text:
\section{Introduction}

Let $G$ be a graph with vertex set  $V(G)$ and edge set $E(G)$. For any $v\in
V(G)$, let $N_G(v)$ denote the set of neighbors of $v$ in $G$. A $k$-walk of
$G$ is a spanning closed walk of $G$ visiting each vertex at most $k$ times. An
$1$-walk of $G$ is a Hamiltonian cycle in $G$. For an integer $m$, denote by $m*G$ the multigraph obtained from $G$ by taking each edge $m$ times.
Obviously, a $k$-walk in $G$, is also a subgraph of $(2k)*G$.
Let $\Omega(G)$ denote the number of connected components of $G$.
The following terminology, due to V.~Chv\'{a}tal \cite{chvatal1973tough}, turned out to be very important in the research of Hamiltonicity.
\begin{definition}
$G$ is $\beta$-{\em tough},
for a positive real $\beta$, if $\Omega(G-S)>1$ implies $|S|\ge \beta\cdot \Omega(G-S)$
for each $S\subset G$.
\end{definition}
That is, $G$ is $\beta$-tough if
$G$ cannot be split into $k$ (with $k>1$) components by removing less than
$k\beta$ vertices.  The {\em toughness} of $G$, denoted $\tau(G)$, is the maximum
value of $\beta$ for which $G$ is $\beta$-tough.  Clearly, if $g$ is
Hamiltonian, then $G$ is 1-tough, however, the converse is not true.  A famous
conjecture of V.~Chv\'{a}tal \cite{chvatal1973tough}, which is still open, claims
that the converse holds at least in an approximate sense.
\begin{conjecture}\label{conj1} There exists a constant $\beta$ such that every
$\beta$-tough graph is Hamiltonian.  \end{conjecture}

The concept of a $k$-walk is a generalization of the concept of a Hamiltonian cycle; in \cite{jackson1990k} B.~Jackson and N.C.~Wormald investigated $k$-walks and obtained the following results.
\begin{theorem}\label{thm1}
Every $1/(k-2)$-tough graph has a $k$-walk.
In particular every 1-tough graph has a 3-walk. \qed
\end{theorem}

In \cite{ellingham2000toughness}, it is proved that
\begin{theorem}\label{thm3}
Every 4-tough graph has a 2-walk. \qed
\end{theorem}
The following well-known conjecture related to $k$-walks appeared in \cite{jackson1990k}.
\begin{conjecture}\label{conj2}
Every $1/(k-1)$-tough graph has a $k$-walk.
\end{conjecture}

Results just mentioned do not apply to the case $k=1$.
For some classes of graphs, there are strong results connected toughness and Hamiltonicity (recall that
a 1-walk is a Hamiltonian cycle). E.g. in \cite {chen1998tough}, G.~Chen, M.S.~Jackson, A.E.~Kezdy, and J.~Lehel proved
\begin{theorem}\label{thm4}
Every 18-tough {\em chordal} graph is Hamiltonian. \qed
\end{theorem}

\begin{definition}
$G$ is said to be {\em split} if $V(G)$ can be partitioned into an independent set $I$ and a clique $C$.
\end{definition}
For split graphs, we have many beautiful results.
E.g. in \cite{kratsch1996toughness} the following is proved.
\begin{theorem}\label{thm5}
Every $3/2$-tough {\em split} graph on at least three vertices is Hamiltonian, and this is best possible in the sense that there is a sequence $\{G_n\}^{\infty}_{n=1}$ of split graphs with no 2-factor and $\tau(G_n)\to 3/2$. \qed
\end{theorem}

Let us consider a superclass of split graphs, named $2K_2$-free graphs. These are graphs which do not contain an induced copy of $2K_2$, the graph on four vertices consisting of two vertex disjoint edges. Obviously, every split graph is a $2K_2$-free graph. What is more, every co-chordal graph, i.e. the complement of a chordal graph, is also a $2K_2$-free graph. That means that the class of $2K_2$-free graphs is as rich as the class of chordal graphs.

Recently, in \cite{broersma2014toughness}, H.~Broersma, V.~Patel and A.~Pyatkin proved the following.
\begin{theorem}\label{thm6}
Every 25-tough 2$K_2$-free graph on at least three vertices is Hamiltonian. \qed
\end{theorem}

In this paper, we prove
\begin{theorem}\label{thm7}
Every 2-tough 2$K_2$-free graph admits a 2-walk.
\end{theorem}

\section{On 2$K_2$-free graphs}

We present several structural properties of $2K_2$-free graphs which turn out to be very useful in the proof of the main theorem.
For a subset $A\subset V(G)$, let $Dom(X)$ denote the set of vertices dominated by $A$, i.e. $Dom(A)=A\cup\{y\in V(G);~there~exists~x\in A~such~that~xy\in E(G)\}$. The set $A\subset V(G)$ is said to be {\em dominating} if $Dom(A)=V(G)$. A {\em dominating clique} of a graph $G$ is a dominating set which induces a complete subgraph in $G$. The following theorem comes from \cite{chung1990maximum}.

\begin{theorem}\label{thm8}
If $G$ is $2K_2$-free and the maximum size of cliques $\omega(G)\ge3$, then $G$ has a dominating clique of size $\omega(G)$. \qed
\end{theorem}
Let us consider a generalization of dominating set. The set $A\subset V(G)$ is said to be {\em weakly-dominating} if for any edge $v_1v_2\in G$, we have $v_1\in Dom(A)$ or $v_2\in Dom(A)$. And, a {\em weakly-dominating clique} of a graph $G$ is a weakly-dominating set which induces a complete subgraph in $G$. We say a clique $Q_j$ of $G$ is weakly-dominated by a clique $Q_i$ of $G$, if for any pair $(v_1,v_2)$ of vertices in $Q_j$ one has that at least one of $v_1$ and $v_2$ is adjacent to a vertex in $Q_i$.

Obviously, a dominating set is a weakly-dominating set.
Then, similarly to Theorem \ref{thm8}, we get:
\begin{theorem}\label{weak}
If $G$ is $2K_2$-free and the maximum size of clique $\omega(G)\ge2$, then $G$ has a weakly-dominating clique of size $\omega(G)$.
\end{theorem}
\begin{proof}
If $\omega(G)\ge3$, by Theorem \ref{thm8}, we get a dominating clique, thus it is also a weakly-dominating clique. If $\omega(G)=2$, for any clique of size 2, say $Q_0=v_1v_2$ and any edge $v_3v_4 \in G$, if $v_1v_3,v_1v_4,v_2v_3,v_2v_4\not\in E(G)$, then $v_1v_2$ and $v_3v_4$ form a $2K_2$.
\end{proof}

In fact, in a $2K_2$-free graph $G$, any edge is weakly-dominating.
The following observation from \cite{broersma2014toughness} is very useful.
\begin{lemma}\label{lm1}
A graph $G=(V,E)$ is $2K_2$-free if and only if for every $A\subset V$ at most one component of the graph $G-A$ contains edges. \qed
\end{lemma}
Using these two properties as tools, we can look at $2K_2$-free graphs more closely.

Given a $2K_2$-free graph $G$, by Theorem \ref{thm8}, we can find one of its maximum weakly-dominating clique, namely $Q_1$. Obviously, any induced subgraph of a $2K_2$-free graph is again $2K_2$-free. Then $G-Q_1$ is also a $2K_2$-free graph. By Lemma 1, $G-Q_1$ is made up by two parts, one is an independent subset (possibly empty) of $G-Q_1$, denoted by $D_1$, another part is a non-trivial component (possibly empty), denoted by $G_1$, which is also $2K_2$-free. For the same reason, we can find a maximum weakly-dominating clique in $G_1$, namely $Q_2$, and a non-trivial component in $G_1-Q_2$, namely $G_2$ and an independent subset in $G_1-Q_2$, namely $D_2$. Repeating this process, we get
\begin{theorem}\label{thm9}
For a $2K_2$-free graph $G=G_0$, we can find a sequence of cliques $\{Q_i;i=1,\ldots,k\}$, where $|Q_i|\ge2$ and $|Q_i|\ge|Q_{i+1}|$, such that $Q_1$ is a maximum weakly-dominating clique in $G_0$ and $Q_{i+1}$ is a maximum weakly-dominating clique in $G_{i}\subset G_{i-1}-Q_{i} ,(i=1,\ldots,k-1)$. Additionally, $G_i$ is the only non-trivial component in $G_{i-1}-Q_i$. The subset $D_i=G_{i-1}-Q_i-G_i$ is an independent set. We call vertices in $D=\cup_{i=1,\ldots,k} D_i$ the first class vertices.  \qed
\end{theorem}

In addition, we get
\begin{theorem}\label{thm10}
A $2K_2$-free graph $G$ can be divided into two parts, a ``clique tower'' $Q=\cup_{i=1,\ldots,k}Q_i$ and an independent set $D=\cup_{i=1,\ldots,k}D_i$, where $V(G)=V(Q)\cup V(D)$ and $V(Q)\cap V(D)=\emptyset$. Note that we allow any of these sets to be empty. \qed
\end{theorem}

\section{The proof of the main result}

In short, the proof is divided into two parts. In the first part, we construct an auxiliary graph $\Gamma$, which is an Eulerian (multi)graph. There are two kinds of edges in $\Gamma$, namely blue edges and red edges. In the second part, with the help of $\Gamma$, we find a subgraph $H$ of $2*G$, which is Eulerian and with all vertices of degree 2 or 4, where $2*G$ denotes the multigraph obtained by doubling each edge of $G$ into a pair of parallel edges. $H$ is the 2-walk we want. In $H$, there are three kinds of edges, namely first-class edges, second-class-edges and third-class edges. The first-class edges are corresponding to the blue edges in $\Gamma$, the second-class edges are corresponding to red edges in $\Gamma$, and the third-class edges are used to make sure $H$ is connected and to adjust the vertex degrees to 2 or 4.

\subsection{The proof of Theorem \ref{thm7}}

Let $G$ be a 2-tough $2K_2$-free graph. If it has only 2 vertices, this is a trivial case and nothing to prove. So, we assume there are at least three vertices. The sequence of cliques defined in Theorem \ref{thm9} is $\{Q_1,\ldots,Q_k\}$, where each $Q_i$ is weakly-dominated by $Q_j$, when $j<i$, and $|Q_i|\ge|Q_{i+1}|\ge2$.

First, if $|Q_1|=2$, then $G$ is triangle-free, then, by \cite[Theorem 4]{broersma2014toughness}, $G$ is Hamiltonian, and thus $G$ has a 2-walk.
Additionally, if there is only one clique $Q_1$ in the sequence, i.e. $k=1$, then $G$ is split graph. By \cite[Theorem 3.3]{ kratsch1996toughness}, $G$ is Hamiltonian, and thus has a 2-walk.

Now, we assume $k\ge2$ and $|Q_1|\ge3$. The independent set (also called the
first-class vertex set) is denoted by $D$, as in Theorem \ref{thm9}.  Let $D_0\subseteq D$.
By 2-toughness, the size of the neighbor
set $N_G(D_0)$, of $D_0$ in $Q$ is at least $2|D_0|$, i.e.
$|N_G(D_0)|\ge2|D_0|$, otherwise, after deleting $N(D_0)$, there are at least
$|D_0|$ components (isolated vertices), since $D_0$ is an independent set.  By
the polygamous form of Hall theorem, there is a subset $Q'$ of $Q$,
$|Q'|=2|D|$, and each vertex in $D$ is adjacent to two distinct vertices in
$Q'$. That means there is a subset $E'\subset E(G)$ where each $e\in E'$ is
connected to a vertex in $D$ and a vertex in $Q'$. Moreover, each vertex in
$Q'$ is incident to exactly one edge in $E'$, and each vertex in $D$ is
incident to exactly two edges in $E'$. We call the edges in $E'$ the {\bf
first-class edges} in $G$, (also in $H$, we will see that later).

\subsubsection*{The construction of $\Gamma$}

Now, let us construct the auxiliary graph $\Gamma$.  First, the vertex set of
$\Gamma$, $V(\Gamma)=\{w_1,\ldots,w_k\}\cup D'$, each $w_i$ corresponds to the
clique $Q_i$, and each $v'_j\in D'$ corresponds to  $v_j\in D$.  For each
first-class edge $e\in E(G)$, we draw the corresponding edge $e'$ on $\Gamma$,
i.e., if $e=v_iv_j\in E(G)$, with $v_i\in D$ and $v_j\in Q_t$, then we have
$v'_iw_t\in E(\Gamma)$. We call it a {\bf blue edge} in $\Gamma$. Note
that we allow parallel edges in $\Gamma$, and degrees of
vertices count parallel edges with multiplicity.

After drawing the blue edges on $\Gamma$, let us look at the components of
$\Gamma$ (some of them may be trivial components, i.e. single points).
Obviously, each component has even number of vertices with odd degree.

\subsubsection*{Case 1}
If there is only one component, then pair up all the
odd degree vertices by adding edges, that means drawing a maximum matching
between these odd degree vertices. And the edges in the matching are called the
{\bf red edges}. Then $\Gamma$ becomes an Eulerian graph, with each vertex
incident to at most one red edge. And note that only vertices $\{w_i\}$ are
possibly incident to a red edge.

\subsubsection*{Case 2}
If there are at least two components, say $C_1,\ldots,C_n$, where $n\ge2$,
let us select some {\bf representative vertices} in each of them.
For any component, say $C_i$,
with some odd degree vertices, select two odd degree vertices, denoted by
$v_i^+$, $v_i^-$, from them as representative vertices. Note that they
are not in $D'$, since all vertices in $D'$ have degree 2. On the other hand,
for any component, say $C_j$ with only even degree vertices, select one vertex,
denoted by $v_j$, as representative vertex. Note that we can require
$v_j\not\in D'$, since each component has at least one vertex $w_t$. For
convenience, we denote $v_j^-=v_j^+=v_j$ in this case. Then, we draw
$v_1^+v_2^-,~v_2^+v_3^-,\ldots,v_{n-1}^+v_n^-,~v_n^+v_1^-$ on $\Gamma$ (if
$n=2$ and both components have only even degree vertices, this circle is a pair
of parallel edges $v_1^+v_2^-,v_2^+v_1^-$), and we also call them the {\bf red
edges}. For the odd degree vertices which are not selected as representative
vertices, we pair them up within their components, that means drawing a
matching on these vertices with all these matching edges do not cross different
components. These matching edges are also called the {\bf red edges}.

Checking {\bf Cases 1 and 2}, we find that for each vertex $w_i$ one
of the following holds.

\begin{enumerate}
\item $w_i$ is not incident to any red edges.
\item $w_i$ is incident to one red edge as representative vertex.
\item $w_i$ is incident to two red edges as representative vertex.
\item $w_i$ is incident to one red edge for pairing up.
\end{enumerate}

Now, $\Gamma$ is an Eulerian (multi)graph, since it is a connected graph with
all vertices of even degree. Note that all red edges are only incident
to vertices $\{w_i\}$, and each vertex in $D'$ is incident to exactly two blue
edges.

\subsubsection*{The construction of $H$}
Now with the help of $\Gamma$ we are going to find a spanning subgraph $H$ of $2*G$.

First, the vertex set of $H$, is set to be the vertex set of $G$. So, we use the same notation for these vertices in $H$ and $G$. Additionally, when we talk about any $Q_i$ in $G$, we mean the clique $Q_i$, on the other hand, when we talk about $Q_i$ in $H$, we are talking about the subset of vertices.

{\bf Step 1.} Add all the first-class edges connecting $Q'$ and $D$ to $H$. That means the first-class edges in $G$ and the first-class edges in $H$ are exactly the same set.

{\bf Step 2.} (Finding second-class edges in $H$.)

For each red edge $w_iw_j\in\Gamma$, (we assume $i<j$), we want to find an edge
in $G$, with one endpoint in $Q_i$ and another in $Q_j$. This is quite an easy
task. By Theorem \ref{thm9}, $Q_j$ is weakly-dominated by $Q_i$, that means,
in $G$, some vertices in $Q_j$ are adjacent to some vertices in $Q_i$. Now, we
can arbitrarily select one edge, with one endpoint in $Q_j$ while another in
$Q_i$, from $G$ into $H$. Such edges are called {\bf second-class edges}.

{\bf Step 3.} (Finding third-class edges in $H$.)
The final step in the construction is to find some so-called {\bf third-class
edges} for $H$. After adding all the first-class edges and all the
second-class edges, let us look at each $Q_i$.

In any $Q_i$, the sum of vertex degrees (corresponding to first-class and
second-class edges) is obviously even, because $\Gamma$ is an Eulerian graph,
and the sum of vertex degrees in $Q_i$ equals the degree of $w_i$ in $\Gamma$.
So, in $Q_i$, there must be even number of odd degree vertices, if any.

In $Q_i$ there is an even number (maybe 0) of odd degree (in $H$) vertices, and by
properties of $\Gamma$ and by construction of $H$ carried so far at most one of
these vertices, say $v_x$, has degree 3, while the rest of them have degree 1.
Now, select a maximum matching, of {\bf third-class edges}, on them. Now $v_x$,
if it exist at all, has degree 4, and the remaining vertices in $Q_i$ have
degree 0 or 2.

Now we connect all the vertices in $Q_i$ (except $v_x$, if it exists), by a circle of {\bf third-class edges}.
More precisely, if $v_x$ is present, and $|Q_i|=2$, we do nothing, and in case we need to connect
just two vertices by a circle we use a pair of parallel edges.

After drawing all these first-, second-, and third-class edges on $H$, we observe that:
\begin{enumerate}
\item $H$ is connected multigraph.
\item $H$ is a subgraph of $2*G$.
\item each vertex in $H$ has degree 2 or 4, where the degree of parallel edges is counted with multiplicity.
\end{enumerate}

We conclude that $H$ is Eulerian, and  $H$ is a 2-walk in $G$. \qed

\medskip

We conclude this paper  with the following
\begin{conjecture}
Every 2-tough $2K_2$-free graph on at least three vertices has a 2-trail,
i.e.  a 2-walk with each edge appearing in the walk at most once.
\end{conjecture}

redpajama_set_name: RedPajamaArXiv


text:
The Year of Rembrandt – 350 Years of Golden Age Art
By Oscar O'ConnorMay 10, 2019 Cities
2019 marks the 350th anniversary of the death of Rembrandt van Rijn. Widely considered to be the greatest Dutch artist of all time (sorry van Gogh, Vermeer, and Tiësto), Rembrandt was a prolific painter, whose oeuvre stretched across a diverse range of subject matter. His work is characterized by a stark division of light and shadow to create a brooding duskiness – a technique known as chiaroscuro – that's just as beguiling now as it was in the 1600s.
Never content with just painting boring old portraits for aristocrats and merchants, and moody self-portraits (although he certainly did them in style), Rembrandt is remembered for his ability to conjure breathtaking landscapes, dramatic historical scenes, biblical allegories, and Classical mythology, with a murky atmosphere haunting every brushstroke. He also liked to draw elephants.
This year, museums around The Netherlands are putting together the largest nationwide celebration of Dutch Golden Age art, since… well… the Dutch Golden Age! The Year of Rembrandt assembles a remarkable array of special exhibitions that revisit this defining chapter in Western history, and the masterful works of art – from Rembrandt and other contemporaries – that blossomed throughout it.
So if you're planning a trip to the Netherlands in 2019, make sure you check out some of these cultural gems.
All the Rembrandts at the Rijksmuseum
Amsterdam's Rijksmuseum is home to the single-largest collection of Rembrandt's works in the world, and as the name of this exhibition suggests, they're wheeling them all out at once and presenting them together. It's the first time something like this has ever happened.
Rembrandt's masterpiece, The Night Watch, or, Militia Company of District II under the Command of Captain Frans Banninck Cocq, to give it its full title, is the Rijksmuseum's year-round centerpiece. The giant military group portrait actually had its sides chopped off in 1715 so that it could fit into its frame in Amsterdam's town hall. This is perhaps history's most cautionary tale against taking Dutch pragmatism too far!
In All the Rembrandts, The Night's Watch is joined by 21 paintings, 60 drawings, and more than 300 prints that span Rembrandt's entire career and evolution as an artist. It's a total must if you're into once-in-a-lifetime cultural events.
Discover Rembrandt – His Life and All His Paintings at RAI Amsterdam
Anything you can do RAI can do better. That's the message from RAI Amsterdam to the Rijksmuseum. Discover Rembrandt takes the concept of 'All the Rembrandts' to the next level, by digitally recreating every single Rembrandt artwork in known existence. Of the artist's 350 paintings, only 41 of them are in Dutch collections.
Also, Rembrandts are naturally in high demand. In fact, his paintings have been stolen over 81 times, and one painting in particular so often, it came to be known as the 'Takeaway Rembrandt'.
While the Rijksmuseum is confined to showing original works from its admittedly immense collection, RAI brings together those works, plus stolen paintings, ones that are housed in private collections, and other museums in 18 different countries.
It's a thought-provoking exhibition that gives the most comprehensive overview of Rembrandt's entire career. These digital facsimiles are so accurate down to the tiniest detail that you may not even be able to tell the difference.
The Rembrandt House Museum
You can learn a lot about someone just by walking around their home. So if you're looking for an even more intimate portrait of Rembrandt, then visit the house in which he lived. The Rembrandt House Museum is a time capsule of Golden Age upper-middle-class living and 17th-century elegance, nestled in the heart of Amsterdam.
Exploring Rembrandt's house is a surreal experience. It's funny to think of him shuffling about these antique rooms, eating breakfast in his PJs before setting to work on paintings that would outlive him by centuries. It's here that he crafted much of his art and ran the largest painting studio in the Netherlands. You'll see sketches, studies, and finished works he rushed through to maintain an artist's lifestyle. He eventually went broke and died a poor man, but the legacy he left behind is priceless.
The Rembrandt House Museum is also getting in on the Year of Rembrandt action, with three special exhibitions that are sure to make the experience of the house even more memorable.
Rembrandt's Social Network – runs until May 19, 2019
We tend to think of artists as singular geniuses who summon amazing feats of creative expression out of thin air, and that's partially true, yet it's only half the story. This unique exhibition explores the roles Rembrandt's friends, family, and contemporaries had on the artist's work.
Rembrandt's Social Network will be staged at the Rembrandt House until mid-May and shows documents and imagery of important figures in the artist's life. Some of these works have never been displayed in The Netherlands before. Rembrandt's Social Network provides an intimate insight into the Dutch master's human side, and it's a nice reminder of the importance of people in our own lives too.
Inspired by Rembrandt – runs from June 7 – September 1, 2019
In addition to being the former abode of one of the greatest artists of all time, the Rembrandt House is a fully fledged art museum in its own right, too. Inspired by Rembrandt presents the museum's eclectic collection of original works by the house's former tenant, prints by his predecessors and contemporaries, as well as modern and contemporary artists who drew inspiration from him.
Original etchings and drawings from Rembrandt are presented alongside works by Hercules Segers, Edgar Degas, Pablo Picasso, Horst Janssen, Willem den Ouden, Charles Donker, and Glenn Brown.
Laboratory Rembrandt –runs 21 September 2019 – 16 February 2020
Using the latest state-of-the-art technology, Laboratory Rembrandt fuses scientific inquiry with creative curiosity and peels back the centuries on Rembrandt's work to reveal secrets and insights about Rembrandt's enigmatic artworks.
Enter a lab-like setting to see the forensic techniques that art historians and scientists use to glean tiny details from antique canvases and paper that the naked eye could never catch. It's a fascinating journey into the creative process of a genius, and a window into the past. This interactive exhibition is a total must-see for anyone with an obsessive streak for art and science.
Hermitage Amsterdam Museum – Portrait Gallery Of The Golden Age
If The Night's Watch has ignited a spark in you for gigantic Golden Age group portraits, then fan the flame with a visit to the Portrait Gallery Of The Golden Age. This exhibit is actually a collaboration between the Rijksmuseum, the Amsterdam Museum, and the Hermitage Amsterdam Museum.
Feast your eyes on civic guards, regents, merchants of all ranks, and feasting tables of dandy-looking men in tights! There's also a famous painting by Rembrandt titled 'The Anatomy Lesson of Dr. Deijman', which presents an unsettling portrait of 17th-century brain dissection. It's mind-opening, to say the least!
The Dutch Golden Whatnow?
At some point, you might be thinking, 'wait, what exactly was this famous Dutch Golden Age anyway?' Long story short, this was the period in history that spanned across the 17th and 18th centuries, when the Dutch won their sovereignty and basically became masters of the world. After gaining independence from Spain in the Eighty Years War, thanks to William of Orange, the Dutch wasted no time in becoming the economic and cultural superpower of Europe.
The Dutch East India Company (VOC) was actually the first to ever to list an official stock exchange, and the booming trade brought economic prosperity and scientific advances that transformed Dutch society. People became healthier and wealthier; populations grew, and a middle class emerged that had an appreciation for the finer things in life.
A renaissance in philosophy and the arts soon followed. Enter Rembrandt, Vermeer, Frans Hals, Baruch Spinoza, and many other inspirational artists, architects, and thinkers.
Rembrandt & Golden Age Walking Tour
All those people needed somewhere to live, and so the Golden Age saw the rapid development of Amsterdam's canal ring into a densely populated metropolis of gingerbread-style houses and ornate bridges connecting its winding waterways. The city has a fairy-tale charm to it that seduced UNESCO into declaring the entire center of Amsterdam a World Heritage Site. Central Amsterdam is essentially an open-air museum of the Dutch Golden Age.
The best way to explore this living, breathing, cultural heritage site is with a guided walking tour of Rembrandt & Golden Age. This tour will let you literally walk in the footsteps of Rembrandt, visiting the scenes he painted, while your guide shares intriguing details about the artist's life. The tour lasts two full hours and will take you to all of the defining places in Rembrandt's life.
Amsterdam isn't where all the action is. The Museum Prinsenhof Delft has its fair share of Golden Age history too and is worth a visit if you fancy a trip outside of the well-trodden walking tours and museums of the capital. Museum Prinsenhof Delft has a large array of Delft Blue pottery. If you don't know what that is, it might become familiar to you once you see it. This iconic blue and white pottery was the Dutch answer to the grand ceramics of China – and Delft mastered the art of crafting it, putting this small city on the world map.
The Museum Prinsenhof Delft is also the building where William of Orange was assassinated. The bullet holes from his murder are still visible in the walls here. The assassination was one of the most influential moments in Dutch history, without which, there may never have been a Dutch Golden Age. So it's definitely worth a visit!
For more unique art and cultural events in Amsterdam, and around the world, keep an eye on the Tiqets Blog.
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Oscar O'Connor
Oscar is an Irish copywriter who likes to wax philosophical about music, culture, and all things football. His natural habitats include beer gardens, parks, cafes, and snackbars around his beloved Amsterdam.
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redpajama_set_name: RedPajamaCommonCrawl


The Federal Reserve Board and the Federal Deposit Insurance Corporation (FDIC) on Friday permitted 84 firms with limited U.S. operations to file reduced content resolution plans for their next three resolution plans. The decision is intended to increase clarity and reduce burden by creating more certainty around future filing requirements.
The Dodd-Frank Wall Street Reform and Consumer Protection Act requires that bank holding companies with total consolidated assets of $50 billion or more or foreign banks with $50 billion or more in global consolidated assets periodically submit resolution plans to the FDIC and the Federal Reserve. Each plan must describe the company's strategy for rapid and orderly resolution under the U.S. Bankruptcy Code or other applicable insolvency regime in the event of material financial distress or failure of the company.
The 84 firms have less than $50 billion in total U.S. assets, and are foreign banking organizations with limited U.S. operations. All of the firms have submitted prior plans that provide the agencies with an understanding of their limited U.S. operations. The reduced content plans should focus on changes the firms have made to their prior resolution plans, actions taken to improve the effectiveness of, or that may alter, those plans, and, where applicable, actions to ensure any subsidiary insured depository institution is adequately protected from the risks arising from the activities of nonbank subsidiaries of the firm.
The first of these reduced content plans must be submitted to the agencies by December 31, 2016. To file reduced content plans for the next three years, the firms must maintain less than $50 billion in U.S. assets and not experience any material events.


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Building on Multi-Purpose Test Cases
By developing layers of reusable test cases and data, SPR provides a new test architecture for the future
A leading vendor of computer hardware, software and services needed to integrate a wide variety of internal applications to comply with the new federal ASC606 accounting standard for Revenue Recognition. Neither their technical IT personnel nor their business end users had a consistent approach to multi-application work flows, typically validating only one application per project team. Automated regression existed in a pre-production environment, separate from those used for development and testing.
The client was very familiar with the HP Application Lifecycle Management suite, having used HP Quality Center for test cases and defects, and QTP for automation, for many years. The testing team from SPR started work on the project by creating a set of functional test plans and cases in HPQC for each application in the Revenue Recognition suite. The test cases covered the variety of "what" (create, modify, write off, delete, etc.) types of orders for each product supported by the various applications. Test cases also identified specific data combinations which could affect the rules of revenue recognition.
Next, SPR worked with the automation team to modify their existing QTP solutions and scripts to be used for regression testing in the development environments. In this setting, automation could also be used as a means to generate order data, saving large amounts of manual effort with each execution.
The functional tests were then reused as the basis of end-to-end system tests, mapped to each use case defined by the business team. Rather than being created from scratch, the system test cases referred to a functional test case from each application in the various workflows. This approach provided not only reuse, but flexibility for the testers to use their own pass/fail judgment in short, modular test cases for lengthy, complex scenarios. The SPR team also identified functional test cases which were missed in the initial rounds of testing, providing coverage support which would have not be available without this approach.
The functional test plans and automated data creation became the foundation of User Acceptance Test planning and execution. The UAT team started by identifying which test cases had already been defined, allowing them to focus on other aspects of the Revenue Recognition workflow. UAT testing was executed out of HP Quality Center for the first time at this client because of the perceived value in support created by the previous functional test cases and data.
The client not only had successful integration of various testing cycles into one Revenue Recognition solution, but a blueprint for future projects involving multiple applications. The functional cases and automation created for this project will provide the basis for future end-to-end testing efforts at this client for years to come.
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General plantation shutters offer a much greater versatility than ordinary blinds and curtains by enabling full control of the amount of light coming into a house. Modern and contemporary styling is the greatest selling point of these products which easily fit into any house or workplace to instantly transform its appearance. Superb quality, security, safety and eco-friendliness are just a few of the many properties that set plantation shutters apart from curtains or blinds. Plantation shutters' quality also means that they have heat and noise retention characteristics; resulting in a warmer, more peaceful home on the inside.


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About IOM ›
Constitution and Basic Texts of the Governing Bodies ›
The IOM Constitution provides a framework for the purposes, functions, legal status, finance, membership and other issues necessary for the functioning of the Organization.
The present text incorporates into the Constitution of 19 October 1953 of the Intergovernmental Committee for European Migration (former designation of the Organization), which entered into force on 30 November 1954, the amendments adopted on 20 May 1987 by the 55th Session of the Council (Resolution no. 724), which entered into force on 14 November 1989, and the amendments adopted on 24 November 1998 by the 76th Session of the Council (Resolution No. 997), which entered into force on 21 November 2013.
Chapter I: Purposes and Functions
Chapter II: Membership
Chapter III: Organs
Chapter IV: Council
Chapter V: Administration
Chapter VI: Headquarters
Chapter VII: Finance
Chapter VIII: Legal Status
Chapter IX: Miscellaneous Provisions
THE HIGH CONTRACTING PARTIES, RECALLING
the Resolution adopted on 5 December 1951 by the Migration Conference in Brussels,
RECOGNIZING
that the provision of migration services at an international level is often required to ensure the orderly flow of migration movements throughout the world and to facilitate, under the most favourable conditions, the settlement and integration of the migrants into the economic and social structure of the country of reception,
that similar migration services may also be required for temporary migration, return migration and intraregional migration,
that international migration also includes that of refugees, displaced persons and other individuals compelled to leave their homelands, and who are in need of international migration services,
that there is a need to promote the cooperation of States and international organizations with a view to facilitating the emigration of persons who desire to migrate to countries where they may achieve selfdependence through their employment and live with their families in dignity and self-respect.
that migration may stimulate the creation of new economic opportunities in receiving countries and that a relationship exists between migration and the economic, social and cultural conditions in developing countries,
that in the cooperation and other international activities for migration the needs of developing countries should be taken into account,
that there is a need to promote the cooperation of States and international organizations, governmental and non-governmental, for research and consultation on migration issues, not only in regard to the migration process but also the specific situation and needs of the migrant as an individual human being,
that the movement of migrants should, to the extent possible, be carried out with normal transport services but that, on occasion, there is a need for additional or other facilities,
that there should be close cooperation and coordination among States, international organizations, governmental and non-governmental, on migration and refugee matters,
that there is a need for the international financing of activities related to international migration,
DO HEREBY ESTABLISH
The INTERNATIONAL ORGANIZATION FOR MIGRATION, hereinafter called the Organization, and ACCEPT THIS CONSTITUTION.
CHAPTER I – PURPOSES AND FUNCTIONS
The purposes and functions of the Organization shall be:
to make arrangements for the organized transfer of migrants, for whom existing facilities are inadequate or who would not otherwise be able to move without special assistance, to countries offering opportunities for orderly migration;
to concern itself with the organized transfer of refugees, displaced persons and other individuals in need of international migration services for whom arrangements may be made between the Organization and the States concerned, including those States undertaking to receive them;
to provide, at the request of and in agreement with the States concerned, migration services such as recruitment, selection, processing, language training, orientation activities, medical examination, placement, activities facilitating reception and integration, advisory services on migration questions, and other assistance as is in accord with the aims of the Organization;
to provide similar services as requested by States, or in cooperation with other interested international organizations, for voluntary return migration, including voluntary repatriation;
to provide a forum to States as well as international and other organizations for the exchange of views and experiences, and the promotion of cooperation and coordination of efforts on international migration issues, including studies on such issues in order to develop practical solutions.
In carrying out its functions, the Organization shall cooperate closely with international organizations, governmental and non-governmental, concerned with migration, refugees and human resources in order, inter alia, to facilitate the coordination of international activities in these fields. Such cooperation shall be carried out in the mutual respect of the competences of the organizations concerned.
The Organization shall recognize the fact that control of standards of admission and the number of immigrants to be admitted are matters within the domestic jurisdiction of States, and, in carrying out its functions, shall conform to the laws, regulations and policies of the States concerned.
CHAPTER II – MEMBERSHIP
The Members of the Organization shall be:
the States being Members of the Organization which have accepted this Constitution according to Article 29, or to which the terms of Article 30 apply;
other States with a demonstrated interest in the principle of free movement of persons which undertake to make a financial contribution at least to the administrative requirements of the Organization, the rate of which will be agreed to by the Council and by the State concerned, subject to a two-thirds majority vote of the Council and upon acceptance by the State of this Constitution in accordance with its constitutional processes.
Any Member State may give notice of withdrawal from the Organization effective at the end of a financial year. Such notice must be in writing and must reach the Director General of the Organization at least four months before the end of the financial year. The financial obligations to the Organization of a Member State which has given notice of withdrawal shall include the entire financial year in which notice is given.
A Member State which is in arrears in the payment of its financial contributions to the Organization shall have no right to vote if the amount of its arrears equals or exceeds the amount of the contributions due from it for the preceding two years. However, the loss of voting rights shall become effective one year after the Council has been informed that the member concerned is in arrears to an extent entailing the loss of voting rights, if at that time the Member State is still in arrears to the said extent. The Council may nevertheless, by a simple majority vote, maintain or restore the right to vote of such a Member State if it is satisfied that the failure to pay is due to conditions beyond the control of the Member State.
Any Member State may be suspended from membership by a two-thirds majority vote of the Council if it persistently violates the principles of this Constitution. The Council shall have the authority to restore such membership by a simple majority vote.
CHAPTER III – ORGANS
There are established as the organs of the Organization:
the Council;
the Administration.
CHAPTER IV – COUNCIL
The functions of the Council, in addition to those mentioned in other provisions of this Constitution, shall be:
to determine, examine and review the policies, programmes and activities of the Organization;
to review the reports and to approve and direct the activities of any subsidiary body;
to review the reports and to approve and direct the activities of the Director General;
to review and approve the programme, the Budget, the expenditure and the accounts of the Organization;
to take any other appropriate action to further the purposes of the Organization.
1. The Council shall be composed of representatives of the Member States.
2. Each Member State shall have one representative and such alternates and advisers as it may deem necessary.
3. Each Member State shall have one vote in the
Council.
The Council may admit, upon their application, nonmember States and international organizations, governmental or non-governmental, concerned with migration, refugees or human resources as observers at its meetings under conditions which may be prescribed in its rules of procedure. No such observers shall have the right to vote.
The Council shall meet in regular session once a year.
The Council shall meet in special session at the request of:
one third of its members;
the Director General or the Chairman of the Council in urgent circumstances.
The Council shall elect, at the beginning of each regular session, a Chairman and other officers for a one-year term.
The Council may set up such subsidiary bodies as may be required for the proper discharge of its functions.
The Council shall adopt its own rules of procedure.
CHAPTER V – ADMINISTRATION
The Administration shall comprise a Director General, a Deputy Director General and such staff as the Council may determine.
The Director General and the Deputy Director General shall be elected by a two-thirds majority vote of the Council and may be re-elected for one additional term. Their term of office shall normally be five years but may, in exceptional cases, be less if a two-thirds majority of the Council so decides. They shall serve under contracts approved by the Council, which shall be signed on behalf of the Organization by the Chairman of the Council.
The Director General shall be responsible to the Council. The Director General shall discharge the administrative and executive functions of the Organization in accordance with this Constitution and the policies and decisions of the Council and the rules and regulations established by it. The Director General shall formulate proposals for appropriate action by the Council.
The Director General shall appoint the staff of the Administration in accordance with the staff regulations adopted by the Council.
In the performance of their duties, the Director General, the Deputy Director General and the staff shall neither seek nor receive instructions from any State or from any authority external to the Organization. They shall refrain from any action which might reflect adversely on their position as international officials.
Each Member State undertakes to respect the exclusively international character of the responsibilities of the Director General, the Deputy Director General and the staff and not to seek to influence them in the discharge of their responsibilities.
Efficiency, competence and integrity shall be the necessary considerations in the recruitment and employment of the staff which, except in special circumstances, shall be recruited among the nationals of the Member States of the Organization, taking into account the principle of equitable geographical distribution.
The Director General shall be present, or be represented by the Deputy Director General or another designated official, at all sessions of the Council and any subsidiary bodies. The Director General or the designated representative may participate in the discussions but shall have no vote.
At the regular session of the Council following the end of each financial year, the Director General shall make to the Council a report on the work of the Organization, giving a full account of its activities during that year.
CHAPTER VI – HEADQUARTERS
The Organization shall have its Headquarters in Geneva. The Council may, by a two-thirds majority vote, change its location.
The meetings of the Council shall be held in Geneva, unless two thirds of the members of the Council have agreed to meet elsewhere.
CHAPTER VII – FINANCE
The Director General shall submit to the Council an annual budget covering the administrative and operational requirements and the anticipated resources of the Organization, such supplementary estimates as may be required and the annual or special accounting statements of the Organization.
The requirements of the Organization shall be financed:
as to the Administrative part of the Budget, by cash contributions from Member States, which shall be due at the beginning of the financial year to which they relate and shall be paid promptly;
as to the Operational part of the Budget, by contributions in cash, in kind or in services from Member States, other States, international organizations, governmental or non-governmental, other legal entities or individuals, which shall be paid as early as possible and in full prior to the expiration of the financial year to which they relate.
Member States shall contribute to the Administrative part of the Budget of the Organization at a rate agreed to by the Council and by the Member State concerned.
Contributions to the operational expenditure of the Organization shall be voluntary and any contributor to the Operational part of the Budget may stipulate with the Organization terms and conditions, consistent with the purposes and functions of the Organization, under which its contributions may be used.
All Headquarters administrative expenditure and all other administrative expenditure except that incurred in pursuance of the functions outlined in paragraph 1 (c) and (d) of Article 1 shall be attributed to the Administrative part of the Budget;
all operational expenditure and such administrative expenditure as is incurred in pursuance of the functions outlined in paragraph 1 (c) and (d) of Article 1 shall be attributed to the Operational part of the Budget.
The Council shall ensure that the management is conducted in an efficient and economical manner.
The financial regulations shall be established by the Council.
CHAPTER VIII – LEGAL STATUS
The Organization shall possess full juridical personality. It shall enjoy such legal capacity, as may be necessary for the exercise of its functions and the fulfilment of its purposes, and in particular the capacity, in accordance with the laws of the State:
to contract;
to acquire and dispose of immovable and movable property;
to receive and disburse private and public funds;
to institute legal proceedings.
The Organization shall enjoy such privileges and immunities as are necessary for the exercise of its functions and the fulfilment of its purposes.
Representatives of Member States, the Director General, the Deputy Director General and the staff of the Administration shall likewise enjoy such privileges and immunities as are necessary
for the independent exercise of their functions in connection with the Organization.
These privileges and immunities shall be defined in agreements between the Organization and the States concerned or through other measures taken by these States.
CHAPTER IX – MISCELLANEOUS PROVISIONS
Except as otherwise expressly provided in this Constitution or rules made by the Council, all decisions of the Council and all subsidiary bodies shall be taken by a simple majority vote.
Majorities provided for in this Constitution or rules made by the Council shall refer to members present and voting.
No vote shall be valid unless a majority of the members of the Council or any subsidiary body concerned are present.
Texts of proposed amendments to this Constitution shall be communicated by the Director General to Governments of Member States at least three months in advance of their consideration by the Council.
Amendments involving fundamental changes in the Constitution of the Organization or new obligations for the Member States shall come into force when adopted by two thirds of the members of the Council and accepted by two thirds of the Member States in accordance with their respective constitutional processes. Whether an amendment involves a fundamental change in the Constitution shall be decided by the Council by a two-thirds majority vote. Other amendments shall come into force when adopted by a two-thirds majority vote of the Council.
Any dispute concerning the interpretation or application of this Constitution which is not settled by negotiation or by a two-thirds majority vote of the Council shall be referred to the International Court of Justice in conformity with the Statute of the Court, unless the Member States concerned agree on another mode of settlement within a reasonable period of time.
Subject to approval by two thirds of the members of the Council, the Organization may take over from any other international organization or agency the purposes and activities of which lie within the purposes of the Organization such activities, resources and obligations as may be determined by international agreement or by mutually acceptable arrangements entered into between the competent authorities of the respective organizations.
The Council may, by a three-quarters majority vote of its members, decide to dissolve the Organization.
This Constitution shall come into force, for those Governments Members of the Intergovernmental Committee for European Migration which have accepted it in accordance with their respective constitutional processes, on the day of the first meeting of that Committee after:
at least two thirds of the Members of the Committee, and
a number of Members whose contributions represent at least 75 per cent of the Administrative part of the Budget,
shall have communicated to the Director their acceptance of this Constitution.
Those Governments Members of the Intergovernmental Committee for European Migration which have not by the date of coming into force of this Constitution communicated to the Director their acceptance of this Constitution may remain Members of the Committee for a period of one year from that date if they contribute to the administrative requirements of the Committee in accordance with paragraph 2 of Article 20, and they shall retain during that period the right to accept the Constitution.
The English, French and Spanish texts of this Constitution shall be regarded as equally authentic.
1 The present text incorporates into the Constitution of 19 October 1953 of the Intergovernmental Committee for European Migration (former designation of the Organization), which entered into force on 30 November 1954, the amendments adopted on 20 May 1987 by the 55th Session of the Council (Resolution no. 724), which entered into force on 14 November 1989, and the amendments adopted on 24 November 1998 by the 76th Session of the Council (Resolution No. 997), which entered into force on 21 November 2013.
2 Articles 29 and 30 were implemented upon the entry into force on 30 November 1954 of the Constitution of 19 October 1953 (at that time Articles 33 and 34) of the Intergovernmental Committee for European Migration (former designation of the Organization).
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Migration Governance Framework (MiGOF)
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Constitution and more
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Adopted in 1954 and last amended by the Council in 2008, the Regulations govern the financial administration of IOM.
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MD Goenka Girls College, established in 1995, has always nourished the dream towards the cause of the human and social upliftment specially women education. Steered by the dynamic vision of Late Smt. Mohinidevi Goenka, the college of its credit has numerous achievements. The new chapter is ready to strengthen girl students by making them technically sound.
Mohini Devi Goenka Girls College, Sikar offers various graduate courses as well as Post Graduate courses.
Mohini Devi Goenka Girls College, Sikar is affiliated to University of Rajasthan, Jaipur.
List of facilities available at Mohini Devi Goenka Girls College, Sikar for students.
This page was last modified on 29 July 2015 at 12:07.