
    float wr = 100;
    float hr = 100;

    float rr = 0;
    float gr = 0;
    float br = 255;

    public void setup()
    {
        background(rb, gb, bb);
    }

    public void settings()
    {
        /* size(500, 500); */
        size(xs, ys);
    }

    public void draw()
    {
        int ecolor = color(re, ge, be);
        fill(ecolor);
        ellipse(xe, ye, we, he);

        int rcolor = color(rr, gr, br);
        fill(rcolor);
        rect(xr, yr, wr, hr);
    }
}

Could you help me ?
Thanks

A: Calling the PApplet.main() function builds a window for you and displays your Processing sketch in that window.
Then you create a second JFrame and display that. But that second JFrame doesn't know anything about your Processing sketch. You only ever add an empty JLabel to it, so it doesn't have anything to display.
Before Processing 3, you used to be able to embed a PApplet directly in a JFrame. But after Processing 3, you can no longer do that since PApplet doesn't extend Applet anymore.
You can still get to the underlying Component by going through the PSurface class, but that's not exactly friendly to novices. Alternatively, you could use Processing as a Java library and build a PGraphics yourself, but that's not exactly trivial either.

A: Kevin Workman say me :
Stop passing in "--present" as an argument. That's what's telling it to go full screen.


It's a question many businesspeople have quietly asked themselves: Just what do consultants do for their money?
According to a federal indictment unsealed Monday, the answer for one former partner at McKinsey & Company's Chicago office and his colleague at State Farm was "not much."
McKinsey partner Navdeep Arora, 51, allegedly teamed up with former State Farm employee Matthew Sorensen, 49, to bilk McKinsey and State Farm out of nearly $500,000 in bogus consulting fees for work that was never done over an eight-year period beginning in 2004.
Arora received another $400,000 from McKinsey, State Farm and other McKinsey clients by making false expense claims for personal travel to cities including Vail, Miami, Las Vegas, New York, London, Prague and Munich, as well as for hotel, dining and theater expenses in Chicago, according to the eight-count wire fraud indictment.
Arrested Sunday at JFK International Airport in New York, Arora, who now lives in London, was ordered to be detained Monday during a brief court appearance in New York. Sorensen, of downstate Bloomington, is due to make his first appearance in court in Chicago Jan. 11.
According to the indictment, Arora oversaw consulting services provided by McKinsey to State Farm. Together with Sorensen, who worked as an internal consultant at State Farm, he allegedly used two companies — "Gabriel Solutions" and "Andy's BCB" — to bill McKinsey, State Farm and another client for nonexistent work, the feds say.
Sorensen, who faces five counts of wire fraud, kept the lion's share of that money, according to the indictment, pocketing nearly all of the $38,265 paid to Andy's BCB and keeping $370,000 of the $452,710 paid to Gabriel Solutions.
Arora kept more than $400,000 from the expenses scam, it's alleged.
Each count carries a maximum sentence of 20 years in prison, plus up to twice the amount allegedly stolen.
Phil Supple, a spokesman for Bloomington-based State Farm, said that State Farm alerted federal investigators in 2012 when it discovered the alleged fraud. Sorensen has not worked for State Farm since then, Supple said, adding that State Farm has not had any "contractual relationship" with McKinsey since 2012.
McKinsey spokeswoman Rachel Grant said, "We discovered this matter in 2011, notified the affected client, terminated the employee involved and worked closely with the authorities on their subsequent investigation."


LORI S. HOBERMAN is a well-known force in the in the New York City venture community. She advises entrepreneurs and investors on how to build successful businesses and strategically guides them through the emerging, later stages and exits of their companies. As a lawyer and mentor, Lori works with clients in a range of industries, including mobile, biotechnology, artificial intelligence, e-commerce and advertising. She also counsels angel and institutional investors in their investments and in the formation of investment funds. Lori is a co-founder of IMG Labs, a new innovation incubator. She is also a co-founder of mobile advertising company, Mojiva Inc., and an occasional angel investor. Lori is a frequent speaker and media resource on entrepreneurialism. She is a Mentor to 37 Angels and she chairs the NYC Chapter of the MIT Enterprise Forum, through which she recently organized a week-long summer program in entrepreneurship for NYC high school girls. NYC startup news blog, AlleyWatch, recently named Ms. Hoberman as one of "20 Awesome People in the New York Tech Scene You Need to Know About." After years of advising entrepreneurs, first as the head of Fish & Richardson's Venture Capital practice and most recently, as Chair of Chadbourne & Parke's Emerging Companies/Venture Capital Practice, she has decided to become an entrepreneur herself. She founded her own firm, Hoberman Law Group, in the fall of 2014.


This project emerged from the 2015 Ministerial Conference on the Canadian Francophonie in Toronto, which brought together the provincial and territorial ministers responsible for Francophone affairs.
A warm thank you to all those who contributed from near or far to the Francophone heritage, culture and tourism Corridor major project (see list below).
In particular, we would like to thank our close collaborators, as well as our members, who invested countless hours and energy to help turn this into the exceptional project it has become.
A big thank you as well to the Chaire de recherche en patrimoine ethnologique de l'université Laval for their outstanding work.
Canadians and visitors from around the world, the Corridor is dedicated to you.
Laurier Turgeon, Project management, interviews, content review and validation.
Alain Guindon and friends, member of the organizing committee for the Kapuskasing Lumberjack Festival, and former employee of Spruce Falls Power & Paper Co.
Stéphane Cloutier, Director, Official Languages, Culture and Heritage Division, Government of Nunavut.


text:
Quality Planning and Asssurance in Manufacturing
Standards, Quality Control, and Measurement Sciences in 3D Printing and Additive Manufacturing
Authors: Chee Kai Chua Chee How Wong Wai Yee Yeong
Imprint: Academic Press
Published Date: 5th June 2017
Print - Paperback
Standards, Quality Control and Measurement Sciences in 3D Printing and Additive Manufacturing addresses the critical elements of the standards and measurement sciences in 3D printing to help readers design and create safe, reliable products of high quality. With 3D printing revolutionizing the process of manufacturing in a wide range of products, the book takes key features into account, such as design and fabrication and the current state and future potentials and opportunities in the field. In addition, the book provides an in-depth analysis on the importance of standards and measurement sciences.
With self-test exercises at the end of each chapter, readers can improve their ability to take up challenges and become proficient in a number of topics related to 3D printing, including software usage, materials specification and benchmarking.
Helps the reader understand the quality framework tailored for 3D printing processes
Explains data format and process control in 3D printing
Provides an overview of different materials and characterization methods
Covers benchmarking and metrology for 3D printing
Engineers and Researchers entering the field for the first time, experienced readers in industry and academic
1. Introduction to 3D Printing or Additive Manufacturing (AM)
2. Roadmap on AM standards
3. Measurement Sciences Roadmap for AM
4. Quality Management Framework in AM
5. Software and Data Format
6. Process Control and Modelling
7. Material Characterization and Qualification
8. Equipment Qualification
9. Benchmarking of AM parts
© Academic Press 2017
Chee Kai Chua
Executive Director of Singapore Centre for 3D Printing and a Professor at the School of Mechanical & Aerospace Engineering in the College of Engineering at Nanyang Technological University.
Executive Director, Singapore Centre for 3D Printing and Professor, School of Mechanical and Aerospace Engineering, College of Engineering, Nanyang Technological University, Singapore
Chee How Wong
Associate Professor & Associate Dean at the School of Mechanical & Aerospace Engineering in College of Engineering at Nanyang Technological University.
Associate Professor and Associate Dean, School of Mechanical and Aerospace Engineering, College of Engineering, Nanyang Technological University, Singapore
Wai Yee Yeong
Assistant Professor at the School of Mechanical & Aerospace Engineering in the College of Engineering at Nanyang Technological University
Assistant Professor, School of Mechanical and Aerospace Engineering, College of Engineering, Nanyang Technological University, Singapore


text:
Globe Live Media > World > Davinson Sánchez, from Mourinho's 'amulet' to one of the most depreciated players in the Premier League
Davinson Sánchez, from Mourinho's 'amulet' to one of the most depreciated players in the Premier League
Posted by Melissa Galbraith December 19, 2020
Aíto returns to train Alba Berlin after overcoming COVID-19
Despite being part of the Premier League team, Colombian central defender Davinson Sánchez is not having a good time at this dream start to the season for Tottenham Hotspur.
For the Portuguese José Mourinho, DT of the 'Spurs', Sánchez is not part of the short and medium term plans. Despite the stature and corpulence of the central defender, Mourinho does not call the Colombian to the matches. When he enters the call to play the Premier League, the experienced coach does not move the player from Cauca from the bank.
In addition, during the season, the top-level defender has received scolding from the Portuguese for his poor performance in the continental Europa League tournament. According to several English media, the statistics do not help the player from Caloto. The goals with Sánchez on the field of play are more than when the Colombian is on the bench or watching the game from home.
Although the comparison is made, the player has only played 12 games in the season. Four of them have been played in the Premier League, while Tottenham have played 13 games in total per league. The remaining 8 games were played in the continental tournament.
The variation of the price of Sánchez
This decline in performance has been reflected in the devaluation of the player's commercial value, according to TransferMarket. According to the website, Sánchez continues to be the fourth most valuable player in the Tottenham squad and the most valuable in the entire Colombian National Team. This price is justified by the youth of the defender, who is only 24 years old and is already part of one of the largest teams on the old continent.
In turn, he is ranked 12th among players with the highest value in the age range and is the 18th highest-priced central defender in the world. Overall, it ranks 123rd in the world, based on business value.
Although the projection for the moment is good, it has been devaluing since April of this year. The Colombian player presented his peak value in December 2019, when it cost 60 million euros. After this, it had a significant devaluation five months later.
In April 2020, months in which the world was already enduring the pandemic, at the age of 23, the Colombian lowered his price by 12 million euros. This figure, despite not being modest compared to other players on the same team, is a significant loss for any player of his age and led to the Colombian cost 48 million euros.
From April to October, 6 months later, Davinson registered another important drop in a short time that took him to 45 million euros, 3 million less than in the fourth month of the same year.
For December and in less than two months, Sánchez lowered his price again: this time by 5 million euros. By January 2021, the Colombian central will have a price of 40 million euros. In short, the Caloto native cost 60 million euros in October 2019 to have a value of 40 million in December of the following year; that is to say, a detriment of 20 million euros in a little over a year.
Melissa Galbraith
Melissa Galbraith is the World News reporter for Globe Live Media. She covers all the major events happening around the World. From Europe to Americas, from Asia to Antarctica, Melissa covers it all. Never miss another Major World Event by bookmarking her author page right here.
Tags: amulet Davinson depreciated League Mourinhos Players Premier Sanchez
Melissa Galbraith December 19, 2020
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text:
Comprehensive Guide to Mergers & Acquisitions, A: Managing the Critical Success Factors Across Every Stage of the M&A Process (Paperback)
By Yaakov Weber, Shlomo Tarba, Christina Oberg
Published Jun 8, 2017 by FT Press.
Dimensions: 7" x 9-1/8"
Leverage today's most complete and practical framework for driving superior business value from mergers and acquisitions -- both domestic and international.
A Comprehensive Guide to Mergers and Acquisitions Management focuses on critical success factors across every stage of the process, including planning, screening, negotiation, due diligence, transition management structures, post-merger integration, leadership and trust, cultural integration, HR practices, control, monitoring, and more. Authored by Yaakov Weber, an international expert in M&A management, strategic alliances, and strategic management, this book's uniquely interdisciplinary approach fully addresses both operational and cultural requirements, supporting participants in every role. Replete with recent examples and cases, it pays special attention to crucial strategic and behavioral linkages between pre- and post-merger stages, explaining why they are so important and how they can be managed to create maximum value. Throughout, Weber provides practical tools, tables, and figures that can help M&A implementers ensure best performance and achieve success where others have failed. As just one example, he provides proven instruments for analyzing cultural differences and the potential for synergy, and translating that potential into reality. For multiple audiences, including board members and top executives who must evaluate the strategic and financial issues associated with M&A; investment bankers, VCs, and other investors who must screen and select acquisitions; managers who must execute business combinations; consultants in strategy, HR, culture, and other areas; and faculty and students in executive education, MBA, and BA-level business programs.
Dark Side of Valuation, The: Valuing Young, Distressed, and Complex Businesses, 3rd Edition
By Aswath Damodaran
Credit Derivatives, Revised Edition: A Primer on Credit Risk, Modeling, and Instruments, 2nd Edition
By George Chacko, Anders Sjöman, Hideto Motohashi, Vincent Dessain
Financial Intelligence for Supply Chain Managers: Understand the Link between Operations and Corporate Financial Performance
By Steven M. Leon


This is the modern era, and technology is advancing at a rapid pace than ever and has become very important because it's used for almost everything. There are several benefits of using advanced technology for almost all types of business practices. However, unfortunately, many business owners tend to avoid adopting technology in their business operations and practices because it keeps changing at a faster pace. It's important for almost every business owners to hire IT professionals in case they are not sure about how to implement modern technology and are not aware of the benefits they can reap from technology.
Technology solutions are always advancing by bounds and leaps and have completely changed the way in which the hotel industry conducts its business. When seen from a marketing perspective, advanced technology allows the hospitality industry to target their customers and prospects better.
Today, the hospitality industry cannot survive without modern technology. Right from booking hotels rooms to making payment and ensuring that guests visit again, all the processes are dependent on IT tools and platforms. The advanced technology keeps the hospitality technology solutions services unique and updated.Look at the following ways technology solutions can help businesses in the hotel industry stay competitive and relevant and save both time and money.
Your guests and customers trust you in order to protect their personal information and data- contact address, phone number, transaction details and more. So, instead of storing the details of the guests in your systems, cloud-based computing is a good option. There are many modern software applications that include backup and cloud storage services. Cloud computing services are becoming the norm and the hotel industry is increasingly replacing their outdated infrastructure with cloud technology.
Nowadays, people are more likely to recommend hotels or resorts that are up-to-date. This is why it's so important for all hoteliers to stay ahead of the technology edge by opting for modern devices into their establishments such as smart room locks and keys, room controls, modern digital signage and other digital equipment. For the hospitality service provider, using the smart devices in this digital era is quite important to remain in the business.
If you are new to the hotel industry, then it's important for you to know that your guests do not like waiting in a long queue. Using smart devices like tablets or other smart devices at the front desk of your hotel can greatly streamline both check-in and check-out process. This will not only improve the customer satisfaction but also save a considerable amount of time to focus more on improving your guest experience.
These were some of the ways that modern technology solutions continue to improve the business operations in the hospitality industry.


Performed at the hall at least once prior to 1966. He is known as "Canada's Polka King.". Delhi was the town of one of Walter Ostanek's first out of town gigs. He also performed many years in a row at the club as a fundraiser for the Catholic Parent Teacher Association (CPTA) of St. Anthony Daniel School, Scotland, ON.


[FIX] Was trying to update via Sparkle on every Flash load. (rentzsch).
@rentzsch screwed up migrating software update hosting from Amazon S3 to github.
If you were automatically updated to ClickToFlash 1.5 or 1.5.1, you'll need manually download and upgrade to 1.5.2 or later yourself. Sorry.
[FIX] Unchecking 'automatically check for updates' only stopped the check on startup, not subsequent ones.
[FIX] Changed 'Open YouTube.com page for this video' to open in the current window in the host app rather than in a new window in Safari.


text:
New Multi-Stakeholder Council To Accelerate Sustainable Purchasing Launching in July
Jennifer Elks
A group of leaders from government, industry, academia, standards organizations and NGOs are joining forces to solve the biggest obstacle to sustainable institutional purchasing: a lack of standardization in how sustainable purchasing is defined, guided, measured and rewarded.
The Sustainable Purchasing Leadership Council will launch with a free, live webcast from Washington, DC on July 23 at 1pm EST.
SPLC's founding members include the cities of San Francisco and Washington DC, California Department of General Services, Office Depot, FedEx, Ecolab, Arizona State and Michigan State universities, UL Environment and FairTradeUSA. Founding partners include the American National Standards Institute, Institute for Supply Management, National Association of State Procurement Officers and the Product Stewardship Institute.
SPLC will help organizations optimize their purchasing for maximum benefit to themselves, society and the planet by:
Convening leaders from across the institutional purchasing marketplace to codify the practice of sustainable purchasing;
Recommending methods for measuring the impacts of an organization's spending;
Identifying existing leadership standards for addressing those impacts; and
Defining a leadership recognition program for sustainability in institutional procurement similar to the U.S. Green Building Council's LEED program.
SPLC has emerged from and builds on four years of work by the Green Products Roundtable, a multi-sector and multi-stakeholder forum convened by the Keystone Center in 2008.
"The average procurement professional facilitates hundreds of dollars in spending for every one dollar spent by the average American consumer," says SPLC's Jason Pearson. "By providing organizations with credible guidance and a leadership recognition program that rewards them for choosing sustainable solutions, we will empower institutional purchasing to lead the transformation of our economy."
Find out more about the July 23 webcast on the SPLC website.
Published Jun 28, 2013 8pm EDT / 5pm PDT / 1am BST / 2am CEST
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Climate Action Plans: How Do We Know If We're Making Real Progress?


Preston J. Skarloken, 90, of Volga, formerly of Estelline, died Thursday, June 7, 2018, at the Brookings hospital.
Funeral services are at 2 p.m. Wednesday at Trinity Lutheran Church, in Estelline. Visitation will be from 5 to 7 p.m. Tuesday at the church. Geise Funeral Home is assisting the family with arrangements.
He was a member of Trinity Lutheran Church in Estelline, a lifetime member of the Brookings VFW, and the American Legion in Estelline. He was also a member of the Sons of Norway. He served as mayor and on the city council for the City of Estelline.
Preston enjoyed traveling and going to auctions and flea markets as a buyer and a seller and would collect pocket knives and caps. He also was a collector of toy tractors and cars. Preston held a special place in his heart for his grandchildren. He was always sure to let them get away with a little more and would make sure they were spoiled.
He is survived by his wife of nearly 62 years, Alyce Skarloken of Volga; two children, Vickie (Kelly) VanderWal of Volga and Keith Skarloken, of Jackson, Michigan; four grandchildren; a sister, Betty Stroschein of Clear Lake; sister-in-law, Betty Skarloken, of Tracy, California, and four nephews.
He was preceded in death by his brother, Rolland and brother-in-law, Maynard Stroschein.


and simple components for reliable 6 wire ISP.
- Allows HW pin control Reset to Start U:0000.
- Valid Baud choices are remembered in a list.
- This allows faster ISP, with user any target frequency.
- If your system uses non-baud Xtals, the FT232H is the most granular device.
New feature: In-System Programming via SPI and via Bootloader.
- Simple UART-SPI bridge examples are provided, for 12cy and 1cy bridge engines.
For software and schematic diagrams see the Examples section.
- Same extended Baud features as Boot feature.
ISPviaSPI allows read & pgm of all Fuses, Signature bytes, EE, Flash.
Improved:    Improved Virtual terminal Baud Simulation, to avoid rounding errors.
to real Silicon timing, for testing baud-timing-critical software like AutoBaud.
New feature: Three Cycle Counters in the View->Registers & Cycles panel.
Can be cleared, or copied to clipboard.
New feature: Turbo51 Assembler able to use the C51ASM compiler.
You can select between ASEM-51 and C51ASM in the Options menu.
C51ASM not included in this package, you need to download it separately.
changed during pause and stop (as well as run), to better interact with Breakpoint and Step modes.
the Atmel Instruction Set Extensions and MAC support.
ADC and DAC, SPI and TWI interfaces, and Flash memory access.
New feature: ERAM available in the External Memory.
New feature: Enable or disable user hints in the Options menu.
New feature: Nano Terminal. This is a real terminal program.
of the hexadecimal and invisible characters.
- Displays and shows/controls the handshake lines signals.
Improved:    All Serial components are more Add/Remove-while-active tolerant.
Improved:    The complete execution module replaced.
Now supports Atmel LP51 family 1 Cycle, and 12/6 cycle opcode sim engines.
instead of added C51ASM include files.
Do not forget to edit the source files!
Fixed bug  : Some failures in the editor.
Fixed bug  : Connecting two pins with Simulator Button and Switch.
Fixed bug  : Program crashes after clean install.
Installer  : Fixed installation directories.
This is the first released version of Turbo51 Studio.


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Ms Perrett, 37, suffered 15 rib fractures as well as 82 areas of external bruising and abrasions. O'Malley-Keyes, 38, was found guilty of murder following a day trial. He was sentenced to life at Winchester Crown Court after a jury rejected his defence that Ms Perrett's injuries were self-inflicted. The pair were seen arguing as they walked between pubs at about BST before Ms Perrett walked away from the group to sit at a the best bournemouth for girlfriend stop. Passers-by later saw her lying on the pavement, apparently due to being drunk, and saw no visible injuries before O'Malley-Keyes approached them to say he was her boyfriend and would look after her.
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In fact I've probably known the Monarch longer than anyone else on board. The pair were seen arguing as they walked between pubs at about BST before Ths Perrett walked away from the group to sit at a bus stop.
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The engine is still doing well although it is 70 years old - the same age as the ship. They lowered the single gangway onto Bournemouth pier and the Monarch butted her tons stern first out into Bournemouth Bay.
During the war he was on contraband work, as was the Monarch herself. So that's how I became one of the hardy passengers bbest the twin funnelled Monarch's first run of the season from Bournemouth to Swanage.
When the Monarch is at sea there are no licensing laws and there is a bar. All the summer small boys and bigger ones too pester him with countless questions.
You can ascertain her age by asking how she refers to clubs in town. He assured me " I've been taking trips on the Monarch for about 40 years.
The ship's radio blared out dance music but the only thing dancing aboard was my stomach. Neighbours told police they heard raised voices from Ms Perrett's flat at about His mother went to the flat and dialled at after her son told her he was "scared" to call an ambulance himself, police said. She can carry passengers and 15 crew.
dor We did the measured mile in 4 minutes 18 seconds, which is more than 12 knots. I escaped to the engine room where, for the second season running, Chief Engineer A D Williams is looking after the Monarch's engines which can develop 1,hp.
Unusual thing about these boilers is their low pressure which is only 30lbs, or less than the pressure in the average car tyre. Great big waves did their best to stop her but they only managed to rock her. Related Topics.
He is taking his thhe, John, aged 11, and daughter, Julia, aged 10 to Norway for a holiday soon. He was sentenced to life at Winchester Crown Court after a jury rejected his defence that Ms Perrett's injuries were self-inflicted.
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Ms Perrett, 37, suffered 15 rib fractures as well as 82 areas of external bruising and abrasions. 'The Opera House' or 'O2.
They burn eight or nine tons of coal between them every day in the season. The followingby the journalist Harry Hamilton, gives a fascinating insight into the first trip of that season from Bournemouth to Swanage aboard the Monarch on Monday 5th May. 'Circo and Elements', or 'The Cage and Zoo'?
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