text:
\section{\textbf{Introduction and preliminaries}}
The concept of Hom-Lie algebras was first introduced by Hartwig et al. \cite{h2006}, as a part of a study of deformations of the Witt and the Virasoro algebras. A Hom-Lie algebra is basically a non-associative algebra satisfying the skew-symmetry and the Hom-Jacobi identity twisted by a linear map. If we take this linear map as the identity map, then the Hom-Lie algebra becomes a Lie algebra. Therefore, the generalizations of the known theories from Lie algebras to the Hom-Lie play a crucial role as these generalizations are not straight forward. Also, because of the close relation to discrete and deformed vector fields and differential calculus, Hom-Lie algebras are widely studied recently \cite{c2015, c2017, p2020}.

The notion of isoclinism for Lie algebras was first introduced by Moneyhun \cite{km1994} in 1994. Eshrati et al. \cite{es2016} studied various properties of isoclinism in $n$-Lie algebras. Isoclinism of various algebraic structures have been exploid, for more details see \cite{kh2022,m2009, m2013, m2018, sn2020, p2020, rud2022, r2020, sa2021, saf2021,n2022}. Recently in 2020, Arabyani and Sheikh-mohseni  \cite{ar2020} introduced the concept of isoclinism on the relative central extensions of pairs of Lie algebras. Lately, isoclinism has been defined and studied for Hom-Lie algebra by Padhan et al. \cite{p2020}. In this paper, we study the relative central extensions of pairs of Hom-Lie algebras.

Firstly,x we define the notions such as isoclinism between a pair of Hom-Lie algebras, Hom-action and relative central extensions. In Section 2, we introduce the concept of isoclinism on the relative central extensions of a pair of Hom-Lie algebras which is a generalization of the work in \cite{ar2020}. We also give some equivalent conditions under which two relative central extensions are isoclinic. In Section 3, we define the concept of factor sets in the context of relative central extensions of a pair of Hom-Lie algebras. Then we show that under certain conditions, two concepts of isoclinism and isomorphism between the relative central extensions of a pair of finite dimensional Hom-Lie algebras are same. In fact, we show that under some conditions two finite dimensional relative central extensions are isoclinic if and only if they are isomorphic.

\begin{definition}
A Hom-Lie algebra $(L,\alpha_L)$ is a non-associative algebra $L$ together with a bilinear map $[.,.]:L\times L\rightarrow L$ and a linear map $\alpha_L:L\rightarrow L$ satisfying
\vspace{0.2cm}

\hspace{1cm} $[x,y]=-[y,x]$ \hfill (skew-symmetry)
\vspace{0.1cm}

\hspace{1cm} $[\alpha_L(x),[y,z]]+[\alpha_L(y),[z,x]]+[\alpha_L(z),[x,y]]=0$ \hfill (Hom-Jacobi identity)
\vspace{0.2cm}

for all $x,y,z\in L$.
\end{definition}

A Hom-Lie subalgebra $(H,\alpha_H)$ of a Hom-Lie algebra $(L,\alpha_L)$ is a vector subspace $H$ of $L$ closed under the product, i.e., $[x,y]\in H~\forall ~x,y\in H$, together with the endomorphism $\alpha_H:H\rightarrow H$ being the restriction of $\alpha_L$ on $H$. A Hom-Lie subalgebra $(H,\alpha_H)$ of $(L,\alpha_L)$ is said to be an ideal if $[x,y]\in H~\forall ~x\in H,~y\in L$. The center of a Hom-Lie algebra $(L,\alpha_L)$ is the vector subspace $$Z(L)=\{x\in L~|~[x,y]=0~\forall~y\in L\}.$$
A Hom-Lie algebra $(L,\alpha_L)$ is said to be $multiplicative$ if  $\varphi([l_1,l_2])=[\alpha(l_1),\alpha(l_2)]$ for all $l_1,l_2\in L$. A multiplicative Hom-Lie algebra $(L,\alpha_L)$ is said to be $regular$ if $\alpha$ is bijective.

\begin{definition}
Let $(L_1,\alpha_1)$ and $(L_2,\alpha_2)$ be two Hom-Lie algebras. Then a morphism from $L_1$ to $L_2$ is a linear map $f:L_1\rightarrow L_2$ such that $f([l,m]_{L_1})=[f(l),f(m)]_{L_2}$ for all $l,m\in L_1$ and $f\circ\alpha_{1}=\alpha_{2}\circ f $ i.e., the following diagram commutes;
\vspace{0.0001cm}

 \begin{center}
  \begin{tikzpicture}[>=latex]
\node (x) at (0,0) {\(L_1\)};
\node (z) at (0,-2) {\(L_1\)};
\node (y) at (2.5,0) {\(L_2\)};
\node (w) at (2.5,-2) {\(L_2\)};
\draw[->] (x) -- (y) node[midway,above] {f};
\draw[->] (x) -- (z) node[midway,left] {$\alpha_1$};
\draw[->] (z) -- (w) node[midway,above] {f};
\draw[->] (y) -- (w) node[midway,right] {$\alpha_2$};
\end{tikzpicture}\\
 \end{center}
\end{definition}

\begin{definition}
Let $(M,\alpha_M)$ be an ideal of a Hom-Lie algebra $(L,\alpha_L)$. Then $(M,L)$ is said to be a pair of Hom-Lie algebras and we may define the commutator as
$$[M,L]=\langle [m,l]:m\in M,~l\in L\rangle$$
and the centre of $(M,L)$ can be defined as
 $$Z(M,L)=\{m\in M:[m,l]=0, \forall~l\in L\}.$$
\end{definition}

If $L$ is regular Hom-Lie algebra, then $[M,L]$ and $Z(M,L)$ are ideals of $L$. Now onwards we always assume that the the given Hom-Lie algebra is regular.

\begin{definition}
Let $(M_1,L_1)$ and $(M_2,L_2)$ be two pairs of Hom-Lie algebras. These two pairs are said to be \textit{isoclinic}, denoted by $(M_1,L_1)\sim(M_2,L_2)$, if there exists a pair of Hom-Lie isomorphisms $(\varphi,\theta)$ where, $\varphi:L_1/Z(M_1,L_1)\rightarrow L_2/Z(M_2,L_2)$ is such that $\varphi(\bar{M_1})=\bar{M_2}$, $\bar{M_j}=M_j/Z(M_j,L_j),~j=1,2$ and $\theta:[M_1,L_1]\rightarrow [M_2,L_2]$ satisfies $\theta([m_1,l_1])=[m_2,l_2],$ for all $m_1\in M_1, l_1\in L_1, \bar{m_2}\in \varphi(\bar{m_1}), \bar{l_2}\in \varphi(\bar{l_1})$, and the following diagram is commutative:
\vspace{0.001cm} \\
 \begin{center}
  \begin{tikzpicture}[>=latex]
\node (x) at (0,0) {\(M_1/Z(M_1,L_1)\times L_1/Z(M_1,L_1) \)};
\node (z) at (0,-3) {\(M_2/Z(M_2,L_2)\times L_2/Z(M_2,L_2)\)};
\node (y) at (6,0) {\([M_1,L_1]\)};
\node (w) at (6,-3) {\([M_2,L_2]\)};
\draw[->] (x) -- (y) node[midway,above] {$\mu$};
\draw[->] (x) -- (z) node[midway,right] {$\varphi^{2}$};
\draw[->] (z) -- (w) node[midway,above] {$\rho$};
\draw[->] (y) -- (w) node[midway,right] {$\theta$};
\end{tikzpicture}\\
 \end{center}
 \end{definition}

Observe that when $M_i = L_i$ for $i=1,2$ on the above definition, we have the definition for isoclinism  of Hom-Lie algebras \cite{p2020}.

\begin{definition}
Let $(L,\alpha_L)$ and $(K,\alpha_K)$ be two Hom-Lie algebras. A Hom-action of $L$ on $K$ is a linear map $L\otimes K\rightarrow K,~x\otimes k\mapsto ~^xk$, satisfying the following properties:
\vspace{0.1cm}
\begin{enumerate}
\item $^{[x,y]}\alpha_K(k)=~^{\alpha_L{(x)}}(^yk)-~^{\alpha_L{(y)}}(^xk)$
\vspace{0.1cm}
\item $^{\alpha_L{(x)}}[k,k^\prime]=[^xk,\alpha_K(k^\prime)]+[\alpha_K(k),~^x(k^\prime)]$
\vspace{0.1cm}
\item $\alpha_K(^xk)=~^{\alpha_L{(x)}}\alpha_K(k)$
\end{enumerate}
\vspace{0.1cm}
for all $x,y\in L,$ and $k,k^\prime \in K$.
\end{definition}

It is easy to see that if $K$ is an ideal of $L$, then by Lie multiplication we have an action of $L$ on $K$.

\begin{definition}
A relative central extension of a pair of Hom-Lie algebras $(M,L)$ is a homomorphism of Hom-Lie algebras $\sigma:(M^*,\alpha_*)\rightarrow (L,\alpha_L)$ together with an action of $L$ on $M^*$ satisfying the following conditions:
\begin{enumerate}
\item $\sigma(M^*)=M,$
\item $\sigma(^l{\alpha_*(m)})=[\alpha_L(l),\sigma(\alpha_*(m))],~$ for all $l\in L,~m\in M^*$,
\item $^{\sigma(m^\prime)}\alpha_*(m)=[m^\prime,m],~$ for all $m,m^\prime\in M^*$,
\end{enumerate}
\end{definition}

For a given relative central extension $\sigma: M^*\rightarrow L$, the $L$-commutator and the $L$-central subalgebras of $M^*$ are defined respectively, as follows: $$[M^*,L]=\{~^l\alpha_*(m)|~l\in L,m\in M^*\}$$ and $$Z(M^*,L)=\{m\in M^*|~^l\alpha_*(m)=0,\forall~ l\in L\}.$$
Observe that $\textnormal{Ker}~\sigma\subseteq Z(M^*,L)$ and $\textnormal{Ker}~\sigma\subseteq Z(M^*)$.

\vspace{0.3cm}

\section{\textbf{Isoclinic relative extensions}}

In this section, we introduce the concept of isoclinism on the relative central extensions of pairs of Hom-Lie algebras.

\begin{definition}
Let $(M_1,L_1)$ and $(M_2,L_2)$ be two pairs of Hom-Lie algebras. Let there be two Hom-Lie homomorphisms $\gamma:(L_1,\alpha_1)\rightarrow(L_2,\alpha_2)$ and $\beta: (M_1^*,\alpha_1^*)\rightarrow (M_2^*,\alpha_2^*)$ with $\gamma(M_1)=M_2$ and $\beta([M_1^*,L_1])=[M_2^*,L_2]$ such that $\gamma \sigma_1(m_1)=\sigma_2 \beta(m_1)$, where $\sigma_i:(M_i^*,\alpha_i^*)\rightarrow (L_i,\alpha_i),~(i=1,2)$ are relative central extensions of $(M_i,L_i),~(i=1,2)$ respectively. Then the pair $(\gamma,\beta):\sigma_1\rightarrow \sigma_2$ is called a morphism from $\sigma_1$ to $\sigma_2$. If $\gamma$ and $\beta$ are isomorphic then the pair $(\gamma,\beta)$ is called an isomorphism. The isomorphism between $\sigma_1$ and $\sigma_2$ is denoted by $\sigma_1\cong\sigma_2$.
\end{definition}

\begin{definition}
The relative central extensions $\sigma_1:(M_1^*,\alpha_1^*)\rightarrow (L_1,\alpha_1)$ and $\sigma_2:(M_2^*,\alpha_2^*)\rightarrow (L_2,\alpha_2)$ are said to be isoclinic if there exist Hom-Lie isomorphisms $\gamma:(L_1,\alpha_1)\rightarrow(L_2,\alpha_2)$ with $\gamma(M_1)=M_2$ and $\beta^\prime: [M_1^*,L_1]\rightarrow [M_2^*,L_2]$ such that for all $m_1\in M_1^*,l_1\in L_1$ we have $\beta^\prime(^{l_1}\alpha_1^*(m_1))=~ ^{l_2}\alpha_2^*(m_2)$, where $m_2\in M_2^*,l_2\in L_2$ and  $\gamma\sigma_1(\alpha_1^*(m_1))=\sigma_2(\alpha_2^*(m_2)),\gamma\alpha_1(l_1)=\alpha_2(l_2).$ In this case, the pair $(\gamma,\beta^\prime)$ is called an isoclinism from $\sigma_1$ to $\sigma_2$ and we write $(\gamma,\beta^\prime):\sigma_1\cong\sigma_2$. A morphism $(\gamma, \beta):\sigma_1 \rightarrow \sigma_2$ is called isoclinic if the pair $(\gamma,\beta|_{[M_1^*,L_1]})$ is an isoclinism from $\sigma_1$ to $\sigma_2$.
\end{definition}

Suppose that $(M_1,L_1)$ and $(M_2,L_2)$ be two pairs of Hom-Lie algebras and let for $i=1,2,~\overline{M_i}=M_i/Z(M_i,L_i),~\overline{L_i}=L_i/Z(M_i,L_i)$. If $(\gamma,\beta^\prime)$ be an isoclinism between relative central extensions $\overline{\sigma_1}:\overline{M_1}\rightarrow\overline{L_1}$ and $\overline{\sigma_2}:\overline{M_2}\rightarrow\overline{L_2}$, then $\beta^\prime([\overline{m_1},\overline{l_1}])=[\overline{m_2},\overline{l_2}]$, where $\gamma(\overline{l_1})=\overline{l_2}$ and $\gamma(\overline{m_1})=\overline{m_2}$. Now, if we consider $\beta:[M_1,L_1]\rightarrow [M_2,L_2]$, a Hom-Lie isomorphism defined by $\beta([m_1,l_1])=[m_2,l_2]$, then the pair $(\gamma, \beta)$ will be an isoclinism from $(M_1,L_1)$ to $(M_2,L_2)$. Therefore, two pairs of Hom-Lie algebras $(M_1,L_1)$ and $(M_2,L_2)$ are isoclinic if the relative central extensions $\overline{\sigma_1}$ and $\overline{\sigma_2}$ are isoclinic.

Now we give some examples of isoclinic morphisms.

\vspace{0.1cm}

\noindent{\sc Example 1.} Let $(L,\alpha_L)$ be a Hom-Lie algebra and $A$ be an abelian Hom-Lie subalgebra of $L$, then the maps $\pi_L:L\times A\rightarrow L$ and $i_L:L\rightarrow L\times A$ denote the projective and canonical Hom-Lie homomorphisms, respectively. Let $\sigma:(M^*,\alpha_*)\rightarrow (L,\alpha_L)$ be a relative central extension of the pair $(M,L)$. Then the morphism $\sigma\pi_{M^*}:M^*\times A\rightarrow L$ is a relative central extension of $(M,L)$ together with an action of $L$ on $M^*\times A$ defined by $^l(m,a)=(^lm,a)$. It can be easily verified that $(1_L,\pi_{M^*}):\sigma\pi_{M^*}\rightarrow \sigma$ and $(1_L,i_{M^*}):\sigma\rightarrow \sigma\pi_{M^*}$ are isoclinic epimorphism and isoclinic monomorphism, respectively.

\vspace{0.3cm}

\noindent{\sc Example 2.} Let $\sigma:(M^*,\alpha_*)\rightarrow (L,\alpha_L)$ be a relative central extension of the pair $(M,L)$ and $N$ be an ideal of $M^*$ such that $N\subseteq \textnormal{Ker}{\sigma}$. Let $\bar{\sigma}:M^*/N\rightarrow L$ be the morphism induced by $\sigma$. This $\bar{\sigma}$ along with an action of $L$ on $M^*/N$ given by $^l(m+N)=(~^lm+N)$ forms a relative central extension of $(M,L)$. Let $\rho_{M^*}:M^*\rightarrow M^*/N$ denote the natural epimorphism. Then we find an isoclinic epimorphism $(1_L,\rho_{M^*}):\sigma\rightarrow\bar{\sigma}$ from $\sigma$ to $\bar{\sigma}$.

\begin{lemma} \label{lem1}
Let $\sigma_1:(M_1^*,\alpha_1^*)\rightarrow (L_1,\alpha_1)$ and $\sigma_2:(M_2^*,\alpha_2^*)\rightarrow (L_2,\alpha_2)$ be relative central extensions of the pairs of Hom-Lie algebras $(M_1,L_1)$ and $(M_2,L_2)$, respectively. If $(\gamma,\beta^\prime):\sigma_1\rightarrow\sigma_2$ is an isoclinism, then
\vspace{0.1cm}
\begin{enumerate}
\item $\gamma\sigma_1(x)=\sigma_2\beta^\prime(x)$, for all $x\in[M_1^*,L_1]$.
\vspace{0.1cm}
\item $\beta^\prime(\textnormal{Ker}\sigma_1\cap[M_1^*,L_1])=\textnormal{Ker}\sigma_2\cap[M_2^*,L_2]$.
\vspace{0.1cm}
\item $\beta^\prime(^{l_1}x)=~^{l_2}\beta^\prime(x)$, for all $x\in [M_1^*,L_1],l_i\in L_i,i=1,2$ with $\gamma\alpha_1(l_1)=\alpha_2(l_2)$.
\end{enumerate}
\end{lemma}

\begin{proof}
\begin{enumerate}
\item Let $x\in [M_1^*,L_1]$ such that $x=~^{l_1}\alpha_1^*(m_1)$, for some $l_1\in L_1$ and $m_1\in M_1^*$. Then, $$\gamma\sigma_1(x)=\gamma\sigma_1(^{l_1}\alpha_1^*(m_1))=\gamma[\alpha_1(l_1),\sigma_1(\alpha_1^*(m_1))]=[\gamma\alpha_1(l_1),\gamma\sigma_1(\alpha_1^*(m_1))].$$ Now if $\gamma\alpha_1(l_1)=\alpha_2(l_2)$ and $\gamma\sigma_1(\alpha_1^*(m_1))=\sigma_2(\alpha_2^*(m_2))$ where $l_2\in L_2$ and $m_2\in M_2^*$, then $$\gamma\sigma_1(x)=[\alpha_2(l_2),\sigma_2(\alpha_2^*(m_2))]=\sigma_2(^{l_2}\alpha_2^*(m_2))=\sigma_2(\beta^\prime(x)).$$
\item Let $x\in \textnormal{Ker}\sigma_1\cap[M_1^*,L_1]$, then $\sigma_1(x)=0$ and $x=~^{l_1}\alpha_1^*(m_1)$, for some $l_1\in L_1,~m_1\in M_1^*$. Suppose that $\gamma\alpha_1(l_1)=\alpha_2(l_2)$ and $\gamma\sigma_1(\alpha_1^*(m_1))=\sigma_2(\alpha_2^*(m_2))$, where $l_2\in L_2$ and $m_2\in M_2^*$. Now from the definition of isoclinism we have $\beta^\prime(^{l_1}\alpha_1^*(m_1))=~^{l_2}\alpha_2^*(m_2)$. \\Also we have, $$\sigma_2(^{l_2}\alpha_2^*(m_2))=[\alpha_2(l_2),\sigma_2(\alpha_2^*(m_2))]=\gamma[\alpha_1(l_1),\sigma_1(\alpha_1^*(m_1))]=\gamma\sigma_1(x)=0.$$ Therefore, $\beta^\prime(x)\in\textnormal{Ker}\sigma_2\cap[M_2^*,L_2]$ and the converse is obvious.
\item From (1), we have $\gamma\sigma_1(x)=\sigma_2(\beta^\prime(x))$. So by the isoclinic properties of the relative central extensions $\sigma_1$, $\sigma_2$ and for all $x\in [M_1^*,L_1], l_1\in L_1,\gamma\alpha_1(l_1)=\alpha_2(l_2)$, we can clearly have $\beta^\prime(^{l_1}x)=~^{l_2}\beta^\prime(x)$.
\end{enumerate}
\end{proof}

Let $(M_1,L_1)$ and $(M_2,L_2)$ be two pairs of Hom-Lie algebras and suppose that $\sigma_1:(M_1^*,\alpha_1^*)\rightarrow (L_1,\alpha_1)$ and $\sigma_2:(M_2^*,\alpha_2^*)\rightarrow (L_2,\alpha_2)$ are relative central extensions of these pairs, respectively. Let $\gamma:(L_1,\alpha_1)\rightarrow (L_2,\alpha_2)$ be an isomorphism such that $\gamma(M_1)=M_2$ and $$\overline{M^*}=\{(m_1,m_2)|m_i\in M_i^*,i=1,2,~\gamma\sigma_1(\alpha_1^*(m_1))=\sigma_2(\alpha_2^*(m_2))\}.$$ Then $\overline{M^*}$ is a subalgebra of $M_1^*\times M_2^*$. Also, the homomorphism
\begin{align*}
 \hat{\sigma}:\overline{M^*}&\longrightarrow L_1 \\(m_1,m_2)&\longmapsto \sigma_1(m_1)
\end{align*}
together with an action of $L_1$ on $\overline{M^*}$ defined by $^{l_1}(m_1,m_2)=(^{l_1}m_1,~^{l_2}m_2),$ where $\gamma\alpha_1(l_1)=\alpha_2(l_2)$ is a relative central extension of the pair $(M_1,L_1)$.

\begin{proposition}\label{pro1}
The isomorphism $\gamma:(L_1,\alpha_1)\rightarrow (L_2,\alpha_2)$ induces an isoclinism from $\sigma_1$ to $\sigma_2$ if and only if there exist isoclinic epimorphisms from $\hat{\sigma}$ onto $\sigma_1$ and $\sigma_2$.
\end{proposition}

\begin{proof}
The necessary condition holds true obviously. To prove the converse part, let $\gamma$ induces an isoclinism from $\sigma_1$ to $\sigma_2$. Then there exists an isomorphism $\beta^\prime: [M_1^*,L_1]\rightarrow [M_2^*,L_2]$ induced by $\gamma$ such that the pair $(\gamma,\beta^\prime)$ is an isoclinism from $\sigma_1$ to $\sigma_2$. Now according to the hypothesis and by Lemma \ref{lem1} (1) we have $$[\overline{M^*},L_1]=\{(m_1,\beta^\prime(m_1))|m_1\in [M_1^*,L_1]\}.$$ Let $\beta_i:\overline{M^*}\rightarrow M_i^*$ be the projective homomorphisms and let $\gamma_1=1_{L_1},\gamma_2=\gamma$. Now it can be easily checked that $(\beta_1,\gamma_1):\hat{\sigma}\rightarrow \sigma_1$ and $(\beta_2,\gamma_2):\hat{\sigma}\rightarrow\sigma_2$ are isoclinic epimorphisms and the result follows.
\end{proof}

Let $A=\overline{M^*}/[\overline{M^*},L_1]$. Then $A$ is an abelian Hom-Lie algebra. Thus by example 1, for any central relative extension $\sigma:M^*\rightarrow L$ of the pair $(M,L)$, $\sigma{\pi_{M^*}}:M^*\times A\rightarrow L$ is also a relative central extension. The following proposition explains more of this.

\begin{proposition}\label{pro2}
Let $(\gamma, \beta^\prime)$ be an isoclinism from $\sigma_1$ to $\sigma_2$. Then there exist isoclinic monomorphisms from $\hat{\sigma}$ into $\sigma_1\pi_{M_1^*}$ and $\sigma_2\pi_{M_2^*}$.
\end{proposition}

\begin{proof}
Let's consider a map $\overline{\beta_i}:\overline{M^*}\rightarrow M_i^*\oplus A$ given by $$\overline{\beta_i}(x)=(\beta_i(x),x+[\overline{M^*},L_1]),$$ for $i=1,2$ and $\beta_i$'s are as defined in Proposition \ref{pro1}. Clearly, $\overline{\beta_i}$ is a Hom-Lie homomorphism. Also we have, $[\overline{M^*},L_1]=\{(m_1,\beta^\prime(m_1))|m_1\in [M_1^*,L_1]\}.$ Now if $x=(m_1,m_2)\in \textnormal{Ker}\overline{\beta_i}$, then $m_i=0$ and $m_2=\beta^\prime(m_1)$, which implies that $\textnormal{Ker}\overline{\beta_i}=0$. Hence $\overline{\beta_i}$ is a Hom-Lie monomorphism and it can be easily seen that the morphisms $(\overline{\beta_1},1_{L_1}):\hat{\sigma}\rightarrow\sigma_1{\pi_{M_1^*}}$ and $(\overline{\beta_2},\gamma):\hat{\sigma}\rightarrow\sigma_2{\pi_{M_2^*}}$ are isoclinic monomorphisms.
\end{proof}

\begin{proposition}\label{pro3}
The isomorphism $\gamma:(L_1,\alpha_1)\rightarrow (L_2,\alpha_2)$ induces an isoclinism from $\sigma_1$ to $\sigma_2$ if and only if for some ideal $T$ of $M_1^*\oplus A$ with $T\subseteq \textnormal{Ker}\sigma_1{\pi_{M_1^*}}$, there exist isoclinic monomorphisms from $\sigma_1$ and $\sigma_2$ into the relative central extension $\overline{\sigma_1{\pi_{M_1^*}}}:(M_1^*\times A)/T\rightarrow L_1$.
\end{proposition}

\begin{proof}
The necessary condition is obvious. To prove the converse part, let's suppose that $\gamma $ induces an isoclinism $(\gamma, \beta^\prime)$ from $\sigma_1$ to $\sigma_2$. Let $T=\{(x,(x,0)+[\overline{M^*},L_1])|x\in\textnormal{Ker}\sigma_1\}$. Then clearly $T$ is an ideal of $M_1^*\times A$ with $T\subseteq \textnormal{Ker}\sigma_1{\pi_{M_1^*}}$. \\
\vspace{0.00001cm}
Now, we define two Hom-Lie homomorphisms $\delta_1:M_1^*\rightarrow (M_1^*\times A)/T$ and $\delta_2: M_2^*\rightarrow (M_1^*\times A)/T$ as follows: $$\delta_1(m_1)=(m_1,[\overline{M^*},L_1])+T$$ and $$\delta_2(m_2)=(m_1,(m_1,m_2)+[\overline{M^*},L_1])+T,$$ where $m_i\in M_i^*~(i=1,2)$ and $\gamma\sigma_1(\alpha_1^*(m_1))=\sigma_2(\alpha_2^*(m_2))$. We claim that $\delta_1$ and $\delta_2$ are monomorphisms. If $m_1\in \textnormal{Ker}\delta_1$, then $m_1\in \textnormal{Ker}\sigma_1$ and $\beta^\prime(m_1)=0$ and thereby $m_1=0$. Similarly, $\textnormal{Ker}\delta_2=0$. Now it can be easily checked that the morphisms $(\delta_1,1_{L_1}):\sigma_1\rightarrow\overline{\sigma_1{\pi_{M_1^*}}}$ and $(\delta_2, \gamma^{-1}):\sigma_2\rightarrow\overline{\sigma_1{\pi_{M_1^*}}}$ are isoclinic monomorphisms, as required.
\end{proof}

\section{\textbf{Factor set on an isoclinic relative extension}}

\begin{definition}
Let $(M,L)$ be a pair of Hom-Lie algebras. A relative central extension $\sigma:(M^*,\alpha_*)\rightarrow (L,\alpha_L)$ is said to be \textit{finite dimensional} , if $(M^*,\alpha_*)$ is a finite dimensional Hom-Lie algebra.
\end{definition}

\begin{definition}
Let $\sigma:(M^*,\alpha_*)\rightarrow (L,\alpha_L)$ be a relative central extension of a pair of Hom-Lie algebras $(M,L)$. A \textit{factor set} on $\sigma$ is defined as a skew-bilinear map $$f:(L,\alpha_L)\times (L,\alpha_L)\rightarrow\textnormal{Ker}(\sigma)$$ such that the following conditions are satisfied:
\begin{enumerate}
\item $f(l_1,l_1)=0$
\vspace{0.1cm}
\item $f([{l_1},{l_2}],\alpha_L({l_3}))+f([{l_2},{l_3}],\alpha_L({l_1}))+f([{l_3},{l_1}],\alpha_L({l_2}))=0$
\end{enumerate}
\vspace{0.1cm}
for all ${l_1},{l_2},{l_3}\in L$.
\end{definition}

\vspace{0.3cm}
\begin{lemma}\label{lem101}
Let $f$ be a factor set on the relative central extension $\sigma$ of the pair $(M,L)$. Then the product $\textnormal{Ker}\sigma\times M$ is a Hom-Lie algebra with the bracket defined as, $$[(x_1,m_1),(x_2,m_2)]=(f(m_1,m_2),[m_1,m_2]),$$ along with a linear map ${\alpha_f}:\textnormal{Ker}\sigma\times M\rightarrow\textnormal{Ker}\sigma\times M$ such that ${\alpha_f}(x,m)=(\alpha_*(x),\alpha_L(m)),$ where $\alpha_*$ and $\alpha_L$ are as defined in Definition 3.2.
\end{lemma}
\begin{proof}
First we will check the anti-symmetry
\begin{align*}
[(x_1,m_1),(x_2,m_2)]&=(f(m_1,m_2),[m_1,m_2]) \\&=(-f(m_2,m_1),-[m_2,m_1]) \\&=-[(x_2,m_2),(x_1,m_1)].
\end{align*}
Now to check the Hom-Jacobi identity, we have
\begin{align*}
[\alpha_f(x_1,m_1),[(x_2,m_2),(x_3,m_3)]] &=[(\alpha_*(x_1),\alpha_L(m_1)),(f(m_2,m_3),[m_2,m_3])] \\&=(f(\alpha_L(m_1),[m_2,m_3]),[\alpha_L(m_1),[m_2,m_3]]),
\end{align*}
by performing similar calculations we can find that
\begin{align*}
	[\alpha_f(x_1,m_1),[(x_2,m_2),(x_3,m_3)]] &+[\alpha_f(x_2,m_2),[(x_3,m_3),(x_1,m_1)]] \\&+[\alpha_f(x_3,m_3),[(x_1,m_1),(x_2,m_2)]]=0.
\end{align*}
Therefore $\textnormal{Ker}\sigma\times M$ is a Hom-Lie algebra.
\end{proof}
We denote the above Hom-Lie algebra by $(\textnormal{Ker}\sigma\times M)_f$. Then the projective map,
\begin{align*}
\sigma_f:(\textnormal{Ker}\sigma\times M)_f&~\rightarrow ~L \\(x,m)&~\mapsto~ m
\end{align*}
together with an action of $L$ on $(\textnormal{Ker}\sigma\times M)_f$ defined by $^l(x,m)=(f(m,l),[m,l])$is a relative central extension of the pair $(M,L)$.

\vspace{0.3cm}

\begin{definition}
Let $\sigma:(M^*,\alpha_*)\rightarrow (L,\alpha_L)$ be a relative central extension of a pair of Hom-Lie algebras $(M,L)$.  If $\textnormal{Ker}\sigma\subseteq [M^*,L]$, then $\sigma$ is called as a \textit{stem relative central extension}.
\end{definition}

\begin{lemma}\label{lem11}
Let $\sigma_1:(M_1^*,\alpha_1^*)\rightarrow (L_1,\alpha_1)$ and $\sigma_2:(M_2^*,\alpha_2^*)\rightarrow (L_2,\alpha_2)$ be two relative central extensions of the pairs $(M_1,L_1)$ and $(M_2,L_2)$ of finite dimensional Hom-Lie algebras, respectively. Then,
\begin{enumerate}
\item $\sigma_1$ is a stem relative central extension if and only if $\textnormal{Ker}\sigma_1$ contains no non-zero ideal $N$ satisfying $N\cap[M_1^*,L_1]=0$.
\item If $\sigma_1$ and $\sigma_2$ are isoclinic stem relative central extensions, then $\textnormal{Ker}\sigma_1\cong\textnormal{Ker}\sigma_2$. In particular, if the Hom-Lie algebras $M_1^*$ and $M_2^*$ are finite dimensional, then $\textnormal{dim}M_1^*=\textnormal{dim}M_2^*$.
\end{enumerate}
\end{lemma}

\begin{proof}
\begin{enumerate}
\item Let's suppose that $\sigma_1$ is stem and $N$ is an ideal of $M_1^*$ with $N\subseteq \textnormal{Ker}\sigma_1$ and $ N\cap[M_1^*,L_1]=0$. But we know that $\textnormal{Ker}\sigma_1\subseteq Z(M_1^*,L_1)$. Also, since $\sigma_1$ is stem, so $\textnormal{Ker}\sigma_1\subseteq[M_1^*,L_1]$. Therefore, we have $$N\subseteq N\cap\textnormal{Ker}\sigma_1\subseteq N\cap Z(M_1^*,L_1)\cap [M_1^*,L_1]=N\cap [M_1^*,L_1]=0,$$ and the result follows.

\vspace{0.1cm}

Conversely, let $ \textnormal{Ker}\sigma_1\subsetneq Z(M_1^*,L_1)\cap [M_1^*,L_1].$ Then there exists a non-zero element $x\in\textnormal{Ker}\sigma_1\setminus (Z(M_1^*,L_1)\cap [M_1^*,L_1]) $. Now $\langle x\rangle$ is clearly a central ideal of $M_1^*$ and consequently, by hypothesis, we have $\langle x\rangle\cap [M_1^*,L_1]\neq 0$. So, for some non-zero element $a\in F, ~ ax\in [M_1^*,L_1]$, which is a contradiction. Therefore, $\textnormal{Ker}\sigma_1\subseteq Z(M_1^*,L_1)\cap [M_1^*,L_1]$ and $\sigma_1$ is a stem relative central extension.

\item Let $\sigma_1$ and $\sigma_2$ be isoclinic stem relative central extensions, then there exists an isomorphism $\gamma :(L_1,\alpha_1)\rightarrow (L_2,\alpha_2)$ with $\gamma(M_1)=M_2$. Therefore, $\textnormal{dim}M_1=\textnormal{dim}M_2$. Also, by Lemma \ref{lem1} (2), $\textnormal{Ker}\sigma_1\cong \textnormal{Ker}\sigma_2$. If $M_1^*$ and $M_2^*$ are finite dimensional, then by the isomorphism theorems, we have $\textnormal{dim}M_1^*=\textnormal{dim}M_2^*$.
\end{enumerate}
\end{proof}

The next result shows that every isoclinic family of the relative central extensions of pairs of Hom-Lie algebras contains a stem relative central extension.

\begin{corollary}\label{cor1}
 Any relative central extension is isoclinic to a stem relative central extension.
\end{corollary}

\begin{proof}
Let $\mathcal{A}=\{N|N \textnormal{~is~an~ideal~of~Ker}\sigma ~\textnormal{and}~N\cap[M^*,L]=0\}$, where $\sigma:M^*\rightarrow L$ is a relative central extension of $(M,L)$. Then the set $\mathcal{A}$ is non-empty, as it contains the zero ideal. Now if we define a partial ordering on $\mathcal{A}$ by inclusion then by Zorn's lemma, we can find a maximal ideal $N$ in $\mathcal{A}$. Since, $N\subset\textnormal{Ker}\sigma$, by example 2, $\overline{\sigma}:M^*/n\rightarrow L$ is a relative central extension and $\sigma\sim\overline{\sigma}$.

\vspace{0.1cm}

Now, let $K/N$ is an ideal of $M^*/N$ such that $K/N\subseteq\textnormal{Ker}\overline{\sigma}$ and $K/N\cap[M^*/N,L]=0$. Then $(K\cap[M^*,L]+N)/N=0$ and hence $K\cap[M^*,L]\subseteq N$. Since $N\cap[M^*,L]=0$, we conclude that $K\in \mathcal{A}$. Also, we have $N\subseteq K$. So by the maximality of $N$, it follows that $K=N$. Therefore, $K/N$ is zero ideal and hence $\overline{\sigma}$ is a stem relative central extension by Lemma \ref{lem11} (1).
\end{proof}

\begin{lemma} \label{lem2}
Let $\sigma_1:(M_1^*,\alpha_1^*)\rightarrow (L_1,\alpha_1)$ and $\sigma_2:(M_2^*,\alpha_2^*)\rightarrow (L_2,\alpha_2)$ be relative central extensions of the pairs of Hom-Lie algebras $(M_1,L_1)$ and $(M_2,L_2)$, respectively. Then
\begin{enumerate}
\item There exists a factor set $f:(L_1,\alpha_1)\times (L_1,\alpha_1)\rightarrow\textnormal{Ker}(\sigma_1)$ such that the relative central extensions $\sigma_1$ and $\sigma_{1f}$ are isomorphic.
\item If $\sigma_1$ and $\sigma_{2}$ are stem and $(\gamma,\beta^\prime):\sigma_1\rightarrow\sigma_{2}$ is an isoclinism, then there exists a factor set $g:(L_1,\alpha_1)\times (L_1,\alpha_1)\rightarrow\textnormal{Ker}(\sigma_1)$ such that the relative central extensions $\sigma_1$ and $\sigma_{1g}$ are isomorphic.
\end{enumerate}
\end{lemma}

\begin{proof}
\begin{enumerate}
\item Let $T_1$ be the vector space complement of $\textnormal{Ker}(\sigma_1)$ in $M_1^*$. Then for any $m_1\in M_1$, there is a unique element $t_{m_1}\in T_1$ with $\sigma_1(t_{m_1})=m_1$.
Therefore we have
\begin{align*}
\sigma_1(t_{[m_1,m_2]})=[m_1,m_2]=-[m_2,m_1]&=-\sigma_1(t_{[m_2,m_1]})\\&=\sigma_1(-t_{[m_2,m_1]}),
\end{align*}
which implies that $t_{[m_1,m_2]}=-t_{[m_2,m_1]}$ for all $m_1,m_2\in M_1.$

\vspace{0.1cm}

Again since $\sigma_1$ is a homomorphism, so we have
\begin{align*}
\sigma_1([t_{[m_1,m_2]},t_{\alpha_1(m_3)}])=[\sigma_1({t_{[m_1,m_2]}}),\sigma_1({t_{\alpha_1(m_3)}})]=[[m_1,m_2],\alpha_1(m_3)]=\sigma_1(t_{[[m_1,m_2],\alpha_1(m_3)]})
\end{align*}
$$\implies[t_{[m_1,m_2]},t_{\alpha_1(m_3)}]=t_{[[m_1,m_2],\alpha_1(m_3)]}.$$

\vspace{0.1cm}

Let's define a map $f:(L_1,\alpha_1)\times (L_1,\alpha_1)\rightarrow\textnormal{Ker}(\sigma_1)$ given by $f(m_1,m_2)=[t_{m_1},t_{m_2}]-t_{[m_1,m_2]}$ for all $m_1,m_2\in M_1$ and $f(x,y)=0$, if $x,y\in L_1\setminus M_1$. We will show that $f$ is a factor set.

\vspace{0.1cm}

From the definition it is clear that $f$ satisfies all the conditions of a factor set on $L_1\setminus M_1$. So it only remains to show that $f$ is also a factor set on $M_1$. It is obvious that $f(m_1,m_2)\in\textnormal{Ker}(\sigma_1)$. Now to check the skew-symmetric property of $f$, we take for all  $m_1,m_2\in M_1$
\begin{align*}
f(m_1,m_2)&=[t_{m_1},t_{m_2}]-t_{[m_1,m_2]}\\&=-[t_{m_2},t_{m_1}]+t_{[m_2,m_1]}\\&=-\{[t_{m_2},t_{m_1}]-t_{[m_2,m_1]}\}\\&=-f(m_2,m_1).
\end{align*}

To check the Jacobi identity, we take for all $m_1,m_2,m_3\in M_1$
\begin{align*}
f([m_1,m_2],\alpha_1(m_3))=[t_{[m_1m_2]},t_{\alpha_1(m_3)}]-t_{[[m_1,m_2],\alpha_1(m_3)]}=0,
\end{align*}
and similarly, $f([{m_2},{m_3}],\alpha_1({m_1}))=0=f([{m_3},{m_1}],\alpha_1({m_2}))$.
\\i.e., $f$ also satisfies the Jacobi identity and hence is a factor set. Now consider the mapping $\beta:(\textnormal{Ker}\sigma_1\times M_1)_f\rightarrow M_1^*$ given by $\beta(x_1,m_1)=x_1+t_{m_1}$. Then we have, $(x_1,m_1)=(x_2,m_2)\Leftrightarrow x_1+t_{m_1}=x_2+t_{m_2}\Leftrightarrow \beta{(x_1,m_1)}=\beta{(x_2,m_2)}$ i.e., $\beta$ is well defined and obviously bijective. Also,
\begin{align*}
\beta([(x_1,m_1),(x_2,m_2)])=\beta(f(m_1,m_2),[m_1,m_2])&=f(m_1,m_2)+t_{[m_1,m_2]}\\&=[t_{m_1},t_{m_2}]\\&=[x_1+t_{m_1},x_2+t_{m_2}]\\&=[\beta{(x_1,m_1)},\beta{(x_2,m_2)}].
\end{align*}
i.e., $\beta$ preserves the bracket operation. Again, we know that the relative central extension $\sigma_1:(M_1^*,\alpha_1^*)\rightarrow (L_1,\alpha_1)$ being a Hom-Lie homomorphism satisfies $\sigma_1\alpha_1^*=\alpha_1\sigma_1$. So, we have $\sigma_1\alpha_1^*(t_m)=\alpha_1\sigma_1(t_m)=\alpha_1(m)$, which implies that $\alpha_1^*(t_m)=t_{\alpha_1(m)}$. Now for some $(x,m)\in (\textnormal{Ker}\sigma_1\times M_1)_f$, we get
\begin{align*}
\beta{\alpha_f}(x,m)=\beta(\alpha_1^*(x),\alpha_1(m))&=\alpha_1^*(x)+t_{\alpha_1(m)}\\&=\alpha_1^*(x)+\alpha_1^*(t_m)\\&=\alpha_1^*(x+t_m)\\&=\alpha_1^*\beta(x,m),
\end{align*}
i.e., $\beta{\alpha_f}=\alpha_1^*\beta$, which confirms that $\beta$ is a Hom-Lie isomorphism. Therefore, $(1_{L_1},\beta):\sigma_{1f}\rightarrow \sigma_1$ is an isomorphism between the central extensions $\sigma_{1f}$ and $\sigma_1$.
\vspace{0.1cm}
\item By Lemma \ref{lem1}(2), we have $\beta^\prime(\textnormal{Ker}\sigma_1)=\textnormal{Ker}\sigma_2$. Since $\sigma_2$ is a stem relative extension, so from the above proof, we can conclude that there exists a factor set $h:(L_2,\alpha_2)\times (L_2,\alpha_2)\rightarrow\textnormal{Ker}(\sigma_2)$ such that the relative central extensions $\sigma_2$ and $\sigma_{2h}$ are isomorphic. Define a map $g:(L_1,\alpha_1)\times (L_1,\alpha_1)\rightarrow\textnormal{Ker}(\sigma_1)$ given by $g(m_1,m_2)=\beta^{\prime-1}(h(\gamma(m_1),\gamma(m_2)))$ for all $m_1,m_2\in M_1$ and otherwise $g(x,y)=0.$ It can be easily shown that $g$ is a factor set.
\vspace{0.1cm} \\
Now consider a map $\theta:(\textnormal{Ker}\sigma_1\times M_1)_g\rightarrow (\textnormal{Ker}\sigma_2\times M_2)_h$ defined by $\theta(x_1,m_1)=(\beta^\prime(x_1),\gamma(m_1))$. It is obvious that $\theta$ is well defined and bijective. Also $\theta$ is a Hom-Lie homomorphism as,
\begin{align*}
\theta[(x_1,m_1),(x_2,m_2)]_g&=\theta(g(m_1,m_2),[m_1,m_2])\\&=\theta(\beta^{\prime-1}(h(\gamma(m_1),\gamma(m_2))),[m_1,m_2])\\&=(\beta^{\prime}(\beta^{\prime-1}(h(\gamma(m_1),\gamma(m_2)))),\gamma([m_1,m_2]))\\&=(h(\gamma(m_1),\gamma(m_2)),[\gamma(m_1),\gamma(m_2)])\\&=[(\beta^\prime(x_1),\gamma(m_1)),(\beta^\prime(x_2),\gamma(m_2))]_h\\&=[\theta(x_1,m_1),\theta(x_2,m_2)]_h,
\end{align*}
and if $\alpha_g$ and $\alpha_h$ are the linear maps in the Hom-Lie algebras $(\textnormal{Ker}\sigma_1\times M_1)_g$ and $(\textnormal{Ker}\sigma_2\times M_2)_h$ respectively, then
\begin{align*}
\theta\alpha_g(x_1,m_1)=\theta(\alpha_1^*(x_1),\alpha_1(m_1))&=(\beta^\prime\alpha_1^*(x_1),\gamma\alpha_1(m_1))\\&=(\alpha_2^*\beta^\prime(x_1),\alpha_2\gamma(m_1))\\&=\alpha_h(\beta^\prime(x_1),\gamma(m_1))\\&=\alpha_h\theta(x_1,m_1).
\end{align*}
i.e., $\theta$ is a Hom-Lie isomorphism and hence $(\gamma,\theta)$ is an isomorphism between $\sigma_{1g}$ and $\sigma_{2h}$. Therefore, $\sigma_{1g}\cong\sigma_{2h}\cong\sigma_{2}$.
\end{enumerate}
\end{proof}

\begin{proposition}\label{pro4}
Let $\sigma:(M^*,\alpha_*)\rightarrow (L,\alpha_L)$ be a finite dimensional relative central extension and $f,g: (L,\alpha_L)\times  (L,\alpha_L)\rightarrow\textnormal{Ker}\sigma$ be factor sets on $\sigma$ such that $\textnormal{dim}(\textnormal{Ker}\sigma\times M)_f=\textnormal{dim}(\textnormal{Ker}\sigma\times M)_g$, $\sigma_f$ is a stem relative extension and the extensions  $\sigma_f$ and $\sigma_g$ are isoclinic. Then $\sigma_f$ and $\sigma_g$ are isomorphic.
\end{proposition}

\begin{proof}
Let $(\gamma,\beta^\prime)$ be an isoclinism between $\sigma_f$ and $\sigma_g$. Then from Lemma \ref{lem1}(2), it follows that $\beta^\prime (\textnormal{Ker}\sigma_f)=\textnormal{Ker}\sigma_g$. Now for all $m\in M,l\in L$, we have $$\beta^\prime(^l(0,m))=~^{\gamma(l)}(0,\gamma(m))=(g(\gamma(m),\gamma(l)),\gamma([m,l])),$$ and $$\beta^\prime(^l(0,m))=\beta^\prime(f(m,l),[m,l])=\beta^\prime(f(m,l),0)+\beta^\prime(0,[m,l]).$$

\vspace{0.1cm}

Let $d([m,l])$ be the first component of $\beta^\prime(^l(0,m))$. Then we can define a linear map $d:[M,L]\rightarrow\textnormal{Ker}\sigma$ satisfying $\rho\beta^\prime(f(m,l),0)+d([m,l])=g(\gamma(m),\gamma(l))$, where $\rho:\textnormal{Ker}\sigma_g\rightarrow\textnormal{Ker}\sigma$ is the projective map. If we take $d$ to be zero on the vector space complement of $[M,L]$ in $M$ then $d$ can be defined on whole $M$. Now it is easy to see that the map $\lambda:(\textnormal{Ker}\sigma\times N)_f\rightarrow(\textnormal{Ker}\sigma\times N)_g$ given by $\lambda(x,l)=\beta^\prime(x,0)+(d(l),\gamma(l))$, is an isomorphism. As $\lambda|_{\textnormal{Ker}\sigma_f}=\beta^\prime|_{\textnormal{Ker}\sigma_f}$ and $(\lambda,\gamma):\sigma_f\rightarrow\sigma_g$ is a morphism, we conclude that $\sigma_f$ and $\sigma_g$ are isomorphic.
\end{proof}

\begin{corollary}\label{cor2}
Let $\sigma_1:(M_1^*,\alpha_1^*)\rightarrow (L_1,\alpha_1)$ and $\sigma_2:(M_2^*,\alpha_2^*)\rightarrow (L_2,\alpha_2)$ be finite dimensional stem relative central extensions of the pairs $(M_1,L_1)$ and $(M_2,L_2)$ respectively. Then $\sigma_1$ and $\sigma_2$ are isoclinic if and only if they are isomorphic.
\end{corollary}

\begin{proof}
Let $\sigma_1$ and $\sigma_2$ are isoclinic. Then by lemma \ref{lem2}, there exist factor sets $f,g:(L_1,\alpha_1)\times  (L_1,\alpha_1)\rightarrow\textnormal{Ker}\sigma_1$ such that $\sigma_1\cong \sigma_{1f}$ and $\sigma_2\cong \sigma_{1g}$. Therefore, $ \sigma_{1f}$ and $ \sigma_{1g}$ are isoclinic and since $(\textnormal{Ker}\sigma_1\times M_1)_f$ and  $(\textnormal{Ker}\sigma_1\times M_1)_g$ are finite dimensional, so we can have $\textnormal{dim}(\textnormal{Ker}\sigma_1\times M_1)_f=\textnormal{dim}(\textnormal{Ker}\sigma_1\times M_1)_g$. Hence by Proposition \ref{pro4}, $\sigma_{1f}\cong\sigma_{1g}.$ Therefore, $\sigma_1\cong\sigma_{1f}\cong\sigma_{1g}\cong\sigma_2$ and the result follows.
\end{proof}

\vspace{0.1cm}

\noindent{\sc Example 3.} Let $\sigma:(M^*,\alpha_*)\rightarrow (L,\alpha_L)$ be a relative central extension of $(M,L)$. Let $T$ be a Hom-Lie subalgebra of $M^*$ such that $M^*=T+\textnormal{Ker}\sigma$ and also $\sigma(T)=M$. Then the map $\sigma_T:T\rightarrow L$ defined by $\sigma_T(t)=\sigma(t)$ for all $t\in T$ is a relative central extension of $(M,L)$ and $(1_L,i):\sigma_T\rightarrow \sigma$ is an isoclinic monomorphism, where $i:T\rightarrow M^*$ is an inclusion map.

\vspace{0.1cm}

The next theorem helps to determine the structure of all the relative central extensions in an isoclinism family of a given relative central extension.

\begin{theorem}\label{thm1}
Let $\mathcal{C}$ be an isoclinism family of finite dimensional relative central extensions. Then $\mathcal{C}$ contains a stem relative central extension $\sigma_1:(M_1^*,\alpha_1^*)\rightarrow (L_1,\alpha_1)$ and relative central extension in $\mathcal{C}$ is the form of $\sigma_1\pi_{M_1^*}:M_1^*\times A\rightarrow L_1$, in which $A$ is a finite dimensional abelian Hom-Lie algebra.
\end{theorem}

\begin{proof}
From Corollary \ref{cor1}, it is clear that $\mathcal{C}$ contains a stem relative central extension $\sigma_1$. We know that for any finite dimensional abelian Hom-Lie algebra $A$, the relative central extensions $\sigma_1:M_1^*\rightarrow L_1$ and $\sigma_1\pi_{M_1^*}:M_1^*\times A\rightarrow L_1$ are isoclinic and consequently $\sigma_1\pi_{M_1^*}\in \mathcal{C}$.

\vspace{0.1cm}

Now, let $\sigma:M^*\rightarrow L$ be an arbitrary relative central extension in $\mathcal{C}$. Then there exists an ideal $N$ of $\textnormal{Ker}\sigma$ such that $\textnormal{Ker}\sigma=N\times(\textnormal{Ker}\sigma\cap(M^*)^2)$, where $(M^*)^2$ is the derived Hom-Lie subalgebra of $M^*$ and by the proof of Corollary \ref{cor1}, and example 2, the map $\bar{\sigma}:M^*/N\rightarrow L$ is a stem relative central extension in $\mathcal{C}$. If we choose the subspace $T$ of $M^*$ such that $(M^*)^2\subseteq T$ and $T\times N=M^*$, then $T$ is a Hom-Lie subalgebra of $M^*$ with $\sigma(T)=M$ and, $\sigma_1$ and $\bar{\sigma}$ are isoclinic. By Corollary \ref{cor2}, we get $\sigma_1\cong\sigma_T$. Therefore, $\sigma\cong\sigma_T\pi_T\cong\sigma_1\pi{M_1^*}$, where $\sigma_T\pi_T:T\times N\rightarrow L$ and $\sigma_1\pi{M_1^*}:M_1^*\times N\rightarrow L$ are relative central extensions of the pair $(M,L)$ and $N$ is a finite dimensional Hom-Lie algebra.
\end{proof}

redpajama_set_name: RedPajamaArXiv


text:
Q: JPA - A NullPointerException was thrown while extracting a value from the instance variable I'm building an enterprise application for a subject, and I have some objects inserted in a database all mapped with JPA from the following classes:
Aula.java, Sessao.java, Instalacao.java
Both Aula.java and Instalacao.java are  @Entity and Sessao.java is @Embeddable and it's @Embedded in the Instalacao.java.
The algorithm used goes something like this:
I query for a specific Aula and perform some changes to it.
I query for a specific Instalacao, create a new Sessao with info from the Aula retrieved and add it to the queried Instalacao, which has a list of Sessao
Here are some of the classes mentioned:
public void ativarAula(String nome, String instalacao, Calendar inicio, Calendar fim, int maxAlunos)
        throws ApplicationException {

    EntityManager em = emf.createEntityManager();

    AulaCatalog aulaCatalog = new AulaCatalog(em);
    InstalacaoCatalog instalacaoCatalog = new InstalacaoCatalog(em);

    try {
        Instalacao instal = instalacaoCatalog.getInstalacao(instalacao);
        Aula aula = aulaCatalog.getAula(nome);

        em.getTransaction().begin();
        aulaCatalog.activateAula(aula, instal, inicio, fim, maxAlunos);
        em.getTransaction().commit();
    } catch (Exception e) {
        // Exceptions
    } finally {
        em.close();
    }
}

public void activateAula(Aula aula, Instalacao instalacao, Calendar inicio, Calendar fim, int maxAlunos)
        throws ApplicationException {

    // Verifications

    aula.setActivo(true);
    aula.setDataInicio(inicio);
    aula.setDataFim(fim);
    aula.setInstalacao(instalacao);
    aula.setMaxAlunos(maxAlunos);

    createSessoes(aula, instalacao);
}

private void createSessoes(Aula aula, Instalacao instalacao) {

    List<Calendar> datas = aula.getAulaSpecificDates();

    for (Calendar dia : datas) {
        Sessao novaSessao = new Sessao(aula.getNome(), dia, aula.getDuracao(), aula.getMaxAlunos());
        instalacao.setSessao(novaSessao);
    }
}

============ Sessao.java =============
@Embeddable
public class Sessao implements Comparable<Sessao> {

    public static final String DATE = "data";

    public static final String AULA = "nomeAula";

    @Column(nullable = false)
    private String nomeAula;

    @Column(nullable = false)
    @Temporal(TemporalType.TIMESTAMP) private Calendar data;

    @Column(nullable = false)
    private int duracao;

    @Column(nullable = false)
    private int vagas;

    /**
     * Constructor needed by JPA.
     */
    protected Sessao() {
    }

    public Sessao(String nomeAula, Calendar data, int duracao, int vagas) {
        this.nomeAula = nomeAula;
        this.data = data;
        this.duracao = duracao;
        this.vagas = vagas;
    }

//Getters and setters

============ Aula.java =============
@Entity
@NamedQueries({
    @NamedQuery(name=Aula.FIND_BY_NAME,
            query="SELECT a FROM Aula a WHERE a.nomeAula = :" + Aula.NAME),

    @NamedQuery(name=Aula.FIND_BY_MODALIDADE,
                query="SELECT a FROM Aula a WHERE a.modalidade = :" + Aula.MODALITY),

    @NamedQuery(name=Aula.FIND_ATIVAS_BY_MODALIDADE,
                query="SELECT a FROM Aula a WHERE a.modalidade = :" + Aula.MODALITY
                + " AND a.activo = :" + Aula.ACTIVE),
})
public class Aula {

    // Named query name constants
    public static final String FIND_BY_NAME = "Aula.findByName";
    public static final String NAME = "nomeAula";

    public static final String FIND_BY_MODALIDADE = "Aula.findByModalidade";
    public static final String MODALITY = "modalidade";

    public static final String FIND_ATIVAS_BY_MODALIDADE = "Aula.findAtivasByModalidade";
    public static final String ACTIVE = "activo";

    @Id private String nomeAula;

    @ManyToOne @JoinColumn(name = "MODALIDADE", nullable = false)
    private Modalidade modalidade;

    @Column(nullable = false) private LocalTime horaInicio;

    @Column(nullable = false) private int duracao;

    @ElementCollection @CollectionTable(name = "DIAS_SEMANA_AULA")
    private List<DiasSemana> diasSemana;

    private boolean activo;

    private int maxAlunos;

    @Temporal(TemporalType.DATE) private Calendar dataInicio;

    @Temporal(TemporalType.DATE) private Calendar dataFim;

    @ManyToOne @JoinColumn(name = "INSTALACAO")
    private Instalacao instalacao;

    /**
     * Constructor needed by JPA.
     */
    protected Aula() {
    }

    public Aula(String nome, Modalidade modalidade, LocalTime horaInicio, int duracao, List<DiasSemana> diasSemana) {
        this.nomeAula = nome;
        this.modalidade = modalidade;
        this.horaInicio = horaInicio;
        this.duracao = duracao;
        this.diasSemana = diasSemana;
        this.activo = false;
        this.dataInicio = null;
        this.dataFim = null;
        this.instalacao = null;
        this.maxAlunos = 0;
    }
//Getters and setters

============ Instalacao.java =============
@Entity
@NamedQueries({
    @NamedQuery(name=Instalacao.FIND_BY_NAME,
                query="SELECT i FROM Instalacao i WHERE i.nome = :" + Instalacao.NAME),

    @NamedQuery(name=Instalacao.GET_ALL_NAMES,
                query="SELECT i.nome FROM Instalacao i"),

    @NamedQuery(name=Instalacao.FIND_SESSOES_BY_DATE,
                query="SELECT s FROM Instalacao i inner join i.sessoes s"
                + " WHERE i.nome = :" + Instalacao.NAME
                + " AND s.data = :" + Sessao.DATE),

    @NamedQuery(name=Instalacao.FIND_SESSOES_BY_AULA,
                query="SELECT s FROM Instalacao i join i.sessoes s"
                + " WHERE i.nome = :" + Instalacao.NAME)
                + " AND s.nomeAula = :" + Sessao.AULA),

    @NamedQuery(name=Instalacao.FIND_SESSOES_BETWEEN_DATES,
                query="SELECT s FROM Instalacao i join i.sessoes s"
                + " WHERE i.nome = :" + Instalacao.NAME
                + " AND s.data <= :" + Sessao.DATE
                + " AND s.data >= :" + Sessao.DATE),
})
public class Instalacao {

    public static final String FIND_BY_NAME = "Instalacao.findByName";
    public static final String NAME = "nome";

    public static final String GET_ALL_NAMES = "Instalacao.getAllNames";

    public static final String FIND_SESSOES_BY_DATE = "Instalacao.findSessaoByDate";

    public static final String FIND_SESSOES_BY_AULA = "Instalacao.findSessaoByAula";

    public static final String FIND_SESSOES_BETWEEN_DATES = "Instalacao.findSessaoBetweenDates";

    @Id private String nome;

    @Column(nullable = false)
    private int lotacao;

    @Enumerated(EnumType.STRING) @Column(nullable = false)
    private TipoInstalacao tipo;

    @ElementCollection
    @CollectionTable(name = "MODALIDADES_INSTALACAO", joinColumns = @JoinColumn(name = "NOME_INSTALACAO", nullable = false))
    private List<String> modalidades;

    @ElementCollection
    @CollectionTable(name = "SESSOES_INSTALACAO", joinColumns = @JoinColumn(name = "NOME_INSTALACAO", nullable = false))
    private List<Sessao> sessoes;

    protected Instalacao() {
    }

    public Instalacao(String nome, int lotacao, TipoInstalacao tipo, List<String> modalidades) {
        this.nome = nome;
        this.lotacao = lotacao;
        this.tipo = tipo;
        this.modalidades = modalidades;
        this.sessoes = new ArrayList<>();
    }
//Getters and setters

Here is the error given:
[EL Warning]: 2020-04-21 03:02:48.04--UnitOfWork(1262548561)--Exception [EclipseLink-69] (Eclipse Persistence Services - 2.6.2.v20151217-774c696): org.eclipse.persistence.exceptions.DescriptorException
Exception Description: A NullPointerException was thrown while extracting a value from the instance variable [nomeAula] in the object [business.main.sessao.Sessao].
Internal Exception: java.lang.NullPointerException
Mapping: org.eclipse.persistence.mappings.DirectToFieldMapping[nomeAula-->NOMEAULA]
Descriptor: RelationalDescriptor(business.main.sessao.Sessao --> [])
Erro a ativar aula: Exception [EclipseLink-69] (Eclipse Persistence Services - 2.6.2.v20151217-774c696): org.eclipse.persistence.exceptions.DescriptorException
Exception Description: A NullPointerException was thrown while extracting a value from the instance variable [nomeAula] in the object [business.main.sessao.Sessao].
Internal Exception: java.lang.NullPointerException
Mapping: org.eclipse.persistence.mappings.DirectToFieldMapping[nomeAula-->NOMEAULA]
Descriptor: RelationalDescriptor(business.main.sessao.Sessao --> [])

If you need any info just say so!
Thanks for your help!

redpajama_set_name: RedPajamaStackExchange


text:
Faculty Notes for April 2020
CHRIS ANSON
Chris Anson had the following scheduled items canceled due to the coronavirus: a presentation at the 10th Annual Learning and Analytics conference in Frankfurt, Germany (March 24); a presentation at the CCCC conference in Milwaukee (March 28); a a program review at St. Joseph University in Hartford, CT (April 9-10); a keynote address at the Writing on the Range Conference at the University of Denver (April 17).
SHERYL CORNETT
Sheryl Cornett's poem "Easter Irises" is forthcoming in the anthology Viral Verse: Poetry of the Pandemic, juried and collected by Cathy Warner. The anthology will be published in May.
DAUN DAEMON
On April 11, Deep South Magazine published Daun Daemon's poem "Double-jointed." On April 25, the magazine published two more of her poems: "That First Poem" and "On Trying to Write a Prayer for Forgiving My Parents."
PAUL FYFE
This month, Paul Fyfe was scheduled to give the following presentations, which were cancelled due to coronavirus:
"The Boundaries of Digital Humanities." Digital Humanities Initiative, University of North Carolina–Wilmington
"Lajos Kossuth and the International Press System," with Jana Keck (Univ Stuttgart) and Mila Oiva (Univ Turku) at the workshop "Close and distant: reading(-viewing) journals" hosted by the Journalliteratur reading group at University of Bochum
"Computing the Nineteenth-Century Periodical Press" at the DH in the Disciplines Series, Franklin Humanities Center, Duke University
MARSHA GORDON
Now through May 8, Marsha Gordon's latest documentary, All the Possibilities … Reflections on a Painting by Vernon Pratt, will stream online as part of the RiverRun International Film Festival's virtual program of NC short films.
Additionally, All the Possibilities … Reflections on a Painting by Vernon Pratt was awarded the Best Documentary Short jury award from the Longleaf Film Festival, sponsored by the North Carolina Museum of History.
MARVIN HUNT
Marvin Hunt has been named to the board of advisors of the new Rasmussen-Hines rare book and manuscript collection in Reno, NV. The library has established a short-term research fellowship in his honor.
KYESHA JENNINGS
On March 25, Kyesha Jennings was a panelist on a virtual webinar series — AERA Hip-Hop Theories, Praxis, and Pedagogies SIG Webinar Series Pt. 2: Past, Current, and Future Directions in Hip-Hop Based Education Research — hosted by AERA's Hip-Hop Education Special Interest Group.
Her article on North Carolina rapper Rapsody, "From Snow Hill to Raleigh to the Billboard Charts, Rapsody Is Redefining Success," was the cover story for the INDY's March 10 edition.
The Popular Culture Association awarded Jennings the William E. Brigman Award for Outstanding Graduate Student Paper for her essay "City Girls, Hot Girls and the Re-imagining of Black women in Hip-Hop and Digital Spaces," the second award this essay has won. She was scheduled to present this same research on April 19 in Philadelphia, but the event was canceled. This research will also appear in the inaugural issue of the Global Hip-Hop Studies Journal next month.
Jennings was invited to contribute a chapter to Hip Hop Feminist Pedagogies of Renewal, a collection of essays edited by Aisha Durham and Ruth-Nicole Brown scheduled for publication this fall. Her chapter is titled "Ratchet and Intelligent as Ever: A Critical Reading of Cardi B as a Digital Hip-Hop Feminist."
SUSAN KATZ
Susan Katz reports that in 2007 she worked on an article titled "Implications of Diffusion of Innovations Theory for A Culturally Sensitive Multi-sectoral Approach to HIV/AIDS Prevention" with two colleagues from the Communication Department (James Kiwanuka-Tondo and Jessica Katz Jameson). They submitted the article to many journals, revising significantly several times, and then gave up. She and the other authors learned recently that, unbeknownst to them, the article was published in the Clinical Journal of HIV & AIDS in 2017. Her message to everyone is never give up!
After two postponed conference presentations in late March and early April (as well as a poetry reading at the Museum of Nebraska Art), Jason Miller will discuss "F.B. Eyes on Langston Hughes and Martin Luther King, Jr." as an invited Zoom presentation on May 30 for the State Libraries and UNC Greensboro. This pilot program is part of a workshop on teaching primary sources from a multidisciplinary approach pitched for high school educators throughout Winston-Salem and Forsyth County Schools.
JENNIFER NOLAN
Jennifer Nolan was to have given a lecture, "'Early Success:' The Dawn of the Jazz Age in Fitzgerald's Short Fiction," and serve as one of four faculty at a workshop on teaching Fitzgerald, sponsored by Humanities Texas (the state affiliate of the NEH) in Dallas, TX, on March 31. The event has been postponed with hopes of rescheduling during the upcoming academic year.
TIM STINSON
Tim Stinson received an NEH Summer Stipend to work on an article entitled "Jerusalem's Fall and England's Rise: Josephan History, the Prose Brut, and the Framing of a Medieval English Nation."
John Wall presented "Recreating Time: The Virtual St Paul's Cathedral Project and the Re-Presentation of Early Modern Worship" at the NTRS-DH@RSA Virtual Conference, held on April 2 via Internet and Twitter. This paper was originally scheduled to be delivered at the annual conference of the Renaissance Society of America, which was canceled due to the coronavirus pandemic.

redpajama_set_name: RedPajamaCommonCrawl


How can I see what I have paid for?
You can see payments that have been made or are currently pending from your online account.
Simply click on the payment tab, you will see there is a option you can click on that says 'Paid'.
This will present you with a description of what you made a payment for; the amount you have paid; the date it was paid as well as the method and status. If you paid a direct debit or bank transfer then the status will show 'pending' or 'paid' depending of if the transaction process has been completed.


text:
Review: Lucy
Review: Into The Storm
Review: Frank
by Jess Brooman on August 17, 2014
Darkly funny, witty, refreshingly original and boasting one of Michael Fassbender's most towering performances to date, "Frank" has just about all you need in a film.
After the first images of Michael Fassbender wearing a Frank Sidebottom mask began to surface, everyone seemed to think Lenny Abrahamson's "Frank" would be a Chris Sievey biopic. During the late 80's and early 90's, the late Sievey (who originally led a punk rock band named The Freshies) used to host television programs and play music whilst wearing a giant cartoon mask – much like the one we see in this film. Now whilst some of Sievey's antics may have inspired Lenny Abrahamson's film, for the most part it appears to be unrelated to his life, aside from the iconic papier-mâché head that takes center stage here. An interesting role choice for Fassbender – after his consistent stream of raw performances, he decides to take a dive and cover himself up. Is this the actor testing new, niche waters?
"Frank" is an especially sharp and witty satire of what the music business has morphed into since social media began to play such a major role in dictating the success of a performer. To call the music Frank makes with his band "Soronprfbs" indecipherable and new age just about sums it up. The music is almost non-existent, hardly worthy of the title 'music.' Rather, the band is like a piece of avant garde performance art, saved from being labeled pretentious by the fact that the band leader is certifiably insane. However, insanity has always been a marketable asset, and that's what the film spends a lot of the time exploring.
The protagonist throughout isn't Frank, but instead the ambitious keyboarder Jon (Domhnall Gleeson) who fills in during a spontaneous gig and soon finds himself apart of the band. Unbeknownst to the other members, Jon begins filming their antics and rehearsal sessions, during an endless period of recording a new album. Uploading videos to YouTube, or posting on Twitter, Jon slowly gives them a following before they've even recorded or released a note. Meanwhile, Clara (Maggie Gyllenhaal) the band's theremin player as well as Frank's confidant, pushes the band in the other direction, with her constantly fighting against even the vaguest idea of success – ultimately distrusting Jon's ambition, and jealous at the prospect of having to share Frank with anybody else.
In the titular role, Michael Fassbender is terrific, despite the fact that his head is always obscured. Frank is like a more innocent, musical version of Tyler Durden, leading his not-so-merry band astray with his ambitious art, which is so taxing that his last keyboardist committed suicide. The film starts off as a wry-eyed, witty satire on the lure of fame, with Jon seduced by Soronprfbs and their bizarre leader; eager to please despite his obvious creative shortcomings. For half of the film, Frank acts as a know-it-all guru, only to shift demeanor and become vulnerable as the film changes pace in the second half, in which the band finds itself invited to South by Southwest festival after the YouTube videos become a viral sensation. Jon, as the innocent with an agenda, strikes a nice balance between wide-eyed naivety and ambition. Scoot McNairy also gives a strong performance as one of the more devoted members of Frank's entourage, and the band's default manager. However it is at this juncture that Abrahamson noticeably changes tack, diluting the film into a more formulaic, and sadly less interesting, morality tale about selling out and forgetting your roots.
The last thirty minutes or so sees our broken, emotionally drained keyboardist unearthing the source of both Frank's ingenuity and mood-killing despair, with the volatile Fassbender revealed at last to his expectant audience. Such a grand climax should be the peak of the film given the teasing that had come before, but there is a sense that Abrahamson reduced his out-there British dramedy into an 'issue film' with a social conscience. This is somewhat disappointing given the subtlety of Abrahamson's past endeavors, and perhaps a sign that it is the filmmakers, rather than Frank and his posse, that have compromised their original creative vision in the hunt for mainstream acceptance.
This film is difficult to classify. It's darkly humorous, but at the same time it's filled with a surprising amount of drama, especially in the final act, where the question of Frank's sanity becomes the central theme. It also tries to say something about the current state of the music business, where bands can become sensations without ever having to prove themselves, just because they are a gimmick. At a relatively brisk ninety-five minutes, Abrahamson's film covers a lot of territory without feeling rushed, over-saturated, or abrupt.
"Frank" is perhaps a little too bizarre to ever really connect with a mainstream audience, but certainly has a lot of cult potential. Indie music fans, and lovers of strange cinema should be quick to embrace it in all its quirky glory. It manages to be both a clever satire, and unexpectedly moving towards the end, with the film's faults being few and far between.
1 hr. 35 min.
Michael Fassbender, Maggie Gyllenhaal, Domhnall Gleeson, Scoot McNairy
(All Reviews), Comedy, Drama, Issue #16, Reviews
Domhnall GleesonFrankLenny Abrahamsonmaggie gyllenhaalMichael FassbenderScoot McNairy
Domhnall Gleeson, Frank, Lenny Abrahamson, maggie gyllenhaal, Michael Fassbender, Scoot McNairy
Jess Brooman
Jess is a 21 year old university student studying English Literature. Born and raised in England, she's an aspiring writer and film lover, with a strong affinity for cats.
Domhnall GleesonFrankmaggie gyllenhaalMichael Fassbender
Review: Ex Machina
by Jess Brooman on January 25, 2015
"Ex Machina" is a refreshingly chilling and complex story with some faultless performances; the moments that make us gasp in horror are masterfully balanced with the thought-provoking and the humorous, thus keeping the darker elements from overshadowing the final intent.
Review: Unbroken
by Josef Rodriguez on December 8, 2014
"Unbroken" benefits from gorgeous cinematography and a stellar lead performance from Jack O'Connell, but Angelina Jolie's sophomore feature is ultimately too disjointed and dull to have any lasting impact.
Review: Calvary
by Taylor Sinople on August 10, 2014
The must-see performance from Brendan Gleeson aside, "Calvary" also offers smart, pitch black comedy and a unique structure.


text:
News Sports Business Life & Events Granville Sentinel Obituaries E-Edition Legals
Bond hearings
The following people appeared before Licking County Common Pleas Court Magistrate Mattie Klein for bond hearings. The cases may be reviewed by a grand jury for possible indictment or additional charges.
Anthony T. Bell, 31, last known address 7895 York Road, Pataskala, was charged with theft, a fifth-degree felony.
On Feb. 1, Bell was suspected of stealing a license plate off a vehicle, according to a statement of facts.
Klein released Bell on his own recognizance.
Andrew H. Painter, 24, last known address 672 Saratoga Ave., Newark, was charged with felonious assault, a second-degree felony.
Between Jan. 31 and Feb. 1, Painter was suspected of hitting a person with a baseball bat, according to a statement of facts.
Klein set bond at $100,000.
Austin M. Hickey, 22, last known address homeless, was charged with felonious assault, a second-degree felony.
Between Jan. 31 and Feb. 1, Hickey was suspected of hitting a person with a vehicle, according to a statement of facts.
Contact Us Support Local Advertise Your Business Advertising Terms and Conditions Buy and Sell Help Center Subscriber Guide My Account Give Feedback Licensing & Reprints
© 2021 www.newarkadvocate.com. All rights reserved.


text:
Q: addons removed in angular-cli.json whats the replacement angular-cli RC 1 has removed addons in the .angular-cli.json file.
Before I was doing this:
    "addons": [
    "../node_modules/font-awesome/css/fontawesome-webfont.woff"
  ],

So now when the addons tag has been removed how do I import the webfonts?


text:
var AngularAskModule = angular.module('angularAsk', ['ng']);
AngularAskModule.config(['$provide', function($provide){
	$provide.decorator('$rootScope', ['$delegate', function($delegate){
		Object.defineProperty($delegate.constructor.prototype, '$onRootScope', {
			value: function(name, listener){
				var unsubscribe = $delegate.$on(name, listener);
				this.$on('$destroy', unsubscribe);

				return unsubscribe;
			},
			enumerable: false
		});

		return $delegate;
	}]);
}]);

AngularAskModule.directive('ngask', [
	function(){
		return {
			restrict: 'EAC',
			link: function(scope, elem, attrs){
				var themeHref = document.getElementById('angularAskTheme').getAttribute('href');
				var fullScreenBlur = themeHref.indexOf('fullscreen');
				scope.$onRootScope('ngAskConfirm', function(e, title, content, callback){
					var container = document.createElement('div');
					container.className += 'angular-ask';
					if ( typeof title == 'string' && title.length !== 0) {
						var titleContainer = document.createElement('p');
						titleContainer.className += 'title';
						titleContainer.innerHTML = title;
						container.appendChild(titleContainer);
					}
					if ( typeof content == 'string' && content.length !== 0) {
						var contentContainer = document.createElement('p');
						contentContainer.className += 'content';
						contentContainer.innerHTML = content;
						container.appendChild(contentContainer);
					}
					var operationsContainer = document.createElement('div');
					operationsContainer.className += 'operations';
					var cancelBtn = document.createElement('button');
					cancelBtn.className += 'cancel';
					cancelBtn.innerHTML = 'Cancel';
					var okBtn = document.createElement('button');
					okBtn.className += 'ok';
					okBtn.innerHTML = 'OK';
					operationsContainer.appendChild(cancelBtn);
					operationsContainer.appendChild(okBtn);
					container.appendChild(operationsContainer);
					var ngaskDom = document.getElementById('ngask');
					ngaskDom.appendChild(container);
					if(fullScreenBlur >= 0){
						$('.ngask-blur').css({
							'filter': 'blur(4px)',
							'-webkit-filter': 'blur(4px)',
							'-moz-filter': 'blur(4px)',
							'-o-filter': 'blur(4px)',
							'-ms-filter': 'blur(4px)'
						});
					}
					var btnClicked;
					cancelBtn.addEventListener('click', function(){
						$(container).remove();
						if(fullScreenBlur){
							$('.ngask-blur').removeAttr('style');
						}
						btnClicked = false;
						if($.isFunction(callback)){
							callback(btnClicked);
						}
					});
					okBtn.addEventListener('click', function(){
						$(container).remove();
						if(fullScreenBlur){
							$('.ngask-blur').removeAttr('style');
						}
						btnClicked = true;
						if($.isFunction(callback)){
							callback(btnClicked);
						}
					});
				});
				scope.$onRootScope('ngAskPrompt', function(e, title, placeholder, callback){
					var container = document.createElement('div');
					container.className += 'angular-ask';
					if ( typeof title == 'string' && title.length !== 0) {
						var titleContainer = document.createElement('p');
						titleContainer.className += 'title';
						titleContainer.innerHTML = title;
						container.appendChild(titleContainer);
					}
					var form = document.createElement('form');
					var input = document.createElement('input');
					input.setAttribute('type', 'text');
					if ( typeof placeholder == 'string' && placeholder.length !== 0) {
						input.setAttribute('placeholder', placeholder);
					}
					form.appendChild(input);
					container.appendChild(form);
					var operationsContainer = document.createElement('div');
					operationsContainer.className += 'operations';
					var cancelBtn = document.createElement('button');
					cancelBtn.className += 'cancel';
					cancelBtn.innerHTML = 'Cancel';
					var okBtn = document.createElement('button');
					okBtn.className += 'ok';
					okBtn.innerHTML = 'OK';
					operationsContainer.appendChild(cancelBtn);
					operationsContainer.appendChild(okBtn);
					container.appendChild(operationsContainer);
					var ngaskDom = document.getElementById('ngask');
					ngaskDom.appendChild(container);
					input.focus();
					if(fullScreenBlur >= 0){
						$('.ngask-blur').css({
							'filter': 'blur(4px)',
							'-webkit-filter': 'blur(4px)',
							'-moz-filter': 'blur(4px)',
							'-o-filter': 'blur(4px)',
							'-ms-filter': 'blur(4px)'
						});
					}
					var btnClicked;
					var userInput;
					cancelBtn.addEventListener('click', function(){
						$(container).remove();
						if(fullScreenBlur){
							$('.ngask-blur').removeAttr('style');
						}
						userInput = undefined;
						btnClicked = false;
						if($.isFunction(callback)){
							callback(btnClicked, userInput);
						}
					});
					okBtn.addEventListener('click', function(){
						$(container).remove();
						if(fullScreenBlur){
							$('.ngask-blur').removeAttr('style');
						}
						userInput = input.value;
						btnClicked = true;
						if($.isFunction(callback)){
							callback(btnClicked,userInput);
						}
					});
				});
			}
		};
	}
]);

redpajama_set_name: RedPajamaGithub


text:
In the Dead of the Night: How NC Republicans Used Deception to Hurt Our Teachers
January 5, 2012 January 10, 2012 Elena Botella
At 1:17 a.m., in what Governor Perdue called an "unprecedented, unconstitutional power grab," House Republicans used a surprise, late-night congressional session to override Perdue's veto of SB727, which stops the North Carolina Association of Educators from collecting dues from teachers' paychecks via payroll deduction.
Not surprisingly, the NCAE has been vocal in our state against the Republican education cuts in the last two years that have ravaged a once great school system that dropped our state to 49th in the nation in per pupil funding. The Republicans are trying to punish NCAE for speaking out against the NC GOP assault on schools, and as noted by the Associated Press, the GOP has done little to refute arguments that the vetoed bill was designed as punishment. Other state employees will still be able to have automatic deductions to their professional organizations (like the Public Service Workers Union and the State Employees Association of North Carolina); "the fact that it picks and chooses one group out of many is a blatant violation of due process," said Rep. Rick Glazier, D-Cumberland. It's not by chance that just the NCAE was singled out: the committee actively rejected a change that also would have cut off payroll deductions for all other employee associations including three unions — the State Employees Association of North Carolina, the Teamsters, and the Public Service Worker's Union.
WRITTEN BY: SAM SPENCER, Young Democrats of North Carolina President
Just after 1 a.m. this morning, the Republicans in the North Carolina House pulled off another legislative coup in the dead of night.While Democratic Representative Larry Womble was in critical but stable condition after a tragic accident; and after Representative William Wainwright had to excuse himself due to a serious illness; Speaker Thom Tillis and the House Republicans held a session that was at best incredibly immoral and at worst unconstitutional.
The Republicans made a deal with Democrats earlier in the day, and subsequently broke the deal when they decided to exceed the scope of yesterday's session. They passed a bill that had already been vetoed and defeated by calling a surprise legislative session that had not been announced to the public.
Republicans lacked the votes to override the veto legitimately, but by early this morning they were able to override Governor Perdue's veto for the sake of nothing more than political payback. Speaker Tillis said earlier this year that Republicans were pushing this bill to attack the North Carolina Association of Educators because "[we] just want to give them a little taste about what's to come." They even had the gall to ask members to pray for Rep. Womble – who is currently in intensive care in Winston-Salem – while blatantly exploiting his absence.
Last year, Speaker Tillis said that "[Republicans] are living up to their commitment to be more transparent." Unfortunately, this week's actions speak for themselves: surprise midnight votes are a far cry from "transparency." Even worse, the multiple recesses and the unnecessary day cost North Carolina up to $55,000; all the while, Representatives were watching football on the taxpayer dime until it got late enough to vote.
National Committeewoman Montica Talmadge and other YDNC members were there in Raleigh, standing up for those of us who couldn't make it. While Speaker Tillis still believesthat teachers "don't care about kids" and "don't care about classrooms," Montica reports that "Rep. Rick Glazier led the charge for teachers and gave an eloquent explanation of the unconstitutionality of the whole session."She couldn't be more right. When you consider midnight sessions, redistricting, attempts to change our voting laws, and many other bills proposed and passed over the past year, the real unconstitutionality becomes clear: Democrats are losing equal protection of the laws in North Carolina.
Today's cloak-and-dagger actions are a new low for this General Assembly. Please take action today:
Contact Speaker Tillis and ask that he apologize for this farce of a session.
Forward this e-mail to your friends and share it on Facebook & Twitter so that they know what the Republicans did.
Contribute to our fight to empower young people across the state to fight the radical Republican agenda.
The Cause Endures,Sam Spencer
President, Young Democrats of North Carolina
beverly perdue education labor north carolina politics rick glazier
Previous Post Which North Carolina bills were bought by corporations?
Next Post Duke Democrats Iowa Caucus Roundup
4 thoughts on "In the Dead of the Night: How NC Republicans Used Deception to Hurt Our Teachers"
FLPatriot says:
"the fact that it picks and chooses one group out of many is a blatant violation of due process," said Rep. Rick Glazier, D-Cumberland.
I agree that this is flawed, it should apply to all public unions. All workers should have the right to choose whither to pay dues to a union or not and how to pay that dues.
Still not sure how this hurts teachers though. Could you clarify how this hurts teachers?
Hi FLPatriot!
The NCAE plays an important role in fighting to make sure our state has the educational resources it needs, fighting against budget cuts, and make sure teachers (who understand classrooms best) have a seat at the table in education reform. Some of their 2010 legislative successes are explained here:http://www.ncae.org/Images/Users/6/NCAELegislativeWin10crp.pdf
I can understand the perspective that dues for organizations should be voluntary, but I think there's a good argument against having them be voluntary
I don't know where you fall on big/small government, but imagine in your head some number that you think would be needed from each person to make sure our country had the services you think are vital (like stoplights, police officers, and so on). Would you want to make paying those taxes voluntary? Probably not–when there is a good that benefits a lot of people equally, too many people would be tempted to "free load" off of the people who do pay in.
NCAE helps protect all teachers, and all teachers will suffer without the voice that NCAE provides.
That's my two cents!
-Elena
Michael Gustafson says:
To play devil's advocate – paying taxes for government services seems dramatically different from automatic payroll deductions for union dues… Beyond that, this does not keep teachers from joining NCAE nor from paying dues; it blocks a convenient way of doing so.
That's where my hypothetical advocacy ends, though, because certainly the process by which this happened and the singular focus on the NCAE – with the active exclusion of other unions – for this…action…falls well outside that for which I am able to even hypothetically advocate 🙂
I see where you're coming from Dr. G. If the overwhelming majority of the employees of your company would like the dues to their professional organization to be paid via payroll deduction, it seems discourteous to not offer them a box to check at least. If I were in the NCGA, I would probably vote in favor of legislation that allowed you to either opt-in or opt-out to automatic payroll deduction (assuming this change happened to all state employees at the same time as opposed to happening to only the organization that a particular political party has a beef with).


text:
Q: Сохранить данные из курсора в Excel Есть курсор с полями:

*

*word типа character (100),

*translation типа memo.

Как сохранить данные из этого курсора в книгу MS Excel?

A: Перелить данные из курсора в таблицу командой
copy to ExportData type fox2x

и открыть полученный файл Excel'ем.


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Sharp Becomes SportsGrid's Lead Pro Football Analyst
Tagged: Analyst, Football, Lead, Pro, Sharp, SportsGrids
SportsGrid, a provider of live sports news and odds, has reinforced its team with Warren Sharp as its new lead pro football analyst. The NFL specialist will host live reports and keep sports fans updated on the latest developments in the league.
Sharp Joins SportsGrid
Sharp joins the sports news company amid the National Football League preseason. His job will be to provide coverage of the regular NFL season once it kicks in. Sharp will also appear on various panels during the season playoffs, including Ferrall Coast to Coast, In-Game Live All Access and Pro Football Today.
Sharp's responsibility as SportsGrid's lead pro football analyst will be to provide coverage of the hottest topics in the NFL, to share his opinions on the latest developments and to provide fans with unique betting insights.
The famed analyst will also appear on promotional social media content and help SportsGrid boost its digital presence. Furthermore, Sharp will help to promote SportsGrid's new mobile application upon its launch.
SportsGrid Is Happy to Have Sharp on Board
Warren Sharp is a former NBC Sports analyst who is well-versed in the world of professional football. He will be an important asset in SportsGrid's arsenal of specialists ahead of the new NFL season.
Sharp spoke about his new position as SportsGrid's new lead pro football analyst. He shared that he believes SportsGrid is a great place where NFL fans and sports bettors can find news about the latest developments in football.
When I look at the future of sports gambling coverage, I see SportsGrid as an outstanding place to reach the fans who want the NFL insight I provide on a regular basis.
Warren Sharp, lead pro football analyst, SportsGrid
Sharp added that his new job will provide him with the freedom to keep his personality during his reports. This is a major benefit for him and he believes that this content strategy would resonate with NFL fans and bettors.
Adam Kaplan, SportsGrid's chief operating officer, also shared his thoughts on the matter. He welcomed Sharp to the company and said that the entire team is glad to have him on board. Kaplan then praised Sharp is known for his deep knowledge of football and his reputation as one of the best analysts in sports.
Warren's well-known insights and deep analysis of the NFL teams, players and betting markets have developed his reputation as one of the foremost experts in the sports betting industry.
Adam Kaplan, COO, SportsGrid
A few days ago, SportsGrid launched its network on FuboTV's platform. A few days prior, SportsGrid teamed up with WynnBet for an insight-driven betting partnership.
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Amber Heard 'cried,' 'yelled' and 'screamed' on her deposition day, Johnny Depp's lawyer claims
Tim Kenneally
Aug 10th 2016 10:55AM
Amber heard did pretty much everything but testify on the day she was supposed to sit for a deposition in her domestic violence case against estranged husband Johnny Depp. At least, that's the suggestion of court papers filed by Depp's attorney.
In a motion filed on Tuesday, Depp's lawyer, Laura Wasser, accused Heard of dragging her feet and making a scene on Saturday, when she was scheduled to be deposed.
"Amber continues to delay litigation," the court papers read. "After showing up nearly two hours late to her Court-ordered deposition, Amber refused to go on the record to testify at all. She refused to testify despite repeated requests from Johnny's counsel and instead sat with her lawyers, cried on the telephone, yelled, screamed and paced in a separate room."
Also Read:Amber Heard to Present More Evidence of Johnny Depp's Alleged Domestic Abuse
The papers continued, "Amber's conduct on August 6, 2016 is just one example of her blatant gamesmanship and disregard for the Court's orders."
See photos of Amber Heard and Johnny Depp together:
Johnny Depp and Amber Heard
LONDON, ENGLAND - JANUARY 19: Actors Johnny Depp (L) and Amber Heard attend the UK Premiere of 'Mortdecai' at Empire Leicester Square on January 19, 2015 in London, England. (Photo by Dave J Hogan/Getty Images)
LONDON, ENGLAND - JANUARY 19: Johnny Depp and Amber Heard attend the UK Premiere of 'Mortdecai' at Empire Leicester Square on January 19, 2015 in London, England. (Photo by Karwai Tang/WireImage)
Johnny Depp and Amber Heard are married!The lavish island wedding is still to come, but People reports that The Rum Diary co-stars made it official Tuesday, marrying each other at their home in Los Angeles.People reports that Depp, 51, and Heard, 28, signed the papers to become man and wife in advance of their ceremony this weekend on Depp's private island in the Bahamas.The couple got engaged over the holidays in 2012 after meeting on the set of The Rum Diary in 2011.
LONDON, ENGLAND - JANUARY 19: Johnny Depp and Amber Heard attend the UK Premiere of 'Mortdecai' at Empire Leicester Square on January 19, 2015 in London, England. (Photo by Anthony Harvey/Getty Images)
US actor Johnny Depp (L), accompanied by his fiancee US actress and model Amber Heard (R), arrive at Tokyo International Airport on January 26, 2015 for the Japan premiere of his latest movie 'Mortdecai'. The action comedy movie will be screened in Japan from February 6. AFP PHOTO (Photo credit should read YOSHIKAZU TSUNO/AFP/Getty Images)
US actress and model Amber Heard, accompanied by her fiance US actor Johnny Depp (unseen), arrives at Tokyo International Airport on January 26, 2015 for the Japan premiere of his latest movie 'Mortdecai'. The action comedy movie will be screened in Japan from February 6. AFP PHOTO (Photo credit should read YOSHIKAZU TSUNO/AFP/Getty Images)
LONDON, ENGLAND - JANUARY 19: (EDITORS NOTE: Retransmission of #461785548 with alternate crop.) Johnny Depp and Amber Heard attend the UK Premiere of 'Mortdecai' at Empire Leicester Square on January 19, 2015 in London, England. (Photo by Karwai Tang/WireImage)
US actor Johnny Depp (L) jokes with fiancee US actress and model Amber Heard (R) as they arrive for the UK premiere of the film 'Mortdecai' in London on January 19, 2015. AFP PHOTO / LEON NEAL (Photo credit should read LEON NEAL/AFP/Getty Images)
LOS ANGELES, CA - JANUARY 15: Johnny Depp and Amber Heard are seen at 'Jimmy Kimmel Live' on January 15, 2015 in Los Angeles, California. (Photo by RB/Bauer-Griffin/GC Images)
SANTA MONICA, CA - JANUARY 10: Actor Johnny Depp and actress Amber Heard arrive at The Art Of Elysium 8th Annual Heaven Gala at Hangar 8 on January 10, 2015 in Santa Monica, California. (Photo by Jon Kopaloff/FilmMagic)
SANTA MONICA, CA - JANUARY 10: (L-R) Johnny Depp and Amber Heard attend the Art of Elysium and Samsung Galaxy Marina Abramovic's HEAVEN Gala at Hangar 8 on January 10, 2015 in Santa Monica, California. (Photo by Tibrina Hobson/Getty Images)
LOS ANGELES, CA - JANUARY 10: Honoree Amber Heard (L) and actor Johnny Depp attend the 8th Annual HEAVEN Gala presented by Art of Elysium and Samsung Galaxy at Hangar 8 on January 10, 2015 in Los Angeles, California. (Photo by Jason Merritt/Getty Images for Art of Elysium)
LOS ANGELES, CA - JANUARY 10: Actors Johnny Depp and Amber Heard attend the 8th Annual HEAVEN Gala presented by Art of Elysium and Samsung Galaxy at Hangar 8 on January 10, 2015 in Los Angeles, California. (Photo by Jason Merritt/Getty Images for Art of Elysium)
TOKYO, JAPAN - JANUARY 26: Johnny Depp and Amber Heard are seen upon arrival at Haneda Airport on January 26, 2015 in Tokyo, Japan. (Photo by Jun Sato/GC Images)
TOKYO, JAPAN - JANUARY 26: Amber Heard is seen upon arrival at Haneda Airport on January 26, 2015 in Tokyo, Japan. (Photo by Jun Sato/GC Images)
SANTA MONICA, CA - JANUARY 10: Actors Johnny Depp (L) and Amber Heard attend the The Art Of Elysium 8th Annual Heaven Gala at Hangar 8 on January 10, 2015 in Santa Monica, California.(Photo by Jeffrey Mayer/WireImage)
Actor Johnny Depp attends the cast of 'Benny & Joon' present Planet Hollywood with memorabilias from the film on March 22, 1993 at Planet Hollywood, California.
BEVERLY HILLS,CA - MARCH 25: Actor Johnny Depp attends the 'Benny & Joon' Beverly Hills Premiere on March 25, 1993 at the WGA Theatre in Beverly Hills, California. (photo by Ron Galella, Ltd./WireImage)
UNITED STATES - OCTOBER 01: Johnny Depp and Guest (Photo by The LIFE Picture Collection/Getty Images)
1988 File Photo of Johnny Depp at the Nosotros Benefit in Los Angeles, California taken May 13, 1988 in Los Angeles, California (Photo by Barry King/WireImage)
Nicolas Cage & Johnny Depp (Photo by Barry King/WireImage)
Actor Johnny Depp attends the 18th Annual Los Angeles Police/Celebrity Golf Tournament on May 14, 1988 at Rancho Park Golf Course in Los Angeles, California.
SHERMAN OAKS,CA - DECEMBER 13: Actor Dustin Nguyen, actor Johnny Depp and actor Peter DeLuise attend the FOX Television Stars Feed the Homeless on December 13, 1987 at Sherman Oaks Galleria in Sherman Oaks, California. (photo by Ron Galella, Ltd./WireImage)
POMPANO BEACH, FL - AUGUST 29: Johnny Depp greets fans after performing as part of the Sheila Witkin Memorial Reunion Concert at Club Cinema on August 29, 2008 in Pompano Beach, Florida. (Photo by Mike Franklin/FilmMagic)
UNITED STATES - AUGUST 22: Matthew Perry and Johnny Depp in New York to promote their first network series on the Fox Network in 1987 (Photo by Vinnie Zuffante/Getty Images)
LONDON - JANUARY 10: Johnny Depp attends the Sweeney Todd film premiere held at the Odeon Leicester Square on January 10, 2008 in London, England. (Photo by Eamonn McCormack/WireImage)
SANTA MONICA, CA - JANUARY 10: Johnny Depp; Amber Heard attend the The Art Of Elysium 8th Annual Heaven Gala at Hangar 8 on January 10, 2015 in Santa Monica, California.(Photo by JB Lacroix/WireImage)
SANTA MONICA, CA - JANUARY 10: Actors Johnny Depp and Amber Heard arrive at The Art Of Elysium's 8th Annual Heaven Gala at Hangar 8 on January 10, 2015 in Santa Monica, California. (Photo by Gregg DeGuire/Getty Images)
LOS ANGELES, CA - JANUARY 10: Actor Johnny Depp (L) presents the Spirit of Elysium award to honoree Amber Heard during the 8th Annual HEAVEN Gala presented by Art of Elysium and Samsung Galaxy at Hangar 8 on January 10, 2015 in Los Angeles, California. (Photo by Michael Buckner/Getty Images for Art of Elysium)
NEW YORK, NY - MAY 05: Johnny Depp and Amber Heard attend the 'Charles James: Beyond Fashion' Costume Institute Gala at the Metropolitan Museum of Art on May 5, 2014 in New York City. (Photo by Andrew H. Walker/Getty Images)
NEW YORK, NY - MAY 05: Johnny Depp and Amber Heard attend the 'Charles James: Beyond Fashion' Costume Institute Gala at the Metropolitan Museum of Art on May 5, 2014 in New York City. (Photo by Axelle/Bauer-Griffin/FilmMagic)
NEW YORK, NY - MAY 05: Johnny Depp and Amber Heard attend the 'Charles James: Beyond Fashion' Costume Institute Gala at the Metropolitan Museum of Art on May 5, 2014 in New York City. (Photo by George Pimentel/WireImage)
LOS ANGELES, CA - FEBRUARY 12: Actor Johnny Depp (L) and his fiancee actress Amber Heard arrive at the premiere of Relativity Media's '3 Days To Kill' at the Arclight Theatre on February 12, 2014 in Los Angeles, California. (Photo by Kevin Winter/Getty Images)
HOLLYWOOD, CA - FEBRUARY 12: Johnny Depp and Amber Heard arrives at the '3 Days To Kill' at ArcLight Cinemas on February 12, 2014 in Hollywood, California. (Photo by Steve Granitz/WireImage)
Actor Johnny Depp kisses actress Amber Heard as they attend the US premiere of '3 Days To Kill,' at Arclight Cinemas, February 12, 2014 in Hollywood, California. AFP PHOTO ROBYN BECK (Photo credit should read ROBYN BECK/AFP/Getty Images)
Actor Johnny Depp and actress Amber Heard attend the US premiere of '3 Days To Kill,' at Arclight Cinemas, February 12, 2014 in Hollywood, California. AFP PHOTO ROBYN BECK (Photo credit should read ROBYN BECK/AFP/Getty Images)
Heard filed for divorce from the "Pirates of the Caribbean" star in May after little more than a year of marriage, and obtained a temporary restraining order against Depp days later. Heard claims that Depp had been abusive to her throughout their relationship, and cited in particular an alleged May 21 incident at the couple's Los Angeles residence, during which she claims Depp injured her by striking her in the face with a cell phone.
A hearing on whether Heard should be granted a restraining order against Depp is scheduled for next week, but in Tuesday's papers Wasser claims that Heard has "severely limited" Depp's ability to prepare for the hearing.
Also Read:Johnny Depp Divorce: Amber Heard Has 'Inexplicably Refused' to Sign Confidentiality Agreement, Lawyer Says
"Amber has repeatedly obstructed Johnny's efforts to obtain evidence of her claims and has severely limited his ability to prepare for the August 15/16, 2016 hearing," the papers read. "Amber has provided innumerable excuses: I am in London. I am at a wedding. I have a costume fitting. My lawyer is unavailable. Amber is truly not interested in having the veracity of her claims examined."
Pamela Chelin contributed to this report.
Read original story Amber Heard 'Cried,' 'Yelled' and 'Screamed' on Her Deposition Day, Johnny Depp's Lawyer Claims At TheWrap
RELATED: Amber Heard was a no show at her first deposition hearing:
johnny depp divorce
Laura Wasser
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Fight the virus, not the infected person
By ( chinadaily.com.cn )
A person who contracted the novel coronavirus in Harbin is facing harassment on social networking sites after the authorities made her name and address public to help those who might have come in contact with her to get tested.
A number of cases have emerged in Harbin, capital of Northeast China's Heilongjiang province, after a fresh outbreak was reported there on Sept 20. Ever since the local authorities named the woman who tested positive after returning to Harbin from another place, some people have been blaming her for exposing others to the virus.
How many more times does one need to reiterate that the enemy is the virus, not any infected person? The woman has every right to go wherever she wants, so long as she adheres to social distancing and quarantine norms. Those targeting her are undermining the fight against the pandemic.
While the authorities have a broad idea of an individual's movements, there are finer details that the individual alone can reveal, in good faith, to strengthen the fight against the virus.
Such details are made public to make up for any oversight and enable everyone who might have come in contact with the infected person to get tested.
However, the ordeal that those giving details are subjected to might deter others from being more forthcoming with details when they test positive. Some might avoid reporting to medical authorities even after exhibiting COVID-19 infection symptoms.
However, the authorities, too, must ensure that not every detail of an infected person is made public. Maybe the personal details, such as the Harbin woman's name and address, that in no way aid the fight against the virus, should not have been made public. The authorities in Harbin could learn from Shanghai, where only the names of districts reporting infection cases are made public and not the names of infected people. That is the right way.
Harbin environmental treatment sees results
Environmental treatment in Harbin has made achievements.
Harbin's shanty town renovation projects advance
Pingfang launches aviation industry development layout for next 5 years
Pingfang district officially launched its aviation industry development plan for the 14th Five-Year Plan period (2021-25).
Heilongjiang releases aviation industry development layout
The Heilongjiang Provincial Government recently issued the Development Plan of the General Aviation Industry in Heilongjiang Province During the 14th Five-Year Plan Period (2021-25).
Harbin's modern industrial system sees massive growth
The total scale of Harbin's "4+4" modern industrial system reached 621.37 billion yuan in 2020.


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For Hugh Hanna B ????, Co. Down, with a father forenamed David, I found 1 rcd, 1879, 1st Rathfriland PR parish.
For James Hanna B ????, 1st Rathfriland PR parish, with a father forenamed David, I found 1 rcd 1876, within a relevant range.
For Joseph Hanna B ???? ditto, I found 1 rcd, 1874.
For David Hanna B ????, ditto, I found 2 rcds: 1872, and 1866. The 1872 rcd seems the more likely.
For David Hanna M 1870 +/- 2 yrs, in a PR parish, Co. Down, I found 2 rcds: 1871 Clonduff PR parish, and 1871 Newry & Mourne PR parish. A view of the detailed rcds MAY show a bride named Eliza(beth).


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Solution to world hunger? Eat less meat, new study urges
By: Andy Blatchford
This article was published 12/10/2011 (3383 days ago), so information in it may no longer be current.
MONTREAL -- A newly published blueprint for doubling the global food supply includes a key suggestion about how everyone can contribute to this increasingly pressing ambition: eat less meat.
An international team of researchers has developed solutions to respond to what it calls one the greatest challenges of the 21st century -- boosting food production while slashing the environmental impact of agriculture.
ADRIAN WYLD / THE CANADIAN PRESS ARCHIVES Three-quarters of the world�s agricultural land is devoted to raising livestock and beef is the most resource-intensive animal product of all, scientists say.
The research, which will be featured on the cover page of the Oct. 20 edition of the journal Nature, comes as international concern grows over how the planet will feed the rapidly expanding human population.
With the world's population expected to climb from 6.9 billion to 9 billion by 2050, the issue of food was put at the top of this year's G20 agenda. The study, published online Wednesday, says there are already a billion people who don't have enough to eat.
McGill University's Navin Ramankutty, one of the team leaders on the paper, said the research is the first of its kind to quantify both food production and ecological consequences in the same analysis.
He added that it's also the first study to examine these factors while considering the specific environmental characteristics of different regions of the planet.
Ramankutty said limiting meat consumption is one of several ways to increase food production.
He estimates that simply dedicating prime cropland to growing food for humans -- rather than growing biofuels or feed for animals -- could spike the global output by nearly 50 per cent.
The study says that three-quarters of the world's agricultural land is devoted to raising livestock, either for grazing or for growing feed.
Ramankutty added that beef is the most resource-intensive animal product of them all.
"That doesn't mean we all have to become vegetarians and vegans, but even if you... eat meat one or two days less a week, you can hugely contribute to the amount of food that's needed," Ramankutty, himself a meat-eater, said.
"It would have a huge impact, but this also happens to be one of those things where people are much more personally attached to it."
He said that scientists in his field rarely raised diet as an issue in the past because they didn't want to infringe on a person's right to choose.
But Ramankutty said fewer researchers are staying quiet on this subject, particularly when the consequences have global environmental impacts.
Changes to the human diet are only one component of the study's strategy to double the global food supply.
The research also calls for improved crop management to increase yields; an end to deforestation to make way for farmland; and a cutback on food waste, which accounts for as much as half of the planetary food production.
The catch? Ensuring these strategies are adopted on a global scale.
Ramankutty laughed when asked about the likelihood of these tactics being implemented in his lifetime.
"To be honest, I'm probably pessimistic about it, but I always think that optimism is the only choice we have," the geographer said.
-- The Canadian Press