text:
\section{Introduction}

The multiple-scattering series (MSS) has played a prominent role in the study of meson-
nucleus interactions. The sum of all rescattering terms where meson scatters back and
forth between a pair of static nucleons, i.e., in the Fixed Centers Approximation (FCA) was derived
by Foldy \cite{Foldy45} in 1945. It was applied to the $\pi d$-scattering by Br\"{u}ckner \cite{Bruckner53} in 1953.
According to Br\"{u}ckner, the $\pi d$-scattering amplitude is the FCA amplitude averaged over the deuteron wave function:
\begin{equation}
\label{1_1}
F_{\pi d}=\int |\psi_d({{\bf r}})|^2 \frac{f_1+f_2+2\frac{f_1f_2}{r}e^{ikr}}{1-\frac{f_1f_2}{r^2}e^{2ikr}}d{\bf r}.
\end{equation}
Here $f_1 (f_2)$ are the $\pi N$ scattering amplitudes on the first (second) nucleon of the deuteron
and $\psi_d({\bf r})$ is the deuteron wave function, $\int |\psi_d({\bf r})|^2d{\bf r}=1$. Expression (\ref{1_1})
was first obtained in \cite{KolKud72} by summing the set of the multiple-scattering diagrams.
More recently the terms of the MSS have been discussed in the context of the effective-field-theory (EFT) treatment
of $\pi$-nucleus scattering. The first EFT calculation of the $\pi d$ scattering amplitude was
performed by Weinberg \cite{Wein92}. Different aspects of the MSS in EFT formalisms have been refined
in the next twenty years, see, e.g., \cite{refs}. Expression (\ref{1_1}) for $F_{\pi d}$
in an EFT framework was first recreated in \cite{Rus}.
In our recent publication \cite{Baru12} we discussed from the point of view of an EFT
the fact that, if the meson-nucleon scattering is approximated by the scattering length,
the individual terms of the series are divergent and enhanced
with respect to the straightforward expectation from the chiral perturbation theory ($\chi$PT).
We also showed in that work that the divergences cancel if the series is resummed.

In the present paper we make an attempt to analyse the status of the resummed expression for
the $\pi d$ scattering amplitude (\ref{1_1}). Considering the case of equal amplitudes $f_1=f_2=a$, we
get the following expression for the resummed MSS amplitude $F(a)$ in the coordinate space at zero energy:

$$F(a)=F^{(1)}(a)+F^{(2)}(a),$$
where $F^{(1)}(a)=2a$ is the single scattering contribution and

\begin{equation}\label{1_2}
F^{(2)}(a)=2a^2\int |\psi_d({\bf r})|^2 \frac{1}{r-a}d{\bf r}.
\end{equation}
Here $F^{(2)}(a)$ is the sum of the double-scattering term $f^{(2)}(a)$, the triple-scattering term $f^{(3)}(a)$
and so on:

$$F^{(2)}(a)=f^{(2)}(a)+f^{(3)}(a)+...+f^{(n)}(a)+...,$$
where

$$f^{(n)}(a)=2a^n\int |\psi_d({\bf r})|^2\frac{d{\bf r}}{r^{n-1}}\,.$$
Note that we define the scattering length as $a=f(k=0)$,
so the case of $a>0$ corresponds to effective attraction in the $\pi N$-subsystem.

In our previous paper \cite{Baru12} we concentrated mainly on the case of
the negative scattering length, $a<0$. In this case integral (\ref{1_2}) for the amplitude $F^{(2)}(a)$ is well defined.
However, in the case of attraction ($a>0$) the expression for $F^{(2)}(a)$ (\ref{1_2})
becomes formally divergent and one needs additional information
as to how to deal with the pole singularity in Eq. (\ref{1_2}). The first step
towards solving this problem has been done in \cite{Baru12}.
We showed there that the Fourier transform $P(Q)$ of the function $(r-a)^{-1}$ that enters the integral in (\ref{1_2}),
\begin{equation}
P(Q)=\int e^{i{\bf Q}{\bf r}}\frac{1}{r-a}d{\bf r}=\frac{4\pi}{Q^2}+\frac{4\pi a}{Q}f(-aQ),
\end{equation}
where
\begin{equation}
f(y)=\int\limits_0^{+\infty}\frac{\sin x}{x+y}dx=\Ci(y)\sin y+\left(\frac{\pi}{2}-\Si(y)\right)\cos y
\end{equation}
with $\Si(y)$ and $\Ci(y)$ being the sine and cosine integral functions, acquires a cut from $aQ=0$ to $aQ=+\infty$,
due to the cosine integral having a branch point at $y=0$.
It means that at $a>0$ the function $P(Q)$ becomes complex, i.e., it has a nonzero imaginary part.
Returning to the integral representation for $F^{(2)}(a)$ (\ref{1_2}),
we conclude that $F^{(2)}(a)$ has to be considered as an analytic function of the complex parameter
$a=a_1+ia_2$. This leads us to define the amplitude $F^{(2)}(a)$ for real and positive $a>0$
as the limit of $F^{(2)}(a_1+ia_2)$ as $a_2\rightarrow 0$. This prescription
gives for $F^{(2)}(a)$ at $a>0$:
\begin{equation}\label{1_3}
F^{(2)}(a)=8\pi a^2\ \Vp\int |\psi_d(r)|^2\frac{r^2 dr}{r-a}+i\cdot 8\pi^2a^4\psi_d^2(a).
\end{equation}

According to (\ref{1_3}), the $\pi d$ scattering length is complex even
when no inelastic channels are present.
It might mean that the 3-body meson-deuteron scattering problem is not well defined if the meson-nucleon off-shell
amplitude is approximated by the constant scattering length. To check this hypothesis, we can try to find
a representation of the sum of the MSS terms different from that given by Eq. (\ref{1_2}).

Our paper is structured as follows.
In Section 2 we calculate and resum the MSS in the momentum space.
In contrast to what we had in the coordinate space, here we get a reasonable
answer for the amplitude $^m\! F^{(2)}(a)$. However, this answer still reflects the presence of the singularity in
the expression for $F^{(2)}(a)$ (\ref{1_2}). The resulting solution in the momentum space, obtained numerically,
appears to be an oscillating function of the size of the discretization grid.
To finally decode the answer, we need to introduce a finite range into the elementary $\pi N$-amplitude.
This procedure allows us to sum all the MSS terms and to get finite answers in both the coordinate and
the momentum space representations and to perform a comparison of the results. This is done
in Section 3. In Section 4 we discuss the applicability of both representations of $F^{(2)}(a)$
to the cases of complex and real negative scattering lengths $a$. In the Conclusions we
summarise the results of our research.
In particular, we discuss the physical reasons
behind the final answer for the MSS amplitude becoming ill-defined when the range of the elementary $\pi N$ amplitude goes to zero.

\section{The basic equation for the MSS in the momentum space}

Using the Feynman diagram technique one can easily obtain (see, e.g., \cite{KolKud72,BaruKud97})
3-dimensional expressions for the multiple-scattering amplitudes $f^{(n)}(a)$ in the FCA:

\begin{equation}\label{2_1}
f^{(n)}(a)=\int\frac{\varphi_d({\bf p})}{(2\pi)^3}\Sigma^{(n)}({\bf p},{\bf p}\,')
\frac{\varphi_d({\bf p}\,')}{(2\pi)^3}d{\bf p}d{\bf p}\,',\ n=2,3,...,
\end{equation}
where $\varphi_d({\bf p})$ is the deuteron wave function in the momentum space, normalized such that
$\int |\varphi_d({\bf p})|^2d{\bf p}=(2\pi)^3$, and
\begin{equation}
\begin{split}
  \Sigma^{(2)}({\bf p},{\bf p}\,')=&2a^2\frac{4\pi}{({\bf p}-{\bf p}\,')^2+{\varkappa}^2},{}\\
  \Sigma^{(3)}({\bf p},{\bf p}\,')=&2a^3\int\frac{d{\bf s}}{(2\pi)^3}
  \frac{4\pi}{({\bf p}-{\bf s})^2+{\varkappa}^2}\frac{4\pi}{({\bf s}-{\bf p}\,')^2+{\varkappa}^2},{}\\
  \Sigma^{(4)}({\bf p},{\bf p}\,')=&
\nonumber
\end{split}
\end{equation}
\begin{equation}\label{2_2}
\begin{split}
  2a^4\int\frac{d{\bf s}d{\bf t}}{(2\pi)^6}
  \frac{4\pi}{({\bf p}-{\bf s})^2+{\varkappa}^2}\frac{4\pi}{({\bf s}-{\bf t})^2+{\varkappa}^2}
  \frac{4\pi}{({\bf t}-{\bf p}\,')^2+{\varkappa}^2}\,,
\end{split}
\end{equation}
and so on.
To avoid the IR singularities in the integrals for $\Sigma^{(n)}({\bf p},{\bf p}\,')$, we introduce
the IR cutoff $\varkappa$ everywhere in the denominators of the pionic propagators.
Taking into account only the leading S-wave part of the deuteron wave function,
one can perform all the angular integrations in (\ref{2_1}), resulting in
\begin{equation}
\begin{split}
  f^{(2)}(a)=2a^2\frac{1}{4\pi^3}&\int\limits_0^{+\infty}p\varphi_d(p)\{\ln_{\varkappa}(p,p')\}\varphi_d(p')p'dpdp',{}\\
  f^{(3)}(a)=2a^3\frac{1}{4\pi^3}\times&
\nonumber
\end{split}
\end{equation}
\begin{equation}\label{2_3}
\begin{split}
\int\limits_0^{+\infty}p\varphi_d(p)\left(\int\limits_0^{+\infty}\frac{ds}{2\pi}
  \ln_{\varkappa}(p,s)\ln_{\varkappa}(s,p')\right)\varphi_d(p')p'dpdp',
  \end{split}
\end{equation}
and so on, where we denote
$$\ln_{\varkappa}(p,p')=\ln\frac{(p+p')^2+\varkappa^2}{(p-p')^2+\varkappa^2}.$$
The answer for the full MSS amplitude $^m\! F^{(2)}(a)=\sum\limits_{n=2}^{+\infty}f^{(n)}(a)$
in the momentum space representation then reads:
\begin{equation}\label{2_4}
  ^m\! F^{(2)}(a)=2a^2\frac{1}{4\pi^3}\int\limits_0^{+\infty}p\varphi_d(p)R(p,p')\varphi_d(p')p'dpdp',
\end{equation}
where the function $R(p,p')$ is a solution of the integral equation:
\begin{equation}\label{2_5}
  R(p,p')=\ln_{\varkappa}(p,p')+a\int\limits_0^{+\infty}\frac{ds}{2\pi}\ln_{\varkappa}(p,s)R(s,p').
\end{equation}
It is convenient to introduce dimensionless variables $x,y,z$ and a parameter $L$:

$$p=p_0x, \enskip p'=p_0y, \enskip s=p_0z; \enskip \varkappa=p_0L.$$

To solve equation (\ref{2_5}) numerically we introduce the upper limit of the integration (regularization),
$\Lambda=Np_0$. We take the parameter $N$ to be an integer.
To satisfy the boundary conditions $R(p,0)\equiv R(0,p')\equiv 0$,
the parameters $p_0, \varkappa$ and $\Lambda$ have to satisfy $p_0\ll\varkappa\ll\Lambda$
(or $1\ll L \ll N$). Now we introduce a dimensionless integer-valued grid of size $N$ with the step 1.
The discrete version of our basic equation (\ref{2_5}) reads:
\begin{equation}\label{2_6}
  R_N(i,j)=\ln_L(i,j)+\epsilon\sum\limits_{k=1}^N\ln_L(i,k)R_N(k,j),
\end{equation}
where we denote $R_N(i,j)\equiv R_N(x_i,y_j)$,
$\ln_L(i,j)\equiv \ln_L(x_i,y_j)$, $x_i=i-\frac{1}{2}, y_j=j-\frac{1}{2}, 1\leq i,j\leq N$ and
$\epsilon=\displaystyle\frac{ap_0}{2\pi}$. The solution $R_N(i,j)$ of equation (\ref{2_6}) depends on the size $N$ of the grid, and is a matrix
$N\times N$.

Solving Eq. (\ref{2_6}) numerically, we found that $R_N(i,j)$ nontrivially depends on $N$.\footnote{Note that special
efforts were performed to check stability of the results of our numerical procedure. In particular, we varied scale
$p_0\to\widetilde{p}_0=p_0/n$ and $N\to\widetilde{N}=N\cdot n$ ($n=2,3,4$) and found that numerical results survive.}
Some examples of the solution $R_N(x,y)$ at different $N$ are presented in Figs.~\ref{Fig01}, \ref{Fig02}.
\begin{figure}
\centering
\includegraphics[width=\linewidth]{Figure01.eps}
\caption{The dependence of the function $R(x,y)$ on $x$ at $y=0.5$ for some typical cutoffs $N$ (here $N$ is the size of the grid).
The solid curve 1 corresponds to $N=50$; 2 -- to $N=150$; 3 -- to $N=190$; 4 -- to $N=200$; 5 -- to $N=210$; 6 -- to $N=220$.
The first critical point $N_{crit}^{(1)}=205$. The dashed-dotted curve shows the Born perturbative term
$R_0(x,y)=\ln\frac{(x+y)^2+L^2}{(x-y)^2+L^2}$, also at $y=0.5$. The parameters used in the calculation:
$a=10^{-3}\ \mathrm{MeV}^{-1}$, $p_0=10\ \mathrm{MeV}$, $L=2.5$.}
\label{Fig01}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=\linewidth]{Figure02.eps}
\caption{The same as in Fig.~\ref{Fig01} but for larger $N$. Curve 1 corresponds to $N=290$; 2 -- to $N=350$; 3 -- to $N=450$; 4 -- to $N=510$; 5 -- to $N=540$; 6 -- to $N=560$.
The second critical point $N_{crit}^{(2)}=525$.}
\label{Fig02}
\end{figure}
The evolution
of $R_N(x,y=0.5)$ as a function of $N$ is the following. At small $N$ the exact solution behaves similarly
to the function $R_0(x,y)$, which is the leading perturbative approximation for $R_N(x,y)$ in terms of the parameter $\epsilon$,
$$R_0(x,y)=\ln\frac{(x+y)^2+L^2}{(x-y)^2+L^2}.$$
The function $R_0(x,y=0.5)$ is pictured in Fig.~\ref{Fig01} by the dashed-dotted line. We see that
the solid curves 1 and 2 in Fig.~\ref{Fig01} behave similarly to $R_0(x,y)$. However, with growing
$N$ the solution $R_N(x,0.5)$ deviates sharply from $R_0(x,0.5)$.
At $N$ near $N_{crit}^{(1)}=205$, the solution blows up to the positive infinity,
then changes its sign to become the negative infinity
and continues its evolution as $N$ increases (compare curves 4, 5 and 6 of Fig.~\ref{Fig01}).
Simultaneously, at $N>N_{crit}^{(1)}$ solution $R_N(x,0.5)$ develops a node at small $x$.
This node moves to the right with the growth of $N$ (compare curves 5 and 6 of Fig.~\ref{Fig01}).

The evolution of $R_N(x,0.5)$ with $N$ further increasing is shown in Fig.~\ref{Fig02}.
The solution blows up again at $N$ near the second critical point $N_{crit}^{(2)}=525$ and the story repeats.
At $N>N_{crit}^{(2)}$, the second node of $R_N(x,0.5)$ emerges, see curves 5 and 6 in Fig.~\ref{Fig02}.

The further observed evolution of $R_N(x,0.5)$ with $N$ appears to be periodic or cyclic --- there is an infinite
series of critical points ${N_{crit}^{(i)}}$, and the solution $R(x,0.5)$ blows up in the vicinity of each $N_{crit}^{(i)}$.
This behavior of the amplitude $^m\! F_N^{(2)}$ versus $N$ is demonstrated in Fig.~\ref{Fig03} for some selected scattering lengths $a$.
\begin{figure}
\centering
\includegraphics[width=\linewidth]{Figure03.eps}
\caption{The dependence of the scattering amplitude $^m\! F^{(2)}(a)$ on the grid size $N$.
The calculation is performed with the following parameters: i) $a=0.0035\ \mathrm{MeV}^{-1}$; ii) $a=0.005\ \mathrm{MeV}^{-1}$; iii) $a=0.01\ \mathrm{MeV}^{-1}$.}
\label{Fig03}
\end{figure}
Within the accuracy of calculation the distance between two adjacent critical points $(N_{crit}^{(i+1)}-N_{crit}^{(i)})$
was found to be independent of $i$. This observation means the dependence of $N_{crit}^{(i)}$ on $i$ is linear,
which is demonstrated in Fig.~\ref{Fig04} for different scattering lengths $a$.
\begin{figure}
\centering
\includegraphics[width=\linewidth]{Figure04.eps}
\caption{The dependence of pole positions $N_{crit}^{(i)}$ on $i$ for different values of $a$.
Line 1 corresponds to $a=0.0035\ \mathrm{MeV}^{-1}$, 2 -- to $a=0.005\ \mathrm{MeV}^{-1}$ and 3 -- to $a=0.01\ \mathrm{MeV}^{-1}$.}
\label{Fig04}
\end{figure}

Note that in the vicinity of any $N_{crit}^{(i)}$ the amplitude $^m\! F_N^{(2)}(a)$ behaves similarly
to the situation when a new bound state is created at threshold: it grows to infinity and then changes its sign.
We can argue that what we observe in our numerical calculation is an evidence
that, in the limit $\Lambda\rightarrow\infty$, the 3-body system we are studying has an infinite number of bound states.
To prove this hypothesis conclusively, we need to search for the source
of creation of the series of bound states in the $\pi d$-system. For this purpose we are going to introduce a finite range $r_0$
of the force (which is equivalent to a formfactor) for the elementary $\pi N$-system
and to study the dependence of the amplitude $F^{(2)}(a)$ on $r_0$. This scenario will be the subject of the next section.

\section{Introducing a formfactor into the elementary $\pi N$-amplitude}

The elementary $\pi N$-interaction potential is, in general,
characterized by a certain finite range of force and hence the $t$-matrix is momentum dependent.
The impact of the inclusion of a formfactor in the function $F^{(2)}(a)$
in the coordinate space was already discussed in \cite{Baru12}. Here we want to introduce
formfactor in the momentum space and to compare the results of both approaches.

Consider the full off-shell $\pi N$ amplitude in the separable form:
$$f(p,p';E=0)=ag(p)g(p'),$$
where we take
$$g(p)=\frac{M}{\sqrt{M^2+p^2}}\,.$$
The limit of the zero-range $\pi N$-interaction corresponds to $M$ going to infinity.

In the coordinate space, the introduction of this formfactor leads to the following modification
of the expression for $F^{(2)}(a)$ (\ref{1_2}):
\begin{equation}\label{3_1}
\begin{split}
  F_M^{(2)}&(a)=2a^2\frac{M^2}{M^2-\varkappa^2}\times\\
&\int |\psi_d({\bf r})|^2 \frac{e^{-\varkappa r}-e^{-Mr}}{r-\left( \frac{M^2}{M^2-\varkappa^2} \right)a(e^{-\varkappa r}-e^{-Mr})}d{\bf r}.
\end{split}
\end{equation}
In the limit $\varkappa \rightarrow 0$ this expression coincides with that discussed in \cite{Baru12}.
In contrast to what we had in the point-like limit (\ref{1_2}), this expression for $F_M^{(2)}(a)$ is well defined in the
region $\displaystyle Ma<1+\frac{\varkappa}{M}$.
At $\displaystyle Ma>1+\frac{\varkappa}{M}$ the pole singularity in the denominator emerges again.

In the momentum space, the expression for the amplitude $^m\! F_M^{(2)}(a)$ with the formfactor $g(p)$ reads:
\begin{equation}\label{3_2}
\begin{split}
  ^m\! F_M^{(2)}(a)=&2a^2\frac{1}{4\pi^3}\left(\frac{M^2}{M^2-\varkappa^2}\right)\times\\
&\int\limits_0^{+\infty} p\varphi_d(p)R_M(p,p')\varphi_d(p')p'dpdp',
\end{split}
\end{equation}
where $R_M(p,p')$ is the solution of the following integral equation (cf.\ Eq.~(\ref{2_5})):
\begin{equation}\label{3_3}
\begin{split}
  R_M(p,p')=&\ln_{\varkappa,M}(p,p')+\\
&a\frac{M^2}{M^2-\varkappa^2}\int\limits_0^{+\infty}\frac{ds}{2\pi}\ln_{\varkappa,M}(p,s)R_M(s,p'),
\end{split}
\end{equation}
where
$$\ln_{\varkappa,M}(p,p')=\ln_{\varkappa}(p,p')-\ln_M(p,p').$$

Comparing the functions $F_M^{(2)}(a)$ and $^m\! F_M^{(2)}(a)$,
calculated in both the coordinate and
momentum space representations, we find that they practically coincide for the values of
the parameter $M\leq M_0$, where $M_0$ is determined from the equation:
\begin{equation}\label{3_4}
  M_0 a=1+\frac{\varkappa}{M_0}.
\end{equation}
For $M>M_0$ the function $F_M^{(2)}(a)$ in the coordinate representation is formally divergent similar to the point-like case discussed in the previous section.

The function $^m\! F_M^{(2)}(a)$, calculated in the momentum space according to Eq.~(\ref{3_2}), is well defined also for $M>M_0$.
Some examples of the solution for $^m\! F_M^{(2)}(a)$ in the momentum space versus $a$ are demonstrated in Fig.~\ref{Fig05}
\begin{figure}[h]
\centering
\includegraphics[width=\linewidth]{Figure05.eps}
\caption{The function $^m\! F_M^{(2)}(a)$ versus $a$ for different values of $M$.
Curve 1 corresponds to $M=150\ \mathrm{MeV}$; 2 -- to $M=220\ \mathrm{MeV}$; 3 -- to $M=250\ \mathrm{MeV}$; 4 -- to $M=300\ \mathrm{MeV}$; 5 -- to $M=500\ \mathrm{MeV}$.}
\label{Fig05}
\end{figure}
for some different values of $M$. All calculations were carried out with the cut-off parameter $\Lambda=2500$ MeV.
For $M>M_0$ these functions depend crucially on $M$.
The amplitude $^m\! F_M^{(2)}(a)$, calculated in the momentum space representation at
$a=5\cdot 10^{-3} \mathrm{MeV}^{-1}$ as a function of $M$, is shown in Fig.~\ref{Fig06}.
\begin{figure}
\centering
\includegraphics[width=\linewidth]{Figure06.eps}
\caption{The function $^m\! F_M^{(2)}(a)$ versus $M$ for $a=0.005\ \mathrm{MeV}^{-1}$, $M_0=222\ \mathrm{MeV}$.}
\label{Fig06}
\end{figure}
One can see the set of critical points $M_{crit}^{(i)}$ which appear as spikes.
All the singular points $M=M_{crit}^{(i)}$ are located to the right from the point $M=M_0$ (\ref{3_4}),
$M_{crit}^{(i)}>M_0$. At $M<M_0$ the amplitude $^m\! F_M^{(2)}(a)$ is smooth, positive and finite.
For $M\rightarrow M_{crit}^{(1)}$ \quad $^m\! F_M^{(2)}(a)$ goes to $+\infty$, then changes its sign and continues its further evolution
with $M$. A similar behavior is seen near the second critical point $M_{crit}^{(2)}$.
The function $R_M(x,y=0.5)$ is nodeless for $M$ being in the interval
$M\in(\varkappa,M_{crit}^{(1)})$, while it develops its first node in the interval $M\in(M_{crit}^{(1)},M_{crit}^{(2)})$.
Some typical pictures for the function $R_M(x,y=0.5)$ are demonstrated in Fig.~\ref{Fig07}. The further evolution of
$R_M(x,y=0.5)$ with $M$ also appears to be cyclic.
\begin{figure}
\centering
\includegraphics[width=\linewidth]{Figure07.eps}
\caption{The function $R_M(x,y=0.5)$ versus $x$ at different typical $M$: a) $M=150\ \mathrm{MeV}$; b) $M=260\ \mathrm{MeV}$; c) $M=280\ \mathrm{MeV}$; d) $M=330\ \mathrm{MeV}$; e) $M=380\ \mathrm{MeV}$.}
\label{Fig07}
\end{figure}

We conclude that for $M<M_0$ the 3-body system under our study
appears to be in an attractive but perturbative regime without forming any bound state.
At $M=M_{crit}^{(1)}$ the attraction is getting strong just enough to form the first bound state.
The amplitude $F_M^{(2)}(a)$ for $M>M_{crit}^{(1)}$ becomes negative, which
corresponds to the effective repulsion. With the further
growth of $M$ this picture repeats periodically. In the limit $M\rightarrow +\infty$
an infinite set of bound states in the $\pi d$-system is formed. Hence we conclude that the perturbative approach
is not applicable in this extremely nonperturbative case of positive scattering length $a$.
Looking again at Fig.~\ref{Fig06}, we also conclude that the function $^m\! F_M^{(2)}(a)$
behaves akin to $\tan M$, i.e., periodically oscillates from minus to plus infinity.
It means that this function has no definite limit as $M$ goes to infinity, i.e., in the point-like limit. This observation is in line
with the fact that the function $F_M^{(2)}(a)$ in the coordinate representation
is not well-defined for $M>M_0$. On the other hand, treating $F^{(2)}(a)$ as an analytic function of
$a=a_1+ia_2$, we come to expression (\ref{1_3}).

Thus, the straightforward solution of the integral equation for the function $R_M(p,p')$
at real positive values of scattering length $a$ tells us
that the function $^m\! F^{(2)}(a)=\lim\limits_{M\rightarrow +\infty}^{\phantom{I}} {\phantom{I}} ^m\! F_M^{(2)}(a)$ does not exist.
The analyticity hypothesis for the function $F^{(2)}(a)$, on the other hand,
gives us a unique solution for $F^{(2)}(a)$ (see Eq.~(\ref{1_3})).
The situation looks rather ambiguous. To make the correct choice and to solve the problem
we should study the properties of the function $F^{(2)}(a)$ in the
complex $a$-plane. It will be the subject of discussion in the next section.

\section{Inclusion of absorption}

In the real $\pi d$-system the effect of absorption is not the leading one because both
elastic $\pi N$-amplitudes ($\pi^-p\rightarrow\pi^-p$ and $\pi^-n\rightarrow\pi^-n$) are real.
The role of absorption is more crucial in the $K^-d$-scattering problem because of
the presence of open inelastic two-body channels $K^-N\rightarrow\pi\Sigma(\pi\Lambda)$.
The FCA is widely used for the $K^-d$ scattering problem, see, e.g., \cite{Kamalov}.
For more recent publications see \cite{Oset} and references therein.

Note that expression (\ref{1_2}) for the amplitude $F^{(2)}(a)$ is well defined
only if the imaginary part of the scattering length $a=a_1+ia_2$ differs from zero, $a_2\neq 0$.
On the other hand, we may solve Eq.~(\ref{3_3}) for the function $R_M(p,p')$ considering the parameter $a$
as a complex one. Calculating this function $^m\! F_M^{(2)}(a)$ in the momentum space, one can compare the
results of calculations for $F_M^{(2)}(a)$ in both the momentum and the space representations.
This comparison is demonstrated in Figs.~\ref{Fig08}--\ref{Fig12} for the cut-off parameter in Eq.~(\ref{3_3}) $\Lambda=2500$ MeV.
\begin{figure}
\centering
\includegraphics[width=\linewidth]{Figure08.eps}
\caption{The function $^m\! F_M^{(2)}(a)$ for scattering length $a=0.005\ \mathrm{MeV}^{-1}$.}
\label{Fig08}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=\linewidth]{Figure09.eps}
\caption{Real (dashed curve) and imaginary (solid curve) parts of the functions $F_M^{(2)}(a)$ (plot ({\it a})) and $^m\! F_M^{(2)}(a)$ (plot ({\it b})) for the scattering length $a=0.005+0.0001i\ \mathrm{MeV}^{-1}$.}
\label{Fig09}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=\linewidth]{Figure10.eps}
\caption{Real (dashed curve) and imaginary (solid curve) parts of the functions $F_M^{(2)}(a)$ (plot ({\it a})) and $^m\! F_M^{(2)}(a)$ (plot ({\it b})) for the scattering length $a=0.005+0.0003i\ \mathrm{MeV}^{-1}$.}
\label{Fig10}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=\linewidth]{Figure11.eps}
\caption{Real (dashed curve) and imaginary (solid curve) parts of the functions $F_M^{(2)}(a)$ (plot ({\it a})) and $^m\! F_M^{(2)}(a)$ (plot ({\it b})) for the scattering length $a=0.005+0.0005i\ \mathrm{MeV}^{-1}$.}
\label{Fig11}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=\linewidth]{Figure12.eps}
\caption{Real (dashed curve) and imaginary (solid curve) parts of the functions $F_M^{(2)}(a)$ (plot ({\it a})) and $^m\! F_M^{(2)}(a)$ (plot ({\it b})) for the scattering length $a=0.005+0.001i\ \mathrm{MeV}^{-1}$.}
\label{Fig12}
\end{figure}
The real part of the scattering length was fixed, $$a_1=5\cdot 10^{-3} \mathrm{MeV}^{-1}\,,$$
and we varied the imaginary part starting from very small positive $a_2$.
The starting point is Fig.~\ref{Fig08} that reproduces the function $^m\! F_M^{(2)}(a)$ versus $M$
for real and positive $a=a_1=5\cdot 10^{-3} \mathrm{MeV}^{-1}$. The function $^m\! F_M^{(2)}(a)$ in this figure is analogous
to what is shown in Fig.~\ref{Fig06}. We see quite a regular behavior of $^m\! F_M^{(2)}(a)$ at small $M<M_0$
and several singular points (or spikes) at $M>M_0$. The imaginary part of $^m\! F_M^{(2)}(a)$ is equal to zero.

In Fig. \ref{Fig09}{\it b} we draw the real and imaginary parts of the function $^m\! F_M^{(2)}(a)$, calculated in the momentum space
for complex scattering length $a=0.005+0.0001i\, (\mathrm{MeV}^{-1})$. Both $\Real\: ^m\! F_M^{(2)}(a)$ and $\Imag\: ^m\! F_M^{(2)}(a)$ are shown in this figure.
The behavior of the real and imaginary parts of $^m\! F_M^{(2)}(a)$ at $M$ near each of the $M_{crit}^{(i)}$
looks similar to their behavior in the vicinity of a Breit-Wigner resonance.
The next step of the evolution of the function $^m\! F_M^{(2)}(a)$ with increasing $\Imag a=a_2$ is shown in Fig.~\ref{Fig10}{\it b}
($a_2=0.0003\enskip \mathrm{MeV}^{-1}$). Although for this value of $a_2$ the peaks at this figure are still separated,
their corresponding regions already start to overlap. This tendency is better seen in Fig.~\ref{Fig11}{\it b} ($a_2=0.0005\enskip \mathrm{MeV}^{-1}$)
where the isolated peaks are seriously squeezed or deformed. Further evolution of $^m\! F_M^{(2)}(a)$ with
the growth of $a_2$ is demonstrated in Fig.~\ref{Fig12}{\it b}. We see in this figure that isolated
peaks disappear and both the real and imaginary parts of the function $^m\! F_M^{(2)}(a)$ become smooth
functions --- no peaks any more. We observe therefore that if the absorption ($\Imag a$) is not extremely small, i.e., $a_2$
is comparable with $a_1$, all the calculated curves behave quite regularly.

Now it is time to compare these results with what we get in the coordinate
representation, i.e., with the integral representation given by Eq. (\ref{3_1}). In Fig. \ref{Fig09}{\it a} the real
and imaginary parts of $F_M^{(2)}(a)$, calculated according to Eq. (\ref{3_1})
for $a=0.005+0.0001i\, (\mathrm{MeV}^{-1})$, are shown. Both functions look quite regular
and smooth. Note that $\Imag F_M^{(2)}(a)$ is extremely small at small $M<M_0\approx 220$.
This is a consequence of the fact that $\Imag a=a_2$ is taken extremely small. The growth of
$\Imag F_M^{(2)}(a)$ for $M>M_0$ looks like a threshold phenomenon. The origin of this non-negligible
imaginary part is similar to what is given in the r.h.s.\ of Eq.~(\ref{1_3}) for the point-like case.
This contribution may be called the ``unphysical'' part of $\Imag\: ^m\! F_M^{(2)}(a)$.
In the limit $a_2 \rightarrow 0$ and $M\rightarrow\infty$ the function $\Imag F_M^{(2)}(a)$
coincides with the imaginary part given in Eq.~(\ref{1_3}).
Further evolution of $F_M^{(2)}(a)$ at different values of $a_2$ is demonstrated in Figs.~\ref{Fig10}{\it a} -- \ref{Fig12}{\it a}.
As it is seen, the contribution of the ``physical'' absorption is getting more prominent with
growing $a_2$, which is intuitively clear as absorption on each individual scatterer is getting stronger.

It is instructive to compare Figs.~\ref{Fig09}{\it a} and \ref{Fig09}{\it b},
drawn for the same values of $a_2$. At extremely small $a_2$ they look absolutely different.
The function $^m\! F_M^{(2)}(a)$, calculated in the momentum space for small $a_2$, is an
oscillating function of $M$ with singular points. Because of the oscillating character no definite answer for this function
in the point-like limit $M\rightarrow +\infty$ exists. However, with the growing $a_2$ $^m\! F_M^{(2)}(a)$
is getting smooth and for large $a_2$ the profiles of the functions $F_M^{(2)}(a)$ and $^m\! F_M^{(2)}(a)$
calculated by different methods, coincide with each other (compare, e.g., the curves in Figs.~\ref{Fig12}{\it a} and \ref{Fig12}{\it b}).
Note that at relatively large $a_2$
$$\lim\limits_{M\rightarrow\infty} F_M^{(2)}(a)=F^{(2)}(a),$$
where $F^{(2)}(a)$ is the point-like limit for scattering amplitude given by Eq. (\ref{1_2}).

Concluding this section, we would like to stress that we used the momentum-space
representation to check the validity of the simple coordinate-space representation, given by Eq.~(\ref{1_2}).
We came to the conclusion that almost everywhere in the complex plane of parameter $a$ one can
use Eq.~(\ref{1_2}) to calculate the MSS. However, this equation gives incorrect answer
in a narrow region of complex $a$. This exceptional region is shown in Fig.~\ref{Fig13}
\begin{figure}
\centering
\includegraphics[width=\linewidth]{Figure13.eps}
\caption{The region of complex parameter $a$ in which the functions $F_M^{(2)}(a)$ and $^m\! F_M^{(2)}(a)$, calculated with $\Lambda=2500$ MeV,
don't coincide with accuracy better than 1\%.}
\label{Fig13}
\end{figure}
for the particular value $\Lambda=2500$ MeV.
The border of the dashed area is chosen under condition that functions $F_M^{(2)}(a)$ and $^m\! F_M^{(2)}(a)$,
calculated in the two different representations,
coincide with accuracy better than 1\%. Everywhere outside the marked area the FCA given by the simple and useful expression
(\ref{1_2}) is applicable. In the case of real negative $a\leq 0$,
the answers for the amplitudes $F_M^{(2)}(a)$ and $^m\! F_M^{(2)}(a)$ practically coincide identically as well.

Note that the results mentioned above were obtained at $\Lambda=2500$ MeV,
but we have also performed calculations with larger values of $\Lambda$.
We observed that the accordance between $F_M^{(2)}(a)$ and $^m\! F_M^{(2)}(a)$ increased with increasing $\Lambda$,
and the marked region in Fig.~\ref{Fig13} is reduced.

\section{Conclusions}

In this paper we demonstrated that the pion-deuteron scattering amplitude $F_{\pi d}$,
calculated in the Fixed Centers Approximation according to Eq.~(\ref{1_2}),
is correct and can be used in a rather wide region of the complex scattering length $a$.
Simultaneously, we proved that the coordinate representation in the FCA (\ref{1_2})
is getting incorrect and so cannot be used in a narrow region surrounding the real positive $a$ half-axis.
This region is marked in Fig.~\ref{Fig13}. For $a$ belonging to this region the interaction
between the incident light particle and the pair of the fixed centers, while being attractive,
becomes anomalously strong. Due to this anomalously strong attraction, an infinite set of $\pi NN$ bound states is formed.

An analogous situation, where an infinite set of bound states emerges as well, occurs in
the problem of the motion of a particle in a singular attractive potential, e.g.,

$$V(r)=-\frac{\beta}{r^n},$$
with $\beta >0$ and $n>2$, see, e.g., \cite{LL}, \S\S18, 35. The discrete part of the spectrum for
this problem is unbounded from below, i.e., the binding energy of the ground state is
infinite, whereas the size $r_0$ of the ground state goes to
zero. This is the phenomenon of ``the falling down to the center''.

Vitaly Efimov \cite{Efimov} showed in 1970 that the three-body system of identical bosons in the
limit of large two-body scattering length $a$ displays a specific discrete scale invariance. As
a consequence, there is an infinite number of 3-body bound states
and the ratio of binding energies of two successive 3-body bound states is approximately 515.
This cyclic behavior of the 3-body spectrum in the limit $a \rightarrow\infty$ has been rederived as the
leading order prediction of an EFT, see, e.g., \cite{Bedaque}. Note that the Efimov effect was
demonstrated to survive also in a model consisting of two heavy particles and a light one
when the light-heavy interaction leads to a zero-energy two-body bound state, see \cite{Fonseca}.

In our case, we found a similar (but not identical) cyclic behavior of the
spectrum of the system of a light particle interacting with a pair of fixed
centers, arising when the scattering length $a$, corresponding to the scattering
of the light particle on each of the fixed centers, is positive.

To study this problem,
we developed a method of getting the FCA amplitude by summing the
MSS in the momentum space.
In this representation we solved the problem numerically. To compare the results of both methods, we introduced
a finite range of interaction $r_0=M^{-1}$ for each of the scatterers.
The point-like limit corresponds to the case $M\rightarrow\infty$. The solutions of Eqs.~(\ref{2_5}) and (\ref{3_3})
for positive values of the scattering length $a$ confirmed the existence of an infinite set of bound states in
the $(\pi NN)$-system. Along with that, we found that no unique solution for the
$\pi d$-scattering length exists in the momentum representation for the case of $a>0$. The function $^m\! F_M^{(2)}(a)$,
which represents the $\pi d$ scattering length as a function of $a$ and $M$, is an oscillating function of $M$
and hence gives no well-defined answer in the point-like limit $M\rightarrow\infty$.
We conclude therefore that the $\pi d$ scattering lenght is not well-defined for positive values of $a$.

It is also instructive to discuss expression (\ref{1_3}) for the scattering amplitude $F^{(2)}(a)$.
As seen from Eq.~(\ref{1_3}), $F^{(2)}(a)$ is complex even for real values of $a$.
At the same time the imaginary part of $F_M^{(2)}(a)$, calculated in the coordinate space according to Eq.~(\ref{1_3})
even with extremely small values of the imaginary part of $a$, is also non negligible, see, e.g., Fig.~\ref{Fig09}.
Obviously, expressions (\ref{1_2}) and (\ref{1_3}) violate unitarity!
This violation of unitarity is a direct consequence of the singularity of the interaction we
are dealing with. In the case of a singular attractive potential,
due to the phenomenon of ``the falling down to the center'',
there is a sink of particles and hence the unitarity violation.
We have a similar picture in the FCA: the interaction is getting supersingular, and the unitarity is violated.

Still, in the physically interesting cases like the $K^-d$ scattering
the imaginary part of the elementary ($K^-N$ in the example at hand) scattering length is comparable with the real
part. In this case the interaction in the 3-body system is not singular any more. As shown in Section 4,
formula (\ref{1_2}) is applicable in this case and both the coordinate and momentum space approaches to the 3-body scattering problem
give practically the same answers for the scattering amplitude $F^{(2)}(a)$.

It is interesting, however, to understand better the physical interpretation of this
``unphysical'' imaginary part. In hadronic atoms the imaginary part of the scattering length is
usually proportional to the width $\Gamma_{nl}$ of the atomic level. In the absence of a phyiscal absorption
it is difficult to say what this additional width means.

In the end it is worth to stress that the problem we studied here is a special case
of the general 3-body scattering problem, which is usually formulated in terms of the Faddeev equations.
We took the elementary $\pi N$-amplitudes to be constant and found that for positive and real scattering lengths $a$
the 3-body system has an infinite number of bound states. The introduction of a formfactor (or a finite range of the
interaction) does not resolve the problem completely: for values of $M$ larger than some critical value $M_0$, $M>M_0$, the system also
has bound states.

To solve this problem, we first need to understand what are the minor modifications of the elementary amplitudes that
will allow us to avoid the singularity that arises in the FCA with constant amplitudes or to decipher its nature.

\section*{Acknowledgments}

\begin{sloppypar}
We thank V.~E.~Tarasov and V.~G.~Ksenzov for useful discussions, C.~Hanhart and E.~Epelbaum
for their interest to our work.
We are extremely grateful to V.~A.~Lensky for careful reading of our manuscript and for
many useful questions and remarks. We are also thankful to V.~V.~Baru for useful and constructive criticism.
This work was supported partly by the grant NSh-3172.2012.2. One of the authors (AEK) thanks also the DFG and NSFC
grant CNC 110 for partial support.
\end{sloppypar}

redpajama_set_name: RedPajamaArXiv


We now have a Quest Lab located inside of our office. This allows not only our cash-pay patients, but also those who use their insurance for labs to use Quest within our office for blood work. You no longer have to go to another location. We are excited to be able to expand our services in this way!
CAUTION: For those of you with insurance, it will often be less expensive to pay "out-of-pocket" for labs. CFP's contracted prices with Quest are much lower than what you will pay if your insurance denies coverage because it does not deem the tests "medically necessary" or because CFP is out-of-network. If your insurance denies coverage, you will pay what is called "delayed billing prices" which are 100-600% higher than what you would otherwise pay when you pay CFP directly at the time of service.
Please come for your labs prepared to tell us whether you plan to pay cash or have Quest bill your insurance. We cannot answer questions about your individual insurance plan's pricing, or whether your lab tests will be covered. Just as you have always done in the past, you need to contact your insurance company or the Quest Billing department at 1-800-377-8448 if you need help deciding whether or not to use it.
*Please note that only established patients can use the walk-in lab; new patients must be seen by a CFP practitioner first.


text:
Two Hands restaurant opens in Tribeca | Well+Good
Cult-Fave Cafe Two Hands Opens a New Full-Blown Restaurant in Tribeca
Kristy Mucci・April 20, 2016
Photos: Two Hands
New Yorkers are picky about their cafes and their options are endless, a combination which makes it nearly impossible for establishments to build a devoted following. But Two Hands—which sits on the border between Little Italy and Chinatown and has arguably the most Instagrammed avocado toast in town (no small feat)—has done exactly that, cultivating legions of fans obsessed with its awesomely low-key approach to healthy eating.
Now, its Aussie owners have opened a second, more ambitious location in Tribeca, this one a full-blown restaurant. Much of what made Two Hands cafe a smash remains, but there's also a much larger menu (yay!) and alcohol (double yay!). The goal with Two Hands Restaurant and Bar is to really introduce New Yorkers to what co-owner Henry Roberts calls "modern Australian" cuisine. Basically, stealth health food.
"Rather than screaming 'organic' or 'vegan' or shoving raw kale down your throat, we're primarily letting the produce speak for itself," Roberts says.
"I really dislike going to a health food restaurant and reading a menu and it saying, 'gluten-free, dairy-free, soy-free, sugar-free, free free free,' you know?" echoes Two Hands' other owner, Giles Russell. "For a customer that's really daunting."
Two Hands' new menu is fresh, vegetable-focused, and healthful—but also satisfying. Case in point: The brassicas bowl with charred broccolini, Brussels sprouts, kale, hummus, egg, and avocado, topped with pickled shallots. Sure, it's gluten-free, but that's not the focus; the goal is simply to celebrate the type of nourishing dishes and flavors Two Hands' owners grew up loving.
"Australian food is really simple. We eat fresh vegetables with really good grass-fed and free-range meats with eggs, and that's the style of food that we want to do here," says Russell. The restaurant is currently open daily from 8 a.m. to 5 p.m., but a dinner service will be starting soon (no hard date yet). Head chef Frankie Cox, also an Aussie, has been busy fine-tuning a menu that highlights the flavors of the season.
As for the space itself, it's significantly larger than the Mott Street spot, and gorgeously bright and airy. There's also a distinctly friendly, laid-back vibe shared by the staff that Russell and Roberts take a lot of pride in.
"When [customers] walk out and feel good on the inside and on the outside…it's super epic that you have that ability to affect someone like that," Russell says. "From a restaurant standpoint, that's the number-one goal." It's also a good way to establish a hardcore following.
Two Hands Tribeca, 251 Church St., New York, NY, 10013, twohandsnyc.com/restaurant/
If healthy exports are your thing, check out the jackfruit—it may just be the next big thing in plant-based protein.
Tags: Healthy Eating Tips

redpajama_set_name: RedPajamaCommonCrawl


text:
Expect more Sony first-party titles for the PC in the future
God of War on the PC soon?
August 31, 2020 By Chris Garcia 2 Mins Read
This year alone, Death Stranding and Horizon Zero Dawn have made their way into PC's everywhere and if Sony's corporate is any indication of things to come, then we can see more first-party titles make the jump.
Sony has recently published their 2020 Corporate Report, which discusses a lot of the efforts and plans for the company. A segment in the report, which you can find on Page 42 and 43, talks about their "Gaming & Network Services", and has a particularly interesting quote:
SIE aims to achieve robust revenue growth by accelerating the virtuous cycle that has been established for the PlayStation Platform. This entails increasing active users and play time, enhancing network services and reinforcing content IP so that consumers select PlayStation as their platform of choice. Targeted outcomes include growth in active users, stronger retention and a shorter cash conversion cycle, from which expanded cash flow can be expected. We will explore expanding our 1st party titles to the PC platform, in order to promote further growth in our profitability.
While it is not necessarily a bad thing, the underlying worry is that interest in the PlayStation 5 may dwindle due to these exclusive not being exclusives anymore. That may be true, but we'd like to think Sony are smart enough to have thought of that too, and similar to Horizon Zero Dawn, it is likely that these first-party titles will not be making the jump on day one, or maybe even within the year of launch.
It can be argued that some other high profile first party titles like Days Gone, God of War, and Spider-Man could see a resurgence in sales if and when they release for the PC, just like what Sega has done for Persona, so it really is an enticing option to take.
In the mean time, the PlayStation 5 still has some big first-party titles lined up like Spider-Man: Miles Morales and Ratchet & Clank: Rift Apart, which are expected to bolster hardware sales when it releases.
Virtual Pop Group K/DA is making a comeback
Review: Captain Tsubasa: Rise of New Champions – Hitting the goalpost


Going to the Cable Show?
Join research firm Parks Associates at a lunch presentation, Engaging the Consumer: Opportunities and Challenges in the Evolution of TV, on Thursday, April 2 at 12:45.
This special lunch session, sponsored by Macrovision, discusses the challenges for operators as they develop and deploy innovative services and business models. In addition, the participants will address the impact of open standards such as tru2way, both in the short term on operators' ability to develop interactive applications and their long-term influence on the evolution of the TV viewing experience.


text:
Institutional psychotherapy (also known as institutional analysis) is a French psychiatric reform movement and approach to group psychotherapy influenced by Marxism and Lacanian psychoanalysis starting in the 1950s. The Association of Institutional Psychotherapy was founded in November 1965. Those associated with the approach include François Tosquelles, Jean Oury, Felix Guattari, Frantz Fanon, and Georges Canguilhem. Institutional psychotherapy proposed a radical restructuring of the insane asylum and the mental health clinic where patients actively participated in running the facility. The approach began in Saint-Alban-sur-Limagnole with Tosquelles, Fanon and Oury, and then continued at the La Borde clinic founded by Oury and where Guattari worked until his death. Institutional psychotherapy is also practiced by Patrick Chemla at the Centre Artaud in Reims and has spread to Spain and Italy.

Although similar to anti-psychiatry in its institutional critique, the founders of institutional psychotherapy were adamant about distinguishing their approach from it, claiming that anti-psychiatry failed to account for the reality of mental illness, arguing that psychosis is not merely a social construct and were open to neuroleptics and even at times to electroshock treatment. Guattari wrote of a "systematic failure" of many psychiatrists to understand "what was going on outside the hospital walls", leading to a tendency to psychologize social problems. The goal according to Guattari was to "never to isolate the study of mental illness from its social and institutional context, and...to analyze institutions on the basis of interpreting the real, symbolic and imaginary effects of society upon individuals."

Institutional psychotherapy and the terminology used by the group of psychoanalysts associated with the approach took on a noticeable evolution throughout the 1960s to 1980s. After Guattari began to distance himself from the concept of schizoanalysis only one year after the publication of Anti-Oedipus (1972), later Guattari proposed that "institutional analysis" be used instead of "institutional psychotherapy". This change in nomenclature represented Guattari's intention to direct the practice at La Borde in a more political direction, calling for "a political analysis of desire. Guattari offered an extensive critique of institutional psychotherapy in the beginning of Molecular Revolution (1984) and introduced the concept of "institutional analysis". Guattari referred to the interactive transference that occurred at the La Borde clinic as "transversality", while Oury called it "transferential constellation".

See also
 Schizoanalysis
 Anti-psychiatry
 La Borde clinic
 Institutional pedagogy

External links
 http://www.bbk.ac.uk/hiddenpersuaders/blog/robcis-interview/
 Jean Oury and La Borde. Conversation with Camille Robcis. http://somatosphere.net/2014/jean-oury-and-clinique-de-la-borde-a-conversation-with-camille-robcis.html/
 Susana Caló, The Grid, 2016. https://www.anthropocene-curriculum.org/contribution/the-grid
 https://epg.pubpub.org/pub/03-institutional-therapy/release/1
 Susana Caló, Can an Institution be Militant?, 2019. https://www.academia.edu/38568214/Can_an_Institution_be_Militant

Further reading
 Felix Guattari, The Molecular Revolution: Psychiatry and Politics, 1984 - https://machinicunconsciousmachine.files.wordpress.com/2014/02/molecularrevolutions.pdf
 Georges Canguilhem, The Normal and the Pathological, 1991 - https://monoskop.org/images/b/b6/Canguilhem_Georges_The_Normal_and_the_Pathologic_1991.pdf
 Francois Dosse, Gilles Deleuze and Félix Guattari: Intersecting Lives, 2011

Psychotherapy

redpajama_set_name: RedPajamaWikipedia


text:
Is this why Google's Project Ara phones have been pushed to 2016?
Chris Smith, August 19, 2015 9:44 pm BST
Earlier this week Google announced it was pushing its Project Ara modular phone tests into 2016, but wasn't kind enough to inform the world as to why.
Flash forward a couple of days and the culprit may have been revealed; the electropermanent magnets that were being used to hold the components together aren't up to scratch.
In a pair of tweets posted from the Project Ara account on Wednesday, the team admitted the solution had failed the drop test and a "signature experience" was now being tested as a replacement.
https://twitter.com/statuses/634048152249634816
What Google has in mind for the replacement remains to be seen as no further information was revealed in the tweets.
On Monday Google announced it was cancelling plans to test Project Ara in Puerto Rico before the end of 2015, adding that it was now looking for alternative test locations in the US market for next year.
See also: What is Google's Project Ara all about?
The hugely ambitious endeavour seeks to free smartphone users from the need to update their device every two years.
If Project Ara comes to fruition users will be able to build their own custom handsets, replacing components as better cameras and more powerful processors become available.
Can you envision a modular future? Share your thoughts below.
Unlike other sites, we thoroughly review everything we recommend, using industry standard tests to evaluate products. We'll always tell you what we find. We may get a commission if you buy via our price links. Tell us what you think – email the Editor


Elton Fred Schlimmer died March 19, 2019.
He was born September 27, 1929, to Fred and Ida Schlimmer.
He graduated from Rutland High School in 1947, joined the National Guard, and was activated to Camp Carson, Colorado. There he married Evelyn Meyer, before returning to South Dakota to farm. They retired to Ocala, Florida, in 2009.
Elton is survived by his wife, Evelyn; three children: David, of Lake City, Florida; Carol (Ruano), of Quetzeltenango, Guatemala; Marvin, of Rochester, Minnesota, and a brother, Leland, of Volga.


text:
Die LASH-Schiffe des MARAD Design C9-S-81d wurden von 1971 bis 1975 in neun Einheiten bei der Werft Avondale Shipyards in New Orleans gebaut.

Geschichte
In den 1960er Jahren entwickelte der amerikanische Schiffbauingenieur Jerome L. Goldman das LASH-System und gründete zur Vermarktung des patentierten Systems die Lighter Aboard Ship Corporation. Hintergrund der Entwicklung waren die seinerzeit üblichen sehr langen Hafenliegezeiten, die mit der hohen Umschlagsleistung des LASH-Systems von über 1000 Tonnen pro Stunde verkürzt werden sollten. Noch vor der Indienststellung der ersten LASH-Schiffe Acadia Forest und Atlantic Forest in den Jahren 1969 und 1970 bestellten mehrere US-amerikanische Reedereien eine Serie von elf LASH-Schifen bei der Avondale-Werft in New Orleans. Diese begann 1970 mit dem Bau der Serie. Die ersten drei jeweils 28,5 Millionen US-Dollar teuren Schiffe des Typs wurden im Jahr 1973 an die Reederei Delta Line aus New Orleans abgeliefert, die sie als Delta-Mar-Klasse betrieb. 1974 folgten drei baugleiche Schiffe für die Waterman Steamship Corporation in Mobile, deren Stückpreis mit je 27,9 Millionen US-Dollar etwas günstiger ausfiel. Danach lieferte die Avondale-Werft 1974/75 schließlich drei Einheiten an die ebenfalls in New Orleans ansässige Central Gulf Lines, die mit je 27,5 Millionen US-Dollar pro Einheit einen nochmals geringeren Baupreis aufwiesen.

Zwei der Schiffe befinden sich noch heute in der Ready Reserve Force, die von der United States Maritime Administration (MARAD) unterhalten wird. Sie sind zwei von 48 RRF Schiffen in dessen "Sealift Program Office".

Technische Daten und Besonderheiten
Die sieben Laderäume der Schiffe, vier davon vor dem Maschinenraum, sind in insgesamt 18 Zellen zum Stauen von Leichtern und Containern unterteilt. Um ein optimales Laderaumvolumen zu erreichen, befinden sich die Deckshäuser weit vorn und die Maschinenräume der Schiffe so weit achtern wie technisch möglich. Die Übernahme der Leichter erfolgt am Heck mittels eines 460-Megapond-Portalkranes. Das Be- und Entladen mit 20-Fuß-Container– die sogenannten TEU (Twenty-foot Equivalent Unit) – und 40-Fuß-Container FEU (Forty-foot Equivalent Unit), kann ein 30-Megapond-Portalkran sowohl auf der Backbord- als auch auf der Steuerbordseite übernehmen. In der doppelwandigen Schiffskörperhülle, zwischen Laderaumlängsschott und der eigentlichen Außenhaut, befinden sich Wasser-, Treibstoff- und Öltanks.
Angetrieben werden die Schiffe von einer Zweiwellen-Getriebeturbine mit einer Leistung von 23.536 kW. Die Bordversorgung mit elektrischer Energie wird durch je einen 2000-kW-Turbo bzw. Dieselgenerator sichergestellt.
Die Wohnräume für die Besatzung befinden sich im Haupt- 1. und 2. Deck der Aufbauten. Die Bordverpflegung der Besatzung wird in speziellen 10-Fuß-Containern angeliefert und von einem separaten Schwenkkran auf der Steuerbordseite übernommen.

Die Schiffe

Literatur
 K. Dreßler: Jahrbuch der Schiffahrt 1975. transpress VEB Verlag für Verkehrswesen, Berlin, S. 95

Weblinks
 Artikel über die C9-S-81d-LASH-Schiffe bei globalsecurity (englisch) abgerufen am 22. Februar 2012
 Liste von in den USA gebauten LASH-Schiffen (englisch) abgerufen am 21. Februar 2012

Einzelnachweise

Containerschiffstyp
Frachtschiffsklasse
Avondale Shipyard


In recent years, the rise of ride sharing apps such as Uber and Lyft have changed the landscape for commercial driving services. California legislators are only now enacting legislation that specifically addresses ride sharing drivers. In 2017, new laws went into effect regarding how DUI laws apply to Uber and Lyft drivers. As many people want to work as an Uber or Lyft driver, it is important to understand what laws apply and what restrictions are now or will soon be in effect.
Prior to the adoption of Assembly Bill 2687, most ride sharing drivers operating a non-commercial vehicle were subject to a 0.08 percent BAC limit. In most cases, it would be legal to drive after consuming alcohol, as long as the driver's BAC was below 0.08 percent.
A lower legal limit applies to commercial drivers. Under California Vehicle Code Section 23152(d) VC, it is unlawful to drive a commercial motor vehicle, such as a truck, with a BAC of 0.04 percent or higher. A commercial vehicle is defined as any vehicle requiring a Class A or Class B license.
Under the previous DUI law, Uber and Lyft drivers, who were allowed to drive on their non-commercial Class C license and operate their personal vehicle, would only be subject to the 0.08 legal limit. However, the California legislature has amended the DUI statute. California Vehicle Code Section 23152(e) VC now reads "Commencing July 1, 2018, it shall be unlawful for a person who has 0.04 percent or more, by weight, of alcohol in his or her blood to drive a motor vehicle when a passenger for hire is a passenger in the vehicle at the time of the offense." This means that an Uber or Lyft driver who currently has a passenger for hire would no longer be subject to a 0.08 percent BAC limit, but instead would have a 0.04 percent limit and could be charged with a DUI offense for having a BAC of 0.04 percent or higher.
It is important to remember that this higher BAC only applies when the Uber or Lyft driver has a passenger for hire in his or her vehicle. Otherwise the driver would be subject to the regular 0.08 percent BAC limit. Legislators want to ensure that ride sharing drivers are driving safely and change in the law reflects this.
In addition, California legislators have enacted a new law that requires backgrounds checks for potential ride sharing drivers and prevents them from driving if convicted of certain offenses. Under Assembly Bill 1289, ride sharing companies would have to conduct criminal background checks on all applicants and would face steep fines and penalties if a driver is found to have committed a misdemeanor assault or battery, a domestic violence offense, a DUI offense or other specific crimes within the previous seven years.
This means that any person convicted of a DUI would be not be allowed to drive for Uber or Lyft for seven years. This is expected to affect many drivers who have old DUI convictions and who currently drive for Uber and Lyft as well as drivers who have been arrested for a new offense and rely on ride sharing for their income.
If you are a Los Angeles area Uber or Lyft driver who has been arrested for DUI, it is critical you review you case with a knowledgeable DUI attorney right away. Michael Kraut is a former Deputy District Attorney with over 14 years of prosecutorial experience who understands the severe consequences that a DUI can trigger and works hard to ensure his clients receive the best representation possible.
For more information about Los Angeles DUI and ride sharing services, and to schedule your free consultation, contact Michael Kraut at the Kraut Law Group located at 6255 Sunset Boulevard, Suite 1480, Los Angeles, CA 90028. Mr. Kraut can be reached 24/7 at 888-334-6344 or 323-464-6453.


Last month was a good month! Here's the latest from South Lake Union, Seattle.
We're big fans of everything Apple added to iOS 11. OmniFocus, OmniGraffle, and OmniPlan all adopted new features in these releases like Drag and Drop, Siri integration (for OmniFocus), and Files support, all there on September 19th. At the very beginning of this month—just a bit of lag time—OmniOutliner's update dropped.
Check out the blog post from launch day!
macOS High Sierra followed on the heels of iOS 11, along with our Mac compatibility updates.
Plus, even OmniDiskSweeper is being updated! Though still in Test, OmniDiskSweeper v1.10 includes APFS (the new file system introduced in High Sierra) and Folder Drop support. Folder Drop adds "ad hoc" folder-sweep functionality: just drop a folder on to the Dock icon.
Finally, OmniGraffle for Mac implemented a lot of fixes, along with a few new features for Omni Automation. (If you didn't know, that's our relatively new Cross-Platform application-scripting setup for Mac and iOS.) Check out the release notes if you're looking for a fix, and let us know if you've created any useful scripts!
Having a hand to hold when starting something new can be extremely helpful. In addition to our existing help and support resources, we've had users ask us to offer new ways of interacting with other members of the community, seasoned pros and beginners alike. So we're thrilled to introduce live community chat with Slack, Omni, and people like you!
If that sounds interesting or helpful, please do sign up and ask & answer questions, share your own workflows, and see what others have to offer. But remember that this is an experiment, and it's not an official place for support.
David Sparks and Brett Terpstra just released their second volume of Mac Tips, an ebook that includes an incredible number of useful tips in screencast form.
Sound handy? (It is.) Check out 60 Mac Tips: Volume 2 in the iBooks Store.
We're still planning to ship OmniOutliner 3 for iOS this quarter; it will start its public TestFlight within the next few weeks.
The OmniFocus features discussed in this year's roadmap will debut next quarter (Q1, 2018) with the public TestFlight of OmniFocus 3 for iOS.
Enjoy the rest of October!


text:
Rumor: The Order 1886 Sequel in Development
By Tyler Fischer - July 28, 2019 07:09 pm EDT
UPDATE: Jordan Mychal Lemos has clarified that he doesn't know if a sequel is in development, rather that's what articles in the past have lead him to believe.
Before this gets any more out of hand, I know nothing about a sequel. These are the types of articles I read last year and I remembered reading 11 months later as there was one coming. Sorry to disappoint. pic.twitter.com/tVPKGzavOJ
— Jordan Mychal Lemos (@crypticjordan) July 28, 2019
According to a new report/rumor, a sequel to The Order 1886 is in development, presumably for either PS4 or PS5 (or both). The news comes way of Jordan Mychal Lemos, a writer at Sucker Punch Productions who's currently working on Ghost of Tsushima, and who has worked at Ubisoft in the past on Asssasin's Creed Odyssey. More specifically, when talking about The Order 1886, and why everyone should play it with The Gamerheads podcast, Lemos revealed that the team over at Ready at Dawn is cooking up a follow-up.
"Everyone should play The Order 1886, especially since -- I guess they're making a sequel, which I don't know if it's The Order 1887 or-." At this point Lemos is cut off by the host of the show, who asks if Ready at Dawn is actually doing a sequel, which prompts Lemos to claim that last he heard the developer was making a second entry, which he says he's excited for.
Now, it's a bit unclear what Lemos means by "last time he heard." Did he hear this from someone at Ready at Dawn, or is this just something he picked up from a random Internet rumor? The former appears to be the case, but it's not 100 percent clear. In other words, take this with a grain of salt. In fact, even if it's the former, still take this with a grain of salt, like you would any unofficial information.
That all said, given that Sony Interactive Entertainment owns the IP, if a sequel is actually in development, it would have to have been greenlighted by it. And given the reception to the first game, it's hard to believe Sony would order a sequel. However, while The Order 1886 was criticized at launch for its length and lack of actual gameplay, it had massive potential. The world and characters were interesting, the custom-built engine was impressive, and what was there was decent. There just wasn't much of it. In other words, maybe Sony sees its potential, and decided to take a shot at a sequel. Unfortunately, at this point all we can do is speculate.
For those that don't know: The Order 1886 released back in February 2015. It was one of the first big PS4 exclusives, and perhaps PlayStation's biggest fumble this generation, garnering a very middling 63 on Metacritic.
As always, feel free to leave a comment or two with your thoughts or hit me up on Twitter @Tyler_Fischer_ and let me know over there. Would you like to see a sequel to The Order 1886?
Thanks, Reset Era.
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text:
package broker_deregistrar
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* File Generated by enaml generator
* !!! Please do not edit this file !!!
*/
type BrokerDeregistrarJob struct {

	/*Cf - Descr: Password of the admin user Default: <nil>
*/
	Cf *Cf `yaml:"cf,omitempty"`

	/*Broker - Descr: Basic Auth password for the service broker Default: <nil>
*/
	Broker *Broker `yaml:"broker,omitempty"`

}

redpajama_set_name: RedPajamaGithub


Heating And Air Service Susquehanna Pa - Everyone around the world air conditioner repairs 4 seasons every year. Since of the continuous modifications in environment, it is not constantly simple for people there to adjust, particularly when extreme weather condition is available in such as extremely hot days throughout summer season and freezing solid cold throughout winter season new heating and air - Heating And Air Service Susquehanna Pa.
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Nevertheless, people should first have their home location assessed if geothermal heat pumps can be set up. If their area satisfies the requirements, then they need to work with licensed contractors to do the job of setting up the geothermal heat pumps. People must keep in mind that they need to not put their comfort and life at stake during the severe seasons simply to conserve loan. They must have their own A/C in order to fight the severe cold throughout winter and the extreme heat during summer.


text:
Another Disaster in the Russian Navy
Publication: Eurasia Daily Monitor Volume: 5 Issue: 216
By: Roger McDermott
November 11, 2008 06:03 PM Age: 12 years
(Above) Russian Akula-class submarines The Amur submarine yard
On November 8 Russia's President Dmitry Medvedev ordered Defense Minister Anatoliy Serdyukov to instigate a full and thorough investigation into a fire on board a nuclear-powered submarine, the latest accident to afflict the Russian navy. Russian officials refused to identify the submarine, but a source in the Amur shipyard administration said the vessel was the K-152 Nerpa, a submarine of the Project 971 Shchuka-B type, or Akula-class by NATO classification, according to RIA Novosti. Sources in the Pacific Fleet command said that the accident took place in the bow section of the submarine, which represented no threat to the reactor, which is in the submarine's stern (RIA Novosti, November 8). This comes after a series of grave naval accidents: in 2000 the nuclear submarine Kursk sank in the Barents Sea after an explosion on board, resulting in 118 deaths; in 2003 nine sailors were killed in the Barents Sea on board a K-159 submarine, while it was being towed to port for decommissioning; and in 2005 a mini-submarine became snared in a fishing net requiring the assistance of a British rescue team.
(CLICK HERE FOR AN INTERACTIVE MAP)
Among the Nerpa's 20 dead were three naval officers and 17 civilians, all victims of suffocation as a result of Freon gas accidentally released to quell a non-existent fire. The 21 injured on board were airlifted to a Pacific Fleet hospital and treated for poisoning, and the submarine returned to the port of Bolshoi Kamen in Russia's Far East, the site of a large refitting shipyard, where the 20 dead were taken ashore. Conflicting reports suggested that a lack of gas masks and over reliance on automated procedures could have combined with a lack of safety training for the civilians on the submarine. As the investigation began, the usual cycle of speculation and state secrecy, marked by a failure for anyone in officialdom to admit accountability, masked the underlying darker story of the Nerpa disaster. (RIA Novosti, Moscow, November 8, 9; Interfax, Moscow, November 9).
In the context of such a serious naval tragedy, the Russian Naval top brass were eager to keep the disaster from further damaging the already weakened image of Russia's beleaguered navy. The navy command said that the 8,140-ton submarine had not yet entered service in the Russian navy. "The nuclear submarine has not come into service with the navy and was at the stage of shipyard sea trials that are conducted by a shipyard's trial crew. The handover was scheduled for the end of the year," explained naval spokesman Captain Igor Dygalo. The response from the authorities was predictable, with the Prosecutor-General's Office already talking publicly about instituting "criminal proceedings," in a bid to reassure the Russian public that culprits would be found for this latest disaster (NTV, November 9).
In late October representatives from the Amur shipyard announced that running tests of the Nerpa nuclear-powered submarine (Project 971 Shchuka-B, NATO classification Akula) had begun in Maritime Territory. The Nerpa (Seal) was originally ordered in 1991, but the collapse of the USSR resulted in constant setbacks in its construction. By the mid-1990s it seemed almost an embodiment of the problems facing the post-Soviet Russian navy. At that time it was named Bars (leopard) and was around 85 per cent complete but with no progress on its final stage of construction. After years of non-activity, in which it lay in Russia's Far East awaiting completion, it was finally renamed the Nerpa and scheduled for sea trials in 2008 (RIA Novosti, November 8). Problems at the Amur shipyard, including pay stoppages and the arrest of a shareholder in December 2007, further delayed completion and may also have contributed to safety problems in the submarine.
Russia's Pacific Fleet had been earmarked to receive two nuclear-powered submarines and a modern aircraft carrier, according to its commander Vice Admiral Konstantin Sidenko. It is planned to add an aircraft carrier of a new class to the fleet within the next decade, and two nuclear missile submarines of the 955 Borey project equipped with the advanced missile system Bulava are scheduled for introduction by 2012. "The government and the president of the Russian Federation have approved a program on the development of a concept of building an aircraft carrier of a new class for the Pacific Fleet. Within the next ten years, we will probably receive it," Admiral Sidenko suggested. He knows the past record of his political masters well enough, however, to add the caveat "probably." Currently the Russian Pacific Fleet is comprised of five strategic missile submarines, 18 multipurpose submarines, and 56 warships of various classes. The Pacific Fleet reportedly faces personnel cuts starting next year, which will include the removal of more than 4,500 officer posts (ITAR-TASS, October 27). Sidenko may look with some alarm at this latest disaster, as the Nerpa was apparently due to be leased to the Indian navy prior to securing a $2 billion deal for Russia to supply the Indian navy with two submarines. In theory, the Nerpa should have been a cutting edge example of what Russia can export to foreign navies; the reality, however, turned out far from an exemplary model, instead underscoring the continuing crisis in Russia's navy and its overall military reform plans.
Nonetheless, in his recent address to Russia's Federal Assembly President Medvedev said, "Regarding the re-outfitting of the army and navy with new, modern equipment, I have already made the relevant decisions." Russia's navy is plagued by problems that emanate from the continued dream of the Kremlin to attain a blue-water navy that can once again compete with the United States. Until this approach is finally jettisoned and planners are tasked with reforming and equipping the type of navy Russia actually needs, rather than one it cannot afford and is not able to build and maintain, then more such disasters can be anticipated. With the Nerpa due for lease to India's navy, the latest disaster may also damage Russia's international reputation as an arms exporter.
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Chinese Anti-Ship Ballistic Missile Development: Drivers, Trajectories and Strategic Implications
China's anti-ship ballistic missile (ASBM), the DF-21D, has reached the equivalent of Initial Operational Capability. Although it probably has been deployed in small numbers, additional challenges and tests remain. This 160-page monograph examines the ASBM's capability and history, showing how the DF-21D meets multiple priorities in Chinese defense modernization... MORE


A British mom is suing her son's school for indoctrinating students with pro-LGBTQ ideology without parental permission. Izoduwa "Izzy" Montague, 35, accuses Heavers Farm Primary School in London of "the systematic proselytization of its young and vulnerable pupils" after children were forced to participate in the school's LGBTQ "Proud to Me" event last summer. Montague is seeking a "five-figure sum" from the school. She has also filed a formal complaint to Damian Hinds, the Education Secretary for England and Wales.


This is Volume 7 of the Mastering the Basics series and is further confirmation that the word 'basics' is not to be taken too literally. The book starts with an interesting discussion of general principles then gives examples from professional games which focus on the decisions on how to handle moyos. The bulk of the book is taken up with 151 problems in the usual Kiseido format.
These I found quite eye-opening in the variety of techniques and ideas discussed. We move beyond the simple binary choices of: invade — to live or run out; versus reduce – and build an outside position. Many problems address the messy situation where there are more than two areas of interest and the flow of moves needs careful evaluation. While the ideas would likely give 8-10 kyu players a greater awareness, most of the text and problems would be challenging to low SDK and probably low dan too.
Last updated Mon Nov 23 2015. If you have any comments, please email the webmaster on web-master AT britgo DOT org.


GREENSBURG, Pa., Jan. 14, 2014 /PRNewswire/ -- West Penn Power, a subsidiary of FirstEnergy Corp. (NYSE: FE), has completed scheduled reliability projects for 2013 designed to further enhance the electrical system and reliability in its 24-county service area. Major projects included transmission improvements, completion of new distribution circuits, replacement of underground cables, inspection and replacement of utility poles and ongoing vegetation management programs.
West Penn Power's 2013 enhancements have both localized and widespread system benefits to customers throughout the service area. Upgrades to the distribution system included installation of new wire, cable, fuses, crossarms and lightning arrestors to enhance service reliability. The company also completed transmission expansions and enhancements intended to increase the capacity and robustness of its high-voltage transmission system. The work is part of West Penn Power's overall $115 million investment in 2013 designed to help enhance service reliability.
Additionally, West Penn Power completed multiple reliability inspection programs, including inspecting all 2,600 miles of its subtransmission network, as well as overhead facilities on 130 distribution circuits and underground facilities on 132 distribution circuits. The inspections help identify equipment for replacement to help minimize unplanned service interruptions.
"These infrastructure investments, vegetation management programs and annual inspections are designed to help maintain our system on a day-to-day basis to benefit West Penn Power customers now while helping to prepare our system for future load growth," said David W. McDonald, president of West Penn Power. "We are committed to delivering the quality service our customers expect and deserve."
Completing vegetation management along about 5,000 miles of distribution and transmission lines at a cost of approximately $30 million.
Completion of a $5 million project to install a 500-kilovolt (kV) transformer at a substation near Mt. Morris in Greene County to reinforce the regional transmission system.
Construction of the final 8.5 miles of a new transmission line and adding breakers to the Whiteley Substation in Greene County, a $13 million project to enhance the transmission network in southwestern Pennsylvania.
Upgrading equipment on 18 distribution circuits to enhance reliability for 20,000 West Penn Power customers in communities including Butler, Westmoreland City, North Irwin, Ligonier, and Uniontown.
Spending more than $25 million to expand the company's distribution system throughout the service area.
Replacing underground distribution cables in several communities including Greensburg at a cost of about $240,000 to enhance service.
Inspection of about 52,000 utility poles and replacement of about 125 poles.
West Penn Power serves about 720,000 customers in 24 Pennsylvania counties. Visit FirstEnergy on the web at www.firstenergycorp.com, and follow West Penn Power on Twitter @W_Penn_Power.


text:
Give the structure and name of the product produced from the reaction of cis-2-butene with {eq}Br_2 {/eq}.
Bromination Reaction:
The reaction of bromine molecule with C-C double bond is known as bromination reaction. It takes place with the carbon tetrachloride and via the formation of a three-membered transition state.
The reaction of cis-2-butene with bromine molecule is stereospecific i.e., products of different stereochemistry will be formed. The name and structure of the product formed by the reaction of cis-2-butene and bromine are given below.
Organic Chemical Reactions: Addition, Substitution, Polymerization & Cracking
Chapter 18 / Lesson 10
Organic chemical reactions refer to the transformation of substances in the presence of carbon. This lesson will explore organic chemical reactions dealing with hydrocarbons, including addition, substitution, polymerization, and cracking.
Give the structure and name of the products produced from the reaction of trans-2-butene with Br2.
Give the name for the product from the hydrogenation for 2-methyl-2-butene.
Predict the product of the reaction of 1-butene with bromine (The IUPAC name).
What is the IUPAC name of the expected major product formed upon reaction of HCl with 3-methyl-1-butene? a. 1-chloro-2-methylbutane b. 1-chloro-3-methylbutane c. 2-chloro-2-methylbutane d. 2-chloro-3-methylbutane
A. Name the product when CH_3-CH-CH-CH_2-CH_3 reacts with Br_2. \\ B. Name the type of reaction in part A.
Name the organic product of the following nucleophilic substitution reaction: OH- + CH3I
Name the organic product of the following nucleophilic substitution reaction: OH + CH3CH2I
Provide the IUPAC name for the primary organic product of the following reaction.
Name the following alkyne, and predict the products of their reaction with H2 in the presence of a Lindlar catalyst.
There are three products that might form on reaction of toluene (methylbenzene) with Br_2. Draw and name them.
In the esterification reaction of ethnic acid and 2-butanol. What is the final product? Provide the name and the structure of the product.
Suggest a structure for alkene that give the reaction product below. There may be more than one structure.
Write the name and structure of the product forms on oxidation of methanol with chromic acid. Write the mechanism of the reaction.
Write the name and structure of the product that forms on oxidation of methanol with chromic acid. Write the mechanism of the reaction.
Identify (i.e., name) the organic product for the reaction of 2-pentanol with sulfuric acid.
Predicate and name the product when HI is added to 2-Butene.
Name the following alkyne, and predict the products of their reaction with H3O+ in the presence of HgSO4.
What are the structural formula and the name of the organic product that would result from the hydrogenation (addition of hydrogen) reaction of propene?
Write an example reaction that would yield a dihalogenated alkane. Name the organic reactant and product in each reaction.
Name the organic product of the following nucleophilic substitution reaction. OH^- + CH_3CH_2CH_2Cl =>
What would be the major organic product of the following reaction and provide its IUPAC name?
What is the name of the major product formed when a quantity of water is added to 1-butene in the presence of an acid catalyst?
What is the product(s) when 2-Butene reacts with HI?
Write the structural formula of the main product formed in the following reaction. 2-methyl butene + chlorine
Starting with 3-hexene, provide the name and structure of the product when it is reacted with: a. 1. H+, h20 2. Jones reagent B. 1. BH3 2. H2O2/OH- 3. Jones reagent C. 1. O3 2. ZN, H+
Name the alkyne below, and predict the product of its reaction with (i) H2 in the presence of a Lindlar catalyst and (ii) H3O+ in the presence of HgSO4.
Name the given alkyne, and predict the product of its reaction with (i) H2 in the presence of a Lindlar catalyst and (ii) H3O+ in the presence of HgSO4.
Which of the following is the product formed by the chlorination of 1-butene? A. 2-chlorobutane B. 1,1-dichlorobutane C. 1,2-dichlorobutane D. 1-chlorobutane
What is the product(s) of the following reaction? 1-butene and Cl2 at 400 degrees C.
Provide the structure of the major organic product that results when the reagents below are combined, and name the mechanism through which this reaction is proceeding. CH_3 C?C:-Na+ + CH_3CH_2CH_2I
What would be the product of this reaction? Draw the molecule and name it: Propene + Water \rightarrow X
What will be the major product of the reaction of 2-methyl l-2-butene with each of the following reagents?
Predict the major product of the reaction shown below: a) 3,3-dimethyl-1-butene b) 2,3-dimethyl-2-butene c) 2,3-dimethyl-1-butene d) None of the above
Some 2-methyl-2-butene may be produced in the reaction as a by-product. Give a mechanism for its production.
Give the name of the product from the hydrogenation of cyclohexene. Spell out the full name of the compound.
What are the IUPAC names for the following structures? Draw the major elimination product you would expect for this reaction:
Provide the IUPAC name of the major organic product isolated from the reaction of 3-hexyne with the following: Hydrogen (1 mole), Lindlar catalyst followed by reaction of this product with bromine.
Provide the IUPAC name of the major organic product isolated from the reaction of 3-hexyne with the following: hydrogen (1 mole), Lindlar catalyst.
Write the name of the major organic product obtained from the reaction between: Write the name of the major organic product obtained from the reaction between: a) styrene and 1 mol H_2 over Pd ethylb
What is the major product in the Friedle-Craft Alkylation reaction using 1,4-dimethoxybenzene and 3-methyl-2-butanol, also included in the reaction are H_2SO_4 and CH_3COOH. What is the mechanism behind this reaction? What is the structure and IUPAC name
Give the name of the product from the hydrogenation of 3-methyl 2-pentene Spell out the full name of the compound. Give the name of the product from the hydrogenation of cyclohexene Spell out the f
What product would you expect from reaction of cis-2-butene with meta chloroperoxybenzoic acid? Show the stereochemistry.
Name the ester formed when butyric acid reacts with cyclo pentanol?
Write the name of the major organic product obtained from a reaction between 1-bromo-1-phenylethane and sodium ethoxide inethanol.
1. Write the name and structure of the product forms on oxidation of methanol with chromic acid. 2. Write the mechanism of the reaction. 3. Know the rule to predict the major/minor products in the e
Name all reactants and the product using IUPAC nomenclature rules; provide reaction conditions and draw an appropriate experimental setup. Outline a complete reaction mechanism(s) for the synthesis. D
What is the product formed when HBr is added to 1-butene?
Write the name of the major organic product obtained from a reaction between 1-bromo-1-phenylethane and sodium ethoxide in ethanol.
Give the name of the product from the complete hydrogenation of cyclohexene.
Provide the IUPAC name of the major organic product isolated from the reaction of 3-hexyne with the following: chlorine (1 mole).
Suggest structure(s) for alkene that gives the given reaction product.
Name and provide the structure of the major organic product which results when (R)-3,3-dimethyl-2-butanol is heated in the presence of HBr.
Suggest structure(s) for alkene that gives the reaction product below.
Name the given alkene, and predict the products of its reaction with (i) KMnO4 in aqueous acid and (ii) KMnO4 in aqueous NaOH.
Name the alkene below, and predict the products of its reaction with (i) KMnO4 in aqueous acid and (ii) KMnO4 in aqueous NaOH.
Provide the IUPAC name of the major organic product isolated from the reaction of 3-hexyne with the following: Chlorine (2 moles).
1. In the reaction sulfonation of benzene, the name of the product is A) Benzene sulfanilic acid B) Benzene sulfonamide C) Sulfanilic acid D) Benzenesulfonic acid E) Nitrobenzene 2. Phenanthrene
Give the correct IUPAC name of the major product of the reaction of PBr3 with sec-butyl alcohol.
What compound was condensed in an aldol reaction to produce (2E)-5-methyl-2-isopropylhex-2-enal? Type the systematic IUPAC name.
What is the major product of the reaction of 2-methyl-2-butene with Br_2/CH_3OH?
Give the IUPAC name for the missing reactant in the reaction shown below. (Image)
Give the structure of the alkene formed in the following reaction.
Provide the IUPAC name of the major product for the given reaction in the basic solution. 1-ethyl-3-methylcyclohexene + KMnO4
Draw the organic product of the reaction of 1-butene with H2O, H2SO4
A) When ethylbenzoate undergoes hydrolysis, ethanol is one product. Draw the structure of the other product. B) Name the ester formed by the reaction of heptanoic acid and ethanol. Spell out the full
Provide the structure for alkene that gives the reaction product below. There may be more than one structure.
Name the following alkenes, and predict the products of their reaction with (1) meta-chloroperoxybenzoic acid, (2) KMnO4 in aqueous acid, and (3) O3, followed by Zn in acetic acid:
Write the name of the major organic product obtained from the reaction between 1-phenyl-1-ethanol and concentrated sulfuric acid when heated.
Given 1-butene as the reactant, it reacts with the following compounds in the given order, 1) MCPBA 2)NaSH 3)H_2O. What will the final product be?
Give the IUPAC name to the simple ester produced by the reaction between ethanoic acid and the following: 1-butanol
What products would form after the hydrogenation of 2-methyl-1-butene? After halogenation (cl2)?
Name the organic product that would result from the following process: 3-pentanol is subjected to an excess of an oxidizing agent. Select one: a. pentane. b. pentanal. c. pentanoic acid. d. 1-pentanone.
Provide the IUPAC name of the major organic product isolated from the reaction of 3-hexyne with the following: Hydrogen chloride (2 moles).
Use Markovnikov's rule to predict the major organic product product formed in the reaction of hydrogen chloride with cis-2-butene.
What product would you expect from the reaction of 1-phenyl-2-butene with NBS? Explain.
Name the type of reaction illustrated by the two reaction above glucose to ethanol and ethanol to ethane.
1. Name the following alkene. (Include E/Z designations if appropriate. 2. Draw the product(s) of the reaction of the alkene below with meta-chloroperoxybenzoic acid. (Image)
Provide the IUPAC name of the major organic product isolated from the reaction of 3-hexyne with the following: hydrogen (2 moles), palladium-carbon.
Identify the product in the reaction of an alkene with a peroxyacid. a) Cyclopropane. b) Epoxide. c) Alcohol. d) Ether.
What is the major organic product obtained from the following reactions? a. 1 b. 2 c. 3 d. 4 What is the major organic product obtained from the following reaction? a. butane b. 1-butene c. cis-2-but
Write down the Criegee produced in the ozonolysis of the following alkenes: a. ethene b. trans-2-butene c. cis-2-butene d. 2,3-dimethyl-2-butene e. 2-methyl-2-butene f. cyclopentene g. isoprene
Write a possible dehydration reaction for 4-methylhexan-3-ol and name the alkene products without citing cis or trans.
Predict product when HBr is added to the 1-butene.
Draw the major and minor product (s),if any, for each of the following EI reaction and name each alkene formed: Draw the complete reaction mechanism for part (ii)
Using line diagrams, represent the reaction of cyclohexene with bromine. Using IUPAC rules, name the product. Identify the reaction type.
Describe the preparation of three aldehydes from alcohols, and write appropriate equations. Name all reactants and products.
The name the following alkene and the product(s) of their reaction with (1) meta-chloroperoxybenzoic acid, (2) KMnO4 in aqueous acid, and (3) O3, followed by Zn in acetic acid:
Name and assign R or S stereochemistry to the product(s) you would obtain by reaction of the following substance with ethyl magnesium bromide. Is the product chiral? Is it optically active? Explain.
The addition of HBr to 2-butene produces: a. 1-bromobutane b. 2-bromobutane c. 1,2-dibromobutane d. 2,3-dibromobutane e. no reaction
Write the reaction for the hydrogenation of \\ A) 2-butene B) Oleic acid
1 hexyen reacts with excess HBr, then the product is? Use IUPAC naming system for the answer
How would trans-2-butene react with [1] R2BH [2] H202, HO-
What is the name of the product of the hydrogenation of 3,6,6-trimethyl-4-nonene?
Predict the major product B from the reaction sequence shown below. a. Trans-2-butene b. 2-butyne c. Cis-2-butene d. 1-butyne Butane
What products would you expect from the reaction of the following alkene with NBS? If more than one product is formed, show the structures of the given.
Using IUPAC substitutive nomenclature rules, write the name of the major organic product when cycloheptanol reacts with concentrated sulfuric acid under heated conditions.
Give an example of an oxidation reaction that involves alcohol as a reactant Be sure to provide the name for the organic reactant and product.
Give the structure and name of the product produced from the reaction of cis-2-butene with Br2.


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text:
Sederholm är ett efternamn som burits av bland andra:

Bertil Sederholm, svensk grosshandlare och konsul
Carl Robert Sederholm, finländsk militär och religionsfilosof
Edvard Sederholm, svensk läkare
Edward Sederholm, svensk godsägare, riksgäldsfullmäktig och riksdagsman
Gustaf Sederholm, svensk politiker, ämbetsman och riksdagsman
Henrik Sederholm, svensk ämbetsman
Jakob Johannes Sederholm, finländsk geolog
 Jan Sederholm (1924–2012), svensk arkitekt
Johan Sederholm, finländsk affärsman
Karl Sederholm, finländsk filosofisk och teologisk skriftställare
Mortimer Sederholm (1888–1975), svensk militär
Theodor Sederholm, finlandssvensk publicist

Se även
Sederholmska huset

Svenska efternamn


text:
Ure Routes
Winckelmania
Collectors Curators Cataloguers
Grace Ernestine Holding (c. 1878-1943)
19th December 2019 3rd January 2020
By Amara Thornton (Research Officer, Ure Museum)
Grace Ernestine Holding was born in London in around 1878. She obtained a B. A. degree from the University of Wales, attending University College of South Wales and Monmouthshire at Cardiff where she was a student of Ronald Burrows, Professor of Classics. She later recalled his teaching as inspirational, stating for George Glasgow's biography of Burrows that "More than one Cardiff student, who began his college life uncertain what his special subject should be, made his decision for Classics before the end of his intermediate year."
Holding taught at the County School for Girls in Pontypool before moving back to London to become Classics Mistress at the North London Collegiate School for Girls in early 1905. Within a year of her arrival she obtained her M. A. from the University of Wales. This degree was awarded for a thesis entitled "The Structure and Scenic Effects of the Greek Theatre". Two years later, she was on a sabbatical from the North London Collegiate School, taking a working-holiday in Greece. She had been asked to undertake drawings and photography for excavations at Rhitsona, directed by her old University lecturer Ronald Burrows, working with a young Classics Lecturer at the University of Wales, Percy Ure. Her work appeared in subsequent publications on the excavation.
Detail of Grace Holding's signature, from an undated letter to Ronald Burrows (Ure Museum archives, Drawer C)
She returned to the School in early 1909, bringing with her a photograph of Athens which was displayed in the new Classics room at the School. She took an active role in the School's Classical Society, delivering lectures in the 1910s and 1920s on topics such as the "Greek Vases", "The Oracle at Delphi" (featuring slides of her own photographs of the site), "Athens" (including anecdotes from her experiences in the city) and "Pompeii". While at NLCS, she was a member of both the Classical Association and the Hellenic Society. She retired from the School in 1935 and died in London in 1943.
The Ure Museum archive holds letters from Grace Holding during her work on the Rhitsona excavations.
Further Reading/References
Burrows, RM & Ure, PN 1907/8. Excavations at Rhitsona in Boeotia. Annual of the British School at Athens 14 (226-318).
Gill, D. 2002. "The Passion of Hazard": Women at the British School at Athens before the First World War. Annual of the British School at Athens 97: 491-510.
Glasgow, G. 1924. Ronald Burrows: a memoir. London: Nisbet & Company.
North London Collegiate School Magazine, February 1905; February 1909, March 1916, March 1917, March 1922, July 1923, November 1935.
archaeology archives Classics education Percy Ure research Rhitsona women
Africa Allen Seaby Ancient Anglo Saxon Britain Annie Ure archaeology archives art British School at Athens Brucciani & Co. Caroline Amy Hutton Cast children Classics education Egypt Eric Stanford events exhibition Grace Holding Hellenic Society history Leon of Messalia Lowbury Hill Modern museum Mythology Percy Ure publishing Reading research Rhitsona Roman Britain Romano-British Museum Rome Ronald Burrows Sculpture Sculpture Trail student suffrage University College Reading University History Collection women