text:
Thieves Stole Pope John Paul II's Blood
Vial filled with Pope's blood was taken from a church in mountains east of Rome
By Andrew Katz Jan. 27, 2014
L'Osservatore Romano / Associated Press
Pope Francis prays in front of the tomb of Pope John Paul II, at the Vatican Tuesday, April 2, 2013, on the eighth anniversary of the much-beloved pontiff's death.
Follow @TIMEWorld
A group of thieves broke into a church near Rome favored by the late Pope John Paul II over the weekend and stole a vial filled with his blood.
Pope John Paul II, who died in 2005, was known to visit the Abruzzo region, east of Rome, to hike or ski or pray in the small stone church of San Pietro della Ienca, near the city L'Aquila. Six years after he died, his former secretary gave the local community some of the late Pontiff's blood as a token of his love for that region. The blood was set in a gold and glass circular case and kept in the church.
A custodian of the church, Franca Corrieri, said Monday she discovered a broken window on Sunday morning and alerted authorities. The relic and a crucifix were taken in the heist. "In a sense, a person has been stolen," she told Reuters.
Italian authorities said Monday they thought the theft was commissioned, NBC News reports, as many other valuables were left inside the church.
The Polish-born John Paul held the papacy for 27 years. He survived an assassination attempt in St. Peter's Square in May 1981, after which some of his blood was saved. He is due to be made a saint of the Roman Catholic Church later this year, which would boost the value of the stolen blood.
[Reuters]
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It usually comes as a big surprise to those who haven't checked it out before; the calorie count for alcohol is a substantial one. So before you get all smug thinking you've got your total weekly food calories calculated exactly, don't forget to add on that extra glass of wine - or three.
People who strictly monitor what they are eating, and find they can't lose those extra pounds, may need to check out their drinks tally.
Only fat has more calories per gram than alcohol, and the alcohol calories add absolutely nothing in the way of nutrition.
There is evidence to suggest that, as well as being relaxing and fun, some alcohol, taken in moderation, can have medicinal benefits. In the long term, however, drinking more than a glass or two a day can seriously damage your health. You must weigh the benefits against the danger of developing a harmful habit.
If you are watching your weight, you have to count the calorie cost of 7 calories per gram of alcohol. That is about 85 calories for a modest, standard pub glass of red wine. If you drink your wine out of the goblets used in many homes and restaurants, you could be consuming twice the calories.
Low alcohol wines are much lower in calories. Low alcohol drinks can make a good alternative as long as they are not taken in larger amounts. They still contain varied amounts of alcohol and it is important to check the labels for strength. It is also important to remember that low alcohol drinks contain more chemical additives than full strength drinks.
With beers, the calorie difference between low alcohol and standard beers is not so marked. Low alcohol beers range from 40 to 80 calories for a half pint, compared to around 85 for a small can of ordinary beer or lager to as many as 175 calories for a pint.
Strong beers are very high in calories, having 170 for a small can and 350 for a full pint.
Hard spirits like gin and vodka have around 50 calories or more in a single shot, depending on the proof strength, plus the calories contained in whatever is your mixer drink of choice. If you are drinking spirits keep the calorie count down by using slim line mixers.
Liqueur, like coffee liqueur, is even higher in calories at 160 for a 1.5 ounce shot. Fruity tropical drinks like pina coladas will put your calorie count through the roof.
Alcohol is a diuretic, that is it makes the body lose water, so it dehydrates you. For the sake of your health it is best if you do drink to try to limit your drinking to three or four drinks a week, preferably red wine. When drinking alcohol it helps to drink some water with it, to prevent dehydration.
The recommended levels of alcohol consumption are measured in units, with the current acceptable limits for men set at 21 units per week and for women 14 units per week.
Bear in mind that these measures for wine are for standard glasses and not goblets.


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text:
\section{Introduction}

In the papers \cite{BS, Kor} it was observed
that the six-vertex $R$-matrix at root of unity intertwines not
only the six-vertex $L$-operators, but also some other
$L$-operators (which are called cyclic $L$-operators).
These $L$-operators def\/ine $n$-particle
Bazhanov--Stroganov quantum chain (BSQC) by the standard procedure
in quantum inverse scattering method: the product of $L$-operators
def\/ines the monodromy matrix
\begin{gather} \label{mmintro}
{T}_n(\lambda)=L_1(\lambda)L_2(\lambda)\cdots L_n(\lambda)= \left(
\begin{array}{cc}
A_n(\lambda)& B_n(\lambda)\\[2mm]
C_n(\lambda)& D_n(\lambda) \end{array} \right),
\end{gather}
which in turn provides us with commuting set of operators ---
Hamiltonians of quantum chain. It was observed by Baxter that the
so-called ``Inverse SOS'' model discovered by him \cite{BaxtInv}
is equivalent to Bazhanov--Stroganov quantum chain. Thus the same
model (which is called the $\tau_2$-model) has two formulations:
the formulation as face model by Baxter and the formulation as
quantum chain (or vertex model) by Bazhanov and Stroganov. The
connection between six-vertex model, $\tau_2$-model and chiral
Potts model gave a possibility to formulate the system of
functional relations \cite{BS,BBP} for transfer-matrices of these
models. This system provides the main tool for derivation the free
energy \cite{BaxtEV} and the order parameter \cite{BaxtOP} for
chiral Potts model.

The goal of this contribution is to f\/ind common eigenvectors of
the set of commuting Hamiltomians ${\boldsymbol H}_k$,
$k=1,2,\ldots,n$, of open $n$-particle BSQC. These Hamiltonians
are def\/ined by the coef\/f\/icients of the $A_n(\lambda)$ given
by (\ref{mmintro}):
\[
A_n(\lambda)=1+\lambda {\boldsymbol H}_1+\lambda^2 {\boldsymbol
H}_2+ \cdots+\lambda^n {\boldsymbol H}_n.
\]
The main idea how to f\/ind the eigenvectors is to use iterative
procedure. Namely we build the eigenvectors of $A_n(\lambda)$
using the eigenvectors of $A_{n-1}(\lambda)$ which is the
generation function of Hamiltonians for open $(n-1)$-particle
BSQC. This procedure in essential is an adaptation of iterative
procedure by Kharchev and Lebedev \cite{KhL} for quantum Toda
chain. The mentioned idea has origin in the paper by Sklyanin
\cite{Skl}, where he used separated variables of subsystems to
construct the separated variables of the whole system. The models
where the iterative procedure was realized are relativistic Toda
chain \cite{KhLS}, Toda chain with boundary interaction \cite{IS},
periodic Bazhanov--Stroganov model \cite{GIPS}. It is worth to
note that these models do not admit algebraic Bethe ansatz
procedure because in the case of generic parameters these models
do not possess ``highest weight vectors''. The method used in this
contribution is an evolution of the method of separated variables
(or functional Bethe ansatz method).

At the end of the introduction we would like to mention that the
Bazhanov--Stroganov model at special values of parameters reduces
to the relativistic Toda chain at a root of unity. Also it is worth
noting {\it direct} (not through the chiral Potts model!) relation
\cite{BIS} between lattice formulation of the model at $N=2$ and Ising
model. This relation gave a possibility to find the eigenvalues \cite{BIS}
and the eigenvectors \cite{Lis}
of the transfer-matrix by means of auxiliary grassmann field technique.

\section[Bazhanov-Stroganov quantum chain]{Bazhanov--Stroganov quantum chain}

Let $\omega=e^{2\pi{\rm i}/N}$, $N\ge 2$. For each particle $k$,
$k=1,2,\ldots,n$, of Bazhanov--Stroganov quantum chain (BSQC) with
$n$ particles there corresponds $N$-dimensional linear space
(quantum space)~${\cal V}_k$ with the basis
$|\gamma\rangle_k$,$\gamma\in \mathbb{Z}_N$, and a pair of
operators $\{{\boldsymbol u}_k,{\boldsymbol v}_k\}$ acting on
${\cal V}_k$ by the formulas:
\begin{gather}\label{uvact}
{\boldsymbol v}_k|\gamma\rangle_k=\omega^\gamma
|\gamma\rangle_k,\qquad {\boldsymbol u}_k|\gamma\rangle_k=
|\gamma-1\rangle_k.
\end{gather}
The space of quantum states of BSQC with $n$ particles is ${\cal
V}={\cal V}_1\otimes{\cal V}_2\otimes\cdots\otimes{\cal V}_n$. We
extend the action of operators $\{{\boldsymbol u}_k,{\boldsymbol
v}_k\}$ to ${\cal V}$ def\/ining this action to be identical on
${\cal V}_s$, $s\ne k$. Thus we have the following commutation
relations
\begin{gather*
{\boldsymbol u}_j {\boldsymbol u}_k={\boldsymbol u}_k {\boldsymbol
u}_j,\qquad {\boldsymbol v}_j {\boldsymbol v}_k={\boldsymbol v}_k
{\boldsymbol v}_j,\qquad {\boldsymbol u}_j {\boldsymbol v}_k=
\omega^{\delta_{j,k}} {\boldsymbol v}_k{\boldsymbol u}_j.
\end{gather*}

For each particle of BSQC model we put into correspondence the
cyclic $L$-operator
\begin{gather}\label{bazh_strog}
L_k(\lambda)=\left(
\begin{array}{cc}
1+\lambda \varkappa_k {\boldsymbol v}_k &  \lambda {\boldsymbol u}_k^{-1} (a_k-b_k {\boldsymbol v}_k)\\
{\boldsymbol u}_k (c_k-d_k {\boldsymbol v}_k) & \lambda a_k c_k +
{\boldsymbol v}_k {b_k d_k}/{\varkappa_k }
\end{array}
\right),\qquad k=1,2,\ldots,n,
\end{gather}
where $\{a_k,b_k,c_k,d_k,\varkappa_k\}$ are (in general complex)
parameters attached to $k$th particle. In the papers \cite{BS,Kor} it
was observed that the six-vertex $R$-matrix
\begin{gather*}
{R}(\lambda,\mu)=\left(\begin{array}{cccc}
\lambda-\omega\mu & 0 & 0 & 0 \\[1mm]
0 & \omega(\lambda-\mu) & \lambda (1-\omega) & 0 \\[1mm]
0 & \mu (1-\omega) & \lambda-\mu & 0 \\[1mm]
0 & 0 & 0 & \lambda-\omega\mu \end{array}\right).
\end{gather*}
at root of unity $\omega=e^{2\pi {\rm i}/N}$ intertwines not only
the six-vertex $L$-operator, but also the cyclic
$L$-operators~(\ref{bazh_strog}):
 \begin{gather*} R(\lambda,\mu)\,  L^{(1)}_k\, (\lambda) L^{(2)}_k(\mu)=
L^{(2)}_k(\mu)\, L^{(1)}_k(\lambda)\, R(\lambda,\mu),
\end{gather*}
where $L^{(1)}_k(\lambda)= L_k(\lambda)\otimes\mathbb{I}$,
$L^{(2)}_k(\mu)=\mathbb{I} \otimes L_k(\mu)$. In fact the formulas
for $L$-operators and $R$-matrix given in this contribution are
close to formulas from the paper by Tarasov \cite{Tarasov}.
Original formulas given in \cite{BS} and \cite{Kor} are a bit dif\/ferent (but
equivalent). The monodromy matrix for the BSQC with $n$ particles
is def\/ined as
\begin{gather}\label{mm}
{T}_n(\lambda)=L_1(\lambda)L_2(\lambda)\cdots L_n(\lambda)= \left(
\begin{array}{cc}
A_n(\lambda)& B_n(\lambda)\\[2mm]
C_n(\lambda)& D_n(\lambda) \end{array} \right)
\end{gather}
and satisf\/ies the same intertwining relation
\begin{gather}
R(\lambda,\mu) \, {T}^{(1)}_n(\lambda)\, {T}^{(2)}_n(\mu)=
 {T}^{(2)}_n(\mu)\, {T}^{(1)}_n(\lambda)\, R(\lambda,\mu).
\label{rtt}
\end{gather}

The intertwining relation (\ref{rtt}) gives
$[A_n(\lambda),A_n(\nu)]=0$. Therefore $A_n(\lambda)$ is the
generating function for the commuting set of operators
${\boldsymbol H}_1,\ldots,{\boldsymbol H}_n$:
\[
A_n(\lambda)=1+\lambda {\boldsymbol H}_1+\lambda^2 {\boldsymbol
H}_2+ \cdots+\lambda^n {\boldsymbol H}_n.
\]
We interpret these operators ${\boldsymbol
H}_1,\ldots,{\boldsymbol H}_{n}$ as Hamiltonians of the open BSQC.
The simplest Hamiltonians are
\begin{gather*}
{\boldsymbol H}_1=\sum_{k=1}^n  \varkappa_k {\boldsymbol v}_k
+\sum_{1\le l<k\le n}\!\! {\boldsymbol
u}_l^{-1}(a_l-b_l{\boldsymbol v}_l)\prod_{s=l+1}^{k-1}\frac{b_s
d_s}{\varkappa_s}{\boldsymbol v}_s\cdot {\boldsymbol u}_k
(c_k-d_k{\boldsymbol v}_k), \qquad {\boldsymbol H}_n=\prod_{k=1}^n
\varkappa_k {\boldsymbol v}_k.
\end{gather*}
At $b_k=0$ and $c_k=0$, the BSQC model reduces to Relativistic
Toda Chain (RTC) at root of unity. The corresponding $L$-operators
are
\begin{gather*
L_k^{\rm RTC}(\lambda)=\left(
\begin{array}{cc}
1+\lambda \varkappa_k {\boldsymbol v}_k &  \lambda a_k {\boldsymbol u}_k^{-1} \\
- d_k {\boldsymbol u}_k {\boldsymbol v}_k  & 0
\end{array}
\right),\qquad k=1,2,\ldots,n.
\end{gather*}
As in BSQC model $A_n^{\rm RTC}(\lambda)$ is the generating
function for the commuting set of operators ${\boldsymbol
H}_1^{\rm RTC},\ldots,{\boldsymbol H}_n^{\rm RTC}$. The simplest
Hamiltonians for RTC are
\[
{\boldsymbol H}_1^{\rm RTC}=\sum_{k=1}^n  \varkappa_k {\boldsymbol
v}_k -\sum_{1\le l \le n-1} a_l d_{l+1} {\boldsymbol
u}_l^{-1}{\boldsymbol u}_{l+1}{\boldsymbol v}_{l+1}, \qquad
{\boldsymbol H}_n^{\rm RTC}=\prod_{k=1}^n \varkappa_k {\boldsymbol
v}_k.
\]
Note that these operators ${\boldsymbol H}_1^{\rm
RTC},\ldots,{\boldsymbol H}_{n}^{\rm RTC}$ are the Hamiltonians of
the RTC with open boun\-dary condition and association with the
standard operators of momenta ${\boldsymbol p}_k$ and positions
${\boldsymbol q}_k$ roughly speaking (up to constants) is
${\boldsymbol v}_k=\exp {\boldsymbol p}_k$ and ${\boldsymbol
u}_k=\exp {\boldsymbol q}_k$. Then ${\boldsymbol H}_n^{\rm RTC}$
is the exponent of the total momentum of RTC and ${\boldsymbol
H}_1^{\rm RTC}$ is the Hamiltonian of relativistic analogue of
usual Toda chain.

\section{Eigenvalues and associated amplitudes}

In this section we give a procedure of obtaining the eigenvalues
for open $n$-particle BSQC Hamiltonians ${\boldsymbol H}_k$,
$k=1,2,\ldots,n$, or equivalently for $A_n(\lambda)$.

In the case of $a_k=b_k=c_k=d_k=0$, $k=1,2,\ldots,n$, we have
$A_n(\lambda)=\prod\limits_{k=1}^n (1+\varkappa_k{\boldsymbol
v}_k)$. We interpret the corresponding Hamiltonians as free
(without interaction between particles) Hamiltonians. Due to
(\ref{uvact}) the standard basis vectors
$|\gamma_1,\gamma_2,\ldots,\gamma_n\rangle =
|\gamma_1\rangle_1\otimes |\gamma_2\rangle_2\otimes \cdots \otimes
|\gamma_n\rangle_n\in {\cal V}$ are eigenvectors of
$A_n(\lambda)$:
\[
A_n(\lambda) |\gamma_1,\gamma_2,\ldots,\gamma_n\rangle =
\prod_{k=1}^n (1+\varkappa_k\omega^{\gamma_k})
|\gamma_1,\gamma_2,\ldots,\gamma_n\rangle.
\]

We claim that in the general case the spectrum of $A_n(\lambda)$
has the form as in the case of non-interacting particles but with
modif\/ied amplitudes $\varkappa_{n,k}$:
\[
A_n(\lambda)|\gamma_1,\gamma_2,\ldots,\gamma_n\rangle
=\prod_{k=1}^n\left(1+\varkappa_{n,k}\omega^{\gamma_{k}}\lambda\right)
|\gamma_1,\gamma_2,\ldots,\gamma_n\rangle,\qquad \gamma_{k}\in
\mathbb{Z}_N.
\]
The corresponding eigenvectors
$|\gamma_1,\gamma_2,\ldots,\gamma_n\rangle$ are not standard basis
vectors of course. To obtain their coordinates in the standard
basis we will use an iterative procedure as was promised in the
introduction. We start from the eigenvectors of open $1$-particle
BSQC. Then we construct eigenvectors of open $2$-particle BSQC by
addition in an appropriate way one more particle. And so on. In
parallel with this procedure we have an iterative procedure of
obtaining the amplitudes:
\[
(\varkappa_{11}:=\varkappa_1)\stackrel{+2^{\rm nd} {\rm \
particle}} \longrightarrow(\varkappa_{21},\varkappa_{22})
\stackrel{+3^{\rm rd} {\rm \ particle}}\longrightarrow \cdots
\stackrel{+n^{\rm th} {\rm \ particle}}\longrightarrow
 (\varkappa_{n1},\ldots,\varkappa_{nn}).
\]
Now we will describe the procedure how to f\/ind these amplitudes
$\varkappa_{m,s}$, $m=1,2,\ldots,n$, $s=1,2,\ldots,m$. We will
need the variables
\begin{gather}\label{xxx}
x^{m,s}_{m',s'}=\frac{\varkappa_{m,s}}{\varkappa_{m',s'}},\qquad
x_m=\frac{c_m}{d_m},\qquad x_{m,s}=\frac{c_m\varkappa_m}{d_m
\varkappa_{m,s}},\qquad \tilde x_{m,s}=\frac{b_m
\varkappa_{m,s}}{a_m\varkappa_m},
\end{gather}
and variables $y^{m,s}_{m',s'}$, $y_m$, $y_{m,s}$, $\tilde
y_{m,s}$. The latter are def\/ined (up to a root of $1$, which
will be f\/ixed later) by condition that points
$p^{m,s}_{m',s'}=(x^{m,s}_{m',s'},y^{m,s}_{m',s'})$, $p_m=(x_m,
y_m)$, $p_{m,s}=(x_{m,s}, y_{m,s})$, $\tilde p=(\tilde
x_{m,s},\tilde y_{m,s})$ belong to Fermat curve $x^N+y^N=1$.
First, we def\/ine $\varkappa_{1,1}:=\varkappa_1$. If we
constructed all the above variables for $m-1$ particles, we
def\/ine the variables $\varkappa_{m,1},\varkappa_{m,2},\ldots,
\varkappa_{m,m}$ by the equations
\begin{gather}\label{rel_m}
\varkappa_{m,1}\varkappa_{m,2}\cdots
\varkappa_{m,m}=\varkappa_{m-1,1}\varkappa_{m-1,2} \cdots
\varkappa_{m-1,m-1} \varkappa_m,
\\
\label{rel_other} \frac{\varkappa_m }{a_{m-1}d_m} \frac{y_{m-1}}{
y_m y_{m-1,l}\tilde y_{m-1,l}} \prod_{s\ne l}
\frac{y^{m-1,s}_{m-1,l}}{y^{m-1,l}_{m-1,s}}
\frac{\prod\limits_{k=1}^m y^{m-1,l}_{m,k}}
{\prod\limits_{s=1}^{m-2} y^{m-2,s}_{m-1,l}}=1, \qquad
l=1,2,\ldots,m-1.
\end{gather}
We would like to mention that this iterative procedure has a similarity to iterative procedures
in \cite{PS,GPS}.
To solve these equations we f\/irst take $N$-th power of them. It
gives us system of linear equations
\begin{gather}\label{rel_mNi}
\varkappa_{m,1}^N \varkappa_{m,2}^N \cdots \varkappa_{m,m}^N=
\varkappa_{m-1,1}^N \varkappa_{m-1,2}^N\cdots
\varkappa_{m-1,m-1}^N \varkappa_m^N,
\\
\label{rel_otherNi} \frac{\varkappa_{m-1,l}^N }{a_{m-1}^N d_m^N}
\frac{y_{m-1}^N}{ y_m^N y_{m-1,l}^N\tilde y_{m-1,l}^N}
\frac{\prod\limits_{k=1}^m
\big(1-\varkappa_{m,k}^N/\varkappa_{m-1,l}^N\big)}
{\prod\limits_{s=1}^{m-2}
\big(1-\varkappa_{m-2,s}^N/\varkappa_{m-1,l}^N\big)}=1, \qquad
l=1,2,\ldots,m-1.
\end{gather}
with respect to elementary symmetric polynomials in variables
$\{\varkappa_{m,1}^N,\ldots,\varkappa_{m,m}^N\}$. Solving equation
with coef\/f\/icients being the values of the mentioned symmetric
polynomials we obtain the values of
$\{\varkappa_{m,1}^N,\ldots,\varkappa_{m,m}^N\}$. The variables
$\{\varkappa_{m,1},\ldots,\varkappa_{m,m}\}$ can be found up to
$N$-th roots of~$1$. We f\/ix their phases in a way to satisfy
(\ref{rel_m}) and (\ref{rel_other}).

To compare these formulas with the formulas for eigenvalues
proposed by Tarasov \cite{Tarasov} we consider polynomials ${\cal
A}_m(\lambda^N)$ with zeroes $\epsilon/\varkappa_{m,s}^N$, $s=1,$
$2,\ldots,$ $m,$ where $\epsilon=(-1)^N$:
\begin{gather}\label{zerA}
{\cal A}_m\big(\lambda^N\big)=
\prod_{s=1}^{m}\big(1-\epsilon\,\varkappa_{m,s}^N \lambda^N\big),
\quad m\ge 2;\qquad\! {\cal
A}_1\big(\lambda^N\big)=1-\epsilon\varkappa_1^N \lambda^N;
\qquad\! {\cal A}_0\big(\lambda^N\big)=1.\!\!
\end{gather}
Then the relations (\ref{rel_mNi}) and (\ref{rel_otherNi}) can be
rewritten compactly as recursion relation for ${\cal
A}_m(\lambda^N)$, $m\ge 2$:
\begin{gather} {\cal A}_m\big(\lambda^N\big)=\left(\big(1-\epsilon\varkappa_{m}^N\lambda^N\big)+
\frac{c_m^N-d_m^N}{c_{m-1}^N-d_{m-1}^N} \left(\frac{b_{m-1}^N
d_{m-1}^N}{\varkappa_{m-1}^N}- \epsilon \lambda^N a_{m-1}^N
c_{m-1}^N\right)\right)
{\cal A}_{m-1}\big(\lambda^N\big) \nonumber\\
\phantom{{\cal
A}_m\big(\lambda^N\big)=}{}+\frac{c_{m}^N\!-\!d_{m}^N}{c_{m-1}^N\!-\!d_{m-1}^N}
 \frac{\big(b_{m-1}^N \!-\!\epsilon \lambda^N a_{m-1}^N \varkappa_{m-1}^N \big)\!\big(\epsilon \lambda^N c_{m-1}^N
\varkappa_{m-1}^N\! - \!d_{m-1}^N\big)}{\varkappa_{m-1}^N } {\cal
A}_{m-2}\big(\lambda^N\big).\!\!\!\! \label{relAm} \end{gather}
Indeed, the relation (\ref{rel_mNi}) follows from the relation for
coef\/f\/icients in (\ref{relAm}) at $(\lambda^N)^m$. If we f\/ix
sequentially $\lambda^N=\epsilon/ \varkappa_{m-1,l}^N$,
$l=1,$$2,\ldots,$$m-1$, (that is by the zeroes of ${\cal
A}_{m-1}(\lambda^N)$) we obtain the relations (\ref{rel_otherNi}).

This recursion relation for ${\cal A}_m(\lambda^N)$ can be
obtained by means of averaged $L$-operators \cite{Tarasov}. Using
\[
{\cal L}_m(\lambda^N)=\left( \begin{array}{cc}
1-\epsilon \varkappa_m^N \lambda^N & -\epsilon\lambda^N\big(a_m^N-b_m^N\big)\\[2mm]
c_m^N-d_m^N & b_m^N d_m^N/\varkappa_m^N-\epsilon \lambda^N a_m^N
c_m^N
\end{array} \right)
\]
we def\/ine polynomials ${\cal A}_m(\lambda^N)$, ${\cal
B}_m(\lambda^N)$, ${\cal C}_m(\lambda^N)$ and ${\cal
D}_m(\lambda^N)$ by
\begin{gather}\label{calABCD}
\left(\begin{array}{cc}
{\cal A}_m\big(\lambda^N\big) &  {\cal B}_m\big(\lambda^N\big)\\[2mm]
{\cal C}_m\big(\lambda^N\big) &  {\cal D}_m\big(\lambda^N\big)
\end{array}\right)={\cal L}_1\big(\lambda^N\big) {\cal L}_2\big(\lambda^N\big) \cdots {\cal L}_m\big(\lambda^N\big) .
\end{gather}
In particular, we have
\begin{gather}
{\cal A}_m\big(\lambda^N\big)= \big(1-\epsilon \varkappa_m^N
\lambda^N \big) {\cal A}_{m-1}\big(\lambda^N\big)
+\big(c_m^N-d_m^N\big) {\cal B}_{m-1}\big(\lambda^N\big),\nonumber
\\
{\cal B}_m\big(\lambda^N\big)=
-\epsilon\lambda^N\big(a_m^N-b_m^N\big) {\cal
A}_{m-1}\big(\lambda^N\big) +\big(b_m^N
d_m^N/\varkappa_m^N-\epsilon \lambda^N a_m^N c_m^N\big) {\cal
B}_{m-1}\big(\lambda^N\big).\label{AAB}
\end{gather}
Excluding ${\cal B}_{m-1}(\lambda^N)$ from these two relations we
get
\begin{gather*
{\cal B}_m\big(\lambda^N\big)= \frac{b_m^N
d_m^N/\varkappa_m^N-\epsilon \lambda^N a_m^N c_m^N}{c_m^N-d_m^N}
{\cal A}_m\big(\lambda^N\big) -\frac{\det {\cal
L}_m\big(\lambda^N\big)}{c_m^N-d_m^N} {\cal
A}_{m-1}\big(\lambda^N\big).
\end{gather*}
Substituting  the right-hand side of this equation with $m$
replaced by $m-1$ instead of ${\cal B}_{m-1}(\lambda^N)$
in~(\ref{AAB}) we get (\ref{relAm}). Therefore two formulas
(\ref{relAm}) and (\ref{calABCD}) for ${\cal A}_m(\lambda^N)$ are
equivalent. Summarizing, in order to f\/ind amplitudes
$\varkappa_{m,s}$, $s=1,\ldots,m$, for some $m$, we have to f\/ind
${\cal A}_m(\lambda^N)$ using (\ref{relAm}) or (\ref{calABCD}).
Then solving equation ${\cal A}_m(\lambda^N)=0$ of $m$th degree
with respect to $\lambda^N$ and taking into account (\ref{zerA})
we can f\/ind $\varkappa^N_{m,s}$, $s=1,\ldots,m$. This gives us
the set $\varkappa_{m,s}$ up to $N$th roots of $1$. At last step,
we have to f\/ix their values in a way to satisfy (\ref{rel_m})
and (\ref{rel_other}).

It seems to the author that the equation ${\cal A}_m(\lambda^N)=0$
can not be solved explicitly in the case of generic parameters. In
the next section, the solution for the homogeneous RTC is given
explicitly. The author does not know other interesting special
cases of parameters which admit explicit solution for the spectrum
of $A_m(\lambda)$. As shown in \cite{GIPS}, it is possible to give
an explicit solution for the spectrum of $B_m(\lambda)$ in the
homogeneous case of $m$-particle Bazhanov--Stroganov quantum
chain.

\section{Amplitudes for the homogeneous Relativistic Toda Chain}

In this section we sketch the method described in \cite{PS} of
obtaining the amplitudes for the homogeneous RTC: $a_k=a$,
$b_k=0$, $c_k=0$, $d_k=d$, $\varkappa_k=\varkappa$. In this case
the amplitudes $\varkappa_{m,s}$, $s=1,\ldots,m$, can be expressed
in terms of solutions of some quadratic equation. Since
\begin{gather}\label{cLRTC}
{\cal L}^{\rm RTC}_k\big(\lambda^N\big)={\cal L}^{\rm
RTC}(\lambda^N)=\left( \begin{array}{cc}
1-\epsilon \varkappa^N \lambda^N & -\epsilon a^N \lambda^N \\[2mm]
-d^N & 0
\end{array} \right),
\end{gather}
we obtain
\begin{gather*
\left(\begin{array}{cc}
{\cal A}_m\big(\lambda^N\big) &  {\cal B}_m\big(\lambda^N\big)\\[2mm]
{\cal C}_m\big(\lambda^N\big) &  {\cal D}_m\big(\lambda^N\big)
\end{array}\right)=\left({\cal L}^{\rm RTC}\big(\lambda^N\big)\right)^m .
\end{gather*}
Applying the fact that $2\times 2$ matrix $\boldsymbol M$ with
eigenvalues $\mu_+$ and $\mu_-$ satisf\/ies
\[
{\boldsymbol M}^m=\frac{\mu_+^m-\mu_-^m}{\mu_+-\mu_-}{\boldsymbol
M} -\frac{\mu_+^m \mu_--\mu_-^m \mu_+}{\mu_+-\mu_-}{\boldsymbol 1}
\]
for matrix ${\cal L}^{\rm RTC}(\lambda^N)$ we obtain
\begin{gather}\label{Apredv}
{\cal A}_m\big(\lambda^N\big)=\big(1-\epsilon \varkappa^N
\lambda^N \big) \frac{x_+^m-x_-^m}{x_+-x_-}-\frac{x_+^m x_--x_-^m
x_+}{x_+-x_-},
\end{gather}
where $x_+(\lambda^N)$ and $x_-(\lambda^N)$ are eigenvalues of
${\cal L}(\lambda^N)$. These eigenvalues are roots of
characteristic polynomial $x^2-\tau(\lambda^N) x +
\delta(\lambda^N)=0$:
\begin{gather*}
x_{\pm}=\frac{1}{2}\left(\tau\pm \sqrt{\tau^2-4\delta}\right)
\end{gather*}
where, using (\ref{cLRTC}),
\begin{gather}\label{tau}
\tau\big(\lambda^N\big)={\rm tr}\, {\cal L}^{\rm
RTC}\big(\lambda^N\big)=x_1+x_2= 1 - \epsilon \varkappa^N
\lambda^N ,
\\ \label{delta}
\delta\big(\lambda^N\big)= \det {\cal L}^{\rm
RTC}\big(\lambda^N\big) =x_1 x_2= -\epsilon a^Nd^N \lambda^N .
\end{gather}
Taking into account (\ref{tau}) we rewrite (\ref{Apredv}) as
\begin{gather*
{\cal A}_m\big(\lambda^N\big)=\frac{x_+^{m+1}-x_-^{m+1}}{x_+-x_-}.
\end{gather*}

Introducing the variable $\phi$ by $x_+/x_-=e^{{\rm i}\phi}$ we
f\/ind that roots of ${\cal A}_m$ correspond to roots $\phi_{m,s}$
of $e^{{\rm i}(m+1)\phi}=1$ (without $\phi=0$) that is
\begin{gather}
\label{zerphi} \phi_{m,s}=2\pi s/(m+1), \qquad s=1,2,\ldots,m.
\end{gather}
Now we need to f\/ind an explicit relation between $\lambda^N$ and
$\phi$. We have
\[
\tau+\sqrt{\tau^2-4\delta}=e^{{\rm i}\phi} \left(\tau-
\sqrt{\tau^2-4\delta}\right).
\]
Therefore
\begin{gather}
\label{tdphi} \tau^2=4 \delta \cos^2 \frac \phi 2.
\end{gather}
 Taking into account (\ref{tau}) and (\ref{delta}) we
consider (\ref{tdphi}) as quadratic equation with respect to
$\lambda^N$:
\begin{gather*}
\lambda^{2N} \varkappa^{2N} + 2\epsilon \lambda^N \big(a^N d^N +
a^N d^N\cos\phi -\varkappa^N\big) +1=0.
\end{gather*}
The solution $\lambda^N(\phi)$ of this equation describes the
relation between the variables $\lambda^N$ and $\phi$. Therefore
we can translate the zeroes (\ref{zerphi}) of ${\cal
A}_m(\lambda^N(\phi))$ in terms of variable $\phi$ to zeroes
$\lambda^N(\phi_{m,s})$ in terms of $\lambda^N$. Finally, taking
into account (\ref{zerA}) we f\/ind
\begin{gather*}
 \varkappa_{m,s}^N=\epsilon/ \lambda^N(\phi_{m,s}),\qquad s=1,2,\ldots,m.
\end{gather*}

\section{Eigenvectors and eigenvalues}

In order to give explicit formulas for the eigenvectors of
$A_n(\lambda)$ we remind the def\/inition (see for example
\cite{BB}) of $w_p(s)$ which is an analogue of $\Gamma_q$-function
at root of unity. For any point $p=(x,y)$ of Fermat curve
$x^N+y^N=1$, we def\/ine $w_p(s)$, $s\in \mathbb{Z}_N$, by
\begin{gather}\label{defw}
\frac{w_p(s)}{w_p(s-1)}=\frac{y}{1-x \omega^s},\qquad w_p(0)=1.
\end{gather}
The function $w_p(s)$ is cyclic: $w_p(s+N)=w_p(s)$.

We will use the notation $|\boldsymbol{\gamma}_n\rangle \in{\cal
V}_1 \otimes\cdots\otimes{\cal V}_n$ for eigenvectors of the
operator $A_n(\lambda)$ of the BSQC with $n$ particles. These
eigenvectors are labeled by $n$ parameters $\gamma_{n,s}\in
\mathbb{Z}_N$, $s=1,2,\ldots,n$, collected into a vector
\begin{gather*}
\boldsymbol{\gamma}_n=(\gamma_{n,1},\ldots,\gamma_{n,n})\in(\mathbb{Z}_N)^n.
\end{gather*}

The following theorem gives a procedure of obtaining the
eigenvectors $|\boldsymbol{\gamma}_n\rangle$ of $A_n(\lambda)$
from the eigenvectors $|\boldsymbol{\gamma}_{n-1}\rangle\in{\cal
V}_1 \otimes\cdots\otimes{\cal V}_{n-1}$ of $A_{n-1}(\lambda)$ and
basis vectors $|\gamma_n\rangle_n\in{\cal V}_{n}$. To f\/ind the
formula for $|\boldsymbol{\gamma}_{n-1}\rangle$ we can use the
same theorem and so on. At the last step we need the eigenvectors
of $1$-particle quantum chain.

From (\ref{bazh_strog}) and (\ref{mm}), it is easy to see that  the vectors
$|{\gamma_{1,1}}\rangle_1\in {\cal V}_1$, $\gamma_{1,1}\in
\mathbb{Z}_N$, are eigenvectors for $A_1(\lambda)$:
\[
A_1(\lambda) |{\gamma_{1,1}}\rangle_1 =
(1+\varkappa_{1,1}\omega^{\gamma_{1,1}})\,
|{\gamma_{1,1}}\rangle_1,
\]
where $\varkappa_{1,1}=\varkappa_1$.

In what follows, the vector $\boldsymbol{\gamma}_n^{\pm k}$ means
the vector $\boldsymbol{\gamma}_n$ in which $\gamma_{n,k}$ is
replaced by $\gamma_{n,k}\pm 1$.

\begin{theorem}
The vector
$|\boldsymbol{\gamma}_n\rangle=|\gamma_{n1},\ldots,\gamma_{nn}\rangle$
\begin{gather}\label{formvect}
|\boldsymbol{\gamma}_n\rangle=\sum_{\boldsymbol{\gamma}_{n-1}\in
(\mathbb{Z}_N)^{n-1}}
 Q(\boldsymbol{\gamma}_{n-1}|\boldsymbol{\gamma}_{n}) |\boldsymbol{\gamma}_{n-1}\rangle\otimes
|\sigma_n\rangle_n
\end{gather}
satisfies
\begin{gather}\label{Alm}
A_n(\lambda)|\boldsymbol{\gamma}_n\rangle
=\prod_{k=1}^n\left(1+\varkappa_{n,k}\omega^{\gamma_{n,k}}\lambda\right)
|\boldsymbol{\gamma}_n\rangle
=\prod_{k=1}^n\left(1-\lambda/\lambda_{n,k}\right)
|\boldsymbol{\gamma}_n\rangle,
\\
\label{Blmk}
B_n\left(\lambda_{n,k}\right)|\boldsymbol{\gamma}_n\rangle=
\frac{a_n \lambda_{n,k}}{ y_n}
\big(1-x_{n,k}\omega^{-\gamma_{n,k}-1}\big)\big(1-\tilde x_{n,k}
\omega^{\gamma_{n,k}}\big) \left(\prod_{s=1}^{n-1}
y^{n-1,s}_{n,k}\right)|\boldsymbol{\gamma}_n^{+k}\rangle,
\\
B_n(\lambda)|\boldsymbol{\gamma}_n\rangle=\lambda\frac{a_n}{ y_n}
\sum_{k=1}^n\left(\prod_{s\ne k}
\frac{\lambda-\lambda_{n,s}}{\lambda_{n,k}-\lambda_{n,s}}\right)\nonumber\\
\label{Blm}
\phantom{B_n(\lambda)|\boldsymbol{\gamma}_n\rangle=}{}\times
\big(1-x_{n,k}\omega^{-\gamma_{n,k}-1}\big)\big(1-\tilde x_{n,k}
\omega^{\gamma_{n,k}}\big) \left(\prod_{l=1}^{n-1}
y^{n-1,l}_{n,k}\right)|\boldsymbol{\gamma}_n^{+k}\rangle,\qquad
n>1,
\\
\label{Blm1} B_1(\lambda)|\boldsymbol{\gamma}_1\rangle=\lambda
a_1\big(1-\tilde x_{1,1} \omega^{\gamma_{1,1}}\big)
 |\boldsymbol{\gamma}_1^{+1}\rangle,
\end{gather}
if
$|\boldsymbol{\gamma}_{n-1}\rangle=|\gamma_{n-1,1},\ldots,\gamma_{n-1,n-1}\rangle\in{\cal
V}_1 \otimes\cdots\otimes{\cal V}_{n-1}$ satisfies the same
relations with $n$ replaced by $n-1$. In the above formulas we
used
\begin{gather}
Q(\boldsymbol{\gamma}_{n-1}|\boldsymbol{\gamma}_{n})=\frac{\omega^{\gamma_{n-1,1}+\cdots+\gamma_{n-1,n-1}}
\prod\limits_{l=1}^{n-1} \prod\limits_{k=1}^n
w_{p^{n-1,l}_{n,k}}(\gamma_{n-1,l}-\gamma_{n,k})}
{w_{p_n}(-\sigma_n-1) \prod\limits_{j,l=1\atop (j\ne l)}^{n-1}
w_{p^{n-1,j}_{n-1,l}}(\gamma_{n-1,j}-\gamma_{n-1,l})}\cdot
\frac{\prod\limits_{l=1}^{n-1} w_{p_{n-1,l}}(-\gamma_{n-1,l}-1)}
{\prod\limits_{l=1}^{n-1} w_{\tilde p_{n-1,l}}(\gamma_{n-1,l}-1)},
\nonumber\\
Q(\boldsymbol{\gamma}_1|\boldsymbol{\gamma}_2)=\frac{\omega^{\gamma_{1,1}}
w_{p^{1,1}_{2,1}}(\gamma_{1,1}-\gamma_{2,1})w_{p^{1,1}_{2,2}}(\gamma_{1,1}-\gamma_{2,2})
} {w_{p_2}(\gamma_{1,1}-\gamma_{2,1}-\gamma_{2,2}-1) w_{\tilde
p_{1,1}}(\gamma_{1,1}-1)},
\nonumber\\
\lambda_{m,s}=-\omega^{-\gamma_{m,s}}/\varkappa_{m,s}, \qquad
\sigma_n(\boldsymbol{\gamma}_{n-1}, \boldsymbol{\gamma}_n)\equiv
\sigma_n=\sum_{k=1}^n \gamma_{n,k} - \sum_{l=1}^{n-1}
\gamma_{n-1,l}. \label{exprQ}
\end{gather}
\end{theorem}

\begin{proof}
We suppose that the formulas (\ref{Alm}) and (\ref{Blm}) with $n$
replaced by $n-1$ are proved. To prove the action formulas
(\ref{Alm}) and (\ref{Blm}) we use the recurrent relations
\begin{gather}\label{recA}
A_n(\lambda)=A_{n-1}(\lambda)\left(1+\lambda \varkappa_n
{\boldsymbol v}_n\right) +B_{n-1}(\lambda)\,{\boldsymbol u}_n
(c_n- d_n{\boldsymbol v}_n),
\\
\label{recB} B_n(\lambda)=A_{n-1}(\lambda)\,\lambda{\boldsymbol
u}_n^{-1}(a_n-b_n {\boldsymbol v}_n) +B_{n-1}(\lambda)
\left(\lambda a_n c_n+\frac {b_n d_n}{\varkappa_n} {\boldsymbol
v}_n\right)
\end{gather}
which follow from (\ref{mm}).

{\it The action formula for $A_n(\lambda)$}: To prove the action
formula (\ref{Alm}) we act by both sides of~(\ref{recA})
on~(\ref{formvect}) and use the formulas (\ref{Alm}) and
(\ref{Blm}) with $n$ replaced by $n-1$. After shifting in an
appropriate way the variables of summation
$\boldsymbol{\gamma}_{n-1}$ we reduce the problem to
verif\/ication of relation
\begin{gather}
\left( \prod_{k=1}^n\left(1-\lambda/\lambda_{n,k}\right)-
\prod_{l=1}^{n-1}\left(1-\lambda/\lambda_{n-1,l}\right) (1+\lambda
\varkappa_n \omega^{\sigma_n})
\right)Q(\boldsymbol{\gamma}_{n-1}|\boldsymbol{\gamma}_{n})\nonumber\\
\qquad{}=\lambda \frac{a_{n-1}}{ y_{n-1}}
\sum_{l=1}^{n-1}\left(\prod_{s=1\atop s\ne l}^{n-1}
\frac{\lambda-\lambda_{n-1,s}}
{\omega\lambda_{n-1,l}-\lambda_{n-1,s}}\right)
\big(1-x_{n-1,l}\omega^{-\gamma_{n-1,l}}\big)\big(1-\tilde x_{n-1,l} \omega^{\gamma_{n-1,l}-1}\big)\nonumber\\
\qquad\quad{}\times \left(\prod_{s=1}^{n-2}
y^{n-2,s}_{n-1,l}\right) \big(c_n-d_n \omega^{\sigma_n+1}\big)
Q(\boldsymbol{\gamma}_{n-1}^{-l}|\boldsymbol{\gamma}_{n}).\label{idQ}
\end{gather}
Using
\begin{gather*}
\frac{Q(\boldsymbol{\gamma}_{n-1}^{-l}|\boldsymbol{\gamma}_{n})}{Q(\boldsymbol{\gamma}_{n-1}|\boldsymbol{\gamma}_{n})}
\frac{a_{n-1}}{ y_{n-1}}
(1-x_{n-1,l}\omega^{-\gamma_{n-1,l}})(1-\tilde x_{n-1,l}
\omega^{\gamma_{n-1,l}-1})
\left(\prod_{s=1}^{n-2} y^{n-2,s}_{n-1,l}\right)\nonumber\\
\qquad{}{} =\frac{\varkappa_n}{\omega d_n}
\frac{\prod\limits_{k=1}^{n}\left(1-\frac{\lambda_{n,k}}{\lambda_{n-1,l}}\right)}
{1-x_n\omega^{-\sigma_n-1}} \prod_{s\ne
l}\frac{1-\omega\frac{\lambda_{n-1,l}}{\lambda_{n-1,s}}}
{1-\frac{\lambda_{n-1,s}}{\lambda_{n-1,l}}
\end{gather*}
which follows directly from (\ref{exprQ}) and (\ref{rel_other}),
we rewrite (\ref{idQ}) as
\begin{gather*}
\prod_{k=1}^n\left(1-\lambda/\lambda_{n,k}\right)-
\prod_{l=1}^{n-1}\left(1-\lambda/\lambda_{n-1,l}\right) (1+\lambda
\varkappa_n \omega^{\sigma_n})
\\
\qquad{}=\lambda \sum_{l=1}^{n-1}\left(\prod_{s=1\atop s\ne
l}^{n-1} \frac{\lambda-\lambda_{n-1,s}}
{\lambda_{n-1,l}-\lambda_{n-1,s}}\right) \frac{-\varkappa_n
\omega^{\sigma_n}}{\lambda_{n-1,l}} \frac{\prod\limits_{k=1}^n
\lambda_{n,k}}{\prod\limits_{s=1}^{n-1} \lambda_{n-1,s}}
\prod_{k=1}^n\left(1-\lambda_{n-1,l}/\lambda_{n,k}\right) .
\end{gather*}
Taking into account
\begin{gather}\label{kpnkpn-1}
-\varkappa_n \omega^{\sigma_n} \frac{\prod\limits_{k=1}^n
\lambda_{n,k}}{\prod\limits_{s=1}^{n-1} \lambda_{n-1,s}}=1,
\end{gather}
which follows from (\ref{rel_m}), we obtain f\/inally
\begin{gather*}
\prod_{k=1}^n\left(1-\lambda/\lambda_{n,k}\right)-
\prod_{l=1}^{n-1}\left(1-\lambda/\lambda_{n-1,l}\right) (1+\lambda
\varkappa_n \omega^{\sigma_n})
\\
\qquad{}=\lambda \sum_{l=1}^{n-1}\left(\prod_{s=1\atop s\ne
l}^{n-1} \frac{\lambda-\lambda_{n-1,s}}
{\lambda_{n-1,l}-\lambda_{n-1,s}}\right) \frac{1}{\lambda_{n-1,l}}
\prod_{k=1}^n\left(1-\lambda_{n-1,l}/\lambda_{n,k}\right) .
\end{gather*}
To verify this equality  we note that both sides are polynomials
in $\lambda$ of degree $n-1$ (not $n$ due to~(\ref{kpnkpn-1}))
without free term. Therefore it is suf\/f\/icient to verify this
relation at $n-1$ dif\/ferent values of $\lambda$. Taking these
values to be $\lambda=\lambda_{n-1,l}$, $l=1,2,\ldots,n-1$, we
easily prove the relation. Thus we proved (\ref{Alm}).

{\it The action formula for $B_n(\lambda_{n,k})$}: Next we show
the validity of (\ref{Blmk}). The action formulas
for~$B_1(\lambda)$ and $B_2(\lambda)$ can be verif\/ied in a
direct way. Thus we suppose $n>2$.

Excluding $B_{n-1}(\lambda)$ from (\ref{recA}) and substituting it
into (\ref{recB}) we get
\begin{gather}
{\boldsymbol u}_n (c_n- d_n{\boldsymbol v}_n) B_n(\lambda)=
\left(\lambda a_n c_n+\omega \frac {b_n d_n}{\varkappa_n}
{\boldsymbol v}_n\right)A_n(\lambda)
\nonumber\\
\qquad{} -\omega \lambda a_n d_n {\boldsymbol v}_n \left(1+
\frac{\lambda c_n \varkappa_n}{\omega d_n}\right)
\left(1+\frac{b_n}{\lambda
a_n\varkappa_n}\right)A_{n-1}(\lambda).\label{recAB}
\end{gather}

Let us apply (\ref{recAB}) to $|\boldsymbol{\gamma}_n\rangle$ for
$\lambda=\lambda_{n,k}=-\omega^{-\gamma_{n,k}}/\varkappa_{n,k}$,
i.e.\ at the zeros of eigenvalue of~$A_n(\lambda)$. This gives, by
virtue of the def\/initions (\ref{xxx}) of $x_{m,s}$ and $\tilde
x_{m,s}$:
\begin{gather}
{\boldsymbol u}_n (c_n- d_n{\boldsymbol v}_n) B_n(\lambda_{n,k})
|\boldsymbol{\gamma}_n\rangle= -\lambda_{n,k} \omega a_n d_n
\big(1-x_{n,k}\omega^{-\gamma_{n,k}-1}\big)
\big(1-\tilde x_{n,k} \omega^{\gamma_{n,k}}\big)\nonumber\\
\qquad{}{}\times  \sum_{\boldsymbol{\gamma}_{n-1}\in
(\mathbb{Z}_N)^{n-1}}\!\!\omega^{\sigma_n}
 Q(\boldsymbol{\gamma}_{n-1}|\boldsymbol{\gamma}_n) A_{n-1}(\lambda_{n,k})
 |\boldsymbol{\gamma}_{n-1}\rangle\otimes |\sigma_n\rangle. \label{ABm}
\end{gather}

From (\ref{Alm}) we know how to apply
$A_{n-1}$ to $|\boldsymbol{\gamma}_{n-1}\rangle$:
\begin{gather}\label{Almnk}
A_{n-1}(\lambda_{n,k})|\boldsymbol{\gamma}_{n-1}\rangle =
 \prod_{s=1}^{n-1}\left(1-\frac{\varkappa_{n-1,s}}{\varkappa_{n,k}}\omega^{\gamma_{n,k}-\gamma_{n-1,s}}\right)
 |\boldsymbol{\gamma}_{n-1}\rangle.
\end{gather}
Using (\ref{uvact}) we f\/ind the action of the inverse of the
operator ${\boldsymbol u}_n (c_n-d_n {\boldsymbol v}_n)$ on
$|\sigma_n\rangle_n$\,:
\begin{gather}\label{invop}
({\boldsymbol u}_n (c_n-d_n {\boldsymbol v}_n))^{-1}
|\sigma_n\rangle_n= \big(c_n-d_n \omega^{\sigma _n+1}\big)^{-1}
|\sigma_n+1\rangle_n.
\end{gather}
Taking into account (\ref{exprQ}) and (\ref{defw}) we get
\begin{gather}\label{QQ}
 Q(\boldsymbol{\gamma}_{n-1}|\boldsymbol{\gamma}_n)
 \frac{\omega^{\sigma_n}\prod\limits_{s=1}^{n-1}
 \left(1-\frac{\varkappa_{n-1,s}}{\varkappa_{n,k}}\omega^{\gamma_{n,k}-\gamma_{n-1,s}}\right)}
 {c_n-d_n \omega^{\sigma_n+1}}=
 -\omega^{-1}\,Q(\boldsymbol{\gamma}_{n-1}|\boldsymbol{\gamma}_n^{+k})
 \frac{\prod\limits_{s=1}^{n-1} y^{n-1,s}_{n,k}}{d_n y_n}.
\end{gather}
Finally, using (\ref{Almnk}), (\ref{invop}) and (\ref{QQ}), we
reduce (\ref{ABm}) to (\ref{Blmk}).

{\it The action formula for $B_n(\lambda)$}:
From (\ref{bazh_strog}) and (\ref{mm}) it is easy to f\/ind that
the operator $B_n(\lambda)/\lambda$ is a polynomial in $\lambda$
of $(n-1)$th order. Due to (\ref{Blmk}) we know the action
formulas for $B_n(\lambda)/\lambda$ at the $n$ particular values
of $\lambda$: $\lambda=\lambda_{n,k}$, $k=1,$ $2,\ldots,n$. This
data is enough to reconstruct the action of the polynomial
$B_n(\lambda)$ on $|\boldsymbol{\gamma}_n\rangle$ uniquely.
Lagrange interpolation formula gives
\[
\frac{B_n(\lambda)}{\lambda}|\boldsymbol{\gamma}_n\rangle=\sum_{k=1}^n\left(\prod_{l\ne
k}
\frac{\lambda-\lambda_{n,l}}{\lambda_{n,k}-\lambda_{n,l}}\right)
\frac{B_n(\lambda_{n,k})}{\lambda_{n,k}}|\boldsymbol{\gamma}_n\rangle.
\]
Finally using (\ref{Blmk}) we get (\ref{Blm}). This completes the
proof of the Theorem.
\end{proof}

\section{Discussion}
In this contribution we applied the iterative procedure
of obtaining the eigenvectors for quantum integrable systems
by Kharchev and Lebedev~\cite{KhL}
(which has origin in~\cite{Skl} by Sklyanin)
to open Bazhanov--Stroganov quantum chain.
We plan to extend this result (along the line of the paper~\cite{IS})
to the case of Bazhanov--Stroganov chain with
integrable boundary interaction.

\subsection*{Acknowledgements}

The author would like to acknowledge the organizers of the Sixth
International Conference ``Symmetry in Nonlinear Mathematical
Physics'' (June 20--26, Kyiv) for their nice conference. The
present paper is the written version of the talk delivered by the
author at this conference. The author is thankful to
Professors G.~von~Gehlen, S.~Pakuliak and V.~Shadura for
collaboration in obtaining the results presented in this
contribution. The research presented here is partially supported
by INTAS (grant No.03-51-3350) and by the French--Ukrainian
project ``Dnipro''.

redpajama_set_name: RedPajamaArXiv


text:
Florence Mayor visits the sites of the HOPE project
On a visit to the Empoli area, Metropolitan Mayor Dario Nardella made a stop in Empoli together with Mayor Brenda Barnini, deputy mayor of the Metropolitan City of Florence.
Nardella made a tour inside the most important public building sites currently underway: buildings in Empoli's historic centre that are undergoing structural redevelopment.
Together with Brenda Barnini, he visited the most evocative spaces of the old 'San Giuseppe' hospital, which, as part of the HOPE project financed by the Region of Tuscany and the European Union, will see the requalification and consolidation of the structures that will become a reference point for services and for citizens passing through the city's historic centre.
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"I sincerely thank Dario Nardella for his visit", said Brenda Barnini Mayor of Empoli. "Empoli has been on the road to urban regeneration for some years now, thanks to an important capacity for planning and intercepting European funds. This capacity will serve us and is serving us very well also to take advantage of the opportunities linked to the National Recovery Plan and the future programming season of European funds. Being an integral part of the Metropolitan City of Florence and therefore having strategic planning tools for the whole area and clear objectives for our city is certainly an advantage that we intend to strengthen and exploit more and more."
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To EUREka! #4
EURE in a three-fold paper
The journey looks long to the final improvement of the 8 policy instruments, but the EURE team is ready to tackle the challenge. Take a look!
Download EURE leaflet
Let's sum up!
Take a look at the 8 summaries of the fourth semester in the 8 regional languages of EURE.
Tweets by EURE

redpajama_set_name: RedPajamaCommonCrawl


Condemned nation Wick Check Pant in Grey. Sophisticated fashion styling with a look that would not be out of place on the golf course thanks to a custom print fabric. Elasticated waist, tapered fit and pockets to side complete.
Fabric: This product is 84% Polyester, 14% Viscose and 2% Elastane.


text:
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 ********************************************************************************
 *     Licensed under MIT License. Read the file LICENSE for more information   *
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redpajama_set_name: RedPajamaGithub


text:
MLB owners lock out players, 1st work stoppage…
Pablo Martinez Monsivais, Associated Press file
FILE – Then-Chicago Cubs' Javier Baez sports an MLB logo tattoo and logos on his hat and jersey as he waits to take batting practice before Game 2 of baseball's National League Division Series against the Washington Nationals at Nationals Park, Saturday, Oct. 7, 2017, in Washington. The clock ticked down toward the expiration of Major League Baseball's collective bargaining agreement at 11:59 p.m. EST Wednesday night, Dec. 1, 2021, and what was likely to be a management lockout ending the sport's labor peace at over 26 1/2 years. (AP Photo/Pablo Martinez Monsivais, File)
By Ronald Blum and Stephen Hawkins | The Associated Press
PUBLISHED: December 1, 2021 at 11:40 p.m. | UPDATED: December 1, 2021 at 11:45 p.m.
The strategy, management's equivalent of a strike under federal labor law, ended the sport's labor peace after 9,740 days over 26 1/2 years.
"We believe that an offseason lockout is the best mechanism to protect the 2022 season," baseball Commissioner Rob Manfred wrote in a letter to fans. "We hope that the lockout will jumpstart the negotiations and get us to an agreement that will allow the season to start on time. This defensive lockout was necessary because the players' association's vision for Major League Baseball would threaten the ability of most teams to be competitive."
"This drastic and unnecessary measure will not affect the players' resolve to reach a fair contract," union head Tony Clark said in a statement. "We remain committed to negotiating a new collective bargaining agreement that enhances competition, improves the product for our fans, and advances the rights and benefits of our membership."
The lockout's immediate impacts were a memo from MLB to clubs freezing signings, the cancellation of next week's annual winter meetings in Orlando, Florida, and banishing players from team workout facilities and weight rooms while perhaps chilling ticket sales for 2022.
Grading the Week: Colorado Rockies have the answer to their recent woes — more Monfort
Rockies-D-Backs schedule exhibitions unlikely due to lockout
MLB labor talks to resume after 42-day break, AP source says
Sterling Monfort, son of the Rockies' owner, now leads pro scouting department
Yankees' Rachel Balkovec to be first female MiLB manager, AP sources say
"We offered to establish a minimum payroll for all clubs to meet for the first time in baseball history; to allow the majority of players to reach free agency earlier through an age-based system that would eliminate any claims of service time manipulation; and to increase compensation for all young players," Manfred wrote. "When negotiations lacked momentum, we tried to create some by offering to accept the universal designated hitter, to create a new draft system using a lottery similar to other leagues."
A union statement claimed the lockout "was specifically calculated to pressure players into relinquishing rights and benefits, and abandoning good-faith bargaining proposals that will benefit not just players, but the game and industry as a whole. … We have been here before, and players have risen to the occassion time and again — guided by a solidarity that has been forged over generations."
Manfred succeeded Bud Selig as commissioner in 2015 following a quarter-century as an MLB labor negotiator. He was unusually critical publicly of the union's stance.
More in MLB
📬 Rockies Mailbag: What is the future of Connor Joe and the Rox outfield?


text:
Rheinsberg (Mark) station is a railway station in the town of Rheinsberg (Mark), located in the Ostprignitz-Ruppin district in Brandenburg, Germany.

References

Railway stations in Brandenburg
Buildings and structures in Ostprignitz-Ruppin
Railway stations in Germany opened in 1899
1899 establishments in Prussia

redpajama_set_name: RedPajamaWikipedia


NVIDIA GeForce 8400 SE is a Display Adapters hardware device. This Windows driver was developed by NVIDIA. In order to make sure you are downloading the exact right driver the hardware id is PCI/VEN_10DE&DEV_0420.
Download the driver setup file for NVIDIA NVIDIA GeForce 8400 SE driver from the location below. This download link is for the driver version 9.18.13.0908 released on 2015-01-30.
This driver was installed by many users and received an average rating of 4.5 stars out of 42602 votes.
Take a look at the list of available driver updates. Scroll the list down until you locate the NVIDIA NVIDIA GeForce 8400 SE driver. Click on Update.


In June of 1560, Imagawa Yoshimoto assembled a large army with a dream of rising above a local daimyo to become shogunate of all Japan. All that stood in his path to Kyoto, Japan's capital city, was an old rival, Oda Nobunaga. Yoshimoto's first objective on the march was to secure the Oda controlled border forts. He ordered Motoyasu to attack Marune and after a sharp attack against the fort, Motoyasu retired to a prepared position. The fort's garrison unwisely pursued the retiring forces and Motoyasu sprung his trap and the garrison force was destroyed and the fort captured.


text:
The FTC's Apex Building
The FTC Joins Huawei on a Misguided Troll Hunt
Qualcomm, the American company whose technology turned cellphones into smartphones, can't seem to get any respect lately. The chip designer was hauled in for trial this month in a suit the Federal Trade Commission filed in the final days of the Obama administration. The FTC claims Qualcomm violates antitrust laws by overcharging phone makers for using its patented technology like 4G in smartphones. The lawsuit threatens to weaken the patents that have secured the key innovations of the modern tech age.
The FTC's star witness in the first days of trial was Huawei, the Chinese telecommunications giant the Trump administration has called out for stealing intellectual property from American companies. Last month, at America's request, Canada arrested a Huawei executive, escalating the trade war resulting from the U.S. challenge to China's intellectual-property theft. Apparently, the FTC missed the irony of having Huawei testify about how a leading U.S. tech innovator is allegedly violating antitrust laws in licensing its patents to Huawei.
The FTC is blinded by a panic about "patent trolls" that has run rampant in Washington for the past decade. Like the fabled troll under the bridge, the story is that patent owners hold up companies from manufacturing new products or services by demanding a toll—a license to use their patents. The moral of the story is that these patent owners are somehow killing innovation by demanding extortionate royalties from companies that must use their technology in making and selling products like smartphones.
Read the full article in the Wall Street Journal
To Compete With China in 5G, America Must Solve Its Spectrum Problem
Arthur Herman
The next generation of wireless network, 5G, has arrived and is being rolled out around the world, including in communities across the United States. ...
Risking Apocalypse? Quantum Computers and the US Power Grid
Arthur Herman & Alexander Butler
Millions without power; stores and banks shut down; vital services running on emergency generators, if at all; lines of hapless people awaiting food a...


Explore options to get on track to an in-demand career in healthcare during ACC's Health Sciences open house. Training programs are available in areas such as dental hygiene, radiology, sonography, surgical technology, nursing, and more!
Learn more about the department and degree programs!
Registration not required to attend, but encouraged.


text:
Radioactive Girl Scout
By Sarah Knudtson October 30, 2013 Arts & Culture
What do we really know about the ground we walk on?
Illustration by Jordan Whitney Martin
When I was a kid, I was a full fledged, sash-wearing, cookie-selling Girl Scout. For two weeks of every summer and countless weekends, I spent time at Camp Welaka, a small site located on the outskirts of the larger Jonathan Dickinson State Park in Hobe Sound, Florida. The camp consisted of army surplus tents mounted on raised platforms to protect us from the seasonal flooding on a sandy terrain speckled with pine trees and palmetto bushes made humid by the Loxahatchee River snaking through the grounds. Each summer spiders and mosquitoes feast on hapless campers only to be killed en masse as trucks spraying pesticides drive along the dirt roads of the camp. One summer my girl scout best friend and I noticed strange red lights emanating from across the park. We devised fantastical stories to explain the glow in the night sky, stories of Red Martians and the invasion of the rival Boy Scout's Camp Tanah Keeta. As the years passed, the red glow became accepted, and like the trucks of pesticide, was not discussed.
C + -Au
Graphite, Distemper and Gold Pencil on Paper, 2013
Sarah Knudtson //photos courtesy of the artist
Flash forward a decade or so, to my stint as a K-12 drawing teacher. I was reassuring a young pupil that she would not get lead poisoning from the shiny grey smears on her hands, and had the realization that although I knew that pencils were graphite and not lead, I didn't actually know their history. I looked into it. The process started benignly enough, with a history that involved shepherds marking their sheep and graphite's amazing properties as a cannonball lubricant. From there I began to make drawings that toyed with these histories. Following the trail from artistic to industrial uses, I started playing with its conductivity. This resulted in drawings that, with the help of electric currents, lit up LEDs. Wanting to explore this material further, I stumbled across an article that mentioned graphite was used in nuclear reactors. I do not pretend to understand nuclear fission, or for that matter life in general, but I do know that the very first reactor ever built used 771,000 pounds of graphite, which equates to a shit ton of drawings by third graders. This discovery was congruent with my arrival in Chicago, the home of that very heavy first reactor, known the world over as Chicago Pile One, CP1 to it's friends. It was built in a squash court under the football field at the University of Chicago in 1942, but by 1943 the reactor moved to it's current location in Red Gate Woods.
Plot M
Infrared Stereoscopic Digital Photograph, 2013
Part of the Cook County Forest Preserve, Red Gate is located just outside of the city. Marked by two monuments reminiscent of gravestones are Plot M, the first nuclear waste pile, and Site A, commemorating the burial site of the reactor. I was intrigued that these sites, visible scars on the landscape, are located within a nature preserve. Researching Red Gate Woods led me to look into the history of other parks and preserves. What I discovered was that many parks also share histories complicated by government regulations that seesaw between masking and exposing the manufacturing refuse of the past.
While digging through Chicago's industrial burial grounds, I recalled those lights that in my youth I had attributed to boy-scout-abducting aliens. Prior to being a Florida State Park, the Jonathan Dickinson grounds had been Camp Murphy, a World War II training ground for the then highly classified radar system. In its heyday the site was made up of one thousand buildings, including a bowling alley. Remnants of those buildings can still be seen on the landscape. It turns out that in the mid 80s the state of Florida sold a parcel of land back to the federal government to build the Jonathan Dickinson Missile Tracking Annex. Atop a large microwave tower protruding from the northern section of the park was the source of the lights that had appeared that summer.
Even though I cannot visit these sites in person, I have developed a way of exploring them visually. Delving into materials made available by the Freedom of Information Act to question the shift that occurs when a place goes from restricted to public access, I create physical remnants of the unseen. In hand-drawn, layered photographic maps I ask, "What do we really know about the ground we walk on?"
Arts & Culture, F Words, Personal Essay, Prose and Poetry
Arts & Culture Radioactive Girl Scout
By Sarah Knudtson
You Can Take the Man Out of the Culture,...
Posthumous Aesthetics
MBS And Friends
'I Was Raised on the Internet' at MCA...
Palestine Roots
127 Hours: CHICAGO


The Pediatric AIDS Chicago Prevention Initiative (PACPI) Perinatal Enhanced Case Manager (PECM) provides client-centered counseling for adolescents, women, and children. This PECM must have a good understanding and background in maternal child health, substance abuse care and treatment, HIV care systems, homelessness, public aid systems and the Department of Children and Family Services (DCFS). In addition, the PECM is expected to possess or develop an understanding of HIV transmission, prevention, and treatment.
PECMs are each assigned to a geographic area in Chicago that is defined by the PACPI program. The geography for this position is defined as: North: Foster to I-90/I-94, East: Lake Michigan, South: I-55, West: Cook County border. The PECM must attend AIDS Foundation of Chicago (AFC) case management trainings, PACPI meetings and Case Management team meetings. Please note that this position requires a vehicle for 80% local travel, which will be reimbursed based on documented mileage.
This position is wholly funded by contractual grant funding which is renewed under provisions set by the grantor of the contract. Employment will be contingent upon the continued receipt of these grant funds and satisfactory job performance.
Assists mothers in preventing their children from becoming a part of the DCFS system and works directly with DCFS to prevent at-risk youth from entering the system by developing relationships with community providers as well as program participants.
Provide intensive services to women and their families in low income and high risk communities in Chicago and must be available 24/7 for all PACPI clients via phone.Must carry a 24/7 Perinatal Hotline pager 2-3 times per year.
Responsible for documentation of all levels of patient and family contacts for both PACPI and AIDS Foundation Chicago (AFC).
Sensitivity to and understanding of issues concerning HIV/AIDS, teen pregnancy, domestic violence, poverty, and chronic illness required.
Detail-oriented with the ability to act as a liaison between clients and service providers required.
Functional knowledge of computers in order to enter client data into web-based reporting system required.
Attention to detail and ability to prioritize independently required.
Ability to maintain confidentiality, problem-solve, reason and communicate effectively in both verbal and written form required.
Strong ability to handle high pressure situations required.
Must have a good understanding and background in maternal child health, substance abuse care and treatment, perinatal HIV care systems, homelessness and public aid systems, and the Department of Children and Family Services (DCFS) required.
Possesses an understanding of perinatal HIV transmission, prevention and treatment required.
Comfortable with frequent communication via phone and e-mail required.
High level of proficiency with time management required.
Fluent bilingual speaking ability in English and Spanish required.Spanish reading skills at a high school or higher level preferred.
Five years of experience working as a case manager or a Bachelor's degree in social work or human service field required.
Bachelorâ™s degree in social work or human service field preferred.
Two years of experience working with children, adolescents and families required.
AFC certified case manager preferred.
Experience working with HIV/AIDS population preferred.


Rick Kenney challenges all copy editors to be prepared to take an ethical standpoint and use critical thinking to challenge and confront — even when they find themselves working solo.
Are you, as an editor, prepared to use your ethical standpoint confront, to change and to do the right thing all by yourself?
Kenney challenged copy editors to ask themselves if they are prepared to use their critical mind, to take an ethical standpoint and to use their "virtue of excellence" to challenge copy.
He said every editor must ask those questions and be prepared to act on their own. With shrinking copy desks, there often is not another person to use as a sounding board. And at one point or another, all copy editors will find themselves alone with a difficult decision to make.
Critical thinking and knowledge are the key elements to making the right decision, he said.
Kenney touched on how important it is for an editor to be knowledgeable when adding and subtracting information in a story.
Copy editors, he said, also must consider the tone of the story and avoid stereotypes when portraying people. Fairness must be part of the equation. Editors should learn to be neutral when working on stories about controversial topics, he said. Language must be consistent.
Another ethical issue is taste. For instance, copy editors should be mindful of the reader when displaying images, he said.
Kenney said that the fewer the editors there are, the less chances there are for collaboration. But with knowledge and by practicing critical thinking, being the last editor standing will not be a problem, he said.


text:
Stage 32 Next Level Webinars
How to Finance Your Short Film
Hosted by JT Mollner
On Demand Webinar -
For immediate download. Unlimited access for 1 year.
Average Rating | Read reviews
Please make sure you use the same email address as the one you use to sign in to Stage 32
apply Promo code: Your coupon will be applied after you agree to terms below.
I have read and agree to the Terms and Guidelines and the Stage 32 Script ServicesWritten Pitch guidelines and understand that failure to comply could lead to forfeiture of my written spot and/or delays in receiving a response.
Spots are limited. Please complete your payment in 5 minutes to guarantee your spot.
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Stage 32® Webinar Service Terms and Conditions
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Satisfaction Rate:
This webinar has a 100% user satisfaction rate.
Philip Nelson	Read reviews »
Webinar hosted by: JT Mollner
Director (Official Sundance Selection 'Outlaws & Angels')
JT Mollner is a feature film director with his latest film "Outlaws & Angels" becoming an official 2016 Sundance selection and released theatrically by MGM/Orion. Mollner's Writer/ Director credits include "The Red Room" (2008), "Henry John and the Little Bug" (2009), and "Sugartown" (2011); all 3 award winning shorts that played the festival circuit and have now been acquired by Shorts International for worldwide distribution -- a rarity in the world of short form cinema. JT has directed numerous commercials and music videos, most noteworthy being a spot for Lincoln MKS that aired during the Grammy Awards in 2011. In 2015, Mollner made an impact by presenting screen legend Dee Wallace (America's Mom) in the against-type role of a drug addicted, chain smoking bad girl in his 16mm short film "Flowers in December" - inspired by the gritty, "blue collar dramas" of the 1970's. His debut feature film, "Outlaws and Angels", Produced by Rosanne Korenberg (Half Nelson, Hard Candy) and Chris Ivan Cevic shoot in late 2015 and was based on his own original screenplay. It's has been described as a brutal, ultra-realistic home invasion drama set in the old west: Peckinpah's "Straw Dogs" meets "Lolita".JT is a proponent of celluloid image capture and has partnered with Kodak Motion Picture Film and Panavision on multiple projects.After winning multiple awards at Hollyshorts Film Festival, JT became a Jury member in 2012 and has remained ever since.Mollner's production company, "No Remake Pictures", is committed to injecting original, unique, and sometimes controversial stories into a market saturated with remakes and safe, formula fare. The company (an advocate of real film stock, and not digital) is a proponent of practical effects over CGI and VFX. Full Bio »
Webinar Summary
So, you want to make a short film - how do you finance it? We're bringing in Sundance director JT Mollner who launched his career making short films - all while learning how to finance them from outside sources. In this exclusive Stage 32 Next Level Webinar, JT will teach you everything you need to know to finance your short film to make your creative dream a reality!
Included - you'll receive a Pitch Deck from JT's film OUTLAWS AND ANGELS which started as a short film proof of concept, and went on to be made as a feature, being selected as an Official Selection at Sundance and selling to Orion films!
Determining Your Budget
We'll go over the various budget ranges and what to expect if you are working within that range.
How To Put a Pitch Deck Together
We'll share an actual pitch deck example and explain the process on how to put it together - what needs to go into a pitch deck? What should be kept out?
Private Investors vs. Crowdfunding
We'll share 3 detailed examples of investors you can approach that are within you reach. You'll learn how to identify them, what motivates them to want to invest and how to tailor your pitch to make them want to work with you.
We'll go over Indiegogo vs. Kickstarter and give you the pros and cons of each that I've learned. We'll go over how to make your crowdfunding campaign work from pre-campaign, launch, during the campaign and after it's complete. I'll discuss incentives that will work for your investors and your film.
Distribution and recoupment
We'll go over self distribution vs. traditional distribution and what your investors can expect, as well as responsibilities on the investor model vs. a crowdfund model.
Q&A with JT
JT Mollner
JT Mollner is a feature film director with his latest film "Outlaws & Angels" becoming an official 2016 Sundance selection and released theatrically by MGM/Orion.
Mollner's Writer/ Director credits include "The Red Room" (2008), "Henry John and the Little Bug" (2009), and "Sugartown" (2011); all 3 award winning shorts that played the festival circuit and have now been acquired by Shorts International for worldwide distribution -- a rarity in the world of short form cinema. JT has directed numerous commercials and music videos, most noteworthy being a spot for Lincoln MKS that aired during the Grammy Awards in 2011. In 2015, Mollner made an impact by presenting screen legend Dee Wallace (America's Mom) in the against-type role of a drug addicted, chain smoking bad girl in his 16mm short film "Flowers in December" - inspired by the gritty, "blue collar dramas" of the 1970's. His debut feature film, "Outlaws and Angels", Produced by Rosanne Korenberg (Half Nelson, Hard Candy) and Chris Ivan Cevic shoot in late 2015 and was based on his own original screenplay. It's has been described as a brutal, ultra-realistic home invasion drama set in the old west: Peckinpah's "Straw Dogs" meets "Lolita".
JT is a proponent of celluloid image capture and has partnered with Kodak Motion Picture Film and Panavision on multiple projects.
After winning multiple awards at Hollyshorts Film Festival, JT became a Jury member in 2012 and has remained ever since.
Mollner's production company, "No Remake Pictures", is committed to injecting original, unique, and sometimes controversial stories into a market saturated with remakes and safe, formula fare. The company (an advocate of real film stock, and not digital) is a proponent of practical effects over CGI and VFX.
Q: What is the format of a webinar?
A: Stage 32 Next Level Webinars are typically 90-minute broadcasts that take place online using a designated software program from Stage 32.
Q: Do I have to be located in a specific location?
A: No, you can participate from the comfort of your own home using your personal computer! If you attend a live online webinar, you will be able to communicate directly with your instructor during the webinar.
Q: What are the system requirements?
A: You will need to meet the following system requirements in order to run the webinar software: Windows 7 or later Mac OS X 10.9 (Mavericks) or later.
If you have Windows XP, Windows Vista and Mac OS X 10.8 (Mountain Lion): The webinar software does not support these operating systems. If you are running one of those operating systems, please upgrade now in order to be able to view a live webinar. Upgrade your Windows computer / Upgrade your Mac computer
Q: What if I cannot attend the live webinar?
A: If you attend a live online webinar, you will be able to communicate directly with your instructor during the webinar. If you cannot attend a live webinar and purchase an On-Demand webinar, you will have access to the entire recorded broadcast, including the Q&A.
Q: Will I have access to the webinar afterward to rewatch?
A: Yes! After the purchase of a live or On-Demand webinar, you will have on-demand access to the audio recording, which you can view as many times as you'd like for a whole year!
FilmmakingFinancing
If you have a generic question about Stage 32 education you can take a look at our frequently asked questions section on our help page, or feel free to contact support with any other inquiries you might have.
Reviews Average Rating: 5 out of 5
Philip Nelson Haven't had time to watch the Q&A yet, but everything leading up to that is very good. Lots of ideas I wouldn't have thought of, as well as details on how to execute those concepts, not just an overview. I would have liked to have seen the difference between the Feature and Short pitch deck, but otherwise I highly recommend this. One of the few webinars I've watched that is actually well worth the money.
John Raucci JT is a good teacher and very personable. He's very direct and presents a good foundation for raising money. I'm in the process of shooting my first short film and this webinar was very helpful.
Other education that may be of interest to you:
Avoiding Pitfalls for a 1st Time Director on a Low Indie Budget
"My film was shot under $1MM, premiered at Sundance, sold to a major distributor and had a theatrical release. I will impart the wisdom I acquired along the way." - Writer/Director JT Mollner Testimonials "I loved it!" - Romina Schwedler "It was great to hear many sides of a situation and how to make the most difficult scenarios work. Thanks!" - Sindy Jeffrey "This webinar was a GREAT way to prep me for what's ahead. I have no delusions about the tough road on which I embark, but knowing some of the pitfalls will certainly help avoid them. Thank you for taking the time to share what you've learned." -Arial Burnz
Basic Principles of Financing a Film Between $1-$3 Million
Stage 32 is honored to bring in Brad Hibbs Wyman, producer of the highly acclaimed film, Monster starring Charlize Theron in her Oscar-winning role, to teach for Next Level Education on the Basic Principles of Financing a Film Between $1MM-$3MM. Having produced over 40 films at all budget ranges (including Freeway starring Oscar-winner Reese Witherspoon and actor Steve Buscemi's directorial debut, Trees Lounge), Brad has learned all aspects of financing and the elements that are needed for a successful raise. Brad will teach the basic principles of motion picture financing for under 3 million dollar features which include: Rule #1 - "GET THE MONEY" Rule #2 - Always remember to "GET THE MONEY" Rule #3 - Never forget to always remember to "GET THE MONEY" Needless to say, the way you will learn will be fun and educational. We are excited to have the Stage 32 community learn from Brad who is such a prolific producer. A portion of Brad's proceeds will be donated to an arts charity. "Brad was great. I loved his style and how frank he was. Really appreciate his demeanor." - Robert G. "It was one of the most amazing experiences. The most entertaining and true presenter I have ever come across." - Ranadeep B. "Awesome experience - great learning opportunity and very well organized. I look forward to more." - Brien Gorham
Hollywood Resume & Cover Letter Workshop - How To Get Your Foot In The Door
Getting a job in Hollywood can seem hard...but it doesn't have to be. If you feel like every job application you send in is a shot in the dark, you may want to rethink your process. Luckily, there are many tangible strategies that can make the job search more efficient. Ultimately, the key is to find a way to stand out in the pack. And we're here to help you do just that. During this 90 minute session, you'll learn how to build a robust network, job search tactics that will get your resume into the right hands, how to craft effective resumes and cover letters, and tips to help you ace any job interview. Whether you're just starting out or are hoping to transition into a new position that will move you closer to your goals, this course is for you. We are professional resume writers, dedicated to helping Hollywood hopefuls find their dream jobs. But unlike most professional resume writers, we are not recruiters or HR executives. Instead, we have actually worked in and hired for entry-level positions across Hollywood. After conducting hundreds of interviews and weeding through even more resumes over the years, we've learned that many qualified candidates simply don't know how to pitch themselves for the Hollywood jobs they want. And, in an industry where most jobs are filled through internal referrals, it's crucial to impress not only the recruiters, but those in the actual departments that are hiring -- and we know what they're looking for because we've worked in those departments ourselves. We're excited teach you the proven networking strategies, resume and cover letter writing techniques, and and interview skills that we have used to succeed in our own careers and watched countless others use to succeed in theirs.
The Keys to a Successful Crowdfunding Campaign
Learn directly from Indiegogo Film Campaign Specialist, John T. Trigonis! Raising funds. Every filmmaker, director, screenwriter, even actors, has experienced the frustration. The introduction of crowdfunding through sites such as Kickstarter and Indiegogo has brought an incredible new opportunity to those looking to find funding for their films. However, running a successful campaign is not easy! Crowdfunding has revolutionized the way film and video projects are funded by taking the power from the corporations and putting it back into the hands of the creators. Because of this, it's not enough to run a simple, run-of-the-mill campaign on crowdfunding platforms like Indiegogo. Today, running a campaign must be an experience for the campaign owners and especially the contributors, and that's where innovation and creativity come into play, oftentimes spelling the difference between a short-lived stint in crowdfunding and a memorable communal experience. In this Stage 32 Next Level Webinar, you will learn the history of crowdfunding, how to pre-market your campaign and you will walk away with basic & advanced techniques of running a crowdfunding experience!
Masters of Craft: Terence Blanchard, Film Composer (Spike Lee, George Lucas)
For over 20 years, Spike Lee's go to composer to score and provide music for his films has been Terrence Blanchard. From Jungle Fever to 25th Hour to Inside Man to Spike's latest critically acclaimed film, BlacKkKlansman, Terrence has created memorable and essential scores. In fact, Terrence has been the lead composer and provided exquisite music for more than 50 films. And now he's here to teach you everything you need to know about how to break in and stay in, how to overcome your anxiety, how to work in full symphony with your director, how to be the best you can be and be hired again and again and so much more in this exclusive Stage 32 Masters of Craft Webcast. You will find this opportunity nowhere else!
6 Pitfalls To Avoid When Working With Tax Incentives
As the Vice President of Three Point Capital, Viviana Zarragoitia is one of the most prolific financiers who routinely lend on tax incentives, both domestically and internationally, on independent films. She is aware of the rules and regulations of tax incentives in many jurisdictions, and have spoken on numerous panels about tax credits. In this exclusive webinar, Viviana will be teaching what producers should be aware of when working with tax incentives. Although there are minor details that change within each state/country, there are some overall issues that come up in each jurisdiction that producers should be aware of when taking advantage of tax incentives for their film/TV project. These include, but are not limited to, things such as: corporate structure of the company applying for the tax incentive, making sure that costs in-state are qualified spend, working with tax incentive offices during pre-production, production and post-production, submitting final costs in a timely fashion, working with production accountants/CPAs on tracking qualified spend, working with lenders and filing tax returns to claim the incentives.
What is an "on-demand" webinar?
On-Demand Webinars are recorded versions of the original live webinars.
Live and interactive functionality discussed on the recording does not apply to On-Demand webinars. You will, however, receive all the content from the webinar and be able to access it as many times as you'd like for up to 1 year through the My Education page.


Have you noticed? Fingers are sometimes too short, fat and clumsy for picking bits of dirt, dried leaves and pebbles from plants with narrow leaf axils, rosette succulents and spiny cacti. Which is why I wouldn't be without my long-handled tweezers.
Not only is debris unsightly, it holds moisture that can rot the crown. I like to groom fleshy or delicate plants with the precise, gentle jabs of a dental hygienist to avoid bruising or scratching the leaves. In particular, those of agaves, echeverias, and aloes last years, so marred areas are truly a shame.
Watch me wield my 12-inch tweezers in my latest YouTube video, How to Weed a Spiky Succulent (2:59).
See more of my favorite tools in the "Success Secrets for Succulents" section of the completely revised and updated second edition of Designing with Succulents.
I'm launching my new book and speaking both days!
Succulent Gardens nursery, Castroville, CA. Free.
At 10:45 each day, to celebrate the release of the second edition of DESIGNING WITH SUCCULENTS, I'll give presentations on the topic of the book. Each is different; Part One is Friday, Part Two, Saturday.
Watch my Highlights of the 2016 Succulent Extravaganza (4:20).
Those long handled tweezers are great for retreiving items that drop down next to the drivers seat in your car. thanks for telling us how to use them with succulents.


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The Dead End of Human Fraternity
Timothy Flanders
If anyone asserts that this sin of Adam…is taken away either by the forces of human nature or by a remedy other than the merit of the one mediator, our Lord Jesus Christ, who has reconciled us to God in his own blood, made unto us justice, sanctification and redemption…let him be anathema; for there is no other name under heaven given to men, whereby we must be saved (Council of Trent, Session Five, Canon Three)
The fundamental truth at the heart of every single religion states: there is a problem with human existence. The word "religion" means "to bind together again." Religion is a force of natural law inclination wherein all men seek to solve the problem of human existence (cf. Summa Theologica, II-II q85 a1). Each religion defines this problem differently, and thus provides different solutions.
Christianity asserts that the problem is the sin of Adam, that is, Original Sin. This means that every person born of Adam is born into sin, and bondage to him who has "the empire of death, that is to say the devil" (Heb. 2:14). By the sin of Adam, man is born with a weakened will, darkened intellect and an inclination to sin. This is why the Council of Trent anathematizes those who say that man can be saved "by the forces of human nature" since the problem is in human nature itself.
Thus does our Savior say "Amen, amen, I say to thee, unless a man be born again of water and the Holy Ghost, he cannot enter into the kingdom of God" (Jn. 3:5). In 2000, the Congregation for the Doctrine of the Faith reiterated this, declaring that the Church "must be primarily committed to proclaiming to all people the truth definitively revealed by the Lord, and to announcing the necessity of conversion to Jesus Christ and of adherence to the Church through Baptism" (Dominus Iesus, 22). Baptism is necessary because the human condition is slavery to the Satan. Hence the Traditional Baptismal Rite excorcizes and rebukes the Devil: "But you, O Devil, depart, for the judgement of God is come."
Fraternity born of Adam—human fraternity itself—is the fraternity of death and slavery to Satan. But Jesus Christ brings the true liberty and fraternity "not such as the Freemasons absurdly imagine, but such as Jesus Christ obtained for the human race…the liberty, We mean, of sons of God, through which we may be free from slavery to Satan or to our passions, both of them most wicked masters; the fraternity whose origin is in God, the common Creator and Father of all" (Leo XIII, Humanum Genus, 34). Baptism makes a soul a child of God in Christ, thus creating true brotherhood by liberation from Satan.
This fundamental truth is combined by Christians with the fundamental virtue of charity, which impels the Church to proclaim the Gospel of Jesus Christ. This is "Good News" because it is the only solution to the problem all religions are trying in vain to solve. The proclamation of the Gospel and "the necessity of conversion to Jesus Christ and…Baptism" is the proof of Christian charity toward non-Christians. The "brotherly love from a sincere heart" (I Pet. 1:22) is the proof of charity among Christians. For true charity manifests holiness, which is liberty from Satan's rule.
This fundamental dogma of the faith must be at the heart of the message of fraternity to the world. Lamentably, it appears to be otherwise with Pope Francis's recent video message of fraternity, directed primarily toward the relationships between Christians, Jews, and Muslims. For this fraternity which is "Francis's Message" is "human fraternity," and by all appearances is nothing else than the fraternity of Adam. He says that "the source of human dignity and fraternity is in the Gospel of Jesus Christ," but then fails to preach the "necessity of baptism," but only the necessity to "come together as brothers and sisters with those who pray according to other cultures, other traditions and other beliefs." How can we have true fraternity if the sons of Adam are in bondage to Satan?
On the other hand, his message does have a similarity to the words of our Lord in the Parable of the Good Samaritan, which our Lord tells to a man who is willing to justify himself (Lk. 10:29). Herein our Lord brings to the Jewish people of his day the most hated racial and religious enemy, the Samaritan, and rebukes the unmerciful self-righteousness of the religious leaders. When we approach the message of Pope Francis with this lens, we do see a crucial truth in loving our neighbor for the sake of Christ. The conspicuous mark of the Christian is the love of enemies (Mt. 5:44), and our Lord reserves for eternal punishment those who hate their brother (Mt. 5:22). Indeed, many critics of the Holy Father would do well to heed this rebuke straight from Jesus Christ, for in their zeal for truth regarding Pope Francis they act against charity, and risk their own eternal damnation.
Rather, the form and foundation of all good works, says St. Thomas Aquinas, is "truth and charity" together (Commentary on Ephesians 4). The difficulty that is presented by Francis's Message is that it gives the appearance that true fraternity can be created by charity alone, and not also truth. Taken with his frequent condemnations of "proselytism," his message presents to the average Catholic nothing else than fraternity "as the Freemasons absurdly imagine." This presents a scandal (that is, an occasion for spiritual ruin) for the little ones—those are innocently ignorant in faith and are easily led astray. St. Thomas says that if something merely has the appearance of sin "it should always be left undone out of that love for our neighbor which binds each one to be solicitous for his neighbor's spiritual welfare" (Summa Theologica, II-II q43 a2). Moreover, our Lord reserves for severe condemnation those who scandalize the little ones (Mt. 18:6).
More than ever today, therefore, we must recover the true spirit of St. Francis of Assisi, which can show us how to act toward Jews and Muslims better than the message of "human fraternity." Against the "purely imaginary figure of the Saint conjured up by the defenders of modern error" (Pius XI, Rite Expiatis), St. Francis burned with zeal for the love of souls. "[A]rdent charity penetrated the heart of St. Francis," especially for "the poorest and most repulsive" (Leo XIII, Auspicato Concessum). Therefore St. Francis said that among the Muslims one can either emphasize truth or charity as two ways to "announce the Word of God" (Rule, XVI). Pope Francis seems to pick one and degrade the other as "proselytism." However, St. Francis, considering the sin of Adam, knew that proselytism itself is an act of charity. Therefore he boldly proclaimed before the Muslim Sultan: "I am sent by the Most High God, to show you and your people the way of salvation by announcing to you the truths of the Gospel."
Many Franciscans were inflamed with the same zeal, and were subsequently martyred by the Saracens. St. Anthony of Padua, seeing the early Franciscan martyrs, promptly joined St. Francis in the same truth and charity. Thus this great saint became "the gentlest of saints" (Unfailing Prayer to St. Anthony) but also "the hammer of heretics." St. Anthony shows up as statuary in a tomato garden holding the infant Christ and at the same time is invoked against demons—behold, truth and charity!
Finally, the true Franciscan spirit is also shown in the new martyr of charity, St. Maximilian Kolbe. He burned with zeal for the Jewish people, as the Jewish convert Marie-Alphonse Ratisbonne did, and thus sought to convert them to Jesus Christ. He did this so vehemently that Kolbe is vilified today as anti-Semitic, a charge that Jewish convert Roy Schoeman dismisses as an "unfounded libel" (Kolbe: Saint of the Immaculata, 181). When the neo-Pagan Nazis invaded Poland, Kolbe instantly became a fierce advocate to shelter the Jews, to the point of giving away his food to them at Auschwitz while he himself was starving and chronically ill (Ibid., 184). As we know, the saint finally gave up his life to be starved to death naked merely to save another man's life and won a glorious crown.
When compared to the true Franciscan spirit, the "human fraternity" preached by Pope Francis seems to be the banal humanitarianism of the United Nations, relying on "the forces of human nature" to save man who is in bondage to Satan. For those who ardently preach charity but fail to announce the "Good News" of the necessity of baptism, there is a grave omission of this fundamental aspect of human nature. The fraternity of Adam is death and Satanic slavery. Either the human fraternity "gospel" lacks the truth about the sin of Adam, or it lacks the charity to give to souls what is necessary for eternal salvation.
[Photo Credit: Vatican Media/CNA]
By Timothy Flanders
Timothy S. Flanders is the author of Introduction to the Holy Bible for Traditional Catholics and a forthcoming book on the spiritual history of culture for TAN Books. In 2019 he founded The Meaning of Catholic, a lay apostolate. He holds a degree in classical languages from Grand Valley State University and has done graduate work with the Catholic University of Ukraine. He lives in the Midwest with his wife and four children.


text:
Q: Character escaping and echo comand Having simple echo commands:
echo "\n"

and
echo "\\n"

both results in the same output
\n

Can someone please explain me in details how does bash process such a commands (char by char) and why the result is the same in both cases?

A: The short answer is that \ is not always special to bash or to echo. Double quotes preserve the literal string value of everything inside except $, `, \, and sometimes !. Outside of double quotes, \ is always special to bash: it preserves the literal string value of the following character. Inside of quotes, the backslash \ is only special when followed by one of five characters: $, `, ", \, or a newline. In the first four cases, it preserves the literal string value of the following character. To the bash version of echo, \ is never special unless the -e flag is provided.
So, in your two cases, what is happening:
echo "\n"

in this case, \ is not followed by one of the five characters mentioned, and so is treated as its literal string value.
echo "\\n"

in this case, the first \ is followed by a second \. The first escapes the second, so that it is interpreted as its literal string value. That is useless here, since it would be interpreted as its literal string value anyway, but it could be useful if you wanted to print a single backslash at the end of a line, like in:
echo "This is a single backslash:\\"

since otherwise the backslash would be interpreted by the shell as escaping ".
All of this information can be gleaned from the part of the bash man page about double quotes, found here.

A: A single \ preserves the literal string value of the character immediately after it.
So in this case:
echo "\\n"

The first \ is preserving the string literal \ that lies before the "n". If you were to type in the following...
echo "\"

...you would need to finish the command since the interpreter would not see the "\" as a string literal but would instead be waiting for user input to escape a "next" character.
However, if the \ is included inside single quotes, then no escape character is waited for as single quotes, by themselves, preserves the literal character(s) of which they enclose.
So for example: echo '\'
This would print the backslash as a string literal and not an escape character so the interpreter will not wait for the user to include a character.
This information, and much more, is included in the bash man page.

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