text:
\section{Introduction}
The motion of an incompressible inviscid fluid in a Riemannian 3-manifold $(M, g)$ is described by a time-dependent vector field $X$ satisfying the \emph{Euler equations}
\[
\frac{\partial X}{\partial t}+\nabla^{LC}_{X}X=-\nabla P ,\,\,\,\, \Div X=0 \,.
\]

Here $\Div$, $\nabla$, and $\nabla^{LC}$ denote the divergence, gradient and covariant derivative on $M$, defined with the metric $g$; and $P$ is
a (time-dependent) function called the pressure, which is also an unknown in the equations.

Solutions to the above equations that do not depend on time are called stationary, or steady, Euler flows. They describe the equilibrium configurations of the fluid. It is straightforward to see that in this case the Euler equations are equivalent to
\begin{equation*}
X\times \curl X=\nabla B\,, \;\; \Div X=0\,,
\end{equation*}
where $B:=P+\frac12|X|^2$ is called the Bernoulli function.

This paper is concerned with the qualitative properties of steady Euler flows and, more precisely, with the existence of closed trajectories amongst the flow lines.

A lot of aspects of steady Euler flows are not yet understood; nonetheless, the study of some of their qualitative properties has proven to be fruitful, revealing many connections with other areas of mathematics (see e.g  \cite{Kh} and \cite{P} for reviews). Arnold's structure theorem~\cite{AKh} is the first major result in this regard. Arnold discovered that, when the Bernoulli $B$ function is analytic, the flow lines outside its critical level sets  are arranged in a very simple manner: as 1-dimensional families of 2-dimensional integrable Hamiltonian systems.

Completely opposite to the situation covered by Arnold's theorem, we have those steady Euler flows whose Bernoulli function has all level sets critical, i.e those having $ B\equiv $ constant. These solutions are often called Beltrami fields.

Arnold conjectured that Beltrami fields should have very complex flow line arrangements, and since then they have attracted a lot of attention \cite{H, DH, EP, EPT}. Interestingly, contact topology has turned out to be a very useful tool for their study, at least in the absence of zeroes in the vector fields. The reason is that nonvanishing Beltrami fields are actually Reeb flows, and vice versa. More precisely, nonvanishing Beltrami fields satisfy the relation $\curl X=f X$ for some well-defined real-valued function $f$; when this function is constant, they are equivalent (after suitable rescaling) to Reeb flows of contact structures, an idea put forward by Sullivan and developed by Etnyre and Ghrist \cite{EG1}. When $f$ is not constant, the correspondence is rather with Reeb flows of stable Hamiltonian structures (also known as volume-preserving geodesible flows), as shown by Rechtman~\cite{RE2,RE}.

It is by means of this correspondence that we know that, on any closed (i.e compact without boundary) 3-manifold which is not a torus bundle, a $C^2$ nonvanishing Beltrami field always has periodic orbits (in a torus bundle it is straightforward to find examples of Beltrami fields without periodic orbits). Indeed this statement, expressed in terms of Reeb flows of stable Hamiltonian structures, was a major recent breakthrough in contact topology due to Hutchings and Taubes \cite{HT}, and independently to Rechtman \cite{RE} in the case of the 3-sphere and in manifolds with non-trivial second homotopy group.

The question of whether, on closed 3-manifolds which are not torus bundles, a general nonvanishing steady Euler field  has a periodic orbit, remains completely open. An a priori promising approach to this problem would be to show that any nonvanishing steady Euler field $X$ is \emph{beltramisable}, i.e that it satisfies $\curl X= f X$ for \emph{some metric} (note that the curl operator depends on the metric). However, this is known to be false in general: Cieliebak and Volkov provided in ~\cite{CV} a construction of smooth solutions to the stationary Euler equations that are not beltramisable.

A very different picture appears if we require the solutions to be analytic, as in Arnold's original set-up. In this case Cieliebak and Volkov show that all nonvanishing steady Euler flows are indeed Beltrami fields for some metric. This implies, in view of the above mentioned Hutchings--Taubes' theorem, the following result (\cite{CV}, Corollary 3), which is also the main theorem that we prove in this paper:

\begin{theorem}\label{main1}
Let $M$ be a closed real analytic
3-manifold equipped with a metric $g$ and a volume form $\mu$ (which we do not assume to be the one induced by $g$). Let $X$ be a nonvanishing vector field $X$ satisfying the stationary Euler equations,
\[
X\times \curl X=\nabla B\,, \;\; \Div X=0\,.
\]
Suppose that $X$, $g$, $\mu$ and $B$ are analytic. Then, if $M$ is not a torus bundle over the circle,
$X$ has a periodic orbit.
\end{theorem}

We recall that given a metric $g$ and a volume form $\mu$ (not necessarily the one induced by $g$), the divergence, curl and vector product operators are defined by
\[
i_{\curl X} \mu= d(i_X g) \,,\,\, i_{X\times Y} g=i_{Y} i_X \mu \,,\,\, L_X \mu= \Div X \mu \,.
\]

The crucial step in the proof of Theorem \ref{main1} that we present is to show the following:

\begin{theorem}\label{main2}

Let $X$ be a nonvanishing vector field in a real analytic closed 3-manifold which is not a torus bundle. If $X$ has a non-trivial analytic first integral, then it has a periodic orbit.

\end{theorem}

The proof of Theorem \ref{main1} is then achieved by combining Theorem \ref{main2} with Taubes' solution to the Weinstein conjecture in dimension three \cite{TA} and Fuller's theorem \cite{FU} on the existence of periodic points of surface homemorphisms.

\subsection*{Comparison with previous results} As we mentioned above, neither Theorem \ref{main1} nor Theorem \ref{main2} are original. The strategy of the proof that we follow here isn't either: it already appears in the works of Etnyre and Ghrist \cite{EG1}, Rechtman \cite{RE2} and Cieliebak and Volkov \cite{CV}; the difference lies in the details of its implementation.

More precisely, Etnyre and Ghrist proved in \cite{EG1} that, in the 3-sphere, a nonvanishing analytic Euler field always has a periodic orbit, and in fact the only thing preventing their arguments from yielding Theorem \ref{main1} was that the Weinstein conjecture in dimension three had not been solved yet. Rechtman's arguments in \cite{RE} also provide a proof of Theorem \ref{main1} along the same lines as the one presented here. Finally, as we have mentioned already, Theorem \ref{main1} is a corollary (\cite{CV}, Corollary 3) of Cieliebak and Volkov's beltramization result, and another proof following the same strategy as we do is presented in Remark 2.2 of their paper.

With regards to Theorem \ref{main2}, there are several results in the same spirit originally discovered by Fomenko in his work on Hamiltonian systems with Morse--Bott first integrals (\cite{FO}, Chapter 2); besides, it follows directly from the arguments in the proofs of Theorem 3.5 in \cite{EG1}, of Lemma 4.2 in \cite{RE} and of Remark 2.2 in \cite{CV}. The key in all of these arguments is to use the stratified geometry of the critical level sets of the first integral to show that, in the absence of periodic orbits, the manifold is foliated by tori; we proceed in a similar manner. Where our approach differs considerably is in the proof of the fact that $M$ does not just admit a foliation by tori, but is a torus bundle over the circle.

The paper is organized as follows: firstly we prove Theorem \ref{main2} in Section \ref{pmain2}, then Theorem \ref{main1} is proven in Section \ref{pmain1}.

\section{Proof of the Theorem \ref{main2}}\label{pmain2}

Let us denote by $h$ the analytic non-trivial first integral of the vector field $X$. We recall that being a first integral of $X$ means that $h$ is constant along the flow lines; in particular, since $h$ is $C^1$, we have $dh(X)=0$.

The idea of the proof is to first show that, if  $X$ has no periodic orbits, the level sets of $h$ define a foliation of $M$ where all leaves are tori; then we prove that this foliation yields actually a torus bundle over the circle.

\subsection{Step 1: the connected components of the level sets of $h$ are all tori}

Let $L$ be a connected component of the level set $h^{-1}(c)$, for some real number $c$ in the image of $h$.

If $c$ is a regular value, then $L$ is an oriented surface, which moreover is invariant under the flow of $X$; since $X$ has no zeroes, $L$ must be a torus.

If $c$ is a critical value, all we know in principle is that $L$ is a connected analytic subset of $M$. \L ojasiewicz proved \cite{LO} that these
sets have a controlled stratified structure. We begin by recalling some of their properties.

\begin{definition}
Let $L$ be an analytic set on a manifold $M$. We say that the rank of $L$
at a point $x\in L$ is $k$, $\text{rank}_L(x)=k$,  if there is an open neighborhood $U$
of $x$ in $M$ and analytic functions $f_{1},...f_{k}$ on $U$ such that
\[
U\cap L=\{f_{1}^{-1}(0)\cap...\cap f_{k}^{-1}(0),\,\text{ and } d_{x}f_{1},...d_{x}f_{k} \text{ are linearly independent}\}
\]

\end{definition}

Thus, if $\text{rank}_{L}(x)=k$, the set $L$ is a submanifold
of codimension $k$ in a neighborhood of $x$.

We now define:
\[
L^{k}=\{x \in L,\,\text{rank}_L(x)=k\}
\]

The subset $L^{0}$ is  called the \emph{singular set} of $L$. We now summarize some standard geometric properties of analytic sets in connected real analytic manifolds that will be important for our purposes (see e.g \cite{BW}, Section 2 of \cite{LM}, or Theorem 6.3.3 in \cite{KP}):

\begin{enumerate}

\item The singular set $L^{0}$ is an analytic subset of $M$. If $L=L^{0}$,    then $L=M$; if $L \neq L^{0}$, then $L^0$ is a closed and nowhere dense
subset of $L$, and consists of the points at the intersection of the sets $\overline{L^{k}}$ with
$k>0$.

\item For any point $x \in L^{0}$ we define rank$^{1}(x):=$ rank$_{L_0}(x)$, the rank of $L^0$ at the point $x$. We can then define analogously the sets $(L^{0})^{k}$; if $x$ is still on the singular set of $L^{0}$, i.e $x \in (L^{0})^{0}$, then we can define rank$^{2}(x)$
as the rank of $(L^{0})^{0}$ at $x$, and so on. This process eventually terminates, i.e, $(((L^{0})^{0})^{...})^{0}=\emptyset$.

\item If the dimension of the manifold is $n$ and $L \neq M$, we can define a finite filtration by closed subsets $L=L_{n-1}...\supset L_{0}$
(here $L_{k}\neq L^{k}$) such that for any $j$, $L_{j}\setminus L_{j-1}$
consists of the points $x$ with rank$_L(x)=n-j$ and of the points $x \in L^{0}$ with rank$^{i}(x)=n-j$ for some $i>0$. In other words, $L_{j}\setminus L_{j-1}$ is either a submanifold of dimension
$j$ or it is empty. We call the connected components of $L_j \setminus L_{j-1}$ the $j$-dimensional strata of $L$.

\end{enumerate}

Take now $L$ to be the connected component of the critical level set $h^{-1}(c)$; our first claim is that the strata $L_{k}\setminus L_{k-1}$ of dimension $k$ are invariant under the flow of $X$.

Indeed, consider the subsets $L^{k} \subset L$ of points with rank$_L= k$. For any $k>0$, it is clear from the definition of rank and the invariance of $L$ that $\phi^{t}_{X}(L^{k}) \subset L^{k}$ (here by $\phi^{t}_X$ we denote the flow of $X$).

Now the singular set $L^{0}$ is clearly invariant since it is the complement in $L$ of the union of the sets $L^{k}$. Then again, by the definition of rank and the invariance of $L^{0}$, the submanifolds $(L^{0})^{k}$ consisting of the points in $L^{0}$ with rank$^{1}(x)=k$ are preserved by the flow.

Arguing repeatedly as above, we conclude that the set of points $x$ with rank$^{j}(x)=k$, for any $j$ and $k$, is invariant by the flow. Since $L_{k}\setminus L_{k-1}$ is a union of such sets, it is also invariant.

We next proceed to analyze the geometry of the strata $L_{k} \setminus L_{k-1}$. First, observe that $L$ cannot have 3-dimensional strata, because then $h$ would be a constant, which is excluded. There cannot be 0-dimensional strata either, since by invariance these would be zeroes of $X$. The absence of 0-dimensional strata implies that any 1-dimensional stratum must be a closed curve, i.e a periodic orbit of $X$, which is also excluded.

So there can only be 2-dimensional strata: $L$ must be a surface embedded in $M$, with the vector field $X$ tangent to it. Since $L$ is a critical level set, we cannot ensure its orientability: from the absence of zeroes of $X$ we can only conclude that $L$ is either a torus or a Klein bottle. However, a vector field tangent to a Klein bottle always has a periodic orbit \cite{GO}, so $L$ must be indeed a torus.

\subsection{Step 2: the foliation defined by the level sets of $h$ is locally trivial}

To finish our proof of Theorem \ref{main2} we need the following:

\begin{proposition}\label{levelsets2}
Let $L$ be a connected component of the level set $h^{-1}(c)$, for any $c$ in the image of $h$. There is an open set $U \subset M$ containing $L$ and a diffeomorphism $\Phi: U \rightarrow (-\delta, \delta) \times \mathbb{T}^2$, for some positive number $\delta$, such that $h \circ \Phi^{-1}(\{t\} \times \mathbb{T}^2)= \{c+t\}$.
\end{proposition}

Indeed, if that is the case, the leaves of the foliation by tori defined by $h$ are separable. Since $M$ is closed, the leaf space of the foliation is a 1-dimensional, compact closed Hausdorff space, i.e a circle. By Ehresmann fibration theorem, the surjective submersion from $M$ to the leaf space $\SS^1$ is a locally trivial fibration, so $M$ is torus bundle over the circle and Theorem \ref{main2} is proven.

The rest of the Section is dedicated to the proof of the above Proposition.

\begin{proof}[Proof of Proposition \ref{levelsets2}]

Choose any connected leaf $L$ of the foliation defined by the level sets of $h$.

Suppose first that the leaf $L$ is a connected component of a level set
$h^{-1}(c)$ with $c$ a regular value. Then the proposition follows trivially: in a sufficiently
small neighborhood $U$ of $L$, the gradient of $h$ does not vanish. We can thus
define the vector field $S:=\frac{\nabla h}{dh(\nabla h)}$ whose flow $\phi_{S}^{t}$ verifies:
\[
\frac{ \partial }{ \partial t}    \, h\big(\phi_{S}^{t}(x)\big)\big\rvert_{t=s}=dh(S)\big(\phi_{S}^{s}(x)\big)=1,\,\,\,\,h\big(\phi_{S}^{0}(x)\big)=c
\]

for any point $x\in L$. So we have $h(\phi_{S}^{t}(x))=h(x)+t$. Moreover, any point $y \in U$ can be uniquely written as $y=\phi_{S}^{t}(x)$ for some $t \in (-\delta, \delta)$ and $x \in L$ (maybe at the expense of taking a slightly smaller open set $U$), so we define the diffeomorphism $\Phi: U \rightarrow (-\delta, \delta) \times \mathbb{T}^{2}$ simply as $\Phi(\phi_{S}^{t}(x))=(t, x)$ for $x \in L$.

Now consider a leaf $L$ which is a connected component of a level set
$h^{-1}(c)$ with $c$ a critical value. Without loss of generality, we can assume that $c=0$. The key in this case is to prove:

\begin{lemma}\label{local}

On a small enough tubular neighborhood $N_{\delta}(L)$
of $L$ we can write $h=g^{k}\cdot u$, with $k$ a positive integer, $g$ an analytic function
such that $\nabla g\neq0$, and $u$ a smooth
function with $u\neq0$.
\end{lemma}

Indeed, assume the above Lemma for the moment: then, on a neighborhood of $L$, the function $q:=g\cdot u^{\frac{1}{k}}$
has the same level sets as $h$ and, moreover, $\nabla q \neq 0$ on a neighborhood of $L$. Arguing exactly as we did in the case of non-critical level sets with $q$ in the role of $h$ we get a locally
trivial foliation near $L$. This concludes the proof of Proposition \ref{levelsets2} \end{proof}

\begin{proof}[Proof of Lemma \ref{local}]

For any point $x \in L$, we define the vanishing order of $h$ at $x$ to be the smallest integer $n$ such that the $n$-jet of the function $h$ at $x$, $J^{n}_{x}(h)$, does not vanish. Of course if $x$ is a critical point, $n$ is greater than 1 ($h(x)=0$ and $\nabla h (x)=0$).

We begin by establishing the following fact:

\begin{lemma}\label{vanishingorder}
Let $L$ be a connected component of $h^{-1}(0)$ with $0$ a critical value. If $X$ does not vanish and has no periodic orbits, all points in $L$ are critical points of $h$ of the same vanishing order.
\end{lemma}

\begin{proof}[Proof of Lemma \ref{vanishingorder}]
Set
\[
K:=\underset{x \in L}{\text{ min }} \,\{n \in \mathbb{N} \,\text{ such that\,}J_{x}^{n}(h)\neq 0\}\,,
\]
and define the following two sets partitioning $L$:
\[
S_{0}:=\{x \in L,\, J_{x}^{K}(h)\neq0 \}
\]
\[
S_{1}:=\{x\,\in\,L,\,J_{x}^{K}(h)=0\}
\,,
\]

that is, the points in $S_{0}$ are those with minimal vanishing
order, and $S_{1}=L\setminus S_{0}$.

Notice that $S_{1}$ is an analytic subset of $L$, since it is defined as the zero set of the $k$-jet of $h$; and it cannot be the whole $L$ because by definition $S_0$ is not empty. Thus the codimension of $S_1$ in $M$ must be at least 2,
that is $S_{1}$ must consist of points and curves.

But it is easy to check that all $n$-jets of $h$ are preserved
by the flow of $X$ (to see this, consider the matter in a flow box of the vector field), so that $S_{1}$
is invariant and thus it consists of zeroes or periodic orbits of $X$. Since this is excluded by our assumptions, we conclude that $S_1$ is empty and $L=S_{0}$, i.e, $h$ has the same vanishing order $K$ for all $x\in L$. \end{proof}

Now, the leaf $L$ has trivial normal bundle, so there
is a smooth function $F$ in $M$ such that $F^{-1}(0)=L$
and $\nabla F |_{L}\neq0$: indeed, we can simply define the function $F(x,\,t):=t$ for coordinates $(x,\,t)$ on a trivialization of a  tubular neighborhood $N_{\delta}(L)\simeq L\times (-\delta, \delta)$; and extend $F$ smoothly to the whole manifold. Observe that although $L=F^{-1}(0)$ is an analytic submanifold, we cannot ensure that $F$ is analytic.

By Whitney's
approximation theorem, we can find analytic functions arbitrarily
close to $F$ in any $C^{k}$ norm. Consider thus an analytic function $G$ very close to $F$ in the $C^{1}$ norm. Thom's isotopy theorem \cite{AR} ensures that, provided we take $G$ close enough, the level set $L'=G^{-1}(0)$
is diffeomorphic to $L$ and, moreover, that there is a \emph{smooth} family of isotopic embeddings
\[
e_{t}:\mathbb{T}^{2}\rightarrow M
\]
with $e_{0}(\mathbb{T}^2)=L$ and $e_{1}(\mathbb{T}^2)=L'$.

But since both $L$ and $L'$ are analytic, we can take the family of isotopic
embeddings $e_t$ to be analytic as well
(in the sense that the images are analytic submanifolds and the dependence
on $t$ is analytic) by a theorem due to Royden \cite{ROYD} (which precisely states that
given a smooth isotopy of embeddings between two analytic submanifolds we can find an analytic isotopy
of embeddings).

We define now a time-dependent vector field associated with the isotopy $e_t$:
\[
Y_s(e_s(q)):=\frac{\partial e_{t}}{\partial t} \Big\rvert_{t=s}(q)
\]
for $q \in \mathbb{T}^2$. Note that for each $s$, $Y_s$ is only defined on the
embedded tori $e_s(\mathbb{T}^2) \subset M$. It is nonetheless straightforward to extend it smoothly to a time-dependent vector field $Y_t$ on the whole $M$. In doing so, $Y_t$ cannot be ensured to be analytic anymore, but we can keep the extension analytic inside a small enough neighborhood of the original domain of definition. As we are going to see, this is enough for our purposes.

The non-autonomous flow $\phi^{t}_{Y_t}$ on $M$ satisfies, for any $p \in L$,
\[
\phi^{t}_{Y_t}(p)=e_t(e^{-1}_0(p))
\]
so that
\[
\phi_{Y_1}^{1}(L)=L'
\,
\]

and furthermore, $\phi_{Y_1}^{1}: M\rightarrow M$ is analytic on a small enough tubular neighborhood of $L$ that we denote by $N_{\delta}(L)$.

Define now the function
\[
g:=G\circ\phi_{Y}^{1}|_{N_{\delta}(L)} : N_{\delta}(L) \rightarrow \mathbb{R}
\]

which is analytic as well, since $G$ and $\phi_{Y}^{1}|_{N_{\delta}(L)}$ are.

We have that $L=g^{-1}(0)$
and $dg|_{N_{\delta}(L)}\neq0$. Now, since by Lemma \ref{vanishingorder} the function $h$ has the same vanishing order at all points $x \in L$, the Weierstrass Preparation Theorem (see e.g \cite{KP}, Theorem 6.3.1) readily implies that, on a neighborhood $V_x$ of any point $x \in L$, we can write $h=g^{K}\cdot u_{V_x}$, with $u_{V_x}$ a nonvanishing analytic function on $V_x$.

We take now a partition of unity $(\rho_{i},\,V_{i})$ of $N_{\delta}(L)$,
such that on each $V_{i}$ we have $h=g^{K}\cdot u_{i}$. Defining
\[
u=\underset{i}{\sum}\rho_{i}u_{i}
\]
we finally have
\[
h=\underset{i}{\sum}\rho_{i}g^{k}u_{i}=g^{k}\underset{i}{\sum}\rho_{i}u_{i}=g^{k}\cdot u\,
\]

Because of our use of a partition of unity, $u$ is not analytic, but it is clearly nonvanishing on $N_{\delta}(L)$. This finishes the proof of Lemma \ref{local}.\end{proof}

\section{Proof of Theorem \ref{main1}}\label{pmain1}

Any nonvanishing solution of the Euler equations is of one of the following four types:

\begin{enumerate}
\item $\curl X=0$.
\item $\curl X= \lambda X$ with some constant $\lambda \neq 0$.
\item $\curl X=fX$ with $f$ not constant.
\item $X \times \curl X=\nabla B$ with $\nabla B$ not identically zero.
\end{enumerate}

We will prove Theorem \ref{main1} case by case. We note that the only cases where the analyticity assumptions will be needed are cases (iii) and (iv).
\subsection{Case (i)} We begin by recalling a result due to Tischler \cite{TI}:

\begin{theorem}[Tischler \cite{TI}]\label{Tis}
Let M be
a closed manifold. If M has a nowhere vanishing closed 1-form
$\alpha$, then for any $\epsilon>0$ there is a surjective submersion $p: M \rightarrow \SS^1$ and an integer $n$ such that the 1-form $p^{*}d\theta$ (where $d\theta$ denotes the standard  length form on $\mathbb{S}^{1}$) satisfies $|n\alpha(Y(x))-p^{*}d\theta(Y(x))|_{C^0(M)} \leq \epsilon n|\alpha(Y(x))|$, for any vector field $Y$ at any point $x$.
\end{theorem}

Since $\curl X=0$ and $X$ has no zeroes, the 1-form $\lambda=i_{X}g$
is closed and nowhere vanishing. By Tischler's theorem, $M$
fibers over $\mathbb{S}^{1}$ and since $M$ is compact, the fibration $p$ is
proper, so it defines a fiber bundle.

Note that by taking $\epsilon$ in the statement of Theorem \ref{Tis} smaller than 1 we ensure that $i_{X}\ p^{*} d \theta>0$, so the vector field $X$ is transverse to the fibers $p^{-1}(\theta)$.

We want to prove that, if $X$ does not have periodic
orbits, the fibers are tori. Take a fiber $\Sigma_{\theta}:=p^{-1}(\theta)$. Since $p^{*}d\theta(X)>0$, all the flow lines come back
to the fiber. We can then define the Poincar\'e recursion map of $X$ in $\Sigma_{\theta}$, which is a diffeomorphism $\psi_{X}:\Sigma_{\theta}\rightarrow\Sigma_{\theta}$ taking any point in the fiber to the first point in its forward trajectory to belong to the fiber again.

A periodic orbit of $X$ corresponds either to a fixed point
of the Poincar\'e recursion map $\psi_{X}$ or, more generally, to a \emph{periodic
point} of it, that is, a fixed point of the iterated
map $\psi_{X}^{k}=\psi_{X}\circ...\circ\psi_{X}$ for some integer
$k>0$.

So the proof of Theorem \ref{main1} in this case reduces to showing that if $\psi_{X}$ has no periodic
points, $\Sigma_{\theta}$ is a torus. This follows from a classical result of Fuller \cite{FU}, but in any case we will present a proof here.

Define the Lefschetz zeta function of $\psi_X$ as
\[
Z_{\psi_X}(s):= \text{exp }\bigg(\sum_{k=1}^{\infty} \frac{\Lambda(\psi^{k}_{X})}{k} s^{k}\bigg)
\]

where $\Lambda(\psi_{X}^{k})$ denotes the Lefschetz number of $\psi^{k}_{X}$,
\[
\Lambda(\psi_{X}^{k})=
\text{Tr}\big((\psi^{k}_{X})_{*0}\big)-\text{Tr}\big((\psi^{k}_{X})_{*1}\big)+\text{Tr}\big((\psi^{k}_{X})_{*2}\big)\,,
\]
and $(\psi^{k}_{X})_{*i}: H_{i}(\Sigma_{\theta}, \mathbb{Q}) \rightarrow H_{i}(\Sigma_{\theta}, \mathbb{Q})$ is the linear map induced by $\psi^{k}_{X}$ on the $i$-th homology group of the fiber $\Sigma_{\theta}$.

Observe that by the Lefschetz fixed point theorem, if $\Lambda(\psi^{k}_{X}) \neq 0$ then $\psi_{X}$ has a periodic point. So if the map $\psi_{X}$ has no periodic points, all Lefschetz numbers are zero and we must have
\[
Z_{\psi_X}(s)=1 \,.
\]
We now claim that the above identity is only possible if $\Sigma_{\theta}$ is a torus. Indeed, the Lefschetz zeta function can be rewritten as
\[
Z_{\psi_X}(s)=\frac{\text{exp}\bigg(-\sum_{k=1}^{\infty} \frac{s^{k}}{k} \text{ Tr}\big((\psi^{k}_{X})_{*1}\big) \bigg)}{\text{exp}\bigg(-\sum_{k=1}^{\infty} \frac{s^{k}}{k} \text{ Tr}\big((\psi^{k}_{X})_{*0}\big) \bigg)\text{exp}\bigg(-\sum_{k=1}^{\infty} \frac{s^{k}}{k} \text{ Tr}\big((\psi^{k}_{X})_{*2}\big) \bigg)}\,.
\]
Recall that for a square matrix $A$ one has
\[
\text{det}(I+A)=\sum_{n=0}^{\infty} \frac{1}{n!}\bigg(-\sum_{k=1}^{\infty} \frac{(-1)^{k}}{k} \text{Tr} A^{k}\bigg)^{n}
\]
where by $I$ we denote the identity matrix. Thus, we have
\[
\text{exp}\bigg(-\sum_{k=1}^{\infty} \frac{s^{k}}{k} \text{ Tr }\big((\psi^{k}_{X})_{*i}\big)\bigg)=\text{det}(I-s (\psi^{k}_{X})_{*i})
\]
so the Lefschetz zeta function reads
\begin{equation}\label{zeta}
Z_{\psi_X}(s)=\frac{\text{det}\big(I-s (\psi_{X})_{*1}\big)}{\text{det}\big(I-s (\psi_{X})_{*0}\big)\text{ det}\big(I-s (\psi_{X})_{*2}\big)}\,.
\end{equation}
In principle, $\text{det}(I-s (\psi_{X})_{*i})$ is a polynomial of degree $n_i \leq b_i$, where by $b_i$ we denote the $i$-th Betti number of $\Sigma_{\theta}$, $b_i:=\text{dim }(H_i(\Sigma_{\theta}, \mathbb{Q}))$. But in fact, we have that the degree is exactly equal to the Betti number. To see this, note that
\[
\text{det}\big(I-s (\psi_{X})_{*i}\big)=s^{b_i} \text{det}\bigg(\frac{1}{s}I-(\psi_{X})_{*i}\bigg)=s^{b_i}p\bigg(\frac{1}{s}\bigg)
\]
where $p(\lambda)$ denotes the characteristic polynomial of $(\psi_{X})_{*i}$, that is, the polynomial whose zeroes are the eigenvalues of $(\psi_{X})_{*i}$. If there is no term of degree $b_i$ in $\text{det }(I-s (\psi_{X})_{*i})$, then there is no term of degree zero in $p(\lambda)$, and thus $\lambda=0$ is an eigenvalue of $(\psi_{X})_{*i}$. But this is impossible, because $\psi_{X}$ is a diffeomorphism, so $(\psi_{X})_{*i}$ is an isomorphism. So $n_i=b_i$.

Now, we have that $b_0=b_2=1$ and $b_1=2g$, where $g$ is the genus of $\Sigma_{\theta}$. Thus, the denominator in Eq. \eqref{zeta} is a polynomial of degree 2, while the numerator has degree $2g$. So for $Z_{\psi_{X}}(s)$ to be identically $1$ we must have $g=1$, i.e, $\Sigma_{\theta}$ must be a torus.

\subsection{Case (ii)} If $X$ satisfies the equation $\curl X= \lambda X$, it is immediate to see that $\alpha=i_X g$ is a contact form and
\[
X':= \frac{X}{\alpha(X)}
\]
is the corresponding Reeb vector field of $\alpha$. Taubes' solution of the Weinstein conjecture \cite{TA} ensures that $X'$ has a periodic orbit, hence so does $X$.

\subsection{Cases (iii) and (iv)} These two cases can be analyzed simultaneously,
as they have a key feature in common: the field $X$ has a non-trivial first integral, $f$ in case (iii) and $B$ in case (iv).

By the assumptions in Theorem \ref{main1}, $f$ and $B$ are  analytic. We can then apply Theorem \ref{main2} to conclude that if $X$ has no periodic orbits, $M$ is a torus bundle over the circle.

\section*{Acknowledgements}

The author thanks Daniel Peralta-Salas for his many valuable suggestions and advice. He is also grateful to the Max Planck Institute for Mathematics for its financial support and hospitality.

redpajama_set_name: RedPajamaArXiv


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Regional Infrastructure Outlook for 2016
REGIONAL DIRECTION
Regional Infrastructure...
Nick Frontino
Categorized As:
Economy League managing director Nick Frontino takes a look at some of the top infrastructure issues to keep an eye on in Greater Philadelphia in 2016.
New leadership in top Philadelphia infrastructure posts
While Philadelphia mayor Jim Kenney's administration is still in its infancy, his selections of top deputies have already changed the infrastructure leadership landscape in the city. Former DALE Corporation executive and Building Industry Association (BIA) president Anne Fadullon will serve as the City's first director of planning and development, a position created via a change to the city charter approved by voters in the fall. Former City Revenue Commissioner and Streets Commissioner Clarena Tolson will assume the new position of deputy managing director for infrastructure and transportation. At Philadelphia International Airport, Kenney has tapped PHL chief operating officer Chellie Cameron to take over for outgoing CEO Mark Gale. In addition to overseeing the airport's day-to-day operations, Cameron will be tasked with guiding the implementation of the facility's ambitious Capacity Enhancement Program. A former deputy is also taking over the reins at the Philadelphia Water Department, where deputy commissioner and director of operations Debra McCarty has stepped into the role of Water Commissioner. McCarty succeeds Howard Neukrug, under whose leadership PWD was recognized as a national and international model for the integration of green infrastructure solutions for stormwater management through its acclaimed Green City, Clean Waters plan. McCarty is the first woman in Philadelphia history to serve as Water Commissioner. As these leaders get settled in their new roles over the next few months, we expect to learn more about the Kenney administration's vision for and approach to infrastructure in the city.
New Jersey Transportation Trust Fund approaches insolvency (again)
Without intervention, New Jersey's Transportation Trust Fund will run out of money by June 30, the end of the state's fiscal year. The fund, established in 1984 as a tool for long-term investment in transportation improvements, is leveraged to the point where nearly all dedicated annual revenues must go to debt service. With over a third of the state's bridges classified as structurally deficient or functionally obsolete, the lack of transportation funding is seen by some as the state's single most pressing problem. The state Legislature overwhelmingly passed a resolution to ask New Jersey voters to constitutionally guarantee that all, as opposed to most, revenue from gas taxes go to transportation projects. Though this show of support is a good first step, the extra $40 million to $50 million would not be enough to fill the funding gap. The real task - raising the tax - will require a heavy lift from legislators during the first half of 2016.
SEPTA identifies preferred route for King of Prussia rail
Planning continues on SEPTA's proposed extension of the Norristown High Speed Line to King of Prussia. Following December's release of the Economy League's Connecting KOP study, which evaluated the project's economic benefits, SEPTA will identify a locally preferred alternative (LPA) from the five routes currently under consideration within the first half of this year. SEPTA will hold public meetings to solicit feedback on the LPA later this year. As part of the federal process to seek New Starts funding for the extension, SEPTA will continue planning and preliminary engineering for the project. If funding is secured, the transit agency estimates that 2023 would be the earliest that KOP rail could be in operation.
Movement on Southport project?
Following years of stop-and-start attempts to expand Philadelphia's port complex south of the Walt Whitman bridge, officials are now considering proposals from a new round of interested parties. As part of Governor Wolf's strategic plan, the Philadelphia Regional Port Authority is seeking a private concessionaire to design, build, finance, operate, and maintain up to 195 acres of PRPA owned property along the Delaware River in South Philadelphia. Six shortlisted respondents to the request for qualifications will be asked to submit financial and development plans for the riverfront property. Proposal submission is anticipated for this summer with construction on the site anticipated to begin next year. Potential uses of the vast site range from a traditional marine terminal to refined and crude oil import/export facility to warehousing and automobile processing space. Expansion could build upon the sustained growth of the Port of Philadelphia over the past five years, help facilitate export activity, and create new jobs.
SEPTA Key makes long-awaited debut
The introduction of SEPTA's much-anticipated and long-delayed new payment technology, officially dubbed SEPTA Key, is slated for the spring of this year. With new fare collection instruments in place on SEPTA buses and trolleys and in stations along the Broad Street Line and Market Frankford El, SEPTA and vendor Xerox are now in the late stages of system testing. SEPTA Key is expected to roll out on buses, trolleys, the subway and the el within the next few months. Regional rail will see the new fare technology in 2017. The new system promises to make SEPTA's infamous tokens a thing of the past and catapult the agency into the vanguard of fare collection technology. Riders will be able to pay with a new contactless SEPTA card or via smartphone. More information is available from SEPTA here.

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St Michael's RC Comprehensive School
Client – Diocese of Hexham and Newcastle
Architect – Darbyshire Architects
Completion – October 2010
Having carried out a series of projects at the school we were asked to tender for and were awarded a contract to extend and remodel the main entrance and admin area for the school. The work mainly consisted of alterations and the construction of an infill extension at the main entrance, but also included some remodelling to other areas including teaching facilities
The work was fairly central to the school and surrounded on three sides by other school buildings. One of the main thoroughfares for the pupils and staff also ran through the middle of the working area, which had to be maintained during the works to enable pupils and staff to circulate around the school. Planning & segregation was critical to ensure the safety of the pupils and staff, and to ensure that the teaching was not affected by noise, dust, etc. Works were also planned out of hours, i.e. at weekend and night to ensure minimal disruption, these works included electrical shut downs and reconfiguration of the schools data cabling. The work involved the demolition of parts of the existing structure to accommodate the new extension and the removal of asbestos materials in the work areas and service routes. Both of these operations had to be planned, managed and organised to ensure the health and safety of the staff, pupils, workers and general public.
The works were completed within the designated time period, to a high standard, within budget, to the satisfaction of and minimal disruption to the school and without any safety incidents.


Fruit has had a big place in online slots, but over the years they have become a bit stale in terms of presentation, as many of the slots are flat and look dated by today's standards. The Fruit Warp slot machine by Thunderkick gives us a fresh take on the fruit topic, and it manages to suspend the objects in a way that I'm sure nobody has seen in an online slot before.
Fruit Warp is a video slot that doesn't really have paylines as such. Instead it just throws nine pieces of fruit up onto the screen on every spin. I use the term spin loosely, as the fruit seems to be thrown at you from some indeterminate point at the back of the screen every time you click. Its kind of reminiscent of the popular mobile video game Fruit Ninja except the fruit doesn't fall off the bottom of the screen and you don't need a sword at your side. Instead the fruits are suspended in fluid, floating around and rotating in the process. Wins are paid when there are three or more identical pieces of fruit on the screen. Four or more of the same fruit generates a warp feature that takes out all other pieces, and gives you a second shot at gaining five pieces of the same fruit.
If you do get five or more identical fruit pieces a free spins round starts that varies depending on the fruit that triggered the feature. As the round plays out you have a meter along the bottom of the game that increments whenever a spin throws out one or more of the fruit that triggered the round in the first place. As you move along the meter, you can pass certain points that grant multiplier bonuses, and even an extra life of sorts. The round ends whenever you perform a spin that fails to throw up at least one of the the fruit that triggered the free spins, unless of course you have one of those extra lives up your sleeve.
There are a lot of great Thunderkick games out there, but Fruit Warp is one that will divide opinion. The presentation is top-notch as always from this developer, but the unusual and repetitive nature of the game can manage to wear on some players. With that being said, I'm sure that there'll be a bunch of people that'll love this game given its unique presentation and relaxing vibe, along with a bonus feature that can be quite lucrative if you manage to get on an extended roll.
Fruit Warp is my favorite Thunderkick game. It was one of the first games I tried and I love the simplicity it has. The symbols are vibrant and the bonus game is fun. I haven't won anything really over 100x bet but it's a great game for small balance.
This is one of the most different slots I have ever played so far.
The game sometimes go some dozens of rounds without giving anything, but, the feature is also very interesting. Not bad game for fun.
Yeah agree with you guys, finally a fresh and completely different look from any other slot that I've seen lately, I like the way the symbols/fruits are thrown at you and I think it's not only fresh looking sot but also a good earning potential I think, definitely will look around for this one.


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Centre international d'études pédagogiques, appelé depuis 2019 France Éducation international (FEI)
 Cycle international d'études politiques de Sciences Po Paris.

Sigle de 4 caractères

redpajama_set_name: RedPajamaWikipedia


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India bound: PE/VC investments break pre-Covid trends
Naliniprava Tripathy — September 21, 2021 comments off
PE/VC investments are drifting away from the 'in favor' platform and technology-enabled businesses to new and upcoming sectors.
By Naliniprava Tripathy and Harsh Alipuria
India has come a long way from the days when its forex reserves were just $5.8 billion in 1991 due to limited foreign investment. It has become one of the world's most favored investment destinations. Over the years, the Union government has taken various steps to make India an exciting investment opportunity, leading to tremendous growth in PE/VC investments. In the last 30 years, the number of active PE/VC funds has increased by over 3600%, going from 8 in 1992 to over 300 in 2021. The amount of investment grew from $30 million to $240,000 million during the period.
Global Financial Crisis of 2008 and the uncertainties in the global markets generated strong headwinds for foreign investment at the beginning of the last decade. Questions around corporate governance, flexibility in the exit options, and contract enforcement discouraged many investors. Investment was stunted in the early part of the last decade, but grew tremendously in the second half due to the government's efforts to make India a viable investment opportunity. Even the downturn triggered by the Covid-19 pandemic hasn't slowed down the PE/VC investment in the country.
READ I India's fledgling e-commerce industry needs a robust policy framework
In 2020, PE/VC investment stood at $47.6 billion, primarily due to the investments in Jio platforms and Reliance retail. The pandemic has also brought a new trend where the funds are looking at new and upcoming sectors to invest in and moving away from 'in favor' sectors of the platform and technology-enabled businesses. EdTech, life sciences, and financial payment companies have increased their businesses during the pandemic, leading to higher interest and investment from the funds.
The PE/VC investments in the last 5 years have increased at a CAGR of 22%. In the last decade alone funds made an investment of $232 billion in India, which is more than twice the value invested in the previous decade. The major investment was in companies like Flipkart, Reliance platforms etc.
With the investments at an all-time high, it is logical to touch upon the exits as well. Exiting an investment has always been a tricky part of the Indian context. The market mood was highly volatile in GFC, leading to muted investment and exit opportunities. As touched upon earlier, the exits are challenging due to the below factors:
Lower than expected Corporate Governance leading to a mismatch between the expectations and the performance of the asset.
Strategic buying and IPOs have been limited as a lot of the investments haven't returned profits that the buyers expect.
Minimal buyable assets are making the environment extraordinarily competitive and assets valuable.
These factors have made secondary exits and open market exits more viable than strategic or IPO exits.
READ I Scrappage policy: A big business opportunity awaits India
Barring the Flipkart-Walmart deal and Alliance Tire – Yokohama Rubber deal, there aren't many big deals that have taken the strategic exit route. Traditionally, investments by PE/VCs in Indian companies have been in sectors that are in high-growth stage and for minority stakes, hence constraining their ability to drive the transaction towards strategic buyers.
With Indian promoters prefer to control majority stakes, strategic buying becomes less of an option. However, this trend might change going forward as there has been an increase in the buyout deals, increasing the potential for strategic sales. Strategic buyers are also opening to the idea of retaining the promoters to manage the business, creating a win-win situation for all stakeholders involved.
High market volatility during the pandemic and the dampened investor mood, IPO exits haven't been the preferred route. With the added burden of limited profit-making investments, IPO exits become even more challenging. But in 2021, the market is highly bullish, resulting in multiple IPO exits, Zomato being the marquee of the lot. IPO exits are expected to increase if the markets continue to perform well.
READ I Targeted incentives can boost manufacturing sector, revive MSMEs
Future outlook for PE/VC investment
Technology-enabled businesses to rule the roost: Technology has become a critical part of all life aspects and continues to disrupt the traditional business models. With EVs and AR/VR on the horizon, the investment in tech enables and technology backed companies will increase.
Construction and infrastructure to emerge: InvITs and REITs have proved to be highly successful investment options in the last decade. With increased focus on infrastructure development and urbanization, expect the investment to continue in these instruments.
Investing in private credit / distressed assets to increase: With the pandemic raging on, multiple start-ups with suitable business modes have gone bust. PE/VCs are looking at such assets and potentially make money by reviving the operations and then selling on for good profits.
Venture debt funding could emerge as an option for cash strapped start-ups: Cash-strapped start-ups don't want to dilute their stake in the entity and seek alternate funding routes. Debt funding by PE/VC funds has emerged as a viable option and is expected to grow in the coming decade.
(Dr Naliniprava Tripathy is Professor of Finance at IIM Shillong. Harsh Alipuria is Consultant, IIM Shillong Alumni.)
Naliniprava Tripathy
Naliniprava Tripathy is an Indian economist based in Shillong. She teaches finance at IIM Shillong.
https://www.policycircle.org/author/naliniprava-tripathy/
Five years of demonetisation: Economy is highly digitised, but cash remains the king
Masala bonds can be a game-changer for the rupee
PE/VC investment


This is the area of high ground that overlooks Laurel to its south. It is in Howard County, just north of the border with Prince George's County. At first glance this might seem to be about as bad a place to site a good telescope. But it would provide a good vantage point and it would be very convenient to the schools in the Laurel area. The area where we preferred to be located on the highest ground (Brewers Court, around the 9800 block of Washington Boulevard) actually already occupied by large Satellite Dishes.
PROS: Convenience, convenience, conevinience. With easy access for several schools in this area from Route 1 (the old north-south artery of the East Coast and in this area named 'Washington Boulevard'), Maryland Route 32 to the north, and from east or west via Routes 216, 198 and 197.
This area provides several of the highest vantage points in this part of the tri-county area. While the highest points are occupied by businesses, our facility could be located high enough that most lighting would be well below the shutter area of the Observatory Dome.
Even with the sky glow from the developed surroundings the topography and atmospheric qualities of the area lend themselves well to high magnification observing with some exceptional nights throughout the year. Viewing a planet from this area can be better than most locations is dark but mountainous areas (Colorado, etc.).
Almost due south of this area is the Laurel Park, a horse track that operates at times that are not likely to impact the Observatory. Furthermore, it is in a notably lower elevation than the Observatory.
The area is probably about as fully congested and developed as it is likely to be for the foreseeable future.
Being a not too congested business district, the infrastructure is very good with choices of high speed Internet access in place by Comcast Cable, and coming gradually by Verizon Fiber Optic.
Howard County government has done a good if somewhat unbalanced job of providing good educational opportunities for primary and secondary school students. This area has among the older, least equipped schools, but with many students interested in the sciences. The nearby Prince George's County has several schools also that could benefit from this location including private and public schools that we have worked with in the past.
CONS: At first glance this entire area does not seem like an appropriate location for an Observatory. However, we suggest doubters to look to Griffith Observatory in Los Angeles, California to see an example of how such a center can operate symbiotically in a metropolitan area.
In a business district "anything goes" is possible. If we had land here a neighbor could build a tall building alongside and obscure our views.
The cost of Real Estate in this area may be prohibitive.
Above: Aerial view of the North Laurel area.


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Q: Adjust length of y-axis using chart.js and bootstrap I have my chart canvas in the following structure:

        <canvas class="chart chart-bubble" chart-data="c.data" chart-options="c.options" chart-series="c.series"></canvas>

Using this, I have my Chart on the right side, and next to it on the left side are two other rows. I want it to look like this:

But for some reason, the height is not fully used by the chart.
It looks like this:

I can't just set another height for the canvas, because then, the chart becomes distorted.
How can I make the y-axis longer, so the height of the chart becomes bigger and the full height of the layout is used?

A: The solution was to set this attribute of the options-object for the chart:
maintainAspectRatio: false

Then I could adjust the height like:
.chart-container {
    position: relative;
    height: 65vh;
}

redpajama_set_name: RedPajamaStackExchange


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Supermarket Retailers
Commissaries
Deli/Prepared Foods
Home » Fresh-cut fruit: more choices, more convenience
Fresh-cut fruit: more choices, more convenience
By John Unrein
The latest quarterly earnings report for Del Monte Fresh Produce, Coral Gables, Florida, revealed a notable jump in fresh-cut fruit sales — indicative of the promise of this fresh convenience category. Del Monte reported third-quarter net sales of $145.3 million for fresh-cut fruit, an increase of 10% over the prior year period.
"Positive trends continue for Fresh Del Monte with a strong financial performance in the third quarter of 2019," Mohammad Abu-Ghazaleh, who has served as Del Monte's chairman and chief executive officer since 1996 and was instrumental in cementing the company's role as one of the world's pre-eminent fresh, fresh-cut and prepared fruit and vegetable producers and distributors, said on an earnings call. "We are emphasizing value-added margin growth in all product lines, generating momentum with global partnerships, introducing trend-forward products, and are opening new state-of-the-art facilities in Mexico and Japan. Our retail store concept in the U.S. will be coming soon."
Value-added fruit offers such promise for Del Monte that the company plans to open its first fresh food and beverage store in the United States, planned for Coral Gables, during first quarter 2020, Abu-Ghazaleh said on the call. Del Monte opened its first retail store in May 2015 at Abyat in Riyadh, Saudi Arabia, where the Del Monte Fresh Market features grab-and-go food and beverage options including smoothies and salads.
Looking at the macro picture, a new Nielsen report reveals that the success of "fresh retail superstars" in the US supermarket industry points to the fact that "fresh is the growth engine of the store, as gains in these perimeter departments translate to total store success." The superstars are succeeding by taking freshness to the next level.
For the most successful retailers, produce (up 2.6% in 52-week sales ended Aug. 24, 2019) and deli (up 4.9%) departments provide the greatest contribution to total perishable sales, according to Nielsen. This debunks the long-standing belief that the meat department contributes the highest impact to the success of the perimeter of the store. It likely reflects, Nielsen reports, consumers' changing wellness needs, as well as their growing demands for convenience. With more than three-fourths of deli sales coming from random weight items, top fresh retailers have honed a more authentic, ready-made feel.
"Entertaining at home is increasing, and demand for party trays is increasing," points out Doug Burris, executive vice president of sales and procurement for The Woodlands, Texas-based Fresh Food Group, which offers cut fruit (including sliced apples) under its Country Fresh and Sun Rich companies. "Convenient packaging has caught up to the fresh produce industry, and consumers have more choices now."
For fresh retail superstars, according to Nielsen, success hasn't come from necessarily carrying more (or fewer) items, but from having the right items in fresh. Today's consumers value health-conscious food options, and top performing fresh retailers have responded by featuring nearly three times as many different plant-based offerings as lesser performers — a savvy move, considering nearly 60% of U.S. consumers value dietary balance between animal and plant foods.
It's important to remember that produce purchasing remains a necessarily tactile, in-person experience for many consumers. Leading fresh retailers understand this and significantly outperform lesser ones in avocados, apples and berries. These produce items are among ones where consumers look or feel to confirm freshness. Consumers crave a destination, not just a store to stock up. Experience, personalization and convenience win. In fact, foodservice offerings are up 10% in sales year over year, Nielsen reports.
A smorgasbord of choices
Walking the exhibit floor of the Produce Marketing Association's 2019 Fresh Summit convention and expo, the variety of fresh-cut fruit options available to today's retailers proved impressive. Pears, mangoes and even jackfruit were among the new value-added fruit options on display at exhibitor booths.
Crunch Pak, a sliced apple specialist based in Cashmere, Washington, introduced fresh sliced, peeled and diced pears. The value-added pears, available in 7-ounce and 32-ounce packages for foodservice customers initially, are made from Anjou and Bartlett varieties. Slicing pears was an original goal of Crunch Pak when the company started in 2000, but the technology didn't exist to achieve the consistency that consumers wanted, so the company kept working to make sure it got it right, says Tony Freytag, executive vice president and co-founder.
"We made a commitment to develop value-added pears many years ago to our growers and customers," Freytag says. "Our location, relative to where the majority of the country's pears are grown, makes us literally neighbors with orchardists and their crops. The countless hours of research and development that was put into the project and the overall commitment of the company to creating this proprietary technology is to be heralded."
Mott's Sliced Dippers, available from Eden Prairie, Minnesota-based Robinson Fresh, come in two varieties: sweet apples with caramel dipping sauce and tart apples with salted caramel dipping sauce.
Prima Fresh-Cut, Fresno, California, introduced yellow sliced peaches, along with sliced nectarines, sliced pears and sliced apples. Convenient attention-grabbing packaging includes 12-ounce family pack, 24-ounce, 2-ounce snack packs and 3-ounce single serve packs. These convenient sliced fruits are a fresh new option for instore foodservice counters as well.
The Ready Snax line of fresh-cut snack packs from Ready Pac Foods, part of Bonduelle Fresh Americas, Irwindale, California, continues to grow. Options now include apples with low-fat caramel dip and cheddar cheese; apples with low-fat vanilla yogurt and trail mix; apples, grapes and cheddar cheese with flatbread; and carrots, grapes and pretzels with cheddar cheese.
Of further note, Bonduelle Fresh Americas announced in a press release that the company has set comprehensive goals for 2025 to transition to a packaging portfolio that is 100% recyclable, reusable or compostable, as well as to reduce virgin plastic inputs by an average of 25%. Numerous studies show that commitment to the environment is a key concern among today's grocery shoppers, who will look to be more brand loyal to companies that share their commitment to reducing environmental impacts.
"We are excited to launch this comprehensive strategy at Bounduelle Fresh Americas, covering issues from water use and packaging to human rights and labor," says Mathew Caldwell, senior manager of CSR for Bonduelle Fresh Americas. "We are prioritizing the right issues, committing ourselves to improving in these areas and engaging all stockholders in these actions — employees, customers, consumers, communities and suppliers."
New from Yuba City, California-based Sunsweet Growers, individually wrapped Ones Amaz!n Prunes are moist, juicy and full of nutritious goodness. They are packaged for convenience, so shoppers can pop a few into their car, purse or lunch. Sunsweet's Ones are available in 6-ounce canisters and 12-ounce value packs.
Earlier this year, Sunsweet launched a new brand campaign, #ToFeelGood, that integrates multiple media channels and reflects the zest for life shared by consumers of Sunsweet Amaz!n Prunes. Sunsweet's new #ToFeelGood campaign looks to infuse positive reinforcement into the healthy habits consumers already employ, while crowdsourcing to inspire others with new ideas. Sunsweet recognizes that people are already taking small actions every day to improve their lives, and that celebrating and sharing these tips helps promote conversation and engagement with the brand.
"We want to encourage people to appreciate the steps they are already taking to feel good in their everyday lives, and to share those tips so that others may be inspired to do the same," says Stephanie Harralson, director of marketing, North America, at Sunsweet.
Fresh-cut fruit caters to convenience needs
FMI: convenience more important than ever, key to retail foodservice growth
Subscribe to Supermarket Perimeter's free newsletters to stay up to date with the latest grocery fresh perimeter news. Subscribe
African, Indian flavors trending in 2020
General Mills points to demand for 'permissible indulgence'
Keto Bake Box available from new hybrid grocer
Retailers are fighting more organized crime


Hey! Thanks for the comment! If I'm not mistaken, didn't you also comment on the DD Forums? Regardless, thanks a ton! And what will happen with her parents, indeed? Whelp, maybe this'll give you and idea. Thanks for reading!
"Why aren't you getting ready for bed, too?" Emily always felt weird about not being dressed the same as everyone else. It felt like she was unprepared for something, and she hated the idea of being different.
Very cute story! I was kinda hoping it was going to be a bit longer, would have loved to see more instances of the virtual nursery thing. Still enjoyed it nonetheless!
That was a real treat. Excellent concept, brilliant execution, and not rushed. I love it.
Beautiful, just beautiful. I love seeing the interaction and humanity between Emmy/Emily and Mommy/Joyce. I wonder 2hat will happen when her parents show up?
I look forward to reading your story, and I'm glad you are still sharing your talented art with us here!
The tiny bronze bell jingled and jangled as a pair of brisk heels shifted from concrete steps and over to a polished floor. The blaring noises and shining sun on the backs of her heels dulled as the door closed She gave the victorian-styled shop a few simple glances, but with an overall indifferent attitude, moved over to the finished wooden counter.
Vivian looked at the banana. She'd eaten many in her life, some of them salaciously, a visual tease to the boys that could see her, making them shift uneasily in their seats.
She wasn't going to eat this one. She'd bought it for another reason, waited for it to ripen, made sure she was alone and could safely play.
All times are GMT-6. This page was generated at 01:25:15 PM.


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"Judaism Discovered," Michael Hoffman's monumental new work on Judaism is subtitled, "A Study of the Anti-Biblical Religion of Racism, Self-Worship, Superstition and Deceit."
But, what does Hoffman really think of Judaism?
We are in crisis. It's time we listened to plainspoken pariahs like Michael Hoffman. Anti-Semitism is on the rise and Hoffman's book explains why this is not irrational "hate." It's more important for Jews than anyone to learn that they are associated with a "religion" they don't really understand.
Two polls, one on August 9, 2007 and one on January 3, 2009, indicated a sharp growth of anti-Semitism in America. The August poll, conducted for the CIA-controlled RAND Corporation of Santa Monica showed 35% of the American public polled displayed moderate to strong anti-Semitic feelings while a similar poll in January of 2009 showed that percentage had jumped to 62%! This corresponds to the progress of the financial crisis. No doubt, Israel's genocidal attack on Gaza has contributed more. Look at one of the slick new anti-Jewish websites sprouting on the Internet like dandelions.
http://jewishcrimenetwork.com/
Many people serve as witting and unwitting agents of the central bankers' plan for world tyranny (the New World Order.) Collaboration is a criterion for "success" today. Increasingly, the NWO is called the "Jew World Order" because of the out-sized role Jews play. Most Jews are just trying to please their mother ("be successful dear") but it's time they learned they are part of a sinister force, and they may end up holding the bag.
Is the NWO driven primarily by the bankers' megalomania or by their adherence to a Jewish corporate agenda? Since many of the bankers are Cabalist Jews, the answer is probably both. The Jewish bankers have expanded their power base by co-opting the decadent gentile elite through intermarriage and Freemasonry (which is based on Jewish Cabalism.) This entity is a Satanic secret society called "The Illuminati Order."
Illuminati bankers are behind the recent financial collapse which is designed to facilitate political change. "Economic crises have been produced by us for the goyim by no other means than the withdrawal of money from circulation." — (Protocols of Zion, 20) As Pastor Lindsey Williams said recently, long term, "these people are out to own and control everything…they are out to break us."
http://www.henrymakow.com/dear_friends_and_family.html
HOFFMAN BOOK
Hoffman's book is required reading for understanding the Satanic mindset driving both the Illuminati and New World Order.
Normally, a 1100-page book would be daunting. But not in this case. "Judaism Discovered" is an encyclopedia in one volume consisting of more than 140 readable articles. The 10 x 7 inch format, large type and generous spacing make the book approachable. Consider it an opulent banquet. I haven't read it all yet.
Hoffman is a Talmudic adepts' worst nightmare. The goyim aren't supposed to learn this stuff. Ordinary Jews aren't supposed to know either. Hoffman has research assistants, some of whom are Jews, who read Hebrew, Yiddish, Aramaic and German. He is a brilliant scholar and an eloquent, courageous writer. He is clearly not motivated by "hate" but rather by a desire to disabuse both Jews and non-Jews. He sees them as victims of an ongoing scam.
A sample of article titles suggests the provocative theme and range:
The Superiority of the Jews The Inferiority of the Gentiles Sexual Intercourse with Little Girls is Permissible Immanuel Kant The X-Rated Talmud Sex Magic Ritual Murder Hasidic Paganism Modern Protestant View of Judaism From Kaballah to Aggadah: A Sexual Progression No "Judeo-Christian" Tradition The Rabbinic World in the Pre-Modern Age The Talmud in the Toilet The Attire of the Pharisaic Male Who are the Jews Today? Rabbi Judah Loew and Queen Elizabeth's Dr. John Dee US Gov't. Lays the Groundwork for Talmudic Courts
SAMPLING THE FEAST
Judaism is a secret Satanic cult posing as a religion. Hoffman's main point is that Judaism represents the repudiation by the Pharisees of both the Old Testament and the Mosaic Code. Judaism is not Monotheistic but Luciferian. Its goal is the replacement of God with the secret Jewish leadership. Both the Talmud and the Cabala are dedicated to the proposition that only Jews are human. "The raison d'etre of the Talmud and Orthodox Judaism is the essential spiritual and racial superiority of the Judaic over the non-Judaic," Hoffman writes. This template has been transferred to the Illuminati elite.
I don't know why this information would offend Jews, most of whom consider themselves "secular humanists." Their Jewishness is cultural. They have contempt and even hatred for Orthodox Jews who return the compliment. However, a larger question is, to what extent is the pagan materialist secular culture dominant today a form of Judaism? Especially, when you consider the widespread acceptance of Cabala- based New Age beliefs (i.e. human divinity, pantheism, goddess & sex worship and the vogue of many other occult practices.)
There is so much in Hoffman's book I can only provide a taste. An essay on Moses Hess (1812-1875) suggests modern history and culture have been contrived by Cabalists to overthrow Christian civilization and enslave society. Hoffman shows how Hess' ideology was at the nexus of Communism, Nazism and Zionism and nurtured all three. In other words, Cabalists control mankind by controlling the Hegelian thesis and antithesis. With Communism, the Cabalist bankers attempted to take our country, property, family, race, religion and liberty (still the goals of the NWO.) The reaction to Communism was Nazism, and the reaction to Nazism was Zionism. All three Frankensteins were built in the same occult laboratory using common parts.
Tellingly, the Nazis did the rabbis' work by killing "unauthorized" opponents of Judaism like Edith Stein, Irene Nemirovsky and Maximilian Kolbe. (Hoffman, p. 650)
A true Christian, Hoffman says the way to stop the Hegelian dialectic is to stop fighting. In a timely reference to Zionist colonizers and Palestinian resisters, he writes that both groups of violent combatants "are mutually draining their enemy and themselves of blood, treasure and most damaging of all, their humanity, since this killing entails the dehumanization of the opposing force and the brutalization of one's own…No authentic Christian engages in this pagan, uroboros, victim-into-executioner cycle. Peace pays the greatest dividends. All you live by the sword die by the sword. (Mathew 26:52)." (86)
PAYING THE PRICE
Our financial woes will expose the moral and political bankruptcy of Western Society. We will pay the price for our complacence, for allowing the Illuminati to seduce us and subvert all our institutions.
While Christian civilization was dedicated to the revelation of the Creator by obeying natural and spiritual (moral) laws governing human life, the New World Order replaces God's Will with the Illuminati bankers'. What is presented to us as "progressive" (e.g. sexual "liberation," the breakdown of gender identity, marriage and family) refers to progress toward Luciferian tyranny.
Michael Hoffman writes: "The core of Judaism, like the core of Gnosticism and Egyptian Hermeticism, is magic, the manipulation of the universe, contra God's creation; i.e. against nature. Gershom Scholem, Professor of Kabbalah at Hebrew University wrote that Kaballah embraced a great deal of "black magic, …a wide realm of demonology and various forms of sorcery that were designed to disrupt the natural order of things…" (Hoffman, p.779.)
(I elaborate on this opposition to God and nature expressed by Jewish and now "modern" culture in my book "Illuminati.")
Babylonian and Egyptian paganism is the progenitor of Judaism, Hoffman writes. "The rabbis hold Egypt in awe as a magical powerhouse. Pharonic Egypt is the model, root and source for Talmudic and Kabalistic priestcraft." (780) This may explain the pyramid on the US dollar and in the logos of so many corporations.
Hoffman seems mindful of the Illuminati when he writes on his website that , "the evil should NOT be assigned to a particular people denominated as "Jewish," but rather to the spirituality and ideology of Pharisaic/rabbinic origin which can, and does, afflict any people who adhere to its tenets, be they Khazars or Sephardim, WASPs such as George W. Bush, or Germans such as the current Pope of Rome."
Modern history and culture reflect a Cabalistic (Satanic) spell cast on the human race. It is dedicated to the fulfillment of prophecy, the eventual enslavement of mankind by the "Jews" who in practice will be the crazed Illuminati Order. But Jews who have no clue about this demented plan will take the blame. That's why it is essential for Jews and non-Jews alike to understand the true nature of Judaism and oppose the NWO. In a spirit of Christian mercy and love, Michael Hoffman has performed an invaluable service to mankind.
Book available at Hoffman's website http://www.revisionisthistory.org/
Related- My "Jews Must face 'Dark' Side of Judaism" http://www.henrymakow.com/jews_must_confront_dark_side_o.html
Henry Makow Ph.D. is the author of "Illuminati-The Cult that Hijacked the World." (www.cruelhoax.ca) His articles can be found at his web site http://www.henrymakow.com He enjoys receiving your comments, some of which he posts on his site using first names only. hmakow@gmail.com
3 thoughts on "Michael Hoffman's 'Judaism Discovered From Its Own Texts'"
Associazione Unicorno said:
"The reaction to Communism was Nazism, and the reaction to Nazism was Zionism."
How is possible that Zionism is a reaction to Nazism, when Zionism was founded decades before Nazism?
zaidpub said:
Hoffman is not the best logician is he ?
I think Hoffman is very logician person, and I agree with him about all. I just didn't agree with him that Nazism is made by Jews like Communism and Zionism, since Nazism is anti-thesis of both. I didn't yet read all his book, I just read a few article like this. But who write this is completely wrong, maybe is not Hoffman?


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Reality check: This is a vulva
by Gail Johnson on February 23rd, 2011 at 10:12 AM
With 18 years' experience as a stripper under her belt, Wrenna Robertson has noticed a recent trend that bothers her: more and more women want to go for labiaplasty, a cosmetic procedure that changes the appearance of the vulva. It's not just the fact that dancers with gorgeous bodies are considering the surgery that irks her. It's the bigger picture.
Given society's impossible beauty ideals and the way in which women are held up to scrutiny in the media, it's not enough anymore to aspire to a Kate Moss–like frame. Instead, women of all ages are opting for everything from Botox to boob jobs. Will plastic surgery to reshape or reduce the labia be the next big thing?
Robertson—who has two bachelor of science degrees and a master's in plant biology—thinks so. She says coworkers have asked for her opinion on whether or not they should go under the knife to make their vulvas more closely resemble the airbrushed versions on display in mainstream porn, such as the "clamshell", in which the labia minora, or smaller, inner lips of the vulva, are barely discernible. Not only did some of her fellow dancers seem ashamed of the way their vulvas looked, but they were genuinely embarrassed by the subject matter too.
"What struck me was that women started talking to me in a very self-conscious, private, shy manner," Robertson says in an interview at a downtown Vancouver office. "If anyone should be comfortable talking about it, it should be these dancers."
So Robertson embarked on a project to get women of all ages, races, sizes, and shapes talking about their sexual organs in a realistic, unabashed way. The result is I'll Show You Mine (Show Off Books, $40), a hardcover book she edited that features life-size, close-up, colour photographs of women's vulvas as well as personal stories about them. No two tales—or images—are alike.
The 60 women who took part in the project range in age from 19 to 65. Some are moms, some are grandmas, some are transgender. Some have piercings, some shave, some have "outie pussies", meaning the labia minora protrude. A few refer to their vagina as their "yoni"; one calls it her "concha".
While Eve Ensler's 1996 play The Vagina Monologues started out as a celebration of female sexuality and evolved into an ongoing international movement aimed at addressing violence against women, Robertson describes I'll Show You Mine as part empowerment tool, part educational resource.
She maintains that easy access to porn, particularly among youth in the Internet age, doesn't give women an accurate frame of reference regarding their physical features. It does, however, contribute to poor body image. And that can have more than just psychological consequences. According to a study published in the U.S.–based Journal of Sex Research in 2005, women who reported being dissatisfied with their bodies ("feeling frumpy") had sex less often and experienced less sexual pleasure than those who didn't.
"What's represented in porn is not reality," Robertson says. "Women don't know what normal is."¦Porn does not at all represent the full range of diversity."¦The purpose of this book is to display a much broader range of diversity." (As someone who makes her living by dancing naked, Robertson isn't against pornography: "This is not an antiporn campaign," she stresses.)
Research backs up the claim that false representation of female genitalia exists in popular media. A study published earlier this year in the Journal of Sex Research found media perpetuation of a "Barbie Doll" ideal, characterized by a low body mass index, narrow hips, a big bust, and "hairless, undefined genitalia resembling those of a prepubescent female".
The London, England–based biannual journal Medical Humanities, meanwhile, ran a study last year concluding that images of female genitals frequently don't accurately reflect true variation in the population. "Women and health professionals should be aware that"¦consultations for genital surgeries should include discussion about the actual and perceived range of variation in female genital morphology," the paper said.
The artificial aesthetic proliferated by porn is having an effect. According to a 2010 study in another London-based semiannual publication, Reproductive Health Matters, a British medical group saw a threefold increase in the number of labiaplasties being performed in 2007–08, while inquiries rose sevenfold over the course of three years. "In almost all cases, labiaplasty is a response to the physical appearance of completely normal labia and a desire for more "˜attractive' genitalia," the paper stated.
If a future surge in labiaplasty rates seems far-fetched, Robertson notes that when breast-augmentation surgery became available in the 1950s, it, too, was considered a fringe procedure.
Even if the demand for labiaplasty continues, Robertson is hopeful that I'll Show You Mine will at least give women more information so that they can make educated choices. She's hoping moms will share the book with their daughters, who might be worried that there's something wrong with their appearance. The book is for men too: Robertson says the prevailing misrepresentation of female genitalia misinforms boys, who grow up thinking female genitals should be a certain size and shape and that large labia minora are undesirable. And she's confident the book will stir dialogue and debate.
"I want to get people talking," she says. "And this book will definitely get people talking."
Partial proceeds from I'll Show You Mine will go to charity, and free copies are being made available to schools, teen centres, and medical offices. It's available through Show Off Books.
Michael Geoghegan
Feb 23, 2011 at 10:55am
as a man who has come across (no pun intended) perhaps a hundred or more vulvas in my life let me state that I found all of them without exception to be wonderful. It is like looking at a flower some have different sized petals or different shades, it's all good.
91 90Rating: +1
Lisa D.
Shocked, horrified and saddened by the news of this latest trend in "body-shaping". What kind of society are we creating?!! I hate to say that I'm glad I didn't have daughters to raise during what will be known as a very confusing time in women's history. I've tried very hard to instill realistic values about outward appearance in my sons, but I see how it flies in the face of what they are bombarded with every day from every source. I feel I'm losing the battle. Thank you Wrenna for your efforts!
100 85Rating: +15
The world is getting ever more superficial...both men and women are going to lengths to augment or alter thier physical being ... I wold also like to indicate that men in porn are also at the fringes of "the norm" average men don't have 6 packs and 10-12 inch penises ...women shouldn't feel the need to surgically alter the vulva...to much emphasis on the external parts and not enough on the character, soul, humor of a person.
89 92Rating: -3
Porn has influenced me to only want to have sex with good looking women, and body imperfections cause me to move on. I only see women as sex objects and the stripper-author is an example of why I view women as sex objects. She dances naked for my physical enjoyment, while her personality doesn't matter at all.
89 104Rating: -15
Angler D
Right on to Michael G. The flower metaphor is perfect. How dull it would be if the only flowers in the world were roses.
Tulips are glorious. And two lips are glorious.
78 92Rating: -14
Marla Singer
Tyler.... The first rule about fight club is your an F'n Idiot!
Tyler is just a troll. He wouldn't know how to find a vulva if you gave him a map and a GPS.
Tyler, ol' buddy, stick with the reliable hand method. Them female bits is way too confusin' for a boy like you.
96 85Rating: +11
We live in the age of illusion, substance of a person does not matter, a clever ruse is all you need. Modern men like myself only care about getting sex from good looking women, why buy the cow when you can get the milk for free? Also, ugly vaginas are a deal breaker because there are so many women that line up to have sex with men, like me, who have money. It's a use-use situation, and it is what generation y has learned to expect. What do you expect from a generation raised on porn?
Angler D, typically the object of trolling is to blatantly insult someone or something and that does not appear to be the case with Tyler. He has stated his opinion on the matter and justified it.
In addition to your self-deemed-witty remark, most GPS units are typically only accurate to within seven feet, should this radius be the error considered when locating a vulva, a labiaplasty might not be such a bad thing. And I hardly believe that a map will clearly show the location of one vagina unless it is depicted on a scale near 1:1. If someone's desire to look a different way than they currently do results in them feeling more comfortable and confident, they should be entitled to take whatever measures necessary. It ain't your snooch.
Actually, Tyler is right!
For the same reason many women wanted breast implants and now are increasingly wanting labiaplasts, men have been conditioned to desire the "perfect" porn they saw as children or adolescents. Why does the advertising world continue to use one type of body for a woman or a man in any of their explicit or suggestive ads?
We are all victims of a society that only allows us to portray our bodies as the same.
107 99Rating: +8
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Established by Cameron Blake and father David in 2010, family-owned-and-operated Blake Machinery Group (BMG) is focused on working with new and existing customers as it closes in on a decade of operations.
The Sunshine Coast-based business specialises in the supply and delivery of quality used earthmoving equipment and parts, priding itself on providing first-rate services to customers across a range of industries, including the civil contracting, mining and private sectors.
Supporting varied earthmoving operations, BMG ranges a wide variety of equipment, and its team of professionals is keenly aware of the importance of delivering tailored outcomes for clients' specific requirements. BMG sells leading-brand construction and earthmoving machines and equipment – including Caterpillar, Komatsu, Volvo, Bomag, Hitachi, Kubota and Yanmar – with its stock encompassing dump trucks, excavators, graders, loaders, rollers, dozers and more.
BMG is also the exclusive agent for Hydrema articulated and compact dump trucks in Queensland, New South Wales, the Northern Territory, Victoria, South Australia and Tasmania, and offers a wide range of Hydrema 912 dump trucks for sale, describing Hydrema vehicles as being "known for their high performance, ease of use, low weight and great overall durability".
The small and agile 912 range can be configured to accommodate a number of applications, including as a dump truck, water truck, concrete agitator and off-road tray truck, and can be fitted with hi-rail running equipment, suitable for the construction and maintenance of railway lines and tracks.
BMG added another element to its business in 2015, expanding into spare parts, with the BMG Parts component of its operations supplying new Hydrema parts, along with Volvo equipment parts and components, with BMG Parts the exclusive distributor for replacement parts and maintenance products provider Blumaq in Australia and New Zealand.
Specialising in Volvo construction and earthmoving equipment parts and components, BMG Parts stock 2700 different new aftermarket parts for Volvo loaders and dump trucks, with access to excavator parts, and used parts, which are in as-is conditions. BMG Parts also has an on-site workshop which rebuilds major components for their service exchange program.
An integral component of its operations, BMG's fully equipped workshop is decked out to ensure that all equipment leaving the BMG yard is fully serviced and prepared.
With mechanics on hand to cater to a wide range of services, BMG specialises in rebuilding and repairing components, including engines, transmissions, drop boxes and differentials, with all rebuilt transmissions and drop boxes also bench-tested by an outside source prior to delivery.
BMG's fitters are specially trained by Hydrema and fully qualified to undertake all service and repairs for Hydrema dump trucks. Its business operations are supported by a sales team with extensive industry knowledge, drawing on over 75 years of combined experience in the equipment industry.
Blake Machinery Group will be exhibiting at the National Diesel Dirt & Turf Expo for the first time in 2019, and is keenly anticipating its involvement in the event. BMG can be found at the Blake Machinery Group stand, #129, and the BMG Parts stand, #63.
Blake Machinery Group will be displaying two Hydrema articulated dump trucks, which it expects will be sure to excite visitors. BMG Parts will have a drop box, rebuilt by one of its mechanics on display at the outdoor stand, along with genuine Hydrema parts and a range of new aftermarket Volvo parts.
Blake Machinery Group will be exhibiting at Diesel Dirt & Turf 2019 visit Stand Outdoor 129 & Indoor 63 to meet the team and information about their leading range of machines.


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Home | Paris | Centre Pompidou Tour | Private Museum Experience
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Centre Pompidou Tour | Private Museum Experience
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Refundable booking
LivTours Private Centre Pompidou Tour takes place in one of Paris's most eye-catching museums. Built in the 1970s, this "factory for the arts" houses thousands of Modernist masterworks and serves as a creative hub for cutting-edge contemporary artists. If you would like to fully appreciate the most earth-shattering innovations in the artistic world, then you should check out LivTours Centre Pompidou Museum Tour.
The unique Pompidou Centre was the creation of former French President Georges Pompidou in 1969 and was built as a contemporary museum and studio for artists in the center of Paris. Constructed in a derelict section of downtown Paris, the Pompidou is credited for transforming central Paris from the moment it opened its doors in 1977.
Enjoying a vast and notable museum on your own can be daunting, so maximize your time in Paris as well as your time in the Pompidou with a private expert guide to lead the way. Your LivTours Centre Pompidou Museum Tour will give you plenty of opportunities to explore the gallery's current Modernist and Contemporary exhibitions and with a collection so vast, that you are sure to always see something new on rotation, giving you a greater appreciation for the arts!
Why book this tour
See Europe's most impressive collection of 20th & 21st century art on a private tour
Learn about avant-garde art movements from Fauvism onwards with a private guide
Soak up the beauty of Modernist masterpieces of Picasso, Matisse, and Modigliani
Visit sensational installations from some of the most daring contemporary artists
Explore cutting edge art in the largest and most important museum for modern art
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Exclusive private Tours and Experiences. Also offered in Spanish, French, Portuguese, Swedish and Russian
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Read more about your Pompidou Tour
Le Centre Pompidou is certainly one of Paris's most eye-catching museums. Built in the 1970s, this "factory for the arts" houses thousands of Modernist masterworks and serves as a creative hub for cutting-edge contemporary artists. If you would like to fully appreciate the most earth-shattering innovations in the artistic world, then you should check out LivTours' Centre Pompidou Museum Tour.
Your LivTours Centre Pompidou Museum Tour will give you plenty of time to explore the gallery's current Modernist and Contemporary displays with a collection so vast, that you are sure to always see something new on rotation, giving you a greater appreciation for the arts.
Your LivTours Private Centre Pompidou Tour will begin with a close look at the building's unique industrial design. Your guide will explain how the museum's designers used architecture to express Le Centre Pompidou's role as an "industry" for contemporary artists. You will also get the chance to see the frequently photographed Fountain Stravinsky located just a stone's throw from the center.
The rest of your tour will focus on the Pompidou Centre's star attraction: The National Museum of Modern and Contemporary Art. With almost 200,000 square feet of space and thousands of artworks, few museums rival Le Centre Pompidou's collection.
In the museum's Modernist wing, your guide will give you a quick refresher on the most influential art movements in Paris during the early 20th century, getting to know genres such as Fauvism, Cubism, and Surrealism. With a thorough understanding of each movement's context, you will grasp just how radical these paintings must have been during their time. On your tour, you might get to see a few representative paintings by artists like Picasso, Matisse, Léger, and Modigliani.
As you advance in the Modernist collection, your guide will explain how many historians trace the roots of Contemporary Art to a urinal displayed in NYC. As strange as it sounds, one of the biggest events in 20th-century art was when Marcel Duchamp tried to get a urinal exhibited in a New York exhibition. Even though it was initially rejected, Duchamp made a point of bringing out his Fountain for photographs. Duchamp's "ready-made" Fountain continues to ignite debate over the nature of the art object and museum censorship. While Duchamp's original Fountain is not on display in this museum, you might get to see a copy or other works by Duchamp and his Dadaist descendants.
As your tour winds down, you will work your way through cutting-edge Contemporary Art movements. From Pop Art and Abstract Expressionism to the latest in multi-media installations, Centre Pompidou has a wide assortment of Contemporary displays. A few famous works which have been on display here include Andy Warhol's Ten Lizes, Joseph Beuy's Plight, and Mark Rothko's Untitled (Black, Red Over Black on Red). You might also have the chance to see the masterpieces of tomorrow by some of today's most daring artists.
When you have finished in the museum's Modernist collection, it is time to visit the Contemporary Art collection. Here you will see some of the most radical films, photographs, sculptures, and art installations from a wide variety of artistic trends. This is a fantastic tour for art lovers visiting Paris.
This tour includes
Guided tour through Centre Pompidou
Fauvism, Cubism, and Surrealism art
Art by Picasso, Matisse, Léger, and Modigliani
Pop Art and Abstract Expressionism
Modern Art Collection
Andy Warhol's Ten Lizes
Joseph Beuy's Plight
Mark Rothko's Untitled
Fully guided experience
Due to these unprecedented times and ongoing safety and regulation changes, some sites may have limited accessibility if the venue can not guarantee social distancing which may lead to unforeseen tour modifications. Thank you for your understanding.
LivTours' is and always has been based on sustainable travel and especially in these new times, we are proud to be at the forefront of innovation, change, and challenges that are presented to us during this post-pandemic time. At the moment, due to Covid-19 safety regulations, museums and sites visited on this tour require wearing a mask while on site. Please bring one for every participant over 6 years of age.
About our Private tours
When you book a LivTours Private Tour or Experience, you are guaranteed a dedicated, expert guide that allows you the flexibility to start your tour at a time which is convenient for you, making planning easy. Our private tours ensure that you will get a tailored experience to meet all your needs so we go at your pace, perfect for families with younger children, elderly, or individuals with accessibility needs. Please be advised that all private tours begin at a base price starting at two people*. Prices are inclusive of entry tickets where applicable.
*Our Tuscan motorcycle tour and some Ferrari private experiences are inclusive of one person only.
Make your day even more unique and comfortable by upgrading your tour with a customizable LivTours optional add on!
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Upgrade for a one way pick-up service directly from your centrally located Paris hotel to the meeting point of the tour. Guaranteed stress-free. One way only.
starting from 75 € 120 $ 67.50 £ 90 $
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For all France and Italy tours that include an indoor activity, a museum or an archeological park visit, it is now National Law in both countries, to present a covid-19 vaccination card OR negative covid-19 test result from the past 48 hrs accompanied by your personal ID to the local authorities for all adults over the age of 12. Lack of ability to present such documentation may result in loss of tour and funds lifting LivTours from all responsibilities.
Worthy of a visit
"The Pompidou center isn't on everyone's must do list but, after having taken LivParis' tour, we can certainly recommend you try to see it. The outside architecture is spectacular in itself and inside, the museum is fascinating. All of it made so much more sense thanks to our guide Richard (art historian) who had great insight into the artists and who delivered his information not as a boring lecture but in an entertaining and entertaining way. He is a long time resident of Paris but hails originally from England so there wasn't the typical difficulties of trying to understand the language. LivTours was recommended to us by friends so we knew we could expect a great experience. We certainly weren't disappointed!"
Wyatt - USA
A fascinating place
"We were so happy we chose to book a guided tour to visit the Pompidou center. It is a fascinating place and to have a guide with you to point out details and share with you the history of the artist and his works made the visit so much more interesting. We learned so much and will remember this visit and what we saw for a long time. It is definitely worth it to take this tour."
Peggy A. - USA
"The Centre Pompidou is a fascinating place, rich with modern art and architecture that you'll never see anywhere else. We visited with LivTour's guide on a private visit and we were very pleased with the tour, with the guide and with the company's organization. We will recommend this tour to all that are interested in modern art and architecture."
Douglas - USA
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DevSpace
A social platform for developers to collaborate. DevSpace allows developers to share their projects, post tech related discussions, and connect with other developers to collaborate on projects.
Pranav Krishna
Holland Pleskac
Kushagra Singh
Shabd Veyyakula
advithi kethidi
We were inspired by social media as a whole and GitHub's audience, developers, with acknowledging the problem of the lack of social contact developers have with each other. We are frequent users of the two applications and were inspired to create an app where developers can socialize and collaborate on projects with one another.
A social platform for developers to collaborate. DevSpace allows developers to share their projects, post-tech-related discussions, and connect with other developers to collaborate on projects. The app includes a home screen where developers can view posts and projects of other developers as well as contact them. It is a platform developers to meet with each other and collaborate on future projects. There is a direct messaging feature that allows them to contact one another included in the app.
We built this app using flutter in android studio and we built the website using bootstrap with HTML 5 and CSS in visual studio code.
We learned languages such as Html5 with CSS3 because we wanted to challenge ourselves with creating a website and app even though most of us had little experience with it. We worked together on developing the idea and divided the work amongst ourselves to execute the project in the most efficient manner. We used current-day social media apps for inspiration on our user interfaces and by using flutter, we were able to develop a professional app with the proper functionality. We had a hard time making a website and an app as it took a lot of time and difficulty. At one point in the middle, we accidentally overrode the project on GitHub which led to the code being lost but luckily we were able to recover it. We built the app and website using, HTML5, CSS3, Flutter, JavaScript, Note.JS, Jquery, and Bootstrap.
https://tinyurl.com/wrqtg4o
https://github.com/Th3-H4xx0r/DevSpaceMobile/
https://github.com/ShabdVeyyakula/DevSpace
https://github.com/Th3-H4xx0r/DevSpaceMobile/blob/master/app-release.apk
LA Hacks 2020
bootstrap, css3, firebase, flutter, google-cloud, html5, javascript, jquery, node.js
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It'd be absolutely lovely if there was some way of figuring out how much CPU a Purr Data patch is eating up right there and then. Would result in better optimization procedures instead of working in the dark. Ideally this CPU meter would state how much CPU specific objects are taking - if possible.
It'd be absolutely lovely if there was some way of figuring out how much CPU a Purr Data patch is eating up right there and then. Would result in better optimization procedures instead of working in the dark. Ideally this CPU meter would state how much CPU specific objects are taking - if possible. Is something like this possible?