text:
\section{Introduction}
We study in this paper a finite dimensional gentle algebra $A$ over an algebraic closed field $k$. The notion of gentle algebras was first introduced by Assem and Skowro\'nski in \cite{AS87} in order to classify the iterated tilted algebras of type
$\widetilde{A_n}.$  The gentle algebras are special string algebras which were introduced and studied in \cite{BR87, WW85}.
It has been shown in \cite{BR87} that each indecomposable module over a gentle algebra is either a string module $M(w)$ defined by a string $w$, or
a band module $M(b,n,\phi)$ defined by a band $b$, a vector space $V=k^n$ and $\phi\in \mbox{Aut}(V)$.
However, we are only concerned about indecomposable modules without self-extensions in this paper, and band modules which always have self-extensions will be neglected.

We first give a sufficient and necessary condition to determine when two string modules do not have extensions.
To do this, we say two strings $w, v$ have extensions from $w$ to $v$ if $w$ and $v$  can be connected as a string by an arrow from
$w$ to $v$, or $v$ contains a factor string which is also a substring of $w$ or $w^{-1}$,
see precise details in Definition \ref{def-int}. We first present our first theorem which shows that the extensions
of two strings determine the extensions of the corresponding string modules.

\newtheorem{theorem}{Theorem}
\begin{theorem}Let $w,v$ be two strings over a gentle algebra $A$. Then $$\Ext^1_A(M(w),M(v))\neq 0$$ if and only if $w,v$ do not admit extensions
from $w$ to $v.$
\end{theorem}
Note that a necessary condition on $\Ext^1_A(M(w),M(v))\neq 0$ has been given by Schr\"oer in \cite{S99}, see Proposition \ref{yan}.
 We call a module $M$ exceptional if $\Ext^1_A(M,M)=0$. Note that plenty of exceptional modules are constructed in \cite{C11} by using so-called up-and-down graph. A string $w$ is said to have self-extensions if there exist extensions from $w$ to itself.
As a direct application of the above theorem, we give a characterization of
exceptional indecomposable modules over $A$:
\newtheorem*{corollary}{Corollary}
\begin{corollary}Let $M(w)$ be a string module, then $M(w)$ is exceptional if and only if the string $w$ does not admit self-extensions.
\end{corollary}

We give another important application of Theorem 1. We study gentle algebras $G_\ggz$, introduced in \cite{ABCP10,LF09}, arising from triangulations $\ggz$ of an unpunctured surface $(S,M)$. It has been shown in \cite{ABCP10} that there is a bijection $\gz\longleftrightarrow w_\ggz^\gz$ between the curves which are not in $\ggz$ and the strings over $G_\ggz$. We denote by $M^\gz_\ggz=M(w^\gz_\ggz)$ the corresponding string module, see section \ref{def-string}. Under this correspondence, the string modules induced by the curves without self-intersections are indecomposable exceptional modules \cite{BZ11}.
An indecomposable exceptional module $M$ is said to be exceptionally determined by its dimension vector if for any indecomposable exceptional module $N$ $\dim M=\dim N$ implies $M\cong N.$ We show

\begin{theorem}Let $\gz$ be a curve without self-intersections which is not in $\ggz$, then $M_\ggz^\gz$ is exceptionally determined by its dimension vector.
\end{theorem}

Note that to find
indecomposable modules uniquely determined (up to isomorphism) by their dimension vectors is a classical question in representation theory, see \cite{G72} about the proof of the Gabriel theorem, see also recent works \cite{GP12, AD12}. Different from this classical question, we want to
find the indecomposable  modules which are exceptionally determined by their dimension vector. Therefore, $M_\ggz^\gz$ in Theorem 2 might not be determined by its dimension vector which means, there might exist a non-exceptional indecomposable module $N$ such that $\dim M_\ggz^\gz=\dim N,$ see Example \ref{ex-1}. Moreover, Theorem 2 also does not hold for all indecomposable exceptional modules, i.e., there exist two non-isomorphic indecomposable exceptional modules with the same dimension vectors, see Remark \ref{rem}.

However, the  indecomposable modules which are exceptionally determined by their dimension vectors in Theorem 2 are related to many important subjects such as cluster algebras, cluster categories (see \cite{FZ02, BMRRT06, A09, K10}). In fact, these exceptionally determined indecomposable modules together with triangulation $\ggz$
correspond to all the generators in the related cluster algebras, also correspond to
all the objects without self-extensions in
the cluster category $\mc_{(S,M)}$ of the marked surface $(S,M)$ without punctures which has been studied in \cite{A09, BZ11} (we refer to \cite{K10} for more details).

The paper is organized as follows:
we first introduce in section 2 the definition of extensions of two strings
 and present Theorem 1 whose proof will be postponed to section 4.
As an application of Theorem 1, we study, in section 3, the gentle algebras from unpunctured surfaces and give the proof of Theorem 2.
Section 4 is devoted to the proof of Theoreom 1.

\section{Main result}

\subsection{Strings}\label{string-alg}
Recall from \cite{AS87, BR87, S99} that a finite-dimensional algebra $A$ is a
gentle algebra if there is a quiver $Q=(Q_0,Q_1)$ and an admissible ideal $I$
such that  $A=kQ/I$ and the following conditions hold:
\begin{itemize}
\item[$(G1)$]at each vertex of $Q$ start at most two arrows and stop at most two arrows,
\item[$(G2)$]for each arrow $\alpha$ there is at most one arrow $\beta$ and at most one arrow
$\da$ such that $\alpha\beta \not\in I $ and $\da\alpha\not\in I,$
\item[$(G3)$]$I$ is generated by paths of length 2,
\item[$(G4)$]for each arrow $\alpha$ there is at most one arrow $\beta$ and at most one arrow
$\da$ such that $\alpha\beta\in I $ and $\da\alpha\in I.$
\end{itemize}

Note that an algebra $A=kQ/I$ with $I$
an admissible monomial ideal is
called a string algebra if it satisfies the two conditions $(G1)$ and $(G2)$.

For each arrow $\bz$, $s(\bz)$ (resp. $e(\bz)$) denotes its starting point (resp. its ending
point). We denote by $\bz^{-1}$ the formal inverse of $\bz$ with $s(\bz^{-1})=e(\bz)$ and $e(\bz^{-1})=s(\bz)$.
A word $w=\az_1\az_2\cdots\az_n$ of arrows and their formal inverses is called a string of length $n\geq 1$ if $\az_{i+1}\neq \az_i^{-1}, e(\az_i)=s(\az_{i+1})$ for all $1\leq i\leq n-1$, and no subword nor its inverse is in $I$. We denote the length of $w$ by $l(w)$.
 Hence, a string can be viewed as a walk in $Q:$
$$w: e_1 \frac{~~~\az_1~}{}e_2 \frac{~~~\az_2~}{}\cdots e_{n-1} \frac{\az_{n-1}}{}e_{n}\frac{~~~\az_n~}{}e_{n+1}$$
where $e_i\in Q_0$ are vertices of $Q$ and $\alpha_i$ are arrows in either direction. For each vertex $e_i,$ we define
two strings $1_{e^{+1}_i}$, $1_{e^{-1}_i}$ of length 0 with $e(1_{e^t_i})=s(1_{e^t_i})=e_i$ and
$1^-_{e^t_i}=1_{e^{-t}_i}$ for $t\in\{-1,+1\}.$

We denote
by $\mathcal{S}$ the set of all strings over $A$.
A band $b=\az_1\az_2\cdots\az_{n-1}\az_n$ is defined to be a
string $b$ with $s(\az_1)=e(\az_n)$ such that each power $b^m$ is a string, but $b$ itself is not a proper
power of any string.

Recall from \cite{BR87} that each string $w$ defines a unique string
module $M(w)$, each band $b$ yields a family of band modules
$M(b,n,\phi)$ with $n\geq 1$ and $\phi\in \mbox{Aut}(k^n).$  We
refer to \cite{BR87} for more definitions on string modules and band
modules.
\begin{thm}[\cite{BR87}]\label{indec}The indecomposable modules over a string algebra are either string modules or band modules. Moreover,
$\Ext^1_A(M,M)\neq 0$ for each band module $M$.
\end{thm}
\subsection{Maps between string modules}
We present in this subsection a nice basis constructed by Crawley-Boevey for the Hom-space of two string modules \cite{C-B89,S99}.

For a string $w\in\mathcal{S},$ define
${\mathcal{S}}_w=\{(D,E,F)\mid D,E,F\in{\mathcal{S}}, w=DEF\},$
and call $(D,E,F)$ a factor string of $w$ if
 \begin{itemize}
  \item[$(F1)$] $l(D)=0$ or $D=\az_1\az_2\cdots\az_n$ with $\az^{-1}_n\in Q_1,$
  \item[$(F2)$] $l(F)=0$ or $F=\bz_1\bz_2\cdots\bz_m$ with $\bz_1\in Q_1.$
\end{itemize}
Dually, $(D,E,F)$ is said to be a substring of $w$ if the following hold:
 \begin{itemize}
 \item[$(S1)$]  $l(D)=0$ or $D=\az_1\az_2\cdots\az_n$ with $\az_n\in Q_1,$
  \item[$(S1)$]  $l(F)=0$ or $F=\bz_1\az_2\cdots\bz_m$ with $\bz_1^{-1}\in Q_1.$
\end{itemize}
Denote by $\ff(w)$ and $\fs(w)$ the set of all factor strings and substrings of $w$ respectively.
Let $w$ and $v$ be two strings over $A$, a pair $(D, E, F)\times (D', E', F')\in \ff(w)\times\fs(v)$ is said to be an admissible pair (or ad-pair)
if $E=E'$ or $E^{-1}=E'.$ It is easy to understand the ad-pair if one has the following picture in mind.

\medskip

\begin{center}
\includegraphics[height=1.5in]{0.jpg}\label{fig}
\end{center}

We call an ad-pair $p=(D,E,F)\times (D',E',F')$ one-sided if one of the following two conditions holds,
\begin{itemize}
  \item[$(O1)$] $l(D)=l(D')=0$ or $l(F)=l(F')=0$ when $E=E'$.
  \item[$(O2)$]  $l(D)=l(F')=0$ or $l(E)=l(F')=0$ when $E^{-1}=E'$.
\end{itemize}
An ad-pair is said to be two-sided if it is not one-sided.

Recall that each ad-pair $p\in \ff(w)\times\fs(v)$ as above yields a canonical homomorphism
$f_p: M(w)\longrightarrow M(v)$ in $\Hom_A(M(w), M(v))$ by identifying the factor module $M(E)$ of $M(w)$ with
the submodule $M(E')$ of $M(v)$. A basis of Hom-space of two string modules can be described as follows:
\begin{thm}[\cite{C-B89}]\label{C-B89} Consider two strings $w$ and $v$ over $A$. Then $\{f_p\mid p\in \ff(w)\times\fs(v)\}$ is a basis of the $\mbox{Hom}_A(M(w),M(v))$.
\end{thm}
\subsection{Extension of two strings}
We present Theorem 1 in this subsection by first introducing the following important definition:
\begin{defn}\label{def-int}
We say two strings $w,v$ have extensions from $w$ to $v$ if one of the following conditions holds
\begin{itemize}
  \item[$(E1)$]There exists $\az\in Q_1$ such that $w\az v$ or $w\az v^{-1}$ is a string.
  \item[$(E2)$]There exists $\bz\in Q_1$ such that $w^{-1}\bz v$ or $w^{-1}\bz v^{-1}$ is a string.
  \item[$(E3)$]$w, v$ admit a two-sided ad-pair in $\ff(v)\times\fs(w)$.
\end{itemize}
\end{defn} A string $w$ is said to have self-extensions if $w=v$ in the above definition.
\begin{example}Consider a gentle algebra $A=kQ/I$ with $Q$ given as follows
\begin{center}
\includegraphics[height=1.5in]{16.jpg}\label{fig}
\end{center}
and $I=<\az^2,\bz\varepsilon,\varepsilon\theta>.$
Then $w=\bz\az^{-1}\bz^{-1}$, $v=\varepsilon^{-1}\az\varepsilon$ have extension from $w$ to $v$ by $(E3).$
In addition, both $\bz$ and $\varepsilon$ have self-extension by $(E1)$ or $(E2)$. However, $\theta$, $\varepsilon$ do not have
extensions from $\varepsilon$ to $\theta,$ note that $\varepsilon$ and $\theta$ only admit an one-sided
ad-pair in $\ff(\theta)\times\fs(\varepsilon).$

\end{example}

Now we state our main theorem whose proof is given in section \ref{pf}
\begin{thm}\label{main-thm}Let $w,v$ be two strings over a gentle algebra $A$. Then $\Ext^1_A(M(w),M(v))\neq 0$ if and only if $w,v$  admit extensions
from $w$ to $v.$
\end{thm}

The following corollary follows directly from the above theorem by taking $v=w.$
\begin{cor}\label{cor-self-ext} Let $w\in\s$, then $M(w)$ is exceptional if and only $w$ does not have self-extensions. That is,
the following conditions hold
\begin{itemize}
  \item[$(1)$]there does not exist $\az\in Q_0$ such that $w\az w\in \s$ or $w\az w^{-1}\in \s,$
  \item[$(2)$]there does not exist $\bz\in Q_0$ such that $w\bz^{-1} w\in \s$ or $w\bz^{-1} w^{-1}\in \s,$
  \item[$(3)$]$w$ only admits one-sided ad-pairs in $\ff(w)\times\fs(w).$
\end{itemize}
\end{cor}

\begin{rem}
  The Theorem \ref{main-thm} does not hold for string algebras as the following example shows. Let $Q$ be the quiver
  $$\circ\overset{\az}{\lra}\circ\overset{\bz}{\lra}\circ\overset{\tz}{\lra}\circ$$
with $I=<\az\bz\tz>.$ Then $A=kQ/I$ is a string algebra and $w=\az\bz, v=\bz\tz$ have extension from $w$ to $v$.
However, $\Ext^1_A(M(w),M(v))=0$ since $M(w)$ is projective.
\end{rem}

\section{An application}
In this section, we study gentle algebras arising from triangulations of a marked surface without punctures. By applying the results in the previous section, we prove the Theorem 2 in the introduction.

\subsection{Triangulation of a marked surface without punctures}\label{notation}
Consider a compact connected oriented 2-dimensional bordered  Riemann surface $S$ and a finite set of marked points $M$ lying on the boundary $\partial S$ of $S$ with at least one marked point on each boundary component.
The condition $M \subset \partial S$ means that we do not allow the marked surface $(S,M)$ to have punctures.

By a curve $\gz$ in $(S,M)$, we mean a continuous function $\gz:[0,1]\rightarrow S$ such that $\gz(0), \gz(1)\in M$ and $\gz(t)\notin M$ for $0<t<1$. An arc is a curve $\gz$ in $(S,M)$ such that $\gz\mid_{(0,1)}$ is injective. We always consider non-contractible curves up to homotopy, and for any collection of curves we implicitly assume that their mutual intersections are minimal possible in their respective homotopy classes. For two curves $\gz',\gz$ in $(S,M)$ we denote by $\Int(\gz',\gz)$ the minimal intersection number of two representatives of the homotopic classes of $\gz'$ and $\gz$ (the intersections at the endpoints do not count).
A triangulation of $(S,M)$ is a maximal
collection $\ggz$ of arcs that do not intersect except at their endpoints.

Let $\ggz=\{\t_1,\t_2,\ldots,\t_n\}$ be a triangulation of $(S,M)$ and $\gz\not\in\ggz$ be a curve  with $d=\sum_{\t\in \ggz}\Int(\t,\gz)$ which is allowed to have self-intersections.
We fix an orientation for the curve $\gz$ and denote $p_0=\gz(0)\in M$ and $p_{d+1}=\gz(1)\in M$. Along its orientation, let $\t_{i_1}, \t_{i_2},\ldots, \t_{i_d}$ be the internal arcs of $\ggz$ that intersect $\gz$ at $p_1=\gz(r_1),\ldots, p_d=\gz(r_d)$ in the fixed orientation of $\gz$, where $0<r_1<r_2<\cdots <r_d<1$. See the following figure.

\begin{center}
\includegraphics[height=1.8in]{1-1.jpg}

Figure I.
\end{center}

We denote the restrictions of $\gz$ by $\gz_0={\gz\mid}_{(0,r_1)},$ $\gz'={\gz\mid}_{[r_1,r_d]}$ and $\gz_d={\gz\mid}_{(r_d,1)}.$
Along its way, the curve $\gz$ is passing through (not necessarily distinct) triangles $ \Delta^\gz_0, \Delta^\gz_1, \ldots, \Delta^\gz_d$.

If $\gz$ is an arc which is not in $\ggz$ and $\t^n_j,{\t^n_k}, {\t^n_l}$ are the three arcs of $\Delta^\gz_n$. If  $\Delta^\gz_n\neq\Delta^\gz_d$ or $\Delta^\gz_0$,  then $\Delta^\gz_n\cap\gz$  consists of segments of $\gz$ as follows:

\begin{center}
\includegraphics[height=1.5in]{1-3.jpg}
\end{center}

Note that $\gz$ can cross $\Delta^\gz_n$ many times.
It is easy to see that the sum of intersection numbers of any two arcs with $\gz$ is not less than that of $\gz$ with the third one,
and we have the following:
$$
\left\{
  \begin{array}{ll}
   \Int(\gz,\t^n_k)+\Int(\gz,\t^n_j)\geq \Int(\gz,\t^n_l), & \\
    \Int(\gz,\t^n_k)+\Int(\gz,\t^n_j)+\Int(\gz,\t^n_l)\in 2\mathbb{Z}.\quad\quad\quad\quad\quad\quad & \hbox{(*)}
  \end{array}
\right.
$$

However, if $n=0, d$, then $\Delta^\gz_n\cap\gz$ can be described as follows in two cases:
\begin{center}
\includegraphics[height=1.5in]{1-4.jpg}
\end{center}
If $\Delta^\gz_0\neq\Delta^\gz_d,$ then $j,k,l$ can be ordered with $\t^n_l=\t_{i_1}$ or $\t^n_l=\t_{i_d}$ such that
$$\left\{
    \begin{array}{ll}
      \Int(\gz,\t^n_k)+\Int(\gz,\t^n_j)+1=\Int(\gz,\t^n_l), &  \\
     \Int(\gz,\t^n_k)+\Int(\gz,\t^n_j)+\Int(\gz,\t^n_l)\in 2{\mathbb{Z}}+1.\quad\quad\quad\quad\quad & \hbox{(**)}
    \end{array}
  \right.
$$

If $\Delta^\gz_0=\Delta^\gz_d,$ then $j,k,l$ can be ordered with $\t^n_l=\t_{i_1}=\t_{i_d}$ such that
$$\left\{
    \begin{array}{ll}
      \Int(\gz,\t^n_k)+\Int(\gz,\t^n_j)+2=\Int(\gz,\t^n_l), &  \\
     \Int(\gz,\t^n_k)+\Int(\gz,\t^n_j)+\Int(\gz,\t^n_l)\in 2\mathbb{Z}.\quad\quad\quad\quad\quad \quad\quad & \hbox{(***)}
    \end{array}
  \right.
$$
In fact, each arc $\gz$ can also be uniquely recovered from its intersection with each arc in $\ggz$:
\begin{thm}[\cite{M83, T10}]\label{mocher} An arc is uniquely determined by the number of intersections with each
arc of the triangulation.
\end{thm}

\subsection{Gentle algebras arising from $(S,M)$}\label{def-string}
Recall from \cite{DWZ08, LF09, ABCP10} that each triangulation $\ggz$ of $(S,M)$ yields
a quiver with potential $(Q_\ggz,W_\ggz)$:
\begin{itemize}
\item[$(1)$] $Q_{\ggz}=(Q_0,Q_1)$ where the set of vertices $Q_0$ is given by the internal arcs of $\ggz$, and the set of arrows $Q_1$ is defined as follows: Whenever there is a triangle $\vartriangle$ in $\ggz$ containing two
internal arcs $a$ and $b$, then there is an arrow $\rho:a \ra b$ in $Q_1$ if $a$ is a predecessor
of $b$ with respect to clockwise orientation at the joint vertex of $a$ and $b$ in $\vartriangle.$
\bigskip

\item[$(2)$]Every internal triangle $\vartriangle$ in $\ggz$ gives rise to an oriented cycle $\alpha_\vartriangle \beta_\vartriangle\gz_\vartriangle$ in
$Q$, unique up to cyclic permutation of the factors $\alpha_\vartriangle, \beta_\vartriangle, \gz_\vartriangle$. We define
$$W_\ggz =\displaystyle\sum_\vartriangle\alpha_\vartriangle \beta_\vartriangle\gz_\vartriangle $$
where the sum runs over all internal triangles $\vartriangle$ of $\ggz$.
\end{itemize}

From \cite{ABCP10} we know that  the Jacobian algebra $G_\ggz$ of the quiver with potential $(Q_\ggz, W_\ggz)$ is a finite-dimensional gentle algebra, and there is a correspondence
$\gz\longleftrightarrow w^\gz_\ggz$ between curves which are not in $\ggz$ and strings over $G_\ggz:$ For each curve $\gz$ which is not in $\ggz$ with $d=\sum_{\t\in \ggz}I(\t,\gz),$ see Figure I as an example, we obtain a string $w^\gz_\ggz$ in $G_\ggz$:
$$w^\gz_\ggz : \t_{i_1} \frac{~~~\az_1~}{}\t_{i_2} \frac{~~~\az_2~}{}\cdots \t_{i_{d-2}} \frac{\az_{d-2}}{}\t_{i_{d-1}}\frac{~~~\az_{d-1}~}{}\t_{i_d}.$$
We denote by $M_\ggz^\gz$ the corresponding string module $M(w^\gz_\ggz)$ over $G_\ggz.$

We call a curve $\gz$  $\ggz-$rigid if
$\Int(\gz,\gz)\neq 0$ and $\Ext^1_{G_\ggz}(M_\ggz^\gz, M_\ggz^\gz)=0.$ Note that $\ggz-$rigid curves are not arcs by definition.
\begin{example}\label{ex} Consider a triangulation $\ggz$ of an annulus with one marked point on one boundary, two on another:
  \begin{center}
\includegraphics[height=1.5in]{17.jpg}
\end{center}

Then the associated quiver $Q_\ggz$ is as follows:
\begin{center}
\includegraphics[height=1.3in]{15.jpg}
\end{center}
and $W_\ggz=\az\bz\zeta.$ Let $\gz$ be a curve with self-intersection in the surface as in the above figure, by definition $w^\gz_\ggz=\bz^{-1}\tz$ does not have self-extensions and it is a $\ggz-$rigid curve.
\end{example}

By using Corollary \ref{cor-self-ext}, we give in the following a characterization of indecomposable exceptional modules by curves in $(S,M).$
\begin{lem}If the string $w^\gz_\ggz$ has self-extensions, then $\Int(\gz,\gz)\neq 0.$
\end{lem}
\begin{pf} It suffices to explain Definition \ref{def-int} by the curves in $(S,M).$ Note that there do not exist
loops in $Q_\ggz$.
If there exists $\az\in Q_0$ such that $w^\gz_{\ggz}\az w^\gz_{\ggz}\in \s$, then $\gz$ can be described as follows:
\begin{center}
\includegraphics[height=1.5in]{11.jpg}
\end{center}
If there exists $\bz\in Q_0$ such that $ w^\gz_{\ggz}\bz^{-1}  w^\gz_{\ggz}\in \s$,  then $\gz$ can be described similarly as above.

Assume $ w^\gz_{\ggz}$ admits a two-sided ad-pairs
$$(D,E,F)\times(D',E',F')\in\ff( w^\gz_{\ggz})\times\fs( w^\gz_{\ggz}).$$
Then we can characterize $\gz$ as follows when  $E=E'$  or $E^{-1}=E'$ respectively:
\begin{center}
\includegraphics[height=2.5in]{12.jpg}

Figure II
\end{center}
\end{pf}

\begin{cor}[\cite{BZ11}]Let $\gz$ be an arc which is not in $\ggz$, then
$$\Ext^1_{G_\ggz}(M_\ggz^\gz,M_\ggz^\gz)=0$$
for any triangulation $\ggz$ of $(S,M).$
\end{cor}
\begin{pf} Assume that $\ggz$ is a triangulation of $(S,M)$ such that
$\Ext^1_{G_\ggz}(M_\ggz^\gz,M_\ggz^\gz)\neq 0,$ then $w_\ggz^\gz$ has self-extensions by Corollary \ref{cor-self-ext}.
Therefore, $\Int(\gz,\gz)\neq 0$ by the above Lemma which contradicts to the fact that $\gz$ is an arc.
\end{pf}

Combining Theorem \ref{indec} together with the above corollary, indecomposable exceptional modules over $G_\ggz$
are either of the form $M_\ggz^\gz$ with $\gz$ an arc which is not in $\ggz$, or of the form $M_\ggz^\da$ with $\da$ a $\ggz-$rigid curve.

Note that the above corollary does not hold for a $\ggz-$rigid curve $\gz$, that is, there always exists a triangulation $\ggz'$ of $(S,M)$ such that
$\Ext^1_{G_{\ggz'}}(M_{\ggz'}^\gz,M_{\ggz'}^\gz)\neq 0,$ see \cite{BZ11}.
However, we can still find some property for a $\ggz-$rigid curve in terms of Corollary \ref{cor-self-ext}.

Let $\da$ be a $\ggz-$rigid curve, then $\Int(\da,\da)\neq 0$ and $\Ext_{G_\ggz}^1(M^\da_\ggz,M^\da_\ggz)=0.$  We substitute $\da$ for $\gz$ and keep the same notation as in section \ref{notation},
Corollary \ref{cor-self-ext} implies that
\begin{itemize}
  \item[$(\ggz1)$]either $\triangle^\da_0\neq\triangle^\da_n,$ or $\triangle^\da_0=\triangle^\da_n$ with $s(\da)=e(\da).$ This is equivalent to
  the conditions $(1)$ and $(2)$ in Corollary \ref{cor-self-ext},
  \item[$(\ggz2)$]$\da'=\da\mid_{[r_1,r_d]}$ is injective and $\da'$ intersects $\da_0$ or $\da_d$ which means that $w^\ggz_\da$ does not admits two-sided ad-pairs.
\end{itemize}
See the following figure for example:
\begin{center}
\includegraphics[height=2in]{13.jpg}
\end{center}

Roughly speaking, $\da$ only intersects itself with $\da_0$ or with $\da_d.$ However, its restriction $\da'$ is injective. We can do the same discussion
as in section \ref{notation}: Let $\t^n_i, \t^n_j, \t^n_k$ be three arcs of $\Delta^\da_n,$ then  we have similarly as in $(*)$ that
$$\left\{
    \begin{array}{ll}
      \Int(\da,\t^n_k)+\Int(\da,\t^n_j)\geq \Int(\da,\t^n_l),&  \\
      \Int(\da,\t^n_k)+\Int(\da,\t^n_j)+\Int(\da,\t^n_l)\in 2\mathbb{Z}. &
    \end{array}
  \right.
$$
when $\Delta^\da_n\neq\Delta^\da_d$ or $\Delta^\da_0.$
Note that $\da'$ might only intersect one of $\da_0$ and $\da_d$, see the above picture for example. Assume $\da'$ intersects $\da_a$ with $a=0$ or $d$, see the following figure
\begin{center}\label{fig1}
\includegraphics[height=1.5in]{1-5.jpg}
\end{center}
If $\Delta^\da_0\neq\Delta^\da_d$, then $\Int(\da,\t^a_i)\neq 0$ for $i=j,k,l.$ And
$$\left\{
    \begin{array}{ll}
      \Int(\da,\t^a_k)+\Int(\da,\t^a_j)\geq\Int(\da,\t^a_l)+1, &  \\
      \Int(\da,\t^a_k)+\Int(\da,\t^a_j)+\Int(\da,\t^a_l)\in 2{\mathbb{Z}}+1.\quad\quad\quad\quad & \hbox{(****)}
    \end{array}
  \right.
$$

If $\Delta^\da_0=\Delta^\da_d,$ then $\Int(\da,\t^a_i)\neq 0$ for $i=j,k,l.$ And
$$\left\{\begin{array}{ll}
     \Int(\da,\t^a_k)+\Int(\da,\t^a_j)\geq\Int(\da,\t^a_l), &  \\
     \Int(\da,\t^a_k)+\Int(\da,\t^a_j)+\Int(\da,\t^a_l)\in 2{\mathbb{Z}}. \quad\quad\quad\quad\quad& \hbox{(*****)}
    \end{array}
  \right.$$
By the above observation, we prove in the following the Theorem 2 in the introduction.

\medskip

\emph{{Proof of Theorem 2:}} Let $\ggz=\{\t_1,\ldots,\t_n \}$ be a triangulation of $(S,M)$ and $N$ be an indecomposable exceptional module with
$$\dim M_\ggz^\gz=\dim N.$$
By Theorem \ref{indec}, we can assume that $N=M^\da_\ggz$ with $\da$  either an arc which is not in $\ggz$ or a $\ggz-$rigid curve.

By definition,
$$(\Int(\gz,\t))_{\t\in\ggz}=\dim M_\ggz^\gz=\dim M_{\ggz}^\da=(\Int(\da,\t))_{\t\in\ggz}$$
and $\Int(\da,\t)=\Int(\gz,\t)$
for each $\t\in\ggz.$ Therefore, if $\da$ is an arc which is not in $\ggz$,
then we get the proof by Theorem \ref{mocher}.

We assume now that $\da$ is a $\ggz-$rigid curve with $d=\sum_{\t\in \ggz}\Int(\t,\gz)=\sum_{\t\in \ggz}\Int(\t,\da)$. We are going to prove the theorem by
showing that the dimension vector of $M^\da_\ggz$ (induced by a $\ggz-$rigid curve) never coincides with that of $M^\gz_\ggz$ (induced by an arc which is not in $\ggz$).

Without loss of generality, we suppose that the restriction $\da'$ of $\da$ intersects $\da_0$. Consider $\Delta^\da_0$ with three arcs $\t^0_j,{\t^0_k}, {\t^0_l},$ then $\Int(\da,\t^0_i)\neq 0$ for $i=j,k,l$ by $(****).$ We have the following two cases:
  \begin{itemize}
    \item[(I)]If $\Delta^\da_0\neq \Delta^\da_d$, one has
$$\left\{
  \begin{array}{ll}
   \Int(\da,\t^0_k)+\Int(\da,\t^0_j)\geq\Int(\da,\t^0_l)+1, & \\
   \Int(\da,\t^0_k)+\Int(\da,\t^0_j)+\Int(\da,\t^0_l)\in 2{\mathbb{Z}}+1, &
  \end{array}
\right.$$
Therefore, there must exist a triangle $\Delta^\gz_m=\Delta^\da_0$  with the same three arcs $\t^0_j,{\t^0_k}, {\t^0_l}$ satisfying $\Int (\gz, \t^0_i)\neq 0$ for $i=j,k,l,$ and
\begin{itemize}
  \item[$\bullet$]$\Int(\gz,\t^0_k)+\Int(\gz,\t^0_j)\geq\Int(\gz,\t^0_l)+1$ which contradicts to $(**),$ since $(**)$ implies that there exists
$\{\t'_j,\t'_k,\t'_l\}=\{\t^0_j,\t^0_k,\t^0_l\}$ such that
$$\Int(\gz,\t'_k)+\Int(\gz,\t'_j)<\Int(\gz,\t'_l).$$
  \item[$\bullet$]$\Int(\gz,\t^0_k)+\Int(\gz,\t^0_j)+\Int(\gz,\t^0_l)\in 2{\mathbb{Z}}+1$ which contradicts to $(*),(***).$
\end{itemize}
\item[(II)]If $\Delta^\da_0=\Delta^\da_d$, then we have by $(*****)$ that, for each $0\leq n\leq d$
$$\left\{
    \begin{array}{ll}
     \Int(\da,\t^n_k)+\Int(\da,\t^n_j)\geq\Int(\da,\t^n_l), & \\
      \Int(\da,\t^n_k)+\Int(\da,\t^n_j)+\Int(\da,\t^n_l)\in 2{\mathbb{Z}}, &
    \end{array}
  \right.$$
where $\t^n_j, \t^n_k, \t^n_l$ are three arcs of triangle $\Delta^\da_n.$ Therefore, we also have in $\Delta^\gz_0$ with three arcs $\t'_k,\t'_j,\t'_l$ that
$$\left\{
    \begin{array}{ll}
     \Int(\gz,\t'_k)+\Int(\gz,\t'_j)\geq\Int(\gz,\t'_l), & \\
     \Int(\gz,\t'_k)+\Int(\gz,\t'_j)+\Int(\gz,\t'_l)\in 2{\mathbb{Z}}.&
    \end{array}
  \right.$$
We consider the following two subcases:
   \begin{itemize}
     \item[(II.1)]If $\Delta^\gz_0\neq\Delta^\gz_d,$ it contradicts to $(**).$

     \item[(II.2)]If $\Delta^\gz_0=\Delta^\gz_d,$ it contradicts to $(***)$ which implies that $j,k,l$ can be ordered such that
$$\Int(\gz,\t'_k)+\Int(\gz,\t'_j)<\Int(\gz,\t'_l).$$
   \end{itemize}
\end{itemize}
Therefore, the dimension vector of $M^\da_\ggz$ is always different from that of $M^\gz_\ggz$ which
completes the proof. \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad $\Box$

\medskip

Note that in the proof of the above theorem, we do need that $N$ is an exceptional module. If not, the Theorem 2 does not hold, see the following example:
\begin{example}\label{ex-1}Consider the following annulus with a triangulation $\ggz$:
\begin{center}
\includegraphics[height=2in]{18.jpg}
\end{center}
where $\gz$ is an arc and $\da$ is a curve with self-intersection. It is easy to find that $M^\da_\ggz$ has self-extensions by Theorem \ref{main-thm}. However,
$\dim M^\da_\ggz=\dim M^\gz_\ggz.$
\end{example}
\begin{rem}\label{rem}The above theorem does not hold in general for any indecomposable exceptional module.
Reconsider Example \ref{ex}, let $\da$ be a $\ggz-$rigid curve as follows
\begin{center}
\includegraphics[height=1.5in]{14.jpg}
\end{center}
it is easy to find that $\dim M_\ggz^\gz=\dim M_{\ggz}^\da$ and $\Ext^1_{G_\ggz}(M_\ggz^\gz,M_\ggz^\gz)=0=\Ext^1_{G_\ggz}(M_{\ggz}^\da,M_{\ggz}^\da).$ However, $\gz$ is not homotopic to $\da$ which implies that $M^\gz_\ggz\ncong N^\da_\ggz.$
\end{rem}

\section{Proof of the Theorem \ref{main-thm}}\label{pf}

We prove in this section the Theorem \ref{main-thm} by Auslander-Reiten formula in a combinatorial way. Let first recall from \cite{BR87} the Auslander-Reiten theory for a gentle algebra.
\subsection{Auslander-Reiten theory over gentle algebras}
 Let $A=kQ/I$ be a finite-dimensional gentle algebra with $Q=(Q_0,Q_1)$ and $\mathcal{S}$ the set of all strings over $A$.
 Similarly as in \cite{BR87,S99}, one can define
two maps from $Q_1$ to $\{1,-1\}$ to deal with the concatenation of two strings, especially for the strings of length zero.
However, in this paper the strings of length zero can always be chosen such that the concatenation is well-defined and we only use $1_{e_i}$ to denote
the chosen one, i.e., either $1_{e^{-1}_i}$ or $1_{e^{+1}_i}.$

As for a string $w=\az_1\az_2\cdots\az_n$, we denote by $e(w)=e(\az_n),$ and $s(w)=s(\az_1).$ We say $w$ starts (or ends)  on a peak if there is no arrow $\az \in Q_1$ with $\az w \in \ms$ (or $ w\az^{-1} \in \ms$); likewise, a string $w$ starts (or ends) in a deap if there is no arrow $\bz \in Q_1$ with $\bz^{-1}w \in \ms$ (or $ w\bz \in \ms$).

A string $w=\az_1\az_2\cdots\az_n$ with all $\az_i \in Q_1$ is called direct string, and a string of the form $w^{-1}$ where $w$ is a direct string is called inverse string.
Strings of length zero are both direct and inverse. For each arrow $\az \in Q_1$, let $N_\az= {V_\az}\az U_\az$ be the unique string such that $U_\az$ and $V_\az$ are inverse strings and $N_\az$ starts in a deep and ends on a peak (see the following figure).
\begin{center}
\includegraphics[height=.25in]{3-1.jpg}
\end{center}
If the string $w$ does not start on a peak, we define $_hw=V_\az\az w$ and say that $_hw$ is obtained from $w$ by adding a hook on the starting point $s(w)$. Dually, if $w$ does not end on a peak , we define $w_h=w\bz^{-1}{V_\bz}^{-1}$ and say that $w_h$ is obtained from $w$ by adding a hook on the ending point $e(w)$ (see the following figure).
\begin{center}
\includegraphics[height=1in]{10.jpg}
\end{center}
Suppose now that the string $w$ starts on a peak. If $w$ is not a direct string, we can write $w=\az_1\cdots\az_s\az^{-1} {_cw}=U_\az^{-1}\az^{-1} {_cw}$ for some $\az\in Q_1$ and $s\geq 0$. We say in this case that $_cw$ is obtained from $w$ by deleting a cohook on $s(w)$. If $w$ is a direct string, we define $_cw=0$.
Dually, assume that $w$ ends on a peak. Then, if $w$ is not an inverse string, we can write $w=w_c\bz\bz_1^{-1}\cdots\bz_t^{-1}=w_c\bz U_\bz$ for some $\bz\in Q_1$ and $t\geq 0$. We say that $w_c$ is obtained from $w$ by deleting a cohook on $e(w)$, and if $w$ is an inverse string, we define $w_c=0$ (see the following figure).

\begin{center}
\includegraphics[height=1.2in]{8.jpg}
\end{center}

The following theorem summarizes the results from  \cite{BR87} concerning AR-sequences between string modules:

\begin{thm}[\cite{BR87}]\label{BR87} For  a string algebra $A$, let $w$ be a string such that  $M(w)$ is not an injective $A-$module. Then the AR-sequence starting in $M(w)$ is given
\begin{itemize}
\item[(1)] if $w$ neither starts nor ends on a peak by
 $$0\lra M(w) \lra M(w_h)\oplus M(_hw) \lra M(_hw_h) \lra 0,$$

\item[(2)] if $w$ does not start but ends on a peak by
$$0\lra M(w) \lra M(w_h)\oplus M(_cw) \lra M(_cw_h) \lra 0,$$

\item[(3)] if $w$ starts but does not end on a peak by
$$0\lra M(w) \lra M(w_c)\oplus M(_hw) \lra M(_hw_c) \lra 0,$$

\item[(4)] if $w$ both starts and ends on a peak by
$$0\lra M(w) \lra M(w_c)\oplus M(_cw) \lra M(_cw_c) \lra 0.$$
\end{itemize}
\end{thm}
\subsection{Proof of Theorem \ref{main-thm}}
We first consider the special case: $M(v)$ is an injective module or $M(w)$ is an projective module.
\begin{lem}\label{lem-inj} Let $w,v$ be two strings over $A$,
if either $M(v)$ is injective or $M(w)$ is projective, then $w,v$ do not have extensions from $w$ to $v$
\end{lem}
\begin{pf}We only consider the case that $M(v)$ is injective which means there does not exist an arrow $\az$ or $\bz$ such that $\az v$ or $v\bz^{-1}$ is a string. Hence
$(E1)$ and $(E2)$ do not hold for any $w$ with $v.$

Assume $p=(D,E,F)\times (D',E',F')\in\ff(v)\times\fs(w)$, then either $l(D)=0$ or $l(F)=0$ by property of injective modules. Without loss of generality,
we let $l(D)=0$ and consider the following two cases:
\begin{itemize}
\item[$(1)$] If $E=E'$, then $l(D')=0.$ Otherwise, there exists an arrow $\az$ such that $\az E'=\az E$ is a string by definition of substrings. It contradicts to
the fact that $v$ starts on a peak.
\item[$(2)$] If $E^{-1}=E'$, then $l(F')=0$. Otherwise there exists an arrow $\bz$ such that $E'\bz^{-1}=(\bz E)^{-1}$ is a string by definition of substrings. It contradicts again to
the fact that $v$ starts on a peak.
\end{itemize}
Therefore any $p\in\ff(v)\times\fs(w)$ is an one-sided ad-pair. This completes the proof.
\end{pf}

When $w,v$ admit a two-sided ad-pair in $\ff(v)\times\fs(w),$ Schr\"oer constructed in Proposition 4.9 of \cite{S99} a non-split exact sequence
from $M(v)$ to $M(w)$ which gives the following proposition:

\begin{prop}[\cite{S99}]\label{yan} If $w, v$ admit a two-sided ad-pair in $\ff(v)\times\fs(w)$, then
$$\Ext^1_A(M(w),M(v))\neq 0.$$
\end{prop}
The following corollary comes directly from Definition \ref{def-int} and the above proposition.
\begin{cor}\label{cor-imp}Let $w, v$ be two strings which have extensions from $w$ to $v,$ then
$$\Ext^1_A(M(w),M(v))\neq 0.$$
\end{cor}
\begin{pf} In case $(E1)$, let $u=w\az v$ (or $u=w\az v^{-1}$) if $w\az v$ (or $w\az v^{-1}$) is a string.
Then there is a non-split exact sequence
$$0\lra M(v)\lra M(u)\lra M(w)\lra 0$$
which implies that $\Ext^1_A(M(w),M(v))\neq 0.$
The case $(E2)$ is similar to the case $(E1)$, and the case $(E3)$ follows from Proposition \ref{yan}.
\end{pf}

To prove the main theorem, we need to find out that the morphisms induced by some ad-pairs factor through projective modules.

\begin{lem}\label{lem-important}Let $w, v$ be two strings over $A$ and suppose $v=V_\az \az v_0$ for some $\az\in Q_1, v_0\in {\mathcal{S}}.$ If $p=(D,E,F)\times (D',E',F')\in\ff(v)\times\fs(w)$ such that
$DE=V_\az$ with $l(E)>0$. Then $f_p$ factors through a projective module if one of the following conditions holds
\begin{itemize}
  \item[(1)]$E=E'$ and $l(F')>0.$
  \item[(2)]$E^{-1}=E'$ and $l(D')>0.$
\end{itemize}
\end{lem}
\begin{pf} We only prove $(1)$ since $(2)$ follows from $(1)$ if we consider $w^{-1}$ instead of $w.$

Let $V_\az=\az_n^{-1}\cdots\az^{-1}_2\az^{-1}_1$ with $n\geq 1$ since $l(V_\az)\geq l(E)>0.$
Suppose $D=\az^{-1}_n\az^{-1}_{n-1}\cdots\az^{-1}_{j+1}$, $E=\az^{-1}_{j}\cdots\az^{-1}_2\az^{-1}_1,$ where $1\leq j\leq n$ with
$\az^{-1}_{n+1}:=1_{e(\az_n)}.$

By definition of substring, $l(F')>0$ implies that there exists
an arrow $\bz$ such that $w=D'E'F'=D'E'\bz^{-1}F'_0$ with $e(\bz)=s(\az), F'_0\in {\mathcal{S}}$  Since $E'\bz^{-1}=E\bz^{-1}$ is a string, $\bz\az_1\not\in I$. It means
$\bz\az\in I$ by definition of gentle algebras. Let $u=V_\az\bz^{-1}V^{-1}_\bz=DE\bz^{-1}\bz_1\bz_2\cdots\bz_m$ with $m\geq 0$ and $\bz_0:=1_{s(\bz)}$, then $P_{s(\bz)}=M(u)$ is the indecomposable projective module corresponding to $s(\bz)\in Q_0$. One gets the following one-sided ad-pair:
  $$b=(1_{e(\az_n)}, V_\az, F)\times (1_{e(\az_n)}, V_\az, \bz^{-1}V^{-1}_\bz)\quad \quad \quad  (\vartriangle)$$
  $$\in \ff(v)\times \fs(u).$$
  See the following figure
\begin{center}
\includegraphics[height=1.5in]{1.jpg}\label{fig}
\end{center}
  On the other hand, by definition of $U_\bz$ one can rewrite
  $w=D'E'F'=D'E'\bz^{-1}\bz_1\bz_2\cdots\bz_t F'_1$ where $0\leq t\leq m, F'_1\in\s$ such that
  $$(D', E'\bz^{-1}\bz_1\cdots\bz_t, F'_1)\in \fs(w).$$
Therefore, we get an ad-pair
  $$c=(\az^{-1}_n\cdots\az^{-1}_{j+1}, E'\bz^{-1}\bz_1\cdots\bz_t, \bz_{t+1}\cdots\bz_m)\times(D', E'\bz^{-1}\bz_1\cdots\bz_t, F'_1)\quad \quad (\vartriangle\vartriangle)$$
  $$\in\ff(u)\times\fs(w)$$
See the above figure.
Combine $(\vartriangle)$ together with $(\vartriangle\vartriangle)$, we get $f_p=f_bf_c$ which completes the proof.
\end{pf}

The following corollary follows directly from the above lemma if we consider $v^{-1}$ in stead of $v.$
\begin{cor}Let $w, v$ be two strings and suppose $v=v_0\bz U_\bz$ for some $\bz\in Q_1, v_0\in {\mathcal{S}}.$ If $b=(D,E,F)\times (D',E',F')\in\ff(v)\times\fs(w)$ such that $EF=V^{-1}_\bz$ with $l(E)>0$. Then $f_b$ factors through a projective module if one of the following conditions holds
\begin{itemize}
  \item[(1)]$E=E'$ and $l(D')>0.$
  \item[(2)]$E^{-1}=E'$ and $l(F')>0.$
\end{itemize}
\end{cor}

In the following, we always assume that $w,v$ do not have extensions from $w$ to $v$, and show that $\Ext^1_A(M(w),M(v))=0$ by considering $v$ in four different cases as in Theorem \ref{BR87}.

\begin{lem}\label{case1}If $v$ does not start but ends on a peak, then
$$\Ext^1_A(M(w),M(v))=0.$$
\end{lem}
\begin{pf}By Auslander-Reiten formula and Theorem \ref{BR87}, we have
$$\Ext_A^1(M(w),M(v))\cong\underline{\Hom}_A(M(_hv_c),M(w)).$$
By Theorem \ref{C-B89}, it suffices to show that that each $f_p\in \Hom_A(M(_hv_c),M(w))$ with $p=(D,E,F)\times (D',E',F')\in \ff({_hv}_c)\times \fs(w)$
factors through a projective module.

Since $v$ does not start but ends on a peak, there exists $\az\in Q_1$ such that $\az v$ is a string.

\begin{itemize}
  \item[(1)]If $v=U_\az$ is an inverse string, then
$$\t^{-1}M(v)=M({(_hv)}_c)=M(V_\az).$$
   \item[(2)]If $v$ is not an inverse string, one can rewrite
$v=v_0\bz\bz^{-1}_1\cdots\bz^{-1}_m=v_0\bz U_\bz$ with $\bz\in Q_1, v_0\in {\mathfrak{S}}$, where $m\geq 0$, $\bz_0:=1_{e(\bz)}.$
By Theorem \ref{BR87}
$$\t^{-1}M(v)=M({_hv}_c)=M(V_\az \az v_0).$$
  \end{itemize}

{\emph{Claim:}} One gets for each $p=(D,E,F)\times (D',E',F')\in \ff({_hv}_c)\times \fs(w)$ that
$$DE=V_\az.$$

Assume $DE\neq V_\az,$ we are going to prove the claim by constructing a two-sided ad-pair in $\ff(v)\times\fs(w),$ hence get a contradiction
to the assumption.

If $v=U_\az$ is an inverse string, then ${_hv}_c=V_\az$, by definition of  factor string, there is nothing to prove. i,e., one has
$DE=V_\az, F=1_{s(\az)}.$

Assume now that $v$ is not an inverse string, we write $v=v_0\bz U_\bz$, then ${_hv}_c=V_\az\az v_0$. By definition of factor string, $l(DE)\geq l(V_\az)$ and $D\neq V_\az\az.$ We suppose that $l(DE)>l(V_\az)$ and consider the following two cases:
\begin{itemize}
  \item[I.] $l(D)>l(V_\az\az).$ Assume $D=V_\az\az D_0$ with $D_0\in {\mathcal{S}}$ such that $l(D_0)>0$, then
 $$(D_0, E, F\bz U_\bz)\in \ff(v).$$
 Hence there exists a two-sided ad-pair
   $$(D_0, E, F\bz U_\bz)\times (D',E',F')\in \ff(v)\times \fs(w),$$
since $l(D_0)>0$ and $l(\bz U_\bz)>0.$
See the following figure.
   \begin{center}
\includegraphics[height=2in]{2.jpg}\label{fig}
\end{center}
It contradicts to our assumption.
 \item[II.] $l(D)< l(V_\az\az).$ Let $V_\az=\az^{-1}_n\cdots\az^{-1}_2\az^{-1}_1$ with $n\geq 0$ and $\az^{-1}_0:=1_{s(\az)},$
 $D=\az^{-1}_n\az^{-1}_{n-1}\cdots\az^{-1}_{j+1}$ where $0\leq j\leq n$ and $\az^{-1}_{n+1}:=1_{e(\az_{n})}.$
 We can write $E=\az^{-1}_{j}\cdots\az^{-1}_2\az^{-1}_1\az E_0$  with $E_0\in{\mathcal{S}}$ such that $l(E_0)\geq0$ since $l(DE)>l(V_\az)$.
  Then $$(1_{e(\az)}, E_0, F\bz U_\bz)\in \ff(v).$$
See the following figure.
     \begin{center}
\includegraphics[height=2in]{3.jpg}\label{fig}
\end{center}
If $E'=E=\az^{-1}_{j}\cdots\az^{-1}_2\az^{-1}_1\az E_0$, then
  $$(1_{e(\az)}, E_0, F\bz U_\bz)\times (D'\az^{-1}_{j}\cdots\az^{-1}_2\az^{-1}_1\az, E_0, F')\in \ff(v)\times\fs(w)$$
is a two-sided ad-pair since $l(D'\az^{-1}_{j}\cdots\az^{-1}_1\az)>0, l(F\bz U_\bz)>0.$

Similarly, if $E'=E^{-1}$, one gets the following two-sided ad-pair
   $$(1_{e(\az)}, E_0, F\bz U_\bz)\times (D', E^{-1}_0,\az^{-1}\az_1\cdots\az_{j}F')\in \ff(v)\times\fs(w).$$
In both cases, we get a contradiction to the assumption.
  \end{itemize}
It completes the proof of the claim i.e., $$DE=V_\az.$$
Then we use Lemma \ref{lem-important} to show that $f_p$ factors through a projective module.
We first consider the following two cases when $l(E)=l(E')>0:$
\begin{itemize}
  \item[$(1)$]Assume $E=E'$, then $l(F')>0$. Otherwise $e(w)=e(E')=e(E)=s(\az)$, $E\az$ is a string implies
  that $w\az$ is also a string. The definition of gentle algebras  guarantees that $w\az v$ is a string which contradicts
  to the assumption that $w, v$ do not have extensions from $w$ to $v$. Therefore, $l(F')>0.$
   By Lemma \ref{lem-important}, $f_p$ factors through
  projective modules.
  \item[$(2)$]If $E^{-1}=E'$, then $l(D')>0$. Otherwise $s(w)=s(E')=e(E)=s(\az)$, $E\az$ is a string implies ${E'}^{-1}\az$ is a string. Hence
$w^{-1}\az v$ is a string which contradicts
  to the assumption. This implies that $l(D')>0$. Similarly, Lemma \ref{lem-important} implies that $f_p$ factors through
  projective modules.
\end{itemize}
Now, assume $l(E)=l(E')=0$, then $l(F')>0$ or $l(D')>0$. Otherwise, $w=D'E'F'=1_{s(\az)^t}$ with $t=1,-1.$ Hence, either $w\az v$ or $w^{-1}\az v$ is a string which is a contradiction to the hypothesis.

Without loss of generality, let $l(F')>0$ which means there exists
$\bz\in Q_1$ with $e(\bz)=s(\az)$. We rewrite $w=D'E'F'=D'E'\bz^{-1}F'_0$ with $F'_0\in {\mathcal{S}}$ and consider the following two cases:

\begin{itemize}
  \item[(1)]If $\bz\az\in I$, we consider the indecomposable projective module $P_{s(\bz)}$ corresponding to $s(\bz)\in Q_0$, then one gets $f_p$ factors through $P_{s(\bz)}$
as in Lemma \ref{lem-important}.
\item[(2)]If $\bz\az\not\in I$, then $l(D')>0$. Otherwise $w=\bz^{-1}F'_0.$ By definition of gentle algebra, we get $v^{-1}\az^{-1}\bz^{-1}F'_0=v^{-1}\az^{-1}w$ is a string which is again a contradiction.  Therefore, $l(D')>0$ and there exists $\da\in Q_1$ such that $e(\da)=s(\az)$ with $\da\az\in I.$ Similarly as in Lemma \ref{lem-important}, one can find that $f_p$ factors through the indecomposable projective module $P_{s(\da)}$ corresponding to $s(\da)\in Q_0$.
\end{itemize}
Therefore by Auslander-Reiten formula, one gets
$$\Ext^1_A(M(w),M(v))=0.$$
\end{pf}

The following corollary comes directly from the above lemma by considering $v^{-1}$ instead of $v.$
\begin{cor}\label{case2}If $v$ does not end but starts on a peak, then
$$\Ext^1_A(M(w),M(v))=0.$$
\end{cor}

\begin{lem}\label{case3}If $v$ neither starts nor ends on a peak, then
$$\Ext^1_A(M(w),M(v))=0.$$
\end{lem}
\begin{pf}Assume $v$ neither starts nor ends on a peak, then there exists $\az,\bz\in Q_1$ such that $\az v\bz^{-1}$ is a string. Let $u={_hv}_h=V_\az\az v\bz^{-1}V^{-1}_\bz$,
Theorem \ref{BR87} yields that $$\t^{-1}M(v)=M(u).$$
We prove that each non-zero morphism $f_p\in\Hom_A(\t^{-1}M(v),M(w))$ factors through projective modules, where
$p=(D,E,F)\times (D',E',F')\in \ff(u)\times \fs(w)$.

\emph{Claim:} Either $DE=V_\az \mbox{~~or~~} EF=V^{-1}_\bz.$

Similarly as the proof of Lemma \ref{case1}, assume $DE\neq V_\az, EF\neq V^{-1}_\bz$ and we are going to prove the claim by constructing a two-sided ad-pair
in $\ff(v)\times\fs(w)$ which contradicts to our assumption.

By definition of factor string, we have
\begin{itemize}
  \item[(1)]$l(DE)\geq l(V_\az)$ with $l(D)\leq l({_hv} \bz^{-1})$ and $D\neq V_\az\az,$
  \item[(2)]$l(EF)\geq l(V^{-1}_\bz)$ with $l(F)\leq l(\az {v_h})$ and $F\neq \bz^{-1}V^{-1}_\bz.$
\end{itemize}
If $DE=V_\az$ or $D={_hv} \bz^{-1}$, then there is nothing to prove for the claim.
We assume that $l(DE)>l(V_\az)$ with $D\neq {_hv} \bz^{-1}$ and consider the following two cases:

\begin{itemize}
  \item[I.] $l(V_\az\az)<l(D)<l({_hv} \bz^{-1}).$ We rewrite $D=V_\az\az D_0$ with $D_0\in{\mathcal{S}}$ such that $l(D_0)>0$. Note that
  $l(F)<l(\az {v_h})$ and $F\neq \bz^{-1}V^{-1}_\bz$ by $(2)$ above,
   we consider following two subcases related to $l(F):$
  \begin{itemize}
    \item[(I.1)]$l(\az {v_h})>l(F)>l(\bz^{-1}V^{-1}_\bz).$ We rewrite $F=F_0\bz^{-1}V^{-1}_\bz$ with $F_0\in{\mathcal{S}}$ such that $l(F_0)>0.$ Then there exists an ad-pair
   $$(D_0, E, F_0)\times (D',E',F')\in \ff(v)\times \fs(w)$$ which is not one-sided since $l(D_0)>0$ and $l(F_0)>0.$ See the following figure
        \begin{center}
\includegraphics[height=2in]{4.jpg}\label{fig}
\end{center}

    \item[(I.2)]$l(F)\leq l(V^{-1}_\bz).$ Let $V^{-1}_\bz=\bz_1\bz_2\cdots\bz_m$ with $m\geq 0$ where $\bz_0:=1_{s(\bz)}$, and rewrite         $F=\bz_{t+1}\cdots\bz_{m-1}\bz_m$ with $0\leq t\leq m$ where $\bz_{m+1}:=1_{e(\bz_m)}.$ We can rewrite $E=E_0\bz^{-1}\bz_1\cdots\bz_{t}$ with $E_0\in{\mathcal{S}}$. Then we obtain a two-sided ad-pair
    $$(D_0, E_0, 1_{e(\bz)})\times (D', E_0, \bz^{-1}\bz_1\cdots\bz_{t}F')$$
    $$\in\ff(v)\times \fs(w)$$
  when $E=E'$, since $l(D_0)>0$ and $l(\bz^{-1}\bz_1\cdots\bz_{t-1}F')>0$.
  See the following figure
\begin{center}
\includegraphics[height=1.7in]{6.jpg}
\end{center}
    If $E^{-1}=E'$, there is a two-sided ad-pair
    $$(D_0, E_0, 1_{e(\bz)})\times (D'\bz^{-1}_{t}\cdots\bz^{-1}_1\bz, E^{-1}_0,F')$$
    $$\in\ff(v)\times \fs(w).$$
\end{itemize}
 \item[II.] $l(D)< l(V_\az\az).$ Let $V_\az=\az^{-1}_n\cdots\az^{-1}_2\az^{-1}_1$, assume that
  $D=\az^{-1}_n\cdots\az^{-1}_{j+1}$ where $0\leq j\leq n$ with $\az^{-1}_{n+1}:=1_{e(\az_n)}$ and $E=\az^{-1}_{j}\cdots\az^{-1}_1\az E_0$ with $\az^{-1}_0:=1_{s(\az)}$. Then $l(E_0)\geq 0$ since $l(DE)>l(V_\az)$. Similarly as in I, the definition of factor string implies that $l(F)\leq l(\az{v_h}).$
  If $l(F)=l(\az{v_h})$, then there is nothing to prove. We assume $l(F)<l(\az{v_h})$ and consider the following two subcases:
  \begin{itemize}
    \item[(II.1)]$l(\az{v_h})>l(F)>l(\bz^{-1}V^{-1}_\bz).$ We rewrite $F=F_0\bz^{-1}V^{-1}_\bz$ with $l(F_0)>0.$ Then there exists a two-sided ad-pair
   $$(1_{e(\az)}, E_0, F_0)\times (D'\az^{-1}_{j}\cdots\az^{-1}_1\az,E_0,F')$$
   $$\in \ff(v)\times \fs(w)$$
   if $E'=E$, since $l(D'\az^{-1}_{j}\cdots\az^{-1}_1\az)>0$ and $l(F_0)>0.$  Similarly, if $E'=E^{-1}$,
   the following ad-pair
   $$(1_{e(\az)}, E_0, F_0)\times (D',E^{-1}_0,\az^{-1}\az_1\cdots\az_{j}F')$$
   is two-sided in $\ff(v)\times \fs(w).$ See the following figure:
\begin{center}
\includegraphics[height=1.7in]{6-1.jpg}
\end{center}
    \item[(II.2)]$l(F)\leq l(V^{-1}_\bz).$ Let $V^{-1}_\bz=\bz_1\cdots\bz_m$ with $m\geq 0$ where $\bz_0:=1_{s(\bz)}$, and assume $F=\bz_{t}\cdots\bz_m$ with $0\leq t\leq m+1$ where $\bz_{m+1}:=e(\bz_m).$ Therefore, we can rewrite
        $$E=\az^{-1}_{j}\cdots\az^{-1}_1\az v\bz^{-1}\bz_1\cdots\bz_{t-1}.$$
        Then we obtain a two-sided ad-pair
        $$(1_{e(\az)},v,1_{e(\bz)})\times (D'\az^{-1}_{j}\cdots\az^{-1}_1\az, v,\bz^{-1}\bz_1\cdots\bz_{t-1}F')$$
                     $$=(1_{e(\az)},v,1_{e(\bz)})\times ({D"},v,F")\in\ff(v)\times \fs(w)$$
    when $E=E'$. See the following figure
\begin{center}
\includegraphics[height=2.5in]{5.jpg}\label{fig}
\end{center}
 If $E^{-1}=E',$ we get the following two-sided ad-pair
$$(1_{e(\bz)},v,1_{e(\bz)})\times (D'\bz^{-1}_{t-1}\cdots\bz^{-1}_1\bz, v^{-1},\az^{-1}\az_1\cdots\az_{j}F')$$
                     $$\in\ff(v)\times \fs(w).$$
  \end{itemize}
Therefore we complete the proof of the claim.
By using Similar discussion as in Lemma \ref{case1}, Lemma \ref{lem-important} implies that $f_p$ factors through projective module. It completes the proof.
  \end{itemize}
\end{pf}

\begin{thm}Let $w,v$ be two strings over $A$. Then $\Ext^1_A(M(w),M(v))\neq 0$ if and only if $w,v$ admit extensions
from $w$ to $v.$
\end{thm}
\begin{pf} By Corollary \ref{cor-imp}, it suffices to show that if $w,v$ do not have extensions from $w$ to $v,$ then $\Ext^1_A(M(w),M(v))=0.$

By Lemma \ref{case1}, Corollary \ref{case2}  and Lemma \ref{case3}, we only need to consider the case that $v$  both starts and ends on a peak.
It suffices to show that $\Hom_A(\t^{-1}M(v), M(w))=0$ by Auslander-Reiten formula.

Assume $v$ both starts and ends on a peak, Lemma \ref{lem-inj} implies that we only need to consider non-injective module $M(v)$. Therefore, there exists $\az, \bz$ in $Q_1$ such that we can write
$$v=\az_n\cdots\az_1\az^{-1}v_0\bz\bz^{-1}_1\cdots\bz^{-1}_m=U^{-1}_\az\az^{-1}v_0\bz U_\bz$$ with $m,n\geq 0$.
By Theorem \ref{BR87}, we have
$$\t^{-1}M(v)=M({_cv}_c)=M(v_0).$$

Suppose $\Hom_A(\t^{-1}M(v), M(w))=\Hom_A(M(v_0), M(w))\neq 0$ which means by Theorem \ref{C-B89} that $v_0,w$ have an ad-pair
$(D,E,F)\times (D',E',F')\in\ff(v_0)\times \fs(w).$  It implies that
 $$(U^{-1}_\az\az^{-1}D,E,F\bz U_\bz)\in \ff(v).$$
\begin{center}
\includegraphics[height=2in]{7.jpg}\label{fig2}
\end{center}
Therefore there is a two-sided ad-pair
 $$(U^{-1}_\az\az^{-1}D,E,F\bz U_\bz)\times (D',E',F')\in \ff(v)\times \fs(w)$$
which contradicts the hypothesis that $w,v$ do not have extensions from $w$ to $v$. Then
$\Hom_A(\t^{-1}M(v), M(w))=0$ which implies $\Ext^1_A(M(w),M(v))=0.$
\end{pf}

\section*{Acknowledgments}
The author is indebted to professor Feng Luo for pointing out Theorem \ref{mocher} when he was giving series of lectures
in Mathematical center in Tsinghua University. He is very grateful for professor Thomas Br\"ustle, professor Bin Zhu and Yu Zhou
with many helpful discussions and he also thanks professor Jan Schr\"oer for many helpful comments and for telling him that a conjecture in a previous
version of the paper is wrong.

redpajama_set_name: RedPajamaArXiv


The GVG Anuket is a resource extraction vessel designed by the Vasudans. The primary role of the Anuket is to collect resource samples from volatile regions of space and to collect deuterium, which is used to power the fusion engines of all Terran and Vasudan ships. In addition, the Anuket is known to double up as a mobile laboratory on occasion.
The Anuket is an extremely fragile ship—even more fragile than its Terran counterpart, the GTG Zephyrus—with the exact same amount of defensive turrets as the Zephyrus, but with much thinner hull plating.
The discovery of the nebula prompted the Anuket's manufacturers to install the most advanced sensor technology available on all such models, allowing the Anuket to properly navigate even the most severe nebula storms.
The GVG Anuket was originally designed for resource extraction in the volatile environment of gas giants. More recently, the Anuket has been modified for nebular operations. The Anuket has the most sophisticated sensor array available, enabling it to navigate the intense EM maelstroms of supernova remnants. In the nebula, the Anuket plays two important roles. First, the miner collects samples for scientific analysis and serves as a laboratory for field experiments. Second, the Anuket gathers deuterium-rich gas for use in the fusion drives that power the allied fleet.
In Egyptian mythology, Anuket was the goddess of the Nile River. Her name means embracer because the Nile's flooding "embraced" the fields.
This is big, but not very strong or dangerous. Like all miners, an Anuket's explosion is very large.
Probably one of the most beautiful ships in the game. Unfortunately, also one of the most defenceless.
This page was last edited on 3 October 2009, at 08:05.


How much does Better Business Bureau pay?
I returned the shoes, but got nothing in return. I am very disappointed and upset with this company. The repairman from the Hood River shop said he would be here Monday, February 23rd. They took the money, no refund and not even close to when it was promised. There was also an electrical tower imposed on the land. The neighbors in the community in which my brother lives can not believe what this company has done to my brother.
I went to the area's City Hall, spoke with the representative and I was told that its a swamp land. The business also padded their bill and filed a small claims suit against me. Business of all types can be searched and contacted using the app. For reviews of Better Business Bureau see below. In most cases, if your first effort to resolve the problem was not successful, you are not going to change the result just by putting your concerns in writing. Navigate your web browser to the and choose your country of residence. It was a good faith endeavour on our part.
Maybe you could hire more humans to take care of problems people are having, with the companies they want to complain about. During mediation, both sides involved in the dispute meet with a neutral third party, a mediator, to create their own agreement jointly. Only those companies accredited by the Better Business Bureau have the legal right to use the organization's seal or marks and only under certain conditions in their advertising. In arbitration, the third party, an arbitrator, decides how to settle the problem. When you select one of the options, you may be prompted to answer additional questions. He took a substantial amount of money up front and only returned a little when my brother after 30 days of waiting finally cancelled the agreement. They carefully measured my feet and then gave me the wrong size shoes, and their promise that they were non-slip was wrong in the extreme.
You can also search by a specific industry category in order to find new businesses that you may be interested in engaging with. This article was co-authored by. He has shown no professionalism in this matter. This month once again the charges were there! The rating, which will range from A+ to F, will be displayed prominently at the top of the profile page. Sandvick worked as a civil litigator in California for over 7 years. So at 11 years I have a throw away house that I paid a lot of money for. Businesses are given a grade between A+ and F depending on multiple factors that affect their reliability and trustworthiness.
I explained that I do not make these types of calls and that I google this info on my cell phone through another carrier. He left me with no running water in one bathroom. They are awful and it was a mean thing to do. Some of the early answers that you provide will create additional questions. They got my money, and their last and only offer of a solution is to 'patch the cracks'! I asked to return the widgets, but he told me he would not refund my money. You may write as much as necessary to explain your complaint.
They talked me into a 40 gallon tank, when I have a manufactured home and it only needed a 30. He would just charge me for his labor. You should provide the dates and locations of any contacts you made with anyone from the company. That man can't seem to keep a schedule and does sloppy work!! Here are the phone numbers to avoid Ace Cash 347-384-3441 and Jeff Williams at 941-799-8734. I recently rented a room at the Western in the 4500blk of N.
If you have a complaint about wikiHow, that would be a different matter. If you have a problem with a vendor, your first course of action should be to contact the vendor directly. After being told by both places that I qualified for a loan the weird questions started. I saw an add on the internet for Attitude Today;s 2 in 1 Anti-snoring device with a 30-day money back guarantee. I gave him another week and finally went in December 10th. One said he was from Ace Cash, the other I couldn't quite catch, they both spoke in heavy oriental accents. If you are attempting to find information on a specific business, you can search directly from the Better Business Bureau homepage.
Not at all happy with this warranty company. He's an American citizen of 13 years and has lived here for 20, but he isn't the right color and he's a Muslin. Consider carefully before placing too much reliance on any single complaint or customer review. Now is is permanently damaged. I was really upset because of health conditions, that we slept and dined in that filth. This was a big job and they did it cheerfully, quietly, and well. These clauses can prevent you from filing a lawsuit against a company.
While these agencies may not resolve your problem, your complaint helps them investigate fraud. On my recommendation, My niece used Zober Images for her wedding on Labor Day Weekend, 2007. The railings were all cut unevenly and are bowed and falling apart by the day. If this doesn't work, contact a supervisor or manager. Well, he was busy and said he would be here by 3:30. It had been set up for weeks and confirmed the day of the wedding.
Start With Trust About Better Business Bureau is located at the address 300 N Phillips Ave in Sioux Falls, South Dakota 57104. Some companies and industries offer programs to solve disputes. If you have had an unpleasant experience with the company you searched for, it may be a good idea to file a complaint in order to hopefully prevent future consumers from also having a similarly bad experience. Robert Ofelt had the gall to charge my brother for hours worked in which he nor his workers had put in. In fact, he had his wife come over and get a check so he could get it cashed before they left on a trip! Better Business Bureau, any of several American and Canadian organizations formed to protect consumers against unfair, misleading, or fraudulent and selling practices. The coupon for movies came in the mail.


text:
James Isaac Abbott (December 15, 1884 – April 3, 1926) was an American Negro league outfielder in the 1900s.

A native of Brooklyn, New York, Abbott made his Negro leagues debut in 1906 with the Brooklyn Royal Giants. He went on to play for the Cuban Giants the following season. Abbott died in Brooklyn in 1926 at age 41.

References

External links
Baseball statistics and player information from Baseball-Reference Black Baseball Stats and Seamheads

1884 births
1926 deaths
Brooklyn Royal Giants players
Cuban Giants players

redpajama_set_name: RedPajamaWikipedia


text:
Chéri—A Romance in Dance
Alessandra Ferri & Herman Cornejo.
Photo: Joan Marcus
Chéri, based on the novella by Colette, continues Martha Clarke's unique hybrid genre of theater, utilizing movement to advance the story. Clarke—who conceived, choreographed, and directed this Signature Theater production, which runs through December—had the foresight and fortune to engage ABT principal Herman Cornejo and ex-principal Alessandra Ferri as the leads. He is the eponymous Chéri, son of Charlotte (Amy Irving), and lover of his mother's best friend, Lea (Ferri), nearly twice his age. Chéri is a charming, spoiled man who can't resist a glimpse in the mirror, a habit that eventually comes back to haunt him. His mother has put up with the affair for six years, and finally arranges for Chéri to marry a wealthy young woman his age.
We learn fragments about everyone's disparate states of mind in Irving's four brief monologues (by Tina Howe). Irving imbues them with enough salt and snap so that we feel her own vanity, and the guilt in her complicity in the awkward relationship. The two dancers never speak, but they spend a great deal of time embracing, un/dressing, and twirling and spinning in multitudinous ways, often with Ferri's legs and feet as punctuation.
They are both supremely gifted ballet dancers, but Clarke only once indulges in a display of technique, when Chéri undergoes a fit of rage expressed in multiple pirouettes and stag leaps. They do, however, use a refined expressive physicality manifested in every subtle gesture and loaded look, a particular refined gift in certain great dancers such as these. And while Clarke resists showing off her cast, the resulting choreography becomes repetitive and uninspiring after a spell. The chemistry between these two expressive performers is palpable, but one wishes that the staging and movement were more transportive.
Amy Irving and Herman Cornejo. Photo: Joan Marcus
Ferri's legendary high-arched feet, here in soft slippers, are a delightful embellishment. (Cornejo switches from bare feet to jazz shoes.) She has always been able to simultaneously convey both emotional sagacity and physical youthfulness, characteristics handily employed here. She retired from dancing several years ago, so it is rewarding to see her perform again in a different kind of genre. Music is a consistent through-line, a mélange of Ravel, Debussy, and other Romantic compositions for solo piano, played onstage with warmth and sensitivity by Sarah Rothenberg. It completes the intimate, time-worn setting.
In the end, war intervenes, and Chéri succumbs to the demons that have shadowed him as a result of his actions, or by chance. The ending is a shock—for those unfamiliar with the story, and because it abruptly closes the 65-minute performance. If we felt more connected to the characters, we might have felt more loss than feeling as if someone had changed the channel.
Labels: Alessandra Ferri, Amy Irving, Chéri, Herman Cornejo, Martha Clarke, Signature Theater
Ephemeralist's 2013 Highlights
Ailey—Celebrating Matthew Rushing, and 3 Premieres
Juilliard's New Dances Plus: A Pina Bausch Revival...
Glorious Notorious, A Chronicle of Dance Artists

redpajama_set_name: RedPajamaCommonCrawl


Smart Dubai has organised a brainstorming session at its headquarters in Dubai Design District, d3, as part of its Smart Cities Hackathon.
The UAE will generate AED 33.8 billion ($9.2 billion) by 2020 thanks to digital transformation, said Dr. Aisha Bin Butti Bin Bishr, Director-General of the Smart Dubai Office.
"AI has become all the more important as an engine for nation-wide smart transformation following the launch of the UAE's AI strategy," said SDG's CEO Wesam Lootah.
The gathering, which took place after an exciting three-day hackathon, was also graced by the presence of Her Excellency Dr. Aisha Bint Butti Bin Bishr, Director General of Smart Dubai Office, and Wesam Lootah, CEO of Smart Dubai Government Establishment, in addition to ConsenSys executives.
The new service will allow customers to pay for petrol using the Dubai Now app across ENOC's retail network in the UAE, eliminating the need for cash or card payments.


text:
<?php

namespace Assetic\Filter;

use Assetic\Asset\AssetInterface;
use Assetic\Exception\FilterException;

/**
 * Runs assets through OptiPNG.
 *
 * @link   http://optipng.sourceforge.net/
 * @author Kris Wallsmith <kris.wallsmith@gmail.com>
 */
class OptiPngFilter extends BaseProcessFilter
{
    private $optipngBin;
    private $level;

    /**
     * Constructor.
     *
     * @param string $optipngBin Path to the optipng binary
     */
    public function __construct($optipngBin = '/usr/bin/optipng')
    {
        $this->optipngBin = $optipngBin;
    }

    public function setLevel($level)
    {
        $this->level = $level;
    }

    public function filterLoad(AssetInterface $asset)
    {
    }

    public function filterDump(AssetInterface $asset)
    {
        $pb = $this->createProcessBuilder(array($this->optipngBin));

        if (null !== $this->level) {
            $pb->add('-o')->add($this->level);
        }

        $pb->add('-out')->add($output = tempnam(sys_get_temp_dir(), 'assetic_optipng'));
        unlink($output);

        $pb->add($input = tempnam(sys_get_temp_dir(), 'assetic_optipng'));
        file_put_contents($input, $asset->getContent());

        $proc = $pb->getProcess();
        $code = $proc->run();

        if (0 < $code) {
            unlink($input);
            throw FilterException::fromProcess($proc)->setInput($asset->getContent());
        }

        $asset->setContent(file_get_contents($output));

        unlink($input);
        unlink($output);
    }
}

redpajama_set_name: RedPajamaGithub


Melbourne-based VentraIP has acquired the hosting and domain name customers of online solution provider Summit Internet.
The acquisition, VentraIP's fourth this year, will see about 400 customers transferred to the business, constituting more than 1000 hosting and domain name services, while Summit will continue with its core business of telecommunications and enterprise connectivity.
"Unlike most of the other acquisitions we've done in the past, the customers of Summit Internet are premium business customers and we're very pleased to be able to welcome them to the VentraIP Australia family where they will now receive 24x7 technical support offered by our local team," VentraIP Australia chief executive Angelo Giuffrida said.
Summit Internet chief executive Greg Lipschitz said VentraIP had led the way in shared hosting and domain names for some time in Australia.
"It is their core business and they are the best at it. We want to ensure that our customers have the best service and experience possible," Lipschitz said.
VentraIP's Giuffrida said more acquisitions were on the way as it seeks growth amid considerable consolidation in the hosting market.
"We are currently working on others with hopes that we will close them before the end of the financial year. We continue to prove ourselves as a fantastic integrator for acquisitions, but we are also perusing growth through new marketing channels which includes our first radio advertising campaign which is currently on the air in Melbourne," he said.
VentraIP's 2018 acquisition spree has already included On A Cloud, Spiderweb Hosting and Boot Domains, which were folded into the company following customer transferrals.
In January last year, VentraIP acquired Brisbane's Web Access along with 3000 customers and 8000 services, allowing the company to expand into managed services. That was followed up in July when VentraIP acquired 1500 customers from one-man hosting provider Profound Hosting.
VentraIP also gained 4000 shared web hosting customers from Servers Australia in exchange for marketing the company's dedicated servers.


text:
Blue Demons CBI journey marches on with matchup against Longwood
Paul Steeno, Senior Basketball Writer
The most eye catching aspect of the Longwood Lancers, the DePaul Blue Demons opponent for the second round of the College Basketball Invitational, may be the name of one of their star players. Junior point guard Lorenzo Phillips goes by his childhood nickname Shabooty, staking his claim for best n...
Tags: Blue Demons, DePaul, DePaul men's basketball, sports
DePaul to play in the CBI; first postseason tournament apperance since 2007
A disappointing loss to St. John's at Madison Square Garden last Wednesday won't be the last we'll see of the 2018-2019 DePaul Blue Demons. The Roman College Basketball Invitational (CBI) announced the field for its 2019 tournament and DePaul is one of the 16 teams included. DePaul (15-15; 7-11) will...
Reed named most improved in Big East Conference
In a surprise to few who saw him play the last two seasons, DePaul sophomore big man Paul Reed has earned the Big East Conference's Most Improved Player Award for the 2018-2019 season as voted upon by the league's 10 head coaches. The 11.2 points, 8.2 rebounds, and 1.3 blocks per game the Orlando, Fla. reside...
Tags: Blue Demons, DePaul, DePaul basketball, DePaul men's basketball
All-Big East Second Team calls Strus' name
DePaul senior guard Max Strus staked his claim as one of the best players in the Big East Conference this season by earning a selection to the second team All-Big East squad for the first time in his career. Strus joins Sam Hauser (Marquette), Alpha Diallo (Providence), Naji Marshall (Xavier), and...
Tags: DePaul, DePaul Athletics, DePaul men's basketball, sports
So Long, Wintrust
Paul Steeno, Richard Bodee, and Alexa Sandler
It was a heck of a way to go out. If this was the last time that DePaul seniors Femi Olujobi, Eli Cain, and Max Strus play at Wintrust Arena in a DePaul uniform (it'll depend on if DePaul makes a postseason tournament in which case they could host a game), the trio at least went out in style. In a 101-67 stomping of a Georgetown Hoy...
Creighton Bluejays stymie Blue Demon frontcourt; beat DePaul at Wintrust
The Creighton Bluejays (14-13; 5-9) executed head coach Greg McDermott's gameplan nearly flawlessly in a 79-67 win against the DePaul Blue Demons (13-12; 5-9) Wednesday night at Wintrust Arena Force the ball out of the hands of the Blue Demons best players, their frontcourt, instead surrendering open...
"We ran into a buzzsaw:" Golden Eagles sever DePaul at Wintrust
To beat the No. 10 ranked Marquette Golden Eagles (21-4; 10-2) on Tuesday night, the DePaul Blue Demons (13-10; 5-7) would have had to do something special. They hadn't beaten a team ranked in the top 10 since they conquered a Brandon Rush, Mario Chalmers, Darrell Arthur led Kansas team in 2006. Tonight, not...
Tags: Chicago, DePaul, DePaul basketball, DePaul men's basketball
DePaul seeks biggest win of the season against Marquette
It's been a heck of a season for the DePaul Blue Demon men's basketball team. After coming out victorious in Ohio against Xavier on Saturday DePaul now has 13 wins to its name, the most they've accumulated since the 2006-2007 season (20 wins). With five conference wins, the Blue Demons sit in a five-way...
Tags: DePaul, DePaul Athletics, DePaul basketball, DePaul men's basketball
Deep freeze won't stop Blue Demons battle with Villanova Wildcats
Cold is a criminally inadequate adjective to describe the conditions in Chicago when the DePaul Blue Demons (11-8; 3-5) welcome the Villanova Wildcats (16-4; 7-0) to Wintrust Arena tonight for a 7 p.m. bout. When the feels-like temperature is expected to register in the -40s, even a red-hot Villanova...
Blue Demons add Saint Louis University transfer Carte'Are Gordon
DePaul Blue Demon head coach Dave Leitao and his staff have landed another one. Via his Twitter account today, Saint Louis Billikens freshman forward Carte'Are Gordon announced that he is transferring over to DePaul. The 6-foot-9-inch forward played in 13 games for the Billikens this season, aver...
Tags: Blue Demons, DePaul, DePaul Athletics, sports
Pirate attack at Wintrust
When Monday rolls around the DePaul Blue Demon's (8-5; 0-2) next opponent, the Seton Hall Pirates (11-3; 2-0), will likely see their name among the top 25 teams in the country on the AP poll. Winners of seven straight, the Pirates have defeated No. 13 Kentucky, two Big Ten teams in Maryland and Rutgers,...
Tags: Blue Demons, Dave Leitao, DePaul, sports
Sharing is caring: Eli Cain's evolution into the Blue Demons top playmaker
Mired in a back and forth stalemate with Big East Conference rival Xavier on Saturday, things took a turn for the worst when DePaul Blue Demon star Max Strus picked up a fourth foul with 7:52 remaining, forcing head coach Dave Leitao to yank him from the game at a critical juncture Thank goodness for Eli Cain. The 6-foot-6-in...
Tags: Dave Leitao, DePaul, DePaul Athletics, sports


text:
Archive | November 14, 2014
in ICELAND REGION, Quake Swarm, Seismic Swarm
MAGNITUDE 3.4 ICELAND REGION
Depth: 8.7 km
Distances: Latitude, Longitude 64.680 -17.480
(4.9 km NNE of Bárðarbunga)
Earthquake location 14 Nov 23:35 GMT
Time and magnitude of earthquake 14 Nov 23:35 GMT
(4.1 km NE of Bárðarbunga)
(5.5 km SE of Bárðarbunga)
in Canary Islands
MAGNITUDE 2.3 CANARY ISLANDS, SPAIN REGION
Distances: Latitude, Longitude 27.7114 -18.0119
in Cosmic Rays Alert, Earth's Core, Influx Of Energy Alert, Magnetosphere Alert, Massive Dip Spikes Alert
MEGA DIP SPIKES ON THE MAGNETOSPHERE @ APPROX 19:00, 19:30, 19:45, 20:00, 21:15, 21:45 hrs UTC
**VERY URGENT**
MEGA DIP SPIKES ON THE MAGNETOSPHERE @ APPROX 19:00, 19:30, 19:45, 20:00, 21:15, 21:45 hrs UTC. FURTHER EARTHQUAKES, VOLCANO ACTIVITY & ADVERSE WEATHER PATTERNS WILL BE GREATLY INFLUENCED BY THE COSMIC RAYS STRIKING THE EARTH'S CORE
in Earthquake Alert
MAGNITUDE 2.6 SCOTLAND, UNITED KINGDOM
http://www.emsc-csem.org/Earthquake/earthquake.php?id=408603
Distances: 119 km NE of Douglas, Isle of Man / pop: 26,218 / local time: 11:23:58.0 2014-11-14
99 km S of Edinburgh, United Kingdom / pop: 435,791 / local time: 11:23:58.0 2014-11-14
51 km NW of Carlisle, United Kingdom / pop: 72,633 / local time: 11:23:58.0 2014-11-14
4 km W of Locharbriggs, United Kingdom / pop: 6,333 / local time: 11:23:58.0 2014-11-14
MAGNITUDE 5.0 NEW GUINEA, PAPUA NEW GUINEA
Distances: 778 km NW of Port Moresby, Papua New Guinea / pop: 283,733 / local time: 17:52:23.8 2014-11-14
112 km SW of Wewak, Papua New Guinea / pop: 18,230 / local time: 17:52:23.8 2014-11-14
30 km NW of Ambunti, Papua New Guinea / pop: 2,073 / local time: 17:52:23.8 2014-11-14
MAGNITUDE 5.0 OFF EAST COAST OF KAMCHATKA
181 km SE of Petropavlovsk-Kamchatskiy, Russia / pop: 187,282 / local time: 18:09:45.5 2014-11-14
http://earthquake.usgs.gov/earthquakes/eventpage/usc000sx7c#summary
Distances: 239km (149mi) E of Kuril'sk, Russia
476km (296mi) ENE of Nemuro, Japan
492km (306mi) ENE of Shibetsu, Japan
545km (339mi) ENE of Abashiri, Japan
1421km (883mi) NE of Tokyo, Japan


The Omaha Community Playhouse is a performing arts organization that enhances quality of life through live theatre, professional touring and arts education. We are dedicated to enriching the lives of audiences and participants through entertainment, thought-provoking stories and first-hand involvement.
OCP offers opportunities in performing, technical work and support categories to more than 2,000 community volunteers.
Drag On! Omaha Community Playhouse 6915 Cass St.
All events are free and open to the public, however free-will donations of any amount are crucial to continuing adventurous programming.
In this unique comedy, a fledgling drag queen must go through the tests and trials of legendary cosplay divas to find her swagger. An ode to both geek and drag cultures, this refreshingly original piece gives the audience a front row seat to what happens when you combine equal parts fantasy adventure, comic book convention, and drag show.
Alternative Programming includes a series of staged readings, special events and play development collaborations.
All events are held at the Omaha Community Playhouse – 6915 Cass St.
"Sweat" Auditions Omaha Community Playhouse 6915 Cass St.
The Howard Drew Theatre performs Thursdays through Saturdays with a 7:30 p.m. curtain and Sundays with a 2:00 p.m. curtain.
Winner of the 2017 Pulitzer Prize, SWEAT is a head-first dive into working class America. A three-time Tony Award® nominee, SWEAT follows a group of steelworkers whose steady march toward the American dream is uprooted by economic change. As their sense of security slowly unravels, jobs and relationships are left in the wake. Punctuated with lively humor, SWEAT goes to the heart of what it means to be human—both good and bad—when fear and uncertainty take hold. Disclaimer: Contains adult language and violence.
Those auditioning will be asked to read from the script provided at auditions.
Men on Boats Omaha Community Playhouse 6915 Cass St.
Adventure, bravery and humorous absurdity… led by an all-female cast, Men on Boats is the "true-ish" story of ten explorers on four boats charting the course of the Colorado River in 1869. Guided by a one-armed captain, the outlandish but loyal crew encounters various disasters, conflicts and harrowing adventures along the way.
Men on Boats - Gender Perfomance Workshop Omaha Community Playhouse 6915 Cass St.
Join OCP for a gender performance workshop to celebrate Men on Boats. This workshop will be held on Saturday, May. 11 at 6:00 p.m. at the Omaha Community Playhouse and will be taught by Sarah Brown (Nebraska Shakespeare)—Stick around after the workshop for the 7:30 p.m. performance of Men on Boats and an accompanying talkback panel on how the production team brought the characters to life. Cost for the workshop is $10 and includes a drink ticket.
7:30 p.m. | See Men On Boats in the Howard Drew!
9:30 p.m. | Talkback panel life featuring Sarah Brown, OCP Artistic Director Kimberly Faith Hickman and Men on Boats director, Amy Lane.
Ragtime Omaha Community Playhouse 6915 Cass St.
A tragic yet hopeful tale, four-time Tony Award-winning Ragtime explores the pursuit of the American dream and the meaning of family. Set in the melting pot of New York City at the turn of the century, the lives of a wealthy white couple, a determined Jewish immigrant and an African American ragtime musician intertwine, creating a rich tapestry of American life. With soaring ballads and a stunning score, these characters are connected by their compassion, belief and resolution that they, too, will find their place in the world.
Disclaimer: Contains violence and racial tension.
Tara Vaughan's She Rocks Omaha Community Playhouse 6915 Cass St.
Tara Vaughan is a bona fide superstar. Her soulful vocals and piano techniques are reminiscent of a bygone era, but still have a unique and modern sensibility. In her vocal style, you can hear echoes and the influence of legends like Patsy Cline and Sam Cooke. Her abilities on the piano call to mind rock greats Elton John and Carole King. She Rocks celebrates women artists and songwriters of the 1960s–1980s, woven together with songs and stories. Backed by a 4-piece band, Tara performs music from artist like Janis Joplin, Linda Ronstadt, Aretha Franklin, Blondie, Heart and many more. In this unique revue, Tara Vaughan masterfully presents an evening of classic rock and roll with the focus on female artists and songwriters.
2019-2020 Season Musical Adult Auditions Omaha Community Playhouse 6915 Cass St.
Saturday, June 15 @ 11:00 a.m.
Sunday, June 16 @ 6:00 p.m.
* ONCE the musical will include actors playing instruments. If you are interested in this specific musical and have an instrument, please bring the instrument with you and be prepared to play 16 bars of music of your choice. You may also accompany your own singing audition if you prefer.
For more information, contact Breanna Carodine, bcarodine@omahaplayhouse.com, at (402) 553-4890, ext. 110. or go to the webpage.
2019-2020 Season Musical Youth Auditions Omaha Community Playhouse 6915 Cass St.
Saturday, June 22, @ 11:00 a.m.


text:
'Orphan' rare diseases focus of new federal government support plan
November 16, 2018 — 12.00am
The federal government will establish Australia's first National Rare Diseases Framework and Action Plan to support people with rare conditions such as Batten disease, muscular dystrophy and mitochondrial disease.
Advocacy group Rare Voices Australia (RVA) will receive $170,000 to develop the action plan, Health Minister Greg Hunt will announce at the 2018 Rare Diseases Summit in Melbourne on Friday.
Federal Health Minister Greg Hunt will announce the creation of the national action plan on Friday. Credit:Lukas Coch
"Our government recognises the fact that these diseases are statistically rare – with an estimated prevalence of five in 10,000 – therefore special and concerted efforts are needed to address them," Mr Hunt said.
Roughly 8000 rare diseases have been identified worldwide. An estimated 6 per cent to 8 per cent of Australians are affected by one of these life-threatening or debilitating "orphan" conditions and, of those, almost half are children.
Chief executive of RVA Nicole Millis said the healthcare system is overwhelmingly geared towards detecting, treating and managing diseases that affect a large number of patients and is not equipped to respond to the needs of people with rare diseases.
"There are still a number of diseases that don't have the clinical infrastructure to run the clinical trials that are needed," Ms Millis said.
People with rare diseases can bounce between specialists and testing for months, even years before they are correctly diagnosed.
Roughly 30 per cent of people with a rare disease search for more than five years for a diagnosis and 50 per cent have been misdiagnosed at least once, according to RVA.
Many conditions are untreatable and the search for treatments is hampered by a lack of research funding and the tiny patient numbers with any one specific disease.
RVA has called for a national rare disease framework since 2012 that would have six strategic priorities: diagnosis, access to treatment, data collection, co-ordinated care, access to services and co-ordinated research.
"Without a national framework there are always going to be people with rare disease fall through the gaps and the haves and have nots," Ms Millis said.
The Action Plan and Framework will be guided by extensive consultation with people with rare diseases, clinicians, academic experts, policymakers and state and territory governments.
"When someone is diagnosed with a rare disease they need our love and support but also the best possible treatment and care," Mr Hunt said.
"This plan will benefit people with rare diseases, their families and the wider community."
The government's Life Saving Drugs Program funds 14 medicines for nine very rare diseases to 400 Australians. Earlier this month the drug Galafold was added to the program to treat people with fabry disease. The oral drug typically costs about $445,000 a year.


text:
Stock buybacks take off in Japan at record pace
Sony announces first repurchase to bolster sagging shares
Sony announced a stock buyback of up to 100 billion yen on Feb. 8, one of several Japanese companies to do so.
AKIHIRO OTA, Nikkei staff writer February 9, 2019 03:30 JST | Japan
TOKYO -- Japanese businesses are buying up their own shares at a record pace in an apparent attempt to send a message to investors that their stocks are valued lower than they should be based on fundamentals.
Sony joined the trend Friday with its first-ever buyback, announcing that it will repurchase up to 100 billion yen ($910 million) of its shares as a way of "rewarding" its shareholders.
The electronics powerhouse on Feb. 1 reported 14% growth in operating profit on the year to a record 811.5 billion yen for the nine months ended December. Yet its stock price slumped in response to downgraded sales forecasts for some products, sliding to its lowest point in more than a year on Thursday.
"Management must have determined that the shares were underpriced in light of the company's earnings potential," an analyst said. After the buyback announcement, Sony stock shot up 7% at one point Friday before closing the day at 4,906 yen, up 4.1%.
Sony is just one of many companies with strong earnings and weak shares that are turning to repurchases for a boost. When SoftBank Group announced a 600 billion yen buyback Wednesday, Chairman and CEO Masayoshi Son explicitly stated that "I myself as a shareholder feel that the group's stock price is too low." The shares surged the following day.
The annual record for Japanese corporate buybacks since fiscal 2004, when the rules were loosened to allow repurchases via board decisions, is 6.5 trillion yen, set in fiscal 2015, according to I-N Information Systems.
Companies announced 6.32 trillion yen in repurchases so far this fiscal year as of Thursday. Add to this Sony's plans and others announced Friday -- including 30 billion yen at energy and metals company JXTG Holdings, and materials and electronics maker Taiyo Yuden's 3 billion yen -- and the total for the year ending March 31 is all but certain to reach a new high.
Businesses typically repurchase more stock during a price downturn because they can get more shares for the same amount of money. February tends to be a popular month for buybacks, since companies have a good picture of their performance and capital spending for the year soon before they close their books at the end of March.
This year, businesses may be shying away from acquisitions and other growth-oriented spending amid increasing uncertainty about the economy, some say.
"Companies may feel that they have limited options for spending their accumulated cash piles," said Shingo Ide at NLI Research Institute, who expects to see more businesses carrying out buybacks.
Japan's listed companies double shareholder returns over 5 years
Son battles skeptics as SoftBank eyes next Vision Fund


text:
Ymerana pteropoda är en ringmaskart som beskrevs av Holthe 1986. Ymerana pteropoda ingår i släktet Ymerana och familjen Ampharetidae. Inga underarter finns listade i Catalogue of Life.

Källor

Havsborstmaskar
pteropoda


text:
Q: Get Specific Data From Array, Based On Another Value I have an array that outputs these values:
Array (
    [0] => stdClass Object (
        [ID] => 6585
        [COLOR] => red
        [Name] => steve
        )
    [1] => stdClass Object (
        [ID] => 5476
        [COLOR] => blue
        [Name] => sol
        )
    [2] => stdClass Object (
        [ID] => 7564
        [COLOR] => yellow
        [Name] => jake
        )
    [3] => stdClass Object (
        [ID] => 3465
        [COLOR] => green
        [Name] => helen
        )
    )

Now, I will know the ID of the person, and I need the get the COLOR value for that specific value set. How is this best achieved please?

A: Something like this:
function getColorById($arr, $id){
    foreach($arr as $item){
        if ($item->ID == $id)
            return $item->COLOR;
    }
    return "blah!";
}

Use like echo getColorById($arr, 3465);
EDIT:
The way you have the data leads to slowing down access times. A better suggestion is to (since it seems ID is unique), you'd rather have that as the key to your array. You have integer indices to it, now. Construct the array (unless you are receiving it from some area beyond what you have control over) something like the below:
$arr = array();
$arr["ID_4634"] = <object>;

A: You probably want change the way you are storing it up for faster access.
With the current format, you will need to loop through the elements and compare colors until you find a match.
for($i=0;$i<count($array);$i++){
  if($array[$i]['ID'] == $id)
    return $array[$i]['COLOR']
}

alternatively, store it with the ID's as the keys.

A: $users = array();
$count = count($arr);
for ($i = 0; $i < $count; $i++) {
    $users[$arr[$i]['ID']] = array(
        'Name' => $arr[$i]['Name'],
        'COLOR' => $arr[$i]['COLOR']
    );
}
echo $users[$id]['COLOR'];

where $arr represents the array you outputted in your initial post and $id is the id of the person who's color you're trying to access. You can also then get their name by using
echo $users[$id]['Name'];

A: IDTry below :
for($i=0; $i<count($array); $i++)
{
  if($array[$i]['ID'] == $id)
    return $array[$i]['COLOR'];
}

redpajama_set_name: RedPajamaStackExchange


text:
A second Tea Auction House has been set up in Sreemangal
The country's first tea auction centre was set up in Chittagong in 1949 considering the export facilities through the port.
It has been nearly seven decades since then. The auctions now take place on the third floor of the Progressive Tower in Agrabad.
Krishna Pada Chowdhury, secretary of Tea Traders Association of Bangladesh (TTAB), said the auctions were held every Tuesday all the year round.
"As many as 248 tea traders, who are members of TTAB, can purchase tea from the auctions that begin at 8:30am and end at 6:30pm," he said.
The seven Chittagong-based brokers who conduct auctions are National Brokers, KS Brokers Limited, Produce Brokers Limited, Progressive Brokers Limited, Purba Bangla Brokers, Unity Brokers and Planters Brokers Limited.
"They have their respective agreements with the tea growers. First of all, the tea produced in the gardens is sent to a total of 14 bonded warehouses which are mostly located in Chittagong. Later, the brokers receive samples and taste the tea," Chowdhury said.
Tea tasting is the process in which a trained taster determines the quality of a particular tea.
"Due to climatic conditions, topography, manufacturing process and different clones of tea plants, the final product may have vastly differing flavours and appearance," Chowdhury explained.
Then, the brokers prepare catalogues and fix the tentative price of tea. Later, the catalogues and valuation copies are dispatched to all the buyers ahead of the weekly auctions. Then, the traders take part in the auctions and purchase tea. Finally, the tea reaches the retailers and consumers, the TTAB secretary added.
Md Abu Jafar, an official of Unity Brokers, said typically 45 auctions are held a year and the tea sold is mostly bought by domestic buyers.
"In addition to the price of the tea, the buyers have to bear 15% VAT and 1% Advance Income Tax (AIT). On the other hand, the brokers get 1% commission from the tea producers," he said.
"Besides, the brokers get Tk10 for 100 kg of tea from the buyers. The brokers draw 1.5kg tea as sample from each lot of CTC leaf and 0.80 gram from each lot of dust. Each lot of tea contains 550kg," Jafar, who has been working with Unity Brokers for last 24 years, explained.
There are three categories and 10 grades of tea – broken, fannings and dust.
According to Bangladesh Tea Board (BTB), there are 162 tea gardens in Bangladesh. Of them, as many as 90 are in Moulvibazar, 23 in Habiganj, 18 in Sylhet, 21 in Chittagong, one in Rangamati and nine in Panchagarh.
With a total of 133 tea estates, Sylhet contributes to 90% of the tea production in Bangladesh.
According to BTB, 67.38 million kg of tea was produced in 2015 while the production rose to 85.05 million kg in 2016. The following year, 78.94 million kg tea was produced in Bangladesh.
TTAB Vice-Chairman Abdul Hai Chowdhury told the Dhaka Tribune that they were considering introduction of online system to reduce hassles in the auctions.
The tea brokers said that the demand for tea usually rose in the country during the winter.
A second tea auction centre was set up in Moulvibazar's Sreemangal on December 8 last year.
Type:News
In:Tea Auction, TTAB


a traveler comes upon the Dream Chest at the end of a rainbow. The chest has a curious carved star on its scooped lid. The traveler opens the chest. A wise old star emerges (a symbol of the eternal spirit and a mentor figure) and whisks the traveler away on the journey of a lifetime. The story ends with the old star encouraging both the traveler and the reader to pursue their own dreams. The birds in the two final illustrations tie to the Langston Hughes quotation on page 29 in Dream.
This husband-and-wife team have worked together for more than twenty years. They take a collaborative approach in which both artists conceive, draw, design, and paint. They have created artwork for annual reports, brochures, posters, ads, magazines, and even movies -- including Toy Story and A Bug's Life, for which they provided pre-production set and character designs. Their 25 books together include I Walk at Night (Lois Duncan), a New York Times Best Illustrated Book, along with Dr. Seuss's My Many Colored Days and The Boy on Fairfield Street: How Ted Geisel Grew Up to Become Dr. Seuss (Kathleen Krull).
"We always look for art. We see it in the night sky, the glow of light on a child's face, the magic of a good story, the fantastic world of dreams."


text:
Cycle to Break the Cycle is a Wrap!
Kat Fisher
Kat Fisher Published: April 22, 2019
We had such a great time the past four days at the Village in Meridian for Cycle to Break the Cycle! I really didn't know what to expect when we showed up. I had the gist.. that people from the Treasure Valley would be riding bikes and actually powering the radio station through those bikes.
But what I experienced at Cycle was far beyond bikes. Seeing the community come out to power a message and backing something Keke is so passionate about was really inspiring. "It shouldn't hurt to be a child" has so many layers.
April is child abuse prevention month, and I didn't even know that before becoming apart of this campaign. The fact that we get to draw attention to something that's sadly so prevalent in our community and every community is really important.
On Saturday, we found out through a woman who came to the event that a couple who was riding bikes with us just last year were tragically murdered as a result of domestic violence in Meridian a few months ago. Breaking the cycle of abuse is important for so many reasons, and this is one of them. The victim had taken all of the steps necessary to get out of a bad situation, and it still wasn't enough. We were wrecked when we realized who she was.
That's the ugly truth about child abuse, domestic violence and so many other things. You just don't know what could happen, and that's why it's so important to speak out for others who can't speak for themselves.
Thank you to everyone who came to cycle, support and share stories. We are truly inspired and encouraged that one person at a time, the cycle of abuse can be broken.
Filed Under: boise, cycle, keke and kat, Live for 175, newsletter
Categories: Business, Entertainment, Local News, On-Air
Stay In Your Lane! Bike Laws In Idaho
#KatFished: Birthday Gone Wrong!
Should NASCAR Ban Confederate Flags?
Front Yard Entertaining the New Wave?
Republic Records Bans Use of Term 'Urban'
9 Movies to Watch on Systemic Racism


text:
Kernenergiecentrale Tomari (Japans: 泊発電所, Tomari hatsudensho) is een kerncentrale in het dorp Tomari (Shiribeshi) in de prefectuur Hokkaido in Japan. De centrale beschikt over 3 reactoren en kan een vermogen van 2062 MW produceren. De centrale wordt beheerd door Hokkaido Electric Power Co., het hoofdkantoor is gevestigd in Sapporo.

Op 5 mei 2012 werd reactor 3 buiten werking gesteld voor onderhoudsinspecties. De reactor was op dat moment de enige nog werkende kernreactor in Japan.

Tomari
Bouwwerk in Hokkaido


text:
More Journals
Food+Dining
Local moms create nonprofit to help working single parents
Jun 15, 2020 11:02AM ● By Stephanie Yrungaray
Alissa Harrod (second from left) and Meghann Brimhall (fourth from left) with volunteers at a fundraiser at Chick-fil-A. (Photo courtesy of The Single Parent Project)
By Stephanie Yrungaray | [email protected]
Serendipity, fate, a higher power...whatever you want to call it there has been something at work in how quickly the nonprofit organization The Single Parent Project has come together.
Meghann Brimhall had long recognized how valuable her support system was when she was a single mom. As she interacted with other single parents who didn't have as much help, her desire grew to do something about it.
"The vision came to me about how great it would be to pay it forward," Brimhall said. "I wanted to be a support system to somebody else who is a single parent and who doesn't have nearby family or friends."
Brimhall's goal for 2019 was to start a nonprofit organization for single parents. On Dec. 26, she was upset that another year had passed and she hadn't accomplished her goal.
"I started doing research and The Single Parent Project name came to mind," Brimhall said. "There was no group with that name on Facebook so I hurried to create a page. I saw I could use the name on Instagram and there was an available website with that name so I went for it."
In January 2020, Brimhall started working on the Facebook page and added close friends to get feedback. One of her friends misunderstood and shared the fledgling page, and The Single Parent Project took off.
"We raised $1,500 fairly quickly and were able to help three parents right off the bat," Brimhall said. "It was super exciting, and I started posting on social media."
Enter Alissa Harrod.
A former Riverton High classmate, Harrod saw Brimhall's posts and offered to help. She too, had always had a dream of starting an organization to help others.
"I've worked in mental health and was the director of business development for a hospital," Harrod said. "I wanted to have an organization that helped with mental health in general and at the same time Meghann was pushing play I was writing up a program of my own. We were able to mix our drive and passion to help those in need and it has been phenomenal."
Although Brimhall and Harrod had no experience starting or running a nonprofit organization, they have been able to learn and accomplish many goals in a short time frame.
They applied for the nonprofit 501(c)(3) tax-exempt status in February.
"We were told by multiple other nonprofits that for some people it was taking between nine months to three years to get approved," Harrod said. "We got the approval in eight weeks."
They moved into a physical space in Draper in April and in just 12 weeks, The Single Parent Project raised over $15,000 in monetary and in-kind donations. They were able to provide financial help for 120 families that ranged from rent money and daycare expenses to groceries and gas bills and many other expenses in between.
The focus of the Single Parent Project is to help working single parents who fall in the gap between receiving government assistance and making enough money to live comfortably.
"When I was a single mom I applied for Medicaid and got denied," Brimhall recalled. "I had a house payment, and I was also paying for type 1 diabetic insulin and diabetic needs. [Government assistance] doesn't take everything into consideration."
Besides helping with unmet physical needs, Brimhall and Harrod want The Single Parent Project to provide families with mental health resources and a supportive community.
"We are going to provide outpatient service and support groups for families," Brimhall said.
"We're working on programs to help parents with resiliency, trauma and dealing with conflict," Harrod said. "These group settings are important to single parents and we want to help them develop confidence. It's important to take care of yourself so you can be a better mom, a better employee, and a better person all around."
Brimhall and Harrod have a one-year goal to assist 500 families in 2020.
"I would say that we are on track to hit that goal," Harrod said. "We are hoping with grant opportunities we will hit the $150,000 mark and then some. We've already started working on educational courses and support groups."
"Our goals are always changing as we learn all we can do to assist these families," Brimhall said. "We've always said that we want to help with short-term housing and now we also want to assist with long-term housing."
They also hope to help families reach educational goals and would love to partner with local universities and offer scholarships.
The Single Parent Project is a passion project for the cofounders who also have jobs and are moms to a blended family of six kids (Brimhall) and three kids (Harrod). They hope that helping people will one day be their full-time gig.
The duo is amazed and excited about how quickly their project has grown and appreciate all of the support from friends and community members.
"We've had a lot of support from people who were single parents or raised by single parents," Brimhall said. "It has been very rewarding to see these people give back and have our community rally behind us. It is fun to see it grow and have everybody celebrate successes with you."
"To raise the amount of money we have in such little time helps us know that we have found that niche that is overlooked," Harrod said. "This is happening for a reason."
They still need as much help as they can get to reach their goals and assist as many working single parents as possible. Find out more information on how you can help or receive help on their website www.thesingleparentproject.org or their social media pages on Facebook or Instagram @thesingleparentproject.
"Anytime we feel like there is a roadblock something else happens and pushes us forward," Harrod said. "We know we are in the right place doing the right things. It has been a great experience."
The Complete Works of William Shakespeare (Abridged) (Revised)
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How We Drive, the Blog of Tom Vanderbilt's Traffic » Blog Archive » Does Religion Influence Road Safety?
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