text:
\section{All light baryons are rotational excitations}

 The most striking success of the old Skyrme idea \cite{Skyrme} that
 nucleons can be viewed as solitons of the pion (or chiral) field,
 is the classification of light baryons it suggests. Indeed,
 the minimal generalization of spherical symmetry to incorporate
 three isospin components of the pion field is the so-called
 hedgehog form,

 \begin{equation}
 \pi^a(\vec{x})=\frac{x^a}{r}P(r),
 \end{equation}
 where $P(r)$ is the spherically-symmetric profile of the soliton. It
 implies that a space rotation of the field is equivalent to that in
 isospace. Hence, the quantization of the soliton rotation is similar
 to that of a spherical top: the rotational states have isospin
 $T$ equal to spin $J$, and their excitation energies are

 \begin{equation}
 E_{\mbox{rot}}=\frac{J(J+1)}{2I},
 \end{equation}
 where $I$ is the soliton moment of inertia. The rotational states are,
 therefore,
 $(2J+1)^2$-fold degenerate (in spin and isospin). For $J=1/2$ we have the
 four nucleon states; for $J=3/2$ we have the sixteen $\Delta$-isobar
 states.
 By saying that $N$ and $\Delta$ are different rotational states
 of the same object (the ``classical nucleon") one gets certain
 relations between their characteristics which are all satisfied up to
 a few percent in nature \cite{ANW}.

 Quantum Chromodynamics has shed some light into why the chiral soliton
 picture is correct: we know now that the spontaneous chiral symmetry
 breaking in QCD is, probably, the most important feature of strong
 interactions, determining to a great extent their dynamics
 (see, e.g. \cite{D}), while the large $N_c$
 (= numbers of colours) argumentation by Witten \cite{W}
 explains why the pion field inside the nucleon can be considered as a
 classical one, {\em i.e.} as a ``soliton".

 The generalization to hyperons \cite{W, Guad} makes the success of the
 chiral soliton idea even more impressive. The rotation can be now
 performed in the ordinary and in the flavour $SU(3)$ space.
 Its quantization shows
 \cite{Guad, DP, Prasz, Chemtob, ind}

 that the
 lowest baryon state is the {\em octet with spin $1/2$} and the next is the
 {\em decuplet with spin $3/2$} -- exactly what we meet in reality.
 Again, there are numerous relations between characteristics of members
 of octet and decuplet which follow purely from symmetry
 considerations. Perhaps the most spectacular is the Guadagnini formula
 \cite{Guad} which relates splittings inside the decuplet with those in
 the octet: it is satisfied to the accuracy better than one percent,
 see below.

 What are the next rotational excitations? If one restricts oneself to
 only two
 flavours, the next state should be a (5/2, 5/2) resonance; in the
 three-flavour case the third rotational excitation is an
 {\em anti-decuplet with spin $1/2$} \footnote{Probably the existence of the
 anti-decuplet as the next $SU(3)$ rotational excitation has been
 first pointed out by
 the authors at the ITEP Winter School (February, 1984), see ref.
 \cite{DP}.  Other early references for the anti-decuplet include
 \cite{Chemtob, Prasz2, Walliser}.}.  Why do not we have any clear
 signal of the exotic (5/2, 5/2) resonance?  The reason is that the
 angular momentum $J=5/2$ is numerically comparable to $N_c=3$.
 Rotations with $J\sim N_c$ cannot be considered as slow:  the
 centrifugal forces deform considerably the spherically-symmetric
 profile of the soliton field \cite{DPRegge, BR}; simultaneously at $J\sim N_c$ the
 radiations of pions by the rotating body makes the total width of the
 state comparable to its mass \cite{DPRegge,Dorey}. In order to
 survive strong pion radiation the rotating chiral solitons with $J\ge
 N_c$ have to stretch into cigar-like objects; such states lie on
 linear Regge trajectories \cite{DPRegge}.

 The situation, however, might be somewhat different in the
 {\it three}-flavour case. First, the rotation is, roughly
 speaking, distributed among more axes in flavour space, hence
 individual angular velocities are not neccessarily as large as when we
 consider the two-flavour case with $J=5/2$. Actually, the $SU(2)$
 baryons with $J=5/2$ belong to a very high multiplet from the $SU(3)$
 point of view. Second, the radiation by the soliton includes now $K$
 and $\eta$ mesons which are substantially heavier than pions, and
 hence such radiation is to some extent suppressed. Therefore, the
 anti-decuplet baryons may not neccessarily have widths comparable to
 masses. And this is what we, indeed, find below.

 We conclude thus that an expectaction of a relatively light and narrow
 anti-decuplet of baryons is theoretically motivated. Moreover, we are
 in a position to numerically estimate the masses and widths of the
 members of the anti-decuplet, and to point out possible experiments to
 observe them.

 Let us mention that one can altogether abandon the soliton logic:
 the exotic anti-decuplet can be alternatively considered in a primitive
 way as states made of three
 quarks plus a quark-antiquark pair, or else, as a bound state of octet
 baryons with octet mesons. For example, the most interesting member of
 the anti-decuplet, viz. the exotic $Z^+$ baryon can be considered as a
 $K^+ n$ or $K^0 p$ bound state \footnote{It is known that the
 $KN$ phase shift in the $T=0$, $J=(1/2)^+$ state
 corresponds to attraction \cite{Dover}.}.
 Unfortunately, the predictions become
 then to a great extent model-dependent. It is a big advantage of the
 chiral soliton picture that all concrete numbers (for masses and
 widths) do not rely upon a specific dynamical realization but follow
 from symmetry considerations. Actually, only one number would be
 useful to get from dynamics, namely a specific $SU(3)$ moment of
 inertia $I_2$ (see below), and concrete dynamical models give concrete values
 for this quantity. In this paper, however, we prefer to extract this
 quantity from experiment -- by identifying the known nucleon resonance
 $N\left(1710, \frac 12^+\right)$ with the member of the suggested
 anti-decuplet \footnote{A possibility for such an identification has
 been mentioned in ref. \cite{SW} but other members of the
 anti-decuplet have not been addressed there.}.
 We, then, are able to fix completely all the other members of the
 anti-decuplet together with their widths and branching ratios.

 To end up this introduction we draw the $SU(3)$ diagramm for the
 suggested anti-decuplet in the $(T_3,Y)$ axes, indicating its naive
 quark content as well as the (octet baryon + octet
 meson) content, see Fig.~1. In addition to the lightest
 $Z^+$ there is an exotic quadruplet of $S=-2$ baryons (we call them
 $\Xi_{3/2}$). However, the exotic $\Xi^{--}$ and $\Xi^+$ hyperons
 appear to be very heavy and to have large widths, and can
 therefore hardly be detected.  Therefore, apart from peculiar
 branching ratios predicted for the $N\left(1710, \frac 12^+\right)$
 and the $\Sigma\left(1880, \frac{1}{2}^+\right)$ resonances, the
 crucial prediction is the existence of a relatively light and narrow
 $Z^+$ baryon.

\section{Rotational states}

Following Witten \cite{W} and Guadagnini \cite{Guad} we assume the
self-consistent pseudoscalar field which binds up the $N_c = 3$ quarks
in the ``classical'' baryon (i.e. the soliton field) to be of the
form

\begin{equation}
U(\vec{x})\equiv \exp\left(i \pi_A(\vec{x})\lambda^A/F_\pi\right)
= \left(\begin{array}{cc}
\exp \left[i(\mbox{\boldmath{$n$}}
\cdot\mbox{\boldmath{$\tau$}}) P(r)\right] &
\begin{array}{c} 0\\ 0\end{array}\\ \begin{array}{cc}0 &0 \end{array} & 1
\end{array}\right),\;\;\;\; \vec{n}=\frac{\vec{x}}{r},
\la{hedgehog}
\end{equation}
where the spherically-symmetric profile function $P(r)$ is defined by
dynamics. We shall not need the concrete form of this function in what
follows. In \eq{hedgehog} $\lambda^A$ are the eight Gell-Mann $SU(3)$
matrices, and $\mbox{\boldmath{$\tau$}}$ are the three Pauli $SU(2)$
matrices.

In order to provide the ``classical'' baryon with specific quantum
numbers one has to consider a $SU(3)$-rotated pseudoscalar field,

\begin{equation}
\tilde{U}(\vec{x},t)=R(t)U(\vec{x})R^+(t)
\la{rothedgehog}
\end{equation}
where $R(t)$ is a unitary $SU(3)$ matrix depending only on time and
$U(\vec{x})$
is the static hedgehog field given by \eq{hedgehog}.
Quantizing this rotation one gets the following rotational
Hamiltonian \cite{Guad},

\begin{equation}
H^{rot}=\frac{1}{2I_1}\sum_{A=1}^3
J_A^2+\frac{1}{2I_2} \sum_{A=4}^7 J_A^2,
\la{Ham1}
\end{equation}
where $J_A$ are the generators of the $SU(3)$ group; $J_A$ with $A=1,2,3$
are the usual angular momentum (spin) operators, and $I_{1,2}$ are the
two $SU(3)$ moments of inertia, which are model-dependent.
Most important is the additional quantization prescription,

\begin{equation}
J_8=-\frac{N_cB}{2\surd{3}}=-\frac{\surd{3}}{2},\;\;\;\;\;
Y^\prime=-\frac{2}{\surd{3}}J_8=1,
\la{quantiz}
\end{equation}
where $B$ is the baryon number, $B=1$.
In the Skyrme model this quantization rule follows from the Wess-Zumino
term \cite{W,Guad}. In the more realistic chiral quark--soliton model
\cite{DPP} it arises from filling in the discrete level, i.e. from
the ``valence" quarks \cite{mass}. It is known to lead to the selection
rule
\cite{Guad,DP,Prasz,Chemtob,ind}:
not all possible spin and $SU(3)$
multiplets are allowed as rotational excitations of the $SU(2)$
hedgehog.  \Eq{quantiz} means that only those $SU(3)$ multiplets are
allowed which contain particles with hypercharge $Y=1$; if the number
of particles with $Y=1$ is denoted as $2J+1$, the spin of the allowed $SU(3)$
multiplet is equal to $J$.

Therefore, the lowest allowed $SU(3)$ multiplets are:

\begin{itemize}
\item octet with spin 1/2 (since there are {\em two} baryons in the octet
with $Y=1$, the $N$)
\item decuplet with spin 3/2 (since there are {\em four} baryons in the
decuplet with $Y=1$, the $\Delta$)
\item anti-decuplet with spin 1/2 (since there are {\em two} baryons in the
anti-decuplet with $Y=1$, the $N^*$)
\end{itemize}
The next are 27-plets with spin $1/2$ and $3/2$ but we do not
consider them here. The appropriate rotational wave functions describing
members of these multiplets are given in Appendix A.

For the representation $(p,q)$ of the $SU(3)$ group one has

\begin{equation}
\sum\limits_{A=1}^8 J_A^2 = \frac13[p^2+q^2+pq + 3(p+q)],
\end{equation}
therefore the eigenvalues of the rotational Hamiltonian
(\ref{Ham1}) are

\begin{equation}
E_{(p,q)}^{rot} = \frac1{6I_2} [p^2+q^2+pq + 3(p+q)]
+\left(\frac1{2I_1} - \frac1{2I_2} \right) J(J+1)
- \frac{(N_c B)^2}{24I_2}.
\la{rotenerg}\end{equation}
We have the following three lowest rotational excitations:

\begin{eqnarray}
(p,q)=(1,1), & J=1/2& \mbox{(octet)} \\
(p,q)=(3,0), & J=3/2& \mbox{(decuplet)} \\
(p,q)=(0,3), & J=1/2& \mbox{(anti-decuplet)} \, .
\end{eqnarray}
The splittings between the centers of these multiplets are determined by the
moments of inertia, $I_{1,2}$:

\begin{equation}
\Delta_{10-8} =
E_{(3,0)}^{rot} - E_{(1,1)}^{rot} =\frac{3}{2I_1},
\la{octdecspl}\end{equation}
\begin{equation}
\Delta_{{\overline{10}} - 8} =
E_{(0,3)}^{rot} - E_{(1,1)}^{rot} =\frac{3}{2I_2},
\la{oct-antidecspl}\end{equation}
\begin{equation}
\Delta_{{\overline{10}} - 10} =
E_{(0,3)}^{rot} - E_{(3,0)}^{rot} =
\frac{3}{2I_2} - \frac{3}{2I_1}.
\la{dec-antidecspl}\end{equation}

We see that, were the moment of inertia $I_2 > I_1$, the anti-decuplet
would be even lighter than the standard decuplet. Though we do not
know of any strict theorem prohibiting this inequality, all
 dynamical models we know of give $I_1 > I_2$, so that the
 anti-decuplet appears to be heavier.

\section{Splittings in the $SU(3)$ multiplets}

We now take into account the non-vanishing strange quark mass.
The effects of the non-zero $m_s$ are of two kind: first, it splits
the otherwise degenerate masses inside each $SU(3)$ multiplet; second,
it leads to mixing between different $SU(3)$ multiplets.
We shall systematically restrict ourselves to the linear order in $m_s$.
In this order the phenomenologically successful Gell-Mann--Okubo
and Guadagnini formulae are automatically satisfied.

Theoretically, the corrections to baryon masses due to $m_s\neq 0$ are
of two types: i)~leading order, $O(m_sN_c)$ and ii) subleading order,
$O(m_sN_c^0)$.  These corrections perturb the rotational Hamiltonian
(\ref{Ham1}) (for derivation see ref.~\cite{mass}) by

\begin{equation}
\Delta H_m= \alpha D_{88}^{(8)} + \beta Y
+ \frac{\gamma}{\surd 3} \sum\limits_{i=1}^3 D_{8i}^{(8)} J_i \, ,
\label{Ham2} \end{equation}
where $D_{...}^{(8)}(R)$ are the Wigner $SU(3)$ finite-rotation
matrices depending on the orientation matrix of a baryon, see the Appendices.
The coefficients $\alpha, \beta, \gamma$ are proportional to the
mass of the $s$ quark and are expressed through a combination of
the soliton moments of inertia, $I_{1,2}$ and $K_{1,2}$, and the
nucleon sigma term, $\Sigma$ \cite{mass}:

\begin{equation}
\alpha = - \, \frac23 \, \frac{m_s}{m_u + m_d} \, \Sigma
+ m_s \frac{K_2}{I_2} \, ,
\la{a}\end{equation}
\begin{equation}
\beta = - m_s \frac{K_2}{I_2} \, ,
\la{b}\end{equation}
\begin{equation}
\gamma = \frac{2}{3} m_s\left( \frac{K_1}{I_1}
- \frac{K_2}{I_2} \right) \,,
\la{g}\end{equation}
\begin{equation}
\Sigma = \frac{m_u+m_d}{2}\langle N|\bar u u+\bar d d|N\rangle\,.
\la{s}\end{equation}

To get the physical splittings from \eq{Ham2} one has to sandwich it
between the physical rotational states:

\bq{ \Delta m_B = \bra{B} \Delta H_m \ket{B}. }
The mass splittings inside multiplets in terms of the coefficients
$\alpha, \beta, \gamma$ are
listed in Table~1~\footnote{We take the opportunity to thank
M.Praszalowicz and P.Pobylitsa who have
participated in calculating this table back in 1988.}. We call the two
members of the
anti-decuplet with exotic quantum numbers $T=0,\, S=1$ and $T=3/2,\,
S=-2$ as $Z^+$ and $\Xi_{3/2}$, respectively.

\vskip 0.33cm
\begin{tabular}{|c|c|c||c|}
\hline
\hline
octet & $T$ & $Y$ &
$\Delta m_B$ \\
\hline
$N$ & $1/2$ & $1$ &$(3 / 10)\alpha+\beta-(1/20)\gamma$\\
$\Lambda$ & $0$ & $0$& $(1/10)\alpha +(3/20)\gamma$\\
$\Sigma $ & $1$ & $0$& $-(1/10)\alpha -(3/20)\gamma$\\
$\Xi$ & $1/2$ & $-1$ &$-(1/5)\alpha-\beta+(1/5)\gamma $\\
\hline
\hline
decuplet & & & \\
\hline
$\Delta$ & $3/2$ & $1$ & $(1/8) \alpha + \beta - (5/16) \gamma$\\
$\Sigma^\ast$&$1$& $0$ & $0 $\\
$\Xi^\ast$ & $1/2$ & $-1$& $-(1/8)\alpha -\beta +(5/16) \gamma$\\
$\Omega$ & $0$ & $-2$& $-(1/4) \alpha -2\beta + (5/8) \gamma$\\
\hline
\hline
antidecuplet & & & \\
\hline
$Z^+$&$0$ &$2$ & $(1/4) \alpha +2\beta - (1/8) \gamma$\\
$N_{\overline{10}} $&$1/2$&$1$ & $(1/8) \alpha +\beta -(1/16) \gamma$\\
$\Sigma_{\overline{10}}$&$1$ &$0$ & $ 0 $\\
$\Xi_{3/2}$&$3/2$&$-1$ &$ -(1/8)\alpha - \beta + (1/16)\gamma$\\
\hline \hline
\end{tabular} \vskip 0.5cm

Table 1. Mass splittings within multiplets,
$\Delta m_B = \bra{B} \Delta H_m \ket{B}$.
\vskip 0.33cm

One observes that all splittings inside the octet and the decuplet
are expressed through only two combinations of $\alpha,\,\beta$ and
$\gamma$. This is the reason why, in the soliton picture, in addition
to the standard Gell-Mann--Okubo relations,

\begin{equation}
2(m_N+m_\Xi)=3m_\Lambda+m_\Sigma,
\la{GMOo}\end{equation}

\begin{equation}
m_\Delta-m_{\Sigma^*}=m_{\Sigma^*}-m_{\Xi^*}=m_{\Xi^*}-m_{\Omega^-},
\la{GMOd}\end{equation}
there arises a relation between the splittings inside the octet and
the decuplet, the Guadagnini formula \cite{Guad},

\begin{equation}
8(m_{\Xi^*}+m_N)+3m_\Sigma=11m_\Lambda+8m_{\Sigma^*},
\la{Gua}\end{equation}
which is satisfied with better than one-percent accuracy!
The best fit to the splittings in the octet and the decuplet gives
the following numerical values for the two combinations of the
coefficients $\alpha,\,\beta$ and $\gamma$:

\[
\alpha+\frac{3}{2}\gamma = -380\,MeV,
\]
\begin{equation}
\frac{1}{8}\alpha+\beta-\frac{5}{16}\gamma=-150 \,MeV.
\la{abg}\end{equation}

To learn the splittings in the anti-decuplet one needs to
know the third combination of $\alpha,\,\beta$ and $\gamma$, which is
not directly deducible from the octet and decuplet splittings. The only
statement which can be immediatelly made from looking into Table~1 is
that the spectrum in the anti-decuplet is equidistant, as in the normal
decuplet. The third combination can be fixed, however, from the
knowledge of the nucleon sigma term \cite{GLS} and of the current
quark mass ratio \cite{Leut}:

\begin{equation}
\frac{m_s}{m_u+m_d}\approx 12.5,\;\;\;\;\;\Sigma\approx 45\,MeV.
\la{massratio}\end{equation}
These numbers gives for the sum:

\begin{equation}
\alpha + \beta = -\frac{2 m_s}{3 (m_u+m_d)}\Sigma\approx -375\,MeV.
\la{ab}\end{equation}
Combining this knowledge with \eq{abg} we get finally all three
coefficients:

\begin{equation}
\alpha\approx -218\,MeV,\;\;\beta\approx -156\,MeV,\;\;
\gamma\approx -107\,MeV.
\la{abgnum}\end{equation}
The equidistant splittings inside the anti-decuplet are
thus expected to be equal to

\begin{equation}
\Delta m_{\overline{10}}=-\frac{\alpha}{8}-\beta+\frac{\gamma}{16}
\approx 180\,MeV\,,
\la{antispl}\end{equation}
the lightest baryon being the exotic $Z^+$ resonance.

To end up this section we note that the non-zero strange quark mass
leads also to the mixing of octet and anti-decuplet states with otherwise
identical quantum numbers.
In the linear order in $m_s$ these mixings are derived in Appendix A
and can be all expressed through one constant which we call $c_{\overline{10}}$,
where

\begin{equation}
c_{\overline{10}}=-\,\frac{1}{3\surd{5}}\left(\alpha+\frac{1}{2}\gamma
\right)I_2\,.
\la{smesh}\end{equation}

The true hyperon states become superpositions of the octet and
anti-decuplet states:

\vspace{1cm}
\underline{{\it Mainly octet baryons}}

\begin{eqnarray}
|N\rangle&=& |N,8\rangle +c_{\overline{10}}|N,\overline{10}\rangle,\la{first}\\
|\Lambda\rangle&=& |\Lambda,8\rangle ,\\
|\Sigma\rangle&=& |\Sigma,8\rangle +c_{\overline{10}}|\Sigma,\overline{10}\rangle,\\
|\Xi\rangle&=& |\Xi,8\rangle ;
\end{eqnarray}

\underline{{\it Mainly anti-decuplet baryons}}

\begin{eqnarray}
|Z^+\rangle&=& |Z^+,\overline{10}\rangle ,\\
|N_{\overline{10}}\rangle&=& |N,\overline{10}\rangle -c_{\overline{10}}|N,8\rangle,\\
|\Sigma_{\overline{10}}\rangle&=& |\Sigma,\overline{10}\rangle -c_{\overline{10}}|\Sigma,8\rangle,\\
|\Xi_{3/2}\rangle&=& |\Xi_{3/2},\overline{10}\rangle ,
\la{last}\end{eqnarray}

In the linear order in $m_s$ the mixing does not effect the mass
splittings inside the multiplets, discussed above.

Apart from $\alpha$ and $\gamma$, which we know now, the mixing
coefficient $c_{\overline{10}}$ is proportional to the second moment of inertia
$I_2$ which defines the shift of the anti-decuplet center (i.e. the
$\Sigma_{\overline{10}}$ baryon) from the octet center, see \eq{oct-antidecspl}.
We do not know of any symmetry considerations relating
this shift to that between the centers of the octet and the decuplet.
The dynamical (i.e. model) predictions for the moment
of inertia $I_2$ are rather disperse: they range from $0.43$~fm in the
Skyrme model \cite{Prasz2, Walliser}
to $0.55$~fm in the chiral quark--soliton model \cite{mass}. Taken
literally, the last value of $I_2$ would lead to a very light
anti-decuplet, and in particular to a $Z^+$ lying below the $KN$
threshold and thus stable against strong interactions. However,
it should be mentioned that the moments of inertia have $\sim
m_s$ corrections which are not computed yet. On physical grounds
one can argue that the $m_s$ corrections should be negative, since
the account for non-zero quark mass makes the baryons more ``tight".

In any case, we prefer to fix this
fundamental quantity from identifying one of the members of the
anti-decuplet, namely the one with the nucleon quantum numbers,
$N_{\overline{10}}$, with the rather well established nucleon resonance
$N\left(1710, \frac{1}{2}^+\right)$.
Given that $N_{\overline{10}}$ is $\approx 180\,MeV$ lighter than the center
of the anti-decuplet, we find

\begin{equation}
I_2 \approx 0.4\, \mbox{fm}\approx (500\,MeV)^{-1},
\la{I2}\end{equation}
and hence the octet--anti-decuplet mixing amplitude is

\begin{equation}
c_{\overline{10}}\approx 0.084\,,
\la{mixnum}\end{equation}
being not a negligible quantity.

We thus arrive to the following masses of the anti-decuplet:

\[
m_{Z^+} \approx 1530\, MeV,
\]
\[
m_{N_{\overline{10}}} \approx 1710\, MeV {\rm (input)},
\]
\[
m_{\Sigma_{\overline{10}}} \approx 1890\, MeV,
\]
\begin{equation}
m_{\Xi_{3/2}} \approx 2070\,MeV.
\la{masses}\end{equation}

\section{Baryon decays}

In the non-relativistic limit for the initial and final baryons the
baryon-baryon-meson coupling can be written in terms of rotational
coordinates $R$ of the baryon as \cite{ANW}

\begin{equation}
-i \frac{3 G_0}{2 m_B}\cdot \frac 12 \mbox{Tr}(R^\dagger\lambda^m
R\lambda_i)\cdot p_i,
\la{meson-soliton}\end{equation}
where $\lambda^m$ is the Gell-Mann matrix for the emitted meson of flavour $m$,
and $p_i$ is the 3-momentum of the meson.
To make \eq{meson-soliton} more symmetric we use for $m_B$ in the denominator
the half-sum of the initial ($B_1$) and final ($B_2$) baryon masses.
Sandwiching
eq.~(\ref{meson-soliton}) between the rotational wave functions
of initial and final baryons, given by \eqs{wave-functions}{perth},
we obtain the $B_1\rightarrow B_2+M$ transitions
amplitude squared (averaged over the initial and summed over the final
spin and isospin states) in terms of the $SU(3)$ isoscalar factors. The
general formula is given in Appendix~B. Using it we get for
the particular modes of the $10\rightarrow 8 + 8$ decays:
\vspace{0.5cm}

\underline{{\it Decays of the decuplet}}

\begin{eqnarray}
\Gamma(\Delta \rightarrow N\pi)&=&
 \frac{3 G_0^2}{2\pi (M_\Delta+M_N)^2} |\vec{p}|^3
\frac{M_N}{M_\Delta}\cdot\frac 15
= 110\,MeV\;vs.\;110\,MeV\;(exp.),
\label{ww1}
 \\
\Gamma(\Sigma^* \rightarrow \Lambda\pi)&=&
\frac{3 G_0^2}{2\pi (M_{\Sigma^*}+M_\Lambda)^2}
|\vec{p}|^3 \frac{M_\Lambda}{M_{\Sigma^*}}\cdot\frac{1}{10}
= 35\,MeV\;vs.\;35\,MeV\;(exp.),
\\
\Gamma(\Sigma^* \rightarrow \Sigma\pi)&=&
\frac{3 G_0^2}{2\pi (M_{\Sigma^*}+M_\Sigma)^2}
|\vec{p}|^3 \frac{M_\Sigma}{M_{\Sigma^*}}\cdot\frac{1}{15}
=5.3\,MeV\;vs.\;4.8\,MeV\;(exp.), \\
 \Gamma(\Xi^* \rightarrow \Xi\pi)&=&
\frac{3 G_0^2}{2\pi (M_{\Xi^*}+M_\Xi)^2} |\vec{p}|^3
\frac{M_\Xi}{M_{\Xi^*}}\cdot\frac{1}{10}
=8.6\,MeV\;vs.\;10\,MeV\;(exp.),
\label{ww4}
\end{eqnarray}
where $|\vec{p}|=\sqrt{(M_1^2-(M_2+m)^2)\cdot (M_1^2-(M_2-m)^2)}/2M_1$
is the momentum of the meson of mass $m$. To get the concrete numbers we
have used the value of the dimensionless coupling constant in
\eq{meson-soliton} $G_0\approx 19$.

We remind the reader that the usual $SU(3)$ symmetry would require {\em two}
coupling constants ($F$ and $D$) to determine the above widths, and of course
the $SU(3)$ symmetry by itself tells nothing about the relation between
decay constants for {\em different} multiplets. The chiral soliton models,
while preserving the usual $SU(3)$ symmetry, in addition give relations
between various couplings, since they all correspond to different rotation
states of the same object. In particular, the chiral soliton models
predict the $F/D$ ratio to be \cite{Pol}

\begin{equation}
\frac{F}{D}=\frac{5}{9}=0.555...\;\;\;\;vs.\;\;\;\;0.56\pm 0.02\;
({\rm exper.}),
\la{FD}\end{equation}
and the $g_{\pi NN}$ constant to be

\begin{equation}
g_{\pi NN}=\frac{7}{10}\,G_0\approx 13.3\;\;\;\;vs.\;\;\;\;\approx
13.6\; ({\rm exper.}).  \la{gpinn}\end{equation}

Again, we see that the notion of `baryons as rotational excitations'
works quite satisfactory. Therefore, one would expect that {\em the same}
coupling constant $G_0$ should be used for predicting the partial decay
rates of the next rotational excitation, the anti-decuplet.

We remark, however, that in the particular case of the pseudoscalar
couplings we expect rather large $1/N_c$ corrections which need not be
universal for all multiplets. The point is, the baryon-pseudoscalar
couplings are related, thanks to Goldberger--Treiman, to the baryon
axial constants, $g_A$. Meanwhile, it is well known that the real-world
($N_c=3$) value of the nucleon axial constant
$g_A$ differs from its large-$N_c$ limit roughly by a
factor \cite{BR2} $(N_c+2)/N_c=5/3$, which is quite significant.
This value comes from an estimate in a non-relativistic quark model and
is not necessarily exactly true, however it gives an idea of the size of the
$1/N_c$ corrections to the pseudoscalar couplings. Therefore, in order
to perform a reliable estimate of the anti-decuplet widths we have to
take into account, in addition to the leading-order \eq{meson-soliton},
the $1/N_c$ corrections to that formula. The relevant $1/N_c$ corrections
have been treated in ref. \cite{Christov} for the $SU(2)$ case and in
ref. \cite{BPG} for the $SU(3)$ octet and decuplet cases; below we extend
these works to the anti-decuplet couplings.

In the next-to-leading order one has to add to
eq.~(\ref{meson-soliton}) new operators depending on the
angular momentum $J_a$. These operators have the form
\cite{BPG}:

\begin{equation}
i \frac{3 G_1}{2 m_B}\cdot
d_{iab} \cdot \frac 12
\mbox{Tr}(R^\dagger\lambda^m
R\lambda^a) J_b \cdot p_i +
i \frac{3 G_2}{2 m_B\sqrt 3}\cdot \frac 12
\mbox{Tr}(R^\dagger\lambda^m
R\lambda^8) J_i \cdot p_i ,
\la{meson-soliton-rot}\end{equation}
where $d_{abc}$ is the $SU(3)$ symmetric tensor, $a,
b=4,5,6,7$, and $J_a$ are the generators of the infinitesimal $SU(3)$
rotations. The new coupling constants $G_{1,2}$ are suppressed by
$1/N_c$ relative to the leading-order coupling constant $G_0$,
although numerically they can be sizable.

Sandwiching eqs.~(\ref{meson-soliton},\ref{meson-soliton-rot}) between
the rotational wave functions of initial and final baryons and taking
into account the anti-decuplet--octet mixing represented by the
coefficient $c_{\overline{10}}$ (see see \eq{mixnum}), we obtain the following
general formula for partial widths of members of the decuplet and
of the anti-decuplet:

\begin{eqnarray}
\Gamma(B_1 \rightarrow B_2 M)&=&
 \frac{3 G_r^2}{2\pi (M_1+M_2)^2} |\vec{p}|^3
\frac{M_2}{M_1}\cdot (C_1 + \frac{1}{\sqrt 5} C_2\cdot c_{\overline{10}}),
\label{wg}
\end{eqnarray}
The effective coupling constant $G_r$ depending on the multiplet and the
isoscalar factors $C_1$ and $C_2$ for various decays are listed in Table~2. The
pion nucleon
coupling constant $g_{\pi NN}$ and the $F/D$ ratio can be also
expressed in terms of the couplings $G_{0,1,2}$:

\begin{eqnarray}
g_{\pi NN}&=& \frac{7}{10}\cdot (G_0 +\frac 12 G_1 +\frac{1}{14} G_2),\\
\frac{F}{D}&=& \frac 59\cdot \frac{G_0+\frac 12 G_1+\frac 12  G_2}
{G_0+\frac 12 G_1-\frac 16 G_2}\,.
\end{eqnarray}
Substituting in the last equation the experimental value of $F/D = 0.56\pm
0.02$ we find the value of the ratio:

\begin{equation}
\frac{G_2}{G_0+\frac 12 G_1}= 0.01\pm 0.05,
\label{g2num}
\end{equation}
which turns to be very small and will be neglected.
The smallness of $G_2$ is not surprising as it can be related to the singlet
axial constant of the nucleon,

\begin{equation}
G_2=\frac{2 M_N}{3 F_\pi} g_A^{(0)}\,,
\end{equation}
the latter known to be small. We see here another remarkable
prediction of the `baryon as soliton' idea: the smallness of
the singlet axial constant $g_A^{(0)}$ is directly related to
the smallness of the deviation of the $F/D$ ratio from 5/9.

\vskip 0.33cm
\begin{tabular}{|c|c|c|c|}
\hline
\hline
decay & $G_r$ & $C_1$ & $C_2$\\
\hline
\hline
$\Delta \to N\pi$ & $G_0+\frac 12 G_1$ &$\frac 15$ & 0 \\
$\Sigma^* \to \Lambda\pi$ & $G_0+\frac 12 G_1$ &$\frac{1}{10}$ & 0 \\
$\Sigma^* \to \Sigma\pi$ & $G_0+\frac 12 G_1$ &$\frac{1}{15}$ & 0 \\
$\Xi^*\to \Xi \pi $ & $G_0+\frac 12 G_1$ &$\frac{1}{10}$ & 0 \\
\hline
$N_{\overline{10}} \to N\pi$ & $G_0-G_1-\frac 12 G_2$ &
$\frac{1}{20}$ &$ -\frac{23}{40}$ \\
$N_{\overline{10}} \to N\eta$ & $G_0-G_1-\frac 12 G_2$ &
$\frac{1}{20}$ & $-\frac{1}{40} $\\
$N_{\overline{10}} \to \Delta\pi$ & $G_0 + \frac 1 2 G_1 $ &
0 & $\frac 45 c_{\overline{10}}$ \\
$N_{\overline{10}} \to \Lambda K$ & $G_0-G_1-\frac 12 G_2$ &
$\frac{1}{20}$ & $\frac{2}{ 5}$ \\
$N_{\overline{10}} \to \Sigma K$ & $G_0-G_1-\frac 12 G_2$ &
$\frac{1}{20}$ & $\frac{3}{20}$ \\
\hline
$ Z^+\to N K$ & $G_0-G_1-\frac 12 G_2$ &
$\frac{1}{5}$ & $\frac{1}{4}$ \\
\hline \hline
\end{tabular} \vskip 0.5cm

Table 2. Clebsch-Gordan coefficients entering eq.~(\ref{wg}) for the
decays of the decuplet and of the lightest members of the anti-decuplet.
\vskip 0.33cm

From Table~2 we see that the decuplet-octet couplings  are
proportional to $(G_0+G_1/2)$ and hence (if one neglects the
apparently small $G_2$) it can be related to the
pion-nucleon coupling $g_{\pi NN}$. This observation
means that the widths of the decuplet calculated in the leading $1/N_c$ order
in the beginning of this section are actually not affected by the
rotational $1/N_c$ corrections: in the next-to-leading order the
relation of the decuplet widths to the $g_{\pi NN}$ constant is not
changed. One has just to replace the $G_0$ of \eqsss{ww1}{gpinn} by
$G_0+G_1/2$. Therefore, from the decuplet decay width one finds
(cf. \eq{gpinn})

\begin{equation}
G_{10}=G_0+\frac 12 G_1 \approx 19,\;\;\;\;\;
g_{\pi NN} \approx \frac{7}{10}
\left(G_0+\frac{1}{2}G_1\right)\approx 13.3\,.
\end{equation}

However, the situation is different for the anti-decuplet: as seen
from Table~2, its effective couplings are proportional to $(G_0-G_1)$
(again we neglect the small $G_2$), not to $(G_0+\frac 12 G_1)$.
Therefore, with the $1/N_c$ corrections taken into account,
the anti-decuplet--octet coupling is not expressed solely through
$g_{\pi NN}$: to calculate the anti-decuplet decay widths one has
to know the ratio $G_1/G_0$ as well. Unfortunately, it can not be fixed in a
model-independent way -- one has to resort to some model. In
the chiral quark-soliton model \cite{DPP} the ratio $G_1/G_0$ is in
range from $0.4$ to $0.6$ \cite{Christov,BPG} \footnote{M.P. is
grateful to H.-C.~Kim and T.~Watabe for a detailed discussion of this
issue}. A similar calculation of the $G_2$ coupling in the same model
shows that it is substantially smaller than $G_0$ \cite{BPG},
in accordance with the experiment, see \eq{g2num}.
In the estimates below we use the lower value of the ratio,
$G_1/G_0\approx 0.4$, corresponding to the value of the anti-decuplet
decay constant,

\begin{equation}
G_{\overline{10}} \approx G_0-G_1 \approx 0.5\cdot G_{10} \approx 9.5\; .
\la{g1g0}\end{equation}

It should be mentioned that the non-relativistic quark model
(which, to some extent, can be used as a guiding line) predicts
$G_1/G_0=4/5$ and $G_2/G_0=2/5$, which is in a qualitative agreement
with a more realistic calculation in the quark soliton model.
Amusingly, though, these ratios produce exactly zero $G_{\overline{10}}$.
At the moment we are unable to point out the deep reason for
such a cancellation; in any case the non-relativistic quark
model cannot be considered as realistic as it gives also a too large
value of the $F/D$ ratio and of the singlet axial constant.
However, it may indicate that \eq{g1g0} over-estimates $G_{\overline{10}}$,
and that the widths of the anti-decuplet are even more narrow
than we estimate below.

We now present the decay rates of the members of the anti-decuplet
using \eqs{wg}{g1g0} with the Clebsch--Gordan coefficients from Table~2 which
also takes into account the octet--anti-decuplet mixing discussed in section~3.

\vspace{0.5cm}
\underline{$T=0,\; S=1$ state (the exotic $Z^+$ baryon) }

\begin{equation}
\Gamma(Z^+ \rightarrow N K)=
\frac{3 G_{\overline{10}}^2}{2\pi (M_N+M_{Z})^2} |\vec{p}|^3 \frac{M_N}{M_{Z}}
\cdot\frac{1}{5}\bigl(1+\frac{\sqrt 5}{4} c_{\overline{10}}\bigr)
=15\,MeV,
\label{zw}
\end{equation}
Since there are no other strong decay modes, the total width of the $Z^+$
coincides with the above number. \\

\vspace{0.5cm}
\underline{$T=\frac 12,\; S=0$ state (the $N$ resonance)}

\begin{eqnarray}
\Gamma(N_{\overline{10}} \rightarrow N\pi)&=&
\frac{3 G_{\overline{10}}^2}{2\pi (M_N+M_{\overline{10}})^2 } |\vec{p}|^3 \frac{M_N}{M_{\overline{10}}}
\label{w1}
\cdot\frac{1}{20}\bigl(1-\frac{23}{2 \sqrt 5} c_{\overline{10}}\bigr)
=5\,MeV, \\
\Gamma(N_{\overline{10}} \rightarrow N\eta)&=&
\frac{3 G_{\overline{10}}^2}{2\pi (M_N+M_{\overline{10}})^2 } |\vec{p}|^3 \frac{M_N}{M_{\overline{10}}}
\cdot\frac{1}{20}\bigl(1-\frac{1}{2 \sqrt 5} c_{\overline{10}}\bigr)
=11\,MeV, \\
\Gamma(N_{\overline{10}} \rightarrow \Delta\pi)&=&
\frac{3 G_{\overline{10}}^2}{2\pi (M_\Delta+M_{\overline{10}})^2 } |\vec{p}|^3
\frac{M_\Delta}{M_{\overline{10}}} \cdot\frac{4}{5} c_{\overline{10}}^2
=5\,MeV,
\label{w3} \\
\Gamma(N_{\overline{10}}
\rightarrow \Lambda K)&=&
\frac{3 G_{\overline{10}}^2}{2\pi(M_\Lambda+M_{\overline{10}})^2 }|\vec{p}|^3
\frac{M_\Lambda}{M_{\overline{10}}} \cdot\frac{1}{20}\bigl(1+\frac{8}{ \sqrt 5}
c_{\overline{10}}\bigr)
=5\,MeV, \\
\Gamma(N_{\overline{10}} \rightarrow \Sigma K)&=& \frac{3
G_{\overline{10}}^2}{2\pi (M_\Sigma+M_{\overline{10}})^2}
|\vec{p}|^3 \frac{M_\Sigma}{M_{\overline{10}}}
\cdot\frac{1}{20}\bigl(1+\frac{3}{ \sqrt 5} c_{\overline{10}}\bigr)
=0.5\,MeV,
\label{w5}
\end{eqnarray}

These partial widths sum up into 27.5 MeV. However, the quantum numbers
of $N(1710)$ allow decays into, say, $N\pi\pi$ states which are not
fully accounted for above. Allowing a 50\% branching ratio for the
non-accounted decays, we estimate the full width as
$\Gamma_{tot}(N_{\overline{10}})\approx 27.5\,MeV\cdot 1.5 \approx 41\,MeV$,
where from the branching ratios can be deduced, see Table~3.

\vspace{.5cm}\hspace{1cm}
\underline{$T=1,\;  S=-1$ state (the $\Sigma$ resonance)}

\begin{eqnarray}
\Gamma(\Sigma_{\overline{10}} \rightarrow N\bar K)&=&
\frac{3 G_{\overline{10}}^2}{2\pi (M_N+M_{\Sigma_{\overline{10}}})^2 }
|\vec{p}|^3 \frac{M_N}{M_{\Sigma_{\overline{10}}}}
\label{ws1}
\cdot\frac{1}{30}\bigl(1-\frac{9}{ \sqrt 5} c_{\overline{10}}\bigr)
=6\,MeV, \\
\Gamma(\Sigma_{\overline{10}} \rightarrow \Sigma\pi)&=&
\frac{3 G_{\overline{10}}^2}{2\pi (M_\Sigma+M_{\Sigma_{\overline{10}}})^2 }
|\vec{p}|^3 \frac{M_\Sigma}{M_{\Sigma_{\overline{10}}}}
\cdot\frac{1}{30}\bigl(1- \sqrt 5 c_{\overline{10}}\bigr)
=10\,MeV,
\\
\Gamma(\Sigma_{\overline{10}} \rightarrow \Sigma\eta)&=&
\frac{3 G_{\overline{10}}^2}{2\pi (M_\Sigma+M_{\Sigma_{\overline{10}}})^2 }
|\vec{p}|^3 \frac{M_\Sigma}{M_{\Sigma_{\overline{10}}}}
\cdot\frac{1}{20}\bigl(1+\frac{6}{ \sqrt 5} c_{\overline{10}}\bigr)
=9\,MeV,
\label{ws3} \\
\Gamma(\Sigma_{\overline{10}}
\rightarrow \Lambda \pi)&=&
\frac{3 G_{\overline{10}}^2}{2\pi(M_\Lambda+M_{\Sigma_{\overline{10}}})^2 }|\vec{p}|^3
\frac{M_\Lambda}{M_{\Sigma_{\overline{10}}}}
\cdot\frac{1}{20}\bigl(1-\frac{6}{ \sqrt 5}
c_{\overline{10}}\bigr)
=17\,MeV, \\
\Gamma(\Sigma_{\overline{10}}
\rightarrow \Xi K)&=&
\frac{3 G_{\overline{10}}^2}{2\pi(M_\Xi+M_{\Sigma_{\overline{10}}})^2 }|\vec{p}|^3
\frac{M_\Xi}{M_{\Sigma_{\overline{10}}}}
\cdot\frac{1}{30}\bigl(1+\frac{19}{ \sqrt 5}
c_{\overline{10}}\bigr)
=3 \,MeV, \\
\Gamma(\Sigma_{\overline{10}} \rightarrow \Sigma^* \pi)&=& \frac{3
G_{\overline{10}}^2}{2\pi (M_{\Sigma^*}+M_{\Sigma_{\overline{10}}})^2}
|\vec{p}|^3 \frac{M_{\Sigma^*}}{M_{\Sigma_{\overline{10}}}}
\cdot\frac{2}{15} c_{\overline{10}}^2
=2\,MeV.
\label{ws5}
\end{eqnarray}

These partial widths sum up to $47\,MeV$. Multiplying it by a factor of
1.5 as in the previous case we estimate the full width of the
$\Sigma_{\overline{10}}$ to be $\Gamma_{tot}(\Sigma_{\overline{10}})\approx 70\,MeV$. See
Table~4 for the calculated branching ratios and a comparison with the
data.

\vspace{.5cm}\hspace{1cm}
\underline{$T=3/2,\;  S=-2$ state (the exotic $\Xi_{3/2}$ baryon)}

\begin{eqnarray}
\Gamma(\Xi_{3/2}\rightarrow \Sigma K) &=& 52\,MeV, \\
\Gamma(\Xi_{3/2}\rightarrow \Xi \pi) &=& 42\,MeV,\\
\Gamma_{tot}(\Xi_{3/2})&\approx& 140\,MeV.
\la{wx2}\end{eqnarray}

\vskip 0.33cm
\begin{tabular}{|c|c|c|}
\hline
\hline
$N_{\overline{10}}$ & prediction & data \\
\hline
$M_{\overline{10}}$\,, MeV & $1710$ {\rm(input)} & $1710$  \\
$\Gamma_{tot}(N_{\overline{10}})$\,, MeV & $\sim 40$ & 50 to 250\\
$Br(N\pi)$ &$\sim 0.13$ & 0.10 to 0.20\\
$Br(N\eta)$ &$\sim 0.28$ & $0.16\pm 0.10$ \\
$Br(\Delta \pi)$ P-wave &$\sim 0.13$ & --\\
$Br(\Lambda K)$ &$\sim 0.13$ & -- \\
$Br(\Sigma K)$ &$\sim 0.01$ & --\\
$\sqrt{Br(N\pi)Br(N\eta)}$ &$\sim 0.19$ &$0.30\pm 0.08$ \\
$\sqrt{Br(N\pi)Br(\Lambda K)}$ &$\sim 0.13$ &0.12 to 0.18 \\
$\sqrt{Br(N\pi)Br(\Delta \pi)}$ &$\sim 0.12$ &0.16 to 0.22 \\
\hline
\hline
\end{tabular} \vskip 0.5cm

Table 3. Predictions for decay modes of $N_{\overline{10}}$ identified with
$N\left(1710, \frac{1}{2}^+\right)$, confronted with the data from \cite{PDG}.
\vskip 0.33cm

Despite the smallness of the octet--anti-decuplet mixing represented by
the coefficient $c_{\overline{10}}$ (see \eq{mixnum}) it has a large impact on the
decay widths of the anti-decuplet because the decay channels
$8\rightarrow 8+8$ and $8\rightarrow 10+8$ are enhanced ``kinematically"
by large Clebsch--Gordan coefficients. For example, without taking into
account this mixing, the decay $N_{\overline{10}}\rightarrow \Delta \pi$ is forbidden,
however the small mixing probability, $c_{\overline{10}}^2 \sim 0.007$,
is amplified by a huge ``kinematical" factor $\sim 20$.

Finally, we mention that the $Z^+NK$ coupling correspondent to
\eqs{meson-soliton}{meson-soliton-rot}
can be written down in a relativistically-invariant
form as

\begin{equation}
L_{int}=ig_{KNZ}\left[(\bar p\gamma_5 Z^+)\bar K^0 + (\bar n \gamma_5
Z^+)K^- \right]\,.
\la{relinv}\end{equation}
Comparing its non-relativistic
limit with particular projections of
\eqs{meson-soliton}{meson-soliton-rot} we find

\begin{equation}
g_{KNZ}=\frac{3}{\surd{30}}\;\frac{2m_N}{m_N+m_Z}\;(G_0-G_1)\approx
4.1\,.  \la{gKNZ}\end{equation}

For a comparison, the ordinary $\Sigma^+NK$ vertex written in the form of
\eq{relinv} corresponds to $g_{KN\Sigma^+}\approx 5$.

\section{Identification of members of the anti-decuplet}

We see that the predicted branching ratios and total width of the $N(1710)$
are in a reasonable
agreement with the data, given the large errors and inconsistencies in the
data, see \cite{PDG}. Our numbers should be compared also with the
predictions for the $N(1710)$ decays following from the standard $SU(6)$
quark model, performed in ref. \cite{FC}. Assuming $N(1710)$ to be a member
of a normal octet the authors get, in particular, $\Gamma(N\eta) \approx
\Gamma(\Lambda K) \approx 0$, which seems to contradict the data
even though the errors are large. It should be mentioned, however, that
a recent analysis \cite{Batinic} suggests that in the $\sim 1700\,MeV$
region there might be actually two nucleon resonances: one coupled
stronger to pions and another to the $\eta$ meson.

We conclude that the $N(1710)$ nucleon resonance
is a good candidate for the $N_{\overline{10}}$ member of the anti-decuplet. Let us
stress that the octet--anti-decuplet mixing is important for the analysis.
It leads to a considerable reduction of the $N \pi$
branching ratio and of the total width;
simultaneously a non-zero $\Delta \pi$ branching ratio appears, in
accordance with the phenomenology of the $N(1710)$ decays.

There is a fair candidate for the $\Sigma_{\overline{10}}$ member of the anti-decuplet,
namely the $\Sigma(1880)$ from the Particle Data Group baryon listings
\cite{PDG}. The resonance has only a two-star status, and its properties are
not measured properly, including the mass ranging from $1826\pm 20$ to
$1985\pm 50$ MeV. Nevertheless, we compare our predictions for the
$\Sigma_{\overline{10}}$ with what is known about the resonance, see Table~4.

\vskip 0.33cm
\begin{tabular}{|c|c|c|}
\hline
\hline
$\Sigma_{\overline{10}}$ & prediction & data \\
\hline
$M_{\Sigma_{\overline{10}}}$\,, MeV
& $1890$ & $\approx 1880$  \\
$\Gamma_{tot}(\Sigma_{\overline{10}})$\,, MeV & $\sim 70$ &$80$ to 250\\
$Br(N\bar K)$ &$\sim 0.09$ & 0.06 to 0.3\\
$\sqrt{Br(N\bar K)Br(\Sigma\pi)}$ &$\sim 0.11$ &$\sim 0.3$ \\
$\sqrt{Br(N\bar K)Br(\Lambda\pi)}$ &$\sim 0.15$ &0.11 to 0.25\\
\hline
\hline
\end{tabular} \vskip 0.5cm

Table 4. Predictions for decay modes of $\Sigma_{\overline{10}}$, confronted with
the data from \cite{PDG}.
\vskip 0.33cm

What can be said is that the suggested identification does not contradict
the (poor) data on the $\Sigma(1880)$ resonance.

As to $\Xi_{3/2}$ which we predict at $2070\,MeV$, there are several
candidates for the non-exotic components of this quadruplet in the range
of masses between $1900$ and $2100\,MeV$, however even their quantum numbers
are not well established yet. In view of the estimate that our $\Xi_{3/2}$ is
wider than $140\,MeV$  it would be quite difficult to pinpoint
such a state, including its exotic components, $\Xi^{--}$ and $\Xi^+$.
Moreover, a presence of such a wide state would seriously influence the
determination of the parameters of other $\Xi$-type resonances, were they to
appear in this mass region. We sum up our predictions for the
anti-decuplet in Table~5.

\vskip 0.33cm
\begin{tabular}{|c|c|c|c|c|c|}
\hline
\hline
 &T&Y &Mass in MeV & Width in MeV & Possible candidate \\
\hline
$Z^+$&$0$ &$2$ & 1530 & 15 & ---\\
$N_{\overline{10}} $&$1/2$&$1$ & $1710\;{\rm(input)}$ & $\sim 40$ &
$N(1710)P_{11}$\\ $\Sigma_{\overline{10}}$&$1$ &$0$ & 1890 & $\sim 70$&
$\Sigma(1880)P_{11}$\\
$\Xi_{3/2}$ & $3/2$ & $-1$ & 2070 & $>140$ &
$\Xi(2030)?$ \\
\hline \hline
\end{tabular} \vskip 0.5cm

Table 5. Predictions for masses and total widths of the members of the
anti-decuplet and possible candidates for these states.
\vskip 0.33cm

It should be mentioned that the masses of the anti-decuplet have been
estimated in the Skyrme model with the results ranging from
$M_{Z^+}\approx 1500$~MeV \cite{Prasz2} to $\approx 1700$~MeV
\cite{Walliser}. Such an uncertainty arises in the Skyrme model
since one has to make a difficult choice between having the
nucleon mass correct and the $F_\pi$ constant wrong, or {\em vice
versa}. Predictions for the exotic $T=0, S=1$ $P_{01}$ state
in the bag model are grouped around 1750~MeV \cite{corden,bag}, that is
significantly higher than our estimate.

Our considerations have essentially been based on the identification of the
non-exotic member of the anti-decuplet with the rather well established
nucleon resonance, $N\left(1710,\frac{1}{2}^+\right)$. On general grounds,
we cannot exclude the possibility that the anti-decuplet as a whole
lies higher.  For example, the exotic $Z^+$ might, in principle, have a
mass of more than 1750 MeV (lower masses are probably excluded by the
old phase-shift analyses -- see ref. \cite{Dover}). There have been
claims in the past for observing such states (see ref.\cite{obzor} for
a review). In this case, however, there would be difficulties in
finding an appropriate candidate for the $N_{\overline{10}}$ member of the
anti-decuplet.  The only possibility suggested by the Particle Data
baryon listings is the $N\left(2100,\frac 12^+\right)$ resonance.
In this case the moment of inertia $I_2$ determining the shift of the
anti-decuplet center in respect to the decuplet center would be
very small (about $\sim 0.3$~fm).  Such a small moment of inertia can
hardly be obtained in any dynamical realization of the idea of baryons
as solitons, which seems to be so successful everywhere else.
Therefore, we believe that we present a good case for a relatively
light and narrow exotic baryon: it probably has not been observed in
the past just for these reasons.

\section{Conclusions}

The chiral soliton models of baryons, which correctly emphasize the
important role of the spontaneous chiral symmetry breaking in the dynamics of
strong interactions, are extremely successful in explaining relations between
octet and decuplet baryons since in these models they all appear as various
rotational excitations of the same object.

The two lowest rotational states
of chiral solitons are exactly the octet with spin $\frac{1}{2}$ and the
decuplet with spin $\frac{3}{2}$, and it is natural to ask oneself what
is the next rotational state. The answer is
\cite{DP,Chemtob,Prasz2,Walliser}: it is
the anti-decuplet with spin $\frac{1}{2}$, and most of its properties
can be predicted from symmetry considerations only, without entering into
dynamics which is model-dependent. The only unknown parameter (a specific
$SU(3)$ moment of inertia) can be fixed by identifying the nucleon-like
member of the anti-decuplet with the observed
$N\left(1710,\frac{1}{2}^+\right)$
resonance. Its decay modes, as well as masses and decay modes of the
other members of the anti-decuplet can be then fixed unambigiously.
The calculated decay modes of the $N(1710)$ are found to be in a reasonable
agreement with the existing data though the data are not good enough
to make a decisive conclusion.
At least it seems that the standard non-relativistic $SU(6)$
description of this state as a member of an octet, is in trouble with the
data: the anti-decuplet idea fits better.

In a sense, history repeats itself: there are candidates for all members
of the anti-decuplet, except for its vertex -- like in the early 60's when
all members of the now venerable decuplet were known except the
$\Omega^-$ hyperon. In our case it is the exotic $Z^+$ baryon, which
decays into $K^+\,n$ and $K^0\,p$.  Claims for observing such states
have been made in the past (see ref.\cite{obzor} for a review) but they
are all substantially higher than our prediction $m_Z\approx 1530\,MeV$,
with the width lower than $\Gamma_Z\approx 15\,MeV$.

The most direct way to detect the exotic $Z^+$ resonance would be in the
$K^0\,p$ or $K^+\,n$ scattering. Unfortunately, the mass range in question
is too low for kaon beams and probably too high for the $\phi$
factory of kaons.

Another possibility to reveal the exotic $Z^+$ is in the
collisions of non-strange particles. In comparison with direct
production in $KN$ collision, such reactions are more complicated as they
involve many particles in the final states of which
some are neutral and some are charged, therefore a combined detector is
needed. As to the missing-mass-type experiments they seem to be vulnerable
because of severe background conditions and the narrowness of the
$Z^+$.  Let us list several possibilities of the $Z^+$ production in
reactions with non-strange particles.

\begin{itemize}
\item
\underline{Nucleon--nucleon collisions}\\
$pn \to \Lambda Z^+ \to \Lambda K^+ n \; \mbox{or}\; \Lambda K^0 p$,
$\;p_{lab} > 2.60 \;GeV/c$ \\
$pp \to \Sigma^+ Z^+ \to \Sigma^+ K^+ n \; \mbox{or}\; \Sigma^+ K^0 p$,
$\;p_{lab}>2.8\; GeV/c$
\item
\underline{Photon-nucleon collisions}\\
$\gamma p \to \bar K^0 Z^+ \to  \bar K^0 K^+ n
\; \mbox{or}\; \bar K^0 K^0 p$, $\;p_{lab}>1.7 \;GeV/c$ \\
$\gamma n \to K^-Z^+ \to K^- K^+ n
\; \mbox{or}\; K^-K^0 p$, $\;p_{lab}>1.7 \;GeV/c$
\item
\underline{Pion-nucleon collisions}\\
$\pi^- p \to K^-Z^+ \to K^- K^+ n
\; \mbox{or}\; K^-K^0 p$ $\;p_{lab}>1.7 \;GeV/c$ \\
$\pi^+ n \to \bar K^0Z^+\to \bar K^0K^+n
\; \mbox{or}\; \bar K^0K^0p$, $\;p_{lab}>1.7 \;GeV/c$.
\end{itemize}

One of the most promising ways to check the existence of the
$Z^+$ baryon would be in the photon collisions with energies
$>2\,GeV$, since the photon already carries a portion of strange quarks
\footnote{One of us (D.D.) is grateful to E.Paul for a conversation on
this point.}.  Another possibility is to analyze the LASS data
from the 11 GeV $K^+ p$ collisions \footnote{We thank J.~Bjorken
for this suggestion.}.
In any case, a search for a light and narrow exotic $Z^+$ baryon
seems to be a challenging task.

\section{Acknowledgments}
This work has been supported in part by the INTAS grants 93-0283 EXT
and 93-1630-EXT and by a joint grant
of the Deutsche Forschungsgemeinschaft and the Russian Foundation for
Basic Research. M.P. is a
A.v.Humboldt Fellow, and acknowledges warm hospitality by Prof. Klaus
Goeke at the Bochum University.

We thank P.Pobylitsa for a cooperation. M.P. is grateful
to M. Praszalowicz and H.~Walliser for useful discussions.

\setcounter{section}{0}

redpajama_set_name: RedPajamaArXiv


To call the practice at all times, please use the numbers above and listen to the message given- some numbers have changed- see below.
We use divertable numbers on occasions to pass calls through to the duty doctor /surgery.
These are now local rate 0300 numbers. See "when we are closed" section for each surgery.


Looking to do some snorkeling or diving as part of your Mallorcan beaches experience? If your travels take you in the vicinity of stunning Santanyi, be sure to visit Calo des Moro. Nestled between steep pine-tree laden cliffs this small but beautiful Mallorcan beach has much to offer.
Pure crystal clear waters make underwater exploring very easy. Snorkelers and divers alike will have no trouble spotting brightly coloured fish and sea life under the glassy surface. Or if you just fancy a cool swim, Calo des Moro seems to stay temperate all year round. Otherwise you can just stretch out on the golden sandy shores.
Calo des Moro is a cosy intimate cove, so visiting off-peak times is best if you want to avoid feeling crowded. It is not so much that throngs of people flock to Calo des Moro but more that it doesn't take many bods to fill up the 30 metre bay. Weekday or early morning visits are usually a good option.
Getting to this little gem amongst Mallorcan beaches isn't entirely effortless but also not problematic. You'll come to the cove from the Cala s'Almuna fishermen huts. Take a small climb down rather worn stone stairs and you'll find yourself on the beach's glistening Mallorcan sands. Adult tourists won't struggle accessing Calo des Moro. But if you're travelling with a young family this may not be the best Mallorcan beach for you. As well as finding it tricky to get down to the beach, kids will have limited play space too.
Calo des Moro lies some 6km from Santanyi. So this pretty village is a great place to stay during this leg of your Mallorcan beach and holiday experience. Sa Galera is a stately ancient Mallorcan manor offering a great taste of boutique hotels Mallorca. You'll have the choice of 20 individually decorated rooms, each thoughtfully furnished with plenty of comforts.
Looking to get the very most out of your Mallorcan beaches explorations? Or perhaps you'd just appreciate some tips on finding the best accommodation options around Santayni and beyond. Rural Hotels Mallorca would be happy to help. We know both Mallorcan beaches and boutique hotels Mallorca inside out. Just give us a call on 020 3239 4983 (UK number) or get in touch via our contact form. We'll gladly share our inside knowledge with you.


text:
/**
 * This class provides an interface for getting routes between two points; it abstracts the Google Map libraries.
 * @param  {Object} options       The router options
 * @param  {Object} movieInstance The main movie instance
 * @return {Object}
 */
window.streetviewanimator.router = function(options, movieInstance) {

    /**
     * Prevent scope issues by using `base` in callbacks instead of `this`
     * @type {Object}
     */
    var base = this;

    // --------------------------------------------------------------------------

    /**
     * Alias to main namespace
     * @type {Object}
     */
    var $SVA = window.streetviewanimator;

    // --------------------------------------------------------------------------

    /**
     * The API key to use when communicating with Google
     * @type {String}
     */
    base.apiKey = options.apiKey;

    // --------------------------------------------------------------------------

    /**
     * Holds an instance of the direction service
     * @type {Object}
     */
    base.directionService = null;

    // --------------------------------------------------------------------------

    /**
     * Holds an instance of the geocoder
     * @type {Object}
     */
    base.geocoder = null;

    // --------------------------------------------------------------------------

    /**
     * Computes the heading between two points
     * @type {Object}
     */
    base.computeHeading = null;

    // --------------------------------------------------------------------------

    /**
     * A cache of geocoded strings
     * @type {Array}
     */
    base.geocodeCache = [];

    // --------------------------------------------------------------------------

    base.__construct = function() {

        base.log('Constructing');
        base.doReset();

        //  Instanciate the Google services
        if (typeof window.google !== 'undefined' && typeof window.google.maps !== 'undefined') {

            if (typeof window.google.maps.DirectionsService !== 'undefined') {

                base.directionService = new window.google.maps.DirectionsService();

            } else {

                throw('Google Maps Direction Service not available');
            }

            if (typeof window.google.maps.Geocoder !== 'undefined') {

                base.geocoder = new window.google.maps.Geocoder();

            } else {

                throw('Google Maps Geocoder not available');
            }

            if (typeof window.google.maps.geometry !== 'undefined') {

                base.computeHeading = window.google.maps.geometry.spherical.computeHeading;

            } else {

                throw('Google Maps Geometry library not available');
            }

        } else {

            throw('Google Maps Libraries were not found');
        }
    };

    // --------------------------------------------------------------------------

    /**
     * Set the API key to use when communicating with Google
     * @param {String} apiKey The API key to use
     */
    base.setApiKey = function(apiKey) {
        base.apiKey = apiKey;
        return base;
    };

    // --------------------------------------------------------------------------

    base.reset = function() {
        base.log('Resetting');
        base.doReset();
    };

    // --------------------------------------------------------------------------

    base.doReset = function() {
        base.geocodeCache = [];
    };

    // --------------------------------------------------------------------------

    /**
     * Geocode a string and get the coordinates
     * @param  {String} address The address to geocode
     * @return {Object}         A jQuery promise
     */
    base.getCoordinatesFromAddress = function(address) {

        var deferred = new $.Deferred();

        base.log('Geocoding "' + address + '"');

        base.geocoder.geocode({'address': address}, function (results, status)
        {
            if (status === window.google.maps.GeocoderStatus.OK)
            {
                base.log('Successfully geocoded ' + address);
                base.log('Lat: ' + results[0].geometry.location.lat());
                base.log('Lng: ' + results[0].geometry.location.lng());

                var coordinates = {
                    'lat': results[0].geometry.location.lat(),
                    'lng': results[0].geometry.location.lng()
                };

                deferred.resolve(coordinates);

            } else {

                base.log('"' + address + '" could not be geocoded');
                deferred.reject({
                    'error': 'Failed to geocode "' + address + '".',
                    'response': results
                });
            }
        });

        return deferred.promise();
    };

    // --------------------------------------------------------------------------

    /**
     * Returns directions between two coordinates
     * @return {Object} A jQuery promise
     */
    base.getDirections = function(origin, destination, travelMode) {

        var deferred, originObj, destinationObj, request;

        deferred = new $.Deferred();

        originObj = new window.google.maps.LatLng(
            origin.lat,
            origin.lng
        );

        destinationObj = new window.google.maps.LatLng(
            destination.lat,
            destination.lng
        );

        travelMode = travelMode || window.google.maps.DirectionsTravelMode.DRIVING;

        request = {
            'origin': originObj,
            'destination': destinationObj,
            'travelMode': travelMode
        };

        base.log('Getting ' + travelMode + ' directions', request);

        base.directionService.route(request, function(response, status){

            if (status === window.google.maps.DirectionsStatus.OK) {

                base.log('Directions received');
                deferred.resolve(response);

            } else {

                base.log('Directions failed: ', status);
                deferred.reject({
                    'error': 'Failed to get directions, received status "' + status + '"',
                    'response': response
                });
            }
        });

        return deferred.promise();
    };

    // --------------------------------------------------------------------------

    /**
     * Sends an item to the log, prefixing it with a string so that the class
     * making the log is easily identifiable
     * @return {Object}
     */
    base.log = function() {

        $SVA.debug.log('SVA [Router]:', arguments);
        return base;
    };

    // --------------------------------------------------------------------------

    /**
     * Sends an item to the error log, prefixing it with a string so that the class
     * making the log is easily identifiable
     * @return {Object}
     */
    base.error = function() {

        $SVA.debug.error('SVA [Router]:', arguments);
        return base;
    };

    // --------------------------------------------------------------------------

    return base.__construct();
};

redpajama_set_name: RedPajamaGithub


Researchers at Lawrence Berkeley National Laboratory (Berkeley Lab) and UC Berkeley have discovered that as plants develop they craft their root microbiome, favoring microbes that consume very specific metabolites. Their study could help scientists identify ways to enhance the soil microbiome for improved carbon storage and plant productivity.
It turns out your skin is crawling with single-celled microorganisms – and they're not just bacteria. A study by Lawrence Berkeley National Laboratory and the Medical University of Graz has found that the skin microbiome also contains archaea, a type of extreme-loving microbe, and that the amount of it varies with age.
Scientists from Berkeley Lab and PNNL have found that genes and early environment play big roles in shaping the gut microbiome. The microbes retained a clear "signature" formed where the mice were first raised, and the characteristics carried over to the next generation. The findings could potentially be used to develop designer diets optimized to an individual's microbiome.
The initiative will advance the understanding of microbiome behavior and enable the protection of healthy microbiomes, which are communities of microorganisms that live on and in people, plants, soil, oceans, and the atmosphere. Microbiomes maintain the healthy function of diverse ecosystems, and they influence human health, climate change, and food security.
Scientists have for the first time reengineered a building block of a geometric nanocompartment that occurs naturally in bacteria. The new design provides an entirely new functionality that greatly expands the potential for these compartments to serve as custom-made chemical factories.


The logjam in infrastructure financing, 24 October 2014. kw = the long run has caught up with us.
RBI's `wilful default' framework vs. the rule of law, 16 September 2014. kw = Indian bankruptcy code, judicial review.
Response to Raghuram Rajan's speech on FSLRC, Indian Express, 4 July 2014. kw = draft Indian Financial Code, judicial review, RBI turf.
Responding to the distress in Indian banking, Economic Times, 30 June 2014. kw = ARC, Asset management company, moral hazard.
Engineers, not drivers, Economic Times, 10 April 2014. kw = State capacity.
My generation, Economic Times, 13 March 2014. kw = human capital, workforce, literacy, education, learning by doing, human capital obsolescence.
Inflation targeting is the new gold standard, Economic Times, 13 February 2014. kw = adoption of IT all across the world, durable solution, currency crises.
Rule of law and competition in banking, Economic Times, 9 January 2014. kw = bank licensing, RBI.


text:
Courts get different levels of attention at conventions
Aug. 29, 2020 at 5:38 am Updated Aug. 29, 2020 at 11:57 am
Seung-Min Kim
At the Republican National Convention this week, an antiabortion activist lauded President Donald Trump for nominating scores of "pro-life" judges. A California teacher who took her battle against public sector unions to the Supreme Court made the case for Trump's reelection. A Navajo Nation leader thanked the president for tapping Supreme Court picks who upheld the rights of Native Americans.
And Trump used his convention address to brag about the number of federal judges — a figure he inflated — that he expects to have confirmed by the end of his term.
References to the judiciary, long a key motivator for conservative voters, were woven throughout the GOP convention this week and served as a reminder that even if Trump loses reelection in November, his stamp on the courts will last for decades to come.
But Democrats all but ignored the Supreme Court in their four-day convention earlier this month, even after the party spent Trump's first term reckoning with the consequences of Republicans confirming two justices, including a reliably conservative justice who replaced the court's swing vote.
The contrast worries liberal activists who see it as further evidence that the Democratic Party isn't paying enough attention to an area where conservatives have made big inroads in recent years: control of the courts.
"The fact that Democrats spent so little to no time discussing the federal bench failed to take into account that their critically important goals for the future will be challenged in the courts," said Nan Aron, the president of the liberal judicial advocacy group Alliance for Justice.
She added: "It's a major misstep, given the fact that these 200 judges will make it very difficult, if not impossible in many cases, for the Democrats to accomplish their worthy goals going forward."
For activists on both sides, the stakes for the future of the Supreme Court are incredibly high, with two justices in their 80s — including Ruth Bader Ginsburg, who announced last month that her cancer had returned.
The lack of attention on the courts at the Democratic convention came even as a notable shift has occurred in recent years when it comes to how much the party's voters prioritize the judiciary.
A Pew Research Center poll released this month found that 66% of registered voters who support Democratic nominee Joe Biden said the matter of Supreme Court appointments was "very important" in considering their vote for president, compared to 61% of Trump backers. When Pew asked that same question four years ago, 70% of then-candidate Trump's supporters said the issue was "very important," while 62% of backers of Democrat Hillary Clinton said the same.
Yet the sole Democratic speaker to discuss the courts with any notable prominence was Senate Minority Leader Chuck Schumer, D-N.Y., who vowed to "restore a Supreme Court that looks out for people, not corporations" should Democrats win the White House and flip control of the Senate.
Former acting attorney general Sally Yates decried Trump's attacks on institutions such as the FBI and federal judges that are designed to be a check on presidential power. But Sen. Catherine Cortez Masto, D-Nev., the chair of the Senate Democrats' campaign arm, did not mention the courts, even as Democratic senators spent four years vigorously fighting dozens of Trump judicial nominees.
And the appearance of Sara Gideon, the Democratic Senate nominee in Maine, was spent introducing a musical performance, even though she is running against Republican Sen. Susan Collins, whose support for now-Supreme Court Justice Brett Kavanaugh has made her a top target for defeat this November.
"As both 2016 and 2018 reconfirmed, the judicial fight is a winning issue for Republicans," said Mike Davis, the former top nominations counsel for Republicans on the Senate Judiciary Committee. He now runs the Article III Project, a group that promotes Trump's judicial picks. "It unites the party, wins over independents, and even brings in right-thinking Democrats."
Instead, the Democratic Party's changing views on the courts — and the increasing influence on voters — was reflected in its platform. In it, the party acknowledged "it recognizes the need for structural court reforms to increase transparency and accountability." While the platform didn't endorse any specific changes, the inclusion of the language was nonetheless considered a victory for liberal activists who had pushed Democratic presidential candidates to embrace an overhaul of the courts.
Democrats in the platform also vowed to tap judicial nominees with "diverse backgrounds and experiences, including as public defenders, legal aid attorneys, and civil rights lawyers."
"We're definitely moving the dial with actual Democrats," said Christopher Kang, a veteran of the judicial wars in the Obama White House.
Kang, a co-founder and chief counsel for the judicial advocacy group Demand Justice, said he would've been frustrated by the minimal mention for the courts at the Democratic National Convention had there not been an ongoing public health crisis surrounding the novel coronavirus.
"Given the pandemic and seeing how Democrats wove Trump's response to COVID, as well as the Democratic response and the need to come together, the courts didn't really fit as you would've thought in a more policy- and substance-focused convention," he said.
The Democratic National Committee had no comment on why the judiciary went so unmentioned during its convention. The Biden campaign did not return a request for comment.
In contrast, references to the courts were sprinkled throughout the Republican National Convention.
Man lived inside Chicago's O'Hare airport for 3 months before detection, prosecutors say
In a video played the opening night of the convention, Trump vowed that he would appoint justices "who will uphold our laws and our Constitution." Jason Joyce, a lobsterman from Maine, talked about Trump nominating judges "who respect the Constitution and the right to life."
Cissie Graham Lynch, the granddaughter of famed evangelical leader Billy Graham, said Trump nominated judges "who respect the First Amendment" and that while in court, "he ensured religious ministries would not be forced to violate their beliefs."
Eric Trump, the president's second-eldest son, listed Supreme Court justices as a promise kept by his father. And antiabortion activist Abby Johnson cited Trump's "record number of pro-life judges" as she made her case for the president among abortion opponents.
Republicans also invited as speaker Rebecca Friedrichs, whose lawsuit against teachers unions in California positioned her to battle not only the Obama-Biden administration but then-California Attorney General Kamala Harris, now the party's vice-presidential nominee.
"President Trump also strengthened the Supreme Court by nominating strong conservative judges like Neil Gorsuch who supports Native American rights," said Myron Lizer, vice president of the Navajo Nation.
In their respective convention addresses, Vice President Mike Pence said the administration has appointed "more than 200 conservative judges to our federal courts," while Trump one night later said that by the end of his first term, "we will have approved more than 300 federal judges, including two great new Supreme Court justices."
So far during the Trump presidency, the Republican-controlled Senate has confirmed 203 judges. There are 70 vacancies in the federal district courts, with nominees pending for 41 of them.
"We will appoint prosecutors, judges and justices who believe in enforcing the law, not enforcing their own political agenda," Trump said from the South Lawn of the White House in his convention speech.
After a season in which several contenders in the Democratic presidential primary endorsed structural changes to the Supreme Court such as expanding the number of seats or imposing term limits, Senate Majority Leader Mitch McConnell, R-Ky., in his convention appearance Thursday night warned that Democrats "want to pack the Supreme Court with liberals intent on eroding our constitutional rights."
"The stakes have never been higher," McConnell said. "Which is why I'm asking you to support Republican Senate candidates across the country and reelect my friend President Donald Trump."
Conventions aside, the issue of the courts is sure to be an active campaign topic in the coming weeks.
Biden has pledged to nominate a Black woman to a Supreme Court vacancy should he be elected, and advocacy groups are preparing to ramp up publicity and voter engagement efforts around the promise.
Meanwhile, Trump said in a June tweet that he would release a fresh batch of potential Supreme Court nominees — some on the existing list, some not — by Sept. 1, and two people familiar with the plans said the White House was prepared to still to do so next week.
Administration officials have reached out to key allies to craft their new list of nominees, including Sen. Chuck Grassley, R-Iowa, the former chairperson of the Senate Judiciary Committee who has spoken with the White House several times in recent weeks to solicit his input, Grassley spokesman Taylor Foy said.
But even Grassley was rankled this week when the Trump campaign released a list that included dozens of policy priorities for his second term but not any mention of the judiciary.
"[W]hy isn't filling judicial vacancies in 2nd term agenda released 2day?" Grassley, known for his clipped and misspelled social media missives, tweeted at the president this week. "Senate GOP & Trump hv made top priority Talking abt the Supreme Court got Pres Trump elected & it needs 2b center stage again this election 'Lv no vacancy behind' needs 4 MORE YRS"
Foy said Friday that "given the President's comments last night, he's satisfied that voters know judges will continue to be a top priority."
This story was originally published at washingtonpost.com. Read it here.

redpajama_set_name: RedPajamaCommonCrawl


text:
Q: Reading multiple precision binary files through fread in Matlab I have a huge binary file which has records with multiple precision as {'Double','Double',
'Int32','Int8','Char'}. I have used memmapfile to read in the data but its painfully slow to read in the data. Is there a way to read the whole file through fread?

A: You can use the 'skip' option of the FREAD function as well as FSEEK to read the records one "column" at-a-time:
%# type and size in byte of the record fields
recordType = {'double' 'double' 'int32' 'int8' 'char'};
recordLen = [8 8 4 1 1];
R = cell(1,numel(recordType));

%# read column-by-column
fid = fopen('file.bin','rb');
for i=1:numel(recordType)
    %# seek to the first field of the first record
    fseek(fid, sum(recordLen(1:i-1)), 'bof');

    %# % read column with specified format, skipping required number of bytes
    R{i} = fread(fid, Inf, ['*' recordType{i}], sum(recordLen)-recordLen(i));
end
fclose(fid);

This code should work for any binary records file in general, you just have to specify the data types and byte length of the records fields. The result will be returned in a cell array containing the columns.

redpajama_set_name: RedPajamaStackExchange


text:
Q: Doctrine2 Entity PrePersist - Update another entity I have a Doctrine2 entity (call it entity A) in my Symfony2 project. This entity has a ManyToOne relationship with another entity (call it entity B) in the project.
Entity A has a status property which is 'active' or 'inactive'. There's only one 'active' entity A allowed in entity B. So, if a new entity A is added to an existing entity B, the previous entity A, which has an 'active' status, needs to be updated to 'inactive'.
What is the best approach to achieve this?
I was thinking about the LifeCycle methods (prePersist), but I doubt if this works, because it's another entity which is updated than the entity I persist.
A code example:
class EntityA
{
    const ACTIVE = 'active';
    const INACTIVE = 'inactive';

    private $id;
    private $status;
    private $entityB;

    public function prePersist()
    {
        $currentEntityA = $this->entityB->getCurrentEntityA();
        if ($currentEntityA) {
            $currentEntityA->setStatus(self::INACTIVE);
        }
    }
}

class EntityB
{
    private $id;
    private $name;
    private $entityA;

    public function getCurrentEntityA()
    {
        foreach($this->entityA as $row){
            if ($row->getStatus() == EntityA::ACTIVE ) {
                return $row;
            }
        }
        //no entityA found so return null
        return null;
    }
}

A: You should use a prePersist listener / subscriber instead of LifecycleCallbacks in this case.
Read more about them in the documentation chapter - How to register Event Listeners/Subscribers.
btw a subscriber is tagged with doctrine.event_subscriber (currently missing the doc chapter).

A: You can use several approaches

*

*Doctrine Event Listeners

*Service layer

*Database triggers

In your situation I think better to use services and move your business logic there


text:
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Oct 03, 2018 · Exactly how in order to Publish any Rules Article. With some university or college lawful reports training, and inside numerous law the school programs, you can possibly be recommended for you to be able to write a fabulous study newspaper approaching some sort of genuine topic. Those works will be able to often be tough, as a regulation is normally often improving. In order to 80%(41).
Making a good educative essay or dissertation usually means fashioning some sort of coherent arranged regarding suggestions towards a powerful fight. Due to the fact works usually are primarily linear—they present one plan with a new time—they have to present the recommendations during a arrangement which will would make a lot of perception so that you can a fabulous person who reads. Effectively structuring a particular dissertation methods joining to help a new reader's reasoning.


text:
Cerebral palsy is a term used to describe a group of disorders that cause impairments to the brain and nervous system functions. There are several different types of cerebral palsy and the symptoms that manifest may differ widely depending on the type of cerebral palsy and the severity of the damage that caused the disorder. Symptoms can range from mild to severe and can affect one or both sides of the body. Cerebral palsy symptoms can begin to show in children as young as three months old or as old as two years.
Spastic Cerebral Palsy Symptoms
Spastic cerebral palsy is the most common type of cerebral palsy, accounting for about 70 to 80 percent of cases. Symptoms of spastic cerebral palsy often include muscles and joints that are too tight and do not stretch or open up all the way. The gait of children with spastic cerebral palsy is often abnormal. The legs may cross in scissor movements while walking, the knees may touch, or the children may walk on the toes. The arms may also stay tucked in to the sides while moving around and some groups of muscles may entirely lose function and become paralyzed.
Diskenetic Cerebral Palsy Symptoms
Also called extrapyramidal, diskenetic cerebral palsy affects the coordination of muscle movements. There are two main types of diskenetic cerebral palsy, athetoid and ataxic. Athetoid cerebral palsy causes uncontrolled movements of any part of the body, including the face, mouth, and tongue. Ataxic cerebral palsy typically affects the balance, coordination, and depth perception, which can cause symptoms such as unsteady walking or a lack of ability to walk.
Mixed Cerebral Palsy Symptoms
In many cases, the types of cerebral palsy are not clear-cut and cerebral palsy is considered "mixed." A common combination is spastic and athetoid cerebral palsy, in which some symptoms of each type are present. Symptoms may vary widely in cases of mixed cerebral palsy, and may include any combination of physical, cognitive, and developmental impairments that are present in the different types of cerebral palsy.
Developmental Cerebral Palsy Symptoms
Cerebral palsy symptoms are often not identified until children reach six and a half to nine months of age. At this time, children usually start to mobilize and it becomes evident if one side of the body is being favored or if there are issues with muscle coordination. Developmental delays such as issues with grasping objects may also become evident and children may begin to fall behind developmental milestones. As children get older, cerebral palsy symptoms such as learning disabilities and intellectual impairments may inhibit development.
Postural and Visible Symptoms
Depending on the way that cerebral palsy affects the body, some symptoms may be present and identifiable immediately. Babies may hold abnormal posture, with muscles appearing "floppy." Over time, muscle deficits may begin to affect bone growth. Bones require stresses from muscle definition to grow into normal shapes and sizes. When muscle definition is not normal, bones may become thinner or thicker than normal and joint deformities may begin to manifest. Bones may also stop growing sooner than normal, resulting in shorter heights or legs and arms that are different lengths.
Brain and Nervous System Symptoms
Children with cerebral palsy may or may not have intellectual and learning disabilities. Children with cerebral palsy often have communication problems, so it may be difficult for children to articulate knowledge even when cognitive impairments are not present. Cerebral palsy may also cause hearing or vision problems, seizures, and pain as a result of brain and nervous system problems.
Functional Difficulties
Cerebral palsy symptoms may interfere with daily functions, especially as children grow older. Feeding may be difficult, as chewing, swallowing, and controlling mouth movements is often affected by the lack of muscle control and sometimes by tremors. Breathing complications may also be present. Incontinence and drooling are common symptoms of cerebral palsy, which may make it difficult for children to take part in many activities and functions.
"Cerebral Palsy." Medline Plus. U.S. National Library of Medicine, 12 Jan. 2015. Web. 4 Feb. 2015. <http://www.nlm.nih.gov/medlineplus/ency/article/000716.htm>
"Signs and Symptoms." My Child at Cerebral Palsy.org. My Child at Cerebral Palsy.org, 1 Jan. 2015. Web. 4 Feb. 2015. <http://cerebralpalsy.org/about-cerebral-palsy/sign-and-symptoms/>
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Jaxon's daddy posted this inspiring video on his personal Facebook page that was shared by the performer Diddy. I figured I should share it with all of you. As parents of a visually impaired child, we were worried about our son being blind because blindness was not "normal" to us. Everyday, our visually impaired son shows us that overcoming the obstacles associated with blindness is now our "normal" and everyday it gets easier to cope with.
"When the doctor told me at 3 days old (after weeks of uncertainties as to why my son was so tiny before we saw him) that he would be blind, I had to go to corners of the hospital to keep from crying in front of Alyssa. I remember calling my family and tearfully telling them that Jaxon would never see my face, or know what either of his parents look like. I cried in the hallway with Alyssa's mom after the first eye exam with the ophthomologist when Alyssa caught me after hiding it.
This little boy is an example of the unexpected and unrelenting strength that I hoped to impress upon Jaxon. I had never known a blind person, and didn't have the first clue as to how to teach a son that couldn't see how to grow up, but I was determined.
I post this because you might find yourself in what should be the most beautiful moment of your life turn into the most painful day that you'll never forget - either way you will grow, and your child will grow from your strength.
Jaxon now crawls around with limited vision out of one eye, and to us he is "normal". He throws things on the ground, he cries when things are taken from him, and he smiles at you as he glares out of the one good part of his eye to get a good view of you.
He is everything that makes me tear up out of joy just crawling and knowing where he's going. Occasionally he smacks his head on a door, but every placement of hand or knee is a learning moment, and not just for him. Enjoy every step of the way, every movement is a gift and privilege that might not always be there."


The Washington County Railroad (WCRR) is a privately owned large scale railroad whose owners have a special interest in coal fired steam locomotives. It is located at the home of the Brace Family on Campbell Hill in Cherryfield, Maine. Cherryfield is in Washington County, the eastern most county of the United States, where the sun first rises on the United States of America. Therefore, the original WCRR was also known by the name Sunrise Route.
Stop by on the third Sunday of any month and help work on the railroad ... on nice days trains are used haul material to repair the road bed ... helpers ride to work areas. If the weather isn't good, and even in the winter, there's always work to be done in the car barn.
The logo that appears above is that of the original Washington County Railroad. It was incorporated in 1894 and its rails were a short distance from our railroad. Two of John's great uncles were extensively involved. The track existed until 2009, but had not seen any commercial traffic in years. The State of Maine is the owner and in 2009 turned it into a recreational trail. Our bridge is a copy of the nearby train bridge which still spans the Narraguagus River.
Our track gauge is precisely 7.5 inches. The switches have guarded frogs making it possible for 7.25 inch gauge equipment to operate. The guarded frogs make it necessary to require that the wheels on all railroad equipment be at least 3/4 of an inch in width. The wheels on 7 1/2 inch gauge equipment must be no wider than 13/16ths of an inch while the wheels on 7 1/4 inch gauge equipment can be up to 7/8ths of inch in width. The flange profile should conform to the IBLS wheel standards established in 1974.
The minimum radius of the track is 35 feet. The maximum grade is 1.5%. Trains have to climb over 21.5 feet in going from east to west on the track.
Because it a private track access is limited to family and friends who actually do the work of maintaining the railroad.
The main line track circuit is now 5 1/2 scale miles in length. The above picture shows the current track. There is a valley in the foreground with the top of the mountain being at the top of the picture. The spur track that can be seen at the lower left of the picture is the start of the continuation of the main line. It has been laid out for many more miles, but at this time construction is doubtful.
Friends of the family are always welcome as visitors, but call first as we have no public run days. The third Sunday of the month is always a work day, stop by, help out, and learn about the railroad.
Click on the layout for a detailed on-line view or here for the print version.
Video (10:22): Field of Steam, June 26, 2010, my favorite video this year!
October 12, 2003 ... Pictures for John. Come home soon!
George, the Director the WCRR.
Jeremy, the Superintendent of the WCRR.
Wren, the Webmaster of the WCRR.