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Nigeria News Local news
Local newsPolitics
Ondo election: Akeredolu wins again, defeats his challengers at court
6 days ago read comments by Wale Akinola
- Governor Rotimi Akeredolu's nomination as APC candidate has been validated by the court
- This followed the judgement of the Federal High Court Abuja on Wednesday, January 13
- Justice Inyang Ekwo in his judgement dismissed the prayer of Akereolu's challenger, Olajumoke Anifowose
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The Federal High Court in Abuja has dismissed another suit challenging the validity of the emergence of Governor Oluwarotimi Akeredolu as the candidate of the All Progressives Congress (APC) in the July 20, 2020, primary election of the party.
PM News reports that while delivering a ruling, on Monday, January 13, Justice Inyang Ekwo, dismissed the suit filed by an APC aspirant in the poll, Olajumoke Anifowose.
Legit.ng gathered that the judge held that the application was statute-barred on the grounds that being a pre-election matter, it was filed outside the 14 days provided in section 185(9) of the constitution.
Ondo election: PDP candidate tells tribunal to sack APC governor
The Federal High Court sitting in Abuja has thrown out a suit against Governor Akeredolu. Credit: @RotimiAkeredolu
He held that, although the suit, marked: FHC/ABJ/CS/881/20200, which challenged the outcome of the APC's governorship primary election held on July 20, 2020, was originally filed on July 26, 2020 (within 14 days after the occurrence of the cause of action), it was wrongly commenced when the plaintiff chose to sue the governor of Ondo state as against Akeredolu in person.
According to him, the amendment effected by the plaintiff on the originating summons, to substitute the party named as the first defendant – the governor of Ondo state – with Oluwarotimi Akeredolu, was done on August 13, 2020, outside the 14 days allowed by the constitution.
Ekwo stressed that the amendment of the originating process for the purpose of substituting parties in the course of the suit would have been in order if it was done by the plaintiff within the 14 days allowed for the commencement of pre-election cases under Section 185(9) of the constitution.
Prominent APC senator escapes assassination attempt (photos)
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Meanwhile, Legit.ng had previously reported that Governor Akeredolu recorded a victory in a case instituted against him over his emergence as the candidate of the APC during the governorship election in the state.
It was reported that a Federal High Court in Abuja on Wednesday, December 15, dismissed the suit, saying it was statute-barred.
I will conduct free and fair primaries in Ondo - Yahaya Bello | - on Legit TV
Source: Legit
APCFederal Government Of NigeriaPDPOndo election
Nigerian man's grave with Man United's logo gets many emotional as child 'mourns' (photos)

redpajama_set_name: RedPajamaCommonCrawl


By locking a user's account manually, it will only stay locked for the duration specified in the Account Lockout Period field for the user's Security Parameter. As a result users that have locked accounts will be able to access Archer after that lockout period has been met.
Resolution To ensure a user will not be able to login indefinitely, the account should be set to inactive.


text:
from django.apps import AppConfig

class CharityinfoConfig(AppConfig):
    name = 'charityInfo'

redpajama_set_name: RedPajamaGithub


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Categories: Places to See, Puerto Vallarta, Sport & Adventure, Things to Do, Todos Santos
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Baja California's seaside village of Todos Santos is renowned for its rugged mountains, incredible beaches and very challenging surf conditions.
Categories: Getting Around, Places to See, Sport & Adventure, Things to Do, Travel Advice, Valle de Bravo
Valle de Bravo is one of Mexico's Best Kept Secrets
One of the loveliest colonial towns in central Mexico, the town of Valle de Bravo is a perfect getaway for relaxing, great food and paragliding.
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Jeep safaris have become staple adventure options for travelers who want to experience Mexico as an adventurer, especially so on Cozumel Island.
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Steeped in history, from indigenous trading settlements to the birth of the Mexican Revolution, San Miguel is ideal for travel connoisseurs.
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Located on the western coast of the Sea of Cortez, La Paz offers a range of culinary delights from local fresh seafood to international cuisine.
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text:
Gold | Pictorial
Orange Car Crash 14 Times
A man stands in front of Andy Warhol's work titled 'Orange Car Crash 14 Times' at the Museum of Modern Art. New York, NY. 5.5.05.
Elyse Butler (Brooks Institute of Photography)
Silver | Pictorial
Walking in Heaven
Tourists wander through Salar de Uyuni in Bolivia. Salar de Uyuni is a vast salt desert stretching for hundreds of miles and in the rainy season, rain sits atop the salt mounds making the sky and earth meet.
Andrew Henderson (Western Kentucky University)
Bronze | Pictorial
Bobby Parish, of Bowling Green, KY, talks in his bedroom, which is lit by a candle. Parish's electricity was turned off because his Social Security check did not arrive in time for him to pay the bill.
Matt Eich (Ohio University)
Honorable Mention | Pictorial
The photographer's shadow snakes around a corner on Court Street in Athens, OH. The pink dots on the ground were part of an exhibition piece by the Ohio University art department that was intended to highlight litter left on the sidewalk by students.
Danny Ghitis (University of Florida)
Hardly Uniform
Catholic schoolgirls in the rural outskirts of Jinotepe, Nicaragua, who are required to wear identical uniforms to school, express themselves through personality.
Woo Chan Joo (Western Kentucky University)
Twin sisters Myra Hartman, right, a physical therapist assistant, and Marsha Hartman, who teaches English as a second language, watch animation in the Walker Art Center on Hennepin Avenue on Wednesday. The Hartmans, 55, of St. Paul, work at the same school for special-needs children and wanted to visit the newly redesigned and remodeled center before summer break was over.
Michael P. King (Ohio University)
Alex Hamburger of Old Bridge, N.J., walks past a memorial constructed in Staten Island, N.Y., in remembrance of the victims of the Sept. 11, 2001 World Trade Center terrorist attack, Tuesday, Dec. 16, 2004. The memorial, entitled 'Postcards' and designed by Masayuki Sono, contains the profiles of over 250 Staten Island residents who perished. Each crafted profile is unique to the victim it memorializes.
Kevin Benedict (University of Missouri)
Metro commuters leave Judiciary Square station near 3rd Street prior to the inauguration of President George W. Bush on Thursday, Jan. 20, 2005, in Washington, D.C.


Until March 2009 Bill Ives was director of Magdalen College Choir, Oxford, where for 18 years he held the post of Organist, Informator Choristarum and Tutor in Music. During his tenure Magdalen College Choir performed in Japan , the USA and across Europe . In 1999 they made their debut at the BBC Proms, and in association with film composer, George Fenton, they recorded movie soundtracks for Shadowlands, Ever After, and the award-winning BBC television documentary, Blue Planet. In 2001 they gave the first performance of a new choral work by Paul McCartney, Ecce Cor Meum. Magdalen College Choir records for Harmonia Mundi and in 2004 their recording of music by Orlando Gibbons, With a Merry Noyse, was nominated for a Grammy. From 1978-85 Bill was a member of the celebrated British vocal group, The King's Singers. He performed over 800 concerts worldwide, appeared on many radio and television programmes, and made more than 20 recordings, including the frog chorus on Paul McCartney's hit single, We all stand together! As a composer of choral music, his work reflects his broad musical taste. Since his schooldays he has published regularly (as Grayston Ives) and his church music in particular is gaining recognition and regular performances both in the UK and abroad. He is also known for a large number of vocal arrangements of popular music, some of which have been recorded by The King's Singers.


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Robot wars: Student-built robots face off in competition
By Patrick Monahan Monday, June 11, 2018
The first-prize-winning robot, constructed by engineering students Rex Congdon and Wesley Jonson.
SF State engineering students built robots from scratch in just two months
Do you know how your electronics work well enough to explain them? Maybe you do — but could you build them yourself? In San Francisco State's first annual robotics competition, teams of students did just that, going head-to-head to complete a series of challenges using robots that they designed, built and programmed, all in a single semester.
"Maybe these students will be lead design engineers or CEOs in a couple of years," says Assistant Professor of Mechanical Engineering Mojtaba Azadi. "They have the potential — in a matter of just two months, this is what they've done."
Winners Wesley Jonson and Rex Congdon show off their robot.
The competition came out of the mechatronics lab course (Engineering 416). In mechatronics classes, students learn to combine different disciplines — mechanical, electrical, material and computer engineering — to design products that are efficient and cost-effective. For the competition, teams had to construct and program robots that could draw a circle and a square of a specific size on a piece of paper, and also detect and connect randomized colored points on a grid. As a bonus round, the robots could write a given text and draw the SF State logo in detail, which they showed off on May 15 in SF State's Makerspace.
The seven teams each brewed up their own way of tackling the challenges. Some students programmed their robots from scratch, while others scavenged bits of code from online directories and tailored the programs to their needs. The robots themselves were constructed from everything from plywood to fishing line to individually machined pieces of metal, and many included polymer pieces that the students designed and printed using the Makerspace's 3D printer. They ranged in size from something that could be tucked behind a picture frame to an apparatus that would barely fit in an oven.
Patrick Tomsky, Sean Paw and Tan Bui pose with their second-place finisher.
Students Rex Congdon and Wesley Jonson, who won first place in the competition, went the extra mile in every respect. Rather than buying prefabricated pieces, Congdon decided to hand-mill the robot's frame himself. "We were looking at kits and how long it would take to get things delivered, and we realized we could do it cheaper ourselves," Congdon explained. And Jonson not only trained the robot on a neural network to complete the assigned tasks, but also created a user-friendly interface that a non-engineer could use. They received $250 in winnings for their first-place finish.
Other teams elected for style — like one team who constructed a robot with its bulk hidden behind a picture frame. "We wanted ours to be aesthetically pleasing," said student Sean Paw, whose team took second in the competition. Because it draws upright and could be hung on a wall, he says, "it's a conversation piece. You could imagine it drawing at a party."
You can watch the winning team's robot draw the SF State logo here. Azadi doesn't plan to stop at this year's competition. "We'll have another competition next year, maybe even bigger — and hopefully have other labs and colleges enter as well," he said.
Student-led project brings 'soul' into science classrooms
Lecturer and alumna direct documentary on the challenges of older lesbians
History professor looks back on pivotal LGBTQ protests
Climate change may turn important marine organisms into 'junk food'
A Fulbright future for two SF State graduates
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text:
\section{Introduction and motivation}
\noindent
Graph products were introduced by Green \cite{Green}, and are a common generalisation of direct and free products. When all the groups involved are infinite cyclic, the graph products are known as right-angled Artin groups (RAAGs).
In this sense, graph products generalise direct and free products in the same way as RAAGs generalise free abelian and free groups.

Let $\Gamma=(V,E)$ be a simplicial graph, i.e. $V$ a set and $E \subseteq \binom{V}{2}$ a graph with no loops and no multiple edges, and let $\mathcal{G}=\{G_v \mid v\in V\}$
be a family of groups indexed by the vertex set $V$. Note that the set $V$ can be of arbitrary cardinality.
The \emph{graph product} $\Gamma\mathcal{G}$ of the groups $\mathcal{G}$ with respect to the graph $\Gamma$ is defined as the
quotient of the free product $\ast_{v \in V}G_v$ obtained by adding all the relations of the form
$$g_u g_v = g_v g_u \quad \forall g_u\in G_u,g_v\in G_v, \{u,v\}\in E.$$
The groups $G_v\in\mathcal{G}$ are called the \emph{vertex groups} of $\Gamma \mathcal{G}$.

Properties that are stable under direct and free products are often inherited by graph products too.
Green originally proved that a graph product of residually finite (resp.: $p$-finite) groups
is again residually finite (resp.: $p$-finite) \cite{Green}.
More recently, the second named author proved that graph products of residually finite solvable groups are again residually finite solvable \cite[Lemma 6.8]{mf}.
Other examples are soficity \cite{CHR}, (hereditary) conjugacy separability \cite{mf}, Tits alternatives \cite{AnMy}, the Haagerup property or finiteness of asymptotic dimension \cite{AnDr}.

In this work we study residual properties of graph products. We adopt an approach that unifies and recovers the known facts concerning
residual properties. Moreover, it allows us to prove new results in this direction.

If $\C$ is a class of groups, then we say that a group $G$ is \emph{residually} $\C$ if for every non-trivial element $g \in G$ there is a group $C \in \C$ and a surjective homomorphism $\varphi \colon G \twoheadrightarrow C$ such that $\varphi(g)$ is non-trivial in $C$.

\begin{thA}
Let $\C$ be a class of groups closed under taking subgroups and finite direct products. Assume that free-by-$\C$ groups are residually~$\C$, then the class of residually~$\C$ groups is closed under taking graph products.
\end{thA}
In \cite{fb} the first named author considered the class of residually amenable groups.
Among other things, it is proved there that such class is closed under taking free products \cite[Corollary 1.2]{fb}.
As a consequence of Theorem A, we deduce that the class of residually amenable groups is also closed under graph products.

\begin{corA}\label{residually amenable}
The class of residually amenable groups is closed under taking graph products. The same is true
for residually elementary amenable groups.
\end{corA}

Moreover, a result in the same spirit is true for a weaker form of approximation, the one of local embeddability into a class $\C$ (LE-$\C$ for short). See the beginning of Section \ref{last.section} for the precise definitions.

\begin{thB}
Let $\mathcal{C}$ be a class of groups, suppose that $\mathcal{C}$ is closed under taking subgroups, finite direct products and that graph products of residually~$\mathcal{C}$ groups are residually~$\mathcal{C}$.
Then the class of LE-$\mathcal{C}$ groups is closed under graph products.

\end{thB}

This general result allows us to establish that the property of being LE-$\C$ is stable under under graph products for certain classes of groups.
\begin{corB}
Let $\C$ be one of the following classes:
    \begin{enumerate}
        \item finite groups,
        \item finite $p$-groups,
        \item solvable groups,
        \item finite solvable groups,
        \item elementary amenable groups,
        \item amenable groups.
    \end{enumerate}
    Then the class of LE-$\C$ groups is closed under graph products.
\end{corB}

\section{Preliminaries}
\subsection{Notations}
Throughout this work, all graphs considered are simplicial graphs, also if not explicitly stated.

The identity element of a group $G$ is denoted by $e_G$, or simply by $e$ if the group $G$ is clear from the context. Given two elements $h,k\in G$, the commutator $hkh^{-1}k^{-1}$ is denoted by $[h,k]$. If $H,K\leq G$ are two subgroups, $[H,K]$ denotes the subgroup of $G$ generated by the elements $[h,k]$, where $h\in H$ and $k\in K$.
A surjective homomorphism is usually indicated by $\varphi\colon G\twoheadrightarrow H$.

We use the standard notation of an $\mathcal{A}$-by-$\mathcal{B}$ group to denote a group $G$ with a normal subgroup $N\trianglelefteq G$ such that $N\in\mathcal{A}$ and $G/N\in\mathcal{B}$, where $\mathcal{A}$ and $\mathcal{B}$ are given classes of groups (e.g. $\mathcal{A}$ being the free groups and $\mathcal{B}$ being the amenable groups, in the case of a free-by-amenable group).

For a residually finite solvable group we mean a residually (finite solvable) group, not a group which is solvable and, at the same time, residually finite.

\subsection{Graph products}
We recall here some terminology and facts about graph products that will be used in
this paper.
Let $G = \Gamma\mathcal{G}$ be a graph product. Every element $g \in G$ can be obtained as a product of a sequence $W \equiv (g_1, g_2, \dots , g_n)$, where each $g_i$ belongs to some $G_{v_i} \in \mathcal{G}$. We say that $W$ is a \emph{word} in $G$ and that the elements $g_i$ are its \emph{syllables}. The \emph{length} of a word is the number of
its syllables, and it is denoted by $\lvert W\rvert$.

Transformations of the three following types can be defined on words in graph products:
\begin{enumerate}
	\item[(T1)]	remove the syllable $g_i$ if $g_i =e_{G_v}$, where $v \in V$ and $g_i \in G_v$,
	\item[(T2)]	remove two consecutive syllables $g_i, g_{i+1}$ belonging to the same vertex group $G_v$ and replace them by the single syllable $g_i g_{i+1} \in G_v$,
	\item[(T3)] interchange two consecutive syllables $g_i \in G_u$ and $g_{i+1} \in G_v$ if $\{u, v\} \in E$.
\end{enumerate}
The last transformation is also called \emph{syllable shuffling}. Note that transformations (T1) and (T2) decrease the length of a word, whereas transformations (T3) preserve it. Thus, applying finitely many of these transformations to a word $W$, we obtain a word $W'$ which is of minimal length and that represents the same element in $G$.

For $1 \leq i < j \leq n$, we say that syllables $g_i, g_j$ can be \emph{joined together} if they belong to the same vertex group and \lq everything in between commutes with them\rq. More formally: $g_i, g_j \in G_v$ for some $v \in V$ and for all $i < k < j$ we have that $g_k \in G_{v_k}$ for some $v_k\in\mathrm{link}(v) := \{u \in V \mid \{u,v\}\in E\}$.
In this case the words
$$W \equiv (g_1, \dots, g_{i-1}, g_i, g_{i+1}, \dots, g_{j-1}, g_j, g_{j+1}, \dots, g_n)$$ and $$W' \equiv (g_1, \dots, g_{i-1}, g_i g_j, g_{i+1}, \dots, g_{j-1}, g_{j+1}, \dots, g_{n})$$ represent the same group element in $G$, and the length of the word $W'$ is strictly shorter than $W$.

We say that a word $W \equiv (g_1, g_2, \dots , g_n)$ is \emph{reduced} if it is either the empty word, or if $g_i \neq e$ for all $i$ and no two distinct syllables can be joined together. As it turns out, the notion of being reduced and the notion of being of minimal length coincide, as it was proved by Green \cite[Theorem 3.9]{Green}:
\begin{theorem}[Normal Form Theorem]
	\label{nft}
Every element $g$ of a graph product $G$ can be represented by a reduced word. Moreover, if two reduced words $W, W'$ represent the same element in the group $G$, then $W$ can be obtained from $W'$ by a finite sequence of syllable shufflings. In particular, the length of a reduced word is minimal among all words representing $g$, and a reduced word represents the trivial element if and only if it is the empty word.
\end{theorem}

Thanks to Theorem \ref{nft} the following are well defined. Let $g \in G$ and let $W \equiv (g_1,\dots, g_n)$ be a reduced word representing $g$. We define the \emph{length} of $g$ in $G$ to be $|g| = n$
and the \emph{support} of $g$ in $G$ to be
 $$\mathrm{supp}(g) = \{v \in V | \exists i \in \{1,\dots, n\} \mbox{ such that } g_i \in G_v\setminus \{e\}\}.$$

Let $x, y \in G$ and let $W_x \equiv (x_1, \dots ,x_n),W_y \equiv (y_1 \dots, y_m)$ be reduced expressions for $x$ and $y$, respectively.
We say that the product $xy$ is a reduced product if the word $(x_1, \dots, x_n, y_1, \dots, y_m)$ is reduced. Obviously, $xy$ is a reduced product if and only if $|xy| = |x| + |y|$. We can naturally extend this definition: for $g_1, \dots, g_n \in G$ we say that the product $g_1 \dots g_n$ is reduced if $|g_1 \dots g_n| = |g_1| + \dots + |g_n|$.

A subset $X \subseteq V$ induces the full subgraph $\Gamma_X$ of $\Gamma$. Let $G_X$ be the subgroup of $G=\Gamma\mathcal{G}$ generated by the vertex groups corresponding to $X$ and, by convention, let $G_{\emptyset}$ be the trivial subgroup. It follows from Theorem \ref{nft} that $G_X$ is isomorphic to the graph product of the family $\mathcal{G}_X =\{G_v \in \mathcal{G}\mid v \in X\}$ with respect to the full subgraph $\Gamma_X$. Subgroups of $G$ that can be obtained in this way are called \emph{full subgroups}. For such
subgroups, there is a canonical retraction
$\rho_X \colon G \twoheadrightarrow G_X$, defined on the vertex groups as
$$\rho_X(g)=\begin{cases}g&\quad\text{if }g\in G_v\text{ and }v\in X,\\
e&\quad\text{otherwise}.
\end{cases}$$
Thus, $G$ splits as the semidirect product $G \cong \ker(\rho_X)\rtimes G_X$, and full subgroups are retracts of $G$.

\subsection{Special amalgams}
Let $B\leq A$ and $C$ be groups, we define $A \star_B C$, the \emph{special amalgam} of $A$ and $C$ over $B$, to be the free product with amalgamation
$$A \star_B C:=A \ast_B (B \times C)=\langle A,C \parallel [b,c] = e \ \forall b\in B ,\forall c \in C\rangle.$$
Special amalgams generalise the notion of special HNN extensions: every special HNN extension
$$A\ast_{\mathrm{id}_B}=\langle A,t \parallel tbt^{-1}=b\ \forall b\in B\rangle$$
is isomorphic to $A\star_B \langle t\rangle=A\ast_B (B\times\mathbb Z)$.

Graph products can be seen in a natural way as special amalgams of their full subgroups:
\begin{fact}
	\label{graph products split as special amalgams of their full subgroups}
Let $G =\Gamma\mathcal{G}$ be a graph product. Then, for every $v \in V$, we have that $G \cong G_A \star_{G_B} G_C$, where $A = V \setminus \{v\}$, $B = \mathrm{link}(v)$ and $C=\{v\}$.
\end{fact}

Consider $G = A \star_B C$, then every element $g \in G$ can be represented as a product $a_0 c_1 a_1 \dots c_n a_n$, where $a_i \in A$ for $i=0,1, \dots, n$ and $c_j \in C$ for $j = 1, \dots, n$. We say that $g = a_0 c_1 a_1 \dots c_n a_n$ is in a \emph{reduced form} if $a_i \notin B$ for $i = 1, \dots, n-1$ and $c_j \neq e$ for $j = 1, \dots, n$. The following lemma was proved in \cite[Lemma 5.3]{mf}.

\begin{lemma}
\label{normal form theorem for special amalgams}
Let $B \leq A$ and $C$ be groups, and consider $G = A \star_B C$. Suppose that $g = a_0 c_1 a_1 \dots c_n a_n$ is in reduced form, where $a_i \in A$, $c_j \in C$ and $n \geq 1$. Then $g$ is not the trivial element of $G$.

Moreover, suppose that $f = x_0 y_1 x_1 \dots y_m x_m$ is in reduced form, where $x_i \in A$, $y_j \in C$. If $f = g$ then $m = n$ and $c_i = y_i$ for all $i = 1, \dots, n$.
\end{lemma}

Special amalgams satisfy a functorial property.
\begin{fact}
\label{functional property of special amalgams}
Let $B\leq A, C, P, Q$ be groups and let $\psi_A \colon A \to P$, $\psi_C \colon C \to Q$ be homomorphisms. By the universal property of amalgamated free products the homomorphisms $\psi_A$ and  $\psi_C$ uniquely extend to the homomorphism $\psi\colon G \rightarrow H$, defined by
\begin{displaymath}
	\psi(g) =	\left\{\begin{array}{ll}
					\psi_A(a)	& \mbox{ if } g = a \mbox{ for some } a\in A,\\
					\psi_C(c)	& \mbox{ if } g = c \mbox{ for some } c\in C,
			 	\end{array}\right.
\end{displaymath}
where $G:= A\star_BC$ and $H:= P \star_{\psi_A(B)}Q$.
\end{fact}

\section{Pro-$\C$ topologies on groups}

Let $\C$ be a class of groups and let $G$ be a group. We say that a normal subgroup $N \normleq G$ is a \emph{co-$\C$ subgroup} of $G$ if $G/N \in \C$, and we denote by
$\NC(G)$
the set of co-$\C$ subgroups of $G$.

Consider the following closure properties for a class of groups $\C$:
	\begin{itemize}
	    \item[(c0)] $\C$ is closed under taking finite subdirect\footnote{A subdirect product of the family $\{G_i\}_{i\in I}$ is a subgroup $H\leq \prod_{i\in I}G_i$ such that the projections $H\twoheadrightarrow G_i$ are surjective for all $i\in I$.} products,
	    \item[(c1)]	$\C$ is closed under taking subgroups,
	    \item[(c2)]	$\C$ is closed under taking finite direct products.
	\end{itemize}
Note that
$$(c0) \Rightarrow  (c2)\qquad\text{and}\qquad (c1)+ (c2) \Rightarrow (c0).$$
If the class $\C$ satisfies (c0) then, for every group $G$, the set $\NC(G)$ is closed under intersections, that is to say, if $N_1, N_2\in\NC(G)$ then also $N_1\cap N_2\in\NC(G)$. This
implies that $\NC(G)$ is a base at $e_G$ for a topology on $G$.

Hence the group $G$ can be equipped with a group topology, where the base of open sets is given by $$\{gN \mid g\in G,  N \in \NC(G)\}.$$
This topology, denoted by $\proC(G)$, is called the \emph{pro-$\mathcal{C}$ topology} on $G$.

If the class $\C$ satisfies (c1) and (c2), or equivalently, (c0) and (c1), then one can easily see that equipping a group $G$ with its $\proC$ topology is a faithful functor from the category of groups to the category of topological groups. That is to say, for groups $G, H$ every homomorphism $\varphi\colon G\to H$ is a continuous map with respect to the corresponding $\proC$ topologies.

A set $X \subseteq G$ is $\C$-\emph{closed} in $G$ if $X$ is closed in $\proC(G)$: for every $g \notin X$ there exists $N \in \NC(G)$ such that the open set $gN$ does not intersect $X$, that is, $gN \cap X = \emptyset$.
This is equivalent to $gN \cap XN=\emptyset$, and hence $\varphi(g) \notin \varphi(X)$ in $G/N$, where $\varphi \colon G \twoheadrightarrow G/N$ is the canonical projection onto the quotient $G/N$.
Accordingly, a set is $\C$-\emph{open} in $G$ if it is open in pro-$\C(G)$.

The following lemma was proved by Hall \cite[Theorem 3.1]{Hall}.
\begin{lemma}\label{classification of open subgroups}
Let $\C$ be a class of groups closed under subgroups and finite direct products, and let $G$ be a group. A subgroup $H \leq G$ is $\C$-open in $G$ if and only if there is $N \in \NC(G)$ such that $N \leq H$. Moreover, every $\C$-open subgroup of $G$ is $\C$-closed in $G$.
\end{lemma}

The following lemma is crucial for the proofs of the next section.
\begin{lemma}\label{retracts of residually-C groups are C-closed}
Let $\C$ be a class of groups closed under subgroups and finite direct products, and let $G$ be a residually~$\C$ group.
Then a retract $R$ of $G$ is $\C$-closed in $G$.
\end{lemma}

\begin{proof}
	Let $\rho \colon G \twoheadrightarrow R$ be the retraction corresponding to $R$ and let $g \in G \setminus R$ be arbitrary. Note that $\rho(g) \neq g$ as $g \not\in R$. By assumption, there is $C \in \C$ and a homomorphism $\varphi \colon G \twoheadrightarrow C$ such that $\varphi(\rho(g)) \neq \varphi(g)$ in $C$.

	Let $\psi \colon G \to C \times C$ be the homomorphism defined by $\psi(f) = (\varphi(f), \varphi(\rho(f)))$ for all $f \in G$. Let $D = \{(c,c) \in C\times C \mid c \in C\} \leq C\times C$ be the diagonal subgroup of $C \times C$. Clearly $\psi(R) \leq D$ and $\psi(g) \not\in D$, thus $\psi(g) \not \in \psi(R)$. As the class $\C$ is closed under taking subgroups and direct products we see that $\psi(G) \in \C$ and so $\ker(\psi) \in \NC(G)$ and $g\ker(\psi) \cap R = \emptyset$. Hence $R$ is $\C$-closed in $G$.
\end{proof}

When the class $\C$ contains only finite groups this statement has been proved in \cite[Lemma 3.1.5]{RZ}.

\section{Graph products of residually $\C$ groups}
\label{res.section}
The following was proved in \cite[Lemma 6.6]{mf}.
\begin{lemma}	\label{special amalgams of C-groups are free-by-C}
Let $\C$ be a class of groups closed under finite direct products, let $A, C \in \C$ and suppose that $B \leq A$. Then the special amalgam $G = A\star_B C$ is free-by-$\C$.
\end{lemma}

In the following proposition we characterise precisely which special
amalgams are residually $\C$. This should be compared with \cite[Theorem 1.9]{fb}, where a similar statement can be found.
\begin{proposition}
    \label{special amalgams over closed are residually C}
    Let $B \leq A, C$ be groups and suppose that $\C$ is a class of groups closed under taking subgroups, finite direct products and that free-by-$\C$ groups are residually $\C$.

The group $G = A \star_B C$ is residually $\C$ if and only if
$A,C$ are residually $\C$ and $B$ is $\C$-closed in $A$.
\end{proposition}
\begin{proof}
Suppose that $A, B$ are residually $\C$ and that the subgroup $B$
is $\C$-closed in $A$. We need to prove that the group $G$ is residually $\C$.

    Let $g \in G \setminus \{e\}$ be arbitrary and let $g = a_0 c_1 a_1 \dots c_n a_n$, where $a_i\in A$ for $i=0,\dots, n$, $c_j\in C$ for $j = 1,\dots, n$, be a reduced expression.

There are two cases to consider. If $n = 0$, then $g = a_0 \in A\setminus\{e\}$. Note that $A$ is a retract of $G$ and thus for the canonical retraction $\rho_A \colon G \to A$ we have $\rho_A(a_0) = a_0 \neq e$ in $A$. The group $A$ is residually $\C$, so there is a group $H \in \C$ and a surjective homomorphism $\varphi \colon A \twoheadrightarrow H$ such that $\varphi(a_0) \neq e_H$. We see that $(\phi \circ \rho_A)(g) \neq e_H$.

Suppose now that $n \geq 1$. As $B$ is $\C$-closed in $A$, there is a group $Q \in \C$ and a surjective homomorphism $\alpha \colon A \twoheadrightarrow Q$ such that $\alpha(a_i) \notin \alpha(B)$ for all $i=1,\dots, n-1$.
Moreover, $C$ is residually $\C$, so there exists a group $S \in \C$ and a surjective homomorphism $\gamma \colon C \twoheadrightarrow S$ such that $\gamma(c_i) \neq e_S$ for all $i = 1, \dots, n$.
Let $\psi \colon G \to P$, where $P = Q \star_{\alpha(B)}S$, be the canonical extension of $\alpha$ and $\gamma$ given by Fact \ref{functional property of special amalgams}.
It follows that
	\begin{displaymath}
 		\psi(g) = \alpha(a_0) \gamma(c_1) \alpha(a_1) \dots \gamma(c_n) \alpha(a_n)
	\end{displaymath}
	is a reduced expression for $\psi(g)$ in $P$. Hence $\psi(g)\neq e_P$ by Lemma \ref{normal form theorem for special amalgams}.

The group $P$ is free-by-$\C$ by Lemma \ref{special amalgams of C-groups are free-by-C}, and thus residually $\C$ by assumption. Hence, $G$ is residually $\C$.

It remains to prove the other implication. So, suppose that $G$ is residually $\C$.
As $A, C\leq G$ and $\C$ is closed under subgroups, it follows that the groups $A$ and $C$ are residually $\C$.

Looking for a contradiction, suppose that $B$ is not $\C$-closed in $A$. Then there exists an element $a\in A\setminus B$ such that
$\varphi(a)\in\varphi(B)$ for all surjective homomorphisms $\varphi
\colon A\twoheadrightarrow Q$, with $Q\in\C$.

Let $c\in C$ be a non-trivial element, then the element
$g:=[a,c]\in G$ is not trivial, as $a\notin B$ and $C$ only commutes with $B$.

The group $G$ is residually $\C$, hence there exist a group
$Q\in\C$ and a surjective homomorphism $\varphi\colon G\twoheadrightarrow Q$ such that $\varphi(g)\neq e_Q$.
Let $K:=\ker\varphi$.

By the choice of the element $a$, it follows that $\varphi(a)\in \varphi(B)$. Moreover, $B$ and $C$ commute elementwise in $G$, so
$\varphi(B)$ and $\varphi(C)$ commute elementwise in $Q$.
This implies that
$$\varphi(g)=[\varphi(a),\varphi(c)]\in [\varphi(B),\varphi(C)]=\{e_Q\},$$
contradicting the assumption $\varphi(g)\neq e_Q$.
Hence, $B$ is $\C$-closed in $A$.

\end{proof}

\begin{thA}
Let $\C$ be a class of groups closed under taking subgroups and finite direct products. Assume that free-by-$\C$ groups are residually~$\C$, then the class of residually~$\C$ groups is closed under taking graph products.
\end{thA}
\begin{proof}
    Let $\Gamma$ be a graph and let $\mathcal{G} = \{G_v \mid v \in V\}$ be a family of residually~$\C$ groups. We want to prove that the graph product $G:=\Gamma\mathcal{G}$ is residually $\mathcal{C}$.

Let $g \in G$ be a non-trivial element and set $S =\mathrm{supp}(g)$. Consider the canonical projection
$\rho_S\colon G\twoheadrightarrow G_S$ onto the graph product associated to the finite graph
$\Gamma_S$.
As $\rho_S(g)=g\neq e$, without loss of generality we can assume that the graph $\Gamma$ is itself finite.

We proceed by induction on $\lvert V\rvert$. If $\lvert V\rvert = 1$ then $G = G_v$ is residually $\C$ by assumption.

Suppose now that $\lvert V\rvert =r>1$ and that the statement holds for all graph products on graphs with at most $r-1$ vertices.

Fix a vertex $v \in V$ and let
$$A:=V\setminus \{v\},\qquad B:= \mathrm{link}(v),\qquad  C:=\{v\}.$$
From Fact \ref{graph products split as special amalgams of their full subgroups} it follows that $G = G_A \star_{G_B} G_C$. Moreover, $G_A$ is a graph product of residually $\C$ groups with respect to a graph with  $r-1$ vertices, hence $G_A$ is residually $\C$ by the induction hypothesis. Note that $G_C$ is a vertex group, thus it is residually $\C$ by assumption. Finally, $G_B$ is a retract of $G_A$ and thus $G_B$ is $\C$-closed in $G_A$ by Lemma \ref{retracts of residually-C groups are C-closed}.

Hence, applying Proposition \ref{special amalgams over closed are residually C},
we see that $G$ is residually $\C$.
\end{proof}

To give some examples of classes satisfying these properties, we recall here the notion of a root class.
A non-trivial, non-empty, class of groups $\mathcal{R}$ is called a \emph{root class} if it is closed under
taking subgroups, and for every group $G$ and every subnormal series $K\trianglelefteq H\trianglelefteq G$ such that $G/H, H/K\in\C$, there exists $L\trianglelefteq G$ such that $L\subseteq K$ and $G/L \in \C$.

Finite groups, finite $p$-groups, and (finite) solvable groups are
examples of root classes \cite{Gruenberg57}.
This notion was introduced by Gruenberg \cite{Gruenberg57} who proved that, when $\mathcal{R}$ is a root class, a free product of residually $\mathcal{R}$ groups is residually $\mathcal{R}$.
In \cite[Theorem 1.1, Lemma 3.3]{fb}, with the aim to generalise this result, the first named author proved the following.

\begin{lemma}\label{lemma.boh}
Let $\C$ be a non-trivial class of groups such that
\begin{enumerate}
\item $\C$ is closed under taking finite direct products and contains a root class $\mathcal{R}$,
\item every $\mathcal{R}$-by-$\C$ group sits in $\C$,
\item for every group in $\mathcal{C}$ there exists a group in $\mathcal{R}$ of the same cardinality.
\end{enumerate}
Then a free-by-$\C$ group is residually $\C$ and a free product of residually $\C$ groups is again residually $\C$.
\end{lemma}
Root classes satisfy the assumptions of this lemma.
Using Theorem A we extend these results to graph products.

\begin{corollary}\label{resR}
Let $\mathcal{R}$ be a root class. Then the class of residually $\mathcal{R}$ groups is closed under taking graph products.
\begin{proof}
Root classes are closed under taking subgroups, finite direct products and free-by-$\mathcal{R}$ groups are residually $\mathcal{R}$.
Hence we can apply Theorem A.
\end{proof}
\end{corollary}

Using this, we recover Green's result that residually finite and residually $p$-finite groups are closed under taking graph products \cite[Corollary 5.4, Theorem 5.6]{Green}.
Corollary \ref{resR} also covers \cite[Lemma 6.8]{mf} for the class
of residually finite solvable groups. Moreover, it yields
the same statement for residually solvable groups:
\begin{corollary}\label{residually solvable}
Graph products of residually finite groups are residually finite. The same holds for the classes of
residually $p$-finite groups, residually finite solvable groups
and residually solvable groups.
\end{corollary}

On the other hand, the class of amenable groups and the class of elementary amenable groups are not root classes, yet they satisfy the assumptions of Lemma \ref{lemma.boh}. Hence, \cite[Corollary 3.4]{fb} reads as follows.
\begin{fact}
\label{free-by-A}
	If $G$ is a free-by-amenable group, then $G$ is residually amenable. Moreover, if $G$ is free-by-(elementary amenable), then $G$ is residually elementary amenable.
\end{fact}
Hence, as a consequence, these classes are closed under taking free products \cite[Corollary 1.2]{fb}.

The class of amenable groups is closed under taking subgroups and finite
direct products. Moreover, free-by-amenable groups are residually amenable by Fact \ref{free-by-A}. Thus we can apply Theorem A to show that the class of residually amenable groups is closed under taking graph products. In the elementary amenable case we can use the same argument. Hence Corollary A.

\section{Graph products of LE-$\C$ groups}\label{last.section}
We recall here the definition of local embeddability.
Let $G$, $C$ be two groups and $K\subseteq G$ be a finite subset. A map $\varphi\colon G\to C$
is called a $K$-\emph{almost}-\emph{homomorphism} if
\begin{enumerate}
\item $\varphi(k_1k_2)=\varphi(k_1)\varphi(k_2)$ for all $k_1$, $k_2\in K$,
\item $\varphi\restriction_K$ is injective.
\end{enumerate}
A group $G$ is \emph{locally embeddable into} $\C$ (LE-$\C$ for short) if for all finite $K\subseteq G$ there exist a group $C\in\mathcal{C}$ and a $K$-almost-homomorphism $\varphi\colon G\to C$.

For classes $\C$ closed under finite direct products this definition yields a generalisation of being residually $\C$ \cite[Corollary 7.1.14]{CSC}.

Theorem A has an analogue for graph products of LE-$\C$ groups.
\begin{thB}
Let $\mathcal{C}$ be a class of groups, suppose that $\mathcal{C}$ is closed under taking subgroups, finite direct products and that graph products of residually~$\mathcal{C}$ groups are residually~$\mathcal{C}$.
Then the class of LE-$\mathcal{C}$ groups is closed under graph products.
\end{thB}
\begin{proof}
Let $\Gamma=(V,E)$ be a graph, $\mathcal{G} = \{G_v \mid v\in V\}$ be a family of LE-$\C$ groups and let $G:= \Gamma\mathcal{G}$ be the graph product of $\mathcal{G}$ with respect to $\Gamma$. Let $K \subseteq G$ be a finite subset of $G$. The set $\cup_{k \in K}\mathrm{supp}(k)$ is a finite subset of $V$, thus without loss of generality we can suppose that $V$ itself is finite. Set $$K' = K^{-1} K = \{k^{-1} k' \mid k, k' \in K \cup \{e_G\}\}$$ and suppose that $K' = \{g_1, \dots, g_r\}$. Let $W_1, \dots, W_r$ be reduced words in $G$ representing the elements $g_1,\dots, g_r$.

For every $v\in V$ consider the finite subset
$$K_v:=\{e_{G_v}\}\cup\{g\in G_v\mid g \text{ is a syllable of some }W_i\}\subseteq G_v.$$
By assumption, the vertex group $G_v$ is LE-$\mathcal{C}$ for every $v \in V$. Hence, there exist a family of groups $\mathcal{F} = \{F_v \in\C\mid v \in V\}$ and a family of $K_v$-almost-homomorphisms $\{\varphi_v\colon G_v\to F_v \mid v \in V \}$.

As $e_{G_v}\in K_v$ it follows $\varphi_v(e_{G_v})=e_{F_v}$. This implies that
\begin{equation*}\label{welldefined}
	\varphi_v(g)\neq e_{F_v}\quad \forall g\in K_v\setminus\{e_{G_v}\}.
\end{equation*}
Let $F := \Gamma \mathcal{F}$ be the graph product of $\mathcal{F}$ with respect to $\Gamma$.

Let $\mathcal{W}_G$ and $\mathcal{W}_F$ denote the set of all the words in $G$ and $F$ respectively. We define the function $\tilde{\varphi} \colon \mathcal{W}_G \to \mathcal{W}_F$ in the following manner: for $W \equiv (g_1, \dots, g_n)$, where $g_i \in G_{v_i}$ for some $v_i \in V$ for $i = 1, \dots, n$, we set
\begin{displaymath}
	\tilde{\varphi}(W) \equiv (\varphi_{v_1}(g_i), \dots, \varphi_{v_n}(g_n)).
\end{displaymath}
By definition, if $W$ is the empty word in $G$ then $\tilde{\varphi}(W)$ is the empty word in $F$. Let us note that the map $\tilde{\varphi}$ is compatible with concatenation: for all $U,V \in \mathcal{W}_G$ we have $\tilde{\varphi}(UV) = \tilde{\varphi}(U)\tilde{\varphi}(V)$.

Let $g \in G$ be an arbitrary element and let $W \equiv (g_1, \dots g_n)$, $W' \equiv (g_1', \dots, g_m')$ be two reduced words representing $g$ in $G$. By Theorem \ref{nft} we see that $m = n$ and that the word $W$ can be transformed to $W'$ by finite sequence of syllable shufflings. Since the groups $G,F$ are graph products with respect to the same graph, it can be easily seen that the word $\tilde{\varphi}(W)$ can be transformed to $\tilde{\varphi}(W')$ (using the same sequence of syllable shufflings). Hence the words $\tilde{\varphi}(W)$ and $\tilde{\varphi}(W')$ represent the same element in $F$.

We see that the map $\tilde{\varphi}$ induces a well defined map $\varphi \colon G \to F$ given by
\begin{displaymath}
	\varphi(g) = \varphi_{v_1}(g_1) \dots \varphi_{v_n}(g_n).
\end{displaymath}
Clearly, $\varphi \restriction_{G_v} = \varphi_v$ for every $v \in V$ and thus it makes sense to omit the subscripts and write
		\begin{displaymath}
			\varphi(g) = \varphi(g_1)\dots \varphi(g_n).
		\end{displaymath}

We claim that $\varphi$ is a $K$-almost-homomorphism, that is, $\varphi\restriction_K$ is an injective map and $\varphi(kk')=\varphi(k)\varphi(k')$ for all $k,k'\in K$.

First of all, let us show that if the reduced word $W_k\equiv (f_1, \dots, f_n)$ represents $k\in K'$ in the group $G$, then the word $\tilde{\varphi}(W_k)\equiv (\varphi(f_1), \dots, \varphi(f_n))$, which represents $\varphi(k)$ in $F$, is a reduced word in $F$.

As the maps $\varphi_v$ are $K_v$-almost-homomorphisms for every $v \in V$, it follows that $\varphi(f_i) \neq e$ in $F$ for $i = 1, \dots, n$, so no syllable of $\tilde{\varphi}(W_k)$ is trivial. Suppose that $\tilde{\varphi}(W_k)$ is not reduced in $F$. This means that there exist $i<j \in \{1, \dots, n\}$ such that the syllables $\varphi(f_i)$ and $\varphi(f_j)$ can be joined together. However, this implies that the syllables $f_i$ and $f_j$ can be joined in the word $W_k$, which contradicts the fact that $W_k$ is reduced. Hence $\tilde{\varphi}(W_k)$ is reduced.

Now, let us prove that $\varphi(kk')=\varphi(k)\varphi(k')$ for all $k,k'\in K'$.

Let $k,k' \in K$ be arbitrary and let $W,W'$ be reduced words representing $k$ and $k'$ respectively. We want to show that the word $\tilde{\varphi}(WW') \equiv \tilde{\varphi}(W)\tilde{\varphi}(W')$ represents the element $\varphi(kk')$.

Suppose that the product $kk'$ is reduced, i.e. the concatenation $WW'$, which is a word representing $kk'$ in $G$, is reduced. Using a similar argument as above we see that the word $\tilde{\varphi}(WW') \equiv \tilde{\varphi}(W)\tilde{\varphi}(W')$ is reduced. The word $\tilde{\varphi}(W)\tilde{\varphi}(W)$ represents $\varphi(k)\varphi(k')$ in $F$ by definition, but at the same time we see that the word $\tilde{\varphi}(WW')$ represents $\varphi(kk')$ in $F$, and thus $\varphi(kk')=\varphi(k)\varphi(k')$.

Now, suppose that the product $kk'$ is not reduced. Let $c,f,g \in G$ be such that $k$ factorises as a reduced product $k = fc$, $k'$ factorises as a reduced product $k' =c^{-1}g$ and $|c|$ is maximal. Clearly, $kk' = f'g'$. Without loss of generality we may assume that $W \equiv(f_1, \dots, f_n, c_1, \dots c_l)$ and $W' \equiv (c_l^{-1}, \dots, c_1^{-1},g_1, \dots, g_m)$, where $c = c_1 \dots c_l$, $f = f_1 \dots f_n$ and $g = g_1 \dots g_m$.

Consider the word $X \in \mathcal{W}_F$, where
\begin{displaymath}
	X \equiv (\varphi(f_1), \dots, \varphi(f_n), \varphi(c_1), \dots,\varphi(c_l), \varphi(c_l^{-1}), \dots, \varphi(c_1^{-1}), \varphi(g_1), \dots, \varphi(g_m)).
\end{displaymath}
Note that $X = \tilde{\varphi}(WW') = \tilde{\varphi}(W) \tilde{\varphi}(W')$.
The syllable $\varphi(c_l)$ can be joined with syllable $\varphi(c_l^{-1})$. Obviously, $c_l \in G_u$ for some $u \in V$. As $\varphi \restriction_{G_u}$ is a $K_u$-almost-homomorphism and $c_l, c_l^{-1} \in K_u$ we see that $\varphi(c_l)\varphi(c_l^{-1}) = \varphi(c_l c_l^{-1}) = \varphi(e_{G_u})$. As stated before, $\varphi(e_{G_v})=e_{F_v}$ for every $v \in V$ and thus we can remove the trivial syllable. Note that this transformation is compatible with the function $\tilde{\varphi}$:
\begin{displaymath}
	\varphi(k)\varphi(k') = \varphi(f_1 \dots f_n c_1 \dots c_{l-1})\varphi(c_{l-1}^{-1}\dots c_1^{-1}g_1 \dots g_m).
\end{displaymath}
Repeating these two steps $l-1$ more times, the word $X$ can be rewritten to
\begin{displaymath}
	X' \equiv (\varphi(f_1), \dots, \varphi(f_n), \varphi(g_1), \dots, \varphi(g_m))
\end{displaymath}
and thus we see that $\varphi(k)\varphi(k') = \varphi(f)\varphi(g)$.

Note that the word $X'$ is reduced in $F$ if and only if the word $(f_1, \dots, f_n, g_1, \dots, g_m)$ is reduced in $G$. Suppose that the word $X'$ is reduced. Then clearly $$\varphi(k)\varphi(k') = \varphi(f)\varphi(g) = \varphi(fg) = \varphi(kk')$$ and we are done.

Suppose that the word $X'$ is not reduced. As all the syllables of $X'$ are nontrivial we see that two syllables of the word $X'$ can be joined together. The word $(\varphi(f_1), \dots, \varphi(f_n))$ is a subword of $\tilde{\varphi}(W)$, which is a reduced word, and thus it is is reduced, hence no two syllables of $(\varphi(f_1), \dots, \varphi(f_n))$ can be joined together. The same argument applies to $(\varphi(g_1), \dots, \varphi(g_m))$. Hence, we see that there exist $1 \leq i \leq n$ and $1 \leq j \leq m$ such that the syllables $\varphi(f_i)$ and $\varphi(g_j)$ can be joined together in $X'$. Again, $f_i, g_j \in G_u$ for some $u \in V$ and thus $\varphi(f_i) \varphi(g_j) = \varphi(f_ig_j)$ as $f_i, g_j \in K_u$. By the assumptions (as $\varphi\restriction_{K_u}$ is injective), $\varphi(f_i g_j) = e_{F_u}$ if and only if $f_i g_j = e_{G_u}$. However, $f_i = g_j^{-1}$ would be a contradiction with the maximality of $\lvert c\rvert$, hence $\varphi(f_i) \varphi(g_j) \neq e_{F_u}$. As $\varphi \restriction_{G_u}$ is a $K_u$-almost-homomorphism we see that joining the syllable $\varphi(f_i)$ with the syllable $\varphi(g_j)$ is compatible with the map $\tilde{\varphi}$.

Suppose that the syllable $\varphi(f_i g_j)$ can be joined with some $\varphi(f_k)$. By definition, this means that $\varphi(f_k)$ and $\varphi(f_i)$ could have been joined in $\tilde{\varphi}(W)$. This contradicts the fact that $\tilde{\varphi}(W)$ is reduced. By an analogous argument, the syllable $\varphi(f_i g_j)$ cannot be joined with any syllable $\varphi(g_p)$.

By iterating the previous step at most $\min\{n,m\}$ times, we obtain a sequence of transformations compatible with the map $\tilde{\varphi}$. All together, we have shown that the word $\tilde{\varphi}(W)\tilde{\varphi}(W')$ can be rewritten to a reduced word $X''$, that represents the element $\varphi(k)\varphi(k')$ in $F$, and each rewriting step is compatible with the map $\tilde{\varphi}$: if we applied the analogous transformations to the word $WW'$ we would obtain a reduced word $U$, that represents the element $kk'$ in $G$, such that $\tilde{\varphi}(U) \equiv X''$. It follows that $\varphi(kk') = \varphi(k)\varphi(k')$.

To finish, we need to prove that $\varphi\restriction_K$ is an injective map. Let $k, k' \in K \subseteq K'$ be arbitrary such that $k \neq k'$, or equivalently $k' k^{-1} \neq e_G$. We have already shown that $\varphi(k^{-1}k') = \varphi(k^{-1})\varphi(k')$. Consider a reduced word $W_{k'k^{-1}}$ representing the element $k'k^{-1} \in K'$. Note that by the construction of the function $\varphi$ it follows that $\varphi(k) = \varphi(k)^{-1}$ for all $k \in K$. By the previous argumentation, the word $\tilde{\varphi}(W_{k'k^{-1}})$ is reduced in $F$ and thus by Theorem \ref{nft} we see that $\varphi(k'k^{-1})=\varphi(k')\varphi(k)^{-1} \neq e_F$. It follows that $\varphi(k) \neq \varphi(k')$.

Thus, we proved that $\varphi$ is a $K$-almost-homomorphism.

The graph product $F=\Gamma\mathcal{F}$ is residually $\mathcal{C}$ by assumption.
Hence, there exists a surjective homomorphism $\psi\colon F\twoheadrightarrow D\in\mathcal{C}$ which is injective on the finite subset $\varphi(K)\subseteq F$.
Thus, the composition $\psi\circ\varphi\colon G\to D$ is a $K$-almost-homomorphism, and $G$ is LE-$\mathcal{C}$.
\end{proof}

As an immediate corollary we get the following.
\begin{corollary}\label{leR}
Let $\mathcal{R}$ be a root class. Then the class of LE-$\mathcal{R}$ groups is closed under
graph products.
\end{corollary}

Note that the first four cases of Corollary B follow from Corollary \ref{leR}. In the remaining cases the assumptions of Theorem B are met by Corollary A, hence Corollary B.
\section*{Acknowledgments}
\noindent
The main body of work for the presented results was done during November 2014, when Michal Ferov was visiting the University of Vienna. This visit was supported by the European Research Council (ERC) grant of Prof. Goulnara Arzhantseva, grant agreement no.~259527.
Federico Berlai is supported by the European Research Council (ERC) grant of Prof. Goulnara Arzhantseva, grant agreement no.~259527.

redpajama_set_name: RedPajamaArXiv


text:
package net.safedata.spring.boot.training.solace.message;

public abstract class AbstractCommand extends AbstractMessage<AbstractMessageType.CommandMessage> {

    public AbstractCommand(long messageId) {
        super(messageId);
    }
}


The Falkland Islands, a British territory in the South Atlantic, is a cold, windy, and rainy place (more than half the year), as temperatures range between 30 F and 55 F. They neighbor Argentina, 300 miles to the west, the uninhabited Sandwich Islands, to the southeast, and Antarctica, 700 miles to the south. There is virtually no work here, except fishing and shepherding.
The Falklands War broke out in 1982, some 30 years ago, when roughly 3,140 English citizens on the islands witnessed an invasion by thousands of Argentine troops. After ignoring a UN Resolution calling for a withdrawal, a British submarine sank the Gen. Belgrano, an Argentine ship, causing 362 sailors to die at sea, and soon thereafter, Argentina's military junta surrendered. 13 years later, a different government agreed not to invade again, as weekly flights between the islands and Argentina resumed.
Today, Argentina continues to assert that they own the Falklands. They point out Spain was the first European power to claim them, when Magellan sailed past in 1502. Although Englishmen erected a settlement in 1766, they argue Spanish forces evicted them in 1779, just four years later. While a 1771 treaty gave Britain a right to return, they note the English voluntarily gave up the place again in 1776. Argentina asserts Spain subsequently governed the islands, until Argentine independence was declared in 1811. Argentina alleges an unbroken chain of title flowing through Spain, their predecessor-in-interest, all the way back to Magellan.
Britain, on the other hand, has a claim traced back to Capt. Davies who visited in 1592. After Viscount Falkland, a Royal Navy treasurer, went ashore in 1690, the islands were named after him. Although a newly independent Argentina opened a penal colony on the islands in 1828, it was closed down when British citizens started arriving in 1833. The UK argues English descendants have continuously occupied the Falklands since 1833, and the islanders have voted to remain a territory of the United Kingdom.
At the time of the 1982 Falklands War, President Reagan, a light-weight in international affairs, sided with Britain's Margaret Thatcher, and her Conservative government, because he simply did not know any better. He could have reminded Britain that when the people of Latin America rose up against Spanish colonialism, in the early 19th Century, and won their various wars of independence, the U.S. through President Monroe, issued the Monroe Doctrine in which the Americans sided with Argentina, and the other newly independent Latin American republics.
When the British started colonizing the Falklands in 1833, they were in direct violation of U.S. Foreign Policy, under the Monroe Doctrine. At that time, Monroe would have sided with the Argentines and against the British, and if he were alive in 1982 or today, he would take the same anti-colonial stand.
While giving the islands to Argentina now would go against 179 years of ongoing British rule, and the self-determination rights of the islanders, the Falkland Islands will have a more stable future, if they established permanent relations with Argentina, their only real neighbor. The era of colonialism is over, and it is time for Britain, Argentina, and the people of the Falklands to work out a new arrangement.
The Monroe doctrine refers to future colonisation, not defending against attack. Hence "future colonisation".
I agree the Monroe Doctrine refers to future colonization.
The Monroe Doctrine was issued in 1823. Ten years later, in 1833, the British started their current colonization of the Falklands. In 1833, the British were violating the Monroe Doctrine. They fact that they went to war in 1982 to defend their colony does not change the basic point that they acted in violation of the Monroe Doctrine in 1833.


Ready to buy a new home in Aintree? Failing to check that a lawyer is on your lender's list of approved solicitors can put your Aintree home move at risk of delay or failure.
Only LenderPanel.com provides a subset of authorised Aintree conveyancers for over 130 lenders.
The Aintree conveyancing solicitors that I appointed last week on my purchase in Aintree have suddenly shut down. I chose them because I had to have a firm on the Barclays conveyancing panel and my family Aintree lawyer was not. I issued them a cheque for £250 in advance. What do I do now?
Assuming that you have an Estate Agent in the equation then let them know straight away so that they advise the vendors that there may be a slight delay due to the problems encountered. Hopefully they will be sympathetic and urge their lawyer to send a new set of papers to your new solicitors. You should appoint new lawyers that are on the Barclays conveyancing panel and notify the lender. If you have paid over any money, it will hopefully be held by the SRA as money in an intervened firm's bank accounts is transferred to the SRA. Then, the SRA or the intervention agent looks at the intervened firm's accounts to work out who the money belongs to. To claim your money you will need to contact the SRA. If the SRA cannot return money you are owed from the firm's bank accounts, or if they can only return part of the money, you can apply to the Compensation Fund for a grant. Your new solicitors should be in a position to assist.
3 months have gone by since my purchase conveyancing in Aintree concluded. I have checked the Land Registry website which shows that I paid £200,000 when infact I paid £170,000. Why the discrepancy?
How does conveyancing in Aintree differ for new build properties?
Most buyers of new build residence in Aintree contact us having been asked by the builder to exchange contracts and commit to the purchase even before the residence is finished. This is because house builders in Aintree usually purchase the land, plan the estate and want to get the plots sold off as they are building the properties. Buyers, therefore, will have to exchange contracts without actually seeing the house they are buying. To reduce the chances of losing the property, buyers should instruct conveyancing solicitors as soon as the property is reserved and mortgage applications should be submitted quickly. Due to the fact that it could be several months and even years between exchange of contracts and completion, the mortgage offer may need to be extended. It would be wise to use a lawyer who specialises in new build conveyancing especially if they are used to new build conveyancing in Aintree or who has acted in the same development.
My husband and I are one month into a freehold purchase having been recommend to a firm by the estate agent to do our conveyancing in Aintree. I am not happy. Could you help me find new lawyers?
I am purchasing a house and need a conveyancing solicitor in Aintree who is on the lender approved panel. Could you point me in the right direction as regards a firm?
Our service is limited to being a directory service for firms who wish to listed as being on the approved conveyancing panel for the mortgage company who carry out conveyancing in Aintree. We dont recommend any particular solicitor.


text:
Hōdō Nakamura (jap. ; * 29. November 1950 in Arie (heute: Minami-Shimabara), Präfektur Nagasaki) ist ein japanischer Politiker und war von 2010 bis 2022 Gouverneur von Nagasaki.

Leben
Nakamura, Absolvent der Universität Nagasaki, arbeitete seit seinem Abschlussjahr 1973 für die Präfekturverwaltung, zuletzt seit 2009 als Vizegouverneur unter Genjirō Kaneko. Als Kaneko 2010 nicht für eine weitere Amtszeit kandidierte, bewarb sich Nakamura bei der Wahl am 21. Februar 2010 um dessen Nachfolge. Bei einer Wahlbeteiligung von 60 % konnte er sich gegen Tsuyoshi Hashimoto (unterstützt durch die auf nationaler Ebene regierende Demokratische Partei) und fünf weitere Kandidaten klar durchsetzen. Er trat sein Amt am 2. März 2010 an.

Bei den Gouverneurswahlen 2014 und 2018 wurde Nakamura mit expliziter oder impliziter Unterstützung beider großer Parteien, jeweils gegen den Kommunisten Toshihiko Haraguchi als einzigem Herausforderer, klar für zwei weitere Amtszeiten bestätigt. Bei der Gouverneurswahl 2022 spaltete sich die LDP Nagasaki, ein Teil unterstützte Nakamura für eine vierte Amtszeit, ein Teil unterstützte die Kandidatur des über 30 Jahre jüngeren Arztes Kengo Ōishi; Nakamura unterlag knapp.

Weblinks

 Präfekturverwaltung Nagasaki:
 Zenkoku Chijikai (Nationale Gouverneurskonferenz, englisch NGA): Kurzbiografie, abgerufen am 22. Februar 2022.

Einzelnachweise

Gouverneur (Präfektur Nagasaki)
Japaner
Geboren 1950
Mann

redpajama_set_name: RedPajamaWikipedia


Find a great sale price on this 2016 BMW 3 Series at BMW of El Cajon in California. This 2016 BMW 3 Series is located at our BMW dealership in El Cajon. We also serve the cities of San Diego. So if you're looking for a great price on this 2016 BMW 3 Series or just looking to get an auto loan for the vehicle you want... you've come to the right place! BMW of El Cajon.
**BMW CERTIFIED**, Automatic, Automatic Climate Control, Ambent Lighting, Hi-fi sound system, Bluetooth. CARFAX One-Owner. Clean CARFAX.


REALLY Live A Miraculous Life!
Imagine How Divine You Are!
There is never an instant when you are not surrounded in love. You are loved SO MUCH. Feel this love now.
This video begins a series based on the book 12 Powers Of Man written by Charles Fillmore founder of Unity Church. The power shared here is Strength!
Rev. Maria Felipe sits down with author of A Course Of Love Mari Perron to chat on peace and relationships.


Dr. Cunningham has recently introduced BOTOX to her practice. BOTOX ® Cosmetic (Botulinum Toxin Type A) is an FDA-approved agent that can be injected into the muscle just under the skin surface to reduce eye muscle spasm as well as eliminate wrinkles around the eyes and forehead. Wrinkles can be temporarily eliminated, creating a softer, smoother, and more appealing look. After a treatment, wrinkles take only a few days to soften. One treatment usually lasts about 4 months, and can then be repeated as long as you did not experience any allergic reaction or side effect. You might feel some mild discomfort at the injection site, but most people report no side effects. For more information, set up an appointment and go to www.botox.com.


Jr. Youth Sunday School is led by Stephanie Black in the school building on Sunday mornings from 9:30am to 10:30am. Mrs. Black structures every Sunday school lesson to fit her students and to make the information interesting and easy to understand. It is her prayer that each of her students will come to know God as their Rock, even as the world is constantly changing.
Sr. Youth Sunday School is in the Youth House on Sunday mornings from 9:30am to 10:30am. The content and materials studied are based on the current needs and questions of the Sr. Youth and are designed to get teenagers thinking and acting to make a difference in their relationship with God and others.
Join us for Sunday School hour to see how God's Word is still applicable to us today and to learn what your role is as young Christians.
Confirmation is a two year class for 7th and 8th graders that helps them to explore their personal faith and beliefs. Every person needs to decide what they believe and how their beliefs will shape their life. This class aims to walk along side our students to help them determine what they believe. After our two year program, each student gets the opportunity to profess their faith in front of the congregation and to decide what their role in the church will be. Confirmation classes are Wednesday nights in the school building from 6:15pm to 7:30pm. There are 18 classes a year that take place during the school year, excluding the season of Advent and Lent.
At St. John's our youth are provided with monthly opportunities to serve the church and the community of Winston-Salem. Service is a key part of our youth ministry program since being a Christian is all about taking the love and grace Jesus showed us on the cross and sharing that with our neighbor. Many of our service project ideas come from our youth and are based on the personal passions and interests of our teens. Some of our projects include serving foster children in the community, providing care packages for our troops, college students, and the homeless, helping the elderly with yard care, and providing meals for struggling families. The youth also participate in yearly mission trips.
Just like your relationship with your parents, your relationship with God is meant to take place for more than a few hours on Sunday. And just like your relationship with your best friend, your relationship with God is meant to be personal, fun, and based on who you are and what you like. At St. John's we seek to teach each of our youth how to interact with God daily based on their individual hobbies, talents, and learning styles. This puts the faith of the teenager in their own hands which provides them with a personal relationship with God that they will have the skillset to navigate for the rest of their lives.
At St. John's we understand that the most beneficial way to help teens grow in their faith is to have them actually DOING the ministry. Being a leader for God and the Church is a skill that will help these young people maintain their faith as they leave for college and will even help them grow closer to God as they serve him more and more. We want to help our youth be involved in ministries that interest them. If you have an idea of a ministry activity you would like to lead or start, please fill out the form below and hit submit.


text:
IAB Adds Agencies, But May Have Lost Its Way; Can CPGs Stop The Gross Marketing Gimmicks Already?
The "Big Tent" Backlash The IAB announced last week that advertising and media agencies will now be able to join the industry trade association as members. All the big agencies are already partners out of the gate. The IAB makes the case that online advertising must span many categories to work effectively, and the industry... Continue reading »
by AdExchanger	// December 20th, 2021 //
Democrats Call To Revise Section 230; State AGs Condemn Instagram Kids
Here's today's AdExchanger.com news round-up… Want it by email? Sign up here. Section Off Late last week, two House Democrats introduced a bill that would require social media platforms to share and implement content moderation policies and would revise Section 230 by allowing the Federal Trade Commission to bring enforcement actions against tech companies that fail... Continue reading »
60% Of School Apps Are Improperly Sharing Student Data With Third Parties
The kids are online, but their data is not all right. The majority of school utility apps used by kids and parents are pervasively sharing student data with third parties through advertising and analytics software development kits (SDKs), including those provided for free by Google and Facebook. On average, school apps have more than 10... Continue reading »
by Allison Schiff	// May 4th, 2021 //
Just Because You're Compliant With COPPA Doesn't Mean You're Cool Under CCPA Or GDPR
There's not enough awareness that compliance can't be a cut-and-paste job when it comes to kids. Just because you're compliant with Children's Online Privacy Protection Act (COPPA), doesn't mean you're compliant with the California Consumer Privacy Act (CCPA), or the EU's General Data Protection Regulation (GDPR). Plus, US states are coming out with their own... Continue reading »
by Allison Schiff	// January 27th, 2020 //
Some People Are Easing Off Phone Use, Hearts & Science Finds; YouTube Revamps Ad Targeting On Kids Videos
Here's today's AdExchanger.com news round-up… Want it by email? Sign up here. Mobile Detox Are people cutting back on their mobile phone use? Media agency Hearts & Science tracked the phone usage of more than 2,000 Americans over 14 months and found that 64% scaled back their app usage during that period, with the average down... Continue reading »
by AdExchanger	// January 7th, 2020 //


text:
<?php
class Coupon extends MY_Controller{
    public function __construct(){
            parent::__construct();
            $this->load->model('Coupon_model');
            $this->load->model('Category_model');
        $this->db->cache_off();
    }

    public function index(){
            redirect(base_url().'webadmin');
    }

    public function viewlist(){
        $this->load->model('User_model');
            $data=$this->_show_admin_logedin_layout();
            $TopcategoryData=$this->Category_model->get_top_category_for_product_list();
            $AllButtomcategoryData=$this->Category_model->buttom_category_for_product_list();
            foreach($TopcategoryData as $k){
                $SubCateory=$this->Category_model->get_subcategory_by_category_id($k->categoryId);
                if(count($SubCateory)>0){
                    foreach($SubCateory as $kk => $vv){
                        $menuArr[$vv->categoryId]=$k->categoryName.' -> '.$vv->categoryName;
                        $ThirdCateory=$this->Category_model->get_subcategory_by_category_id($vv->categoryId);
                        if(count($ThirdCateory)>0){
                            foreach($ThirdCateory AS $k3 => $v3){
                                // now going for 4rath
                                $menuArr[$v3->categoryId]=$k->categoryName.' -> '.$vv->categoryName.' -> '.$v3->categoryName;
                                $FourthCateory=$this->Category_model->get_subcategory_by_category_id($v3->categoryId);
                                if(count($FourthCateory)>0){ //print_r($v3);die;
                                    foreach($FourthCateory AS $k4 => $v4){
                                        $menuArr[$v4->categoryId]=$k->categoryName.' -> '.$vv->categoryName.' -> '.$v3->categoryName.' -> '.$v4->categoryName;
                                    }
                                }
                            }
                        }
                    }
                }
            }
            //pre($menuArr);die;
            $data['categoryData']=$menuArr;
            $userArr=$this->User_model->get_all_buyer();
            //pre($userArr);die;
            $data['UserDataArr']=$userArr;
            $data['DataArr']=$this->Coupon_model->get_all_admin();
            $this->load->view('webadmin/coupon_list',$data);
    }

    public function add(){
        $code=$this->input->post('code',TRUE);
        $type=$this->input->post('type',TRUE);
        $amount=$this->input->post('amount',TRUE);

        $startDateArr=  explode('-',$this->input->post('startDate',TRUE));
        $startDate=$startDateArr[2].'-'.$startDateArr[1].'-'.$startDateArr[0];

        $endDateArr=  explode('-',$this->input->post('endDate',TRUE));
        $endDate=$endDateArr[2].'-'.$endDateArr[1].'-'.$endDateArr[0];

        $category=$this->input->post('category',TRUE);
        $userId=$this->input->post('userId',TRUE);
        $userUsesType=$this->input->post('userUsesType',TRUE);
        $status=$this->input->post('status',TRUE);

        $dataArr=array(
        'code'=>$code,
        'type'=>$type,
        'amount'=>$amount,
        'startDate'=>$startDate,
        'endDate'=>$endDate,
        'status'=>$status
        );

        if($userId!=""){
            $dataArr['userUsesType']=1;
            $dataArr['usesType']=$userUsesType;
        }else{
            $dataArr['userUsesType']=2;
            $dataArr['usesType']=2;
        }

        //pre($dataArr);die;

        $couponId=$this->Coupon_model->add($dataArr);

        /*$categoryDataArr=$this->Category_model->get_all_parrent_details($category);
        $AddcategoryDataArr=array('couponId'=>$couponId,'categoryId'=>$category);
        //pre($AddcategoryDataArr);die;
        $this->Coupon_model->add_category($AddcategoryDataArr);*/

        if($userId!=""){
            $this->Coupon_model->add_user(array('couponId'=>$couponId,'userId'=>$userId,'userUsesType'=>$userUsesType));
        }

        $this->session->set_flashdata('Message','Coupon added successfully.');
        redirect(base_url().'webadmin/coupon/viewlist');
    }

    public function edit(){
            $code=$this->input->post('Editcode',TRUE);
            $type=$this->input->post('Edittype',TRUE);
            $status=$this->input->post('Editstatus',TRUE);

            $amount=$this->input->post('Editamount',TRUE);

            $startDateArr=  explode('-',$this->input->post('EditstartDate',TRUE));
            $startDate=$startDateArr[2].'-'.$startDateArr[1].'-'.$startDateArr[0];

            $endDateArr=  explode('-',$this->input->post('EditendDate',TRUE));
            $endDate=$endDateArr[2].'-'.$endDateArr[1].'-'.$endDateArr[0];

            $category=$this->input->post('Editcategory',TRUE);

            $couponId=$this->input->post('couponId',TRUE);

            $dataArr=array(
                'type'=>$type,
                'amount'=>$amount,
                'startDate'=>$startDate,
                'endDate'=>$endDate,
                'status'=>$status
                );
            //print_r($dataArr);die;
            $this->Coupon_model->edit($dataArr,$couponId);

            $categoryDataArr=$this->Category_model->get_all_parrent_details($category);
            $AddcategoryDataArr=array('categoryId'=>$category);
            $this->Coupon_model->edit_category($AddcategoryDataArr,$couponId);

            $this->Coupon_model->edit_category($AddcategoryDataArr,$couponId);

            $this->session->set_flashdata('Message','Coupon updated successfully.');
            redirect(base_url().'webadmin/coupon/viewlist');
    }

    public function change_status($couponId,$Action){
            $this->Coupon_model->change_status($couponId,$Action);

            $this->session->set_flashdata('Message','Coupon status updated successfully.');
            redirect(base_url().'webadmin/coupon/viewlist');
    }

    public function delete($couponId){
            $this->Coupon_model->delete($couponId);

            $this->session->set_flashdata('Message','Coupon deleted successfully.');
            redirect(base_url().'webadmin/coupon/viewlist');
    }

    public function add_user(){
        $userId=$this->input->post('addUserId',TRUE);
        $userUsesType=$this->input->post('userUsesType',TRUE);
        $couponId=$this->input->post('couponCodeId',TRUE);

        $this->Coupon_model->add_user(array('couponId'=>$couponId,'userId'=>$userId,'userUsesType'=>$userUsesType));
        $this->session->set_flashdata('Message','User added to coupon successfully.');
        redirect(base_url().'webadmin/coupon/viewlist');
    }
}


A three-member team of auditors from the Food and Veterinary Office of the European Union (EU) is in the country to assess the quality of Ghana's vegetables.
The audit will enable the EU office on food safety to reconsider a three-year-old embargo on vegetables export from Ghana to the EU Market.
The auditors who are expected to end their duty tour by Saturday, September 21, 2017, will among other things thoroughly assess the sanitary and phytosanitary systems in Ghana required for ensuring the safety of food items and fresh produce.
The acting Director, Plant Protection and Regulations Services of the Ministry of Food and Agriculture (MoFA), Mr Eric Quaye, disclosed this at a forum organised by the Ghanaian-German Economic Association (GGEA) in Accra last Wednesday.
He said the country had taken steps to upgrade its sanitary and phytosanitary systems and infrastructure in order to reverse the ban on exports of five vegetables-capsicum, solanum species-aubergines, momordica, luffa and lagenaria (gourd family)-after failing an assessment in 2015 due to high levels of interceptions in the EU Market.
Mr Quaye expressed the confidence that the country would pass the audit following robust measures deployed to correct anomalies in the system.
"We have now put in place the right measures, which include upgrading exporting facilities at the Kotoka International Airport (KIA) and skills of Plant Protection and Regulatory Services Directorate (PPRSD) inspectors to pave the way for the ban on these five vegetables to be reversed," he said.
The EU three years ago banned the exports of chillies, aubergine and other vegetables from Ghana to stop the introduction of pests into the ecosystem of the EU. Also affected are gourds and Asian vegetables.
Ghana is said to have lost more than $30 million worth of exports of the selected vegetables to the EU Market, since the ban three years ago.
Going forward, the President of the GGEA, Mr Stephen Antwi, told the Daily Graphic that the government must also deploy robust plans to prevent any future ban.
"The ban in the first place was as a result of failures on our part to implement certain policies and execute them. Therefore, we need to follow through the stipulated EU guidelines to prevent future ban," he stated.
He said it was the hope of stakeholders in the industry that the ban would be lifted following the measures the government had deployed.
"But we need to be consistent in following the rules of exporting vegetables to the EU Market. Whether in the area of sanitary and phytosanitary systems or warehousing management, let's put robust measure in place to help increase trade," Mr Antwi stated.
The forum, which was the sixth in a series this year, was on the theme: 'Overcoming the Challenges in the Export of Agro Products to the EU Market' and brought participants from the private sector, policy makers and people from government to deliberate on issues affecting businesses in the country.
The forum also gave participants an opportunity to know more about the various developments in the export trade business.


text:
Scala Radio launches Women Composers station
This January, discover something new as Scala Radio adds a brand-new station to the family when they launch their Women Composers station, as part of their ongoing partnership with Donne, Women in Music.
From the 6th of January 2022 listeners will be able to find the channel online as part of the stations available to Scala Radio Premium subscribers.
A first of its kind, the music will focus solely on women classical composers featuring artists such as Clara Schumann, Amy Beach and Augusta Holmès as well as more modern talent like Nainita Desai and Rachel Bruerville.
Scala presenter Penny Smith said "There are many exceptional women composers out there to listen to and discover in the classical genre. By launching this dedicated station Scala Radio is shining a light on these talented women and the music they have produced"
Soprano Gabriella Di Laccio, Founder of Donne said: "It is only through collaboration with others who share our values and ambitions that we can create real change. Music is a powerful instrument of social change and should reflect the diverse richness of all artists. We are absolutely thrilled to continue our partnership with Scala Radio and work together to inspire more listeners and create more impact."
This new station forms part of Scala Radio's ongoing relationship with Donne, Women in Music which was originally formed in Spring 2021.
Donne, Women in Music is a charitable foundation that aims to make a positive change and readdress the gender inequality within the music industry. The charity celebrates, advances and amplifies women in music so that they are seen, heard and appreciated for their talent, as well as leaving a legacy of inspiration for future generations. https://donne-uk.org
Scala Radio's Women Composers station will be available online from 6th January.
Listen to Scala Radio on Digital Radio across the UK, on smart speaker and on the Scala Radio app.
Cat Martin – Communications Director, Bauer Media Audio
T: 0207 432 3317 M: 07932 746 363
Amelia O'Shea – Head of Communications, Bauer Media Audio UK
T: 0207 432 3417 M: 07718 489342
About Scala Radio:
Scala Radio is an entertainment radio station that breaks the mould of classical music in the UK. Presenters include Simon Mayo, Angellica Bell, Penny Smith, Alexis Ffrench and Mark Kermode. Alongside familiar masters such as Mozart, Beethoven and Bach, you can expect to hear contemporary works including film, TV and video game scores, showtunes from musicals and instrumental re-workings of pop and rock songs by the likes of Justin Timberlake, Led Zeppelin and Dua Lipa.


text:
Nash UNC Health Care names hospitalist medical director
Posted Wednesday, August 22, 2018 10:41 pm
Kasarala
For the Times
ROCKY MOUNT — Dr. George Kasarala has been named the hospitalist medical director at Nash UNC Health Care.
The hospitalist program at Nash UNC is partnered with Sound Physicians. Hospitalists are medical providers who specialize in the comprehensive care of the hospitalized patient with 24/7 in-house coverage, guiding patients' care and treatment during their hospital stay. Hospitalists work with the patient's primary care provider to coordinate in-hospital medical care as well as follow-up treatment.
Kasarala started his new role on July 24.
"I am excited to work with the hospitalists and full team at Nash UNC Health Care to support the hospital's mission of providing superior quality health care for this community," Kasarala said. "I am looking forward to collaborating with Nash UNC's medical staff, primary care providers in the community, nursing teams and support staff to improve the full spectrum of care for our patients."
Kasarala has served as a hospitalist in a variety of settings since 2012, most recently with Vidant Medical Center in Greenville. He previously served as associate program director of the Apogee Hospitalist program in Elkhart, Indiana.
"We believe Dr. Kasarala's leadership will help us continue to improve our medical services, especially by focusing on improving communication between doctors and our patients and being attentive to our patients' needs," said Nash UNC president and CEO Dr. L. Lee Isley. "We look forward to seeing the impact Dr. Kasarala will have on our organization and community as a whole."
Kasarala is board-certified in internal medicine by the American Board of Internal Medicine. He also holds a Master's of Business Administration degree from the University of Findlay in Ohio. He completed his residency in internal medicine at Saint Louis University.
Kasarala and his wife have two children.


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Q: Windows 7 laptop fonts DPI is too big breaking certain applications I have just installed windows 7 on a laptop and the fonts seem to be doing weird things, Ive adjusted the DPI back to 100% (was 125% by default) however certain applications (old delphi programmed ones) do not look correct still.
Here is a screen shot comparing my laptop to my PC running the same software (ROCLink RTU configuration software), the PC looks fine but the laptop does not.
Does anyone know where the problem may lie or what I should try next?
Thanks

A: it might be, that the old Delphi-App uses the system default DPI (not user-defined).
The system DPI is not affected by the Control Panel setting.
The system default DPI however is set under following registry path:
HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Hardware Profiles\Current\Software\Fonts\

The Key is named LogPixels and the decimal value should be 96. This corresponds to the 100% scaling setting in the control panel.
After a reboot, you are good to go.

redpajama_set_name: RedPajamaStackExchange


In the above calendar, Green Shaded cells show planetary transits. Red shaded cells show retrograde events and malefic aspects. Blue shaded cells show eclipse dates. All New Moons are labeled as (A) for Amavasya and all Full Moons are labeled as (P) for Poornima.
You can download Vedic calendar for 2017-2018 below. This calendar will give you precise times for various festivals and important lunar days such as Amavasya (New Moon), Ekadashi, Poornima (Full Moon) etc for the whole year.


Areas of Expertise : Civil Litigation, Court of Protection Applications, Powers of Attorney & Injury Claims.
Admitted as a Solicitor in 1972 Keith Jones initially undertook house and commercial conveyancing and probate as his main areas of interest. However over the years he has also became responsible for Injury and Accident Claims and General Litigation such as building disputes and civil disputes requiring Court intervention such as House Re-Possession.
He has added Court of Protection and Office of the Public Guardian work in recent years to advise and assist with Lasting Powers of Attorney and Applications for Deputyship.
He also holds an Honours Degree in Law from London University.
Moving from Liverpool, his home town, first to Chester in 1973 and then to Shotton in 1975, Keith Jones has become a part of the local business community living initially at Northop where he was a Community Councillor and actively involved in the Village School PTA, moving to the Vale of Clwyd in the mid 80's where he now relaxes and enjoys part-time retirement.


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Rand S. April
Mr. April is one of our Class III directors and currently serves as a member of the compensation committee and the nominating and governance committee. Mr. April was a Partner of Skadden, Arps, Slate, Meagher & Flom LLP, an international law firm, for three decades until 2013 and Mr. April served as the leader of Skadden's Los Angeles office from 1994 until 2012. Subsequent to Mr. April's retirement as a Partner in 2013, he was Of Counsel to Skadden until April 2016. During his time at Skadden, Mr. April had an extensive real estate and finance practice, regularly advising both U.S. and international clients in transactions involving a wide variety of real estate asset classes. He has considerable experience with the public and private offering of various types of real estate securities, including REIT and securitized debt offerings. Mr. April serves as a consultant to various real estate related companies, from time to time. In addition, Mr. April is a longtime board member and former Chairman of Public Counsel Law Center, the nation's largest pro bono law firm serving the indigent, where he was interim President and Chief Executive Officer in 2015. Mr. April is also a board member of Town Hall Los Angeles (now known as Los Angeles World Affairs Council Town Hall), where he served as Chairman from 2010 to 2011, and a member of the Advisory Board of the Los Angeles Sports and Entertainment Commission. From July 2016 to June 2019, Mr. April served as general counsel to, and since June 2019 has served as a board member of the Karsh Family Social Service Center, Inc., an organization that provides comprehensive support services for indigent clients and other individuals in the surrounding community. Mr. April holds a B.A., phi beta kappa, from Northwestern University and a J.D. from Columbia University School of Law, where he was a Harlan Fiske Stone Scholar.


For decades, New Jersey lawmakers and governors have failed to address their constitutional obligation to provide a thorough and efficient education to every child in New Jersey but Lisa McCormick will not wait a single day. If school districts have money to spend on multi-million dollar settlements and lawyers, then we can afford to educate every child instead.
We can cut property taxes in half, keep your community involved in every neighborhood school, significantly reduce administrative costs and do a better job impacting the lives of every student by making sense out of our convoluted and corrupt public schools.
It is time to address the problem of failing schools by consolidating the administration of education under state control, ending our reliance on the grossly unfair and antiquated property tax and empowering teacher to do their job well.
We need to restructure the entire school system, insure safe and well-equipped facilities and expand free public education to include pre-K and college, or an alternative training program that qualifies graduates to work in a useful trade.
In process of publishing a book on the dismal state of education in the United States. In fact, I not only critique our educational system, but also suggest meaningful fixes based on various European models.


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"If John Ehlers wrote it, then I will read it. John is one of those rare breed of analysts who dives into the why and how of things and not the often used superficial approach. Cycle Analytics for Traders seemed almost like a composite of much of his work over the last 30+ years, plus considerable new material that makes this book a treasure for anyone who has even the slightest interest in cycles or any periodic associations with market price movements. A must–own book!"


The Phan Foundation, set up by the four children of Padoh Mahn Sha, is asking people from Burma and supporters around the world to hold memorial services for Padoh Mahn Sha on or around 14th February, the first anniversary of his assassination.
On Feb. 14, 2008 Padoh Mahn Sha was assassinated by two gunmen at his home in Mae Sot, Thailand. The gunmen were acting on behalf of the Burmese regime. No-one has been arrested for the murder.
Padoh Mahn Sha was General Secretary of the Karen National Union, and dedicated his life to the struggle for freedom, democracy and human rights in Burma. He was a respected and unifying figure who refused to surrender to the regime, which is why Burma's generals were so afraid of him.
The Phan Foundation was set up in memory of Padoh Mahn Sha and his wife, Nant Kyin Shwe, by their children. It aims to fight poverty and promote education for Karen people, and preserve Karen culture. The Phan Foundation is asking for collections for the Foundation to be made at the memorial services.
For more information contact phanfoundation@googlemail.com.