text:
St. Josef ist die römisch-katholische Pfarrkirche der Pfarrei Passau-Auerbach in Passau.

Die Kirche wurde von 1927 bis 1928 nach den Plänen von Michael Kurz erbaut. Sie ist ein Granitbau mit deutlicher Anlehnung an mittelalterliche Vorbilder. Der Turm ist als Chorturm ausgeführt. Am repräsentativsten brachte Kurz diesen Stil in der zur selben Zeit erbauten Pfarrkirche St. Josef in Memmingen zum Ausdruck.

Ausstattung
Die Gemälde und Fresken entstanden 1931 und stammen von Albert Burkart, mit dem Kurz auch in Memmingen zusammenarbeitete.
Das große Altarkreuz wurde 1932 durch Karl Baur geschaffen.
Die moderne Ausstattung der Kirche schuf Wolf Hirtreiter.

Orgel
Die Orgel wurde 1936 durch die Firma Becker & Hiendl errichtet und hat eine komplette pneumatische Traktur.
1996 wurde die Orgel gegen Holzwurmbefall behandelt und restauriert.
Die acht großen Pfeifen im Prospekt sind blinde Pfeifen.

Disposition:

 Koppeln: II/I, I/P, II/P
 Oktav-Koppeln: Superoktav I, Suboktav II/I, Superoktav II/I, Superoktav II, Superoktav II/P
 Spielhilfen: Freie Kombination für Register und Oktav-Koppeln,  Crescendo-Walze, Tutti, Tremolo, Ped. piano
 Register-Abschaltungen: Hand ab, P. Rankett ab, Posaune ab, II.M. Rankett ab, Trompete ab

Geläut
Das Geläut wurde 1929 bzw. 1930 von der Passauer Glockengießerei Lorenz gegossen. In der Karwoche 1942 wurden die drei schwersten Glocken abgenommen. Der damalige Pfarrer Josef Winkler ließ zu Ostern 1942 aus Protest auch die kleinste Glocke nicht läuten. Nach dem Zweiten Weltkrieg wurden die drei großen Glocken im Glockenlager Hamburg wiedergefunden und zurückgegeben. Das Geläut von St. Josef ist insofern besonders, da es als eines der wenigen zwischen den beiden Weltkriegen gegossenen Geläute bis heute besteht.

Trivia
 In der 15. Auflage des Großen Brockhaus, dem sogenannten "Weimarer Brockhaus", ist St. Josef mit Abbildung des damals noch schmucklosen Chorraumes als Beispiel für den modernen Kirchenbau zu finden.
 Die beim Bau verwendeten Ziegel stammen von der für den Bau des zur selben Zeit gebauten Kachlet-Kraftwerks eigens errichteten Ziegelbrennerei. Dabei wurden in der Granitfassade Klinkerziegel vermauert, welche zum Großteil als Ausschussware galten und somit nichts kosteten.

Weblinks

Pfarrkirche Passau Auerbach St. Josef auf der Homepage des Bistums Passau

Pfarrkirche des Bistums Passau
Josef
Erbaut in den 1920er Jahren
Bauwerk des Historismus in Bayern
Kirchengebäude des Historismus
Passau
Disposition einer Orgel
Kirchengebäude in Europa


text:
\section{Introduction}

Recently there has been great interest in studying nucleon-nucleon (NN)
interactions by using Effective Field Theory
(EFT)~\cite{Weinberg:1990rz, Weinberg:1991um}. EFT is based on the very
simple idea that the effects of short-distance physics can be simulated
by local (contact) interactions, so that a typical (nuclear) EFT-based
potential consists of a series of local interactions (delta function
potentials and their derivatives) and a long-distance part (Yukawa
potential due to one-pion exchange). EFT is valid only below a certain
scale, the cutoff, and the coupling constants of the local interactions
are determined as functions of the cutoff so that the physical
observables are independent of the cutoff. Lowering the cutoff amounts
to the ``integrating'' the short-distance fluctuations, leading to the
change of the coupling constants of the local interactions. This is
nothing but Wilsonian renormalization group (RG)
idea~\cite{Wilson:1973jj}. EFT together with the RG idea is a promising
alternative to the conventional approach based on phenomenological NN
potentials. It is a model independent, systematically improvable
approach, and is related to QCD through chiral symmetry. See
Refs.~\cite{Beane:2000fx, Bedaque:2002mn, Epelbaum:2005pn,
Machleidt:2007ms} for reviews.

One might however think that the use of the ``realistic''
potentials~\cite{Stoks:1994wp, Wiringa:1994wb, Machleidt:1995km,
Machleidt:2000ge}, which describe thousands of data with $E_{lab}\alt
350$ MeV very accurately, together with the RG idea, would be
\textit{more} effective, though such an approach is inevitably
phenomenological. The so-called $V_{\mbox{\scriptsize low k}}$ approach~\cite{Bogner:2000js,
Bogner:2001gq, Bogner:2001jn, Bogner:2002yw, Bogner:2003wn,
Nogga:2004ab} (in its original form) exactly goes along this strategy.

The $V_{\mbox{\scriptsize low k}}$ approach originally emerged as an application of the model
space reduction methods developed in shell-model
theory~\cite{Bogner:2000js}. The model space reduction methods
apparently resemble RG transformations; the effects of the higher-energy
states are taken into account as effective interactions. It has been
shown that ``realistic'' potentials evolve to a universal low-energy
potential by the model space reduction~\cite{Bogner:2001gq}. It appears
to conform to the general idea of ``universality'' in the RG theory. On
the other hand, the universal potential may be useful also in a
practical sense, because it is much smoother than the ``realistic''
potentials so that one may avoid calculating the Brueckner
G-matrix~\cite{PhysRev.100.36, PhysRev.103.1353, ProcRSoc.A238.551,
ProcRSoc.A239.267}, which is energy and nucleus dependent.

A relatively simple RG equation (RGE), which is claimed to be satisfied
by the $V_{\mbox{\scriptsize low k}}$, has been known;
\begin{equation}
 \frac{d}{d\Lambda}V_{\mbox{\scriptsize low k}}^\Lambda(k',k)
  =\frac{2}{\pi}\frac{V_{\mbox{\scriptsize low k}}^\Lambda(k',\Lambda)T^\Lambda(\Lambda, k; \Lambda^2)}
  {1-(k/\Lambda)^2},
  \label{eq:vlowk}
\end{equation}
where $\Lambda$ is the (floating) cutoff, $k$ and $k'$ are the relative
momentum of incoming and outgoing nucleons respectively, and $T$ is the
T-matrix.  The superscript $\Lambda$ indicates that the quantity is
cutoff dependent. Note that we put the superscript $\Lambda$ on the
left-on-shell T-matrix to indicate explicitly that it is, unlike the
right-on-shell T-matrix, a $\Lambda$-dependent quantity. It is important
to note that ``the RG equation lies at the heart of the
approach~\cite{Bogner:2001gq}.'' There are several model space
techniques and, according to Refs.~\cite{Bogner:2000js, Bogner:2001jn,
Bogner:2002yw, Bogner:2003wn, PhysRevC.54.684}, they all satisfy the
same RG equation. In this sense, it is considered that they are all
equivalent and the universal low-energy potential is unique. Because
this is a very nontrivial assertion, it is important to examine the
derivations of the RG equation carefully.

To our best knowledge, however, the derivations of the RG equations
presented in Ref.~\cite{Bogner:2001jn} do not seem to have been
scrutinized, though there are many applications. In this paper, we show
that each of the four derivations presented in Ref.~\cite{Bogner:2001jn}
contains a serious defect. Our arguments are not technically intricate
nor too mathematical so that those who are familiar with the derivations
can easily follow them.

We do not claim that their RGE (\ref{eq:vlowk}) is wrong; we only claim
that all the existent \textit{derivations} are either unjustified or, if
there are bound states, insufficient.  It is however shown that extra
terms arising from the existence of the bound states cancel, keeping
Eq.~(\ref{eq:vlowk}) unmodified~\cite{BFS}, if the bound state
wavefunctions in the reduced theory are required to have the same
low-momentum components as those in the original theory.

We notice that most of the numerical results given in the literature are
not derived directly from the RGE, but from one of the model-space
reduction methods such as Lee-Suzuki (LS) method~\cite{Suzuki:1980yp} or
Kuo-Lee-Ratcliff (KLR) method~\cite{NuclPhysA.176.65}. We emphasize that
numerical results obtained with these methods are not affected by the
present work. The procedure is independent of the actual form of the
RGE, and the effective interactions obtained by these methods in fact
satisfy the condition mentioned above, and hence Eq.(\ref{eq:vlowk}).

We assume that the reader is familiar with Ref.~\cite{Bogner:2001jn},
though we recapitulate the main points. We follow their notations as
closely as possible. In several places, we need to supplement their
arguments by providing the missing intermediate steps which we think
they actually took.

We start with the definition of the so-called $\hat{Q}$-box and the KLR
method in Sec.~\ref{sec:KLR}. By supplementing the intermediate steps,
we point out explicitly where they took a wrong step, invalidating their
second and third derivations. In Sec.~\ref{sec:completeness}, we show
that their completeness relation in the ``model space'' is wrong when
bound states are present, invalidating the first derivation. It is
however shown that, if the bound state wavefunctions in the reduced
theory have the same low-momentum components as those in the original
theory, the extra terms cancel each other, and the RGE is not affected
by the presence of bound states. The fourth derivation is also based on
the same completeness relation, so that it is also invalid in the
presence of bound states as we show in Sec.~\ref{sec:spectral}. Again,
the final result, Eq.~(\ref{eq:vlowk}), can be derived without change
under the same condition as in Sec.~\ref{sec:completeness}. In
Sec.~\ref{sec:summary}, we summarize our results and discuss several
related issues.

\section{$\hat{Q}$-box and the Kuo-Lee-Ratcliff method}
\label{sec:KLR}

Let us start with the ``bare'' Lippmann-Schwinger equation for the
(off-shell) T-matrix,
\begin{equation}
 T=V_{NN}+V_{NN}G_0T,
\end{equation}
where $V_{NN}$ is a ``realistic'' potential. In the partial-wave
notation, this may be written as
\begin{equation}
 T(k',k; \omega) = V_{NN}(k',k)
  +\frac{2}{\pi}\mathcal{P}\int_0^\infty
  V_{NN}(k,p)\frac{p^2 dp}{\omega-p^2}T(p,k; \omega),
\end{equation}
where, following Ref.~\cite{Bogner:2001jn}, we consider the standing
wave boundary condition, but the following arguments are largely
independent of it. (In this paper, we use units with $\hbar=c=M_N=1$.)
Physically speaking, the upper limit should be considered as a very
large cutoff $\Lambda_0$ rather than the infinity.

One would like to replace the ``bare'' Lippmann-Schwinger equation by a
cutoff one, which describes the same physics at low energies. For this
purpose, let us introduce the projection operators, $P$ and $Q$,
satisfying $P+Q=1$, $PQ=QP=0$, $P^2=P$, and $Q^2=Q$. The operator $P$,
which projects states to the low-momentum space, may be written as
\begin{equation}
 P=\frac{2}{\pi}\int_0^\Lambda |k\rangle k^2 dk \langle k|,
\end{equation}
where $|k\rangle$ stands for the plane wave in the partial-wave notation
with the normalization,
\begin{equation}
 \langle k' | k \rangle=\frac{\pi}{2}\frac{\delta(k'-k)}{k'k}.
\end{equation}

The so-called $\hat{Q}$-box may be defined as
\begin{equation}
 \hat{Q}^\Lambda(k',k;\omega)=V_{NN}(k',k)
  +\frac{2}{\pi}\mathcal{P}\int_\Lambda^\infty
  V_{NN}(k,p)\frac{p^2 dp}{\omega-p^2}\hat{Q}^\Lambda(p,k; \omega),
  \label{Qbox-VNN}
\end{equation}
which is the part of the T-matrix, all of the intermediate states of
which are in the $Q$-space. We put the superscript $\Lambda$ to indicate
that it depends on the cutoff. By using $\hat{Q}$-box, the T-matrix may
be written as
\begin{equation}
 T(k',k;\omega)=\hat{Q}^\Lambda(k',k;\omega)
  +\frac{2}{\pi}\mathcal{P}\int_0^\Lambda
  \hat{Q}^\Lambda(k',p;\omega)\frac{p^2 dp}{\omega-p^2}T(p,k; \omega).
  \label{T-Qbox}
\end{equation}
Note that $\hat{Q}$-box is energy dependent. If we restrict $k',\ k \le
\Lambda$, then $\hat{Q}$-box may be identified with the Wilsonian
effective potential $V^\Lambda_{WRG}$ satisfying
\begin{equation}
 \frac{d}{d\Lambda}V^\Lambda_{WRG}(k',k;\omega)=\frac{2}{\pi}
  \frac{V^\Lambda_{WRG}(k',\Lambda;\omega)V^\Lambda_{WRG}(\Lambda,k;\omega)}
  {1-\omega/\Lambda^2},
  \label{wilsonianRGE}
\end{equation}
considered by Birse \textit{et. al.}~\cite{Birse:1998dk}. See
Refs.~\cite{Harada:2005tw, Harada:2006cw, Harada:2007ua} for the field
theoretical formulation. See also Ref.~\cite{Nakamura:2005uw} for the
comparison of $V_{WRG}$ with $V_{\mbox{\scriptsize low k}}$.

First of all, it is important to note that for the \textit{fully
off-shell} T-matrix there is \textit{no} such energy-independent
potential $V^\Lambda$ that satisfies
\begin{equation}
 T(k',k;\omega)=V^\Lambda(k',k)
  +\frac{2}{\pi}\mathcal{P}\int_0^\Lambda
  V^\Lambda(k',p)\frac{p^2 dp}{\omega-p^2}T(p,k; \omega).
  \label{nosuchV}
\end{equation}
Actually, the $\Lambda$-independence of the (off-shell) T-matrix leads
to the RGE (\ref{wilsonianRGE}), which cannot be satisfied by an
energy-independent potential.

On the other hand, for the \textit{half-on-shell} T-matrix, there exists
an energy-independent potential $V_{\mbox{\scriptsize low k}}$,
\begin{equation}
 T(k',k;k^2)=V_{\mbox{\scriptsize low k}}^\Lambda(k',k)
  +\frac{2}{\pi}\mathcal{P}\int_0^\Lambda
  V_{\mbox{\scriptsize low k}}^\Lambda(k',p)\frac{p^2 dp}{k^2-p^2}T(p,k; k^2).
  \label{T-Vlk}
\end{equation}
This may serve as the definition of $V_{\mbox{\scriptsize low k}}$.

A concrete procedure of constructing such a potential is given by the
KLR folded diagram theory~\cite{NuclPhysA.176.65}. Starting with
Eq.~(\ref{T-Qbox}) with $\omega=k^2$, we have
\begin{equation}
 T(k',k;k^2)=\hat{Q}^\Lambda(k',k;k^2)
  +\frac{2}{\pi}\mathcal{P}\int_0^\Lambda
  \hat{Q}^\Lambda(k',p;k^2)\frac{p^2 dp}{k^2-p^2}T(p,k; k^2),
\end{equation}
which should be compared with Eq.~(\ref{T-Vlk}). Although
$\hat{Q}^\Lambda(k',k; k^2)$ almost satisfies Eq.~(\ref{T-Vlk}) for
$V_{\mbox{\scriptsize low k}}^\Lambda$, $\hat{Q}^\Lambda(k',p;k^2)$ in the integrand depends on
three variables. We therefore write
\begin{equation}
 V_{\mbox{\scriptsize low k}}^\Lambda(k',k)=\hat{Q}^\Lambda(k',k; k^2)
  + \sum_{i=2}^\infty \Delta V^{(i)}(k',k),
\end{equation}
where $\Delta V^{(i)}$ is the correction term coming from the folded
diagrams and is of order of the $i$-th power of $\hat{Q}$.

Substituting it into Eq.~(\ref{T-Vlk}) and comparing with
Eq.~(\ref{T-Qbox}), we have
\begin{align}
 \sum_{i=2}^\infty \Delta V^{(i)}(k',k)
  \!=\!
 &\int_p \frac{\Delta
  Q^\Lambda_{(k)}(k',p)}{k^2-p^2}\hat{Q}^\Lambda(p,k)
  +\int_p\int_{p'}
  \frac{\Delta Q^\Lambda_{(k)}(k',p')\Delta Q^\Lambda_{(k)}(p',p)}
  {(k^2-p^2)(k^2-{p'}^2)}T(p,k;k^2)
 \nonumber \\
 &+\!\int_p\int_{p'}
 \frac{\Delta Q^\Lambda_{(k)}(k',p')\hat{Q}^\Lambda(p',p;p^2)}
  {(k^2-p^2)(k^2-{p'}^2)}T(p,k;k^2)
 \!-\!\!
 \int_p\sum_{i=2}^\infty \Delta V^{(i)}(k',p)\frac{T(p,k;k^2)}{k^2-p^2},
 \label{DeltaV-iterative}
\end{align}
where the notations $\int_p\equiv \frac{2}{\pi} \mathcal{P}
\int_0^\Lambda p^2dp$ and
\begin{equation}
 \Delta Q^\Lambda_{(k)}(k',p) \equiv
  \hat{Q}^\Lambda(k',p; k^2) - \hat{Q}^\Lambda(k',p; p^2)
\end{equation}
are introduced.  Eq.~(\ref{DeltaV-iterative}) determines $\Delta
V^{(i)}$ iteratively.

Having shown the existence of the $V_{\mbox{\scriptsize low k}}^\Lambda$ which satisfies
Eq.~(\ref{T-Vlk}), we now turn to the question about what RGE it
satisfies. The authors of Ref.~\cite{Bogner:2001jn} emphasized the
``semi-group composition law,'' and used the following relation,
\begin{equation}
 \hat{Q}^{\Lambda-\delta \Lambda}(k',k; p^2) = V_{\mbox{\scriptsize low k}}^\Lambda(k',k)
  -\delta \Lambda \frac{2}{\pi}\frac{V_{\mbox{\scriptsize low k}}^\Lambda(k',
  \Lambda)V_{\mbox{\scriptsize low k}}^\Lambda(\Lambda, k)}{1-(p/\Lambda)^2}
  + \mathcal{O}(\delta \Lambda^2).
  \label{wrong-Qbox}
\end{equation}
This infinitesimal form is derived from the following finite form,
\begin{equation}
 \hat{Q}^{\bar{\Lambda}}(k',k,p^2)=V_{\mbox{\scriptsize low k}}^{\Lambda}(k',k)
  +\frac{2}{\pi} \mathcal{P}\int^{\Lambda}_{\bar{\Lambda}}
  V_{\mbox{\scriptsize low k}}^{\Lambda}(k',\bar{k})\frac{\bar{k}^2d\bar{k}}{p^2-\bar{k}^2}
  \hat{Q}^{\bar{\Lambda}}(\bar{k},k,p^2),
  \label{twoLambdas}
\end{equation}
where $\bar{\Lambda} \le \Lambda$ is another scale. One might think that
this is the result of integrating Eq.~(\ref{Qbox-VNN}) up to a certain
scale and replacing the ``bare'' potential $V_{NN}(k',k)$ with the
``effective'' one, $V_{\mbox{\scriptsize low k}}^\Lambda(k',k)$,
accordingly. Eq.~(\ref{wrong-Qbox})
can be easily derived by putting $\bar{\Lambda}=\Lambda
-\delta \Lambda$.

It is however easy to see that \textit{there is no such}
$V_{\mbox{\scriptsize low k}}^{\Lambda}$ \textit{that satisfies} Eq.~(\ref{twoLambdas})
\textit{for an arbitrary ${\Lambda}< \Lambda_0$.}  Consider the limit
$\bar{\Lambda} \rightarrow 0$. From Eq.~(\ref{Qbox-VNN}) we see
\begin{equation}
 \lim_{\bar{\Lambda}\rightarrow 0} \hat{Q}^{\bar{\Lambda}}(k',k; p^2)
  = T(k', k; p^2),
\end{equation}
so that Eq.~(\ref{twoLambdas}) becomes Eq.~(\ref{nosuchV}) with
$V^\Lambda(k',k)$ being replaced by $V_{\mbox{\scriptsize low k}}(k',k)$, but, as we emphasized,
there is no such energy-independent potential that satisfies
Eq.~(\ref{nosuchV}). We have thus shown that Eq.~(\ref{wrong-Qbox})
cannot be valid. This is the defect in the second derivation in
Ref.~\cite{Bogner:2001jn}. The same Eq.~(\ref{wrong-Qbox}) is used in
the third derivation too in a crucial way, so that the third one has the
same defect.

\section{Completeness in the model space}
\label{sec:completeness}

Since $V_{\mbox{\scriptsize low k}}$ preserves the half-on-shell T-matrix, one may think of
another way of deriving the RGE, namely, from the $\Lambda$-independence
of the half-on-shell T-matrix in Eq.~(\ref{T-Vlk}). In the case of
$V_{WRG}$, the RGE can be easily derived from the $\Lambda$-independence
of the fully off-shell T-matrix. On the other hand, one cannot follow
the similar manipulation for $V_{\mbox{\scriptsize low k}}$, and the authors of
Ref.~\cite{Bogner:2001jn} invoked information on the cutoff state
vectors. But, as we will show, the relation they used is wrong when
bound states are present.

Consider the ``bare'' Schr\"odinger equation,
\begin{equation}
(H_0+V_{NN}) |\Psi_k\rangle= k^2 |\Psi_k \rangle,
 \label{Schroedinger}
\end{equation}
for a scattering state with energy $0 \le k^2< \Lambda^2$, and the
corresponding reduced one,
\begin{equation}
 (H_0 + V_{\mbox{\scriptsize low k}}^\Lambda) |\chi^\Lambda_k \rangle
  = k^2 | \chi^\Lambda_k \rangle.
  \label{cutoffSchroedinger}
\end{equation}

The potential $V_{\mbox{\scriptsize low k}}^\Lambda$ is a $P$-to-$P$ operator, which may be
constructed by the KLR folded diagram theory or the LS similarity
transformation. In the both cases, the state $|\chi^\Lambda_k \rangle$ is
related to the original state by the projection,
\begin{equation}
 |\chi^\Lambda_k \rangle = P |\Psi_k \rangle.
  \label{stateprojection}
\end{equation}
This condition is nothing but the $\Lambda$-independence of the
half-on-shell T-matrix in the reduced theory. Actually, by applying
$\langle k'| $ with $k' < \Lambda$ to Eqs.~(\ref{Schroedinger}) and
(\ref{cutoffSchroedinger}), we get
\begin{equation}
 \langle k'|V_{NN} |\Psi_k\rangle =(k^2-{k'}^2)\langle k'|\Psi_k\rangle
  \quad\mbox{and}\quad
  \langle k'|V_{\mbox{\scriptsize low k}} |\chi^\Lambda_k\rangle =(k^2-{k'}^2)\langle k'|\chi^\Lambda_k\rangle,
\end{equation}
but the left hand sides of these equations are by assumption equal to
the half-on-shell T-matrix $T(k',k; k^2)$. Therefore the right hand
sides are also equal, and taking into account that $k'$ is arbitrary, we
see that Eq.~(\ref{stateprojection}) is valid. On the other hand, the
preservation of the half-on-shell T-matrix follows
Eq.~(\ref{stateprojection}).

Their first derivation goes as follows: From the cutoff Schr\"odinger
equation (\ref{cutoffSchroedinger}), one gets the corresponding
Lippmann-Schwinger equation,
\begin{equation}
 |\chi^\Lambda_k\rangle = |k\rangle + \frac{2}{\pi}\mathcal{P}\int_0^\Lambda
  dp|p\rangle\frac{p^2}{k^2-p^2}T(p, k; k^2),
\end{equation}
where $k$ is assumed to be small, $k<\Lambda$. Note that the upper limit
of the integral is $\Lambda$ to be consistent with
Eq.(\ref{stateprojection}). Requiring that the half-on-shell T-matrix is
$\Lambda$-independent,
\begin{equation}
 \frac{d}{d\Lambda}T(k',k;k^2)=
  \frac{d}{d\Lambda}\langle k'|V_{\mbox{\scriptsize low k}}^\Lambda|\chi^\Lambda_k\rangle=0,
  \label{hosTinv}
\end{equation}
for $k'< \Lambda$ and using
\begin{equation}
 \frac{d}{d\Lambda}|\chi^\Lambda_k\rangle
  = \frac{2}{\pi}|\Lambda \rangle
  \frac{\Lambda^2}{k^2-\Lambda^2}T(\Lambda, k; k^2),
  \label{derstate}
\end{equation}
one gets
\begin{equation}
 0=\langle k'|\frac{dV_{\mbox{\scriptsize low k}}^\Lambda}{d\Lambda}|\chi^\Lambda_k\rangle
  +\frac{2}{\pi}\langle k'|V_{\mbox{\scriptsize low k}}^\Lambda|\Lambda \rangle
  \frac{\Lambda^2}{k^2-\Lambda^2}T(\Lambda, k; k^2).
  \label{deriv1}
\end{equation}
  The last term may be rewritten by using
\begin{equation}
 \frac{\Lambda^2}{k^2-\Lambda^2}T(\Lambda, k; k^2)
  =\langle \Lambda|V_{\mbox{\scriptsize low k}}^\Lambda \frac{\Lambda^2}{H_0+V_{\mbox{\scriptsize low k}}^\Lambda
  -\Lambda^2}
  |\chi^\Lambda_k\rangle.
\end{equation}

Let us introduce the operator,
\begin{equation}
 J\equiv \frac{2}{\pi} \int_0^\Lambda | \chi^\Lambda_k \rangle k^2 dk
  \langle \tilde{\chi}^\Lambda_{k}|,
  \label{J}
\end{equation}
where we introduced a bi-orthogonal basis $\langle \tilde{\chi}_k^\Lambda|$
for each state $|\chi_k^\Lambda\rangle$,
\begin{equation}
 \langle \tilde{\chi}^\Lambda_{k'}| \chi^\Lambda_k \rangle
  = \frac{\pi}{2}\frac{\delta(k'-k)}{k'k},
\end{equation}
because $V_{\mbox{\scriptsize low k}}^\Lambda$ is not Hermitian.
Note that $J$ is a projection operator, $J^2=J$. One thus obtains
\begin{equation}
 \langle k' |\frac{dV_{\mbox{\scriptsize low k}}^\Lambda}{d\Lambda}J |k\rangle
  =-\frac{2}{\pi}\langle k' | V_{\mbox{\scriptsize low k}}^\Lambda |\Lambda\rangle
  \langle \Lambda |V_{\mbox{\scriptsize low k}}^\Lambda \frac{\Lambda^2}{H_0+V_{\mbox{\scriptsize low k}}^\Lambda
  -\Lambda^2} J|k\rangle.
\end{equation}
If $J$ were the identity operator in the $P$-space, as the authors of
Ref.~\cite{Bogner:2001jn} claimed, then the identity ,
\begin{equation}
 \langle \Lambda | V_{\mbox{\scriptsize low k}}^\Lambda \frac{\Lambda^2}{H_0+V_{\mbox{\scriptsize low k}}^\Lambda
  -\Lambda^2} |k\rangle
  = T^\Lambda(\Lambda, k; \Lambda^2)\frac{\Lambda^2}{k^2-\Lambda^2 },
\end{equation}
would lead us to
\begin{equation}
 \frac{d}{d\Lambda}V_{\mbox{\scriptsize low k}}^\Lambda(k',k)=-\frac{2}{\pi}
  V_{\mbox{\scriptsize low k}}^\Lambda(k',\Lambda)T^\Lambda(\Lambda, k; \Lambda^2)
  \frac{\Lambda^2}{k^2-\Lambda^2 },
\end{equation}
which is nothing but Eq.~(\ref{eq:vlowk}).

In the presence of bound states, however, the operator $J$ cannot be the
identity operator,
\begin{equation}
 J+
  \sum_i
  \left|\chi^\Lambda_{B_i}\rangle
   \langle \tilde{\chi}^\Lambda_{B_i}\right|
  = P,
  \label{correctcomplete}
\end{equation}
where $|\chi^\Lambda_{B_i}\rangle$ are state vectors for the bound
states in the reduced theory,
\begin{equation}
 (H_0 + V_{\mbox{\scriptsize low k}}^\Lambda) |\chi^\Lambda_{B_i} \rangle
  = -k_{B_i}^2 | \chi^\Lambda_{B_i} \rangle,
  \label{eq:BS}
\end{equation}
and $\langle \tilde{\chi}_{B_i}^\Lambda|$ is its conjugate bi-orthogonal
state,
\begin{equation}
 \langle \tilde{\chi}_{B_i}^\Lambda|\chi_{B_j}^\Lambda\rangle=\delta_{ij}.
  \label{biorthonormal}
\end{equation}

Since the first derivation in Ref.~\cite{Bogner:2001jn} uses the claim
that $J$ is the identity operator in the $P$-space in an essential way,
it contains a serious defect in the presence of bound states.

The point is that completeness of the eigenstates of an operator
concerns the whole spectrum, including the bound states.

In the original applications of the KLR folded diagram theory or LS
similarity transformation theory to the shell model problems, the
spectrum of the Hamiltonian is discrete and the model space is finite
dimensional. Everything looks trivial about the completeness.
In the scattering problem, however, even though one is interested in
continuous states, bound states must be included if one talks about
completeness.

One might claim that the reduced theory is designed to reproduce the
scattering amplitudes, so that it does not need to include the bound
states in the spectrum. It is however not correct because the scattering
amplitudes in general reflect some information about the bound states. A
good example is provided by the well known Levinson's
theorem\cite{LevinsonTheorem}, which states that the low-energy
scattering data (the phase shift at zero momentum) for a well-behaved
potential knows the number of the bound states. If the reduced potential
$V_{\mbox{\scriptsize low k}}$ reproduces the half-on-shell, hence the on-shell T-matrix, it
must support the bound states because the existence of which is encoded
in the scattering phase shift.

If one takes into account the correct completeness relation,
Eq.~(\ref{correctcomplete}), one finds the modified RGE given by
\begin{eqnarray}
 \frac{d}{d\Lambda}V_{\mbox{\scriptsize low k}}^\Lambda(k',k)
  &=&\frac{2}{\pi}
  \frac{V_{\mbox{\scriptsize low k}}^\Lambda(k',\Lambda)T^\Lambda(\Lambda, k; \Lambda^2)}
  {1-(k/\Lambda)^2}
  \nonumber \\
 &&{}+\sum_i
  \int_l
  \left(
   \frac{d}{d\Lambda}V_{\mbox{\scriptsize low k}}^\Lambda(k',l)
   -\frac{2}{\pi}\frac{V_{\mbox{\scriptsize low k}}^\Lambda(k',\Lambda)V_{\mbox{\scriptsize low k}}^\Lambda(\Lambda, l)}
   {1+\left(k_{B_i}/\Lambda\right)^2}
  \right)
  \chi^\Lambda_{B_i}(l)\left(\tilde{\chi}^\Lambda_{B_i}(k)\right)^*,
  \nonumber \\
 \label{eq:vlowkmodified}
\end{eqnarray}
where $\chi^\Lambda_{B_i}(k)=\langle k|\chi^\Lambda_{B_i}\rangle$ is the wave
function in momentum space for the bound state, and
$\tilde{\chi}^\Lambda_{B_i}(k)$ is its bi-orthogonal
conjugate.

Interestingly, however, the extra terms are shown to cancel each
other~\footnote{The demonstration below is essentially due to Bogner,
Furnstahl, and Schwenk~\cite{BFS}.}, if we assume that the state
$|\chi^\Lambda_{B_i} \rangle$ is related to the state vector $|\Psi_{B_i}
\rangle$ in the original theory,
\begin{equation}
 (H_0+V_{NN})|\Psi_{B_i}\rangle =-k_{B_i}^2 |\Psi_{B_i}\rangle,
\end{equation}
 through the projection,
\begin{equation}
 |\chi^\Lambda_{B_i} \rangle = P |\Psi_{B_i} \rangle,
  \label{reducedBS}
\end{equation}
in conjunction with Eq.~(\ref{stateprojection}). Note that the
conditions Eqs.~(\ref{reducedBS}) and (\ref{stateprojection}) are
independent.

To see the cancellation, let us first note that the condition
\begin{equation}
 \frac{d}{d\Lambda}\langle k' | V_{\mbox{\scriptsize low k}}^\Lambda |\chi^\Lambda_{B_i}\rangle=0,
  \quad (0\le k' < \Lambda),
  \label{cutoffindepBS}
\end{equation}
and Eq.~(\ref{reducedBS}) are equivalent, as Eqs.~(\ref{hosTinv}) and
(\ref{stateprojection}) are.  Then, from the bound-state
Lippmann-Schwinger equation,
\begin{equation}
 |\chi^\Lambda_{B_i}\rangle=\int_p |p\rangle \frac{-1}{p^2+k_{B_i}^2}
  \langle p | V_{\mbox{\scriptsize low k}}^\Lambda |\chi^\Lambda_{B_i}\rangle,
\end{equation}
 we have
\begin{equation}
 \frac{d}{d\Lambda}|\chi^\Lambda_{B_i}\rangle
  =-\frac{2}{\pi} |\Lambda\rangle \frac{\Lambda^2}{\Lambda^2+k_{B_i}^2}
  \langle \Lambda | V_{\mbox{\scriptsize low k}}^\Lambda |\chi^\Lambda_{B_i}\rangle,
\end{equation}
which corresponds to Eq.~(\ref{derstate}).
From these equations, we have
\begin{eqnarray}
 0
 &=&\langle k' |\frac{dV_{\mbox{\scriptsize low k}}^\Lambda}{d\Lambda}|\chi^\Lambda_{B_i}\rangle
  -\frac{2}{\pi}
  \frac{
  \langle k'|V_{\mbox{\scriptsize low k}}^\Lambda\rangle
  \langle \Lambda |V_{\mbox{\scriptsize low k}}^\Lambda|\chi^\Lambda_{B_i}\rangle
  }{
  1+\left(k_{B_i}/\Lambda\right)^2
  }
  \nonumber \\
 &=&\frac{2}{\pi
  \int_l
  \left(
   \frac{d}{d\Lambda}V_{\mbox{\scriptsize low k}}^\Lambda(k',l)
   -\frac{2}{\pi}\frac{V_{\mbox{\scriptsize low k}}^\Lambda(k',\Lambda)V_{\mbox{\scriptsize low k}}^\Lambda(\Lambda, l)}
   {1+\left(k_{B_i}/\Lambda\right)^2}
  \right)\chi^\Lambda_{B_i}(l),
\end{eqnarray}
thus, the extra terms in Eq.~(\ref{eq:vlowkmodified}) vanish
identically.

In conclusion, though the first derivation in Ref.~\cite{Bogner:2001jn}
does not take into account the existence of bound states at all, and the
completeness relation is wrong when there are bound states, the
RGE~(\ref{eq:vlowk}) is shown to be unmodified irrespective of the
existence of bound states, if we assume  Eq.~(\ref{reducedBS}).

\section{Spectral representation for the $T$ matrix}
\label{sec:spectral}

The fourth derivation of the RGE is given in the appendix of
Ref.~\cite{Bogner:2001jn}. The derivation is based on the following
spectral representation for the T-matrix,
\begin{equation}
 V_{\mbox{\scriptsize low k}}^\Lambda(k',k)=T(k',k;k^2)+ \int_p T(k',p;p^2)\frac{1}{p^2-k^2}
  T^\Lambda(p,k;p^2).
  \label{spectral-T}
\end{equation}

In the following, I will show how this representation is modified in the
presence of bound states.  Let us start with Eq.~(\ref{T-Vlk}) in a bit
different representation,
\begin{equation}
 T(k',k;k^2)=V_{\mbox{\scriptsize low k}}^\Lambda(k',k) + \langle k' | V_{\mbox{\scriptsize low k}}^\Lambda G_0^{(P)}(k^2)
  T(k^2) | k\rangle,
  \label{T-Vlk-2}
\end{equation}
where $G_0^{(P)}(k^2)$ is the free Green function in the $P$-space,
\begin{equation}
 G_0^{(P)}(k^2)=\frac{P}{k^2-H_0}.
\end{equation}
Eq.~(\ref{T-Vlk-2}) may be rewritten by using the full Green function in
the $P$-space,
\begin{equation}
 G^{(P)}(k^2)=\frac{P}{k^2-H^\Lambda}, \quad H^\Lambda=H_0+V_{\mbox{\scriptsize low k}}^\Lambda,
\end{equation}
as
\begin{equation}
 T(k',k;k^2)=V_{\mbox{\scriptsize low k}}^\Lambda(k',k) + \langle k' | V_{\mbox{\scriptsize low k}}^\Lambda G^{(P)}(k^2)
  V_{\mbox{\scriptsize low k}}^\Lambda | k\rangle.
\end{equation}
If the operator $J$ in Eq.~(\ref{J}) were the identity operator in the
$P$-space, then, inserting $J$ and using $H^\Lambda |\chi^\Lambda_p \rangle
= p^2 |\chi^\Lambda_p \rangle$, one would get
\begin{equation}
 T(k',k;k^2)=V_{\mbox{\scriptsize low k}}^\Lambda(k',k)
  +\int_p \langle k' |V_{\mbox{\scriptsize low k}}^\Lambda|\chi_p^\Lambda\rangle
  \frac{1}{k^2-p^2}\langle \tilde{\chi}_p^\Lambda |V_{\mbox{\scriptsize low k}}^\Lambda |k\rangle,
\end{equation}
hence Eq.~(\ref{spectral-T}), with the identification $\langle k'
|V_{\mbox{\scriptsize low k}}^\Lambda |\chi_p^\Lambda \rangle = T(k',p;p^2)$ and $\langle
\tilde{\chi}_p^\Lambda | V_{\mbox{\scriptsize low k}}^\Lambda | k \rangle = T^\Lambda(p,k;
p^2)$. As we have shown, however, the operator $J$ is actually not the
identity operator in the $P$-space in the presence of bound states, this
manipulation is not justified. In the presence of bound states, the
correct equation is
\begin{eqnarray}
 T(k',k;k^2)&=&
  V_{\mbox{\scriptsize low k}}^\Lambda(k',k)
  +\int_p T(k',p;p^2) \frac{1}{k^2-p^2}T^\Lambda(p,k;p^2)
  \nonumber \\
 &&+\sum_i\langle k'|V_{\mbox{\scriptsize low k}}^\Lambda|\chi^\Lambda_{B_i}\rangle
  \frac{1}{k^2+k_{B_i}^2}
  \langle \tilde{\chi}^\Lambda_{B_i}|V_{\mbox{\scriptsize low k}}^\Lambda|k\rangle.
\end{eqnarray}
Similarly, the equation which relate the left-on-shell T-matrix to the
right-on-shell one is also modified as
\begin{eqnarray}
 T^\Lambda(p,k;p^2)&=&T(p,k;k^2)
  +\int_q T(p,q;q^2)
  \left\{
   \frac{1}{p^2-q^2}-\frac{1}{k^2-q^2}
  \right\}
  T^\Lambda(q,k;q^2)
  \nonumber \\
 &&{}+\sum_i
  \langle p |V_{\mbox{\scriptsize low k}}^\Lambda|\chi^\Lambda_{B_i}\rangle
  \left\{
   \frac{1}{p^2+k_{B_i}^2}-\frac{1}{k^2+k_{B_i}^2}
  \right\}
  \langle \tilde{\chi}^\Lambda_{B_i}|V_{\mbox{\scriptsize low k}}^\Lambda|k\rangle.
\end{eqnarray}

The extra terms are however cutoff independent because of
Eq.~(\ref{cutoffindepBS}). Thus they do not contribute to the RGE for
the $V_{\mbox{\scriptsize low k}}$.

\section{Summary and discussions}
\label{sec:summary}

In this paper, we have shown that each of the existent derivations of
the RGE, Eq.~(\ref{eq:vlowk}), has a serious defect. The derivations
based on the ``semi-group composition law'' are shown to be unjustified,
while the derivations based on the completeness must be modified when
bound states are present but the resulting RGE is shown to be
unmodified. After all, the present work shows that, even though the
derivation given in Ref.~\cite{Bogner:2001jn} does not take into account
the effects of bound states, Eq.~(\ref{eq:vlowk}) is correct
irrespective of the existence of bound states, if we assume
Eq.~(\ref{reducedBS}) or, equivalently, Eq.~(\ref{cutoffindepBS}).

It is important to note that, in order to derive Eq.(\ref{eq:vlowk}),
one actually needs to require not only that the half-on-shell T-matrix
is preserved, but also that the matrix elements $\langle p | V_{\mbox{\scriptsize low k}}^\Lambda
|\chi^\Lambda_{B_i}\rangle$ ($0\le p < \Lambda$) is invariant under the
change of the cutoff, $\Lambda$. This latter requirement does not
immediately follow the former. In this sense, the derivation rests on
the stronger (and consistent) requirements, Eqs.~(\ref{stateprojection})
and (\ref{reducedBS}), than just requiring the preservation of the
half-on-shell T-matrix.

It may be interesting to note that the RGE is not directly derived from
the concrete reduction methods such as LS and KLR methods, because the
second and the third derivations of Ref.~\cite{Bogner:2001jn} are now
shown to be invalid. Still, because LS method preserves the
half-on-shell T-matrix (and the matrix elements for the bound states),
it should satisfy the same RGE.

It is also interesting to note that the RGE for $V_{WRG}$ is much
simpler and more easily derived than that for $V_{\mbox{\scriptsize low k}}$.  Furthermore,
since the $V_{\mbox{\scriptsize low k}}$ RGE is too complicated to get a simple picture about
the action under the RG transformations, the usual concepts such as
relevant and irrelevant operators do not seem to be useful, while they
are actually important in the Wilsonian RG approach~\cite{Birse:1998dk,
Harada:2005tw, Harada:2006cw, Harada:2007ua}. To our best knowledge, no
one has ever found the nontrivial fixed point of the RGE for $V_{\mbox{\scriptsize low k}}$,
which plays an essential role for $V_{WRG}$. We thus suspect that the
convergence of ``realistic potentials'' to a universal one is not a
(direct) consequence of ``universality'' of the RG action.

We conjecture that the convergence is best understood in the light of
the inverse scattering problem. (See Chapter 20 of
Ref.~\cite{Newton:1982} or Chapter 12 of Ref.~\cite{AlfaroRegge:1965}
for reviews.) Note that all of the ``realistic'' potentials contain the
information about the phase shifts below $E_{lab}\alt 350$ MeV, and that
the LS reduction preserves the half-on-shell T-matrix elements (hence
the phase shifts), as we will show below. Since the reduced theory does
not contain high energy scattering by construction, the information
about the phase shifts contained in the reduced potential provides more
complete information about the phase shifts ``at all energies'' as the
cutoff is lowered. On the other hand, a result of the inverse problem,
in its simplest case, is that the potential is uniquely determined by
the phase shifts at all energies. Even though careful analysis is needed
to establish the connection between the convergence and the uniqueness
of the potential in the inverse problem, it seems to provide a more
natural way of understanding the convergence than the RG
``universality.''

In Ref.~\cite{Bogner:2006vp} it is reported that the conventional way of
calculating $V_{\mbox{\scriptsize low k}}$ shows a slow convergence and a new method based on
$V_{WRG}$ is proposed. It seems, however, difficult to transform
$V_{WRG}$ to an energy-independent potential analytically, even though
there may be no difficulty in doing so numerically. In
Ref.~\cite{Harada:2005tw}, such a transformation was considered for a
very simple potential as a field redefinition in the path integral
formulation. We found that there is a nontrivial Jacobian, which cannot
be calculated easily.

Recently, there emerges a new approach~\cite{Bogner:2006pc,
Bogner:2007jb, Jurgenson:2007td, Anderson:2008mu} based on the
Wegner-Glazek-Wilson (WGW) similarity RG
transformation~\cite{Wegner:1994, Glazek:1993rc, Glazek:1994qc}. In this
formulation, the RGE is given from the outset so that there is no
problem with the derivation of the RGE. It is however unclear to us if
the WGW similarity transformation preserves the half-on-shell
T-matrix. Note that the LS similarity transformation preserves the
half-on-shell T-matrix because of the particular property of the ``wave
operator'' $\omega$, $P\omega =0$, which leads to
\begin{equation}
 V_{LS}\equiv
  P(1-\omega)(H_0+V_{NN})(1+\omega)P -PH_0P =PV_{NN}(1+\omega)P,
\end{equation}
so that
\begin{eqnarray}
 \langle k|V_{LS}|\chi^\Lambda \rangle
  &=& \langle k|P V_{NN}(1+\omega)P |\chi^\Lambda\rangle
  = \langle k | V_{NN} |\Psi\rangle,
\end{eqnarray}
since $Q|\Psi\rangle = Q\omega P |\Psi \rangle =Q \omega P|\chi^\Lambda\rangle$.
On the other hand, WGW similarity transformed potential $V_s$ is defined
as
\begin{equation}
 V_{s}\equiv U(s)(T_{\scriptsize\mbox{rel}}+V)U(s)^\dagger
  -T_{\scriptsize\mbox{rel}},
\end{equation}
where the operator $U(s)$ is chosen in most papers as
\begin{equation}
 \frac{dU(s)}{ds}U^\dagger(s)=[T_{\scriptsize\mbox{rel}}, V_s].
\end{equation}
One would be interested in the T-matrix of the transformed theory
defined as $\langle k | V_s |\chi_s\rangle $, where $|\chi_s\rangle \equiv
U(s)|\Psi\rangle $ is the eigenstate of the transformed Hamiltonian. Unlike
the LS transformation, the T-matrix does not seem to be invariant under
the change of $s$.

\begin{acknowledgments}
 The author would like to thank NCTS for the financial support (grant
 number: NSC96-2119-M-007-001) for his stay at Taipei, during which the
 initial stage of the present work is done. He is grateful to C.-W.~Kao
 and S.-N.~Yang for the discussions and for the kind hospitality
 extended to him. He thanks S.~X.~Nakamura for the discussions via
 e-mails, and R.~Okamoto for the discussions about the model-space
 reduction methods. Discussions with H.~Kubo are also acknowledged.
 Finally, the author would like to thank S.~Bogner, D.~Furnstahl, and
 A.~Schwenk for pointing out the cancellation of the extra terms.
\end{acknowledgments}

redpajama_set_name: RedPajamaArXiv


text:
The Curve of Binding Energy: A Journey into the Awesome and Alarming World of Theodore B. Taylor (Paperback)
By John McPhee
(ESSAYS)
Theodore Taylor was one of the most brilliant engineers of the nuclear age, but in his later years he became concerned with the possibility of an individual being able to construct a weapon of mass destruction on their own. McPhee tours American nuclear institutions with Taylor and shows us how close we are to terrorist attacks employing homemade nuclear weaponry.
John McPhee was born in Princeton, New Jersey, and was educated at Princeton University and Cambridge University. His writing career began at Time magazine and led to his long association with The New Yorker, where he has been a staff writer since 1965. Also in 1965, he published his first book, A Sense of Where You Are, with Farrar, Straus and Giroux, and in the years since, he has written over 30 books, including Oranges (1967), Coming into the Country (1977), The Control of Nature (1989), The Founding Fish (2002), Uncommon Carriers (2007), and Silk Parachute (2011). Encounters with the Archdruid (1972) and The Curve of Binding Energy (1974) were nominated for National Book Awards in the category of science. McPhee received the Award in Literature from the Academy of Arts and Letters in 1977. In 1999, he was awarded the Pulitzer Prize for Annals of the Former World. He lives in Princeton, New Jersey.
"A book holding, with pretty good authority, that tens of thousands of people know enough about the bomb and are close enough to what they don't know to produce a bomb at home . . . The report's art at its difficult best." —Alvin Beam, The (Cleveland) Plain Dealer
"Though dwellers in the nuclear age should ponder this book, as much for its intellectual excitement as for its warning." —Edmund Fuller, The Wall Street Journal
Publisher: Farrar, Straus and Giroux
Publication Date: April 1st, 1994
Technology & Engineering / Power Resources / Nuclear
Kobo eBook (April 1st, 2011): $11.99
Hardcover (May 22nd, 1974): $30.00

redpajama_set_name: RedPajamaCommonCrawl


text:
Poo Bag Holder
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Awoo is a female-founded and owned business. We are proud feminists. It's hard enough launching a business from scratch but I would imagine it even more challenging without our 'I am woman, hear me roar' mentality. We owe so much of our ability to confidently plow ahead as if there were never any barriers to the one and only RBG.
Ruth Bader Ginsburg was a feminist icon and champion of women's rights. She changed the way the law views gender and actively passed and blocked laws that have paved the way for future generations of women. Women like myself, who take for granted that we can open a bank account without a male co-signer, lease an apartment, and do not need to choose between a career and motherhood. All thanks to RBG.
You can search list after list of RBG quotes worthy of a tattoo or at the very least a T-shirt. She really knew how to eloquently slap you in the face with sound logic. There's one quote that is somewhat less popular but has stuck with me, nonetheless. It is not about dissent or women's rights, but about life and balance.
"When I started law school, my daughter Jane was 14 months. I attribute my success in law school largely to Jane. I went to class about 8:30, and I came home at 4 o'clock. That was children's hour. It was a total break in my day. And children's hour continued until Jane went to sleep. Then, I was happy to go back to the books. So, I felt each part of my life gave me respite from the other and gave me a sense of proportion that classmates trained only on law studies lacked. ...Having Jane gave me a better sense of what life is."
Ruth Bader Ginsburg in The Atlantic, 2017.
While RBG was trailblazing and dismantling the patriarchy, she was also juggling responsibilities and relationships as a wife, mother, daughter, and friend. She created work-life balance before that was even a term, and she viewed that balance as an advantage over her colleagues.
We started Awoo for a myriad of reasons. After 10 years of working in the less than equitable fashion industry for male-owned companies staffed by predominantly white females, we wanted more control. Control of hiring and salaries, along with manufacturing and design. Personally, we also wanted control of our time. Less time spent in an office and more time spent with our dogs. Basically, we wanted a slice of RBG impact with a side of that RBG balance.
There are infinite reasons we admire RBG and just as many reasons that we want to emulate her. Our list is long and this was just a chihuahua-sized glimpse. We will forever be amazed and inspired by her. RBG is a legend and we are forever in her debt.
Thank you, Ruth Bader Ginsburg. Rest in Power.
Now enjoy some photos of pups honoring RBG.
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The project will have a capacity of approximately 800—1000 vessels. The development plan also entails an improvement of the surrounding area and its infrastructure, and includes construction of hotels, apartments, parks, bicycle lanes, shops, restaurants and cafes.
Construction of the new port will be undertaken by the Zenon Consortium, and will cost around 200 million euros.
The building of Cyprus' other new Marina in Limassol is rapidly progressing. The first phase of the project will be completed in 2012.


The Black Student Union held their 5th Annual Save-a-Breast spectacular to raise awareness for breast cancer in the Beckerman Recreation Center on Sunday, Oct. 11. BSU received a lot of support from other student clubs; many RSOs co-sponsored the event. When entering the event, giveaway tickets and t-shirts were handed out and guests were then free to roam to club tables.
Every time a visitor went to a different club table, they received a stamp on a sheet, which vouched as participation in the event and making the visitor eligible to win a prize.
Students Making an Impact on their Living Environment had jeopardy board set up at their table with all sorts of interesting questions pertaining to breast cancer. HOSA had a race to put on as many bras as possible. Some clubs went with a fall theme and had students painting rocks and pumpkins.
Many of the tables had baked goods that disappeared quickly. A lot of the groups had informational activities to help people recognize issues and know the signs of a potential problem related to breast cancer.
Sigma Chi's Joshua Rodriguez let people know that men get breast cancer too. The best of the best were decked out in their black and electric pink shirts and had some fun with everyone; some people were playing a game of the floor is lava with a balloon and others were dancing around.


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Mount Vic Flicks cute little country cinema is 20 minutes away.
But once you arrive you probably won't leave the gates of Tomah.
Please note in summer there are pedestal fans for cooling.
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text:
the fools back pocket
where you been spending your nights?
artistic license; music & lit reviews by the fool…
Review of Future Band album "Moralitas"
written by Caribbean Fool for Future.net
Future's "The Outer of Inside Vol. 1 :: Mortalitas" is comparable to a mini-series, where each episode can be viewed both on its own as well as part of the larger series. Contextually, this allows for a wide range of music styles and interpretations. Just when you think you've finally cracked the code of the album, everything changes, and the best part of it is the bands adeptness at performing entirely different musical genres. Mortalitas transforms from jam-band to funk-rock to rap/spoken word and never skips a beat. Tactical guitar work, a truckload of hooks and downright inspired drums are backed up with driving bass that works as the unifying factor within the music. There's something for everyone on this album, but the pieces are broken up and redistributed in a way that lets the individual talents to the band shine without overwhelming the sound as a whole.
The word "intersection" reappears throughout the lyrics as both signpost and constant reminder to the listener. Connections between ideas, between choices, between decisions and their ultimate outcome are the whole cloth from which the music has been stitched together. Each individual song folds into the following track with ease, even when the band changes style to emphasize a given experience. Tempo and rhythm are altered radically from song to song, but this gives each track a fresh taste when listened to outside the context of the album as a whole.
The album is lyrically reminiscent of other concept albums. Frank Zappa's "Joe's Garage" and Springsteen's "Ghost of Tom Joad" both place the listener over the shoulder of artist in a similar way, if through disparate musical styles. Mortalitas works its way through most of the "big moments" in life, and explicitly deals with the repercussions of decisions made under any number of circumstances. As you move through the album, each song puts the listener a little deeper into the psyche of the main character.
Additionally, there is a fair bit of philosophy sprinkled throughout the album. Cartesian duality appears under the guise of the differentiation between mind and heart; how both ideas and emotions can influence us both as individuals as well as members of society-at-large. Questions of fate and free will are also considered. By and large, many of the questions are raised for consideration instead of judgment. This only acts to improve the consistency of the thematic whole. It is enough to ask the questions and illustrate the possibilities; this can only incite further discussion and deeper thought about the many variables involved with Mortalitas theme.
It should be noted that the depth of the philosophy behind the album does not preclude it from being listened to for plain old enjoyment of the crafted sound. No matter the gravity of the lyrics, the album is still enjoyable simply as music rather than the art it so readily is. The listener will bring whatever degree of connectivity to the music that he/she chooses to, but the album itself still manages to be readily accessible in every sense of the word. Fans of past work will recognize Future from past albums while finding there is a lot more to explore on "The Outer of Inside Vol. 1 :: Mortalitas."
Review of Future Band album "Spiritas"
Spiritas "The Outer Edge of Inside" Vol. 2 reveals a far more stylized side of The Band Called Future showing off a frenetic mastery of sound in ways that would have been impossible for the band just a few short years ago. The band's emphasis on practice and performance is presented with their usual signature, idealized lyrics but made more pertinent by asking deeper, more penetrating/soul-searching questions about the relationship of the individual to a wider society, if not to existence itself. There is a depth to this album as a whole that exceeds the unity-of-purpose imbued first volume. I was left with the image of a devoted respondent awaiting answers to honestly posed questions.
The sonic quality of the album is fabulous from beginning to end. The sound itself is melded in the same way the band manages to meld styles of music without disturbing the core arrangements that bind everything together. Simply listening to the aural signature of the entire album without any attempt toward a connection to the meaning behind the songs gives off the pleasurable rise and fall of an acid trip without any of the queasiness. Rather than a series of initial encounters with individual songs, the album exists as a concept within-itself that teases out complicated issues by tracing different lines of reasoning all seemingly leading to the same aforementioned unanswered questions. A certain ambiguity serves the greater purpose of the album by presenting to the listener a wide array of inspired rhythms, melodies, and beats.
The album is constructed with overlays of repetitious chorus arrangements with the same pulsing intensity as the first installment Mortalitas "The Outer Edge of inside" Vol. 1 but feels far more coherent. The listener is greeted in almost prayer-like fashion with rolling guitars holding back just long enough to breathe and foment the opening words. The opening track on the album, "Jigsaw" sets an aggressive, bold tone that builds slowly but with a special certainty to an overwhelming instrumental conclusion. Track 3, "I've Had Warmer Welcomes" (which features DC hip-hop group Rosetta Stoned) rapidly questions themes of self-confidence, the duality of right and wrong and man's place in larger society placed over the kind of question and answer guitar work that makes even frightening ideas seem a little easier to confront.
"High Noon" is a classic call-back to the spaghetti western theology that lays behind much of the worldwide civil and mental aggression present, but changes the scenery from faux-Western to the band's home outside of Washington, DC. Complete the picture with a wicked horn section (a tip of the hat to the sounds of a tradition of violent conflict in the dogma of the wild West) repeating the melody during the last two minutes of the song and this is easily my favorite track. It serves as the midpoint of the album and effectively plays with preconceived notions any listener might still be clinging to this far into the album.
Other strong songs are "Sentencing" and "Lux." "Sentencing" might be described as the bands judgment of itself, or can be turned inside out to represent perceived reactions to building both message and music in such a way as to offend strict "genre classification" enthusiasts but being so damn good at it that it only strengthens their sound. "Lux" is a seven minute opus demonstrating the philosophy of a band learning as they go, but being pretty damn good as they get even better. The phrase "Into the light" is repeated over and over again, as if to lift the veil just far enough to see that somewhere down the road lay everything they are searching for. Absolutely enjoyable album, highly technical/talented sounds & lyrics.
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virgin suicides tell the strangest stories…
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Where You Can Go To Find Kick Ass Poetry
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Hepatocyte nuclear factor 4α (HNF4α) is a critical factor for hepatocyte differentiation. HNF4α expression is decreased in hepatocellular carcinoma (HCC), which suggests a role in repression of hepatocyte dedifferentiation. In the present study, hepatic expression of HNF4 was increased in liver-specific Hnf4a-null mice. The HNF4 whose expression was increased contained two variants, a known short variant, designated HNF41, and a novel long variant, designated HNF42. HNF4G2 mRNA was highly expressed in small intestine, and the transactivation potential of HNF42 was the strongest among these variants, but the potential of HNF41 was the lowest. Cotransfection experiments revealed that HNF41 repressed HNF4α- and HNF42-dependent transactivation, while HNF42 promoted HNF4α-dependent transactivation. HNF41 and HNF42 were able to bind to the HNF4α binding sites with an affinity similar to that of HNF4α. Furthermore, HNF42, but not HNF41, robustly induced the expression of typical HNF4α target genes to a greater degree than HNF4α. Additionally, HNF42 suppressed proliferation of hepatoma cells as well as HNF4α and HNF41 did, and HNF42 induced critical hepatic functions, such as glucose and urea production, and cytochrome P450 1A2 activity more strongly than HNF4α and HNF41 did. These results indicate that HNF42 has potential for redifferentiation of HCC and thus may be explored as a target for HCC therapy.


Optimum nutritional value is of utmost importance for equine athletes. This can only be achieved through the most current science and research as well as premium quality ingredients. Equina products are designed and created to cover the horse's physiological needs and the quality production process ensures the effectiveness of the active components and that they are not diminished. The result is an easily absorbed, highly effective product. Our premium quality is achieved through top notch ingredients and strict production standards and controls.
Equina Products are formulated with the latest science and research and produced at MIAVIT where quality management is second to none. The MIAVIT certifications ensure the products you receive meet the strictest of standards. Quality management runs through the entire manufacturing process. From formulation to buying of raw materials, receipt and storage of incoming raw materials and on through production and dispatch. In fact, a preventative risk assessment is performed through their HACCP concept so that possible risk can be prevented or minimized in advance of production. MIAVIT quality standard is ensured through analytical monitoring (over 12,000 tests done annually), 100% traceability with their early warning barcode system, separate mixing lines to guarantee highest level or product purity, ongoing, regular employee training that far exceeds the standard and supplier management through continuous assessment, analysis and auditing. In addition, MIAVIT audits all quality management measures regularly, has a very thorough compliant processing system designed to statistically evaluate all complaints and corrective measures in order to prevent and reduce errors. MIAVIT's formulation department not only tests and evaluates their own products, they use a dual review process for customer's formulation development as well.
TUV SUD. This is a global company whose headquarters in in Germany. They specialize in 3rd party solutions and help companies to maximize profitability, ensure quality and sustainability. They certify many industries including food supplements and food packaging. Testing for higher standard, safety, reliability and quality, ensuring a global standard, looking at company regulations and efficacy, and minimizing risk non-compliance are their focus throughout these industries. They asses the company as a whole in order to provide holistic solutions, have cross industry expertise, a global network and are future focused.
FAMI QS. They are a pioneer in the feed ingredient field serve 47 countries and are located in Belgium. They have developed a quality and safety system for specialty feed ingredients and their mixtures. Minimizing risk of unsafe ingredients, feed hygiene regulation and measurements to ensure safety regulations are met are the primary focus. Additionally, they are animal based and their codes are aimed at specialty feed ingredients and mixtures. Training and certification process in intense and they offer training programs geared towards Food Safety awareness and FDA Modernization act. In October of 2017 they launched their revised standards in order to keep up with the developments within the industry. They are present in the United States; however most top feed companies do not carry their certification.
GMP/GMP+. Good Manufacturing Practices and Good Manufacturing Practices + (Plus adds HACCP – Hazards Analysis Critical Control Points). Started in the Netherlands in 1992 as a result of several contamination issues, it has developed and evolved into an international company involving more the 70 countries. The main goal being to ensure consistent quality feed, they believe that food safety starts with the cultivation of products and must continue through all aspects of production until the product reaches the retail outlet, this includes storage, transport and detailed documentation of procedures. They define clear conditions to guarantee safety and sustainability. The addition of the ISO/HACCP certifications resulted from the process evolving into a more preventative and proactive process throughout with a structured approach to risk management. The EWS (Early Warning System) was also implemented to reduce the impact of a contamination. Objective Independent Audits are performed on a regular basis to ensure policies, procedures and guidelines are met and do not need to be updated, changed in order to keep with the companies over growing certifications. GMP+ is one of the most valued and recognized certifications in the industry. It is important to recognize that cGMP registration is gained by meeting facility standards while GMP certification requires actual testing of the end product, the actual supplement. GMP certification is very rare in the United States among the major lines of equine supplements.
Bio Seigel EG. Organic certification. This certification shows the company's products use agriculturally produced products according to EU regulation in organic farming. 95% or more of ingredients in the products must come from organic production. This certification meets German organic food labeling act standards. Producers must also participate as certified operators under controlled system provided for in regulation.
QS Pruzeichen. QS certification mark shows products have been cross staged quality assured for fresh food.
For processes that have a critical impact on food safety or animal welfare, QS goes beyond the legal requirements. For feed supplements QS inspections involve comprehensive feed monitoring. All feeds are regularly tested for certain pollutants (mycotoxins, heavy metals and dioxins). The examination results must be deposited in the QS database. For certain pollutant parameters, QS with stricter limits goes well beyond the legal requirements. QS requires exclusive use of raw materials according to approved/positive list for feed materials or lists of recognized standards. In addition, substances on the QS exclusion list may not be used as feed in the QS system. For deliveries of compound feed (loose goods) to farmers, the VVVO number is documented for traceability. QS has specifications for the cleaning and disinfection of trucks used to transport animal feed.


One of Thailand's leading real estate developers Sansiri has made public their ambitions to tap heavily into the ever-strengthening China buying market.
According to the group Thailand properties provide premium yields of 5%, versus domestic Chinese returns and are five times less expensive on an acquisition basis.
The head of international business for the developer Cobby Leathers has said the group is forecasted THB5 billon in overseas sales in 2016. On a proportional basis the Chinese markets of Singapore, Hong Kong and the Mainland are the key contributors to sales revenue.
In terms of location, the China interest is focused mainly on the major locations of Bangkok. Phuket, Chiang Mai, Hua Hin and Pattaya. As for products, mid-scale condominiums are clearly the top selling units given that freehold foreign ownership is widely available for investors.
Sansiri's retail unit Plus Property has commented that affordable pricing points in Pattaya are seeing strong demand, especially in the Jomtien, followed by Wongamat. New flights from the Mainland into nearby U-Tapao Airport are expected to accelerate the segment as it provides door-to-door access to real estate buyers.
One key success story of Sansiri across it's entire business stream, is the ability to tap into the emerging middle class and last year total turnover for the company was in excess of USD1 billion.
In an ambitious move the group has invested heavily into the new T77 project which is an ambitious inner-city lifestyle community. Within the mixed-use elements Sansiri is brining six different products to the market aimed at different price points and segments. One of the key demand drivers of the area is the inclusion of international educational facilities along with innovative commercial and retail offerings. In effect the concept is a horizontal township which makes sense given Bangkok's sprawling urban landscape.
For Sansiri the China focus simply is rooted in the concept of fishing where the fish are.


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Alicia Keys Shares New "ALICIA" Album Release Date
After much delay, it looks like Alicia Keys' upcoming ALICIA album will see the light of day. Her seventh studio album is set to release this Friday, September 18.
The project was originally supposed to come out in March but that was put on hold because of COVID-19.
Expect the likes of Snog Aalegra, Jill Scott, Khalid, Miguel and more to appear on the effort, as well as Ed Sheeran, who co-wrote "Underdog."
In talking to Apple Music, Mrs. Keys said she named her album ALICIA because she feels like she is full herself now. Naming the album that was a strong feeling for her and she feels like she's not holding anything back for this one.
OS REWIND: Alicia Keys – Love Looks Better
OS REWIND: Alicia Keys – So Done (feat. Khalid) [Music Video]
Dr. Dre Gets Back in the Studio After Brain Aneurysm Diagnosis


In April, May, and June I read some great books. I want to take some time to share what I've learned. Enjoy!
Dr. Frankl practiced psycho-therapy and miraculously survived Nazi work camps. He studied himself and peers throughout the experience. Being in the camps is described as worse than nightmares. Accounts of atrocities committed in the camps are best not paraphrased. Go read it!
One insight taken away is: man finds meaning in love, work, and suffering. The author pulled himself through hell by frequently thinking about his wife, the love of his life.
Jesse Itzler invited a Navy Seal to live with and train him for a month. The ensuing tale is hilarious.
Mind over matter. You have more in you than you think (60% more).
Make big decisions by considering, after it plays out, how great telling the story will be.
Watch out for getting stuck on routines and call in outside help (e.g. Personal trainer) to get unstuck.
The human spirit is powerful, and the mind gives up before the body gives up (usually).
I discovered the book via this YouTube video.
Sandberg abruptly lost her husband. She embarked on a journey to deal with own grief and in the process learned how to give better support to others overcoming tragedy.
Many of the stories in the book refer back to the three P's of tragedy processing.
Personalization – I am the reason this happened. I failed to stop it from happening. It is my fault.
Pervasiveness – Because this happened, every part of my life is ruined.
Permanence – Life is going to be like this forever. It will never get better.
When consoling grief-stricken friends, try not to say things like "let me know if there is anything I can do". The phrase pushes the burden of asking onto them. Instead, take action, show up at the door with a casserole. Help them through the three P's: tragedy isn't their fault, it won't ruin everything, and the feelings are temporary.
The focus of Expert Secrets is how to create and sell information products, after becoming a subject matter expert. Expert Secrets has many nuggets, and I'll share the few most memorable to me.
The reason people buy most things is to increase their status. Status means different things to different people. To some a luxury car is a status symbol, and to others a ten year old junker is a status symbol.
Instead of trying to solve a hundred small problems, look for the biggest domino. The biggest domino, once knocked over, knocks over all the smaller ones.
Most stories follow the format of the heroes two journeys. The hero has an external goal and a more subtle internal struggle. The hero may never achieve the external goal, but while on the journey resolves the inner struggles and completes a transformation.
I think creating less noise is a measure of emotional maturity. Optimize for action instead of talk. Do work, not just press releases.
Parenting: Who is it really for?
A long attention span is a super power when among highly distractible masses. This reminds me of Cal Newport's Deep Work which says a blacksmith may work a single blade for seven hours uninterrupted.
Meaningful, quality work requires an above-average attention span.
Long attention span might be a key to success. It could require a decades long focus to turn vision into reality.
Together we build a world free of fear. What would you do if you were not afraid?
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If you are wondering how to become an independent contractor, I can already tell that you are a pretty smart cookie. If you are looking for full-time work or just a second job, you'll likely find it easier to get hired as an independent contractor rather than as an employee. Why? Because it's much less expensive for an employer to hire a contractor.
The employer saves on taxes, doesn't have to worry about paying you when she doesn't have work, won't have to provide you with tools and equipment (you'll be expected to provide these on your own) and can terminate the relationship without any downsides.
The more you can present yourself as a legitimate independent contractor, the more attractive and easier to hire you'll be. How do you become an independent contractor?
Pick a name that describes what you do and who you do it for. This will be important for marketing later on. Print up invoices and business cards with your business name rather than your own personal name. It just looks much more professional.
In most cases, you'll have to file a fictitious business name statement or a DBA – doing business as – statement. This is very easy to do and it's inexpensive. You can either call your county clerk's office to find out how to get this done, or you can Google "Fictitious Business Name Statement." There are small newspapers that fulfill the publication requirement (for a fee of course), and they'll have all the documents you're country requires. HINT – If you go this route, select the cheapest alternative.
Note: You don't have to get set up as an independent contractor in order to start making money. Here's a cool side gig – driving for a ride sharing company. Once you begin the process of signing up, you can be out making money and working for yourself within a week or so.
Some cities and counties will only let you conduct business if you have a license. This is simply a question of filling out a form and paying a fee. It's usually not a lot of money. Even if you operate out of your home, you should get this done. The penalty for non-compliance will be several times the fee, and you will waste time cleaning up the mess. Go to the city clerk's website to download the forms. Depending on your trade, you might have to apply for a special professional or vocational license. Your trade association will know, so contact them (or your state's website) to learn more.
As an independent contractor, you'll have to take care of all your own tax payments. I strongly recommend you speak to a tax professional about how to set up your business. Should you be a sole proprietor? A Professional LLC? Do it right. The last thing you want is to create tax audit flags.
Your tax person will likely ask you to make quarterly payments (if your business rakes in more than $3,000 or $4,000 a year in gross income). If you don't pull in much money as an independent contractor, you can skip this if you have another day job. Just ask your employer to withhold more from your paycheck.
Remember, taxes are a key benefit of being an independent contractor. You can deduct lots of business expenses that employees can only dream about. You might even be able to create a tax loss and, as a result, lower the income tax due on your other income from your day job.
If possible, start paying estimated taxes. This will strengthen your case and prove that you indeed are an independent contractor.
These three steps will get you set up to become an independent contractor. Once you do that, it will be easier to launch your new business and find work. Make sure to set up good bookkeeping and budgeting for small business systems. And don't forget about getting the right business insurance.
Are you an independent contractor? Does this reduce your tax liability? Is it helpful in other ways?
My wife is being offered a lucrative contract position on a 1099 basis with a large company where she had worked a few years ago. Does she need to set up a company in order to be a 1099 contractor? Also, how does it work if we live in NJ and most of the contract work for this role is in PA?
This would be a good question for your CPA.
my employer is thinking making there only 2 employees (me and my brother-in-law) contract labor instead of employees. and i don't like the sound of that. me and my brother-in law all ready do side jobs. and if all goes well ill be a master plumber and he a JP next month so what do you think we should do??
What don't you like about it? What options do you have? If the boss is trying to do this just to save money, you are going to come up with short end of the stick when it comes tax time. Plus….the boss can only do this if you and your brother in law really are contractors and adhere to the requirements.
lol we really have no options. we just have to do what ever they shove down our throats. they have always seen it like a master slave kind of thing, this is a very old and small family bis. there was a prob on the taxes this year and that is what brought it up so yes im sure it is just to save money. id just like to know what laws i can bring to there attention to persuade them it is best to keep us as employees and not and not try this contract labor thing, that they know nothing about other than thats what other companies do. and not to sound like a know it all jackass but these are just some good ole country boys who know more about hunting and farming than they do about running a business.
I am considering an on-line business and would like to know if I can use an independent Licensed Drug Counselor.
Those considering becoming an independent contractor should also make sure that they do not agree to work with *any* individual or company without reviewing and signing a detailed Independent Contractor's Agreement.
This little bit of due diligence will save you a lot of time and money later on.
During this time of high unemployment, many people are working on a contract basis. I am referring to professionals like lawyers, accountants, etc. They are hoping that it may turn into a permanent job.
Great overview, but I think that you would agree that there are MANY more details to going into business for yourself. I think it is wise to set up a LLC, for the liability protection alone. In this sue-crazy world we live in, you have to protect yourself. Great site. Keep up the good info.


for the casting technique, for smooth and bubble-free castings.
Easy handling by spraying, thus no damage to the cast object.
for the model cast technique, for smoothing, hardening and sealing of model surfaces.
Insulates plaster, resin, metal and porcelain from wax.