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\title{On the massive gluon propagator, the PT-BFM scheme and the low-momentum behaviour of decoupling
and scaling DSE solutions}

\author{J. Rodr\'{\i}guez-Quintero}

\date{}

\begin{document}

\maketitle

\begin{center}
Dpto. F\'isica Aplicada, Fac. Ciencias Experimentales,\\
Universidad de Huelva, 21071 Huelva, Spain
\end{center}

\begin{abstract}

We study the low-momentum behaviour of Yang-Mills propagators obtained from
Landau-gauge Dyson-Schwinger equations (DSE) in the PT-BFM scheme. We compare
the ghost propagator numerical results with the analytical ones obtained
by analyzing the low-momentum behaviour of the ghost propagator DSE in Landau gauge,
assuming for the truncation a constant ghost-gluon vertex
and a simple model for a massive gluon propagator.
The asymptotic expression obtained for the regular or decoupling  ghost dressing function
up to the order ${\cal O}(q^2)$ is proven to fit pretty well the numerical PT-BFM
results. Furthermore, when the size of the coupling renormalized at
some scale approaches some critical value, the numerical PT-BFM propagators tend
to behave as the scaling ones. We also show that the scaling solution,
implying a diverging ghost dressing function, cannot be a DSE solution
in the PT-BFM scheme but an unattainable limiting case.

\end{abstract}

\begin{flushright}
{\small UHU-FP/10-025}\\
\end{flushright}

\Section{Introduction}

The low-momentum behaviour of the Yang-Mills propagators derived either from
the tower of Dyson-Schwinger equations (DSE) or from Lattice simulations in
Landau gauge has been a very interesting and hot topic for the
last few years. It seems by now well established that, if we assume
in the vanishing momentum limit a ghost dressing function behaving as
$F(q^2) \sim (q^2)^{\alpha_F}$ and a gluon propagator as
$\Delta(q^2) \sim (q^2)^{\alpha_G-1}$ (or, by following a notation commonly used,
a gluon dressing function as $G(q^2)= q^2 \Delta(q^2) \sim (q^2)^{\alpha_G}$),
two classes of solutions may emerge (see, for instance, the discussion
of refs.~\cite{Boucaud:2008ji,Boucaud:2008ky}) from the DSE:
(i) those, dubbed {\it ``decoupling''}, where $\alpha_F=0$ and the suppression of
the ghost contribution to the gluon propagator DSE results in a massive gluon
propagator (see \cite{Aguilar:2006gr,Aguilar:2008xm} and references therein);
and (ii) those, dubbed {\it ``scaling''}, where $\alpha_F \neq 0$
and the low-momentum behaviour of both gluon and ghost propagators
are related by the coupled system of DSE through the condition $2 \alpha_F+\alpha_G = 0$
implying that $F^2(q^2)G(q^2)$ goes to a non-vanishing constant when $q^2 \to 0$
(see \cite{Alkofer:2000wg,Fischer:2008uz} and references therein).
As a matter of fact, $F^2(q^2)G(q^2)$, which gives the perturbative running for the
coupling constant renormalized in Taylor-scheme~\cite{Boucaud:2008gn}, is a good
quantity in discriminating the kind of solutions we deal with. It is worth to
remember that, despite the widely accepted nomeclature for the classes
of solutions, neither a scale invariance nor a decoupling of the IR dynamics for the theory
can be inferred from the low-momentum behaviour of such a Taylor coupling.

How both types of IR solutions for Landau gauge DSE emerge and how the transition between them occurs,
being governed by the size of the coupling taken as an integration boundary condition at
the renormalization momentum, was initially discussed in ref.~\cite{Boucaud:2008ji} through the analysis of a
ghost propagator DSE combined with a gluon propagator taken from lattice computations.
It should be remembered that one needs to know the QCD mass scale to predict the QCD coupling at any momentum.
This mass scale should be of course supplied to get a particular solution from DSE and can be
univocally related to the boundary condition needed, after applying a trunctation scheme, to solve
the equation.
The existence of a {\it critical} value for the coupling at any renormalization momentum was suggested
by that partial analysis. No solution was proved to exist for any coupling bigger than the critical one and
the unique scaling solution\footnote{The authors of \cite{Fischer:2006vf} proved there, once the scaling behaviour
is assumed, the uniqueness for Yang-Mills infrared solutions}
appeared to emerge when the coupling took that critical value.
Later, the authors of ref.~\cite{Fischer:2008uz} confirmed, by the analysis of the tower of DSE truncated
within two different schemes and also in the framework of the functional renormalization group, that
the boundary condition for the DSE integration determined whether a decoupling or the scaling solution
occurs. A similar analysis have been recently done in the Coulomb gauge~\cite{Watson:2010cn} leading to
the same pattern of ref.~\cite{Boucaud:2008ji}, although the authors interpreted the boundary condition in terms
of the gauge-fixing ambiguity (see also \cite{Epple:2007ut}).
Furthermore, an analytic study based on the pinch technique in ref.~\cite{Cornwall:2009ud} shows that, within some
approximations, there is a lower limit for the gluon mass, which the IR singularities of QCD still persist below,
that can be also interpreted as an upper limit to the coupling.
Very recently also, a next-to-leading low-momentum asymptotic formula
for the decoupling ghost dressing function solutions was obtained by studying the ghost propagator DSE with the
assumption, for the truncation, of a constant ghost-gluon vertex and of a simple model
for a massive gluon propagator~\cite{Boucaud:2010gr}. In this asymptotic formula, the
ghost-propagator low-momentum behaviour appeared to be regulated by
the zero-momentum effective charge in Taylor scheme~\cite{Aguilar:2009nf}
and by the Landau-gauge gluon mass scale.

In the present note, the work of ref.~\cite{Boucaud:2008ji} will be extended by the analysis of the
results~\cite{Aguilar} obtained by solving the coupled system of Landau gauge ghost and gluon propagators DSE
within the framework of the pinching technique in the background field method~\cite{Binosi:2002ft} (PT-BFM).
Our main goal is investigating whether the same pattern for regular (decoupling) and critical (scaling) solutions in
ref.~\cite{Boucaud:2008ji} is also found for the PT-BFM solutions. In the PT-BFM scheme,
the zero-momentum ghost dressing function will be seen to diverge when the coupling approaches some critical value, as it
should be expected for the scaling solution ($\alpha_F \neq 0$). This seems to support the
suggestion of a transition from one to another solutions controled by
the size of the coupling approaching a critical value~\cite{Boucaud:2008ji}.
The authors of ref.~\cite{Fischer:2008uz} obtained similar results but they applied the zero-momentum
ghost propagator as the boundary condition for the
DSEs integration and missed its connection with the value of the coupling at the renormalization momentum
({\it i.e.} the particular value of $\Lambda_{\rm QCD}$ one applies to build the solutions) or the critical coupling
the scaling behaviour requires to emerge\footnote{These authors furthermore invoked the renormalization
group invariance to claim that such a critical coupling does not appear. Nevertheless, the renormalization group
invariance only requires for the critical values of the coupling at any two fixed renormalized momenta
to be connected by the appropriate renormalization group running (the same, of course, for any decoupling
solution). Indeed, the renormalization flow for the coupling can be defined by $\alpha(q^2) = \alpha(\mu^2) F^2(q^2) G(q^2)$
to satisfy this and it is found to agree, in the perturbative domain, with the perturbative running given by the $\beta$-function
in Taylor scheme~\cite{Boucaud:2008gn}.}. This connection is an important ingredient because it provides us with a manner,
through a comparison with the physical strong coupling, to discuss whether the scaling critical DSE solution could
be allowed by the data. We will also compare the low-momentum analytic results of ref.~\cite{Boucaud:2010gr} with
the PT-BFM results.  In particular, the next-to-leading asymptotic
formula for the ghost dressing function  with $\alpha_F=0$ will be shown to nicely
describe the low-momentum PT-BFM results for different values of the coupling
taken at the renormalization point, as a boundary condition for the DSE integration.
It should be emphasized that the ansatz for the massive gluon propagator applied to derive the
analytical results in ref.~\cite{Boucaud:2010gr} has nothing to do either with the numerical
analysis based on lattice results in ~\cite{Boucaud:2008ji} or with the one based on PT-BFM results in this paper,
both leading to obtain a critical coupling. These analytical low momentum results are applied in
this paper only for comparative purposes. However, as a result of the comparison, this boundary condition will be put in
direct relation to the zero-momentum effective charge in Taylor scheme~\cite{Aguilar:2009nf}
and to the Landau gauge gluon mass. Finally, we will also argue that a scaling solution cannot exist as a solution of the
coupled system of PT-BFM DSE, although the PT-BFM solutions tend to it when the coupling aproaches the critical value.
More generally, a diverging ghost dressing function cannot be obtained when the gluon propagator is massive ($\alpha_G=1$).
Of course, this last claim is not a new result: it is well-known that the scaling solution only can emerge
if the ghost dominance in the gluon propagator DSE, after assuming $\alpha_F < 0 $, implies the gluon
propagator to vanish at zero momentum~\cite{Alkofer:2000wg,Fischer:2008uz}. However, it is not worthless to
emphasize that, for the gluon propagator, being massive implies not to observe
the relation $2 \alpha_F + \alpha_G=0$ and is therefore a sufficient condition for the scaling
solution not to appear. It should be also pointed out that LQCD results
(see~\cite{Cucchieri:2007md,Bogolubsky:2007ud,IlgenGrib,Boucaud:2005ce,Oliveira:2010xc,Bornyakov:2009ug}
and references therein), pinching technique results (see, for instance,
\cite{Cornwall,Binosi:2002ft,Sauli:2009se,Cornwall:2009ud}),
refined Gribov-Zwanziger~\footnote{In addition, K-I. Kondo triggered very recently an interesting
discussion about the Gribov horizon condition and its implications on the Landau-gauge
Yang-Mills infrared solutions~\cite{Kondo:2009ug,Dudal:2009xh,Aguilar:2009pp,Boucaud:2009sd}.}
formalism (see~\cite{Dudal:2007cw}) or
other approaches like the infrared mapping of $\lambda \phi^4$ and Yang-Mills
theories in ref.~\cite{Frasca:2007uz} or the massive extension of the Fadeev-Popov
action in ref.~\cite{Tissier:2010ts} appear to support a massive gluon propagator.

We organized this note as follows: first, we briefly review the low-momentum behaviour for the propagator solutions
of the ghost propagator DSE in section \ref{twosol}; we then compare the PT-BFM results with the low-momentum analytical
expression and discuss their dependence with the size of the coupling at the renormalization point, taken as a
boundary condition for DSE integration, in section \ref{comparing}; and we finally conclude
in section \ref{conclu}.

\Section{The two kinds of solutions of the ghost propagator Dyson-Schwinger equation}\label{revisiting}
\label{twosol}

As was explained in detail in refs.~\cite{Boucaud:2008ky,Boucaud:2010gr}, the low-momentum behavior for
the solutions of the Dyson-Schwinger equation for the ghost
propagator (GPDSE), which can be written diagrammatically as

\vspace{\baselineskip}
\begin{small}
\begin{eqnarray}
\left(\ghostDr\right)^{-1
=
\left(\ghostBr\right)^{-1}%
-
\ghostSD \ ,
\label{ghostSD}
\end{eqnarray}\end{small}%

\noindent can be obtained in Landau gauge by procceeding as follows:

we consider eq.~(\ref{ghostSD}) for two different (although parallel)
external ghost momenta, $k$ and $p$, such that
$p^2-k^2=\delta^2 k^2$ ($\delta$ being an extra parameter that,
for the sake of simplicity, will be taken to be small enough as to
expand on it around 0) and subtract them, as a regularization prescription
for not to have to deal with any UV cut-off. Then, the ghost dressing function,
$F(k^2)$, and the gluon propagator form factor, $\Delta(k^2)$, are renormalized by
applying the MOM prescription,

\begin{eqnarray}
F_R(\mu^2) \ = \ \mu^2 \Delta_R(\mu^2) \ = \ 1 \ ,
\end{eqnarray}

\noindent
where $\mu^2$ is the subtraction point; and, as explained in \cite{Boucaud:2008ky,Boucaud:2010gr},
we choose for the ghost-gluon vertex,

\begin{eqnarray}
\widetilde{\Gamma}_\nu^{abc}(-q,k;q-k) \ = \
i g_0 f^{abc} \left( \ q_\nu H_1(q,k) + (q-k)_\nu H_2(q,k) \ \right) \ ,
\label{DefH12}
\end{eqnarray}

\noindent
to apply the MOM prescription in Taylor kinematics
({\it i.e.} with a vanishing incoming ghost momentum)
and assume the non-renormalizable bare ghost-gluon form factor, $H_1(q,k)=H_1$,
to be constant (at least in the low-momentum regime for the incoming ghost).
Thus, after being cast into a renormalized form and the above-mentioned
subtraction, the GPDSE reads

\begin{eqnarray}
\frac{1}{F_R(k^2)} - \frac{1}{F_R(p^2)}
\ = \
N_C \ g_R^2(\mu^2) \ H_1 \ I(k^2) \ ,
\label{SDRS}
\end{eqnarray}

\noindent
where

\begin{eqnarray}
\label{LamInf}
I(k^2) \ = \  \ \int \frac{d^4 q}{(2\pi)^4}
\left( \rule[0cm]{0cm}{0.8cm}
\frac{F_R(q^2)}{q^2} \left(\frac{(k\cdot q)^2}{k^2}-q^2\right)
\left[ \rule[0cm]{0cm}{0.6cm}
\frac{\Delta_R\left((q-k)^2\right)}{(q-k)^2} -
\frac{\Delta_R\left((q-p)^2\right)}{(q-p)^2}
\rule[0cm]{0cm}{0.6cm} \right]
\rule[0cm]{0cm}{0.8cm} \right) \
\end{eqnarray}

\noindent
and where the ghost dressing function and gluon propagator should be understood as renormalized at
the subtraction momentum, $\mu^2$, and $g_R(\mu^2)$ is the gauge coupling renormalized
at a subtraction point with Taylor kinematics (Taylor MOM scheme).
Then, we cut integral domain of $I(k^2)$ in eq.~(\ref{LamInf}) into two pieces
by introducing some new momentum scale, $q_0^2$, below which
both ghost and gluon are assumed to be well described by the following
ansatze

\begin{eqnarray} \label{gluonprop}
\Delta_R(q^2) &=& \frac{B(\mu^2)}{q^2 + M^2} \
\simeq \frac{B(\mu^2)}{M^2} \left( 1 - \frac{q^2}{M^2} + \cdots \right) \ ,
\\ \label{dress}
F_R(q^2) &=& A(\mu^2) \left( \frac{q^2}{M^2} \right)^{\alpha_F} \left( 1 + \cdots
\rule[0cm]{0cm}{0.6cm} \right) \ .
\end{eqnarray}

\noindent
Thus, we shall look for the ghost dressing function, $F_{\rm IR}$,
its leading behaviour being parameterized through a general power law behaviour
where $\alpha_F > -2$ to keep the integral $I(k^2)$ infrared convergent, and
for a massive~\footnote{This is the massive gluon
propagator where the gluon running mass~\cite{Lavelle:1991}, $M(q^2)$, appears to be approximated by
its frozen value at vanishing momentum, $M(0)$. It should be also noted that, provided
that the gluon propagator is to be multiplicatively renormalized, the mass scale, $M=M(0)$,
does not depend on renormalization scale, $\mu^2$.} gluon propagator, that implies of course a
power law with $\alpha_G=1$, as the current lattice data seems to point to.
It is well-known that the low-momentum behaviour of the
integral $I(k^2)$ in \eq{LamInf} is dominated by the result of the integration over the IR domain,
over $q^2 < q_{0}^2$, and it can be expanded on $\delta^2 = p^2/k^2-1$ around zero with
the subtraction momentum $\mu^2$ kept fixed, as explained in
ref.~\cite{Boucaud:2008ky,Boucaud:2010gr}, to give
\begin{eqnarray}
I(k^2)  \ \simeq \  I_{\rm IR}(k^2)
&\simeq &
- \frac{\delta^2}{M^{2+2\alpha_F}} \frac{2 A(\mu^2) B(\mu^2)}{(2\pi)^3}
\nonumber \\
&\times& \sum_{i=0}^\infty \ (4 k^2)^i  C_i \ \displaystyle \int_0^{q_{0}} q^{3+2i+2\alpha_F} dq \
K_i(q^2;k^2,M^2) \ + \ {\cal O}(\delta^4)
\label{IRKi}
\end{eqnarray}
where
\begin{eqnarray} \label{Rser}
K_i(q^2;k^2,M^2) &=&   \frac {i} {(q^2+ k^2 + M^2)^{2i+1}} - \frac {i}
{(q^2+ k^2)^{2i+1}}  \nonumber \\
&&  \ + \ \ k^2 \left( \frac {2i+1} {(q^2+ k^2)^{2i+2}}
- \frac {2i+1} {(q^2+ k^2 + M^2)^{2i+2}} \right)
\end{eqnarray}
and
\begin{eqnarray}
C_i \ = \ \frac{12 \pi^2 4^{i}}{\Gamma(-3/2-i) \Gamma(1/2-i) \Gamma(5+2i)} \ .
\end{eqnarray}

Now, the two possible cases for the low-momentum behaviour of the
GPDSE solutions will be separately analyzed in the following by applying \eq{IRKi}
to \eq{SDRS}.

\subSection{Critical case: scaling solution}

When $\alpha_F < 0$, one can perform the change $t=q^2/k^2$ and integrate over $t$, the
integration in \eq{IRKi} for any term of \eq{Rser} being (one by one) convergent
as the limit $q_0^2/k^2 \to \infty$ is considered for the upper bound.
Thus, the small-momentum asymptotical behaviour of the r.h.s of \eq{SDRS}
is given by
\begin{eqnarray} \label{IRl0}
I_{\rm IR}(k^2)
&\simeq&
- \delta^2 \ \left(\frac{k^2}{M^2}\right)^{1+\alpha_F} \frac{2 A(\mu^2) B(\mu^2)}{(2\pi)^3}
 \sum_{i=0}^\infty \ 4^i  \frac{C_i} 2 \
\nonumber \\
&\times&
\left( - i \ \int_0^{\infty}dt \frac{t^{1+i+\alpha_F}}{(1+t)^{2i+1}}
\ + (2i+1) \
\int_0^{\infty}dt \frac{t^{1+i+\alpha_F}}{(1+t)^{2i+2}}
\right) \nonumber \\
&+& {\cal O}(\delta^4) \ ,
\end{eqnarray}
while its l.h.s. behaves as:
\begin{eqnarray}
\frac 1 {F_R(k^2)} - \frac 1 {F_R(p^2)} \ \simeq \
\delta^2 \frac{\alpha_F}{A(\mu)} \left( \frac{k^2}{M^2} \right)^{-\alpha_F}
\ + \ {\cal O}(\delta^4)
\end{eqnarray}
Then, we should conclude both
\begin{itemize}
\item[(i)] that $-\alpha_F = 1+\alpha_F \ \ \Rightarrow \ \ \alpha_F=-1/2 $,
\item[(ii)] and, given that
\begin{eqnarray}
\sum_{i=0}^\infty \ 4^i \ C_i \
\left( - i \ \int_0^{\infty}dt \frac{t^{\frac 1 2 +i}}{(1+t)^{2i+1}}
\ + (2i+1) \
\int_0^{\infty}dt \frac{t^{\frac 1 2 +i}}{(1+t)^{2i+2}}
\right) \ = \ \frac {2 \pi} 5 \ ,
\label{rela1}
\end{eqnarray}
one obtains
\begin{eqnarray} \label{crit-be}
N_C  g_R^2(\mu^2) H_1
A^2(\mu^2) B(\mu^2)
\simeq
10 \pi^2 \ .
\end{eqnarray}
\end{itemize}

Thus, we know the asymptotic behaviour for the ghost dressing function in this case
to be :
\begin{eqnarray}
F_R(q^2) \simeq
\frac {\pi}{g_R(\mu^2)}
\left(
\frac{10 }{N_C H_1 \Delta_R(0)}
\right)^{1/2}
\ \left(\frac 1 {q^2} \right)^{1/2}
\end{eqnarray}
This is a so-called scaling solution where, in particular, the low-momentum behavior of
the massive gluon propagator forces the ghost dressing function to diverge at low-momentum
through the requirement~\footnote{This is of course a particular case, with $\alpha_G=1$,
of the more general scaling condition: $2 \alpha_F + \alpha_G=0$.}
for the power exponent, $\alpha_F$, in (i).

If $\alpha_F>0$ is assumed, one would be also left with the contradictory scaling
condition that $\alpha_F=-1$\cite{Boucaud:2005ce,Boucaud:2008ky} and should conclude that no
solution exists for that case.

\subSection{Regular case: decoupling solution}

When $\alpha_F=0$, the previous ressumation cannot be done and
the integral $I(k^2)$ in \eq{LamInf} should be consistently expanded
in powers of $k^2$.
This case has been deeply studied in ref~\cite{Boucaud:2010gr}, where
it is found that

\begin{eqnarray}
I_{\rm IR}(k^2)
\ \simeq \
\delta^2 \ \frac{A(\mu^2) B(\mu^2)}{64\pi^2} \
\frac{k^2}{M^2} \
\left[ \ln{\frac{k^2}{M^2}} - \frac 5 6
\ + \ {\cal O}\left(\frac{M^2}{q_0^2}\right)
\right] \ + \
{\cal O}\left(\frac{k^4}{M^4},\delta^4\right) \ .
\label{demoF}
\end{eqnarray}

\noindent
Then, the ghost dressing  function, including its first correction to the
leading constant term, should behave as~\footnote{It should be also noted
that \eq{demoF} imples to take $M^2/q_0^2 \ll 1$. However,
any correction to that approximation will not play at the order of
the coefficient eqs.~(\ref{coefC2}), that will keep the same
value disregarding that of $M^2/q_0^2$, but at the order of the gluon
mass, $M^2$, inside the logarithm, presummably like the UV part of the
integral $I(k^2)$ that should be proportional to $k^2$ and
vanish at least like $1/\log{(q_0^2/\Lambda^2_{\rm QCD})}$)
when $q_0^2/\Lambda^2_{\rm QCD} \gg 1$.}

\begin{eqnarray} \label{solFIRJo}
F_R(q^2) = F_R(0) \left( 1 \ + \
\frac{N_C H_1}{16 \pi} \ \overline{\alpha}_T(0) \
\frac{q^2}{M^2} \left[ \ln{\frac{q^2}{M^2}} - \frac {11} 6 \right]
\ + \ {\cal O}\left(\frac{q^4}{M^4} \right) \right)
\end{eqnarray}

\noindent where

\begin{eqnarray} \label{coefC2}
\overline{\alpha}_T(0) = \lim_{q \to 0} \left(q^2 + M^2 \right) \frac{\alpha_T(q^2)}{q^2}
\ = \ M^2 \frac{g^2_R(\mu^2)}{4 \pi}
F_R^2(0) \Delta_R(0) ,
\end{eqnarray}
such that the \eq{SDRS} could be satisfied. It should again understood that
the subtraction momentum for all the renormalization quantities is $\mu^2$.
In \eq{coefC2}, $\alpha_T=g_T^2/(4\pi)$ is the perturbative strong coupling
defined in this Taylor scheme~\cite{Boucaud:2008gn}, while $\overline{\alpha}_T$
is the extension of the non-perturbative effective charge definition from
the gluon propagator~\cite{Aguilar:2008fh} to the Taylor
ghost-gluon coupling~\cite{Aguilar:2009nf}.
As a consequence of the appropriate {\it amputation} of a
massive gluon propagator, where the gluon mass scale is the same RI-invariant
mass scale appearing in \eq{gluonprop},
this Taylor effective charge is frozen at low-momentum and gives
a non-vanishing zero-momentum value in terms of which the ghost-dressing-function
subleading correction can be expressed.

\Section{Comparison with numerical results from coupled PT-BFM DSE's}
\label{comparing}

We shall now compare the formulas given by eqs.~(\ref{gluonprop},\ref{solFIRJo})
with some numerical results for the gluon propagator
and ghost dressing function. The aim of the comparison is twofold:
testing the asympotical solution we obtained in the previous section, but
also checking the consistency of a massive-gluon solution and determining
the gluon mass as the best-fit parameter in the comparison.
In particular, we will consider the solutions of the coupled system
of gluon and ghost DS equations obtained by applying the pinching technique
in the background field method (PT-BFM)~\cite{Binosi:2002ft}
(see also \cite{Binosi:2009qm} and references therein)
to compare with. This PT-BFM framework leaves us with an attractive model for gluon
and ghost propagators providing quantitative description of lattice
data~\cite{Aguilar:2008xm,Aguilar:2010gm} and giving well account of their main qualitative features:
finite gluon propagator and finite ghost dressing function at zero-momentum.
Futhermore, the coupled DSE system can be solved with different boundary
conditions (see below), the solutions compared with the analytical formula and
how their behaviour depends on these boundary conditions can be thus
properly studied. This last is the main purpose of this note.

The main feature in the PT-BFM scheme is that the transversality of the gluon self-energy
is guaranteed order-by-order in the dressed-loop expansion, this leading
to a gauge-invariant truncation of the gluon DSE~\cite{Binosi:2002ft}.
In this PT-BFM scheme for the coupled DSE system, the ghost propagator DSE
is the same as given by eqs.~(\ref{ghostSD},\ref{SDRS}), where the bare ghost-gluon
vertex is approximated by $H_1=1$. The gluon DSE is given by
\begin{eqnarray} \label{coupledDSE}
\frac{(1+G(q^2))^2}{\Delta(q^2)} \left( g_{\mu\nu} - \frac{q_\mu q_\nu}{q^2} \right) =
q^2 g_{\mu\nu} - q_\mu q_\nu + i \sum_{i=1}^4 \left( a_i \right)_{\mu\nu}
\end{eqnarray}
where
\begin{eqnarray} \label{gluondiags}
a_1 = \gluonSDi ,  & a_2 = \gluonSDii
\nonumber \\
a_3 = \rule[0cm]{0cm}{1.5cm} \gluonSDiii , & a_4= \gluonSDiv .
\end{eqnarray}
In the diagrams of (\ref{gluondiags}) for the gluon DSE, \eq{coupledDSE}, the external gluons
are treated, from the point of view of Feynman rules, as background fields
(these diagrams should be also properly regularized, as explained in \cite{Binosi:2009qm}).
The last justifies the four field coupling of two background gluons and two ghosts leading to
the contribution $a_4$. The function $1+G$ defined in ref.~\cite{Grassi:1999tp} can be,
in virtue of the ghost propagator DSE, connected to the ghost propagator~\cite{Aguilar:2009nf}.
The coupled system is to be solved, by numerical integration,
with the two following boundary conditions as the only required inputs:
the zero-momentum value of the gluon propagator and that of the coupling at
a given perturbative momentum, $\mu=10$ GeV, that will be used as
the renormalization point. The latter can be done by fixing
different values for the boundary conditions, this providing us
with a family of gluon and ghost propagators solutions so determined.
In particular, solutions obtained by keeping the zero-momentum value of the gluon propagator fixed
(see lefthand plots of fig.~\ref{fig:ghgl}) while $\alpha(\mu^2=100\mbox{\rm~GeV}^2)$ is ranging
from 0.15 to 0.1817 are available~\cite{Aguilar} and can be confronted to the asymptotical
expressions derived in the previous section.

\subSection{Decoupling solutions in the PT-BFM scheme}

Then, as the gluon propagator solutions in the PT-BFM scheme result to behave as massive ones,
the eqs.~(\ref{gluonprop},\ref{solFIRJo}) must account for the low-momentum behaviour of
both gluon propagator and ghost dressing function with $H_1=1$ and
\begin{eqnarray} \label{alphaT033}
\overline{\alpha}_T(0) = \alpha_T(\mu^2) F_R^2(0) B(\mu^2) \ = \
\alpha_T(\mu^2) F_R^2(0) M^2 \Delta_R(0) \ ,
\end{eqnarray}
$\alpha_T(\mu^2)=g_R^2(\mu^2)/(4\pi)$ being fixed, as a boundary condition, at the moment
of the numerical integration of the coupled DSE for each particular solution of the family.
$B(\mu^2)$ and $M$ being determined by the best fit of the \eq{gluonprop} to the numerical solution
for the gluon propagator, we shall be left with one only free parameter,
$F_R(0)$, to account with \eq{solFIRJo} for the numerical solution
for the ghost propagator.
Furthermore, the zero-momentum values of the ghost dressing function, $F_R(0)$, can be also
taken from the numerical integration of the DSE (for any value of the
$\alpha(\mu=10 \mbox{\rm GeV})$); and these altoghether with the zero-momentum values of the
gluon propagator, $\Delta_R(0)$, and the gluon masses, obtained by the fit of \eq{gluonprop} to the
numerical DSE gluon propatator solutions, provide us with all the ingredients
to evaluate, with no unknown parameter, \eq{solFIRJo}.
The gluon masses obtained from the best fits of \eq{gluonprop} to the numerical data (see
the left plots in fig.~\ref{fig:ghgl}) and that of zero-momentum Taylor effective charge,
$\overline{\alpha}_T(0)$, computed by applying \eq{alphaT033}, with
the zero-momentum ghost dressing function taken from numerical data,
can be found in tab. \ref{tab-fits}.

\begin{figure}[hbt!]
\begin{center}
\begin{tabular}{cc}
\includegraphics[width=7cm]{FIGS/gluon015.eps} &
\includegraphics[width=7cm]{FIGS/ghost015-newF.eps} \\
\includegraphics[width=7cm]{FIGS/gluon016.eps} &
\includegraphics[width=7cm]{FIGS/ghost016-newF.eps} \\
\includegraphics[width=7cm]{FIGS/gluon017.eps} &
\includegraphics[width=7cm]{FIGS/ghost017-newF.eps} \\
\end{tabular}
\end{center}
\caption{\small Gluon propagators (left) and ghost dressing functions (right) after the numerical integration of
the coupled DSE system for $\alpha(\mu=10 \mbox{\rm GeV})=0.15,0.16,0.17$ taken from \cite{Aguilar} . The curves
for the best fit of \eq{gluonprop} to the gluon propagator data appear as dotted lines in the lefthand plots.
In the righthand plots, the red dotted lines correspond to apply \eq{solFIRJo} with the gluon mass obtained
from the gluon fits and with $R=\overline{\alpha}_T(0)/M^2$ determined by the zero-momentum values of
gluon propagator and ghost dressing function coming from the numerical integration of the DSE system; the
same for the black dotted lines but retaining only the logarithmic leading term in \eq{solFIRJo}
by dropping the $-11/6$ away.}
\label{fig:ghgl}
\end{figure}

Indeed, the expression given by \eq{solFIRJo} can be succesfully
applied to describe the solutions all over the range of coupling values,
$\alpha(\mu)$, at $\mu=10$ GeV. This can be seen, for instance, for $\alpha=0.15,0.16,0.17$,
in the right plots of fig.~\ref{fig:ghgl}, where the ghost dressing functions
obtained from the numerical integration of the DSE's appear plotted with black-solid
lines and the evaluation of \eq{solFIRJo}, as we explained above, with red-dotted ones.
Thus, {\it with no parameter to be fitted ($F_R(0)$ is taken from the numerical integration),
we nicely reproduce the low-momentum behaviour of the ghost dressing function obtained
through numerical integration}.

In the right plots of fig.~\ref{fig:ghgl}, black-dotted curves obtained by only retaining
the logarithmic leading order in \eq{solFIRJo} appear also drawn. The big discrepancy they
show with respect to the numerical integration clearly implies the necessity of the
next-to-leading correction in \eq{solFIRJo} when assessing the gluon mass from the
low-momentum ghost propagator.

\begin{table}
\begin{center}
\begin{tabular}{|c||c|c|}
\hline
\rule[0cm]{0cm}{0.5cm} $\alpha(\mu)$ & $\overline{\alpha}_T(0)$ & $M$ (GeV) [gluon] \\
\hline
\hline
0.15 & 0.24 & 0.37
\\
\hline
0.16 & 0.30 & 0.39 \\
\hline
0.17 & 0.41 & 0.43 \\
\hline
\end{tabular}
\end{center}
\caption{\small Gluon masses and the zero-momentum non-perturbative effective
charges, obtained as explained in the text, which are applied to describe
the gluon propagator and the ghost dressing function numerical data with
eqs.~(\ref{gluonprop},\ref{solFIRJo}).}
\label{tab-fits}
\end{table}

\subsection{The ``critical'' limit in the PT-BFM scheme}

There appears to be a {\it critical} value of the coupling,
$\alpha_{\rm crit}=\alpha(\mu^2)\simeq 0.182$ with $\mu=10\mbox{\rm ~Gev}$,
above which the coupled DSE system does not converge any longer to a solution~\cite{Aguilar}.
As a matter of the fact, we know from \eq{crit-be} that
the scaling solution implies for the coupling
\begin{eqnarray} \label{ap:crit}
g^2_{\rm crit} \ = \ g_R^2(\mu^2)
\simeq
\frac{10 \pi^2}{3 A^2(\mu^2) B(\mu^2) } \ ,
\end{eqnarray}
where $B(\mu^2)$ is determined by the gluon propagator solution that is supposed to
behave as \eq{gluonprop}, and $A(\mu^2)$ by the ghost propagator that should behave
as
\begin{eqnarray} \label{ap:crit2}
F_R(q^2) \ = \ A(\mu^2) \left(\frac{M^2}{q^2}\right)^{1/2} \ ,
\end{eqnarray}
where again $\mu^2$ is the momentum at the subtraction point.
This is shown in ref.~\cite{Boucaud:2008ji}, where only the ghost propagator
DSE is solved there after extracting a gluon propagator from the lattice data
and applying it to build the kernel of the integral, \eq{LamInf}, appearing in
\eq{SDRS}. In the analysis of ref.~\cite{Boucaud:2008ji}, a ghost dressing
function solution diverging at vanishing momentum appears to exist and
verifies eqs.~(\ref{ap:crit},\ref{ap:crit2}),
while regular or decoupling solutions exist for any $\alpha < \alpha_{\rm crit}$.

Now, we can perform a more complete analysis by studying again the
dressing function computed by solving \eq{coupledDSE} for
the different values of the coupling, $\alpha=\alpha(\mu^2)$, at $\mu^2=100$
GeV$^2$~\cite{Aguilar}.
A ghost dressing function at vanishing momentum, $F(0,\mu^2)$,
diverging as $\alpha \to \alpha_{\rm crit}$ had to be expected, one could
try the following power behaviour,
\begin{eqnarray}
F(0) \ \sim \ (\alpha_{\rm crit} - \alpha(\mu^2))^{- \kappa(\mu^2)} \ ,
\end{eqnarray}
to describe the vanishing-momentum ghost dressing function in terms of
the coupling, $\alpha(\mu^2)$. The coefficient $\kappa(\mu^2)$ should be the
positive critical exponent (depending presummably on the
renormalization point, $\mu^2$) governing the transition from decoupling
($\alpha < \alpha_{\rm crit}$) to the scaling ($\alpha = \alpha_{\rm crit}$)
solutions.

Our strategy will be to let $\alpha_{\rm crit}$ be a free parameter to be fitted
by requiring the best linear correlation for $\log[F(0)]$ in terms of
$\log[\alpha_{\rm crit}-\alpha]$. In doing so, the best correlation
coefficient is 0.9997 for $\alpha_{\rm crit}=0.1822$, which is pretty close to
the critical value of the coupling above which the coupled DSE system does not converge
any more, and then we obtain
\begin{eqnarray}
\kappa(\mu^2) = 0.0854(6) \ .
\end{eqnarray}

\vspace{0.9cm}
\begin{figure}[!hbt]
\begin{center}
\begin{tabular}{cc}
\includegraphics[width=7.5cm]{FIGS/ghost0-F-0.1822.eps}
&
\includegraphics[width=7.5cm]{FIGS/CritGluons.eps}
\\
(a) & (b)
\end{tabular}
\end{center}
\caption{\small (a) Log-log plot of the zero-momentum values of the ghost dressing function, obtained
by the numerical integration of the coupled DSE system in the PT-BFM scheme, in terms of
$\alpha_{\rm crit}-\alpha$. $\alpha=\alpha(\mu=10 \mbox{\rm GeV})$,
the value of the coupling at the renormalization momentum, is an initial condition for
the integration; while $\alpha_{\rm crit}$ is fixed to be 0.1822, as explained in the text,
by requiring the best linear correlation.
(b) Gluon propagator solutions
in terms of $q^2$ for the same coupled DSE system for different values of $\alpha(\mu=10 \mbox{\rm GeV})$,
all very close to the critical value, ranging from 0.18 to 0.1817~.}
\label{fig:ghost0s}
\end{figure}

In fig.~\ref{fig:ghost0s}.(a), the log-log plot of $F_R(0)$ in terms of
$\alpha_{\rm crit}-\alpha$ is shown for $\alpha_{\rm crit}=0.1822$, where
the linear behaviour corresponding to the best correlation coefficient
can be strikingly seen and the negative slope indicates a zero-momentum ghost propagator diverging
as $\alpha \to \alpha_{\rm crit}$. However, {\it no critical or scaling solution of the
coupled DSE system seems to appear with a massive gluon propagator as solution of the coupled
DSE system in the PT-BFM, although the decoupling solutions obtained for any
$\alpha < \alpha_{\rm crit} = 0.1822$
seem to approach the behaviour of a scaling one when $\alpha \to \alpha_{\rm crit}$}.
The absence of the scaling solution can be well understood by analysing \eq{coupledDSE}.
As explained in \cite{Aguilar:2008xm},
after the appropriate regularization and renormalization, the contribution of
$a_3$ to the inverse of the gluon propagator, its momentum vanishing, will be
dominated by~\footnote{The regularisation procedure in \cite{Aguilar:2008xm} implies the
subtraction of the perturbative part, as well as we evaluate \eq{SDRS} for
two different scales and subtract them in order not to have to deal with any
UV cut-off in \eq{SDRS}.}
\begin{eqnarray}
a_3 \rightarrow \int_0^{q_0} d(q^2) \left( F^2(q^2) - 1 \right) \ ,
\end{eqnarray}
where $q_0$ is again some UV cut-off above which the ghost dressing function
can be taken to be perturbative. Provided that one deals with a decoupling solution,
the ghost dressing function reaching some constant as $q^2 \to 0$, this contribution
is finite and negligible (the same happens for $a_4$). On the other hand, had we
considered the scaling solution, the ghost dressing function would behave as $1/q$
and would lead to a divergent contribution and to a vanishing gluon propagator at
vanishing momentum. Then, a massive gluon propagator, as lattice solutions points to and as
required in ref.~\cite{Aguilar:2008xm,Aguilar}, cannot appear as a scaling solution.
The same has been already proven in literature by applying different truncation schemes and also
on general grounds, and indeed agrees with the very well-known infrared behaviour
obtained from the coupled DSE system in refs.~\cite{Alkofer:2000wg,Fischer:2008uz},
where an unique scaling solution with $\alpha_F\simeq - 0.595$ and $\alpha_G=-2 \alpha_F \simeq 1.190$
emerges, the gluon propagator vanishing thus at zero-momentum,
as the inverse of the zero-momentum ghost dressing is assumed to vanish.
However, for the sake of completeness, a very general argumentation addressing this
issue is presented in appendix \ref{C}.
We should recall at this point that the numerical analysis of the ghost propagator
DSE in ref.~\cite{Boucaud:2008ji} left us with a divergent ghost dressing function for
the critical value of the coupling, even after assuming a finite gluon propagator at zero
momentum. However, this resulted from a partial analysis where we dealt only with
the ghost propagator DSE and not with the gluon propagator one.
Thus, we did not solve the gluon DSE and taking a massive gluon propagator from the
lattice to build the ghost-DSE kernel does not
prevent from obtaining a ``{\it wrong}'' scaling solution indeed not satisfying the coupled
DSE system.

When approaching the critical value of the coupling, the gluon propagators obtained
from the coupled DSE system in PT-BFM must be also thought to obey the
same critical behaviour pattern as the ghost propagator.
In the PT-BFM, the value at zero-momentum being
fixed by construction~\cite{Aguilar:2008xm,Aguilar}, one should expect that,
instead of decreasing, the
gluon propagator obtained for couplings near to the critical value increases for low momenta:
the more one approaches the critical coupling the more it has to increase.
This is indeed the case, as can be seen in fig.~\ref{fig:ghost0s}(b).
This implies that, near the critical value, the low momentum propagator does not
obey \eq{gluonprop} and that consequently \eq{solFIRJo} does not work any longer to
describe the low momentum ghost propagator\footnote{This is only true for the
next-to-leading contribution of \eq{solFIRJo}, the leading one being
only determined by the zero-momentum gluon propagator still works.}.

Finally, one can pay attention to the critical value of the coupling, $\alpha_{\rm crit}=0.1822$,
and try to make a comparison with the physical strong coupling values in order get some idea of
whether the current data can exclude or not this critical behaviour. Although the experimental PDG {\it world
average} of the strong coupling in the $\overline{\rm MS}$ scheme, $\alpha_{\overline{\rm MS}}(M_Z)=0.1184(7)$~\cite{PDG},
can be propagated from the $Z^0$ boson mass down to $\mu=10$ GeV
to give $\alpha_{\overline{\rm MS}}(10 \ {\rm GeV})=0.179(2)$, that
incidentally lies on the right ballpark of the above critical value, such a comparison
is meaningless because our coupling corresponds to one in MOM Taylor-scheme for
zero number of flavours. One can use instead the available perturbative four-loop formula describing
the running of the coupling in Taylor-scheme to estimate $\Lambda_{\rm QCD}$ in this particular scheme,
then perform the conversion to $\overline{\rm MS}$ (see for instance eqs.(22,23)
of the first reference in~\cite{Boucaud:2008gn}) and thus obtain the value quoted in tab.~\ref{tabLambda}.
Of course, it would be again meaningless to compare this last value with the one
for $\Lambda_{\overline{\rm MS}}$ that can be
obtained from the PDG value for $\alpha_{\overline{\rm MS}}(M_Z)$, also quoted in tab.~\ref{tabLambda},
but we can refer the comparison to the lattice Yang-Mills determinations of the same parameter\footnote{It should
be noted that the procedures for the lattice determination of $\Lambda_{\overline{\rm MS}}$ mainly work in
the UV domain, where IR sources of uncertainties as the Gribov ambiguity or volume effects are indeed negligible.
In fact, there are unquenched lattice determinations with $N_f=5$ staggered fermions for the strong
coupling~\cite{Davies:2008sw} which
are pretty consistent with the PDG value.}, as for instance the two of them included in tab.~\ref{tabLambda}.
Thus, the lattice estimates of
$\Lambda_{\overline{\rm MS}}$ appear to lie clearly below this critical limit for the PT-BFM DSE
in pure Yang-Mills. However, as no quark flavour loops effect have been incorporated in our
DSE, \eq{coupledDSE}, we cannot neither compare with the physical strong coupling nor conclude
whether the critical limit can be allowed in the ``{\it real world}''.

\begin{table}[htb!]
\begin{center}
\begin{tabular}{|c|c|c|c|}
\hline
$\Lambda_{\overline{\rm MS},{\rm crit}}^{N_f=0}$
&
$\Lambda_{\overline{\rm MS}}^{N_f=0}$~\cite{Luscher:1993gh}
&
$\Lambda_{\overline{\rm MS}}^{N_f=0}$~\cite{Boucaud:2008gn}
&
$\Lambda_{\overline{\rm MS}}^{N_f=5}$~\cite{PDG}
\\
\hline
434 MeV & 238(19) MeV & 244(8) MeV & 213(9) MeV \\
\hline
\end{tabular}
\end{center}
\label{tabLambda}
\caption{\small The critical value of $\Lambda_{\overline{\rm MS}}$ in pure Yang-Mills inferred
from $\alpha_{\rm crit}=0.1822$ (first column), lattice estimates for Yang-Mills $\Lambda_{\overline{\rm MS}}$
taken from literature (second and third columns) and the one obtained from the PDG value
of $\alpha_{\overline{\rm MS}}(M_Z)$ by applying a four-loop perturbative formula for the running of
$\alpha_{\overline{\rm MS}}$ with $N_f=5$.}
\end{table}

\vspace*{1cm}

\Section{Conclusions}\label{conclu}

The ghost propagator DSE, with the only assumption of taking $H_1(q,k)$ from the
ghost-gluon vertex in \eq{DefH12} to be constant in the infrared domain of $q$, can be
exploited to look into the low-momentum behaviour of the ghost propagator.  The
two classes of solutions named ``decoupling'' and ``scaling'' can be indentified and
shown to depend on whether the ghost dressing function achieves a finite non-zero
constant ($\alpha_F=0$) at vanishing momentum or not ($\alpha_F \neq 0$). The
solutions appear to be dialed by the size of the coupling at the renormalization
momentum which plays the role of a boundary condition for the DSE integration.
The low-momentum behaviour of the decoupling solutions results to be regulated by the
gluon propagator mass and by a regularization-independent
dimensionless quantity that appears to be the effective charge defined from
the Taylor-scheme ghost-gluon vertex at zero momentum.

In this note, we have studied the solutions of coupled ghost and gluon propagator DSE in
the PT-BFM scheme
and demonstrated that the asymptotic decoupling formula ($\alpha_F=0$)
successfully describes the low-momentum ghost propagator.
The model applied for the massive gluon propagator is also verified to give properly account
of the gluon solution, at least for momenta below 1 GeV (and for a coupling
not very close to the critical point).
Although we argued that a massive gluon propagator implies that the ghost dressing
function takes a non-zero finite value at vanishing momentum,
we also show that the zero-momentum ghost dressing function
tends to diverge when the value of the coupling dialing the solutions
approaches some critical value. Such a divergent behaviour at the critical coupling
seems to be the expected one for a scaling solution (where, if the gluon
is massive, $\alpha_F=-1/2$). If we consider the zero-momentum value of the ghost
dressing function as some sort of ``{\it order parameter}'' indicating whether the
ghost propagator low-momentum behaviour is suppressed ($\alpha_F=0$ and finite ghost
dressing function) or it is enhanced ($\alpha_F<0$ and divergent ghost dressing
function), the strength of the coupling computed at some renormalization point
seems to control some sort of transition from the {\it suppressed} to
the {\it enhanced} phases for the ghost propagator DSE solutions in the PT-BFM scheme.
The last only takes place as some critical value of the coupling is reached.
Neverteless, it can be proven that, as far as the gluon is massive,
the scaling behaviour for the Yang-Mills propagators appear not to be a
solution but an unattainable limiting case for the PT-BFM DSE solutions.

\bigskip

{\bf Acknowledgements:}
The author is particularly indebted to Ph.~Boucaud, J.P~Leroy, A.~Le~Yaouanc, J.~Micheli and
O.~P\`ene for very fruitful discussions at the initial stages of the work and to
J.~Papavassiliou and A.C.~Aguilar also for very valuable discussions and comments, and
specially for providing me with some unpublished results
which were exploited in this paper. J. R-Q also acknowledges the Spanish MICINN for the
support by the research project FPA2009-10773 and ``Junta de Andalucia'' by P07FQM02962.

redpajama_set_name: RedPajamaArXiv


text:
Become a Mentor with The Girls Network
University of Portsmouth CCI Staff and Alumni are being offered the incredible opportunity to become a mentor, with The Girls Network.
The Girls Network is a non profit organisation, working to inspire, and empower girls from the least advantaged communities, by connecting them with a mentor, and a network of professional female role models.
The Girls Network is already filled with dedicated women, giving their time and support, helping to enable the next generation of young women, across the South West of England, to thrive.
After three years, The Girls Network is now in demand from schools, and in order to reach this growing demand, The Girls Network are looking for new female mentors, to help inspire, empower, and support local young women.
If you have been in work for over three years, and are willing to give a minimum of just one hour a month to support local young women, this could be the ideal opportunity for you.
Becoming a mentor with The Girls Network is an incredible opportunity for you to give your time and support, something that may seem small to you, but could prove invaluable to a young woman.
To find out more about The Girls Network, you can visit their website, and follow them on Facebook @TheGirlsNetwork, Twitter @TheGirlsNet, and Instagram @TheGirlsNetwork.
If you are interested in becoming a mentor, you can fill out this application form.
Tags #opportunityalumniHelpmenteementorMentor systemportsmouthRole modelsschoolStaffsupportThe Girls' Network
CCI Student looking for help from Asthma Sufferers
Amara Competition open to CCI Students
Alison Rowsell
Would be happy to mentor someone. I work full time as a research fellow at Southampton university and have just completed a PhD in psychology at Southampton.

redpajama_set_name: RedPajamaCommonCrawl


PVC flexible strip doors are transparent bulkheads that separate two workspaces. They consist of transparent plastic strips (voids) made of polyvinyl chloride, which are attached to an inoxin bracket that is placed on the opening of the space to be separated. PVC bar curtains have rounded edges, enabling undisturbed passing without injury. The basic purpose is to make industrial halls and warehouses safer, less noisy and more energy-efficient place.
Where to apply flexible industrial PVC curtains?
PVC bar Curtains or more commonly referred to as PVC strip curtains are a very suitable solution for refrigerated, supermarkets, plants in factories, warehouses and distributive centres.
Openings for rail deliveries etc.
How to order PVC strip doors?
In order to maximise the PVC door, it is necessary to correctly select the dimension of PVC strips taking into account the height of the aperture and the degree of overlap.
What are the main advantages of using industrial PVC doors?
Bar curtains are a practical and profitable alternative to complex and expensive bulkhead rocks.
The main flaw of using plastic bar curtains is not a disadvantage in the true sense of the word but its characteristic. Namely, although they are called PVC strip doors, it is not possible to lock them classically.
The product is delivered as a finished system ready for installation and use. The system is fitted with PVC bar curtains and brackets made of stainless steel. The unique design of these elements allows for a quick return of an industrial strip curtain to its original position.
Place the stainless steel bracket to the opening (on the front of the wall beam or below).
Note: If you are setting the bracket to the front of the beam, it should correspond to the width of the opening width, and if placed under the beam, it is necessary to ensure that the sidebar can be moved undisturbed during transit.
When you mark the position of the holes, fasten the mounting bracket to the screws and place the PVC strips on it. Unlike the mounting bracket that is placed on the front of the wall beam, the stainless steel bracket that is placed below should be cut to the required dimension in order to fit into the opening and fit the width of the passage.
When placing the mounting bracket on the front side of the beam, the curtains should be wider than the openings to fill the space between the neck and wall edges and ensure maximum protection.
The edges of the bracket (which are longer than the openings) are useful as places where you will place all the strips, if during the summer months you decide to temporarily remove the door.
Avoid the use of solvents.


text:
SEASON TICKETS JUST £25 FOR UNDER-12S!
Our £25 season tickets for Under-12s proved hugely popular in 2014/15 and there's good news - they're back for 2015/16!
We saw record season ticket sales last season as we embarked on our vision of bringing new faces to Stevenage FC by focusing on the next generation of Stevenage fans and their families. Our special offer saw our youngest supporters receive a terrace or seated season ticket and a Boro polo shirt for just £25, allowing them to watch Football League action at The Lamex for little more than £1 a game and look the part too!
It's just one of the many reasons we were one of just six clubs across the Football League to be nominated for the prestigious Family Club of the Year award at the Football League Awards - a ceremony where we were crowned League 2 Family Club of the Year!
As well as this Under-12 offer continuing, the Under-16, Under-19 and Under-22 categories have also remained to ensure fans of all young ages can once again be part of the Stevenage experience.
Season ticket applications continue to fly in as Stevenage fans pledge their support for 2015/16. Remember there's just 10 days left before the first season ticket deadline, where anyone purchasing by Friday 29th May receives a free entry voucher for one pre-season friendly.
For the full information on prices, the many season ticket holder benefits, the different ways to apply, payment options (including how to pay in monthly instalments) and to discover how you can win back your money, take a look at our Season Ticket Brochure HERE or click on the image below.


I was recently on a video conference call with three other young women, two lawyers and a biologist. The participants were located in Seoul, Miami, Orlando, and Ames. After concluding business, we just started chatting. Before long the topic landed on isolation. We were all feeling isolated, without a support system or friends near by.
After graduating from KU I moved to a suburb of Salt Lake City for a job. This job was exactly what I wanted to be doing. Yet, a few months before I graduated I started to get nervous. I was moving to a new place, that I had only visited once for the interview and booked with ShortNoticeMovers.net right away. I had no family and no friends there. The company wasn't that big and, as far as I knew, I was the only new graduate hire. Some of my peers who went to work for large companies that hired many people right out of college were lumped into a "New Recruit" pool in which they made friends. I knew that wasn't an option for me. There were a few young, single people like me at the company, but they were all men. I found out, after I had been working there for a year, that they had regular camping trips, but I was never invited.
I decided, before I moved, that I was going to become active in organizations with values that I could support. Society of Women Engineers (SWE) was a life-saver for me. We were a small group of women from many different backgrounds and of varying ages. We had social events and volunteering events. Mostly, these women were just my friends. In engineering academia, professional organizations are mostly about working on projects for competitions and publishing papers. SWE does hardly any of that. Men often see SWE as a joke or as a chance for free food. For many women in engineering, SWE is a support system. I was able to score affordable long distance movers trhough contacts I made there. Whenever I have started in a new location, SWE has been there.
I am no longer surprised to be only woman in the room, but I am still bothered by this reality. This is my eighth year in college. I had only two women professors in engineering, the last taught in my sophomore year. This is the first time I have been at a school where there is, in my department, a woman faculty member. She isn't in my specialization, but she is in the department. I have found many men who are my allies, kind guys who have become close friends, but SWE has given me friends, women, peers with experiences similar to my own.
Even here at Geek Feminism there seems to be people searching for community. We are coming together for a sense of shared experience. So I am giving some unsolicited advice, much like I did on that conference call. If you are feeling isolated, find an organization with a purpose you can support. Attend, volunteer, get involved.
This entry was posted in Uncategorized and tagged community, engineering, guest post on 2011/10/27 by elizabethggf.
Thanks! You've prompted me to see what similar organizations my university has.
Might the size of the university make a difference? I did my PhD at one of the smallest universities in the country, and there just weren't enough postgrads (in total numbers) to make much of a community, so even though I'm from the majority demographic for CS postgrads, I felt quite isolated… apply that effect outside the majority, and I guess it might be worth preferring larger universities when applying for PhD places. Or does that bring some other kind of problem?


text:
We All Deserve to be Healthy
Amanda's Journey to Health
Changing her life, inspiring others.
By Anna Fritz, Health and Wellness
Amanda Davies made a decision to overcome obesity after tipping the scales at 270 pounds. Today she's down 75 pounds and has energy like never before. She's sharing her story in the hope that she'll inspire others. Follow Davies' journey through a series of blog posts over the next few months.
Like anyone who's faced a serious health challenge, Amanda Davies found that changing a lifetime of habits isn't easy. But she drew inspiration each time she reached a goal, and experienced a real sense of freedom by letting go of a heavy burden.
Davies faced the challenge of obesity by committing every day to exercise, a nutritious diet, and a healthy mind-set. "I had to change everything about myself," she said. "I took it meal by meal, workout by workout."
At a weight of 270 pounds, Davies didn't feel good physically or emotionally. But it took her "Know Your Numbers" health insurance screening to inspire her to change her entire lifestyle. As the spouse of a St. Luke's employee, she can lower her insurance premiums by achieving fitness goals regarding blood pressure, blood sugar, tobacco use, and BMI (body mass index).
"I was designated 'morbidly obese' at my 'Know Your Numbers' screening last February," she said. "I hated that. I wanted my next measurement to show changes. Little did I know I would be down 75 pounds!"
Her screening also showed issues with insulin resistance, cholesterol, and blood pressure. She's reversed those numbers as well, and dramatically lowered her risk for heart attack, stroke, diabetes, dementia, cancer, and other serious diseases.
Davies began her transformation in February 2015. Just nine months later, her numbers paint an incredible picture:
75 pounds lost
Triglycerides down from 221 to 55
Total cholesterol down from 164 to 123
15 inches off her waist, 10 off her hips, and seven off her chest
Clothing size down from 24 to 14
"Amanda has been successful because her goals are reasonable," said Angela Latta, Davies' OB-GYN nurse practitioner. "She focuses on consistency, healthy foods, portion control, regular exercise, and positive self-talk to achieve long-term changes in her habits and lifestyle. She didn't start out with grand, overwhelming plans—which are usually destined to fail."
Davies' St. Luke's family doctor had long encouraged her lifestyle changes, as had the team at her OB-GYN office. But even with their support, she knew the strength to change had to come from within.
"Amanda's success began because in her mind she believed she could transform herself and feel better again," Latta said. "She never quit believing."
"I knew no one could fix this but me," Davies said. "I had to save my own life."
"Amanda has a beautiful story of success, teaching us all the power of self-belief and just how far it can take us," Latta said. "She's an inspiration to us all, but especially those who harbor self-doubt. That's not something you can get from a healthcare provider."
Along her journey, Davies has been teaching positive habits to her family and getting creative with making recipes healthier. She also shares recipes, tips, and stories on her motivational Facebook page, "Fit and Fabulousness," as well as her blog, to engage with readers in ways that are helpful, healing, and fun.
"Changing my habits changed my life," Davies said. "It's been a gift, and I want to encourage others. We all deserve to be healthy."
Anna Fritz
Anna Fritz is a writer and editor with St. Luke's Communications and Marketing.
Spreading a Positive Message
From a Single Step to a 10K
Creating Nutritious, Delicious Food


The ESVL9 Proportional Solenoid Cartridge Valve is designed to integrate external check valve within the main cartridge. The units allow customers to optimize flow forces and improve metering of flow to the spool. The valve is tested in over 30 design cases with full computational fluid dynamics (CFD) analysis. It uses two springs for increased functionality to control metering of the spool.
Modular Molded Manifold Valves offer broad chemical compatibility.
Solenoid Valve offers single-acting cylinder control.
Cartridge Valve handles pressures up to 15,000 psi.
Rugged Cartridge Valve offers extended service life and uptime.
High-Flow 2- and 3-Way Poppet Valves include cartridge style.
Toggle and Stem Valves have bright dipped brass construction.
Multi-Gun Valve operates at up to 24,000 psi.


text:
Q: volttron multiple platform connection tutorial Hi I am trying to go through this tutorial getting one data collector instance of Volttron (rasp pi) integrated to a volttron central instance (Ubuntu) on a LAN using ZMQ. But the rasp pi doesnt appear to be talking to the volttron central instance.
This is the configuration of the "central" instance on IP address 192.168.0.191:
(volttron) (base) bartlino@bartlino-Latitude-E5530-non-vPro:~/Desktop/volttron$ vcfg

Your VOLTTRON_HOME currently set to: /home/bartlino/.volttron

Is this the volttron you are attempting to setup? [Y]:
What type of message bus (rmq/zmq)? [zmq]: zmq
What is the vip address? [tcp://192.168.0.191]:
What is the port for the vip address? [22916]:
Is this instance web enabled? [N]: Y
What is the protocol for this instance? [https]:
Web address set to: https://bartlino-latitude-e5530-non-vpro
What is the port for this instance? [8443]:

The following certificate and keyfile exists for web access over https:
/home/bartlino/.volttron/certificates/certs/master_web-server.crt
/home/bartlino/.volttron/certificates/private/master_web-server.pem

Do you want to use these certificates for the web server? [Y]:
Is this an instance of volttron central? [N]: Y
Configuring /home/bartlino/Desktop/volttron/services/core/VolttronCentral.
Installing volttron central.
['volttron', '-vv', '-l', '/home/bartlino/.volttron/volttron.cfg.log']
Should the agent autostart? [N]: Y
VC admin and password are set up using the admin web interface.
After starting VOLTTRON, please go to https://bartlino-latitude-e5530-non-vpro:8443/admin/login.html to complete the setup.
Will this instance be controlled by volttron central? [Y]:
Configuring /home/bartlino/Desktop/volttron/services/core/VolttronCentralPlatform.
What is the name of this instance? [bartlino]:
Volttron central address set to https://bartlino-latitude-e5530-non-vpro:8443
['volttron', '-vv', '-l', '/home/bartlino/.volttron/volttron.cfg.log']
Should the agent autostart? [N]: Y
Would you like to install a platform historian? [N]: Y
Configuring /home/bartlino/Desktop/volttron/services/core/SQLHistorian.
['volttron', '-vv', '-l', '/home/bartlino/.volttron/volttron.cfg.log']
Should the agent autostart? [N]: Y
Would you like to install a master driver? [N]:
Would you like to install a listener agent? [N]: Y
Configuring examples/ListenerAgent.
['volttron', '-vv', '-l', '/home/bartlino/.volttron/volttron.cfg.log']
Should the agent autostart? [N]: Y
Finished configuration!

You can now start the volttron instance.

If you need to change the instance configuration you can edit
the config file is at /home/bartlino/.volttron/config

(volttron) (base) bartlino@bartlino-Latitude-E5530-non-vPro:~/Desktop/volttron$

vctl status
(volttron) (base) bartlino@bartlino-Latitude-E5530-non-vPro:~/Desktop/volttron$ vctl start --tag vcp
(volttron) (base) bartlino@bartlino-Latitude-E5530-non-vPro:~/Desktop/volttron$ vctl status
  AGENT                    IDENTITY            TAG                STATUS          HEALTH
0 listeneragent-3.3        listeneragent-3.3_1 listener           running [9827]  GOOD
a master_driveragent-4.0   platform.driver     master_driver      running [9826]  GOOD
b sqlhistorianagent-3.7.0  platform.historian  platform_historian running [9825]  GOOD
c vcplatformagent-4.8      platform.agent      vcp                running [9824]  GOOD
d volttroncentralagent-5.2 volttron.central    vc                 running [9822]  GOOD
(volttron) (base) bartlino@bartlino-Latitude-E5530-non-vPro:~/Desktop/volttron$

The Rasp Pi on IP address 192.168.0.102:
(volttron) pi@raspberrypi:~/volttron $ vcfg

Your VOLTTRON_HOME currently set to: /home/pi/.volttron

Is this the volttron you are attempting to setup? [Y]:
What type of message bus (rmq/zmq)? [zmq]:
What is the vip address? [tcp://192.168.0.102]: tcp://127.0.0.1
What is the port for the vip address? [22916]:
Is this instance web enabled? [N]:
Will this instance be controlled by volttron central? [Y]:
Configuring /home/pi/volttron/services/core/VolttronCentralPlatform.
What is the name of this instance? [raspberrypi]:
What is the hostname for volttron central? [https://bartlino-latitude-e5530-non-vpro]:
What is the port for volttron central? [8443]:
['volttron', '-vv', '-l', '/home/pi/.volttron/volttron.cfg.log']
Should the agent autostart? [N]:
Would you like to install a platform historian? [N]:
Would you like to install a master driver? [N]: Y
Configuring /home/pi/volttron/services/core/MasterDriverAgent.
['volttron', '-vv', '-l', '/home/pi/.volttron/volttron.cfg.log']
Would you like to install a fake device on the master driver? [N]:
Should the agent autostart? [N]:
Would you like to install a listener agent? [N]:
Finished configuration!

You can now start the volttron instance.

If you need to change the instance configuration you can edit
the config file is at /home/pi/.volttron/config

vctl status on the pi:
(volttron) pi@raspberrypi:~/volttron $ vctl status
   AGENT                   IDENTITY              TAG                STATUS          HEALTH
44 bacnet_proxyagent-0.5   platform.bacnet_proxy proxy              running [1581]  GOOD
f3 listeneragent-3.3       listeneragent-3.3_1   listener
13 master_driveragent-4.0  platform.driver       master_driver
4f sqlhistorianagent-3.7.0 platform.historian    platform_historian 0
79 vcplatformagent-4.8     platform.agent        vcp                running [1606]  GOOD

The tutorial is stating at this point on the "central" instance I should see ZMQ certificates to accept but I have none. Any tips greatly appreciated!

redpajama_set_name: RedPajamaStackExchange


Home / Featured / Braves to avenge loss to Prisons tonight?
Braves to avenge loss to Prisons tonight?
Braves of Customs will be in action later today at the Lebanon House Court in Tudu in the CAP 7 Memorial Basketball Tournament.
The team takes on Reformers of Prisons in the competition put together in honour of former Accra Basketball League (ABL) Chairman Benjamin Baafi.
Baafi doubled as Braves Manager and Manager of several Ghana National Teams prior to his death last year. The competition tipped off on September 14 and runs to September 22.
The game is the only fixture in the Women's Division among the quartet of games scheduled to be played at the venue later today.
However, Braves head into the game with its form in flux following a disappointing league campaign thus far losing four games.
Prisons are the last team to beat Braves courtesy a 46-32 win and another victory would represent the perfect start in the nine day tournament.
Home side Tudu Galaxy's matchup against Teshie Rangers in the Men's Division is the final game on CAP 7 Day Two.


Conveniently located on Yellowstone Avenue directly across the street from Winco and Carl's Jr. We repair broken Apple devices, including iPads, iPhones and iPods, most Samsung devices and many more. Our team of battery and light bulbs experts is here to help you find the right battery or bulb for your needs. We carry energy efficient light bulbs, including CFLs and LEDs. Batteries Plus Bulbs in Pocatello offers convenient services, including battery testing, installation, recycling and custom design. In addition to serving your personal battery needs, we offer commercial accounts and special pricing for case quantities. We look forward to working with you today.


COACH RECOMMENDATION REQUIRED. Ages 7/8, Focus will be on basic fundamentals of player development: dribbling, passing, shooting, trapping and how to use them effectively in a game. Players go through weekly sessions of fundamental skill building and competitive drills/games to develop self-confidence in practice and game situations. Player to coach ratio is 10:1.


Adolfo Camarillo High School's Varsity Softball coach was nominated by California Coaches' Association for the honor of Softball Coach of the Year.
Each year, one high school coach is selected for the California Coaches' Association Coach of the Year in each sport. Spring coaches are nominated on their achievements during the 2011 season. Their peers nominate coaches and then five finalists are selected from each section for each sport. In May, the State Coaches of the Year will be announced.


text:
Send Flowers for Myra
Plant a Tree for Myra
Myra G. Burke
February 11, 1936 ~ January 17, 2023 (age 86) 86 Years Old
Myra G. Burke, 86, formerly of Roebuck, SC, died Tuesday, January 17, 2023, at Woodruff Manor. Born February 11, 1936, in Spartanburg, SC, she was the daughter of the late Howard J. and Martha Jane Gurley Sisk and the wife of the late Albert Douglas Burke.
A faithful servant of her Lord. Myra was devoted, loving, and a caretaker to her family. She was a homemaker of all things good, especially in the kitchen.
Survivors include her daughters, Lisa B. Waddle (Ben) of Roebuck, SC and Lori Sellers (Danny) of Spartanburg, SC; grandchildren, Cameron, MaKenzie, Tommy (Donna), Tony, and Cheyenne; eight great grandchildren, Avery, Grady, Emily, Jolie, Jayden, Jacob, Kimberly, and Tyler. She was predeceased by a daughter, Teresa G. Haulbrook.
Graveside service will be 2:00 p.m. Sunday, January 22, 2023, in Greenlawn Memorial Gardens, 1300 Fernwood-Glendale Road, Spartanburg, SC 29307, conducted by The Rev. Kermit Morris. Visitation will follow the graveside service.
The J. F. Floyd Mortuary
Greenlawn Memorial Gardens
1300 Fernwood-Glendale Road
Visitation to follow


Prompting fist pumps from Alien fans everywhere, Neill Blomkamp—who recently decided that he should put all that geeky concept art to good use—says in a new interview with Sky News that his upcoming Alien sequel will take place after James Cameron's Aliens, ignoring Alien 3 and Alien: Resurrection.
Even the staunchest defenders of all four Alien films (discounting Prometheus due to its shortage of Xenomorph money shots) would admit that the first two movies are the best in the franchise. Ridley Scott's original film is a landmark in sci-fi horror, and Cameron's follow-up is a terrific pulse-pounding action thriller. However, many fans also consider Alien 3 too sloppy and nihilistic and Alien: Resurrection too French.
When discussing the tone of the new film, Blomkamp said, "It's a Freudian nightmare. That element to me is what is so appealing. To try to put the audience on the edge of their seat, in a traditional 'monster stalking you in a dark corridor' way." That actually sounds more like a genetic sibling of the original Alien, which was much more about playing hide and seek with an enormous beast that somehow looks like every single pipe and bulkhead on the ship. But whatever, if the man says we don't have to serve time on that prison planet, then sign us up.
The only question now is what to call this new film, as both the singular and plural forms of the noun are taken. Perhaps Blomkamp should look to the possessive (Alien's) or to modifiers (Hungry Alien, Alien Posse). Whatever the movie is called, James Cameron probably will be thrilled with the project, as he's long voiced his displeasure with how Alien 3 treated the characters he created. However, Ridley Scott might be a bit confused, as he recently declared that the "beast is done." Meanwhile, David Fincher, who started his directing career with Alien 3, doesn't care and prefers to be left the hell out of all this, and Jean-Pierre Jeunet would like to point out that everyone still likes Amélie.
Blomkamp's next film, Chappie, hits theaters March 6. The release date for Alienaissance is still undetermined.


For more information on this topic read "Your Potential, Your Privilege," by President Dieter F. Uchtdorf, Ensign, May 2011, 58.
Think of what a glorious thing it is to reach beyond our earthly limitations, to have the eyes of our understanding opened and receive light and knowledge from celestial sources!
"I Am a Child of God," Children's Songbook, p. 2.
Procedure: Show mirror to family, let them see themselves if possible.
Ask: Does a mirror ever give us a true likeness of ourselves? Explain that a mirror throws our reflection back at us in reverse. We are so used to seeing ourselves in the way the mirror show us that few of us would recognize ourselves any other way. We all should seek for a glimpse of ourselves as seen in the sight of God. That wold be most revealing and most helpful.
A beautiful young woman sent me a book entitled Hope for the Flowers (Trina Paulus [Paramus, N. J.: Paulist Press, 1972]). Let me share its message with you.
The yellow caterpillar began fearfully but continued the process until at length she became a butterfly. Then she helped the striped caterpillar learn who he was and leave the pile to become what he was really meant to be. . . .
So it is for us as Latter-day Saints. We too must act worthy of ourselves and the glorious vision of truth and eternity which has been restored to us. That vision of eternal growth and gentle, loving persuasion is too great a dream to let go of when we hunger in our hearts to be one with our Savior.
The power is in you to reach out and claim those blessings. You have the powers within you to be Christlike. It is what you are meant to be.
Grease and flour a 9x13-inch metal baking pan. Preheat oven to 325 degrees.
In a large bowl, beat the eggs lightly with a wire whisk. Beat the sugar into the eggs until combined well. In a separate bowl, sift the flour and baking powder together, and then stir it into the egg mixture; set aside. In a small saucepan, heat the milk over low heat until it is just about to boil. Stir constantly to prevent milk from scorching. Add the butter to the hot milk and stir until the butter melts. Immediately pour the hot milk/butter into the flour and egg mixture. Stir in the vanilla. Pour the batter into the prepared pan and bake for 25 to 30 minutes. Prepare Lazy- Dazy Frosting while cake is baking; pour over the cake while the cake is still hot. Return cake to the oven and turn on the broiler to brown the coconut. Watch carefully, so you don't burn the cake.
Combine all ingredients in a heavy saucepan over medium- high heat. Bring mixture to a boil, stirring consistantly; maintain boil for 31/2 minutes.


In July 1998, Larry Summers appeared before a Senate committee to argue that a financial product, called an over-the-counter (OTC) derivative, did not need to be regulated. He said that there were only two potential reasons for financial regulation—"to protect retail investors from unscrupulous traders" and "to guard against manipulation in markets"—neither of which, Summers concluded, were applicable to OTC derivatives. Summers, who served as Treasury secretary from 1999 to 2001, eventually won the battle over derivatives regulation.
Those derivatives, of course, were at the heart of the 2007/2008 financial crisis.
That's not quite a mea culpa. But comparing that language to his comments in the 1990s is instructive of how Summers's thinking on financial regulation has evolved in the wake of the Great Recession.
Yet, that evolution is not limited to Summers nor to the issue of financial regulation. Skyrocketing inequality and the worst financial crisis since the Great Depression have led many economists, particularly those on the center-left, to rethink their positions. These days, they are sounding a lot like the progressive economists circa 1996. And this change has not gone unnoticed. In interviews with nearly two dozen left-leaning economists, many of whom were involved in the past two Democratic administrations, there is widespread agreement that the policy differences between center-left and progressive economists have narrowed.
Moreover, many progressive economists noted that the differences between the center-left and left have not disappeared. That is evidenced by their policy positions and by reports issued by different think tanks.
And those differences have important implications for Hillary Clinton's campaign and, potentially, her administration. Will she pursue trade deals like the Trans Pacific Partnership, which is loathed by unions and progressive economists? Is she satisfied that Dodd-Frank can prevent the financial system from imploding again? More importantly, what if the economic problems of today aren't the problems of tomorrow? The battles between center-left and progressive economists that defined much of Bill Clinton's White House—and have largely been absent from Barack Obama's White House—might just be ready to make a comeback.
After the financial crisis, it was hard to find any economist, on the left or right, who still believed that the financial industry was capable of effectively regulating itself. Even former Federal Reserve Chair Alan Greenspan, one of the godfathers of that school of thought, admitted he was wrong. So it's no surprise that center-left economists like Summers now support greater financial regulation.
But as Blinder pointed out, the spectrum is still wide. Some center-left economists believe that Dodd-Frank is nearly strong enough to protect the financial system from another crisis. For instance, Martin Baily, who was Council of Economic Advisers chair from 1999 to 2001 and currently is a senior fellow at the Brookings Institute, supported the repeal of a section of Dodd-Frank through a must-pass budget bill in December, a proposition that Massachusetts Democrat Elizabeth Warren railed against, unsuccessfully, on the Senate floor.
On this issue, Summers sides with the progressives. In January, he co-authored a report for the Center for American Progress on ensuring more Americans benefit from a stronger, 21st century economy. He criticized Congress for the backdoor way of chipping away at Dodd-Frank, saying it "must not become a precedent." Elsewhere in the 166-page report, he calls for stronger regulation of the shadow-banking system, for regulators to demand admissions of guilt in settlements with the government, and a review of capital and liquidity requirements at major banks. But financial stability is not a focal point. For instance, Summers mentions too-big-to-fail banks just twice—on pages 91 and 92.
Compare that to a recently released report by the Roosevelt Institute's Joseph Stiglitz, who was the CEA chair from 1995 through 1997. Stiglitz calls for some of the same policies as Summers: higher capital requirements, stronger regulation of the shadow banking system, and stricter penalties on those that break the law. But reforming the financial system is a clear focus of the report. "The Dodd-Frank Act was an excellent start, but the legislation did not change the structure of the dysfunctional system," Stiglitz writes. He calls for enacting a financial transactions tax and breaking up any banks that cannot produce a "living will" that shows regulators how it can wind itself in bankruptcy.
When I asked Summers about those two proposals, he didn't sound that much different than Stigltiz. "No institution should be permitted to continue to function if it's incapable of preparing a resolution procedure in case it fails," he said, although he believed that was already the case under Dodd-Frank. As for a financial transactions tax, Summers worried about potential evasion and implementation difficulties citing Europe's experience but was open to consideration of the idea.
Still, in reading the reports, you get the sense that financial stability and reforming Dodd-Frank is of higher importance to Stiglitz than Summers, who emphasizes his secular stagnation thesis.
In the 1990s, Democratic economists, especially those in the Clinton administration, were largely not paying attention to income inequality. Wages were rising, after all. Even if inequality was widening, it didn't seem like a big deal. But it's impossible to deny the fact now that income inequality has increased dramatically and wages haven't grown for the past 15 years, and economists have reacted accordingly.
"Most of the centrist economists wing of the Democratic Party are definitely espousing the view that income inequality has become a serious issue and that it's worthy of discussion rather than [saying] let's not talk about that," said Austan Goolsbee, an economist at the University of Chicago who was the CEA chair from 2010 to 2011.
Despite those differences, income inequality is a far larger part of the national discourse, on both the right and left, than it was in the '90s. "There's a shared understanding that the central economic problem we face is raising wages for middle class families and expanding mobility for people to get into the middle class and to rise," Furman said.
The question lurking behind this convergence is why it has happened. Just about everyone I spoke with pointed to the events of the past 15 years. The financial crisis and wage stagnation unquestionably caused nearly every economist to rethink the role of the financial system in the economy.
Summers denies that politics has ever influenced his positions. "I've said what I think all along," he said. "I think if you look at things that I've said and wrote about inequality or you read the speeches I gave about financial regulation in the administration, my views have been pretty consistent through time, responding to events." That's true. Summers was one of the first to call for fiscal stimulus, was focused on inequality before the crisis and attacked financial regulators for not forcing capital raises during 2008. And throughout his time as head of the National Economic Council, he made numerous speeches in support of stronger financial regulation.
Is Summers interested in a position in a potential Hillary Clinton administration? People close to him insist he's not. And he told me, "I've got no official role in her campaign." At age 60, Summers is still relatively young and just a few years ago he was eager to lead the Federal Reserve. He may not want a White House position now. But I'm sure he isn't interested in closing any doors.
What Hillary Clinton's economic team looks like will say a lot about the economic policies she intends to pursue as president. (Her campaign didn't respond to a request for comment.) To some extent, that matters less than it sounds. After all, Republicans are all but certain to control the House until at least 2020. Given that, Congress is unlikely to pass major pieces of economic legislation in her first term.
Still, the president is the leader of the party and shapes the national dialogue. If she becomes president, Hillary would also staff regulators and nominate members to the Federal Reserve. She'll release a budget each year and negotiate deals with Republicans on must-pass spending bills. The president's control over the economy may be vastly overrated but it's not non-existent.
If the recent convergence between center-left and left economists is part of a long-term trend, then disagreements among liberal economists are likely to be small, at least compared with those in the 1990s. But the opposite may be more likely to occur. If growth picks up, the labor market tightens and wages rise, we could see a reversal of this convergence. Center-left economists may become increasingly concerned with the long-term debt and insist on raising interest rates to prevent inflation. Progressive may try to keep income inequality a topic in the national conversation and worry that the financial system is still unstable. After eight years of relative agreement during the Obama presidency, those disagreements could reemerge as another Clinton moves into the White House.


The larger leather Malou bag is your everyday companion. The big front snap pocket holds essentials and inside, you'll find open pockets and a zip pocket. The strap extends from shoulder bag to crossbody length. Fully lined in 100% cotton. Top zip closure.
13.8 x 14.6 x 2.2"


Marcus Desaiha doesn't have a personal statement currently.
Music and video games basicly.
Hello brothers and sisters of GMC!
I would like to announce the debute of my new band that was put togheter late this year.
We will be releasing our first single titled 「Wisteria」 on January the 6th!
So I had an "Amp day" all day long yesterday. Went to four diffrent music stores and tried out several amps.
The one I fell for was the dual rectifier. It was just the thing I was looking for.
AMAZING amplifier, but so was the price-tag.
Though, I've noticed that they're alot cheaper in the states, so I was wondering if it is safe to import one of theese babies from the US and plug them in to a wall socket in Sweden? Or will the thing pop?
Since you got 110V in the states while we got juice worth of 210V here in Sweden coming out of our walls.
Do you need a voltage converter/transformer, or is it safe to just plug and play without one? I'd hate having to bring that to every gig I play though, it would be a burden!
Anybody in the EU here on GMC that has any knowledge in this area?
I'd thought I would wish everybody a Merry christmas and Happy holidays here at GMC!
Hope santa has brought everyone a custom made guitar, made in his own workshop this year!
Anybody ever thought of having a green flying V as a christmas tree this year?
I was sitting here practicing the same lick for an one and a half hours straight, increasing the speed by 1% each time I had repeated it 10 times.
Now my head feels like scrambles eggs..
I would like to hear how you practice to build up speed and technique.
I've got some theories of my own regarding the matter of practicing "the right way".
First I wonder if it really pays of to practice hours and hours every day. And if you always should do it slow? Shouldnt you sort of let your mind get used to the higher speed some times just to remind it of where the finishing line is?
When I started getting serious with my guitar playing (while still in school) I remember skipping school days just to sit at home and practice, I could do that for 6-8 hours straight almost every day of the week. Though, now when I think about, was it really worth it?
Could I have wasted thoose days learning and evolving my guitar skills the worst possible way?
Is pushing youself, sitting through five hours straight of full on practicing really the answer? Or could it be better to practice 1 hour, take a break 1-2 hours and then do the other hours of practicing after your brain processed the info you just put in it?
Billy wanted to become lightning fast, he heard that all of his favorite guitar players sat countless of hours practicing in their rooms, so he decided to do the same thing. Billy practiced for six hours straight without any break, he ate dinner and went to bed, during the night his brain tried to process the information he just put in there, and here is the thing, maybe the brain got too much on its hands and maybe thoose last 5-6 hours of practicing was for absolutely no good? Because you see the next day Billy tried to play the same thing and this time he only got an increase of lets say 3%.
If we rewind and tell billy that he should only practice for two hours, take a break, eat dinner, watch some TV, go back and practice one more hour, then go to bed. Maybe the precentage would be even higher the next day, maybe he would have had a 5 or even 10% increase?
Should you perhaps restrict yourself to a max of lets say two hours a day, just to avoid some sort of "overload" in your mind and optimize your learning ability?
The brain works in mysterious ways and I've always been fascinated by how we humans learn things.
I remember when I was a kid, my mom got me a Super Nintendo, you could sit through countless of hours, trying to beat "That certain level" without any achievement, til you gave up, took a break, went back and all of a sudden you cleared it flawlessly?
There are always better and worse times in your guitar career, some times you got such a flow, and you feel unstoppable, other times you feel like you're going nowere. Could it be that you were practicing in a slightly diffrent way during thoose periods of time without knowing it?
Please tell me your stories about how you practice, what you've learned from practicing in diffrent ways, and how you obtain maximum focus when practicing.
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The principal purpose of the Robert H. Goddard Library's Archives and Special Collections Department is to collect, preserve, provide access to, and encourage the use of the archival materials, books, and other items in the department's collection. The Coordinator of Archives and Special Collections is responsible for the development of collections in this department.
The Clark University Archives collects materials that the archives staff deems to be of potential enduring historical value about the university. The staff selectively accessions the non-current records of the university and of certain faculty members. These materials are chosen for their lasting administrative, legal, historical, or research value. Decisions about what to add to the collection are guided by the university's Records Retention Policy and Records Retention Schedule. Clark faculty and staff can get copies of these documents by contacting the archives.
The Special Collections area acquires books about the university, books about the greater Worcester area, and books written by current and former university faculty members. Furthermore, the holdings of special collections include the manuscript collections of certain Worcester authors. In addition, the coordinator of the department and the collections management librarians decide which books are too fragile, rare, or valuable to remain in an unsecured area. These books are then transferred to special collections; this manner of growth is restricted due to the limited availability of shelf space.
Collect – Archives and Special Collections will acquire materials by donation or attempt to purchase materials in this category. In areas of highest priority, Archives and Special Collections staff will be pro-active in seeking out materials of significance. Acquisition funds can be used to purchase materials for existing collections when funds are available.
Maintain – Material in this category represents collections already held in Archives and Special Collections. Collections will be maintained at their current level but, with the exception of donations, additional funds will not be used to expand these collections.


In This posting I will be talking about the Dr Bob Beck Protocol which is the use of a series of treatments that use low voltage currents to provide a cure for HIV and to provide a natural cure for cancer as well.
You may be very sceptical at this point if you have just come across this knowledge for the first time on here. If this is the case please watch the videos on this posting what Dr Bob Beck made a few years ago.
Once you have watched them please continue reading this posting and if you are in need of these treatments desperately please go to my section above named "Order Products" and scroll down to the Dr Bob Beck section where you can get access to devices you need.
Dr Bob Beck was a renowned physicist at this time and had an interest in using micro currents to heal people and after seeing the results from his college's labs. He set his mind to inventing a device that could be a cure for all.
He tested his device once he had made it on himself as well as a HIV sufferer and friends and family. All of them included himself witness huge improvement in their health. Dr Beck's hair even started to grow back in the areas he had been bald before. Which he found amusing and another effect he noticed was his libido had improved also.
Dr Beck was born in 1944 and sadly passed away in 2008 but what a legacy he left behind him. His protocol what he had created involved a four stage treatment which is listed below.
This process uses micro-currents to cleanse the blood of all impurities. Dr Beck discovered these properties while other colleges were doing other related research their laboratories.
The use of micro currents is applied at the wrist area using colloidal silver strips what the current passes through and enters the blood stream. The colloidal silver particles are extremely small but once they are in the blood stream they are attracted to oppositely charged viruses and pathogens.
Once they attach themselves to the pathogens they smother it and the viruses die. All these viruses and pathogens get excreted by the bodies normal methods of waste disposal.
Dr Beck realised that the first stage would kill most of the unwanted viruses and pathogens but some could be hiding in the lymph glands. So he invented a magnetic pulsing system that would neutralise these unwanted quests once and for all.
This method involves putting 99.9% colloidal silver into water and passing a current through it. This energised the water with the ionic silver which should be drunk regularly.
Stage 4 – Orally consuming ozonised water.
After many people had started using his protocol and lot of these individuals was reporting flu like symptoms. This was a result of the toxins not exiting the body quick enough.
Dr Beck needed to come up with a method to solve this, and the method was drinking newly made ozonised water. He knew that ozone was a fantastic at getting rid of toxins but the cost was very high to do this procedure.
Bob built a water ozoniser and this resolved the problem and patients no longer suffered the flu like symptoms as long as they drank lots of ozonised water.
Here is a link to a pdf document that breaks down exactly the amount of treatments and how often as well guides on drinking ozonised water. If you purchase a Bob Beck Protocol system I recommend saving the pdf as it will be invaluable as a guide on its use. I hope you have enjoyed this posting which has now given you access to a natural cure for cancer as well as a cure for HIV.
Fascinating information that you are sharing here, I have actually come across this information before. Just have not really put it all together! Probably not surprising that this information is not readily available to the general public. All the best with your site.
Thank you for the nice comment, glad you appreciate the content I created. I am passionate about getting this information out there and stop people dying unnecessary. Please come back as I am adding content regularly on different cures for different illnesses.