text:
\section{Introduction}
\label{int}

The purpose of this note is to clarify the relation
between the Hamiltonian and Lagrangian approaches to
nonlinear evolution equations. In particular we explain
the least action principle and the Noether theorem in this
context.
The specific
point of view,
adapted from Souriau's book \cite{Sou}, has perhaps not been
presented for nonlinear evolution equations. It seems that
in the mathematics literature, as in \cite{FrSi},\cite{GSS},\cite{HZ1}, and in
references
given there, the Hamiltonian point of view is prevalent.
In the physics  literature,
see for instance \cite{GHW},\cite{OS}, the Lagrangian point of view rules
with the symplectic structure largely neglected. In \S \ref{ed} we
present one possible mathematical reason for that.

\section{The Hamiltonian structure}
\label{rhs}

In this section we recall well known facts about the
Hamiltonian structure of the nonlinear Schr\"odinger equation.
The same point of view applies to other evolution equations, see
for instance \cite{GSS} and references given there.

For simplicity we will consider the case of dimension one, and
\[ V \stackrel{\rm{def}}{=} H^1(\mathbb{R}, \mathbb{C})\subset L^2(\mathbb{R},\mathbb{C})\,,\]
viewed as a {\em real} Hilbert space.
The inner product and the symplectic form are given by
\begin{equation}
\label{eq:omega}\
\langle u,v \rangle  \stackrel{\rm{def}}{=} \Re \int u\bar v \,, \  \
\omega(u,v) \stackrel{\rm{def}}{=} \langle  u , i v \rangle = \Im \int u\bar v\,,
\end{equation}
Let
$H:V\to \mathbb{R}$ be a function, a Hamiltonian.
The associated Hamiltonian
vector field is a map $\Xi_H : V\to TV$,
which means that for a particular point $u\in V$, we have
$(\Xi_H)_u \in T_uV$. The vector field  $\Xi_H$ is defined by the relation
\begin{equation}
\label{eq:Hamvf} \omega(v , (\Xi_H)_u) = d_uH(v)
\,, \end{equation}
where $v\in T_uV$, and $d_uH:T_uV \to \mathbb{R}$ is defined by
$$d_uH(v) = \frac{d}{ds}\Big|_{s=0} H(u+sv) \,. $$
In the notation above
\begin{equation}
\label{eq:nats}  dH_u ( v ) = \langle dH_u , v \rangle \,,
\ \  (\Xi_H)_u = \frac 1 i dH_u  \,.
\end{equation}

If we take $ V = H^1 ( {\mathbb R} , {\mathbb C} ) $ with the symplectic form \eqref{eq:omega},
and
$$H(u) = \int \frac14|\partial_x u|^2 - \frac1 {p+1} |u|^{p+1} $$
then we can compute
\begin{align*}
d_uH(v) &= \Re \int ( (1/2) \partial_x u \partial_x \bar v - |u|^{p-1} u \bar v)\\
&= \Re \int ( - (1/2)\partial_x^2 u - |u|^{p-1} u)\bar v \,.
\end{align*}
Thus, in view of \eqref{eq:nats} and \eqref{eq:Hamvf},
$$(\Xi_H)_u = \frac 1 i \left( - \frac12 \partial_x^2u - |u|^{p-1}u \right) $$
The flow associated to this vector field (Hamiltonian flow) is
\begin{equation}
\label{eq:Hflow}
\dot u = (\Xi_H)_u =  \frac 1 i  \left( -
\frac12 \partial_x^2u - |u|^{p-1}u \right)
\,.
\end{equation}

\section{The Lagrangian point of view and the Noether theorem}
\label{lpv}

According to \cite{Sou} the following point of view towards
dynamics goes back to Lagrange. We consider
\[  {\widetilde V} = V \times {\mathbb R} = H^1 ( {\mathbb R} , {\mathbb C} ) \times {\mathbb R} \,,\]
and the following one form on $ {\widetilde V} $ (we are rather informal
here about dual spaces etc):
\begin{equation}
\label{eq:defal}
 \alpha_{(u,t)} ( v , T ) \stackrel{\rm{def}}{=} \frac 12 \omega ( u , v ) -  H ( u ) T \,, \ \
( v , T ) \in T_{ ( u , t ) } {\widetilde V} \,, \ \ ( u , t ) \in {\widetilde V} \,.
\end{equation}

\medskip

\noindent
{\bf Remark.} The presence of the factor $ 1/2 $ in front of $ \omega $
in the definition of $ \alpha $ is best understood using the
finite dimensional analogy: if $ z = x + i \xi $, $ x, \xi \in {\mathbb R}^n $, then
\begin{equation}
\label{eq:alpha}   \alpha = \frac{1}2 \Im z d\bar z   - H( x, \xi ) dt
= \frac 12 ( \xi dx - x d \xi ) - H ( x, \xi ) dt \,.
\end{equation}

\medskip

We then define the differential of $ \alpha $:
\[ {\widetilde \omega} \stackrel{\rm{def}}{=} d \alpha \,, \]
that is
\[ {\widetilde \omega}_{(u,t)} ( ( v_1 , T_1 ) , (v_2 , T_2 ) ) = \omega ( v_1 , v_2 ) -
dH_{u} ( v_1 ) T_2 + dH_u ( v_2 ) T_2 \,, \]
where we used the notation of \S \ref{rhs}. This calculation is
easily understood using the analogy with \eqref{eq:alpha}:
\[ d ( \xi dx - x d \xi )/2 = d \xi \wedge d x \,. \]

Having $ {\widetilde \omega} $ makes
$ {\widetilde V} $ a presymplectic space in the sense that $ {\widetilde \omega} $ has
a kernel of dimension one. Here, the kernel is
\[ \ker {\widetilde \omega}_{(u,t)} \stackrel{\rm{def}}{=} \left\{ ( v, T )  \in T_{ ( u , t) } {\widetilde V} \; ; \; \
\forall \; (v', T') \in T_{ ( u , t ) } {\widetilde V} \,, \
{\widetilde \omega}_{(u,t)} ( ( v, T ) , ( v' , T') ) = 0 \right\} \,. \]

The following proposition replaces \eqref{eq:Hflow} with a condition
related to $ {\widetilde \omega} = d \alpha $:

\begin{prop}
\label{p:HL}
The curve $ t \mapsto u ( t ) \in V $ is a solution to
\begin{equation}
\label{eq:NLS}
  i u_t = - \frac 12 \partial_x^2 u - |u|^{p-1} u \,,
\end{equation}
if and only if
\begin{equation}
\label{eq:HL}
(\dot u ( t ) , 1 ) \in \ker {\widetilde \omega}_{ u ( t ) } \,.
\end{equation}
In other words,
\[ \ker {\widetilde \omega}_{u} = {\mathbb R} ( \Xi_{ u } , 1 ) \,. \]
\end{prop}
\begin{proof}
We already know that \eqref{eq:NLS} is equivalent to \eqref{eq:Hflow}.
We then check that
\[ \begin{split}
{\widetilde \omega} ( ( (\Xi_H)_u , 1 ) , ( v , T) ) & =
\omega ( (\Xi_H)_u , v  ) - \langle dH_u , T (\Xi_H)_u  - v  \rangle
\\
&  = - \langle dH_u , v  ) -  \langle dH_u ,  T (\Xi_H)_u  - v  \rangle\\
& = T   \langle dH_u , (\Xi_H)_u \rangle
 = T  \langle
dH_u , (1/i ) dH_u \rangle = 0 \,.
\end{split} \]
\end{proof}

A special case of Noether's Theorem (see \cite[(11.12)]{Sou} for a
more general version using the moment map) is now nicely given using
this point of view:

\begin{prop}
\label{p:Noeth}
Suppose that
\[ A ( s) \; : \;
( s , U ) \mapsto U ( s )  \,,  \ \ s \in {\mathbb R} \,, \ \ U \in {\widetilde V} \,, \]
is a
one parameter group acting on $ {\widetilde V} $ and preserving $ \alpha $:
\begin{equation}
\label{eq:Aal}
  A(s)^* \alpha = \alpha \,, \end{equation}
(here the pullback is given by $ f^* \alpha_{(u,t)}  ( v, T )
\stackrel{\rm{def}}{=} \alpha_{ f ( u , t ) }
(f_* ( v , T ) ) $).
Then
\begin{equation}
\label{eq:Noeth} F ( u, t ) \stackrel{\rm{def}}{=} \alpha_{(u,t)} \left ( \frac{d}{ds} A ( s ) (u,t) |_{s=0} \right) \,, \
(u,t)  \in {\widetilde V} \end{equation}
is conserved by the flow \eqref{eq:NLS}.
\end{prop}
\begin{proof}
In the finite dimensional case we use Cartan's formula: if $ (d/ds) f_s|_{s=0}
= X  $ (here $ f_s : {\widetilde V} \rightarrow {\widetilde V} $), then at $ s = 0$,
\[ \frac{d}{ds} f_s^* \alpha = d ( \alpha ( X ) ) + ( d \alpha ) ( X , \bullet)
\,. \]
If we take $ f_s = A( s) $ then the left hand side is $ 0 $ and
$ X = (d/ds) A ( s ) ( u , t ) |_{s=0} $. The invariance of $ F $ is
then equivalent to
\[  d ( \alpha ( X ) ) ( \dot u , 1 ) = 0 \,\]
but since
\[  d ( \alpha ( X ) )  = - {\widetilde \omega} ( X , \bullet)  \,,\]
this follows from Proposition \ref{p:HL}. The same argument applies
formally in the case of evolution equations and can be easily verified.
\end{proof}

\subsection{Standard group actions.}
\label{sga}
The basic group action to consider are
\[ ( u , t ) \mapsto ( e^{ -is } u , t )  \,, \ \
( u , t ) \mapsto ( u ( \bullet - s ) , t ) \,, \ \
( u , t ) \mapsto ( u , t - s ) \,, \]
and in each case we quickly see that $ A ( s ) ^* \alpha = \alpha $.
In the three cases we have
\begin{gather*}  ( d/ds ) A( s) ( u , t) |_{s=0} = (- i u , 0 ) \,, \ \
 ( d/ds ) A( s) ( u , t) |_{s=0} = ( -u_x  , 0 ) \,, \\
 ( d/ds ) A( s) ( u , t) |_{s=0} = ( 0  , -1 ) \,, \ \
\end{gather*}
respectively, and the conserved quantities obtained using
the formula \eqref{eq:Noeth} are easily seen to be
\[ \int |u|^2 dx \,, \ \ \Im \int u_x \bar u dx \,, \ \  H ( u ) \,. \]

A more interesting example is given by considering the Galilean
invariance:
\[  A( s ) ( u , t ) = ( A_0 ( s , t ) u , t ) \, , \ \
A_0 ( s, t ) u \stackrel{\rm{def}}{=} e^{- i t s^2/2 + i \bullet s } u ( \bullet - s t ) \,. \]
We first check that \eqref{eq:Aal} holds. In fact,
\[  [A ( s )_*]_{(u,t)} ( v, T ) = ( A_0 ( s, t ) v + \partial_t (
A_0 ( s , t) u ) T , T ) = ( A_0 ( s, t ) ( v - (i s^2 u /2 +
s u_x ) T), T ) \,, \]
and hence
\[ \begin{split}
  (A( s )^* \alpha)_{( u , t )} ( v ,  T ) & =
\alpha_{ A ( s ) ( u ,t ) } ( [A ( s )_*]_{(u,t)} ( v, T ) ) \\
& = \omega ( A_0 ( s , t ) u ,
A_0 ( s, t ) ( v - ( i s^2u/2 +
s u_x ) T ) ) - 2 H ( A_0 ( s , t ) u ) T \\
& =
\alpha_{( u , t ) } ( v , T )\,,
\end{split} \]
since
\[ \omega  ( A_0 ( s , t ) u ,
A_0 ( s, t )  v) = \omega ( u , v ) \,, \]
and
\[ \begin{split}
H ( A_0 ( s, t ) u ) & = H ( u ) + s^2 \langle u , u \rangle/4
+ s \langle i u , u_x \rangle/2  \\
& = H ( u ) + s^2 \omega ( i u , u )/4
+ s \omega ( u , u_x )/2 \,.
\end{split}
\]

We also see that
\[ \frac{d}{ds} A ( s ) ( u , t ) |_{ s= 0 } =
( i x u - t u_x , 0 ) \,, \]
formula \eqref{eq:Noeth} gives
\[  F( u , t ) = t \Im \int u_x \bar u dx - \int x |u|^2 dx =
F ( u , 0 ) = - \int x |u|^2 dx = 0 \,, \]
which of course corresponds to $ p = m q / t $ where
\[ p = \Im \int u_x \bar u dx \,, \ \ q = \frac1m \int x |u|^2 dx \,, \ \
m = \int |u|^2 dx \,, \]
are the momentum, position, and mass, respectively.

\subsection{Scaling}
\label{sc}

Let us now consider another group action preserving
solutions of \eqref{eq:NLS} ($p > 1$):
\begin{equation}
\label{eq:sc}
( s , u , t ) \longmapsto ( A_0 ( s ) u ,
s^{-2} t ) \,, \ \
A_0 ( s ) u ( \bullet ) \stackrel{\rm{def}}{=} s^{\frac{2}{p-1}} u (  s \bullet )  \,.
\end{equation}
Then
\[ [A ( s )_*]_{(u,t)} ( v , T ) = A(s) ( v, T ) \,, \]
and
\[ (A( s)^* \alpha)_{(u,t)} ( v ,  T) =
\tfrac12\omega(A_0 (s )u , A_0 ( s )v ) - H ( A_0 ( s ) u ) s^{-2} T =
s^{\frac{5-p}{p-1}} ( \tfrac12\omega (u , v ) -  H ( u ) T ) \,.\]
That means that the form is preserved for $ p = 5 $. For $ p \neq 5 $
we still preserve the kernel of $ {\widetilde \omega} = d \alpha $ which is consistent
with \eqref{eq:sc} preserving the solutions.

To see the invariant quantity given by Noether's theorem (formula
\eqref{eq:Noeth}) for $ p = 5 $ we compute
\[ \frac{d}{ds} A ( s ) ( u , t ) |_{s=1} =
( u/2 + xu_x , - 2t ) \,, \]
and the conserved quantity is
\begin{equation}
\label{eq:cons}
 F ( u , t ) = \tfrac12\omega ( u , u/2 + x u_x ) + 2 t H( u ) =
- \tfrac12\Im \int x u_x \bar u + 2 t H ( u ) \,,
\end{equation}
which is a version of the virial identity, typically written
\begin{equation}
\label{E:virial1}
\partial_t \left( \Im \int xu_x \bar u \right) = 4H(u) \,.
\end{equation}

\subsection{Case of $ p=5 $}
\label{p5}

Here the scaling symmetry is part of a more general
scaling property:
\[ u ( t , x ) \longmapsto ( ct + d )^{-1/2} e^{\frac{ i c x^2}{ 2 ( ct + d)}}
u \left( \frac{ at+b} { ct+d} , \frac x{ct+d} \right) \,, \ \
\left( \begin{array}{ll} a & b \\ c & d \end{array} \right) \in
SL_2 ( {\mathbb R} ) \,, \]
see \cite{KS} for this and a recent study of the quintic NLS.

Motivated by this,
for $ g \in SL_2 ( {\mathbb R} ) $ we define the standard action on $ \overline {\mathbb R} $:
\[  g ( t ) = \frac{ a t + b }{ ct + d } \,, \ \
\left( \begin{array}{ll} a & b \\ c & d \end{array} \right) \in
SL_2 ( {\mathbb R} )  \,.\]
Then
\[ A ( g ) \; : \; {\widetilde V} \rightarrow {\widetilde V} \,, \]
is given as follows
\[ A ( g ) ( u , t ) = ( A_0 ( g ) u  ,  g^{-1}(t ) ) \,, \ \
A_0 ( g ) u = (g'(t))^{-\frac14} e^{ -i g''(t) x^2/(4 g'(t)) }
u \left( ( g'(t))^{\frac 12}  x  \right) \,. \]
Since $ g'( t) = ( ct + d )^{-2} $, $ (g'(t))^{\frac 12} =
( c t + d )^{-1} $ is well defined.

The cases of
\[ \left( \begin{array}{ll} a &  \; 0\\ 0 & 1/a \end{array} \right)  \,, \ \
\left( \begin{array}{ll} 1 & b \\ 0 & 1 \end{array} \right) \,, \]
correspond to scaling and translation with the invariant quantities already
discussed.

For
\[ g ( s ) \stackrel{\rm{def}}{=} \left( \begin{array}{ll} \cos s
 & - \sin s  \\ \sin s & \ \cos s \end{array} \right) \,, \]
we obtain
\[ \frac{d}{ds} ( A ( g ( s )) ( u, t ) |_{s=0} =
( (-t/2 + i x^2/2 ) u - t x u_x , 1 + t^2 ) \,, \]
so that the conserved quantity is
\[ F( u , t) = - \frac14 \int x^2 |u|^2 dx + \frac12t \Im \int x u_x \bar u
- H(u)t^2-H(u) \,.  \]
Since $ H( u ) $ is conserved and we also have \eqref{eq:cons}
we conclude that
\begin{equation}
\label{E:virial2}
\int x^2 |u ( x , t ) |^2 dx = \int x^2 |u ( x , 0 ) |^2 dx
+ 2t \Im \int x u_x \bar u - 4H(u)t^2  \,
\end{equation}
which is again a version of the virial identity.  This version of the virial identity is usually written
$$\partial_t^2 \int x^2 |u(x,t)|^2 \, dx = 8H(u)$$
Two time integrations, then substituting the identity
$$\partial_t \int x^2 |u|^2 \, dx = 2\Im \int x \bar u \partial_x u \, dx$$
evaluated at $t=0$, give
$$\int x^2|u(t)|^2 \,dx = \int x^2|u|^2 \,dx \Big|_{t=0}+ 2\Im \int x \bar u \partial_x u \, dx \Big|_{t=0} t + 4H(u)t^2$$
Integrating \eqref{E:virial1} from $0$ to $t$ gives an expression for $\Im \int x \bar u \partial_x u \, dx \Big|_{t=0}$, which substituted here gives \eqref{E:virial2}.

\section{The least action principle}
\label{lap}

To formulate the least action principle we need to define the
Lagrangian. In the last section, although we took the
Lagrangian point of view, we used the form $ \alpha $ given by
\eqref{eq:defal}. The Lagrangian,
\[  {\mathcal L} \; : \; T {\widetilde V} \; \longrightarrow \; {\mathbb R} \,, \]
is defined as follows:
\[ {\mathcal L} ( u , t , X , T ) \stackrel{\rm{def}}{=} \alpha_{(u,t)} ( X , T ) \,, \ \
X \in T_u V \,. \]
If $ t \mapsto u $ is a curve in $ V$ we use a simplified notation

\begin{equation}
\label{eq:defla0}
 {\mathcal L} ( u ) \stackrel{\rm{def}}{=} \alpha_{(u,t)} ( \dot u ,  1) \,.
\end{equation}

For the equation \eqref{eq:NLS} we obtain
\begin{equation}
\label{eq:defla}
 {\mathcal L} ( u ) = \frac12 \omega ( u, \dot u ) - H( u ) =
- \frac 12 \Im \int u_t \bar u - \frac 14 \int |u_x|^2 + \frac1{p+1}
\int |u|^{p+1} \,.
\end{equation}

Action is more natural than considering Lagrangian. Let $ \gamma $
be a curve in $ {\widetilde V} $. Then the action on $ \gamma $ is defined as
\begin{equation}
\label{eq:defac} {\mathcal S}_\gamma \stackrel{\rm{def}}{=} \int_\gamma \alpha \,.
\end{equation}
When the curve is given by $ t \mapsto ( u ( t) , t ) $ we
get, in the notation of \eqref{eq:defla0},
\[  {\mathcal S }_\gamma  \stackrel{\rm{def}}{=} \int {\mathcal L} ( u ) dt \,. \]

The least action principle can be formulated as follows:

\begin{prop}
The curve $ \gamma: s \mapsto ( u ( s ) , t ( s) ) $ is
critical for $ {\mathcal S}_\gamma $ if and only if
$ \dot \gamma (s) \in \ker {\widetilde \omega}_{\gamma (s)} $. In other words
\begin{equation}
\label{eq:delta} \delta {\mathcal S}_\gamma = 0 \;
\Longleftrightarrow \;  \dot \gamma (s) \in \ker {\widetilde \omega}_{\gamma (s)} \,.
\end{equation}
\end{prop}
\begin{proof}
We first give the proof in finite dimensions.
Let $ \gamma_r $ be a smooth family of curves such that $ \gamma_0 = 0 $,
and $ \gamma_r $ is equal to $ \gamma $ outside of a compact subset,
disjoint from $ \partial \gamma $.
Being stationary means that for any such family,
\[ \frac { d} { d r} \int_{\gamma_r } \alpha \; \; \Big|_{r=0} = 0 \,.\]
Let $ F_r $ be a smooth family of diffeomorphism such that, for $ r $
small, $ \gamma_r = F_r ( \gamma ) $, and let $ X = (d/dr) F_r |_{r=0} $
be a vector field defined on $ \gamma $. Then, as in the proof of
Proposition \ref{p:Noeth}, we use Cartan's formula:
\[ \begin{split}
 \frac { d} { d r} \int_{\gamma_r } \alpha \; \Big|_{r=0}
& = \frac { d} { d r} \int_{\gamma } F_r^* \alpha \; \Big|_{r=0}
 = \int_\gamma ( d \alpha ( X , \bullet ) + d ( \alpha ( X ) ) ) \\
& = \int_\gamma \widetilde \omega ( X , \bullet )  + \alpha( X )|_{ \partial
\gamma }
 = \int_\gamma \widetilde \omega ( X , \bullet )
\,,
\end{split}\]
since by the assumptions on $ \gamma_r $, $ X \equiv 0 $ near
$ \partial \gamma$. This means that
\[  \frac { d} { d r} \int_{\gamma_r } \alpha \; \Big|_{r=0} = 0
\ \Longrightarrow \ \widetilde \omega_{\gamma(s)} ( X_{\gamma(s)}  , \dot \gamma(s) ) = 0 \ \forall \; X \ \forall \; s \,, \]
which proves the proposition in finite dimensions.

The same formal argument applies to evolution equation and in our
case we check it by a sandard direct computation:
\[ \begin{split}
{\mathcal S } ( u + \delta u , t + \delta t ) & =
\int ( \omega ( u + \delta u , \dot u + \delta \dot u ) /2 -
H ( u + \delta u ) ( \dot t + \delta \dot t ) ) ds
\,.
\end{split} \]
Integrating by parts and neglecting higher order terms
we obtain the first variation of
$ {\mathcal S } $:
\[ \begin{split} \delta {\mathcal S}
&  = \int ( \omega ( \delta u , \dot u ) - \dot t d_u H  ( \delta u ) +
d_u H ( \dot u ) \delta t ) ds \\
& = \int {\widetilde \omega}_{(u,t)} ( ( \delta u , \delta t ), ( \dot u , \dot t ) ) ds \,,
\end{split} \]
and this vanishes for all $ \delta u $ and $ \delta t $ if and only
if
$ ( \dot u , \dot t ) \in \ker {\widetilde \omega}_{(u,t)} $.
\end{proof}

\section{Effective dynamics}
\label{ed}

Suppose that $ {\widetilde M} \subset {\widetilde V} $ is a submanifold which
is {\em presymplectic} in the sense that
\begin{equation}
\label{eq:const}   \dim \ker {\widetilde \omega} |_{ {\widetilde M} } = k \,, \ \ \text{where $ k $ is
 constant on $ {\widetilde M} $.} \end{equation}
Then $ \ker {\widetilde \omega} |_{{\widetilde M} } $ defines a foliation of $ {\widetilde M} $ with
leaves of dimension $ k $. We note that the fact that $ d {\widetilde \omega} = 0 $
and the formula for $ d \rho ( X, Y , Z ) $,
\[  X \rho ( Y , Z ) - Y \rho ( X ,  Z) +
Z \rho ( X , Y ) - \rho ( [ Y , Z ] , X ) + \rho ( [ X , Z ], Y )
- \rho ( [ X, Y ] , Z ) \,, \]
show that the $ \ker {\widetilde \omega} $ satisfies the Frobenius integrability
condition.

The method of collective coordinates for motion close to $ \widetilde M $
is based on the following principle:
\begin{quote}
Suppose that $ \gamma $ is critical for $ {\mathcal S} $
(for instance  $ t \mapsto u ( t ) $ which satisfies
\eqref{eq:HL} or,
equivalently, \eqref{eq:Hflow}). Suppose also that $ \gamma $
is {\em close} to $ {\widetilde M} $. Then it is close to a fixed leaf of the
above foliation.
\end{quote}

Here is a trivial example to illustrate this. Let $ V = T^* {\mathbb R} $
and $ H ( x , \xi ) = \xi^2/2 $. Then suppose that $ {\widetilde M} = \{ \xi = 0 \}$.
In that case $ \dim \ker {\widetilde \omega} |_{\widetilde M} $ is $ 3 $. If
\[  \gamma ( t ) = (  ( x + t\epsilon  , \epsilon ), t ) \,, \]
then it is close $ {\widetilde M} $, which the only leaf of the foliation.

What one normally wants is (see \cite{OS} for examples from the
physics literature and \cite{FrY} for an implicit application of this
principle in the mathematics literature):
\begin{quote}
Let $ {\widetilde M} $ satisfy \eqref{eq:const} with $ k = 1 $.
Suppose that $ \gamma $ is critical for $ {\mathcal S} $.
Suppose also that $ \gamma $
is {\em close} to $ {\widetilde M} $. Then $ \gamma $ is close to a
$ \gamma_{{\widetilde M}} \subset {\widetilde M} $ which is critical for
$ {\mathcal S}_{\gamma_0 } $, $ \gamma_0 \subset {\widetilde M} $.
In other words, we restrict the Lagrangian to the submanifold
and compute the action there.
\end{quote}

The simplest case is given by $ {\widetilde M} = M \times {\mathbb R} $ with
$ M $ symplectic, that is $ M$ for which $ \omega |_M $ is nondegenerate.
In that case the foliation is given by
\[   s \rightarrow ( \exp ( s \Xi_{H\;|_{M}} ), s ) \,, \]
where $ \Xi_{p }$ is the Hamilton vector field of a Hamiltonian $ p $.
This is very clear in finite dimensions since then, locally,
\[ M = { ( x , \xi ) : x''=\xi''=0 }  \,, \ \ x = ( x' , x'') \,, \ \
\xi = ( \xi' , \xi'') \,, \]
and
\[ {\widetilde \omega} |_{{\widetilde M} } = ( d\xi' + H_{x'} ( x', 0 , \xi' , 0 ) dt ) \wedge
 ( dx' - H_{\xi'}  ( x', 0 , \xi' , 0 )  dt ) \,.\]

However we may have situations in which $ \omega |_M $ is degenerate
yet $ \ker {\widetilde \omega} |_{M \times {\mathbb R} } $ keeps fixed rank $ 1$. That means that the
Hamiltonian formalism is not applicable but the Lagrangian one is.
Here is a simple example:
\begin{gather*}
M = \{ ( x_1 , 0  , \xi_2^2 , \xi_2  ) \} \subset V = T^* {\mathbb R}^2\,,
\ \  H ( x, \xi) = x_1  \,, \\
 \omega |_M =  2 \xi_2 d \xi_2 \wedge dx_1  \,, \ \
\dim \ker  \omega |_{ M \cap \{\xi_2 = 0 \} } = 2 = \dim M \,, \\
{\widetilde \omega} |_{\widetilde M} = ( 2 \xi_2  d \xi_2 + dt )\wedge dx_1  \ \
\dim \ker {\widetilde \omega} |_{\widetilde M} = 1 \,.
\end{gather*}

A complicated example from the physics literature comes from \cite[\S 5]{GHW}.
If one considers $ M \subset V = H^1 ( {\mathbb R} , {\mathbb C} ) $ given by
all sums of time-modulated solitons and time modulated nonlinear ground states
(see \cite[(5.1)]{GHW}),
\begin{gather}
\label{eq:ghw}
\begin{gathered}
 u(x) = u_S (x; \eta, Z, V, \phi) + u_D (x; a, \phi, \psi) \,, \\
u_S ( x  ; \eta, Z, V , \phi) \stackrel{\rm{def}}{=}
\eta \,  \textnormal{sech} ( \eta x - Z) e^{ i Vx - i \phi} \,, \\
u_D (x; a, \phi, \psi) \stackrel{\rm{def}}{=}
 a \, \textnormal{sech} \left( a x + \textnormal{tanh}^{-1} \left(\frac \gamma a\right)\right)
e^{ - i ( \phi + \psi ) } \,,
\end{gathered}
\end{gather}
then in the reduced six dimensional space described by $ ( \eta, Z, V , \phi,
a, \psi ) $ is {\em not} symplectic with respect to $ \omega $ given by
\eqref{eq:omega}. This can be checked by computing the determinant of
a matrix corresponding to $ \omega |_M $ -- see Fig.\ref{f:2}.
Despite that the method of collective coordinates is used by the
authors in constructing an effective Lagrangian \cite[(5.4)]{GHW}
and it is then used to obtained approximate equations of motion
\cite[(5.9)]{GHW}. It is numerically
shown to give a good agreement with the solution of the equation.

\begin{figure}
\begin{center}
\includegraphics[width=5.5in]{plot1s}
\end{center}
\caption{The plot of $ \det ( \omega|_{M \cap \{ V = Z = 0 \}}  ) $ for $ \gamma = 0.1 $ (in the notation of \cite{GHW}), $ \phi = 0 $, $ \psi = \pi/4 $,
$ 0 < \eta < 1.2 $ and $ 0.11 < a < 1.2$. The two lines along
which $ \omega|_{M \cap \{ V = Z = 0 \} } $ is degenerate are clearly visible.
The restriction to $ Z = V = 0 $ is not essential since these two variables
are essentially conjugate.}
\label{f:2}
\end{figure}

Finally we comment on the effective dynamics of solitons interacting
with slowly varying potentials. In \cite{HZ1} we followed \cite{FrSi}
and used a symplectic approach improving the results of \cite{FrSi}
and \cite{FrY} (same method apply to in that setting)
by obtaining equations of motion without errors and
obtaining a better accuracy of approximation by a moving soliton ($ h \rightarrow h ^2 $, where $ h $ is slowness parameter of the potential).
When attempting to reproduce these results using the Lagrangian
formalism we could obtain the same equations of motions (we later learned
that they were implicit in \cite{OS}), but could not obtain the
$ h \rightarrow h^2 $ improvement.

\medskip

\noindent
{\sc Acknowledgments.}
We would like to thank Alan Weinstein for suggesting Souriau's monograph
as a source of geometric interpretation of Noether's theorem and Lagrangian
mechanics.
The work of the first author was supported in part by an NSF postdoctoral
fellowship, and that
of the second second author by the NSF grant DMS-0654436.

redpajama_set_name: RedPajamaArXiv


Immigration is rapidly transforming Western societies. Classic immigration countries, such as Australia, Canada and the United States, are again experiencing large-scale immigration. France, Germany, Great Britain and other European countries are becoming immigrant societies. In both old and new immigration countries, there is deep concern among policy makers and social scientists about the integration of the foreign-born population. Van Tubergen argues that comparing immigrant groups within and across countries provides keen insights into immigrant incorporation. Compiling a unique data set, van Tubergen analyzes immigrant's employment status, occupational status, self-employment, language proficiency and religion in 19 Western countries. Findings show that immigrant integration differs across receiving nations and across sending nations. Results also suggest that the ethnic community is important: some groups are particularly well incorporated in one country, but not in others. It is discussed how the role of immigrant's country of origin, the receiving nation, and the immigrant community can be understood with theories from sociology, economics, and demography.
Frank van Tubergen earned his Ph.D. in 2005 and is currently employed as an Assistant Professor of Sociology at Utrecht University, the Netherlands. He is affiliated with the Inter-University Center for Social Science Theory and Methodology (ICS) and the European Research Center on Migration and Ethnic Relations (ERCOMER).


One of the most commonly asked questions here at Mike Lewis Attorneys is what the rules are concerning driving and cell phone usage. It's hard to keep track when the rules change constantly, and no two states have the same regulations.
Bottom line: here in North Carolina, if you've been injured in an accident, and the driver who caused the accident was distracted by use of a cell phone, it was no "accident" and they are responsible for payment for your injuries.
Let's take a closer look at the cell phone usage laws in North Carolina and how they relate to car accidents.
Distracted driving is operating a motor vehicle while also engaging in some other task. This other task sometimes involves a cell phone. Obviously, if you are talking or texting someone, that counts as distracted driving.
But, there are other situations that apply. Reaching for your cell phone (even if your eyes are only off the road for a split second) can be counted as distracted driving. So can being distracted by a conversation you are having (even on a hands-free device) or a passenger's cell phone usage.
Drivers have one job when they are behind the wheel: operating the vehicle. Anything else you're doing in that car counts as a distraction.
Currently, in North Carolina, you are allowed to use a cell phone while driving. However, you are not allowed to text while the vehicle is in motion. The texting law is written such that an officer does not need to have any other reason to pull you over. They just need to suspect that you are texting.
Imagine if an employee of a company decides to make a work-related call while driving, or sends a work-related text, and then causes an accident. Not only are they at fault for the accident, the company itself may share in the liability. This is why so many companies today have bans on employee cell phone use while driving.
Also, in North Carolina, minors are not allowed to use any device while driving. This includes both handheld and hands-free devices. There have been legal cases where it was argued that the parents of a distracted minor driver were responsible because they gave the phone to the child, who then caused the accident.
Yes, you can! If you are seriously hurt in an accident that another driver caused, and the other driver was using a phone when the crash occurred, they are responsible for the injuries. It's not just the medical bills and the damage to your car; it's also pain, suffering, and lost wages from work.
Anytime you sustain an injury in an automobile accident, whether the accident was caused by a distracted driver or not, you need to find an experienced attorney who can help you figure out an appropriate level of compensation. Do not trust the insurance companies to look out for your best interests. They want a quick settlement for the lowest possible amount.
In the Triad area, Mike Lewis Attorneys are your go-to lawyers in case of an accident, especially if you've been in a car accident caused by cell phone usage on the part of the other driver. Mike Lewis Attorneys have the experience and the skill to help you during a difficult time. The case consultation is free and you do not pay unless you win the case. Simply use the online contact form and a member of the Mike Lewis team will be in touch.


text:
Audio Download 2019
Unexpected Lessons in Love
Imprint: Transworld Digital
The heartwarming Sunday Times bestseller
'Real, heart-breaking - I loved it.' Katie Fforde
'My heart is smashed and repaired for reading this wonderfully romantic and strong piece of fiction.' Milly Johnson
What happens when 'I do' turns into 'I don't know'?
Jeannie always wanted to fall in love, and now she's finally got the whirlwind romance she dreamed of. Dan's gorgeous, he's a successful young vet, and he flew her to New York and proposed on Brooklyn Bridge. Jeannie has to remind herself this is actually her life. It seems too perfect, too magical, to be real. Yet it is.
But now she's on her way to the wedding she can't shake off the tight sensation crushing her chest. Is it just nerves . . . or is this all happening a bit too fast?
Jeannie has one last chance to shout, 'Stop!' But just as she grabs it, a twist of fate throws everything she knows into the air like confetti. What Jeannie learns about Dan, about her own heart, and about the power of love itself, will change her world for ever . . .
Readers adore Unexpected Lessons in Love
***** 'An absolute delight . . . I enjoyed every moment.'
***** 'I couldn't put it down. Lovely story about finding love and being honest with a little twist.'
***** 'A story of family, friendship, loyalty, relationships and new beginnings. This book made me smile but also broke my heart.'
'Real, heartbreaking - I loved it'
'My heart is smashed and repaired for reading this wonderfully romantic and strong piece of fiction.'
A glorious tangle of cold feet and mixed messages, Unexpected Lessons in Love is a heartwarming romantic comedy that tells us to be brave and to listen to our hearts. Suffused with Lucy's trademark warmth and gentle humour (with a splendid canine supporting cast), it's sure to win your heart. Irresistible!
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'Such a great 'what would you do?' book about love, truth, friendship and of course dogs. Kept me guessing all the way.'
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Lucy Dillon's books never fail to make me happy.
Where The Light Gets In
Sunday Times bestselling author Lucy Dillon grew up in Cumbria and read English at Cambridge, then read a lot of magazines as a press assistant in London, then read other people's manuscripts as a junior fiction editor. She now lives in a village outside Hereford with a Border terrier, an otterhound and her husband. Lucy won the Romantic Novelists' Association Contemporary Romantic Novel prize in 2015 for A HUNDRED PIECES OF ME, and the Romantic Novel of the Year Award in 2010 for LOST DOGS AND LONELY HEARTS. You can find out more at www.lucydillon.co.uk, follow her on Twitter @lucy_dillon, on Instagram @lucydillonbooks or find her on Facebook at www.facebook.com/pages/LucyDillonBooks.

redpajama_set_name: RedPajamaCommonCrawl


text:
Make Disciples – Part 1, Discipling a Nation
Church historians sometimes call the 19th Century the missionary century. Following William Carey's publication of An Enquiry into the Obligations of Christians to Use Means for the Conversion of the Heathen in 1792, and his subsequent move to India the following year, hundreds followed Carey in obedience to the missionary call. They travelled to Africa and Asia and South America and to the remote islands of the South Pacific Ocean. Those who survived became legends and heroes of subsequent generations. David Livingstone and Hudson Taylor, Adoniram Judson, John Paton and Lottie Moon are among those we revere.
But of all the 19th Century missionary endeavors, none was as successful as the effort to evangelize the young, expanding nation called the United States of America (Kenneth Scott Latourette, A History of the Expansion of Christianity, vol. 4; also Andrew Walls, The Missionary Movement in Christian History, 227). Rodney Stark documents how this happened in his excellent book The Churching of America. In summary, the United States was churched, not so much by missionary heroes, as by ordinary believers, some of whom were preachers, who evangelized and planted churches as the nation grew to the west. The most successful of these were the Baptists because they were not stymied by denominational polity or steep educational qualifications.
So what did those 19th Century pioneers do to reach the United States for Christ? Simply put, they discipled the nation. Every church leader knows the Great Commission. Or do they? What comes to mind when you hear the term "Great Commission?" If you've studied Matthew's version you know that the key verb is "make disciples," and it is an imperative verb, a single word in the original language. The command is to "disciple all the nations" (Matthew 28:19).
Think about that command – "disciple all the nations." What does that mean? How do you do it? What does a discipled nation look like? Many have understood the command to mean that we are to make "some" disciples from among all the "people groups" in the world. But is that what it means, or does it mean that we are to do precisely what it says – "disciple all the nations?"
Personally, I have never been convinced that our evangelism and missionary strategies should be fashioned so as to "win at least a few converts" from among all of the many thousands of nations (people groups) in the world, so that each will be represented around God's throne in glory. Yes, all the peoples of the world will be represented before the throne, and this will be a "great multitude that no one could count" (Rev. 7:9). But the Scripture also says of God that "He is patient with you, not wanting anyone to perish, but everyone to come to repentance" (2 Pet. 3:9b). That means that God doesn't want a single individual to perish, not one.
I don't intend by this to disregard or lessen in any way those who are spending their lives among isolated peoples, in difficult places, sharing Christ and spending their lives so as to see the first converts from among an unreached people. These missionaries are my heroes and should be supported and encouraged in every way. They are doing the incredibly hard work of going from zero believers to one believer, and zero churches to one church. I'm simply saying that in our preaching and strategizing we should strive to share the gospel with every single individual, in every house and hut, on every hill and in every valley, and in each language spoken on the earth. If 90 percent of the people of a nation have heard the gospel, but my loved ones are among the 10 percent who have not heard, that is a personal disaster which would cause me to deeply grieve because the destination of a person without Christ is hell.
I'll address in a subsequent article how "discipling all the nations" can be applied to a local church or individual, but let's think first about how the United States became a discipled nation (Note: To say that a nation is discipled is not to say that it will remain discipled. Historically many nations were once more discipled than they are at present, including the United States).
In large measure the first Europeans that moved to the land that became the United States were Christians. They weren't all Christians, but they certainly weren't Hindus or Muslims or Zoroastrians. The governing document of the Pilgrims, the Mayflower Compact, stated that they had undertaken "for the Glory of God, and advancements of the Christian faith." Early on, men like John Elliot sought to evangelize Native Americans. The early immigrants were largely a Christian people. I don't mean by this that they all knew Jesus. I simply mean that our nation was largely settled by a people with a Christian background.
When the First and Second Great Awakenings happened in the 18th and 19th Centuries, many colonists and Americans were spiritually converted to faith in Jesus Christ. Differently than converts in Saudi Arabia or India today, however, these early American converts did not "leave" a religion and join a new religion. In many cases they came to a saving faith in the God they already claimed to confess as God.
As the new nation migrated westward, believers did as well. Along the famed Oregon Trail were Christians like David Lenox, who, finding no church where he settled, started one in his cabin west of present day Portland, OR. Lenox was not a preacher, but a Baptist layman who founded the first Baptist church west of the Rocky Mountains on May 25, 1844. Twelve years later there were 26 Baptist churches in Oregon, not because of missionaries sent from the East, but because of laypeople and preachers who started churches wherever they settled.
Evangelizing people and starting churches are the first steps toward discipling a nation. Then, in the United States, schools, and even hospitals, were soon started by Christian settlers. In Portland, OR, Rev. Horace Lyman and Rev. N. Doane were among those who started schools in the early years. A Google search of the first schools in most any town, universities included, will reveal that most of the first schools in the Colonies and in the U.S.A. in the 17th, 18th, and 19th Centuries were founded by Christians. The same is true of hospitals, orphanages, anti-slavery organizations, and temperance societies. Thus, I would propose that the United States became a "discipled nation" because churches were founded, and these churches moved out from the church to begin schools and other organizations that benefited the communities and furthered the mission of the churches. Churches penetrated their communities and transformation occurred as a result.
What does this mean for your church and your community? How do you disciple your community? How do you disciple a church or and individual? These are questions we will explore in subsequent articles.
Tags Baptist, church, Church planting, evangelism, gospel, Leadership Training, Making disciples, missions, Northwest Baptist Convention, Pastors, Rodney Stark
Northwest Baptist Update as We Begin 2017
Make Disciples – Part 2, Discipling a community
2 thoughts on "Make Disciples – Part 1, Discipling a Nation"
Randy this is one of your finest blogs, and they are all great. Loved it.
Thank you Mark!
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text:
Loyola recruit Mike Herlihy looks to play the heavy for Lincoln-Way East in middle
By Logan Malloy
Daily Southtown |
Lincoln-Way East's Mike Herlihy (14) is one of the two Loyola recruits on the roster. (Brian O'Mahoney/Daily Southtown)
There's no need for a countdown. Mike Herlihy already has liftoff.
It took about two years for the 6-foot-6 senior to skyrocket into the volleyball stratosphere, going from a relative unknown to blue-chip recruit, but Lincoln-Way East knew what it had.
"We knew Mike was going to be good early — you saw the raw skills," East coach Kris Fiore said. "Now he's there. He's got all the shots."
It doesn't hurt when you're blasting spikes from heights that few can match. Herlihy rocks nearly an 11-5 touch.
"I'd probably do a 360 slam," Herlihy said when asked what he'd show in a dunk contest. "I started for the varsity basketball team as a sophomore, but going into junior year, I made the decision to stop playing.
"I thought I could go further in volleyball."
Smart choice.
Herlihy put himself on the map with a dominant postseason last spring while matched against some of the top middle hitters in the state. In the process, he helped lift Lincoln-Way East to the state finals in front of a number of college scouts.
The Griffins eventually fell to Glenbard West — now the three-time defending state champion and one of East's biggest obstacles this season. But Herlihy showed enough at state to land a scholarship from Loyola, the 2014 and 2015 NCAA volleyball champion.
"They were one of the first schools to reach out to me," Herlihy said. "I'm stoked they're in the NCAA basketball tournament. Obviously, I'm choosing them to win the whole thing."
Can East do the same?
If the Griffins are to celebrate in June, they'll need Herlihy and an imposing front line to control the net.
Lucky for the Griffins, a trio of middle hitters — Herlihy, Luis Zavala and Wil McPhillips — might be the best in the state.
Zavala led the team in blocks last season, while McPhillips looks primed for a breakout season.
"This will be the best blocking team we've ever had," said Fiore, who guided the program to the 2014 state championship.
McPhillips, a junior, already has an offer from two-time reigning NCAA champion Ohio State, which seems to know the area well. Ohio State's starting lineup features former Southland standouts Sanil Thomas (Andrew) and Jake Hanes (Sandburg).
East's depth and athleticism at middle hitter is a major reason expectations are high. Another reason is outside hitter Ian Piet.
Piet, a player of the year candidate and East's top attacker last season, plans to join Herlihy at Loyola.
"We're here to win state, obviously," Piet said. "Go as far as we can. Top last year."
Piet expects tough outs from Brother Rice and Lincoln-Way West, and as usual, the team that ended their season in three games.
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"Glenbard West graduated a lot of seniors, but I'm sure they're going to be good because they always are," he said.
Piet's jump serve will be among the best in the area and, matched with East's imposing block, should keep teams out of system.
And while there's some uncertainty at setter with three players battling to get into the 6-2 rotation, confidence brims elsewhere.
Daily Southtown Local Scoreboard for Sunday, Jan. 19, 2020
'He accepted the challenge': Terrance Ford takes control as Leo pulls off comeback win over St. Laurence
Gabby Beggs powers Argo to rout of Oak Lawn in front of big crowd: 'It was great that everybody came out to support us'
'Scoring for us is contagious': Juan Avila sparks Oak Forest to easy conference win over T.F. South
Atharva Atreya scores career-high 30 points as Sandburg slips past Stagg: 'I was a little more jacked up than usual'
George Kougan, a 6-7 opposite, bolsters the attack and gives East another dangerous hitter. Mark Wroblewski, a 6-4 outside hitter, should provide a little of everything.
"Mark's probably the biggest hustler on this team," Herlihy said. "People sleep on him."
Nobody's sleeping on East, though.
Logan Malloy is a freelance reporter for the Daily Southtown.


Lycopersicon esculentum f. pyriforme (Dunal) C. H. Müll., Lycopersicon esculentum var. commune L. H. Bailey, Lycopersicon esculentum var. grandifolium L. H. Bailey, Lycopersicon esculentum var. pyriforme (Dunal) L. H. Bailey, Lycopersicon esculentum var. validum L. H. Bailey, Lycopersicon lycopersicum (L.) H. Karst., Lycopersicon lycopersicum var. cerasiforme auct., Lycopersicon lycopersicum var. pyriforme auct., Lycopersicon pyriforme Dunal, Solanum lycopersicum L.
Tomato seeds, a by-product of tomato processing (cannery, tomato paste, tomato juice, etc.), contain about 20-25% of an edible oil rich in linoleic acid (50-60%) and cholesterol (Lazos et al., 1998; Giannelos et al., 2005; Gunstone, 2006). The development of tomato processing in Italy and in the USA at the turn of the twentieth century led to an interest in tomato oil for soap-making and cooking, and in the use of tomato seed cake, the by-product of the oil extraction, in feeds and fertilizer (Rabak, 1917). Today, tomato seeds are usually mixed with the skins and pulp residue to make tomato pomace, and tomato seed oil has become a niche product, used notably in cosmetics. In recent years, there has been a renewed interest both in tomato seed oil for its nutraceutical properties and as a biofuel (Lazos et al., 1998; Giannelos et al., 2005), and in the protein of the seed cake, which is rich in lysine, and, when added to bread, improves loaf volume, texture and crumb quality, due to its anti-staling properties (Sogi et al., 2005).
Tomato seed cake has become a rare feed ingredient that should be available in regions where tomato seed oil is still produced. Production figures are lacking, but most of the recent research concerning tomato seed cake comes from Egypt (Anwar et al., 1978; El Moghazy et al., 1982; El-Din et al., 1997) and India (Rao et al., 1991; Sogi et al., 2005; Kaur et al., 2005).
Historically, the seeds were obtained after drying the pomace and separating the seeds from the skins and pulp using sieves and fans (Rabak, 1917). Newer processes may use a wet flotation and sedimentation system (Kaur et al., 2005). The dried seeds are then deoiled by mechanical extraction and, for a higher extraction rate, using a solvent. The resulting press cake is then ground (El Boushy et al., 2000).
Tomato seed cake is produced by different methods and its chemical composition is, therefore, variable. The deoiled oil cake was often mixed with the skins and other residues resulting in a product similar to the pomace but containing less oil, depending on the extraction rate (Rabak, 1917; El Boushy et al., 2000). True tomato seed cake has a high protein content (36-37%) as well as a high crude fiber content (22-28%). The residual oil content is in the 3-7% range and depends on the extraction process (Rabak, 1917; Anwar et al., 1978; Maymone et al., 1945; El-Din et al., 1997). The protein of the seed cake is rich in lysine (7% of the protein) but may be inadequate in methionine and cystine, especially for poultry (El Moghazy et al., 1982). Because of its high content of fibre, it is mostly used in ruminant feeding (Göhl, 1982).
Tomato seed cake, sometimes mixed with the pomace and molasses, was used to feed cattle in Italy in the first decades of the last century. Tomato seed cake was considered to be similar or superior to linseed cake for the feeding of dairy cows (Rabak, 1917). Like other tomato by-products, tomato seed cake has a somewhat bitter taste and should be used with more palatable feedstuffs. When first introduced, it should be sprinkled with salt and given in small proportions (Göhl, 1982). There have been no recent ruminant trials with tomato seed cake. Maymone et al., 1945 determined the OM digestibility to be rather low (55%), corresponding to a ME value of 9.2 MJ/kg DM.
Tomato seed cake contains large amounts of fibre, is deficient in methionine and should not be given to poultry at rates above 15%. Its ME value is quite low (6.49 MJ/kg DM). Feeding broiler chicks with a diet containing 34% defatted tomato seed cake depressed feed conversion and their performance (final body weight and average daily gain) was lower than those fed a diet containing cottonseed meal. The protein value of tomato seed cake-based diets benefited from the addition of DL-methionine (Anwar et al., 1978).


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text:
Swansea Council
Coroner orders independent expert to examine Swansea's Kingsway
A second pre-inquest review into the death of Daniel Foss on Swansea's Kingsway has heard an outside expert will examine the road's lay-out
Robin Turner
Daniel Foss, 37, from Reynoldston, Gower, who died after an incident on Kingsway in Swansea
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A coroner has ordered an independent highways expert to consider whether the "unconventional lay-out" of Swansea's controversial Kingsway played a part in the death of Gower hotel worker Daniel Foss who was hit by a bus on the city centre road in September 2013.
Speaking at a second pre-inquest review into 37-year-old Mr Foss's death, Colin Phillips, Swansea's acting senior coroner, said bus company First Cymru raised concerns with Swansea council about the safety of pedestrians on the road as early as April 2011.
At an earlier pre-inquest review into Mr Foss' death, Mr Phillips said people were "looking the wrong way" in a number of incidents on the Kingsway where popular Cardiff police sergeant Louise Lucas died and her eight-year-old daughter was injured after a collision with a bus in March.
The Kingsway traffic system, previously labelled "counter-intuitive" by Mr Phillips, had two lanes of normal traffic travelling west on one side of the road, with two lanes of public transport – one going east and one west – on the other side.
After Sgt Lucas' death, east-bound traffic was stopped and safety barriers were put in place along the Kingsway.
Swansea council said it had earlier placed a 20mph limit on the road and had increased signage.
Mr Phillips, who now hopes a full inquest into Mr Foss' death can begin in September, said: "I feel there is a need for an independent expert to consider if the unconventional lay-out of both carriageways of the road may have contributed to the death of Mr Foss."
He also said he wanted to know if adequate warnings to pedestrians were given "in a timely manner" and he wanted a review of the efficiency of road safety auditing regarding the road.
Barrister Simon John, representing Swansea council, questioned the need for an independent highways expert at the full inquest, but Mr Phillips said: "I'll order one".
He said he expected to get an independent expert's report within 28 days.
Deadline set
A representative for Mr Foss' family backed the need for an independent examination of the Kingsway road lay-out saying "an objective view" was required for the full inquest hearing.
Mr Phillips told the hearing that bus company First Cymru had raised concerns about the safety of pedestrians involving east bound buses in a letter to Swansea council on April 8, 2011 and that subsequently, an independent safety review of the road network was commissioned.
He asked Swansea council to provide him with the findings of the safety review which followed First Cymru's concerns by June 12.
He also asked for annual safety reviews of the city centre road network in Swansea to be provided by the same date.
Council representative Mr John said the annual safety reviews looked at the road network in the centre of Swansea as a whole and there were unlikely to be specific break-downs for the Kingsway but he said the authority would do its best to find the information in the coming days.
Following Sgt Lucas' death in March, Mr Phillips sent a Regulation 28 report (under Coroners' Rules) to Swansea council urging the authority to make urgent changes to the road layout.
He said at the time that the road had a "serious design issue", which "must be addressed" by Swansea council and he pointed to a number of previous incidents on the road including a number of "near miss" events.
CourtsMan stabbed friend so deeply knife blade scratched his boneJohn Layton 49, wounded friend Philip Christie at a hostel in Barry after the two became involved in an argument
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Health Check WalesNuffield Health secures national award for its high standards in treating bones and jointsNuffield Health Cardiff and Vale Hospitals offer a tailored programme for hip and knee replacement patients


The entrance should have a doorbell or knock, eye holes and a sign on your house. Always keep your front door shining. Wooden furniture as box furniture, mirror frames, and cabinets you can plan to fill your home. The room towards your front door must have a friendly and not boring appearance. You can remodel bathroom wall decor picturespictures for bathroom wall decorpictures of bathroom wall decor. When decorating a home, the key is not to make the environment too excited, incorporating the use of calm colors will be a good alternative to bold prints, the furniture chosen for the house is also very important, an efficient table is usually the main work chosen, comfortable chairs important items too. Adding decorative shelves to the wall is a great way to display collections, knick-knacks or photographs, wooden shelves can be stained or painted, or you can choose a wrought iron shelf.
Equally important is the chair. The most prominent furniture from the dining room is the dining table, therefore, it is very important to choose a dining table that suits your taste and lifestyle. The color of the chair must match the color of the dining table equipment to create a sense of color coordination in the room, the color red, said to stimulate appetite.Glass table matches a small room because it gives the illusion of spaciousness. For large families with many children, a table that is easy to clean is the best, also must be safe for children so that the glass table is not recommended so a round table and wood are recommended.
Make sure that the kitchen table is large enough, the kitchen table surface is also important, a table with a waterproof surface is preferred this is the same as we would choose a kitchen chair.Make sure kitchen furniture is made of the right ingredients. You might need a kitchen cabinet. The wood that has been used must be of high quality, check to make sure that the wood does not have knots, sanding marks, or grain irregularities. Having the right furniture will make it easier for you to do kitchen work comfortably, you might need a few kitchen chairs, kitchen trains, tables, bar stools and shelves. Start by checking the cabinet face, these are the parts that are visible from the front of the cabinet.
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Anxiety and Shame Getting in the Way?
Avoiding situations due to fear of being judged or humiliated?
Unable to accomplish your goals?
Spending 24/7 second guessing your decisions?
even after you've been told you did a great job?
I will collaborate with you to enlist your mind and your body to be agents of change.
I offer a holistic approach to healing that incorporates talk therapy, mindfulness and sensory awareness; you'll practice using your breath to slow down and make space for reflection and being present; this is the place where change takes hold. Slowing down allows you to notice your thoughts and how your body processes stress. You will learn how to intervene when triggers arise. Our journey will enable you to identify beliefs that often get in the way of change; you'll learn to assess what's fact and what's fiction.
Let's make anxiety be a place you visit rather than your inevitable home.


Yesterday afternoon I went out with some of the old photographs to photograph the scenes and how they look like today.
I find it fascinating what has changed and what hasn't. What certainly isn't a change for the better are the road signs and cars. Not unique to Olhão I know since every city, town and village seems to be overwhelmed by both these days.
I have a quite a few more 'past and present' photographs to share especially of the area around the markets which have changed dramatically with the creation of the gardens and promenades. As with Monday's wildflower post I'll keep these additional photographs for another day.


Michael Hengstermann, born 1987, is responsible for marketing at IPM.
During and after his studies of business administration in Wiesbaden, Mr. Hengstermann worked as a sales assistant for the fleet division at Avalon Premium Cars in Kronberg im Taunus. From 2015 to 2018, he was then responsible for paid advertising at an online performance marketing agency in Hanover.


When most people see a rat on the street corner, they don't really think twice.
But a whole slew of people came to the aid of one very plump sewer rat in Germany.
The chubby sewer rat was found to be stuck in a sewer drain hole.
Apparently, he had been trying to squeeze through a hole in the sewer cap and got stucks when his big booty couldn't fit through.
This poor rat was seriously distressed.
I mean, look how scared this little guy looks.
It looks like he's screaming.
Thankfully passersby weren't about to let this pudgy guy sit there and suffer.
A local family called animal rescuers from Berufstierrettung Rhein Neckar for help.
When rescuers arrived they found that the rat was healthy and not hurt, but he was definitely stuck.
"He was in a really good condition," Andreas Steinbach, spokesperson for Berufstierrettung Rhein Neckar, told The Dodo.
Unfortunately, they couldn't safely pull him out since he was really stuck in there. So, they called for help.
These guys were the professionals and could extricate the rat safely without just yanking him through the hole and risk him being injured.
Once the husky rat was removed he was assessed and let back into his home that is the sewer system.
The firefighters lifted up the sewer cap and shimmied the rat back through the bottom of the hole.
Imagine so many people working to save a creature that many are repulsed by.
It was a truly beautiful thing.
His rescuers said that the rat seemed to be grateful for their efforts.
"He made a brief look back at us as if to say, 'Thank you — and yes, I know I need to go on a diet,'" Steinbach said.
The compassionate effort on behalf of the animal rescuers and firefighters seemed to win them fans.
The children of the family who called for help for the rat immediately ran up to the firefighters after the rescue.
They delivered hand-drawn pictures of the rat as thanks for their selfless efforts.
The firefighters were even treated to some doughnuts.
Some might say a fat rat's life isn't worth saving and isn't worth the trouble of the local volunteer fire department.
But no one on the scene that day thought this.
We happen to think that it's a beautiful story.
Even actor Ron Perlman said that this rat's life was worth saving.
"You watch, that rat will go on to do great things," he said on Twitter.


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Confident England look to dash South Africa's hopes
A semifinal spot virtually assured, in-form England would look to dent South Africa's hopes of reaching the last-four stage when the two teams meet each other in a high-voltage Group 1 Super 12 match of the ICC T20 World Cup here on Saturday.
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T20 World Cup 2022: India to face Pakistan in opening tie at MCG on October 23
Virat Kohli creates history, surpasses Sachin Tendulkar in THIS record list
With a net run rate of +3.183, England are more or less through to the semifinals with four wins from as many games, while South Africa are lying in the third spot with six points from four matches.
Both South Africa and Australia are in close race for the second semifinal spot from Group 1 but the Australians are above the Proteas on the basis of a better net run rate, though they have six points each.
It will all boil down to Saturday's game and South Africa will know what exactly they need to do before facing England as Australia play West Indies in the first match of the day.
The Proteas can't afford to slip even a bit and need a resounding win to keep their hopes alive.
But with form on their side, an ominous-looking England will definitely start as firm favourites against the Proteas.
After three consecutive wins over Bangladesh, Sri Lanka and West Indies, South Africa suffered their first defeat against Australia in their last match, putting questions on their campaign.
England would look to capitalise on it and finish off their group campaign with a perfect record. They have more or less ticked all boxes in their campaign so far.
England looked one of the best teams in the tournament other than Pakistan.
While it hasn't been a cakewalk in all the four matches, the Englishmen were clinical in their approach and somebody or the other stepped out to bail the team out whenever in trouble.
England's batting revolves around Jos Buttler, Jason Roy, Dawid Malan, Jonny Bairstow and skipper Eoin Morgan.
In fact, Buttler achieved two personal milestones in the last match — scored his maiden T20 century (101 not out of 67 balls) and also became the only English cricketer to hit centuries in all formats of the game.
And come Saturday, the opener would be high on confidence to do an encore.
Another good news for England is that skipper Morgan struck form in the last match, scoring 40 off 36 balls and shared 112 runs with Buttler.
On the bowling front, the spin duo of Moeen Ali and Adil Rashid have been excellent so far, while Chris Woakes, Chris Jordan and Liam Livingstone have responded well to the team's call in the pace department.
Uttarakhand Will Get More Tourists In 10 Years Than Last 100 Years: PM
Cruise drugs case: Aryan Khan appears before NCB to mark his weekly presence
Romeo force organises Rural sports Mela at Mendhar
Team India bowling attack was most challenging one for me, says SA batter Keegan Petersen
'Captaincy is not anyone's birthright': Gambhir uses stern words for Kohli's future; 'his role doesn't change one bit'
Report: US cancels vaccine maker's multimillion dollar deal


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text:
Kee Chan, PhD, MBA
The Art and Science of Health & Wellness
Email: keechanphd@gmail.com
LinkedIn: http://www.linkedin.com/in/keechan
Follow me on Twitter: @keechanphd
Subscribe to my YouTube Channel: keechanphd
PhD, Epidemiology and Public Health, Yale University, New Haven, CT
ALM, Finance and Management, Harvard University, Cambridge, MA
MBA, Executive MBA program, Quantic School of Business and Technology, Washington DC.
MS, Biology, University of California, San Diego, La Jolla, CA
BS, Molecular Biology, University of California, San Diego, La Jolla, CA
Certificate in Strategic Management, Harvard University, Cambridge, MA
Certificate in Social Sector Leadership, Berkeley-Haas School of Business, Berkeley, CA
Fellowship and Training:
Instructional Designer Certificate Program, Online Consortium Learning
Institute for Emerging Leadership in Online Learning
Pre-Doctoral Research Fellowship National Human Genome Research Institute (NHGRI), NIH, Bethesda, Maryland.
Agent-Based Modeling Certification, Institute of System Sciences and Health, University of Michigan, Ann Arbor.
AnyLogic Modeling Certification, AnyLogic, Chicago, IL
American Public Health Association (APHA) Maternal and Child Health (MCH) Young Professional Award (2013)
Eric Mood New Professional Award by Yale Alumni Association (2013)
Research Interest:
Medical Decision Making
Infectious Diseases (HIV/AIDS, Hepatitis)
Public Health Genomics and Chronic Diseases
Strategic Management and Financial Analysis
About Kee Chan, Ph.D.:
Dr. Kee Chan is a passionate teacher of the science and management of health and wellness.
Her teaching interest includes the intersection of science and strategic planning, financial analysis, public health management, and medical decision-making analysis. Dr. Chan researches the comparative analysis of new biomedical intervention and testing on improving population health and its impact on healthcare services delivery. Dr. Chan is an expert on developing mathematical models to determine time-saving and cost-effective strategies in improving public health. Dr. Chan is an author a textbook on the"Advanced Management and Leadership in Improving Population Health". Interested in creating your own wellness plan, check out her planner titled "The Wellness Plan" (available on Amazon).
Academic Background:
She received her BS and MS in Biology from the University of California, San Diego (UCSD), and her Ph.D. in Epidemiology and Public Health from Yale University. To extend her interest in creating sustainable healthcare systems in the era of genomic information, Dr. Chan earned her Master's degree in Management at Harvard University. From 2002 to 2007, Dr. Chan conducted research at the National Human Genome Research Institute (NHGRI) at the National Institutes of Health (NIH). From 2009 to 2015, Dr. Chan served as a health economist and research investigator for the Center of Innovation (COIN) at the Department of Veterans Affairs (VA) in Bedford and Boston, MA. For the VA, she conducted business cases analysis and policy modeling on HIV, Hepatitis C, and cancer genomics. Dr. Chan is collaborating with researchers across the U.S. and internationally to evaluate effective public health programs.
Research and Policy Breakthrough:
Her significant contribution to society includes her development of a screening test to detect for T-cell receptor excision circles (TRECs) in newborns, in which the absence of TRECs is indicative of severe combined immunodeficiency (SCID) (Chan and Puck 2005). With screening, babies with SCID are identified early and can be saved by bone marrow treatment and live a healthy life. As of 2019, all the states in the U.S. have implemented newborn screening for SCID to screen for over 4 million babies. In the summer of 2015, Dr. Chan was invited to be a part of the European Expert Panel on SCID Screening in Vienna, Austria, to advocate the life-saving benefits of early screening and cost-savings to the healthcare system. Currently, UK, Israel, Netherlands, Taiwan, and Italy are implementing pilot programs to screen for SCID. Dr. Chan was a member of the Genetic Alliance Consumer Task Force on Baby's First Test, and together, they helped increased the awareness of genetic testing and newborn screening through grassroots efforts.
Popular Publications:
Dr. Chan has led workshops and written papers on professional development in several national forums. Published in the highly-acclaimed The Chronicle of Higher Education, her article on "Translating the 7 Effective Habits for the Classroom" provides a faculty guide on developing and teaching new academic courses. Dr. Chan is also an advisor on careers in science and public health. She has written papers on career advice for scientists, and her paper on "Bridging Your Research Into Public Health" describes effective tips on navigating through the transition (Chan, Science 2012).
Public Services:
Dr. Chan is currently a co-chair I'd subcommittee for improving pregnancy outcomes for the Maternal and Child Health (MCH) Section of the Association Public Health Association (APHA) and is an active member of the Society of Medical Decision Making (SMDM). She served as the event coordinator for the Massachusetts Chapter of the Association for Women in Science (AWIS) where she moderated workshops on negotiation, financial management, and book reviews. She is a member of the Board of Directors of the Association of Yale Alumni in Public Health (AYAPH). She is on the governing council of YaleWomen and is charged with creating a virtual chapter and has helped organize events for Yale alumni. Her paper titled "Our DNA Family Reunion", which illustrates the genomics basis of our humanity, was awarded the APHA Genomics Forum award in 2013.
Visit Dr. Chan's publications at Google Scholar Citations
updated 1/4/2021
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The unauthorized copying of copyrighted material, whether print or computer media, is illegal and is considered an act of academic dishonesty; moreover, such practice makes the violator subject to legal penalty.
Copyright infringement is the act of exercising, without permission or legal authority, one or more of the exclusive rights granted to the copyright owner under section 106 of the Copyright Act (Title 17 of the United Stated Code). These rights include the right to reproduce or distribute copyrighted work without authority constitutes an infringement.
Penalties for copyright infringement include civil and criminal penalties. In general, anyone found liable for civil copyright infringement may be ordered to pay either actual damages or "statutory" damages affixed at no less than $750 and not more than $30,000 per work infringed. For "willful" infringement, a court may award up to $150,000 per work infringed. A court can, in its discretion, also assess costs and attorneys' fees. For details, see Title 17, United States Code, Sections 504,505.
Willful copyright infringement can also result in criminal penalties, including imprisonment of up to five years and fines of up to .$250,000 per offense.
For more information, please see the website of the U.S. Copyright Office at www.copyright.gov, especially their FAQ's at www.copyright.gov/help/faq.


text:
Tumblin Dice Board Game
Introduction to Tumbling Dice Board Game
History of Tumbling Dice Board Game
Benefits of Playing Tumbling Dice Board Game
Tips for Winning at Tumbling Dice Board Game
Variations of Tumbling Dice Board Game
Where to Buy Tumbling Dice Board Game
Tumbling Dice Board Game is an enjoyable and exciting game suitable for all ages of family and friends. In this game, players need to roll their dice against their opponents in order to get a higher score. What's more, the stakes can be raised gradually as the participants become skilled at the game.
At its core, Tumbling Dice is a race game where each player must control their destiny by rolling their dice and managing which pieces go home first. Through strategic thinking and luck of course, players can manipulate the odds in their favor as they try to beat their opponent into submission!
One of the great things about Tumbling Dice is that it's easy to pick up and you're playing within minutes; rules are simple but building strategies can take time so there's something suitable for both casual gamers and strategy buffs alike! As well as testing your nerve against your opponent you'll also develop key strategies & critical thinking skills as you experience how much control you have over your own fates.
For those who would like a bit of visual help when learning how to play Tumbling Dice Board Game, there is a demonstration video online or other graphics locatable online that helps in showing the best way to approach the game. So don't hesitate — hop into an exciting world of racing chance with friends and family today!
Tumbling Dice Board Game has been around for over 50 years and is currently one of the most popular board games in America. The game is closely related to Liar's Dice, a game that has its origin in ancient China and dates back to the 15th century. However, the modern version was developed in 1964 by James Brunot, an American mathematician and expert in probability theory. It was Brunot who developed the rules and system that made Tumbling Dice the game it is today.
The game first became available through Brunot's own company, Cheapass Games, though it now appears under many other names such as Cosmic Wimpout, Farkle, Zilch, Greed, Hot Dice and Dudo. As production increased so did popularity among Americans. Today there are dozens of versions of the game with different rulesets ranging from classic cribbage to unique creations like Midnight Madness or Vegas Challenge.
Tumbling Dice Board Game has become more than just a pastime"it's even made its mark on popular culture. From Terry Pratchett novels to movies like Die Hard with a Vengeance (where Bruce Willis plays Farkle), references to tumbling dice can be found all over pop culture today. This has added to its popularity and cemented its status as an accessible board game for people of all ages across multiple generations.
How To Make And Sell Board Games
Playing Tumbling Dice board game has many health benefits. It is growing in popularity due to its strategic elements which call for exercising of social and problem-solving skills. Additionally, playing board games can improve cognitive functions thanks to its stimulating puzzles. Board games provide a unique way to socialize, allowing players to interact with one another and build relationships. This communication helps improve teamwork as well as decision-making skills. Additionally, it stimulates mental agility making it easier for individuals to challenge their own boundaries when it comes to logical thinking and understanding analytical concepts. Furthermore, playing board games can reduce stress levels as they engage the players entirely in the game and allow them to take a break from reality by focusing on something fun he or she enjoys doing instead. Board games are a great activity that can be enjoyed at any age, making it a good choice when looking for leisure activities.
Strategies for winning at Tumbling Dice Board Game include intelligently and strategically moving pieces around the board with each roll of the dice. This means analyzing all possible moves to ensure you are making the best possible decision. Memorizing important facts such as which locations on the board that are beneficial, or even detrimental is also a great way to increase your chances of success. Seeking advice from experienced players can be an invaluable resource when exploring winnable strategies. Additionally, keeping emotions in check and not allowing yourself to become frustrated when losing is a key tip to help you stay focused and motivated to keep playing. Finally, something simple such as researching the rules in advance can go a long way towards helping you understand the game better and more fully utilize its features. Overall, Tumbling Dice is an exciting strategy-based game; incorporating these tips into your play will help increase your odds of victory!
Alternative Rules
1. Counting Points: Instead of competing to pick up all the dice, the focus is on playing with the most skillful hand. Points are counted based on how many pips are shown between each player's throws.
2. Tumble Ladder: The objects of the game is to move all of your pieces up two stairs at a time while blocking opponents from doing the same by knocking their pieces off as you make your climb.
3. Joker Rules: For an extra challenge, include jokers in the mix and allow for one joker per person for each turn. The goal is to collect 5 points through combinations of luck and skill in either a game or tournament play mode.
4. Chain Rulez: Instead of rolling separately, players must roll all five dice together and score points for each successful pair rolled along with penalty points if any matching pair fails to be found in that particular turn.
Best Board Games For Adults 2 Player
5. Team Competition: Formulate teams of two or three players and compete alongside other teams in tournament rounds among larger groups of competitors!
6. Bonus Die: A bonus die can be included as part of a variant set or randomly drawn during regular gameplay rounds to further complicate strategies when trying to secure five out of six different numbers needed to beat an opponent's total score overall winner!
Tumbling Dice Board Game is a fun, 2-4 player game for all ages. It focuses on strategy and luck as players try to win the most chips by rolling their dice and navigating the board. The brightly colored board and madcap challenges bring an added dose of excitement to every round.
If you're looking to purchase Tumbling Dice Board Game, there's no shortage of options! You can buy it online from retailers such as Amazon and Walmart or in store from specialty game shops, department stores, and toy stores. Shopping around is the best way to find competitive prices and special offers – discounts like free shipping or exclusive content can make a big difference in your final cost when making a purchase. Additionally, some sites offer bundle packages that include other board games at discounted rates. Of course, if you are hoping to nab a present for any special occasion, ensure you check the delivery times beforehand; holding out for those timely specials could save you money long-term.
Tumblin Dice board game is a great game for all ages. It is fun and yet challenging enough to keep players engaged, as it requires strategy and critical thinking skills in order to be successful. This game also has important life lessons relating to teamwork and trustworthiness, further making it a valuable asset for families and friends of all kinds. For those looking for a bit of mental stimulation while still having an enjoyable time, Tumblin Dice certainly offers up that perfect combination of both!
Overall, this board game is worth playing as it provides a fantastic way to pass the time with friends or family members while still engaging in an interesting activity. Whether you're simply spending quality time together or attempting to outwit each other Strategy-wise Tumblin Dice has something to offer everyone! Its underlying message of working together and keeping your word resonates with most people, making it a usable tool for sparking conversations we wouldn't otherwise have. A quality pastime, full of fun and learning alike " who wouldn't want in?
Board With Pegs Game
Board Games For A Crowd


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Baylor > ECS > Undergraduate Programs > Computer Science > ACM Programming Contest
The ACM-ICPC Programming Contest Web Site and management is hosted by Baylor University. The contest is the world's largest academic problem-solving competition. Each year, teams from over 1100 of the world's most prestigous universities in 75 countries compete in regional contests throughout the world for regional championships and the privelege of advancing to the World Finals. There they compete for bragging rights, prizes, and scholarships.
The Baylor School of Engineering and Computer Science, the 1982 world champion, is proud to work with ACM and IBM in bringing this event to the academic world. Directed for over a decade by Dr. William B. Poucher, Professor of Computer Science, the contest encourages thousands of the world's most talented students to develop their problem-solving acumen, programming skills, and team work on the stage of this grueling competition. While under Dr. Poucher's direction, sponsors have directed over $60,000,000 in computing resources, scholarships, travel funds, technical assistance, and media relations to the universities that compete in the ACM International Collegiate Programming Contest.


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Will Eating Bananas Prevent Coronavirus Infection?
Bananas are a good source of various nutrients, but eating them doesn't offer solid protection against COVID-19.
Image via Brent Hofacker / Shutterstock
Eating bananas is a preventative against the COVID-19 coronavirus disease.
Amidst the plethora of misleading preventatives and cures for the COVID-19 coronavirus disease offered online during the pandemic of early 2020 was a video posted to Facebook that suggested consuming bananas could ward off infection by the novel coronavirus:
However, the video did not stem from any reputable news agency, nor did it offer anything documenting that the consumption of bananas was an effective preventative against COVID-19. It misleadingly combined clips from a January 2020 ABC Australia news segment and a February 2020 Wall Street Journal news video about efforts by scientists at the University of Queensland and the National Institutes of Health to develop a coronavirus vaccine, interspersed with added inserts and overlays about bananas that touted the supposed health benefits of the fruit, as follows:
Bananas are one of the most popular fruits worldwide. such as Vitamin C. All of these support health. people who follow a high fiber diet have a lower risk of cardiovascular disease. Bananas contain water and fiver, both of which promote regularity and encourage digestive health. Research made by scientists and the University of Queensland in Australia have proven that bananas improve your immune system due to the super source of Vitamins B-6 and helps prevent coronavirus. Having a banana a day keeps the coronavirus away.
It is true that bananas, consumed in moderation, are fairly good sources of fiber, dietary potassium, vitamin B6, and vitamin C, all of which are important components of a healthy diet.
However, other than contributing in a modest way to general good health, the consumption of bananas does not specifically do anything to "prevent coronavirus," nor have scientists at the University of Queensland asserted any such claim.
The most effective methods to protect yourself against contracting COVID-19 do not involve eating any specific food, but rather maintaining a safe distance from others who might spread the virus to you and regularly following basic sanitary/hygienic procedures:
o Wash your hands regularly for 20 seconds, with soap and water or alcohol-based hand rub
o Avoid close contact (1 meter or 3 feet) with people who are unwell
o Stay home and self-isolate from others in the household if you feel unwell
o Don't touch your eyes, nose, or mouth if your hands are not clean
WebMD. "The Health Benefits of Bananas."
3 February 2017.
Ferguson, Vicky. "Ask the Dietitian: Bananas Do Contain Some Vitamin C."
The Grand Rapids Press. 13 October 2010.
World Health Organization. "Basic Protective Measures Against the New Coronavirus."
Accessed 22 March 2020.
National Institutes of Health. "Potassium."
Ipatenco, Sara. "How Much B6 Is in a Banana?"
SFGate. 26 October 2012.


The collections contain over 40 000 works. Here are a few tools for grouping the material.
Browse the works by type.
Choose decade here, works starting from 15th century.
The collections of Finnish National Gallery contains sketchbooks too. Find published sketchbooks below.
The keywords describe the key contents of the works in the Finnish National Gallery's collections.


text:
package org.apache.struts.taglib.logic;

import javax.servlet.jsp.JspException;

/**
 * Evaluate the nested body content of this tag if the specified variable
 * and value are equal.
 *
 * @version $Rev$ $Date$
 */

public class EqualTag extends CompareTagBase {

    /**
     * Evaluate the condition that is being tested by this particular tag,
     * and return true if the nested body content of this tag
     * should be evaluated, or false if it should be skipped.
     * This method must be implemented by concrete subclasses.
     *
     * @exception JspException if a JSP exception occurs
     */
    protected boolean condition() throws JspException {

        return (condition(0, 0));

    }

}

redpajama_set_name: RedPajamaGithub


Welcome to the Wolds Day Nursery at Stragglethorpe. We are extremely proud of the high quality day care we offer and are confident that you will be delighted with the level of service provided from our leadership team.
Located between Radcliffe- on-Trent and Cotgrave, set in the beautiful woodland grounds behind the Shepherds restaurant, our nursery is a single story, purpose-built facility providing a bright, airy, homely and secure environment.
There is a large parking area for parents, alongside a 'pocket park and ride', with regular buses going to West Bridgford and Nottingham.
All the staff are friendly, caring, supportive and good fun :-). The children get to experience so many activities and the opportunity to develop in a lovely environment including exploring the surrounding facilities and countryside. The food they provide is excellent home cooked and well balanced.
Wow! A beautiful setting with wonderful staff. I have absolute confidence in leaving my little boy in their capable hands every day. He is always happy when I leave him in the morning, which is a good sign. Can't praise it highly enough & I's so pleased we found you!


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· Published May 31, 2020
Paid Rioters? Infiltrators Evident in Cities Across America
By Faye Higbee
We've written about this kind of situation before. Ferguson, Missouri; Baltimore, Maryland; Portland, Oregon; Charlottesville... Antifa and other left wing groups infiltrate the legitimate protests and work to increase the violence to create chaos. Their agenda is destruction of everything America stands for. And there are Antifa members inside what has been occurring all across the country. Some who have infiltrated are paid rioters.
It is not a "protest" it is a coup attempt, according to Dan Bongino, former Secret Service agent.
Surprisingly, even Keith Ellison, Minnesota's AG and a Democrat, has reported that he has evidence of outside influence in the rioting.
"We have evidence that outsiders have been present and, in some cases, have played a very negative role. But I've been talking with protesters and trying to get a sense of who some of these folks are and I've heard mixed things. Some of the negative stuff has come from people in Minnesota and some of it has come from people on the outside. What I'd say is we've got enough to handle on our own and that what we really need to do is refocus on justice for Mr. Floyd. And the negative behavior, looting, arson, does not help us achieve that goal." Keith Ellison
The legitimate protests over the death of George Floyd were hijacked…no commandeered… by Antifa and other leftist groups. Their purpose is to create destruction, kill cops, and take down this President. They do not care about communities or families…they want destruction. At least 3 are dead, businesses looted and destroyed by fire, and dozens of people injured so far.
Oh, and by the way, Biden campaign staff has been donating money to those posting bail for some of these losers (Fox). The Democrat Minneapolis Mayor has been giving out face masks to the rioters. There is a sad backwards thinking in Democrat circles.
Some of the peaceful protesters have become heroes in the midst of this mayhem by saving the lives of police officers just trying to keep the peace. We wrote about some yesterday from Louisville, Kentucky who formed a human chain around a lone officer who had become separated from his unit during the rioting.
Then there were the officers trying to arrest a person and were attacked by a violent mob, dragged, and protesters forced the mob back so that the officers could get up. Their injuries are unknown at this point. The suspect apparently didn't get arrested due to the violence of the mob.
This is brutal. Protesters had to come to the defense of the police against rioters. pic.twitter.com/iHhaSE1jhw
— Ian Miles Cheong (@stillgray) May 30, 2020
In 2016, MoveOn.org hired PAID agitators to protest Trump in various cities on an ongoing basis. The protesters were paid $15.22 per hour and someone would bail them out if they were arrested. Paid protesters bussed in from out of state is what Minneapolis and other cities are dealing with, and it's not peaceful in any sense of the word.
With the injection of Antifa, the situation becomes vicious and violent. Are they being paid again now to hijack the protests and create destruction? Antifa hates everybody. They don't care about you, your community, or the businesses you've built with your own hard-earned money.
In Minneapolis armed men stood guard over a business to protect it against looters. This is what needs to take place. People protecting their own against the thugs who are trying to destroy their community.
Lawful black firearms owners standing guard outside their businesses. https://t.co/UyV5uHw3cW
— Ezra Levant 🍁 (@ezralevant) May 28, 2020
"Those who participate in the destruction are just puppets." David J Harris Jr
David J Harris Jr. has something to say about what's been happening. Is this a coup against the President? Absolutely. Is this about George Floyd's death? Not even a little bit. The attention need to be refocused on his death and the attitudes of Minneapolis police – all police. But the rioting serves only to ingrain those attitudes, not remove them. That is what the radical left wants: to destroy the country. They have no desire to change the attitudes of police or bring peace.
A post shared by David Harris Jr (@davidjharrisjr) on May 30, 2020 at 12:51pm PDT
Featured photo: a weeping bar owner who poured his life savings into his business, only to lose it to rioters who destroyed it and even tried to steal his safe.
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Q: Using string template like eval I'm working with react/redux stack, and I have a section with dynamic state.
I have this structure
state:{formvalues:{email1:'',confirmEmail1:'',email2:'',confirmEmail2:'', etc }}

with dynamic emails,
I need to check if email1 is equal confirmEmail1 and the same thing for every mail.
I have found a solution with eval
v = `props.formValues.email${e} !== props.formValues.email${e}`;
eval(v);

And it work, but I cannot use the eval
I tried to use the template string in some differents way, but I have not found the solution,
I really hope that someone could help me,
Thank you very much for your help

redpajama_set_name: RedPajamaStackExchange


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