text:
Le Championnat de Turquie de football de deuxième division, actuellement appelé TFF First League ou plus couramment 1. Lig, est la deuxième ligue la plus importante du pays. Elle est l'antichambre de la Süper Lig.

Organisation
Trois équipes sont promues en , le Championnat de Turquie de football. Les deux premiers se qualifient directement, et une troisième équipe qui remporte une série de matches éliminatoires opposant les clubs classés , ,  et  du championnat accède également à l'élite.

Les trois dernières équipes du classement de cette ligue descendent au troisième niveau national, la Ligue 2 de TFF.

Au cours de la saison 2006-2007, Türk Telekom devient le sponsor de la compétition, qui prend alors le nom de . Cette dénomination évolue à nouveau pour la saison 2007-2008, la compétition devenant la . À la deuxième moitié du championnat, un nouveau sponsor fait son apparition, la Bank Asya, et la ligue prend le nom de . De 2012 à 2016, le championnat est nommé  avant de reprendre son ancienne appellation, la .

TRT Spor diffuse tous les matchs de la TFF 1st League.

Palmarès

Les champions du Championnat de Turquie de football D2 :

Bilan

Meilleurs buteurs

Notes et références


text:
Police investigate weekend shootings in South Bend
South Bend Tribune Report
SOUTH BEND — Police are investigating shootings that led to two people being hospitalized over the weekend in South Bend.
Shortly before 4 p.m. on Sunday, police responded to High Street in the Miami Hills Neighborhood for reports of a shooting. They found a female who had been shot and she was taken to the hospital with non-life-threatening injuries.
Police also responded to a reported shooting in the 900 block of East Corby Boulevard around 2 a.m. Monday morning.
According to an email sent to university students by the Notre Dame police department, the victim was walking near the intersection of Corby and Notre Dame Avenue when a man approached the victim, pointed a gun at him and demanded his belongings. The suspect then shot the victim in the leg, according to the email. The victim then threw his belongings and ran to get help.
The South Bend Police Department's Shooting Response Team are handling both on going investigations.
Officers also responded to Olive Street early Monday morning and found a car that had been struck by gunfire, though there were no reported injuries.
Police ask that anyone with information about either incident call Michiana Crime Stoppers at 574-288-STOP or the SBPD Investigative Bureau at 574-235-9263.

redpajama_set_name: RedPajamaCommonCrawl


text:
\section{Introduction}
Consider three identical bosons (or fermions with spin and isospin) that occupy a spatially symmetric
$s$-state. Efimov predicted in 1970 that the spectrum obeys a geometrical scaling law,
such that the ratio of the successive energy eigenvalues of the system is
a constant.\cite{efimov} This scaling results in an accumulation
of states near zero energy, with the size of the system growing larger by a factor of about $22.7$ for identical bosons for every state approaching zero energy. The number of these three-body bound states is infinite when the
dimer binding is zero. However, the number of
three-body bound states is actually reduced as the two-body interaction is made more attractive.
More remarkable is the fact that the Efimov effect is independent of
the details of
the interaction, for example, whether it is between atoms with a pair-wise van der Waals
interaction, or between nuclei with a nuclear force. The effect persists even with
unequal masses, as long as two of the three dimer bonds have near-zero binding.
These statements will be made more precise in the following.

A rigorous proof of Efimov's prediction followed in 1972.\cite{amado}
Recently, an analytical solution
for three identical bosons exhibiting the Efimov spectrum has been obtained.\cite{gogolin} Efimov examined the triton and
$^{12}$C (the latter as a bound state of three alpha particles) for manifestations of his prediction. However, for nuclear systems, the interaction between two nucleons cannot be adjusted to yield a two-body zero-energy bound
state. Also, the Coulomb potential between protons often restricts the examples for which two of the three
participants are loosely bound neutrons\cite{mazumdar} in the field
of a nuclear core. However, for ultra-cold neutral atoms with tunable
interaction strengths, these drawbacks are absent. The experimental observation of the Efimov effect was first made by Kraemer {\it et al.}\cite{kraemer} with an optically trapped
dilute gas of $^{133}$Cs atoms at 10\,nK. At such low temperatures, thermal motion does not mask quantum effects. Moreover, the two-body interaction between atoms may
be fine-tuned using ``Feshbach resonance.''\cite{fesh, cohen, chin}
Under such conditions, the recombination losses increase sharply due to
the formation of Efimov trimers, giving the experimental signature of the effect. More recently, Barontini {\it et al.}\cite{bar} have found evidence for two kinds of
Efimov trimers in a mixture of $^{41}$K and $^{87}$Rb; namely
KKRb and KRbRb.

Although there are excellent reviews of Efimov physics (see, for example, Ref.~\onlinecite{braaten}),
beginning graduate or senior undergraduate students unfamiliar
with the quantum three-body problem might find them inaccessible.
The Efimov effect arises from the
large-distance (asymptotic) behavior of the
inverse square interaction. The spectrum resulting from such a
potential is well-known,\cite{coon, griffiths, rajeev} and its implications
for Efimov physics are discussed in
Ref.~\onlinecite{braaten}.

The main goal of this article is to
derive, using elementary quantum mechanics, the effective inverse square
interaction in coordinate space of the three-body system. To achieve
this goal, we use the separable form of two-body potential,
for which the algebra is tractable. The
Efimov effect is universal and does not depend on this
special choice of a separable potential. A choice of the more familiar
local form for the potential would entail more advanced
aspects of the three-body problem, while not adding to the essential
physics. Our
hope is that this article can be used as the
basis for introducing the fascinating
Efimov effect in an advanced undergraduate, or first year graduate course
in quantum mechanics.

The outline of our paper is as follows. In Sec.~II we briefly
review the low-energy scattering of two particles.\cite{pat}
The rationale for utilizing a
nonlocal separable two-body potential near a resonance for the analysis of
the three-body system\cite{fonseca} is introduced at this
stage. Short discussions of the separable potential, and Feshbach
resonance follow. The relevant properties of the inverse
square interaction for an understanding of the Efimov effect are given in
Sec.~III.  Our discussion of the properties of the inverse square interaction sets the
stage for the derivation of the Efimov effect in the three-body problem in Sec.~IV.
Recent experimental evidence for the Efimov effect, which has
resulted in a renewed interest in this topic,\cite{phys} is briefly
presented in Sec.~V. Our concluding remarks are in Sec.~VI.

\section{The two-body problem}
\subsection {Low energy parameters}
In the elastic scattering of two particles, the initial and the final
energies are the same, and only momentum transfer may take place. The scattering amplitude is said to be ``on the
energy shell.'' The
scattering cross section and other observables may be described in
terms of a phase shift that occurs in each partial wave of the asymptotic (relative) two-body wave
function. We assume that the
two-body interaction is central, and falls off faster than $r^{-2}$,
where $r$ is the distance between the two particles. If
three or more particles are involved, the situation is not so simple,
even when the particles interact only pair-wise. If a third particle
is present near the pair, it might take away some energy in the
scattering process. The two-body scattering amplitude is then said to
be ``off the
energy shell," and depends on the short-distance behavior of the
two-body wave function.

The exact
description of the three-body problem is given by three coupled integral
equations involving the two-body off-the-energy-shell scattering
amplitudes.\cite{fad}
The Efimov effect in the three-body problem is remarkable
in the sense that its existence is dictated only by the low-energy two-body
elastic scattering properties, and not by the off-shell
behavior. The Efimov effect arises as long as the two-body
interaction between at least two of the pairs is tuned to resonance, regardless of
the interaction potential being, for example, local or nonlocal, of zero range or falling off as $r^{-6}$. At resonance, the two-body wave function is just about bound, and
extends over a large distance.  The tuning of the two-body interaction to resonance is all-important in giving rise to the
Efimov effect.

In this paper we choose a
specific form of a nonlocal potential, called a separable potential,
that gives an analytical form for the two-body wave function, and
for which the treatment of the three-body Faddeev equations is
simpler.\cite{amado} In the example of the
three-body problem that we discuss in Sec.~IV, we avoid solving the
Faddeev equations explicitly, while still obtaining the Efimov spectrum.

For two-body scattering at very low energies, the interaction is
effective only in
the relative $s$-state, because the centrifugal barrier in the higher partial
waves suppresses the particles from coming close together. The $s$-wave
scattering amplitude is well-known to be given by
\begin{equation}
f_0(k)
=\frac{1}{k}
\exp(i\delta_0(k)) \sin \delta_0(k) =(k\cot \delta_0(k)-ik)^{-1},
\label{f0}
\end{equation}
where $\delta_0(k)$ is the $s$-wave phase shift. The differential
cross-section for $s$-wave scattering is isotropic and is given
by $|f_0(k)|^2$.
The scattering
between the two particles is well-described\cite{bethe, blatt} at
low energies by two
shape-independent parameters, the scattering length $a$, and the
effective range $r_0$, where
\begin{equation}
k\cot \delta_0(k)=-\frac{1}{a}+\frac{1}{2} r_0 k^2
+ \ldots
\label{ranger}
\end{equation}

The effective range $r_0$ is a measure of the range of the
two-body potential, and the scattering length is the intercept of the
asymptotic zero-energy $s$-wave wave function. The reader unfamiliar with this description of the two-body problem
should study Fig.~1 and read Ref.~\onlinecite{pat}, Sec.~II A.

Consider a situation where the attractive potential is not
strong enough to support a two-body bound state, in which case the sign of the
scattering length is negative.\cite{pat}
As the potential is made more attractive, the scattering
length becomes more and more negative, and goes to $-\infty$
at resonance (that is, a ``bound state'' at $E=0$), and then flips to
$+\infty$ as the strength of the attractive potential is increased. A further increase in the attractive strength
drives the scattering length to smaller positive values (but
with $a \gg r_0$), resulting in the formation of a dimer.\cite{pat}
For a zero-range potential, only the first term on the right-hand side of
Eq.~(\ref{ranger}) survives, and it follows from Eq.~(\ref{f0}) that the
scattering amplitude is given by $f_0=-(1/a+ik)^{-1}$.
If we extrapolate the wave number to complex values $k=i\kappa_0$ for a
bound state at $k^2=-\kappa_0^2$, we see that the resulting dimer has
energy $E_b = -\hbar^2/M a^2$, where $M$ is
the mass of each isolated atom. The corresponding wave function for
$r>r_0$ is given by
\begin{equation}
\psi_0(r)\sim \frac{\exp (-r/a)}{r}.
\label{wave}
\end{equation}
For $r\ll a$, Eq.~(\ref{wave})
reduces to $\psi_0 \sim (1/r-1/a)$, showing the connection of the
intercept to the scattering length.

\subsection {Separable two-body potential}
A separable potential is a special form of nonlocal interaction which
has been extensively used in the three-body problem in nuclear
physics.\cite{mitra, tabakin}
It results in
considerable simplification of the Faddeev integral equation, which
Amado and Noble\cite{amado} exploited to give a rigorous treatment of
the Efimov
effect. The work of Amado and Noble was further developed in Ref.~\onlinecite{adhikari}.
In the following we give the Schr\"{o}dinger equation for two particles
interacting by a separable interaction, and consider the scattering of a heavy
particle of mass $M$ interacting with a light one of mass $m$, with
the mass ratio $\cm=M/m$.  The relative energy is given by
$E_2 ={k^2}/{\nu'}$, where we have set $\hbar=2m=1$ and
$\nu'=\cm/(\cm+1)$. For simplicity, we assume $\cm \gg 1$, and
take $\nu'=1$.
The eigenvalue equation (after the center-of-mass has been removed) is
\begin{equation}
\label{this1}
(k^2-H_0)|\psi_k\rangle=V|\psi_k\rangle,
\end{equation}
where $H_0$ is the kinetic energy operator. In {\bf r}-space Eq.~\eqref{this1}
takes the form (where ${\bf r}$ is the relative coordinate between the two particles)
\begin{equation}
(k^2+\nabla^2) \psi_k({\bf r})=\!\int \langle{\bf r}|V|{\bf r'}\rangle \psi_k({\bf r'})\,d^3 r',
\end{equation}
and in {\bf p}-space Eq.~\eqref{this1} becomes
\begin{equation}
(k^2-p^2)\psi_k({\bf p})=\!\int \langle{\bf p}|V|{\bf p'}\rangle \psi_k({\bf p'})\,
d^3 p'.
\label{scat}
\end{equation}

A separable potential in Hilbert space may be written as
$V=-\lambda |g\rangle\langle g|$, where the negative sign is taken for attraction,
and $\lambda > 0$ determines the strength of the potential. In the coordinate representation, the
attractive separable potential in the $s$-state is given by
$\langle{\bf r}|V|{\bf r'}\rangle=-\lambda g(r) g(r')$, where $g(r)$
is taken to be real. When a bound state is present, the Fourier
transform of $g(r)$ is closely related to the bound state wave
function.
The Schr\"{o}dinger equation in ${\bf p}$-space for
a bound state, $k^2=-\kappa_0^2$, is given by
\begin{equation}
(\kappa_0^2+p^2)\psi_{\kappa_0}({\bf p})=\lambda g(p)\!\int\!g(p')\psi_{\kappa_0}({\bf p}') d^3 p'.
\label{kappa}
\end{equation}
In Eq.~\eqref{kappa},
\begin{equation}
g(p)=\!\int\!\langle{\bf p}|{\bf r}\rangle g(r) d^3 r = \frac{1}{(2\pi)^{3/2}}\!\int
\exp(- i{\bf p}\cdot{\bf r}) g(r) d^3 r.
\end{equation}
We may write Eq.~(\ref{kappa}) as
\begin{equation}
\psi_{\kappa_0}(p)=\lambda C_{\kappa_0} \frac{g(p)}{(\kappa_0^2 + p^2)},
\label{yama}
\end{equation}
where $C_{\kappa_0}=\!\int g(p') \psi_{\kappa_0} (p') d^3 p'$ is a nonzero
constant. If we multiply
both sides of Eq.~\eqref{yama} by $g(p)$, and integrateover $d^3
p$, we obtain the
equation that determines the binding energy $\kappa_0^2$ for a given
potential
\begin{equation}
\lambda\!\int\! \frac{g^2(p)}{(\kappa_0^2+p^2)} d^3 p =1.
\label{two}
\end{equation}
In the next section, a similar equation for the three-body bound state
will be obtained.

For explicit calculations we choose the popular Yamaguchi form\cite{yamaguchi}
$g(p)=(p^2+\beta^2)^{-1}$, giving
\begin{equation}
g(r) = \frac{1}{(2\pi)^{3/2}}\!\int\!\exp( i{\bf p}\cdot{\bf r}) g(p) d^3p =
\sqrt{\frac {\pi}{2}}\frac{\exp(-\beta r)}{r}.
\label{short}
\end{equation}
We substitute this choice of $g(p)$ in Eq.~(\ref{yama}), and take its
Fourier transform. After a little algebra, we find that
\begin{equation}
\psi_{\kappa_0}(r)=\lambda C_{\kappa_0}
\sqrt{\frac {\pi}{2}}\left(\frac{\exp(-\kappa_0 r)}{r}-
\frac{\exp(-\beta r)}{r}\right)
\label{guchi}
\end{equation}
For small binding, $\kappa_0$ is only slightly greater than zero. We
choose a short range potential, so that $\beta\gg \kappa_0$, and
asymptotically Eq.~(\ref{guchi}) becomes the same as Eq.~(\ref{wave})
obtained from the zero-range approximation.
The universal nature of the Efimov effect is independent of the
specific choice of $g(r)$, as long as $g(r)$ is short range.

\subsection{Feshbach resonance}
The strength of the interaction of a zero-range potential is
controlled by the scattering length $a$. For cold-atoms the
scattering length may be varied by
a magnetic field, making use of the Feshbach resonance.\cite{fesh, cohen, chin}
Near a Feshbach resonance, two unbound
atoms with relative energy $E$ slightly larger than zero
may scatter off each other through a potential. This scattering process is said to occur in the
``open channel.''
When the same two atoms come close together in a different total
spin state, they may encounter a different potential, and form a bound or
quasi-bound state at energy $E_{\rm res}>E$.  The process leading to the formation
of a bound or quasi-bound state is called a ``closed''
channel.
The scattering state at energy $E$ does not
exist in the closed channel, because the closed channel requires $E_{\rm res}>E$ to
dissociate the atoms.  Nevertheless, there may be interchannel coupling
through a spin-dependent potential that might cause a virtual transition
between the two channels.
The two atoms in the open channel have different magnetic moments
than when they are in the quasi-bound state, and hence the energy gap
between the states may be
controlled by the relative Zeeman shifts. As a result, the mixing between the
two states is more pronounced when the Zeeman energy gap is reduced.
In a single-channel description,\cite{cohen} the two atoms in the
open channel may make a virtual transition to the closed channel state
and back, giving an effective single-channel scattering length in the open
channel that is
inversely proportional to the energy gap, $\Delta E$, between the two states, where $\Delta E= \Delta \mu (B-B_0)$.
Here, $\Delta \mu$ is the difference in magnetic moments of the two-atom system in the two channels, and $B_0$ is the magnetic field at which the scattering length diverges
(at resonance) and changes sign.
When $B$ is very different from the resonance value $B_0$, the effect of the
coupling is small, and the scattering length reduces to its natural
``background'' value $a_{\rm bg}$. More details in the context of
ultra-cold atoms may be found in Refs.~\onlinecite{moer} and \onlinecite{chin}.
\begin{figure}[hbt!]
   {\includegraphics[angle=0, width=96mm]{./Slide1.eps}}
   \caption{\label{fig1}%
            Adapted from Fig.~1 in Ref.~\onlinecite{phys}.
For $a<0$, even though there is no two-body bound state (dimer), more and more
three-body bound states (trimers) are formed as the potential becomes
more attractive. The solid lines represent these Efimov trimer states
which emerge at $E=0$, and $a<0$.  For $a>0$ on the right, the
trimers break up at the atom-dimer continuum
, indicated by the
  dotted curve}
  \end{figure}
\section{ Efimov spectrum and the Inverse square potential}
For three identical bosons interacting pairwise via short-range potentials, Efimov predicted
an infinite number of { three-body} bound
states with geometrical scaling, when the two-body interactions are resonant, that is, $|a| \rightarrow \infty$.

Figure 1 (following Ref.~\onlinecite{phys}) depicts the Efimov
scenario where the
energies of some of the three-boson states are plotted as a function of
$1/a$; for $E>0$ the energies of the three-atoms form a continuum. The bound Efimov states are shown schematically
by solid lines, with a scaling factor (ratio of successive energy eigenvalues) set artificially at 2 rather than $22.7$. The Efimov states break up on the positive side of $a$ in the atom-dimer continuum given by $-\hbar^2/(Ma^2)<E<0$ (see the dotted curve in Fig.~1).

The Efimov spectrum of the three-body problem is the signature of an attractive central potential which falls off asymptotically as the
inverse square power of the distance. A three-body
long-range potential is suggested by noting that for large positive $a$, the size of the
dimer is very large, and the presence of another atom, even if very
distant, may be ``sensed'' by the dimer. For large negative $a$ the two atoms, even
if not bound, are spatially correlated over a distance of order $|a|$ in a quasi-bound state.

To obtain the geometric scaling of the
spectrum, it is sufficient to consider the simpler problem of a single particle of mass $m$ in an inverse square
potential $V(r)=(\hbar^2/2m)\lambda/r^2$, where $\lambda$ is
a dimensionless coupling constant. Classically the equation of motion in
this potential is
scale invariant under the continuous transformations ${\bf r} \rightarrow \alpha {\bf r}$, and $t\rightarrow\alpha^2 t$. Quantum mechanically, for
$\lambda>-1/4$, there is no bound state, and the continuous
scale-invariance is valid. A zero-energy state appears for $\lambda=-1/4$, and the system is anomalous for $\lambda < -1/4$, due to the short-distance
singularity of the potential.\cite{coon,griffiths} A direct
consequence of the anomaly for $\lambda < -1/4$ is that there is no longer a lower limit in
the energy spectrum, and a regularization is required.\cite{rajeev} We are
interested
in the situation where the potential is inverse square only
for $r>r_c$, where $r_c$ is taken as the short-distance
cut-off. We impose the boundary condition that the eigenfunctions vanish at $r=r_c$, which results in a discrete
spectrum. The geometric scaling property, namely that the
ratios of the adjacent energy eigenvalues remain a constant, is
independent of $r_c$.

We write the Schr\"{o}dinger equation in the $s$-state for $r>r_c$ as
\begin{equation}
\left[-\frac{d^2}{d r^2}-\frac{(s_0^2+1/4)}{r^2} \right]
u(r)=\frac{2m}{\hbar^2} E u(r),
\label{inverse}
\end{equation}
where at this stage, $s_0^2\geq 0$ is
just a way of parametrizing the strength of an inverse square potential
that is greater than $1/4$. For bound states, we set $(2m/\hbar^2) E=-\kappa^2$, and require that wave functions vanish
at infinity. We then obtain the solution $u(\kappa r)=\sqrt{\kappa r} K_{is_0}(\kappa r)$, where $K_{is_0}$ is the modified Bessel
function of the third kind of pure imaginary order ${is_0}$.~\cite{braaten}
The boundary condition that $u(\kappa r_c)=0$ makes $\kappa$
discrete, such that $K_{is_o}(\kappa_n r_c)=0$, with $n$ a positive integer. For shallow bound
states such that $(\kappa_n r_c\ll 1)$, the zeros of the Bessel
function $K_{is_0}(\kappa_n r_c)$ are given by
\begin{equation}
\kappa_n r_c=\exp\Big(\frac{-n\pi}{s_0}\Big)(2 e^{-\gamma})[1+O(s_0)+\ldots],
\end{equation}
where $\gamma$ is Euler's constant.
Equation (14) leads to the desired result
\begin{equation}
\frac{E_{n+1}}{E_{n}}= \exp (-2\pi/s_0), \hspace{1cm} n=1,2, \ldots\infty
\label{scaling}
\end{equation}
which is the geometric scaling mentioned previously. Note that the actual value of $E_n$
scales as $r_c^{-2}$, but geometric scaling holds for the shallow states. Also note that as $n$
becomes larger, the states become shallower, with an infinite number of
states accumulating at zero energy. In the three-body problem in which three particles interact pair-wise,
there are six degrees of freedom after the
center-of-mass motion is eliminated. This problem is commonly treated in
hyperspherical coordinates\cite{nielsen} with a hyperradial variable
$R$, and five angles. For equal mass particles,\cite{note} $R=\sqrt{(r_{12}^2+r_{23}^2+r_{31}^2)/3}$. In the adiabatic
approximation\cite{macek}
for fixed $R$, we solve the Schr\"{o}dinger equation
for the angular variables, thus obtaining a complete set of adiabatic eigenvalues $\varepsilon (R)$ and corresponding eigenfunctions. The solution shows that in the resonant limit $a\rightarrow
\pm\infty$, neglecting channel coupling, the same
inverse square potential as in Eq.~(1) appears in hyperspherical
coordinates, with $r$ replaced by $R$.

For identical bosons, $\exp (\pi/s_0)\simeq 22.694$, (that is, $s_0 \approx 1.00624$) but in general, $s_0$ depends on the mass
ratios. If $a$ is finite and very large, with $|a| \gg r_0$, the inverse square interaction $\varepsilon
(R)$ is cut-off at a short distance of the order of $r_0$, and at a
long distance of the order of $|a|$. The number of shallow bound states is given approximately by\cite{fonseca}
\begin{equation}
N \simeq \frac{s_0}{\pi} \ln \frac{|a|}{r_0}.
\label{tom}
\end{equation}
A simplified derivation of Eq.~(\ref{tom}) is given in the
Appendix.

\section{The three-body model}
Our objective of obtaining an inverse square interaction in the
three-body problem is best served by taking two identical heavy particles
$1$ and $2$, each of mass $M$, and particle $3$ of mass
$m \ll M$, as shown in Fig.~2.
\begin{figure}[hbt!]
   {\includegraphics[angle=0, width=86mm]{./Slide2.eps}}
   \caption{\label{fig2}%
            A schematic illustration of the relative coordinates used in the three-body problem.  See the text for details.}
\end{figure}

The coordinates of the
particles are labeled ${\bf r}_1$, ${\bf r}_2$, and
${\bf r}_3$, as measured from an arbitrary origin not shown in Fig.~2. The three-body analysis is simplified if the relative coordinates
${\bf R}=({\bf r}_1-{\bf r}_2)$, and ${\bf r}={\bf r}_3-({\bf r}_1+{\bf r}_2)/2$ are introduced. Following the common convention, we denote by $V_1$ the interparticle potential between particles $2$ and
$3$, and likewise for $V_2$ and $V_3$ in cyclic order. The three-body Schr\"odinger equation is given by ($\cm=M/m$, and recall that $\hbar=2m=1$)
\begin{equation}
H \Psi ({\bf r}, {\bf R}) = E \Psi({\bf r}, {\bf R}),
\label{muon}
\end{equation}
with
\begin{equation}
H = -\frac{1}{\mu} \nabla^2_R-\frac{1}{\nu}\nabla^2_r +V_1+V_2+V_3, \quad \mu=\cm/2, \quad \nu=2\cm/(2\cm+1),
\end{equation}
where $E$ is the energy of the three-body system. For $\cm \gg 1$, $\nu \rightarrow 1$, and the motion of the heavy particles is very slow compared to that of the light particle of mass $m$, which is in the spirit of the Born-Oppenheimer approximation. Following Ref.~\onlinecite{fonseca} we may apply the adiabatic Born-Oppenheimer approximation to
solve the three-body Scho\"odinger equation in two stages. First, the wave function is decomposed according to
\begin{equation}
\Psi({\bf r}, {\bf R})=\psi({\bf r}, {\bf R}) \phi({\bf R}),
\end{equation}
where $\psi({\bf r},{\bf R})$, with eigenenergy $\varepsilon(R)$, is first solved for the relative motion of the light-heavy system,
keeping ${\bf R}$ a parameter. For fixed ${\bf R}$, the relative kinetic energy of the heavy particles is zero, and the potential energy $V_3(R)$ is a constant shift in energy. Equation (\ref{muon}), with $\nu=1$, becomes
\begin{equation}
\left [-\nabla_r^2 + V_1 ({\bf r}-{\bf R}/2) +V_2 ({\bf r} +{\bf R}/2)\right]\psi({\bf r},{\bf R})=
\varepsilon(R) \psi ({\bf r}, {\bf R}).
\label{sr}
\end{equation}
Next, the two-body Schr\"{o}dinger equation with $\varepsilon(R)$ as the
adiabatic potential between the two heavy particles is solved for the ground state energy, $E$, within the adiabatic approximation:
\begin{equation}
\left[-\nabla_R^2/\mu +V_3 (R) +\varepsilon(R)\right] \phi(R)= E \phi(R).
\label{heavy}
\end{equation}
Because the interatomic potential $V_3(R)$ falls off faster than
$1/R^2$, it does not affect the asymptotic behavior of $\varepsilon(R)$,
and we set $V_3(R)=0$. For $V_1$ and $V_2$ in Eq.~(\ref{sr}), we take short-range
separable potentials $-\lambda |g\rangle\langle g|$. Thus, for a fixed
parameter ${\bf R}$, we have
\begin{equation}
\langle {\bf r}'-{\bf R}/2|V_1|{\bf r}-{\bf R}/2\rangle=-\lambda \langle {\bf r}'-{\bf R}/2|g\rangle \langle g|{\bf r}-{\bf R}/2\rangle,
\end{equation}
and likewise for $V_2$, with $-{\bf R}/2$ replaced by
$+{\bf R}/2$.

If we introduce the displacement operator, $D_{{\bf R}/2}=\exp\left(i{\bf p}_r\cdot {\bf R}/2 \right)$, we can write $|{\bf r}+{\bf R}/2\rangle=D_{{\bf R}/2}|{\bf r}\rangle$,
where ${\bf p}_r$ is the momentum conjugate to ${\bf r}$. In operator form, Eq.~(\ref{sr}) becomes
\begin{equation}
\left[-\nabla_r^2-\lambda \left( D|g\rangle \langle g|D^{-1} + D^{-1}|g\rangle \langle g|D\right)\right]|\psi\rangle =\varepsilon (R)
|\psi\rangle ,
\label{milan}
\end{equation}
with the subscripts on $D$ suppressed for brevity. Equation~(\ref{milan}) bears a striking similarity to the two-body equation in operator notation given by
$\left[-\nabla_r^2-\lambda |g\rangle \langle g|\right]|\psi\rangle =E_2
|\psi\rangle$. In Eq.~(\ref{milan}), let $\varepsilon(R)=-\kappa^2(R)$, $G=(-\nabla^2_r+\kappa^2)^{-1}$,
and $\langle g|D|\psi\rangle =N({\bf R}/2)$. The light-heavy wave function
$\psi({\bf r},{\bf R})$ has a definite parity under core-exchange, ${\bf R}\rightarrow -{\bf R}$, so that for the lowest energy state with energy $E$ [recall that we are solving Eq.~(\ref{heavy})], we take the wave
function to be symmetric. We define
$\langle g|D^{-1}|\psi\rangle\equiv N(-{\bf R}/2)=N({\bf R}/2)$, thereby reducing Eq.~(\ref{milan}) to
\begin{equation}
|\psi\rangle =\lambda G \left( D^{-1}|g\rangle + D|g\rangle \right) N({\bf R}/2).
\end{equation}
We multiply both sides by $\langle g|D$, note that $[G,D]=0$ and $N({\bf R}/2)\neq 0$, and obtain
\begin{equation}
\lambda \left( \frac{\langle g|g\rangle + \langle g|D^2|g\rangle }{(-\nabla_r^2+\kappa^2)} \right)=1.
\end{equation}
In the momentum representation, Eq.~(20) takes the form
\begin{equation}
\label{three}
\lambda\!\int\! \frac{g^2(p_r)}{p^2_r + \kappa^2}d^3p_r +
\lambda\!\int\!\frac{g^2(p_r)\exp(i{\bf p_r}\cdot {\bf R})}{p^2_r + \kappa^2}d^3p_r = 1,
\end{equation}
which is analogous to Eq.~(\ref{two}) for the two-body problem. Note that Eq.~(\ref{three}) assumes $\cm\gg 1$, so that
$\nu'\simeq \nu$.  Recall that $\nu' \equiv \cm/(\cm+1)$ and $\nu=2\cm/(2\cm+1)$.
The coupling constant $\lambda$ may be eliminated by fixing the binding $\kappa_0^2$ of the two-body problem. For the Yamaguchi form $g(p)=(p^2+\beta^2)^{-1}$, the integrals in
Eq.~(\ref{three}) may be performed analytically, giving
\begin{equation}
1-\left (\frac{\beta+\kappa_0}{\beta+\kappa}\right )^2= \left (\frac{\beta+\kappa_0}{\beta+\kappa}\right )^2
\left[ \frac{2\beta}{(\beta-\kappa)^2}\frac{e^{-\kappa R}-e^{-\beta R}}{R}
-\frac{\beta+\kappa}{\beta-\kappa} e^{-\beta R} \right ].
\label{four}
\end{equation}

As the distance $R$ between the two heavy atoms is increased, the
light atom will tend to attach to one of them, and
$\kappa^2(R)\rightarrow \kappa_0^2$. We are particularly interested in
this large $R$ behavior of $\varepsilon (R)$ as the two-body binding $\kappa_0^2$ goes to zero. To deduce the functional form of $\varepsilon
(R)=-\kappa^2(R)$ for large $R$, it is convenient to define $\xi\equiv \kappa -\kappa_0$, and substitute it into Eq.~(\ref{four}). From Eq.~(\ref{short}), we see that $g(r)$ is short-ranged for $\beta \gg 1$. In the resonant limit, consider $a\rightarrow \infty$
from the positive side. Then $\kappa_0=1/a\rightarrow 0$. We consider two possible cases in turn:

(1) $\kappa_0 \ll \beta$, $\beta R \gg 1$, $R/a \rightarrow 0$, $\xi \ll \beta$ for which $\exp (-\beta R) \rightarrow 0$, and $\exp (-\kappa_0 R)\rightarrow 1$. Some algebra yields the
equation
\begin{equation}
\frac{e^{-\xi R}}{\xi R}=1,
\end{equation}
which has the solution $\xi R=A$, where $A=0.5671\ldots$. Hence $\kappa=\kappa_0+\xi= \kappa_0+A/R$. In the limit of
$a\rightarrow\infty$, $\kappa_0\rightarrow 0$, we see that $\varepsilon(R)=-\kappa^2=-A^2/R^2$, giving the desired inverse square
potential. In our analysis, we set $\nu=1$, which only
approximately holds for $\cm \gg 1$. However, setting $\nu=1$ is not necessary, and Fonseca {\it et al.}\cite{fonseca} have shown that $\varepsilon(R)=-A^2/(\nu R^2)$. The effective potential including the kinematic factors that appear in the equation analogous to Eq.~(\ref{inverse}) may be easily deduced
from Eq.~(\ref{heavy}) to be $-\mu A^2/(\nu R^2)=-1/4 A^2(1+2 \cm)/R^2$. Therefore the scaling parameter $s_0$ in the Efimov
spectrum, as defined in Eq.~(\ref{inverse}), depends on the mass ratio $\cm$.

(2) Let the scattering length be large but finite, and consider a distance $R$ that is even larger, so that $R/a \gg 1$. $R/a \gg 1$ implies
that $\kappa_0 R \gg 1$, even though the other conditions are the same as in case (1). Thus, in spite of being able to set $\exp (-\beta R)=0$, we cannot set $\exp(-\kappa_0 R)$ to unity. We may show that
for $R \gg a$, Eq.~(\ref{four}) yields the Yukawa form
\begin{equation}
\varepsilon(R) \simeq -\frac{2}{\nu}\frac{e^{-R/a}}{aR}
\label{yu}
\end{equation}
This form of a static Yukawa potential arises naturally in nuclear
physics due to the exchange of a light mass boson (for example, a pion)
between two heavy mass nucleons. In nuclear physics the range of the potential is
determined by the square root of the mass of the light particle; in
our case, it is the square root of the binding energy of the light
atom that plays the analogous role. This situation is depicted in
Fig.~3. In region I, $R\leq R_0$, where $R_0$ is the range of the interatomic potential\cite{newref} between the two heavy particles. We cutoff the potential for the shallow states at this distance. In region II there is a $1/R^2$ potential, which extends to distances $R \ll a$, hence for all $R$ as $a\rightarrow \infty$, as in case (1). Region III is for $R\sim a$, where the transition to the Yukawa form takes place. Region IV contains the asymptotic behavior of the potential.
\begin{figure}[hbt!]
   {\includegraphics[angle=0, width=86mm]{./Slide3.eps}}
   \caption{\label{fig3
The effective potential $\varepsilon (R)$ between
     the two heavy-mass particles that arises in the adiabatic
approximation due to the interaction
     with the light-mass particle. For
$R<R_0$, the interatomic potential is irrelevant for the Efimov
effect. The scattering length $a$ is marked on the horizontal
axis. As $a\rightarrow \infty$, the two-body binding $\kappa_0^2$ goes
to zero, and $\varepsilon (R)\rightarrow R^{-2}$ for all $R>R_0$.
The four regions of the potential
$\varepsilon (R)$, are discussed in the text. }
\end{figure}
As the two-body binding $\kappa_0^2$ goes to zero,
the long-range potential $\varepsilon (R)$ takes the inverse square form, which has no length scale. From
dimensional considerations, because $\hbar^2/M$ has the dimensions of
$E L^2$, an inverse square potential is the only form possible in the
absence of other mass scales or coupling constants.

From Fig.~3, a related prediction associated with the collapse of the
three-body system called the Thomas effect\cite{thomas} may also be
deduced. Consider a two-body system of range $r_0$ with a fixed binding $\kappa_0^2$. Let the range parameter $r_0$ become smaller
and smaller, adjusting the strength of the two-body potential so that $\kappa_0^2$ remains constant. The Thomas effect asserts that the
three-body system will collapse as $r_0\rightarrow 0$, with its
deepest bound state going to $-\infty$. In Fig.~3, the short distance cut-off $R_0$ of the inverse
square potential $\varepsilon(R)$ goes to zero as $r_0$ goes to
zero. Such a behavior near the origin causes a collapse in the
three-body energy. The Thomas effect does not require the asymptotic form of the
potential to be inverse square, but rather is associated with the short
distance singularity of the potential. From Eq.~(\ref{tom}) we note
that the number of three-body bound states diverges when the ratio $a/r_0 \rightarrow \infty$, which may be brought about either by
letting $a\rightarrow \infty$ with $r_0$ finite, as in the Efimov effect,
or letting $r_0 \rightarrow 0$, with $a$ finite, which corresponds to the
Thomas effect.\cite{fred} Unlike the Efimov effect, the Thomas effect is not amenable to experimental verification because
the range of the two-body potential cannot, as of now, be tuned to zero.

\section{Experimental Evidence}
Starting with the pioneering work of Kraemer {\it et al.}\cite{kraemer} with ultra-cold Cs atoms in 2006, several experiments\cite{zacc, gross, pollack} have confirmed Efimov's predictions by measuring the three-body recombination losses
of atoms through the reaction $A+A+A \rightarrow A_2+A$. The experiment with heteronuclear atoms was done by Barontini {\it et al.}\cite{bar}
All these experiments require very low temperature $ k_BT\leq \hbar^2/Ma^2$ for a very large scattering length
$a$ to avoid break up of the dimers. For example, for Cs atoms, $T=10$\,nK was required to largely eliminate thermal effects.

The atoms in a gas have a tendency
to form lower energy dimers directly for scattering length $a>0$. But
two atoms alone cannot form a bound state and preserve momentum and
energy at the same time. Dimer formation is possible if a third atom
is nearby within a distance of the order $a$. This problem was studied
in a gas of identical atoms with number density $n$, while looking at atomic losses in Bose-Einstein condensates.\cite{fed} Let the number of three-body recombinations
per unit volume per unit time be denoted by $\nu_{\rm rec}$, which is proportional to $n^2 (\sigma v) (na^3)$. Here $n^2 (\sigma v)$ is the
probability of two atoms being in the interaction volume $(\sigma v)$, where
$\sigma$ is the elastic scattering cross section and $v$ is the
relative speed between the two atoms. The probability of finding a third atom
within a distance $a$ is $n a^3$. Because $v=\hbar k/m\simeq \hbar/(m a)$, and $\sigma \propto a^2$, we obtain
\begin{equation}
\nu_{\rm rec}= C(a) n^3 \left(\frac{\hbar}{m} a^4\right),
\end{equation}
where $m$ is the mass of each atom, and $C(a)$ is a dimensionless
constant. The variation of $C(a)$ with the scattering length $a$ exhibits the
emergence of an Efimov trimer (negative $a$), and its subsequent
dissolution to dimer plus atom (positive $a$), see Fig. 1. It has been
calculated from theory.\cite{fed, nielsen2,esry}
The recombination length (the ordinate of Fig.4) is defined as
$\rho_3=(2\sqrt{3} C(a))^{1/4}a$, where the numerical factor is
included to take into account the reduced mass of the trimer, and the fact that
three atoms are lost for each trimer.
\begin{figure}[hbt!]
   {\includegraphics[angle=0, width=136mm]{./Slide4.eps}}
   \caption{\label{fig4}%
            Adapted from Fig.~2 of Ref.~\onlinecite{esry2}.  The solid circles
            are experimental data points~\cite{kraemer} at $10$ nK for the
            observed three-body
recombination: $Cs+Cs+Cs \rightarrow Cs_2 + Cs$.  The scattering
length is measured in units of the Bohr radius $a_0$.}
\end{figure}
To understand the experimental peak in the measured recombination
length $\rho_3$ (see Fig.~4), note that shallow
dimers are not formed directly for $a <0$. The potential
$\varepsilon (R)$ of Fig.~3 develops a potential barrier for
large $R$, followed by an attractive potential at shorter distances.
Such a potential emerges from a hyperspherical calculation for equal
mass bosons.\cite{macek}
There may result, for certain negative values of $a$, shape resonances
of the trimer at $E>0$. When the energy of the three atoms matches a
resonance, there is enhanced barrier penetrability to form an Efimov
trimer. The enhanced barrier penetrability allows the system to relax
to a deeply bound dimer state (from the interatomic potential), with the excess
energy being carried away by the third atom. The peak $\rho_3$ on the negative
side is at $a=-850 a_0$, where $a_0$ is the Bohr radius. The next
peak should be at a value of $a$ that is $22.7$ times larger, that is,
$a=-19,295$, which is outside the range of experimental observation.
Nevertheless, these multiple peaks were observed in later
experiments.\cite{zacc, gross, pollack}
Even though multiple resonance peaks were not seen in the Kraemer {\it et al.}\cite{kraemer} experiment, the interference minimum
observed on the positive
$a$ side is convincing evidence for the Efimov effect.\cite{esry2}
Hyperspherical calculations for $a>0$ not only give an attractive
potential as in Fig.~3 for $\varepsilon (R)$, but also a barrier for
positive energies that falls off for large $R$. The three incoming
atoms may be reflected by the barrier, and form $A_2+A$ on the way
out, interfering with the incoming dimer plus atom system following
the large-$R$ attractive channel of Fig.~3.
The out-of-phase interference between the two paths leads to
the curve that fits the experiment for positive $a$ (see Fig.~2 of
Ref.~\onlinecite{esry2}).

\section{Closing remarks}
It is remarkable and not foreseeable in 1970 that
the Efimov effect has been experimentally verified
using ultra-cold atoms. We have considered a
simple case for which two of the atoms are very heavy compared
to the third. The light heavy pairs are treated very differently, as
evidenced by the adiabatic approximation. The light particle is almost
unbound, and can be very distant from the heavy partners.
The overall size of the shallow Efimov trimer is large in
comparison to the short-range of the two-body interaction.

As is clear from Sec.~IV, it is the dynamics of the light particle that
generates the attractive long-range interaction between the heavy
ones. We may regard the
light particle as being exchanged back and forth to generate this
potential between the two heavy particles.
Even for equal mass particles,
Efimov\cite{comments}
has stressed this intuitive picture for the inverse square potential.
A different approach must be
taken for three identical particles, as indicated briefly in
Sec.~III for three identical bosons. Each particle has to be treated
the same way, and hyperspherical coordinates are well-suited to
describe the shallow Efimov states.
The size of these states is large, and
the small binding results in the formation of floppy triangles. For
these shallow states, the
coupling between the hyperradial variable $R$ and the hyperangles is
small. The coupling vanishes for $|a|\rightarrow \infty$, and the
hyperangular contribution just adds a centrifugal term for angular
motion to the adiabatic potential $V(R)$. The deepest potential is
attractive enough (for $L=0$) to yield the Efimov effect.

For three nucleons the overall wave function under
the exchange of any two has to be antisymmetric. As was originally found by Efimov,~\cite{efimov}
imposing these symmetries results in only the spatially symmetric angular
momentum state $L=0$ (with the spin-isospin combination antisymmetric) leading
to an attractive interaction. Unlike charge neutral ultra-cold atoms,
it is not possible to manipulate the strength of the nucleon-nucleon interaction.

Given that there is suggestive experimental evidence for the
Efimov effect in the
four-body sector (see for example, Ref.~\onlinecite{pollack}), it is clear that
Efimov physics in ultra-cold atoms will continue to be an active
area of research.

redpajama_set_name: RedPajamaArXiv


text:
Windows into the Middle East
By Jim Fletcher
Published July 22, 2009 at 12:33am
I just finished two of the most extraordinary books I've read in a long time. Michael Oren wrote both.
The newly named Israeli ambassador to the U.S. – a real renaissance man – is both a scholar and former officer in the Israel Defense Forces. The two works I am reviewing this week, "Six Days of War," and "Power, Faith, and Fantasy: America in the Middle East, 1776 to the Present," are absolutely must-haves for pro-Israel Christians in particular.
Although Oren's agenda isn't to point out the supernatural miracle of modern Israel, the reader will easily be able to discern God's hand at work.
In "Six Days of War," Oren provides a riveting account of the 1967 Six-Day War, including the escalation leading up to the conflict, its scintillating action and far-reaching conclusion.
For example, Oren shows how Arab intransigence – particularly that of Nasser of Egypt – propelled them into a tragicomedy of strategic errors. Time and again, the Israelis signaled to the West (and to the Soviets) that war was not a foregone conclusion.
As Nasser's genocidal threats grew louder, Egypt's defense minister, Shams Badran, uttered an inanity that could have come from the lips of "Baghdad Bob," Saddam Hussein's clueless spokesman, a generation later:
"If the [U.S.] Sixth Fleet intervenes in our struggle with Israel," Badran boasted, "our bombers together with our missile boats can destroy its largest carriers."
Oren notes that Badran was "convinced that Egypt was now invincible."
This theme occurs throughout the book. Truly, had the Arabs not adopted hubris as a war policy, the Middle East today would look very different.
Just one of the many fascinating facets of this important work is the American reaction to, and handling of the conflict between, Israel and Egypt.
President Lyndon Johnson, for example, a man who seemed to have some genuine fondness for the young Jewish state, would not give much public warning to the Arabs prior to June 5, 1967.
In fact, during a conversation with Israeli Foreign Minister Abba Eban, the tall Texan said: "You won't be alone, unless you go it alone."
Of course, it's possible Johnson meant it, but had the Israelis placed their safety in Western hands, we might be lamenting the late, great Israel.
As it was, Prime Minister Levi Eshkol, not exactly a decisive fellow, fretted about international opinion. After Nasser closed the Straits of Tiran to Israeli ships – an act of war – Eshkol dithered for a time. Then, as the Arab forces' irrationality and international cowardice further solidified, Israel's "men of war," the military echelon, stepped forward with a bold plan: an initial assault on Egyptian airfields that could give Israel a major advantage in the war's genesis.
In fact, that's exactly what happened. And this is just one of many instances in Oren's book that points to the intervention of help beyond this world.
As Israel's fighter jets headed out over the Mediterranean, just before turning sharply west and to the enemy's airfields, the pilots realized there was little wind and perfect visibility. This combination allowed Israel to destroy half the Egyptian air force within 30 minutes.
Pinpoint planning had also carried the day: Air Force chief Ezer Weizman had been refining a plan codenamed "Focus" for several years. A key element of this plan involved the turnaround time for refueling and rearming after a sortie. Israeli pared its turnaround time to eight minutes. Egypt's, by contrast, was eight hours. Amazing.
The war's conclusion, which saw Israel now controlling the Sinai Peninsula, the West Bank and the Golan Heights, left a diplomatic mushroom cloud around the globe. No one quite knew what to "do" with a suddenly strong Israel.
As Oren points out, the subsequent negotiations, featuring a still-stubborn, prideful Arab League, laid a firm foundation for the ongoing conflict. For students of this era, "Six Days of War" is the ultimate guide to Israel's lightning victory.
"Power, Faith, and Fantasy," Oren's study of U.S. involvement in the region, details America's diplomatic efforts in the Middle East from the time of the American Revolution until our time. For people who think they know a lot about the subject, Oren's page-turner provides context and detail for a rich period of American history. One can see clearly that the world's current superpower has been vexed and perplexed by radical Islam for much longer than eight years.
Presidents Thomas Jefferson and John Adams both dealt with the draconian Muslim stance toward "infidels." One of the first clashes came when Algerian pirates took captive 21 American sailors. The Muslim ruler, upon seeing the hostages paraded before him, declared: "Now I have you, you Christian dogs, you shall eat stones."
As early as the 1770s, North African pirates were calling themselves mujahideen, Islamic holy warriors, and attacking American ships. Lacking gunboats, America initially paid ransom to free cargo and crews, but eventually resolve stiffened and the U.S. settled into a period of real influence in the area.
In fact, as Oren's research points out, it was American missionaries to the Middle East that not only played a large role in 19th century policy, but also laid the groundwork for policy today. Frustrated by their inability to convert Muslim populations to Christianity, missionaries like Maine's Cyrus Hamlin established colleges in Arab lands and slowly became enamored of their hosts. Jettisoning the need to exclusively preach the gospel, these missionaries began to foster Arab nationalism, a major source of unrest in our world today.
In fact, as Oren points out, those 19th century missionaries are the ancestors of many Washington diplomats today, which explains the State Department's mendacity as regards the Jewish state. Career "Arabists" in the diplomatic corps have little use for Israel.
A particularly useful line of research in "Power, Faith, and Fantasy" involves Oren's look into the personal views of American presidents. While Adams, U.S. Grant, Teddy Roosevelt and Harry Truman ("His Bible reading had led him to accept the notion of Jewish restoration in the Holy Land," Oren writes) all contributed to warm relations with the Jewish effort to settle Palestine, others, such as Jimmy Carter, saw things differently. Even Richard Nixon, who ordered his Air Force chiefs to send "everything that will fly" to help rearm a desperate Israel during the 1973 Yom Kippur War, was soaked in anti-Semitism.
Michael Oren has provided Middle East aficionados with two remarkable volumes that chronicle seismic political and cultural events in that volatile area of the world. These two books are so good, I wouldn't sell you my heavily underlined copies for any amount of Saudi oil, which, by the way, directly impacts all our lives in ways we can scarcely comprehend.
For example … well, on second thought, get the books and find out for yourself!
Blogger and researcher Jim Fletcher has worked in the book publishing industry for 15 years, and is now director of the apologetics group Prophecy Matters. His new book, "Truth Wins," provides important analysis of Rob Bell and his Emergent friends.
Spreading the Gospel in funny ol' ways
Meet the man behind the 'Coast to Coast' microphone
Are you 'mad as hell'?
When pastors tweet nonsense
Hey Deplorables: Need some guidance?


text:
Agitators Seeking Separate Nations Have Committed No Crime — Lagos Assembly Speaker, Obasa
June 16, 2021 admin Latest, Metro Gists, Politics 0
Newsie Events Media:
Mudashiru Obasa, Speaker of the Lagos State House of Assembly has stated that there's no known crime committed by agitators clamouring for the disintegration of Nigeria and seeking to belong to other nations.
According to Daily Post, the lawmaker, while speaking during the debate on a motion on Nigeria's democracy raised by Setonji David, on Tuesday, cautioned the military against the deployment of personnel to suppress agitations for secession.
Obasa insisted that applying force will not bring about the desired result since it is part of democracy for citizens to speak out about leadership. He said although 22 years of unbroken democratic rule in Nigeria is worth celebrating, there are issues causing chaos in the country.
He urged the Nigerian government to dialogue with the agitators across the country.
"Those that elected have the right to protest when they think things are not working. The right to protest should not be taken away from them.
"There is no crime in seeking for separate nations within an existing nation. Those representing the people through the ideology of social contract must listen," Obasa added.
Regarding the ban on open grazing by herdsmen, Obasa urged governors of Southern states to remain resolute in their decision.
"Having stated their position, they should not go to sleep. They should follow it through. We will continue to call for state police and devolution of power," he said.
Obasa hailed President Muhammadu Buhari for signing an executive order granting autonomy to state legislature and judiciary and for honouring the late MKO Abiola with the declaration of June 12 as Democracy Day.
The House observed a minute's silence in honour of Abiola, winner of the 1993 presidential election, and all those who died in the course of the struggle.
NEWSIE EVENTS MEDIA TEAM Follow Us On Twitter: @NewsieEvents, Instagram: newsieevents, Facebook: Newsie Events (Subscribe to our YouTube Page: Newsie Eventsng.
Twitter refused FG's request to delete Nnamdi Kanu's account – Lai Mohammed
Onyema Nwachukwu takes over from Yerima as Army spokesman .


MenHealing Weekends of Recovery are open to any man, 18 or older, who has been sexually victimized as a child and/or assaulted or raped as an adult. Registration will open June 18, 2019. You are encouraged to register early as our weekends frequently fill quickly. All participants must be registered in advance of this event; NO walk-in registrations accepted.
Hope Springs is a 501c3 Not For Profit Retreat Center in Ohio's Southern Appalachian foothills providing intentional space for mindful, creative, and healthy private group retreats. Hope Springs also sponsors profoundly transformative workshops on topics which include women's issues, empowered leadership, and personal growth. We have been conducting Weekend of Recovery retreats at Hope Springs since 2007.
This was my first time here. I will return.
Private meeting spaces are available for all Weekend of Recovery sessions. The weekend is designed to provide a mixture of full participant community activities and small group break out sessions.
Large group sessions are conducted in a wonderfully-designed Studio Building and small groups are conducted in several comfortable physical spaces in the Farmhouse. Special attention is given to creating safe environments that allow participation at whatever level is authentic for each participant.
The Studio Building and Farmhouse provide comfortable lodging.
Hope Springs is carefully integrated into farmland and the forest ecosystem. The weekend incorporates mindfulness skills as a tool for managing difficult emotions such as anxiety.
Abundant green space and a contemplative labyrinth provide wonderful settings for expanded mindfulness and program activities.
The weekend allows ample leisure time for reflection and to enjoy the restorative setting of an expansive Appalachian Woodland. This woodland sanctuary includes user-friendly trails and creates an environment of solitude. Optional time for meditation walks and a low-impact recreational hike are included in the program agenda.
Careful attention is given to nutritious food. The meals at Hope Springs are delicious cuisine, featuring both animal protein, vegetarian and gluten free options. Special dietary requests are accommodated to insure that each participant has ample, high quality, and enjoyable food throughout the weekend.
For further information about Hope Springs, click here . You can also visit their website for more information.
Weekend of Recovery (WOR) Retreats provide complementary support for any male – 18 or older – who is a survivor of sexual trauma as a child and/or as an adult. By engaging participants in creating an environment that supports safety needs for male survivors, our program format seeks to acknowledge and honor the authentic diversities of attendees at each WOR (racial, ethnic, class, spirituality, sexuality, gender, etc.). Alumni of WOR retreats report the experience contributed to easing their suffering; to enabling higher functioning; to facilitating healthier relationships with friends, partners, children; to inspiring activism; and to diminishing the cycle of victimization.
involving accessibility issues and/or special needs.


1. Department of Physical Medicine and Rehabilitation, Taichung Tzu Chi Hospital, Buddhist Tzu Chi Medical Foundation, Taichung City 427, Taiwan.
2. Department of Physical Medicine and Rehabilitation, School of Medicine, Tzu Chi University, Hualien 970, Taiwan.
3. Graduate Institute of Sports Science, National Taiwan Sport University, Taoyuan 33301, Taiwan.
5. Graduate Institute of Metabolism and Obesity Sciences, Taipei Medical University, Taipei 11031, Taiwan.
Current treatment options for muscle injuries remain suboptimal and often result in delayed/incomplete recovery of damaged muscles. In this study, the effects of dextrose prolotherapy on inflammation and regeneration of skeletal muscles after a contusion injury were investigated. Mice were separated into five groups, including a normal control (NC), post-injury with no treatment (mass-drop injury, MDI), post-injury with 10% dextrose (MDI + 10% dextrose), post-injury with 20% dextrose (MDI + 20% dextrose), and post-injury with 30% dextrose (MDI + 30% dextrose). The gastrocnemius muscles of the mice were subjected to an MDI, and muscle samples were collected at 7 days post-injury. Results showed the serum creatine kinase (CK), blood urea nitrogen (BUN), creatinine (CREA), and low-density lipoprotein (LDH) of the MDI-alone group were significantly higher than those of the normal control group (p<0.05). However, levels of serum CK, BUN, CREA, and lactate dehydrogenase (LDH) significantly decreased with different concentrations of dextrose. In addition, dextrose suppressed the macrophage response (F4/80 protein decreased) and promoted muscle satellite cell regeneration (desmin protein increased). In conclusion, dextrose prolotherapy can effectively help repair muscles; therefore, it may be one of the methods for clinically treating muscle injuries.
Keywords: dextrose, prolotherapy, contusion, mass-drop injury (MDI), diclofenac (DCF).
Among sports injuries, up to 35%~55% are soft-tissue injuries . Soft-tissue injuries can cause significant pain, swelling, and bruising to the affected muscle, ultimately leading to delayed and impaired functionality . The pathophysiology of muscle injuries includes a series of complex stages which may occur simultaneously, including degeneration, inflammation, regeneration, and the formation of fibrotic scar tissue [3-6]. Depending on the intensity of the injury, damages to skeletal muscle may also be accompanied by capillary rupture, infiltrative bleeding, inflammation, oxidative stress, and fibrosis. Inflammation plays a key role in these processes, since inflammatory cytokines mediate the cellular environment, which largely controls the progress of other repair processes. Therefore, inflammation seems the best target for developing effective treatments for faster repair.
Recent research focused on modulating inflammation to improve muscle regeneration, for example, by targeting immune cells activated during the inflammatory phase [7,8]. During inflammation, chemotactic signals draw neutrophils and macrophages to the site of injury for phagocytosis [5,9,10]. Neutrophils, macrophages, and satellite cells damage the surrounding tissues unaffected by the primary injury by producing reactive oxygen species, resulting in oxidative stress, and causing secondary muscle damage. Despite the fact that macrophages in the early stage may participate in sustaining the inflammatory response and contribute to secondary damage, these cells also release various growth factors which directly accelerate tissue repair and regeneration [5,11]. In addition, both neutrophils and macrophages stimulate T cells to secrete cytokines such as interleukin (IL)-1, IL-6, and IL-8 as well as other chemotactic factors, and recruit satellite cells, fostering a greater capacity for muscle regeneration [5,12,13]. Therefore, it could be concluded that although inflammation is conducive to secondary damage, it is also a critical factor in repairing muscle cells after an injury. This is also the reason why when the inflammatory response is severely blocked for a prolonged period of time, for example, by non-steroidal anti-inflammatory drug (NSAID) treatment, it might not result in successful clinical outcomes, due to delayed and/or incomplete tissue healing and excessive scar formation, which increase the risk of injury recurrence.
Bertrand et al.  found that injection with hypertonic dextrose in patients with painful rotator cuff tendinopathy on painful entheses resulted in better long-term pain improvement and patient satisfaction than did an injection of saline, and results of enthesis injections were intermediate. While the regenerative effect could not account for such differences, dextrose prolotherapy may improve standard care for painful rotator cuff tendinopathy in certain patients. Lee et al.  showed that prolotherapy can improve the pain, disability, isometric strength, and shoulder acute rupture of membranes (AROM) in patients with refractory chronic rotator cuff disease. Therefore, dextrose prolotherapy may be a potential candidate for further development as an effective treatment for clinical use to repair muscles after sterile contusion injury. Nevertheless, as far as we know, dextrose prolotherapy for contusion-induced muscle injuries in mice remains unreported. In this study, we evaluated the effects of dextrose prolotherapy on contusion-induced muscle injuries in mice by investigating the serum lactate dehydrogenase (LDH) and creatine kinase (CK) as well as the expressions of F4/80 and desmin after muscle injuries.
Male ICR mice (8 weeks old; 30~40 g) were purchased from BioLASCO (A Charles River Licensee, Yi-Lan, Taiwan). Experimental animals were given 1 week to acclimatize to the environment and diet. All animals were fed a chow diet (no. 5001; PMI Nutrition International, Brentwood, MO, USA) and distilled water ad libitum, and were maintained on a regular cycle (12-h light/dark) at room temperature (24±2 °C) and 60%~70% humidity. The bedding was changed and cleaned twice a week. All animal experimental protocols were approved by the Institutional Animal Care and Use Committee (IACUC) of National Taiwan Sports University, and the study conformed to guidelines of protocol IACUC-10505-M approved by the IACUC ethics committee.
As shown in Fig. 1A, 48 mice were randomly assigned to six groups (8 mice/group), namely: (1) a normal control (NC), animals injected with saline with no injury; (2) mass-drop injury (MDI), animals injected with saline at 2 h post-injury; (3) MDI + 10% dextrose, animals injected with 10% dextrose at 2 h post-injury; (4) MDI + 20% dextrose, animals injected with 20% dextrose at 2 h post-injury; (5) MDI + 30% dextrose, animals injected with 30% dextrose at 2 h post-injury; and (6) MDI + DCF (diclofenac, an NSAID), animals injected with DCF at 2 h post-injury. On day 7 after injury at the end of the experiment, mice were sacrificed. Serum was collected by centrifugation at 1500 ×g and 4 °C for 10 min. The liver, muscles, lungs, kidneys, heart, and epididymal fat pad tissues were collected and weighed. Muscle tissues were snap-frozen and stored at -80 °C until further analysis.
Contusion injury to a mouse hind-limb was produced using a mass-drop injury method as described in a previous study  with slightly modification. Briefly, the technique entails dropping a 50-g weight from a height of 60 cm onto the medial surface of the left gastrocnemius muscle after exposure to 4%~5% isoflurane (Fig. 1B). This contusion injury had a medium intensity and did not cause bone injury or gait abnormalities in the MDI groups.
At the end of the experiments, after an 8-h fast, mice were sacrificed by 95% CO2 asphyxiation, and blood was withdrawn by cardiac puncture. Serum was collected by centrifugation, and levels of blood urine nitrogen (BUN), creatinine (CREA), lactate dehydrogenase (LDH), and creatine kinase (CK) were assessed as our previous study .
The liver, muscles, lungs, kidneys, heart, and fat tissues were removed at the end of the experiment, and fixed in 10% neutral buffered formalin for 24 h before being processed for a histopathologic analysis as we previously described . Tissues were embedded in paraffin and cut into 4-μm-thick slices for morphological and pathological evaluation, then stained with hematoxylin and eosin (H&E) and examined with a light microscope equipped with a CCD camera (BX-51, Olympus, Tokyo, Japan). For IHC, paraffin-embedded samples were cut into 5-μm-thick sections, deparaffinized, and rehydrated through an alcohol-to-water gradient, and then treated with boiling water for 15 min. Sections were incubated in 3% hydrogen peroxide for 10 min to block endogenous peroxidase activity and then incubated overnight at 4 °C with the primary rabbit monoclonal antibody, F4/80 (MA5-16363; Thermo Scientific, Waltham, MA, USA), working dilution 1:100 and the rabbit polyclonal antibody, desmin (SC-14026; Santa Cruz Biotechnology, Santa Cruz, CA, USA), working dilution 1:25. For antigen retrieval, the sections were immunostained with the VECTASTAIN® ABC kit (UNIVERSAL, VECTOR, USA) in accordance with the manufacturer's specifications. Diaminobenzidine (DAB) was used for staining development, and sections were counterstained with hematoxylin. In the negative controls, normal serum was substituted for the primary antibodies.
(A) The schedule of dextrose prolotherapy treatment for contusion-induced muscle injuries in mice. (B) The gastrocnemius muscle of mice was subjected to a mass-drop injury (MDI). Mice were randomly assigned to six groups (8 mice/group), namely: (1) normal control (NC), animals injected with saline without injury; (2) MDI, animals injected with saline at 2 h post-injury; (3) MDI + 10% dextrose, animals injected with 10% dextrose at 2 h post-injury; (4) MDI + 20% dextrose, animals injected with 20% dextrose at 2 h post-injury; (5) MDI + 30% dextrose, animals injected with 30% dextrose at 2 h post-injury; and (6) MDI + DCF (diclofenac, an NSAID), animals administrated DCF at 2 h post-injury.
All results are expressed as the mean±standard error of the mean (SEM) (n = 8). The significance of the difference was calculated by a one-way analysis of variance (ANOVA) with Duncan's post-hoc test, and values of < 0.05 were considered significant.
Results of the one-way ANOVA indicated that there were no significant differences in body weight, food intake, liver mass, muscle mass, lung mass, kidney mass, heart mass, or epididymal fat pad mass of mice in the MDI + 10% dextrose, MDI + 20% dextrose, and MDI + 30% dextrose groups compared to the MDI group.
Effect of dextrose prolotherapy on serum blood urea nitrogen (BUN) on contusion-induced muscle injuries in mice. Mice were randomly assigned to five groups (8 mice/group), namely: (1) normal control (NC), animals injected with saline without injury; (2) mass-drop injury (MDI), animals injected with saline at 2 h post-injury; (3) MDI + 10% dextrose, animals injected with 10% dextrose at 2 h post-injury; (4) MDI + 20% dextrose, animals injected with 20% dextrose at 2 h post-injury; and (5) MDI + 30% dextrose, animals injected with 30% dextrose at 2 h post-injury. Data are the mean±SEM (n = 8 mice/group). Different letters indicate a significant difference at p<0.05 by a one-way ANOVA.
Effect of dextrose prolotherapy on serum creatinine (CREA) on contusion-induced muscle injuries in mice. Mice were randomly assigned to five groups (8 mice/group), namely: (1) normal control (NC), animals injected with saline without injury; (2) mass-drop injury (MDI), animals injected with saline at 2 h post-injury; (3) MDI + 10% dextrose, animals injected with 10% dextrose at 2 h post-injury; (4) MDI + 20% dextrose, animals injected with 20% dextrose at 2 h post-injury; and (5) MDI + 30% dextrose, animals injected with 30% dextrose at 2 h post-injury. Data are the mean±SEM (n = 8 mice/group). Different letters indicate a significant difference at p<0.05 by a one-way ANOVA.
In vehicle control mice, the serum BUN level was 21.2 ± 0.8 mg/dL. In animals with a contusion-induced muscle injuries, the serum BUN level was elevated to 26.1 ± 1.5 mg/dL. Therefore, the serum BUN level showed an increase of 23.3% compared to the vehicle control (p<0.05). As shown in Fig. 2, serum BUN levels of the MDI + 10% dextrose (20.7±0.7 mg/dL), MDI + 20% dextrose (18.8±0.5 mg/dL), and MDI + 30% dextrose (18.9±0.3 mg/dL) groups were significantly lower compared to the MDI-alone group (26.1 ± 1.5 mg/dL) (p<0.05). Therefore, mice injected with 10%, 20%, and 30% dextrose after injury had significantly lower serum BUN levels by 20.6%, 27.9%, and 27.5%, respectively, than the MDI-alone group. But, there was no significant dose-dependent effect on the serum BUN level.
Compared to vehicle control mice (0.23±0.02 mg/dL), the serum CREA level of the MDI-alone group (0.27±0.02 mg/dL) significantly increased by 21.0% (p<0.05) (Fig. 3). Serum CREA of the MDI + 10% dextrose group was 0.21±0.01 mg/dL (23.7% lower than that of the MDI-alone group, p<0.05); serum CREA of the MDI + 20% dextrose group was 0.15±0.01 mg/dL (46.6% lower than that of the MDI-alone group, p<0.05); and serum CREA of the MDI + 30% dextrose group was 0.13±0.01 mg/dL (53.9% lower than that of the MDI-alone group, p<0.05). There was a significant dose-dependent effect on the serum CREA level (p<0.05). Therefore, animals injected with 10%, 20%, and 30% dextrose had significantly reduced serum CREA.
Although LDH is abundant in tissue cells, blood levels of the enzyme are normally low. However, when tissues are damaged by injury, they release more LDH into the bloodstream. Thus, serum LDH is known to serve as an accurate indicator of muscle trauma. As shown in Fig. 4, the serum LDH level of the MDI-alone group (681±26 U/L) showed an increase of 25.1% compared to the vehicle control group (544±26 U/L) (p<0.05). However, animals injected with 10%, 20%, and 30% dextrose showed significant reductions in serum LDH by 13.9%, 21.5%, and 27.4%, respectively, compared to the MDI-alone group (p<0.05). Results showed that dextrose prolotherapy reduced serum LDH levels due to contusion-induced muscle injuries in mice.
A contusion can cause physical damage, and then lead to sarcomeric damage and muscular cell necrosis . Muscle cells release CK into the blood indicating that muscle damage has occurred or is occurring. Clinically, CK is known to serve as an accurate indicator of muscle damage. As shown in Fig. 5, the serum CK level of the MDI-alone group (1586±229 U/L) showed an increase of 239.5% compared to the vehicle control (467±48 U/L) (p<0.05). However, serum CK levels of the MDI + 10% dextrose (959±144 U/L), MDI + 20% dextrose (908±91 U/L), and MDI + 30% dextrose (1003±116 U/L) groups decreased compared to the MDI-alone group (1586±229 U/L). Thus, animals injected with 10%, 20%, and 30% dextrose showed significant reductions in serum CK by 39.6%, 42.8%, and 36.7%, respectively, compared to the MDI-alone group (p<0.05). In this study, dextrose prolotherapy reduced serum CK levels in mice with contusion-induced muscle injuries.
Effect of dextrose prolotherapy on serum lactate dehydrogenase (LDH) on contusion-induced muscle injuries in mice. Mice were randomly assigned to five groups (8 mice/group), namely: (1) normal control (NC), animals injected with saline without injury; (2) mass-drop injury (MDI), animals injected with saline at 2 h post-injury; (3) MDI + 10% dextrose, animals injected with 10% dextrose at 2 h post-injury; (4) MDI + 20% dextrose, animals injected with 20% dextrose at 2 h post-injury; and (5) MDI + 30% dextrose, animals injected with 30% dextrose at 2 h post-injury. Data are the mean±SEM (n = 8 mice/group). Different letters indicate a significant difference at p<0.05 by a one-way ANOVA.
As shown in Fig. 6, groups did not differ in histological observations of the liver, lungs, kidneys, heart, or fat tissues of mice in the MDI, MDI + 10% dextrose, MDI + 20% dextrose, MDI + 30% dextrose, and MCD + DCF groups compared to the vehicle control group. Figure 6 shows the therapeutic effect of dextrose prolotherapy against contusion-induced muscle injuries using H&E staining. Histological evaluation of muscle tissues showed that the blunt force to the muscle markedly disrupted and damaged the muscle fibers, resulting in red blood cell accumulation in the interstitial spaces after contusion-induced muscle injuries in mice. However, injection of dextrose and DCF could recover disruption of the muscle tissues in contusion-induced muscle injuries. Among four treatments, 10% dextrose exhibited the best recovery effect, and the therapeutic effect of 10% dextrose was better than that of DCF (the positive control).
Effect of dextrose prolotherapy on serum creatine kinase (CK) on contusion-induced muscle injuries in mice. Mice were randomly assigned to five groups (8 mice/group), namely: (1) normal control (NC), animals injected with saline without injury; (2) mass-drop injury (MDI), animals injected with saline at 2 h post-injury; (3) MDI + 10% dextrose, animals injected with 10% dextrose at 2 h post-injury; (4) MDI + 20% dextrose, animals injected with 20% dextrose at 2 h post-injury; and (5) MDI + 30% dextrose, animals injected with 30% dextrose at 2 h post-injury. Data are the mean±SEM (n = 8 mice/group). Different letters indicate a significant difference at p<0.05 by a one-way ANOVA.
The indicator desmin was used to evaluate the regeneration of muscle satellite cells. As shown in Fig. 7A, desmin protein expression of the MDI-alone group showed an increase compared to the vehicle control. In addition, animals injected with 10%, 20%, and 30% dextrose showed significant increases in desmin protein expression compared to the MDI-alone group. The data indicate that dextrose prolotherapy resulted in more-effective muscle repair after contusion-induced muscle injuries. These results indicate that a dextrose injection can elevate desmin expression with a contusion, which in turn can promote the regeneration of muscle satellite cells. George et al.  found that desmin expression steadily increased after injury, with the highest values at 7 days after injury. In this study, desmin expression also increased for 7 days after the contusion. George et al.  showed that Prosopis glandulosa significantly elevated desmin expression, thereby facilitating more-effective muscle recovery. Thus, in this study, dextrose prolotherapy elevated desmin expression, thereby promoting muscle recovery in contusion-induced muscle injuries.
Effects of dextrose prolotherapy on pathological histology of (A) the liver, (B) muscles, (C) lungs, (D) kidneys, (E) heart, and (F) epididymal fat pad tissues on contusion-induced muscle injuries in mice. Mice were randomly assigned to seven groups (8 mice/group), namely: (1) vehicle + 30% dextrose, animals injected with 30% dextrose without injury; (2) vehicle control, animals injected with saline without injury; (3) mass-drop injury (MDI), animals injected with saline at 2 h post-injury; (4) MDI + 10% dextrose, animals injected with 10% dextrose at 2 h post-injury; (5) MDI + 20% dextrose, animals injected with 20% dextrose at 2 h post-injury; (6) MDI + 30% dextrose, animals injected with 30% dextrose at 2 h post-injury; and (7) MDI + DCF (diclofenac, an NSAID), animals administrated DCF at 2 h post-injury.
The indicator F4/80 was used to evaluate macrophage infiltration. As shown in Fig. 7B, the muscle tissue distribution of the murine macrophage-specific antigen, F4/80, was assessed using IHC. F4/80 protein expression of the MDI-alone group showed an increase compared to the vehicle control. However, animals injected with 10%, 20%, and 30% dextrose exhibited reduced F4/80 protein expressions compared to the MDI-alone group. In addition, F4/80 protein expressions with 10%, 20%, and 30% dextrose were less than that with DCF. Furthermore, 10% dextrose produced the most obvious decrease in F4/80 protein expression among the four treatments. Data indicate that dextrose prolotherapy resulted in more-effective muscle repair after a contusion than the NSAID, DCF. These results indicate that mice with a contusion-induced muscle injuries injected with dextrose prolotherapy exhibited decreased F4/80 protein expression compared to the MDI-alone group; so dextrose prolotherapy could decrease macrophages in the repair of muscle after contusion-induced muscle injuries.
Proliferative therapy has become established worldwide since the 1930s. In a clinical trial, Dr. Hackett found that the main cause of musculoskeletal pain may be ligament injuries, and thus developed prolotherapy which included an injection of autologous platelet extraction and high-concentration glucose [20,21]. In the past 2 years, hyperplasia therapy has been continually applied for clinical implementation in rehabilitation departments in Taiwan. High-concentration glucose water was proven to be effective in clinical outcomes [14,15,22], but the mechanism of dextrose prolotherapy on contusions remains unclear. Therefore, we investigated the effects of dextrose prolotherapy on contusion-induced muscle injuries in a murine model. During contusion injury, myocytes and other surrounding cells release chemotactic factors, which causes immune cells to be attracted and move to the site of damage [3,9,23]. In this study, we proposed that dextrose prolotherapy is a potential candidate for treating contusion injuries. We assessed the effects of macrophages infiltrating into the injured area, and their influence on the situation of regeneration. We found that dextrose was associated with restraining the response of macrophages to contusion injury.
IHC staining of (A) F4/80 protein and (B) desmin protein in muscle tissues after contusion-induced muscle injuries in mice. Mice were randomly assigned to seven groups (8 mice/group), namely: (1) vehicle + 30% dextrose, animals injected with 30% dextrose without injury; (2) vehicle control, animals injected with saline without injury; (3) mass-drop injury (MDI), animals injected with saline at 2 h post-injury; (4) MDI + 10% dextrose, animals injected with 10% dextrose at 2 h post-injury; (5) MDI + 20% dextrose, animals injected with 20% dextrose at 2 h post-injury; (6) MDI + 30% dextrose, animals injected with 30% dextrose at 2 h post-injury; and (7) MDI + DCF (diclofenac, an NSAID), animals administrated DCF at 2 h post-injury.
Nevertheless, dextrose prolotherapy actually facilitated more-effective muscle recovery with increased F4/80 expression in muscle cells, while it decreased the infiltration of macrophages during the process of muscle repair after contusion-induced muscle injuries (Fig. 7B). Inflammatory cells which infiltrated into the injured muscle, as well as the satellite cells, appear to be the most crucial to successful regeneration. Among these inflammatory cells, monocytes/macrophages play key roles in this repair process. These cells responded to local vascular damage, and molecules released by degenerating myofibers extravasated from the blood and infiltrated into injured areas, to phagocytose myofiber debris. In addition to this critical function, inflammatory cells also produce growth factors, cytokines, inflammatory mediators, and damage signals that deeply affect the state of satellite cells during the repair process . Along with monocyte/macrophage recruitment, resting satellite cells are activated by damage/inflammation-associated signals and begin to proliferate, supplying enough myonuclei for the formation of new myofibers. As shown in Fig. 7A, mice injected with 10%, 20%, and 30% dextrose showed significant increases in desmin protein expression compared to the MDI-alone group. Therefore, these results reveal that dextrose can promote desmin expression in mice with contusion-induced muscle injuries by facilitating muscle satellite cell regeneration. Consistent with our other data, desmin expression significantly increased after dextrose treatment, inducing better conditions for muscle fiber repair. In contrast, desmin expression after NSAID treatment was significantly lower than with dextrose treatment, again implying an inhibitory ability of NSAID toward repair, as suggested in the literature . George et al.  pointed out that the initial suppression of repair by NSAIDs can be overcome if NSAID administration is limited to 1~2 days post-injury, but it was proven that NSAID treatment should not be administered after these very early time points post-injury.
In this study, dextrose prolotherapy suppressed the macrophage response (F4/80 protein decreased) and promoted muscle satellite cell regeneration (desmin protein increased) after contusion injury. In addition, dextrose prolotherapy decreased serum LDH and CK levels by improving muscle damage after contusion-induced muscle injuries in mice. Thus, dextrose prolotherapy facilitated effective muscle recovery after contusion-induced muscle injuries. The present results suggested that injection with 10% dextrose once after contusion-induced muscle injuries showed a better therapeutic effect than 20% dextrose, 30% dextrose, and DCF. Therefore, these results showed that 10% dextrose has great potential for more-effective muscle repair after sterile contusion injury.
This research was supported by the Ministry of Science and Technology of Taiwan (grant no. MOST 105-2314-B-303-004 to Sen-Wei Tsai and MOST 106-2313-B-038-003-MY2 to Yu-Tang Tung), and institutional grants to Dr. Tsai (Taichung Tzu Chi Hospital, Buddhist Tzu Chi Medical Foundation) and to Dr. Tung (grant no. TMU106-AE1-B15, Taipei Medical University). The authors are grateful to Dr. Chien-Chao Chiu for technical assistance with animal experiments.
Sen-Wei Tsai, Chi-Chang Huang, and Yu-Tang Tung designed the experiments. Sen-Wei Tsai, Yi-Ju Hsu, Chi-Chang Huang, and Yu-Tang Tung carried out the laboratory experiments. Sen-Wei Tsai, Hao-En Huang, and Yu-Tang Tung analyzed the data, interpreted the results, prepared the figures, and wrote the manuscript. Sen-Wei Tsai, Hao-En Huang, Chi-Chang Huang, and Yu-Tang Tung revised the manuscript. Sen-Wei Tsai, Chi-Chang Huang, and Yu-Tang Tung contributed reagents, materials, and analytical platforms.


text:
Q: Errors Installing previous version of ggvis Upon updating ggvis to 0.4.3, the shiny application I built was no longer working.  I am therefore trying to revert ggvis back to the previous version, however, when I run the following code:
foo <- "https://cran.r-project.org/src/contrib/Archive/ggvis/ggvis_0.4.2.tar.gz"
install.packages(foo, repos=NULL, type="source")

based on this post: Installing older version of R package
This is the result in the console.  I have replaced the name of the company and user in the directories with "company" and "user" respectively for discretion.
Installing package into '\\company/user/R/win-library/3.3'
(as 'lib' is unspecified)
trying URL 'https://cran.r-project.org/src/contrib/Archive/ggvis/ggvis_0.4.2.tar.gz'
Content type 'application/x-gzip' length 728345 bytes (711 KB)
downloaded 711 KB

'\\company\user'
CMD.EXE was started with the above path as the current directory.
UNC paths are not supported.  Defaulting to Windows directory.
* installing *source* package 'ggvis' ...
** package 'ggvis' successfully unpacked and MD5 sums checked
** R
** data
*** moving datasets to lazyload DB
** demo
** inst
** preparing package for lazy loading
** help
*** installing help indices
** building package indices
** installing vignettes
Warning in file(con, "w") :
  cannot open file '\\company/user/R/win-library/3.3/ggvis/doc/index.html': No such file or directory
Error in file(con, "w") : cannot open the connection
ERROR: installing vignettes failed
* removing '\\company/user/R/win-library/3.3/ggvis'
* restoring previous '\\company/user/R/win-library/3.3/ggvis'
Warning in install.packages :
  running command '"C:/PROGRA~1/R/R-33~1.1/bin/x64/R" CMD INSTALL -l "\\company\user\R\win-library\3.3" "C:/Users/user/AppData/Local/Temp/RtmpuOIfA9/downloaded_packages/ggvis_0.4.2.tar.gz"' had status 1
Warning in install.packages :
  installation of package 'C:/Users/user/AppData/Local/Temp/RtmpuOIfA9/downloaded_packages/ggvis_0.4.2.tar.gz' had non-zero exit status

The result is either ggvis stays as version 0.4.3.
I tried the exact same code to revert back to 0.4.2 on another machine running the same version of RStudio (3.3.1) on a mac instead of my windows machine and it worked just fine.  I am at a loss as to why I am not able to reinstall 0.4.2 of ggvis on my machine.
Thanks

redpajama_set_name: RedPajamaStackExchange


Konecranes has said its business has slowed down in the UK and it is confident the decision to scale back its UK operations in 2018 was the right move.
With the announcement of its fourth quarter and 2018 results, Konecranes' president and CEO, Panu Routila, stated that decision making within certain customer sectors is slowing down and economic activity among its UK customers stagnated during 2018 "amid Brexit uncertainty", but the company, which has 12 locations throughout the UK, expected a limited impact.
Mr Routila said: "We are the only foreign vendor in our industry with local manufacturing in the UK. While our local presence can potentially be a relative benefit to us in the case of hard Brexit, we are confident that the scaling-down of our UK operations in 2018, as a part of our integration activities, was rightly timed.
Overall, "the momentum in Port Solutions right now is good" and product demand is stable in EMEA, the Americas and APAC, though Konecranes last year decided to ramp down its joint venture port crane factory in Seoul, China, which came with a MHPS acquisition.
The order intake in the fourth quarter of 2018 was "the highest ever in the history of Konecranes," growing in all business areas and in all three regions. The value of the order book at the end of December totalled approximately EUR1.7bn, approximately 180m higher compared to the beginning on 2018.


When moviegoers first met Anne Hathaway, she was a frizzy-haired teen named Mia Thermopolis who lived in a firehouse and just happened to be royalty. The Princess Diaries was Hathaway's silver screen debut, but that wasn't the only notable thing about director Garry Marshall's family flick. He managed to snag semi-retired Dame Julie Andrews to play Mia's grandmother, the queen of (fictional) Genovia. Also in the cast? A secret Coppola and an actual politician. Read the details on Marshall's casting choices, as well as his sly Pretty Woman references, below.
1. ANNE HATHAWAY GOT THE PART BY FALLING OUT OF HER CHAIR.
How did 18-year-old Anne Hathaway land her first movie? Simple: by falling on her face. Hathaway was apparently so nervous during her audition that she slid off her chair, which immediately endeared her to Garry Marshall. He cast her as klutzy Mia based on that audition alone.
2. GARRY MARSHALL WAS A JULIE ANDREWS SUPERFAN.
3. IT WAS FILMED ON THE SAME STAGE AS MARY POPPINS.
Andrews returned to a sentimental place for this shoot. The Princess Diaries was filmed on Stage 2 in Walt Disney Studios—which is also where Robert Stevenson shot the movie that made Andrews a star, Mary Poppins. "Karma, I tell you," she said in an interview. "When I went onto that soundstage, there was a little plaque on the door that says, 'Mary Poppins was filmed here' and suddenly I became very nostalgic." The set got another plaque in 2001 when it was rechristened "Julie Andrews Stage 2" to honor the actress.
4. IT WAS ORIGINALLY CALLED THE PRINCESS OF TRIBECA.
The film's first title referenced its literary roots. In Megan Cabot's book series The Princess Diaries, Mia and her mom live in Manhattan. This was the original plan for the movie, too, so it was called The Princess of Tribeca. But the location was changed to San Francisco further into production, which meant the name had to be tweaked as well.
5. THE CAST WAS FULL OF FAMILY MEMBERS.
For Marshall, The Princess Diaries was a family affair. His daughter Kathleen played Queen Clarisse's assistant, Charlotte Kutaway; his wife Barbara played Lady Jerome; and his granddaughters Lily and Charlotte played the two girls who ask Mia for her autograph. He wasn't the only one roping family members into roles. Marshall's longtime friend Hector Elizondo (who acted in every single movie Marshall made, including this one) got his granddaughter, Juliet, a small part as the Genovian prime minister's daughter, Marissa Motaz.
6. JULIE ANDREWS AND HECTOR ELIZONDO CONSPIRED TO MAKE THEIR CHARACTERS A COUPLE.
7. ROBERT SCHWARTZMAN'S FAKE BAND PLAYED A SONG BY HIS REAL BAND.
Mia's love interest, Michael Moscovitz, plays keyboard for a fictional band called Flypaper. Coincidentally, the actor who played Michael has a band of his own. Robert Schwartzman is the frontman for Rooney, whose single "Blueside" appears in the movie. Schwartzman actually plays the song onscreen at a Flypaper band practice, along with another real-life Rooney bandmate, Ned Brower.
8. HE'S ALSO PART OF A HOLLYWOOD DYNASTY.
Schwartzman has only acted in a handful of films, but you might've seen his brother Jason in a Wes Anderson movie or two. If not, he's got plenty of other famous family members. Robert's mom is Talia Shire, his uncle is legendary director Francis Ford Coppola, and his cousins include Sofia Coppola and Nicolas Cage. No wonder he showed up in Sofia's first two movies, Lick the Star and The Virgin Suicides.
9. THERE'S A PRETTY WOMAN CONNECTION.
Marshall's movie Pretty Woman has a lot in common with The Princess Diaries. Both films have a Pygmalion-esque transformation story and actors like Elizondo and Patrick Richwood. But they also contain an identical joke: In The Princess Diaries, Mia accidentally breaks a glass at her first fancy dinner. A sympathetic waiter immediately runs over and assures her that "it happens all the time." Similarly, in Pretty Woman, Vivian embarrasses herself at a posh dinner when she accidentally flings an escargot across the room. A waiter catches it mid-air and tells her "it happens all the time." The craziest part? Both waiters are played by the same actor, Allan Kent.
10. THE MAYOR OF SAN FRANCISCO PLAYED HIMSELF.
11. WHITNEY HOUSTON WAS A PRODUCER.
Whitney Houston was one of four credited producers on the film. She also returned to produce the sequel, The Princess Diaries 2: Royal Engagement. See if you can spy her at the end of this B-roll footage.
12. THE MOVIE NEARLY COST HATHAWAY LATER ROLES.
While promoting 2015's The Intern, Hathaway admitted that she struggled to be taken seriously after The Princess Diaries. "It was a great first job. It was a hit," she told The Huffington Post. "But at the same time, it was a hard thing to be like, 'You know, Robert Rodriguez, I swear: I can do one of your movies.' It was hard to get into rooms to be taken seriously for roles that weren't princesses." In one case, this bias nearly cost her a job. Hathaway's director on Becoming Jane, Julian Jarrold, initially didn't want to meet with her at all. Her first audition didn't impress him either, but she won him over in the second one. Weirdly, she did this by showing up sleep-deprived.