text:
\section{Introduction}

The study of multiparticle production in low-$p_T$ processes has been
pursued for over twenty years.  Since they involve soft interactions,
they cannot be treated in perturbative QCD.  In the absence of any
reliable theoretical approach to the problem, many models have been
proposed, most of which are represented in the review volumes
published ten years ago \cite{car,hx}.  Nearly all of those models have
since been shown to be inadequate in light of the data on fluctuations
and intermittency \cite{ddk,see}.  Indeed, there are very few models
that have the appropriate dynamical content capable of reproducing
the scaling behaviors observed in the experiments.  Even though
perturbative QCD cannot be used, it seems that some kind of branching
process is needed to generate the property of self-similarity, as the
resolution scale is varied.  In this paper we propose a model that
incorporates some aspects of nonperturbative QCD and is capable of
generating the features of the intermittency data, which are shown in
the last figure of this paper.  To our knowledge those data have not
been fitted by any model that contains some features of the color
dynamics.  To reproduce those data has become the main motivator
for this work.

Our approach embraces many time-honored properties of hadronic
collisions.  Since hadrons are extended objects, the eikonal formalism is
at the foundation of our model.  Thus it is not difficult for our model to
possess the virtues of geometrical scaling \cite{ddd} and approximate KNO
scaling \cite{kn}.  In order to build into the model features of
chromodynamics, it is necessary to introduce quarks and gluons into
the eikonal formalism, so the parton model is an essential gateway
into the microscopic domain of color interactions.  Once we enter that
domain, we embark on an unconventional journey of studying color
mutation of the constituents as a dynamical process by which the
colors of the quarks evolve through the emission and absorption of
gluons.  The smallness of
$\alpha_S$ is never assumed, so the evolution is not perturbative.
With all partons taken into consideration globally, we follow the
evolution of the configuration in the color space.  When the
configuration exhibits color neutral subclusters, we allow branching to
take place with a possible contraction  of the cluster size in
accordance to a reasonable rule consistent with confinement
dynamics. Successive branching leads to smaller and smaller clusters,
until they are finally identified as particles and resonances. The decay of
resonances are also taken into account before the final state of an
event is determined. Evidently, the model contains many features of
soft interaction that are familiar and desirable at a qualitative level.
Here we put them on a quantitative basis.

We shall call this model ECOMB, which stands for eikonal color
mutation branching. Only the eikonal part overlaps with an earlier
model, called ECCO, an eikonal cascade code \cite{hp}. Whereas
branching is put in by hand in ECCO, it is a consequence of the color
dynamics in ECOMB. Since the partons play a fundamental role in this
model, it is significantly closer to QCD than any eikonal model on soft
hadronic collisions has ever been.

There are a few parameters in the model. They are adjusted to fit  a
large body of experimental data on low-$p_T$ processes for
$\sqrt{s} \stackrel{<}{\sim} 100$ GeV. They include
$\sigma_{el}$,
$\sigma_{inel}$,
$\left<n\right>$, $C_q$, $dn/dy$, $P_n$, and $F_q$ for all $s$ in the
range
$10 < \sqrt{s} <100$ GeV, and all rapidity intervals. $F_q$ are the
normalized factorial moments, whose power-law dependence on the
rapidity bin-size $\delta$ has been referred to as the intermittency
behavior \cite{bp}.  Except for $F_q$, all the other pieces of datga are
global in nature; i.e., examined in or averaged over all rapidity space.
They can be fitted by many models.  $F_q$ in small rapidity intervals
exhibit local fluctuations, which are what invalidate most of those
models.

There is one important aspect about our model that should be
commented on in these introductory remarks. ECOMB is built upon the
parton model, and therefore represents an approach to multiparticle
production at low $p_T$ that is opposite to that of the more familiar
models, such as the Lund string model \cite{lun}, and the dual parton
model \cite{dpm}. The basic idea of those models is that the
momentum of an incident hadron is carried mainly by a few of the
valence quarks, which upon collision drag a color flux tube or a string
that subsequently fragment due to confinement forces. The parton
model, on the other hand, as originally proposed by Feynman for soft
processes \cite{fey}, regards the hadron momentum as being carried
by all partons, whose momentum distribution is frozen by a hard
collision  process (except for $Q^2$ evolution). For production at low
$p_T$ the partons cannot be regarded as being momentarily free. It
does not mean that the parton model is invalid; it only means that the
model cannot be naively applied, as in hard processes. In describing
the inclusive cross section of  $pp$ collision in the large $x_F$ region,
the Lund model \cite{lun} had one extreme view in that the produced
hadrons are the result of string fragmentation, while the
recombination model \cite{rec} had the other extreme view in that
the partons that are originally in the incident hadrons recombine to
form the detected hadrons. Whereas the Fritiof model \cite{fri} is a
refinement of the original Lund model, ECOMB represents an
enormous step of upgrading of the original recombination model. Most
importantly, it treats hadronization in the central region with due
regard to hadron size as well as color dynamics.

The paper is organized as follows. In Sec. 2 we review the Geometrical
Branching Model (GBM) with emphasis on the eikonal formalism for
multiparticle production. Then the parton model is incorporated into
the GBM in Sec.\ 3. The parton number distribution at each impact
parameter is used   only as the initial condition for the dynamical
evolution process of color mutation, which is discussed in Sec.\ 4. The
comparison of the results from Monte Carlo calculation with the data
on intermittency is carried out in Sec.\ 5. Some concluding remarks are
made in the final section.

\section{A Review of the Geometrical Branching Model}

The aim of GBM is to describe multiparticle production in hadronic
collisions through soft interaction \cite{gbm}. To focus on processes in
which hard subprocesses are unimportant, we confine our attention to
the energy range $10<\sqrt{s}<100$ GeV, which covers the CERN ISR
energies. The model is constructed to possess the properties of
geometrical scaling \cite{ddd} and approximate Koba-Neilsen-Olesen (KNO)
scaling
\cite{kn} that are observed in that energy range. It consists of two
parts: the geometrical part that is based on the eikonal formalism of
hadronic collisions, and the branching part that describes how
hadrons are produced. The details of the later will be modified and
improved in the following sections. Here we review the general
framework of how the two parts are put together.

In terms of the eikonal function $\Omega(b)$, which is assumed
known from an independent source, the elastic, inelastic, and total
cross sections are
\begin{eqnarray}
\sigma_{el}=\int {d^2b\, (1-e^{-\Omega(b)})^2} \quad ,
\label{2.1}
\end{eqnarray}
\begin{eqnarray}
\sigma_{inel}=\int {d^2b\, (1-e^{-2\Omega(b)})} \quad ,
\label{2.2}
\end{eqnarray}
\begin{eqnarray}
\sigma_{tot}=\int {d^2b\, 2(1-e^{-\Omega(b)})} \quad .
\label{2.3}
\end{eqnarray}
In the energy range stated above there is geometrical scaling; i.e.,
$\sigma_{el}$/$\sigma_{tot}$ is roughly constant \cite{ddd}. That
property can be guaranteed, if $\Omega$ depends only on the scaled
impact parameter $R$, where
\begin{eqnarray}
R = b/b_0(s) \quad,
\label{2.4}
\end{eqnarray}
so that (\ref{2.1})-(\ref{2.3}) may be written as
\begin{eqnarray}
\sigma_{el}=\pi b_0^2(s)\int^\infty_0 {d R^2\, (1-e^{-\Omega(R)})^2} \quad ,
\label{2.5}
\end{eqnarray}
\begin{eqnarray}
\sigma_{inel}=\pi b^2_0(s)\int^\infty_0 {d R^2\, (1-e^{-2\Omega(R)})} \quad ,
\label{2.6}
\end{eqnarray}
\begin{eqnarray}
\sigma_{tot}=\pi b^2_0(s) \int^\infty_0 {d R^2\,
2(1-e^{-\Omega(R)})} \quad .
\label{2.7}
\end{eqnarray}
In order that the inelasticity function
\begin{eqnarray} g(R)=1-e^{-2\Omega(R)}
\label{2.8}
\end{eqnarray} satisfies the normalization condition
\begin{eqnarray}
\int^\infty_0 {d R^2 g(R)}=1 \quad ,
\label{2.9}
\end{eqnarray} we are free to set the scale $b_0(s)$ by requiring
\begin{eqnarray}
\sigma_{inel}=\pi b^2_0(s)\quad .
\label{2.10}
\end{eqnarray} The function $g(R)$ describes the probability of
having an inelastic collision at $R$.

The multiplicity distribution $P_n$ is a result of sampling the
multiparticle production processes by many collisional events, each of
which may have a different impact parameter. Hence, $P_n$ should
have the form
\begin{eqnarray} P_n=\int{d R^2 g(R) {\bf Q}_n (R)} \quad ,
\label{2.11}
\end{eqnarray}
where ${\bf Q}_n(R)$ is the probability of producing $n$
particles at impact parameter $R$. Both
$P_n$ and ${\bf Q}_n$ are normalized by
\begin{eqnarray}
\sum_n P_n=\sum_n {\bf Q}_n=1 \quad .
\label{2.12}
\end{eqnarray}

The eikonal formalism is, of course, quite general. It satisfies
unitarity, which relates elastic and inelastic scattering amplitudes.
Furthermore, it emphasizes the spatial properties of the colliding
hadrons, which are known to be extended objects. Any treatment of
the collision process that ignores the geometrical aspects of the
hadrons leaves out some part of the physics of the problem, which cannot be
unimportant for soft processes.

The inelasticity function $g(R)$, defined in (\ref{2.8}), can be
expanded in a power series
\begin{eqnarray}
g(R)=\sum^\infty_{\mu=1} \pi_{\mu}(R)
\label{2.13}
\end{eqnarray}
where
\begin{eqnarray}
\pi_{\mu}(R)= {\left[2\Omega (R)\right]^{\mu}\over{\mu !}}
e^{-2\Omega (R)}.
\label{2.14}
\end{eqnarray}
The $\mu$th-order term may be regarded as the
$\mu$th-order rescattering contribution, and can be related to the
$\mu$-cut-Pomeron $\cite{ani,hp}$. In this paper we use
$\mu$-cut-Pomeron only as a terminology in reference to the
$\mu$th term in the expansion (\ref{2.13}). For $\mu\ge 2$,
$\pi_{\mu}$ is small compared to $\pi_1$ except at small $R$ for any
reasonable $\Omega (R)$. For $pp$ collisions the well-determined
form for the eikonal function is $\cite{cy}$
\begin{eqnarray}
\Omega(R)=-\ell n\left(1-0.71e^{-1.17R^2}\right) \quad,
\label{2.15}
\end{eqnarray}
which has been used to give a good description of
$d\sigma/dt$ $\cite{cy2}$. To get an estimate of the average $\mu$,
let us define
\begin{eqnarray}
\bar{\mu}(R) = \sum ^\infty_{\mu=1}
\mu\pi_{\mu}(R)/\sum^\infty_{\mu=1} \pi_{\mu}(R)
\label{2.16}
\end{eqnarray}
and
\begin{eqnarray}
\left<\mu\right>=\int{dR^2 \, g(R)\bar{\mu}(R)} =
\int{dR^2 \, 2\Omega(R)}.
\label{2.17}
\end{eqnarray}
Using (\ref{2.15}) in (\ref{2.17}), one gets
$\left<\mu\right>=1.6$ \cite{hw}. Thus unless
$R\simeq 0$, high-order terms involving $\mu > 2$ are negligible. But
for the high-$n$ behavior of the multiplicity distribution $P_n$, small
$R$ collisions are very important.

As far as the geometrical aspect of the collision problem is concerned,
the above discussion summarizes all that is important. To go further
in multiparticle production, it is necessary to model the dynamics of
soft interaction. Before we enter into the details of that, we consider
here the connection between particle production and geometry. At
each $R$, $\pi_{\mu}(R)$ gives the probability of having
$\mu$-cut-Pomerons, for which we use ${\bf B}^{\mu}_n$ to denote
the probability of producing $n$ particles. Thus the overall $P_n$ is a
convolution
\begin{eqnarray} P_n=\int
dR^2\sum^\infty_{\mu=1}\pi_{\mu}(R){\bf B}^{\mu}_n
\label{2.18}
\end{eqnarray} with $\sum_n {\bf B}^{\mu}_n=1$. Going back to the
general formula (\ref{2.11}), it is clear from (18) that ${\bf Q}_n$ is a
weighted average of ${\bf B}^{\mu}_n$:
\begin{eqnarray}
{\bf Q}_n(R)=\sum^\infty_{\mu=1}\pi_{\mu}(R){\bf
B}^\mu_n/\sum^\infty_{\mu=1}\pi_{\mu}(R),
\label{2.19}
\end{eqnarray} where (\ref{2.13}) has been used.

Using (\ref{2.14}) and (\ref{2.15}), the dependence of $\pi_{\mu}(R)$
on $R$ is shown in Fig.\ 1 for various values of $\mu$.  Evidently, at
large values of $R$ only the $\mu =1$ term is important. At $R\equiv
0$, terms up to $\mu = 6$ can still make   small contributions. The
sum in (\ref{2.13}), when truncated at $\mu = 6$, is shown by the heavy
dashed line in Fig.\ 1, and well approximates $g(R)$ shown by the
heavy solid line in Fig.\ 1. Thus we see in (\ref{2.19}) that at smaller
$R$ more terms in the sum over $\mu$ are needed, resulting in more
particles produced, as is physically reasonable.

\section{Incorporation of the Parton Model}

In an earlier version of the GBM \cite{hp}, a self-similar branching
process is assumed for ${\bf B}^\mu_n$, whose $n$ dependence is
determined by simulation. The defect of that approach is that the
dynamics of branching is {\it ad hoc}, not based on QCD. The
guiding principle is self-similarity, i.e., a cluster of mass
$m$ branches into two subclusters of masses $m_1$ and $m_2$ with
probability
$D(m, m_1, m_2)$ that is independent of any specific mass scale. The
aim is to reproduce the intermittency phenomenon observed, as the
resolution scale is varied \cite{ddk}. We now want to improve the
model by incorporating nonperturbative QCD to the extent feasible.
Branching becomes a derived property in the present approach,
instead of an assumed property in ECCO \cite{hp}.

To do so, it is necessary to put the model in a framework in
which the interactions of quarks and gluons can be examined
in detail, with hadrons being the end product of the
hadronization process. Since our aim is to study soft
interaction in low-$p_T$ production processes, rigorous
calculation from first principles is not possible. Even the use of
the parton model may be questionable when the virtuality
$Q^2$ that is relevant to the process is not high. However,
bearing in mind that Feynman's  first paper on the parton
model addresses specifically the soft interaction problem
\cite{fey}, we shall similarly frame our investigation in the
language of partons without using perturbative
approximations. Indeed, it is because the interactions are soft
that we have to follow the time evolution of the partons.

An important departure from the usual application of the parton
model is that we combine the property of hadrons being spatially
extended objects with the property of hadrons being made up of
smaller constituents. Clearly, for most collisions whose impact
parameters are nonzero, only portions of the partons in the incident
hadrons overlap and interact, so the number of hadrons produced
depends on that overlap. The event-to-event fluctuation of the
particle multiplicity therefore depends strongly on the
impact-parameter fluctuation, and the event averaged parton
distributions, as determined from the structure functions, are of no
use in that respect.

To implement our amalgamation of the two properties stated above,
we adopt the eikonal description of Sec. 2 and modify (\ref{2.19}) to
refer to parton number instead of hadron number. Thus let us define
${Q}_ \nu (R)$ to be the probability of involving $\nu$ partons in
soft interaction in the overlap region when the two incident hadrons
are separated by a scaled impact parameter $R$; let $B^{\mu}_{\nu}$ be
the probability of having $\nu$ partons in the
${\mu}$-cut Pomeron.  Note that we have
used $Q_\nu$ and $B^{\mu}_{\nu}$ in place of ${\bf Q}_n$ and
${\bf B}^\mu_n$,
when we refer to the $\nu$ partons instead of the $n$ particles. The
parton and particle distributions are, of  course, very different. As in
(\ref{2.19}), $Q_\nu$ and $B^{\mu}_{\nu}$ are related by
\begin{eqnarray} {Q}_ \nu (R) = g^{-1}(R) \sum^{\infty}_{\mu = 1}
\pi_{\mu}(R) B^{\mu}_{\nu} \quad .
\label{3.1}
\end{eqnarray} We emphasize that in (\ref{3.1}) the subscripts $\nu$
refer to the number of partons that initiate the evolution process
leading toward the hadrons produced in the central rapidity region.
The nonoverlapping portions of the incident hadrons produce the
leading particles in the fragmentation regions.
If we use ${\cal E}_{\nu\rightarrow n} \{\cdots\}$ to denote  the evolution
process that takes the $\nu$ partons to the $n$ hadrons, we may express
the relationship between $Q_\nu(R)$ and ${\bf Q}_n(R)$ symbolically as
\begin{eqnarray}
{\bf Q}_n(R) =  {\cal E}_{\nu\rightarrow n}
\{\,{Q}_\nu(R)\,\}
\quad.
\label{3.5a}
\end{eqnarray}
The description of ${\cal E}_{\nu\rightarrow n}$ is the main task of this
paper.

A way of thinking about $B^{\mu}_{\nu}$ is to consider the
$\mu = 1$ case, for which we have a one-Pomeron exchange diagram
for the elastic scattering amplitude with the Pomeron being cut to
expose the internal lines on mass shell.  If the Pomeron is represented
by a ladder of gluons with quark loops, then cutting it reveals the
gluons, quarks and antiquarks, which constitute the partons of
$B^1_{\nu}$.  Being the probability (i.e., absolute square of the amplitude
for $p+p\rightarrow \nu$ partons) of having $\nu$ partons in the one
cut-Pomeron,
$B^1_{\nu}$ is, of course, more general than any specific model
approximating that Pomeron by ladders or otherwise.  Similarly,
$B^{\mu}_{\nu}$ is the corresponding probability, when $\mu$ Pomerons
in the elastic amplitude are cut.

Since there exists no rigorous derivation of $B^{\mu}_{\nu}$,
we shall assume that it is Poisson distributed around some mean
number $\bar{\nu}$ of partons.  It is reasonable, since it is known
that a cut ladder corresponds to a multiperipheral diagram for a
$\nu$-particle production amplitude, whose rapidity distribution is
uniform, and multiplicity distribution Poissonian.   The mean number
$\bar{\nu}(\mu, s)$ can depend on both $\mu$ and $s$, since we
expect $\bar{\nu}$ to increase with $\mu$ and $s$.  Lacking any
information on that dependence, except that the $s$ dependence
should be logarithmic, this being $\log{s}$ physics, we adopt the following
parameterization
\begin{eqnarray}
\bar{\nu} (\mu, s) = \hat{\nu} (s) \mu^{a(s)} \quad ,
\label{3.2}
\end{eqnarray}
where
\begin{eqnarray}
\hat{\nu} (s) = \nu_0 + \nu_1\, {\rm ln} s \quad ,
\label{3.3}
\end{eqnarray}
\begin{eqnarray}
a(s) = a_0 + a_1\,  {\rm ln} s +a_2\, {\rm ln}^2 s \quad .
\label{3.4}
\end{eqnarray}
We shall use these in
\begin{eqnarray}
B^{\mu}_{\nu} ={1 \over \nu!} \left[\bar{\nu}
(\mu , s) \right]^{\nu} e^{-\bar{\nu} (\mu , s)} \quad ,
\label{3.5}
\end{eqnarray}
which in turn is used in (\ref{3.1}) to determine
${Q}_ \nu (R)$.

In the next section we describe the algorithm for parton evolution in
color space event by event.  For each event we simulate a scaled
impact parameter $R$.  For that $R$, we use ${Q}_ \nu (R)$ to
simulate an initial parton configuration involving $\nu$ partons.
After the completion of the evolution process, symbolized by ${\cal
E}_{\nu\rightarrow n}$,
$n$ particles are produced for that event.  Repeated simulation of many
such events results in a multiplicity distribution $P_n$ at each $s$, a
process expressed analytically by (\ref{2.11}).
 From $P_n(s)$ we can
calculate the average multiplicity
$\left<n\right>(s)$, and the standard moments
\begin{eqnarray}
C_q(s) = \left<n^q\right> /\left<n\right>^q \quad .
\label{3.6}
\end{eqnarray}
We vary the parameters in (\ref{3.3}) and (\ref{3.4})
to fit the data on $\left<n\right>(s)$ and
$C_q(s)$ for $s$ in the range $10 < \sqrt{s} < 70$ GeV.

Although the hadronization procedure has not yet been described, we
give the result here first to close our discussion on the initial parton
distribution.  We do this so as not to lose sight of the global features of
multiparticle production, when our attention is turned to the local
properties in the following sections.  The data that we want to fit are
$\left<n\right>_{\rm ch}$ and $C_q$ from Refs.\ \cite{dat}.
They are shown in Figs. 2 and 3.  The solid lines are our
calculated results using
\begin{eqnarray}
\nu_0 &=& -5.10\, ,\quad \quad \nu_1 = 4.03\, ,\nonumber\\
a_0 &=& -1.1\, ,\quad a_1 = 0.41\, , \quad a_2 = -0.025 \, ,
\label{3.6a}
\end{eqnarray} in (\ref{3.3}) and (\ref{3.4}) with $s$ in units of
GeV$^2$.  The relative $s$-independence of
$C_q(s)$, which is a manifestation of the KNO scaling, is nontrivial
when $\left<n\right>(s)$ more than doubles over the energy range
considered for soft production only.  The fits in Figs.\ 2 and 3
are evidently very satisfactory.

Before we go into the details of the color dynamics that is responsible
for the calculated results, let us show the parton number distributions
${Q}_ \nu (R)$.  They are plotted in Fig.\ 4 for four
representative values of $R$ and for $\sqrt{s}= 52$
GeV.  Note that the peak does not move below $\nu=25$, as $R$ is
increased; it is due to the fact that the minimum $\nu$ is 1, no matter
how large $R$ is.
 Note  also that the typical parton numbers are not
large by the standards of hard processes at much higher
energies.  That is connected with the nature of those partons
that initiate the evolution process, a subject we turn to next.

\section{Color Mutation}

We now consider the color dynamics of soft interaction. The initial
state is that there are $\nu$ partons distributed in some fashion in a
linear array in rapidity space. This is a consequence of the parton
model in that the partons are in the incident hadrons to begin with,
and the collision rearranges those partons and sets off the evolution
process that takes those partons to the final state, where the produced
hadrons are decoupled. The evolution process involves quarks and
antiquarks emitting and absorbing gluons. Since the process is not
perturbative, there is no analytical method to track the time development
of the process. Thus we shall use Monte Carlo simulation to generate
the configuration at each time step.

There are two spaces in which we must track the motion of the color
charges. One is the two-dimensional color space; the other is the
one-dimensional rapidity space. The latter can be extended to include
the azimuthal angle
$\phi$ and the transverse momentum $\left|\vec{p}_T\right|$, but in
our first attempt here we integrate over those variables and examine
the simpler problem of a 1D system. As for the color space, it is 2D,
and can be spanned by the ($I_3$,$Y$) axes, as in $SU(3)$ flavor. The
configuration in the two spaces are coordinated in the following sense.
Starting from the extreme left end of the rapidity ($\eta$) space, for
which the system that contains no partons is by definition color neutral
and therefore is
represented by a point at the origin of the  color space, we move in
the positive direction in $\eta$ space until we cross a color
charge. At the point to the right of that color charge, the
corresponding point in the color space jumps from the origin
to a position that represents the color of the charge that has
been crossed. Let us denote that jump by a vector. Then each
time we cross a color charge in the
 $\eta$ space, there is a corresponding vector added to the previous
point in the color space. The succession of additions of those vectors,
each one starting from the tip of the previous one, forms a path. Since
the whole parton system is color neutral, by the time we have
moved to the extreme right in the $\eta$ space, the path in the color
space returns to the origin, thus forming a closed loop. Such a loop
may be self-intersecting at various points. We call such a closed path
a configuration of the system in color space.

The essence of our evolution process is to track the configuration of
the system at each time step. The configuration  changes because the
colors of the partons can mutate, as they interact through the
emission and absorption of gluons. The way that each color
charge mutates is determined by the use of an energy
principle, which is proposed on the grounds that the system
attempts to lower its energy by changing its color
configuration, but fluctuating forces at the microscopic level
cause the changes to be erratic. At the same time, the
confinement force tends to reduce the distances among the
color charges, which are separated initially because of the
initial momenta that the partons possess, while being
constituents of the incident hadrons. Since we work in the 1D
$\eta$ space and cannot use perturbative QCD, we do not treat the
scattering problem among the partons in either the momentum or the
coordinate space. The evolution of the configuration in the color space
is what is important.

When the closed path in the color space evolves to a configuration in
which the path crosses the origin, a point in the evolution is then
reached that requires special attention. At that point, the
configuration may be regarded as having two closed paths,
corresponding to two color neutral subsystems. We assume that a
subsystem with no net color charge (i.e. $I_3$ and $Y=0$ in color
space) is in the lowest $SU(3)$ representation, that is, a singlet.
This assumption is based mainly on the expectation that a
nonsinglet system requires more energy to sustain it than
a singlet system.  Relaxation to the lowest energy state,
despite fluctuations, is the principle that guides the
evolution.  Since two spatially separate singlet subsystems do
not interact, we regard a branching process to have taken
place: the original large cluster of partons has partitioned
itself into two smaller color neutral subclusters.  Thereafter,
we repeat our procedure of color mutation, but now applied to
the two subclusters separately. This process is repeated again
and again until all subsystems consist of only quark-antiquark
pairs that cannot branch any further. However, a $q\bar{q}$
subsystem can be a resonance, in which case it can decay into
pions and kaons.

So far, we have described only qualitatively the evolution process of
color mutation and branching. The quantitative implementation of the
procedure will be given below. The conceptual basis of our approach
to soft production incorporates many features of strong interaction
that are generally regarded as being reasonable and physical, but
lacking calculational schemes with results for comparison with data.
We now amend that defect. The procedure that we adopt to carry out
the calculations is not unique, and can be modified and improved in
time. But the framework of  ECOMB is fixed by the combination of
eikonalism, color mutation, and branching. Our present procedure is as
follows.

\subsection*{A. Initial Distributions of the Partons}

As described in Sec.3, we start out with $\nu$ partons for a given
event. It is a number generated by use of the eikonal formalism with
variations in the impact parameter taken into account. How the $\nu$
partons are distributed in rapidity is drawn from the parton model. An
important basis of our model is that partons are in the incident hadrons
before the collision, and are not to be regarded as $q\bar q$ pairs that are
excited from the vacuum due to the stretching of strings in the string
model. Thus our partons have a momentum-fraction distribution as
determined in leptoproduction, but with $Q^2$ as small as can be achieved.

In the parton model there has always been a question of how gluons
hadronize in low-$p_T$ processes, when the produced particles are
predominantly pions. In the recombination model for particle
production in the fragmentization region \cite{rec}, the problem is
handled by saturating the sea, i.e., by converting all gluons to quarks
and antiquarks at the outset. The normalization of the hadronic
inclusive cross section turns out to be correct, when the recombination
mechanism is applied to all quarks and antiquarks that are nearby in
phase space. We now use the same saturation of the sea in our
problem here, as we attempt to treat the central region. Thus when we
refer to partons in the following, we shall mean only quarks and
antiquarks. The $\nu$ partons are therefore color triplets and
antitriplets of equal numbers so that collectively they form a color
neutral system. Their distributions in rapidity and color spaces are to
be considered separately.

\subsubsection*{(1) Distribution in rapidity space}

By rapidity we mean space-time rapidity $\eta$, where
\begin{eqnarray}
\eta = {1\over 2}\, \ell n\, {t + z \over t - z} \quad .
\label{4.1}
\end{eqnarray}
Momentum rapidity $y$ will not be used throughout
the calculation until the end, when the momentum  of a produced
particle is to be determined. We use the $\eta$ variable because the
spatial separations between partons change during the evolution process
due to the color forces.

The usual parton distribution in momentum fraction (at the lowest accessible
$Q^2$) implies roughly a flat $\eta$ distribution with rapid
damping toward zero at large $\eta$. We approximate that distribution for
the forward-going incident hadron by
\begin{eqnarray}
\rho^{(f)}(\eta) =
\rho_0\, , \hspace{1.2in} 0 \le \eta \le
\eta_c\,  ,\hspace{1.5cm}\nonumber\\
\rho_0 \, {\eta_{\rm max} - \eta \over
\eta_{\rm max}- \eta_c}\,
,\quad \hspace{.25in}\eta_c \le \eta
\le \eta_{\rm max}\, ,\hspace{.5in}
\label{4.2a}
\end{eqnarray}
where $\rho_0=\nu/(\eta_{\rm max}+\eta_c)$,
which corresponds to a total of $\nu/2$ partons when integrated over
$\eta>0$. For the partons belonging to the backward-going incident hadron,
the
$\eta$-distribution is
\begin{eqnarray}
\rho^{(b)}(\eta) =
\rho_0\, , \hspace{1.2in} -\eta_c \le \eta \le 0
\,  ,\hspace{1.5cm}\nonumber\\
\rho_0 \, {\eta_{\rm max} + \eta \over
\eta_{\rm max}- \eta_c}\,
,\quad \hspace{.25in}-\eta_{\rm max} \le \eta
\le -\eta_c\, .\hspace{.5in}
\label{4.2b}
\end{eqnarray}
The partons in each of  $\rho^{(f)}$ and $\rho^{(b)}$ should add up to be
color neutral. The overall parton distribution in the initial state is then
\begin{eqnarray}
\rho(\eta)=\rho^{(f)}(\eta)+\rho^{(b)}(\eta)\, .
\label{4.2}
\end{eqnarray}
 For each event, the
partons are, to first approximation, distributed randomly in $\eta$
according to $\rho(\eta)$.

The above distribution describes the rapidities of the partons before the
collision of the incident hadrons. Upon collision those partons  interact,
even if only softly. The conventional wisdom about soft interaction is that
the range of interaction in rapidity is short. That follows from the known
fact that the correlation between produced particles is short-ranged. Thus
apart from a limited range
$(\, -\eta_0 \le \eta \le \eta_0\, )$ in the central region where the partons
from the two incident hadrons interact, most partons outside that range
are undisturbed by the collision.  We describe the effect of the interaction
by modifying the initial distributions $\rho^{(f)}(\eta)$ and
$\rho^{(b)}(\eta)$ in that interaction region to $\rho^{(1)}(\eta)$ and
$\rho^{(2)}(\eta)$, respectively, where
\begin{eqnarray}
\rho^{(1)}(\eta) = \rho_0{\eta + \eta_0 \over 2 \eta_0 }\,
\theta(\eta+\eta_0)\, \theta(\eta_0 - \eta) + \rho^{(f)}(\eta)\,
\theta(\eta-\eta_0) ,
\label{29.2}
\end{eqnarray}
\begin{eqnarray}
\rho^{(2)}(\eta) = \rho_0{-\eta + \eta_0 \over 2 \eta_0 }\,
\theta(\eta+\eta_0)\, \theta(\eta_0 - \eta) + \rho^{(b)}(\eta)\,
\theta(-\eta-\eta_0) .
\label{29.3}
\end{eqnarray}
Note that the total parton distribution is unchanged, i.e.,
\begin{eqnarray}
\rho^{(1)}(\eta) + \rho^{(2)}(\eta) = \rho(\eta)\, .
\label{29.4}
\end{eqnarray}
The shapes of $\rho^{(1)}(\eta)$ and $\rho^{(2)}(\eta)$ are now
trapezoidal: some of the partons initially between $\eta=0$ and
$\eta_0$  in
$\rho^{(f)}(\eta)$ are dragged to the negative $\eta$ region, and some
between
$\eta_0$ and 0 in
$\rho^{(b)}(\eta)$ are dragged to the positive $\eta$ region.   Fig.\
5 illustrates how the distributions look like at a low energy where
the trapezoids are almost triangular. This rearrangement may not seem
 significant for the inclusive cross section of the produced hadrons,
since $\rho(\eta)$ is unchanged, but it turns out to be important for
multiplicity fluctuations in smaller bins. The point is that $\rho^{(f)}$ and
$\rho^{(b)}$ are two color-neutral clusters, coming from the two incident
hadrons.  The rearrangement caused by the collision creates an
overlapping region so that there is no smaller segment within the entire
range,
$-\eta_{\rm max} \le \eta \le \eta_{\rm max}$, where one can find color
neutrality, except by accident. The  color mutation process is sensitive to the
fact that the partons distributed according to $\rho^{(1)}(\eta) +
\rho^{(2)}(\eta)$ has no color-neutral subclusters, so that the evolution
must begin from the whole cluster, not from the two neutral subclusters,
$\rho^{(f)}$ and $\rho^{(b)}$, separately.

One can find a rough parallel between our $\rho^{(1,2)}(\eta)$ and the
strings in the Fritiof model \cite{fri} or in the dual parton model
\cite{dpm}.  However,  a string in DPM is stretched between a quark in one
incident proton with a diquark in another proton. Our
$\rho^{(1)}(\eta)$ is a color-neutral cluster of partons distributed from
$-\eta_0$ to $\eta_{\rm max}$.

To summarize, whereas $\rho^{(f)}(\eta)$ and $\rho^{(b)}(\eta)$ are the
initial parton distributions of the incident hadrons, $\rho^{(1)}(\eta)$ and
$\rho^{(2)}(\eta)$ are the parton distributions after the hadrons pass
through the interaction region.  The  evolution of the color dynamics
begins thereafter starting with $\rho^{(1)}(\eta)$ and
$\rho^{(2)}(\eta)$.

\subsubsection*{(2) Distribution in color space}

In the color space spanned by $I_3$ and $Y$, a quark is represented
by a vector, which has the coordinates of one of the triplets: $(1/2,
1/3), (-1/2, 1/3)$, and $(0,\,-2/3)$. An antiquark is
represented by a vector directed opposite to one of the above.
As a distribution of partons in the $\eta$ space is generated, say, $
\rho^{(2)}(\eta)$ between $-\eta_{\rm max} \le \eta \le \eta_0$,  we assign
to each parton a color vector
consistent with the requirement that the quarks and antiquarks come in
pairs, but their
orderings in the $\eta$ and the color spaces are totally random.
The partons in $\rho^{(1)}(\eta)$ are distributed similarly, but completely
independently, between $-\eta_0 \le \eta \le \eta_{\rm max}$. The total
distribution $\rho(\eta)$ in $-\eta_{\rm max} \le \eta \le \eta_{\rm
max}$ is the sum of these two sets, whose partons are merged in the
$\eta$ and the color spaces.
 Thus as we move from the extreme left in  the
$\eta$ space in the $+\eta$ direction, we begin at the origin of the color
space, and, each time when we move over a parton in the $\eta$
space, we add a vector (corresponding to its color) with its tail
to the head of the previous vector (or to the origin if it is the
first parton). A succession of such vectors forms a trajectory in
the color space. The trajectory eventually ends at the origin,
thus forming a closed path, when $\eta$ reaches the extreme
right.

Note that the path in the color space is dual to the ``path'' in the 1D
$\eta$ space in the sense that the segment between two partons in
the $\eta$ space is mapped to a point in the color space, while the
point where a parton is located is mapped to a segment of the path in
the color space. Thus the closed path is made up of $\nu$ short
segments. An example of a path in color space is shown in Fig.\ 6. The
sequence of color charges represented by the vectors is indicated by
$r\bar{b}rg \cdots \bar{b}r$ in the figure. We have used the
notation
$r=(1/2, 1/3)$, $g=(-1/2, 1/3)$, and $b=(0,\, -2/3)$. The origin
is labeled by 0.

\subsection*{B. Evolution in the color and rapidity spaces}

We now consider the evolution of a configuration due to QCD
dynamics. A nonperturbative treatment of $\nu$ simultaneously
interacting color charges is, of course, too difficult to contemplate here.
We reduce the problem by considering pairwise near-neighbor
interaction via the exchange of a gluon in any of the $s$-, $t$-, or
$u$-channel, whichever is applicable. Starting from the extreme
left in the $\eta$ space, we regard the ordered chain of $\nu$
partons as having $\nu-1$ links (with varying link lengths). Its
dual path in the color space has $\nu$ vectors, meeting at
$\nu-1$ vertices, not counting the endpoints, which are located
at the origin. Pairwise near-neighbor interaction means that we
consider the $\nu-1$ links  in $\eta$ space one at a time, according to a
rule to be specified below. After the interactions at all $\nu-1$ links
are considered, the evolution of the whole configuration is
regarded as having taken one time step, and the process is then
repeated.

\subsubsection*{(1) Color interaction}

Consider any link in the chain, i.e., a pair of partons. Suppose that the
pair is ($r,\bar{g}$). The only possible outcome of an interaction by
the emission and absorption of a gluon, besides remaining as
($r,\bar{g}$), is ($\bar{g}, r$), since the sum of the two color vectors
must remain invariant. If the pair consists of quarks, such as ($r,g$),
the only outcome of an interaction is again either ($r,g$) or ($g,r$).
Only in the case of a color-neutral pair, such as ($r,\bar{r}$), can the
outcome be any such pair, i.e., ($r,\bar{r}$), ($g,\bar{g}$),
($b,\bar{b}$) or their exchanged pairings. To determine the specific
outcome of an interaction, we use a statistical method.

For every global configuration $\alpha$ of the $\nu$ partons, there is
an associated energy $E_{\alpha}$. How
$E_{\alpha}$ is determined will be described in the following
subsection. Whenever a local pair of partons interact, the outcome
may or may not affect the global configuration. Let $c$ be the total
number of possible configurations. From the foregoing discussion $c$
can only be 2 or 6, the latter being for a color-neutral pair. Our
statistical approach to the determination of the global configuration
$\alpha$, consistent with favoring the lowest energy state, requires that
the probability for configuration $\alpha$ to occur is
\begin{eqnarray} P_{\alpha}=e^{-\beta E_{\alpha}}/Z, \qquad
Z =
\sum^c_{\alpha=1}e^{-\beta E_{\alpha}},
\label{4.3}
\end{eqnarray} where $\beta$ is a free parameter.

Using the Metropolis algorithm, we use $P_{\alpha}$ to determine the
outcome of a local interaction at every link. The result affects only one
vertex of the closed path in the color space, one vertex at a time. As
we go down the chain, every vertex is then tested for possible
changes. At the end of one complete sweep for one time step, the
whole closed path has undergone a color mutation, resulting in a new
path. Note that our procedure  incorporates several features of the
dynamics governing the system. Locally, there is the QCD dynamics of
gluon exchange between quarks and antiquarks. The outcome of the
local interaction depends on the global configuration in the color
space. The statistical treatment takes into
account the fluctuating nature of the many-body problem.

\subsubsection*{(2) Energy of a color configuration}

The color mutation process is an attempt by the dynamical system to
relax to its lowest energy state. It starts initially at a high energy state
because the collision puts the partons in a spatially spread-out
domain by virtue of the initial momenta of the partons that are essentially
uninterrupted by the soft collision, i.e., no large momentum transfers.
Color charges that are dispersed in space have high potential energy.
Since soft interactions do not result in significant changes in the
parton momenta, the energy of the system is controlled mainly by the
potential energies residing at all the links in the $\nu$-parton chain.

Specifically, consider the $i$th link in a chain, where
$i= 1, \,2, \cdots ,  \nu -1$.  The net color charge that
the link sees on the left side is
\begin{eqnarray}
\vec{C}_i=\sum^i_{j=1}\vec{c}_j \quad ,
\label{4.5}
\end{eqnarray}
where $\vec{c}_j$ is the vector in color space
representing the color of the $j$th parton. Due to the color neutrality
of the whole system, the net color that the link sees on the right side
is $-\vec{C}_i$. Since the potential energy
at the link $i$ is proportional to the net  color charges on the two sides
of the
link,  we write the energy
$E_i$ of the
$i$th link in the simple form
\begin{eqnarray}
E_i=\left|\vec{C}_i\right|^2 \quad ,
\label{4.6}
\end{eqnarray}
where the proportionality factor is
absent for the following reason. The confinement potential should be
proportional to the distance between color charges. Here $\vec C_i$ is the
total color of all the partons to the left of the $i$th link, so the relevant
effective distance should be measured from the center of those partons on
the left side to the center of the partons on the right side. That is a
global distance that is roughly half the total $\eta$ range, insensitive
to the position of the $i$th link. Since $E_\alpha$ is never used
without $\beta$ in (\ref{4.3}), the omission of the proportionality
factor in (\ref{4.6}) is equivalent to letting it be absorbed in the
definition of $\beta$.
 The energy associated with the whole configuration
$\alpha$ is
\begin{eqnarray}
 E_{\alpha}=\sum^{\nu -1}_{i=1} E_i \quad ,
\label{4.7}
\end{eqnarray}
where the sum obviously depends on the particular
path in color space that the configuration $\alpha$ takes.

It is this energy $E_{\alpha}$ in (\ref{4.7}) that the system attempts to
lower by color mutation, as it changes from one configuration
$\alpha$ to another, $\alpha^{\prime}$. Because of the additive nature of
$E_{\alpha}$ in (\ref{4.7}), the probability of mutation is determined
by the local energy difference, as can be seen in the following example.
Consider a link for which the number of possible configurations is two, i.e.,
$c=2$ in (\ref{4.3}). Then
$P_{\alpha}$ can be written as
\begin{eqnarray}
P_\alpha = {1\over 1+e^{-\beta\, \Delta E}}\, ,
\label{4.7a}
\end{eqnarray}
where $\Delta E$ is the change of energy in going to the new configuration
$c'$
\begin{eqnarray}
 \Delta E=E_{\alpha^{\prime}}-E_\alpha=E^{\prime}_i-E_i\, .
\label{4.7b}
\end{eqnarray}
$E^{\prime}_i$ is the energy at the $i$th link in the new configuration.
Note that $\Delta E$ is now locally determined at the link $i$. However, the
energy $E_i$ and $E'_i$ depend on the global configurations in the color
space, due to (\ref{4.5}) and (\ref{4.6}).

Since the net color charge of all the partons on one side of a link can be
large,
$E_i$ can also be large, according to (\ref{4.6}). Thus unless $\beta$ is a
small number, (\ref{4.7a}) can give a probability distribution $P_{\alpha}$
that can have an abrupt change at $\Delta E=0$. To round off the edges,
$\beta$ would have to be quite small.

\subsubsection*{(3) Spatial fluctuations}

The length of the $i$th link in the $\eta$ space is
\begin{eqnarray}
d_i=\eta_{i+1}-\eta_i \quad,
\label{4.4}
\end{eqnarray}
where $\eta_i$ is the rapidity of the $i$th parton,
counting from the left at $\eta=-\eta_{\rm max}$.
For a spatially extended color-neutral system, we have positive link
lengths, $d_i\ge 0$. We put $d_i=0$, when two partons are in the
same $\eta$ bin. The rapidity range,
$-\eta_{\rm max}\le\eta\le\eta_{\rm max}$, is divided into 256 bins in our
numerical calculation, so the smallest bin size is $2\eta_{\rm max}/256$,
which, of course, depends on the collision energy. As far as the
problem regarding the spatial distribution is concerned, we shall
assume energy independence and work only in the space that has 256
basic units, whatever $\eta_{\rm max}$ is. We denote the width of the
basic unit by
$\delta\eta$.

On the basis of  (\ref{4.3}) and (\ref{4.6}) the system undergoes color
mutation, as it evolves toward the final state.  In addition to the fluctuation
of the color charge $\vec C_i$, the length of the $i$th link, $d_i$, which is
an integer in units of $\delta \eta$, can also fluctuate.  Whether the link
length contracts or expands depends on the attractiveness or repulsiveness
of the net color forces that act on the two ends of the link.  To determine the
nature of that force is beyond the scope of this treatment.  We shall model
the change in link length by a stochastic approach, consistent with how we
have handled the color mutation part of the dynamics of the complex
system.   We allow $d_i$ to change by an integer $m_i$, i.e., $d_i \rightarrow
d_i+m_i$, where the probability for $m_i$ is specified by a distribution
${\cal P}_i(m)$.
Apart from the consideration that a contraction cannot render $d_i$
negative, we would set ${\cal P}_i(m)$ to be a uniform distribution from
$-m_-$ to $m_+$, where $m_{\pm}\ge 0$. However , if $m_->d_i$, we
truncate
${\cal P}_i(m)$  at
$m=-d_i$ and place the probabilities for contraction from $-d_i$ to $-m_-$
at
$m=-d_i$. Thus our two-parameter formula for ${\cal P}_i(m)$ can be
rewritten in the form that has
 a constant term plus a Kronecker delta term  at $-d_i$. That is, with
$\gamma_1$ and $\gamma_2$ as the two revised parameters, we have
\begin{eqnarray}
{\cal P}_i(m) = \gamma_1\, \theta(m+d_i)\, \theta(\gamma_2-m)
+[1-\gamma_1(\gamma_2+d_i)]\, \delta_{m,-d_i} \quad,
\label{4.7c}
\end{eqnarray}
which satisfies $\sum_{m=-d_i}^{\gamma_2}{\cal P}_i(m)=1.$
This distribution allows $m$ to be positive (expansion) uniformly up to
$\gamma_2$, and negative (contraction) down to $-d_i$.  The net
probability for expansion is
$\gamma_1\gamma_2$, and for contraction is $1-\gamma_1\gamma_2$.

Confinement implies that there should be a net contraction between the
subcluster of charge $\vec C_i$ and the opposite subcluster of charge
$-\vec C_i$. However, these two subclusters are at an effective distance
much larger than $d_i$, which is the length of the link specifying the
separation between the boundaries of the two subclusters. At the $i$th
link, there are microscopic color forces that can be attractive or repulsive.
${\cal P}_i(m)$ is a two-parameter description of that stochastic force,
which should lead to a net macroscopic contraction for the whole cluster.
That property is related to the value $\gamma_1\gamma_2$, which
should be less than 0.5, if contraction dominates over expansion. Of course,
this change of $d_i$ should be tested at all links in the neutral cluster
before a net effect is known.

\subsection*{C. Branching}

As we have discussed in the introduction of this section, the evolution
process described here is a branching process. A fission of the
color-singlet cluster occurs, when it contains two color-singlet
subclusters, since no confining force exists between them. The
partitioning takes place when the closed path of the mother cluster
evolves to a configuration where the path passes through the origin in
the color space so that there are two color neutral subsystems.
Thereafter, the color mutation process is applied to the two
subsystems separately and independently. This is repeated again and
again until all subclusters consist of only $q\bar{q}$ pairs.

During color mutation, it is possible that a baryon-like singlet can be
formed with a $(r,g,b)$ closed loop. Since baryon-antibaryon pair
production in $pp$ collision is rare at energies where soft
interaction is dominant, we shall ignore 3$q$ and 3$\bar{q}$
singlets, (since mass inhibition is not explicitly taken into
account), and require color mutation to continue until only
mesons are produced. If in the middle of a color chain there is
a color neutral $q\bar{q}$ pair, such as $r\bar{r}$, it is not
allowed to break off from the chain; it must continue to
mutate until a genuine neutral subcluster, counting from the
extreme left or right in the $\eta$ space, is formed.

In Fig.\ 7 we show an example of how 24 partons evolve under color
mutation, and how branching takes place. Thirty-two time steps are taken
to get to the final state of $q\bar q$ subclusters only, when hadronization
occurs.

To gain some insight on how long a typical  evolution process takes for a
cluster to partition into two, we show in Fig.\ 8(a) the distribution in
time steps for $10^3$ initial clusters each consisting of ten pairs of
$q\bar{q}$ with random color ordering. The average is about 3.5 steps for
just one branching. For the evolution processes to complete, the daughter
clusters must continue to branch successively, and the overall distribution
at the end of the evolution is shown in Fig.\ 8(b). Note that on the
average quite a large number of time steps is required for the
evolution of an average-sized cluster, much larger than what is
usually involved in a hard porcess where high virtuality is degraded
by branching.

At every stage of the evolution process, a cluster shrinks due to overall
spatial contraction. We always keep the center of the cluster invariant
to conserve momentum. When a branching occurs, the two daughter
clusters will have their own respective centers, which will remain
invariant during contraction, until they themselves branch. At the end
when a hadron is formed from a $q\bar{q}$ pair, the hadron
momentum rapidity $y$ will be identified with a value of
$\eta$ taken randomly between the $\eta$ values of the quark and
antiquark. The reason for doing this is that without knowing the mass
and the transverse momentum $p_T$ of the hadron, a precise
determination of its $y$ is not possible, nor meaningful. A random
value within a small range is good enough. A rough identification of $y$
with
$\eta$ is justified for free particles at high energy. We do not expect
that our
measure of fluctuations in the final result will be sensitive to this
$y$-$\eta$ identification.

\subsection*{D. Hadronization}

The branching process terminates, when all the neutral subclusters
are reduced to the composition of $q\bar{q}$ pairs only. Those
subclusters are identified as hadrons, which may be pions, kaons, or
resonances. Those resonances must be allowed to decay before the
total number and distribution of particles are counted for the final
state of the event. The probabilities of producing various resonances
and stable (in strong interaction) particles have been studied
experimentally in $pp$ collisions in \cite{res}. We use that reference
as a generic guide for the proportions of all particles produced in any
general hadronic collision.

In our simulation we use that guide to determine whether a neutral
subcluster is a resonance or not. In either case we give it a transverse
momentum according to a specified distribution. Let us use $k_T$ to
denote the transverse momentum of a $q\bar{q}$ pair. The
distribution we use is
\begin{eqnarray}
{dn \over dk^2_T}=
{1 \over \left<k^2_T\right>}e^{-k^2_T / \left<k^2_T\right>}
\quad ,
\label{4.8}
\end{eqnarray}
where $\left<k^2_T\right>$ is a parameter to be varied. If the
$q\bar{q}$ pair forms a pion or a kaon, then that $k_T$ becomes
the
$p_T$ of the particle without any change. However, if the
$q\bar{q}$ pair forms a resonance, then we assume an isotropic
decay distribution in the rest frame of the resonance. The
azimuthal angle
$\phi$ of $\vec{k}$ is assigned randomly. After boosting back to
the cm system, the 3-momenta $\vec{p}$ of the decay particles
are then determined. The collection of all the final-state particles results in
the exclusive distribution in the $(y,\vec p_T)$ space for the event
generated.

The charges of the particles are chosen randomly subject to the
constraint that the total charge can only be either 0, 1, or 2, on the
grounds that the leading particles in a $pp$ collision can be doubly-,
singly-, or un-charged. The particles that we treat are all the produced
particles, excluding the leading particles. Once the charge of a specific
particle or resonance is generated, the decay of the resonance is then
assigned the usual branching fractions into different channels according to
the particle data book.

\section{Results}
In the previous section we have introduced seven parameters:
$\eta_c$ and  $\eta_{\rm max}$ in (\ref{4.2a}) and (\ref{4.2b}), $\eta_0$ in
(\ref{29.2}) and (\ref{29.3}), $\beta$ in (\ref{4.3}),
$\gamma_1$ and $\gamma_2$ in (\ref{4.7c}),
and
$\left< k^2_T\right>$ in (\ref{4.8}).  They are to be varied to fit the data on
inclusive distributions and on fluctuations of the exclusive distributions.
The properties of fluctuations will be quantified in terms of the normalized
factorial moments, $F_q(\delta)$ for farious bin sizes $\delta$.

The parameters  $\eta_c$, $\eta_{\rm max}$, and  $\left< k^2_T\right>$
are essentially kinematical; they set the boundaries of the phase space in
which the partons are placed.  They do not affect the dynamics of
color mutation and the spatial fluctuation of the clusters.  The
data used to determine them are the rapidity distribution $dn/dy$
\cite{thom} and the
transverse mometum distribution $g(p_T)$ of the produced
particles in the final state.  The energy range of the data in \cite{thom}
is $22 < \sqrt{s} < 63$   GeV, for which hard scattering is negligible.
The values of $\eta_c$ and $\eta_{\rm max}$ depend on $s$. To fit the
data, we have used the values given in Table I. The value of
$\left( \left< k^2_T\right> \right)^{1/2}$ is chosen to be 400 MeV.
In Fig.\ 9 we show the rapidity distributions where the
histograms are the results of our calculation, while the data are from
\cite{thom}.  There, $\eta$ refers to pseudaorapidity, not space-time
rapidity.  The agreement is clearly satisfactory. Although in carrying
out our calculation the other parameters need to be specified also, we
have not given them in Table I because the results on
$dn/d\eta$ are insensitive to them. They will be given below.

\begin{center}
\begin{tabular}{|c|c|c|c|c|c|c|c|c|c}
\hline
$\sqrt{s}$ & 22.0 & 23.6 & 30.8 & 45.2 & 53.2 & 63.2  \\
\hline
$\eta_c$   & 1.76  & 1.55   & 1.42   & 0.889   & 0.762 & 0.635  \\
\hline
$\eta_{max}$ & 5.0 & 6.6 & 6.6  & 6.5  & 6.5 & 6.5 \\
\hline
\end{tabular}
{\\TABLE 1. The parameters for the initial condition of partons in the evolution }
\end{center}

 The multiplicity distribution at $\sqrt s =22$ GeV is shown in Fig.\ 10
for $|y|<2.5$. The calculated result evidently agrees very well with the
data \cite{ada}, especially at the high $n$ end. At the low end, there is
a slight discrepency, which could very well be due to the fact that we
have not included diffractive production. That portion of the
distribution will have negligible effect on our calculation of the
factorial moments.  We have not included in Fig.\ 10 the $P_n$ for
narrow rapidity windows, since essentially the same physical content
will be conveyed by the $F_q(\delta)$ to be presented below.  We have
not considered the UA1 and UA5 data at higher energies because
those data contain significant contributions from hard subprocesses.
The inclusion of such perturbative processes is not difficult
\cite{ch,wang}, and should be investigated in order to extend the
energy range where ECOMB can be applied.

The  parameters that influence the evolution process of
mutation and branching are $\eta_0$ , $\beta$, $\gamma_1$ and
$\gamma_2$. $\eta_0$ specifies the overlap region of the initial
color-neutral clusters,
$\beta$ pertains to the probability of color mutation, and
$\gamma_1$ and $\gamma_2$ characterize the fluctuations of the link
lengths. The data used to determine them are on factorial moments and
their variants
\cite{ddk}. It is here that we can underline the importance of
those data on fluctuations, without which we have no guidance
on how to restrict the detail dynamics of particle production.
Putting that in another way, in the absence of a procedure to
calculate from first principles, any model that fails to fit the
fluctuation data is missing some aspect of the basic dynamics. To
the extent of our awareness, very few models on soft interaction
have been put to the test of confronting those data on the factorial
moments for varying bin sizes.

The normalized factorial moments, first suggested by Bia\l as
and Peschanski \cite{bp}, can be expressed as
\begin{eqnarray}
F_q={1\over M}\sum_k{{\left<n(n-1)...(n-q+1)\right>_k\over
\left<n\right>_k^q}}
\quad ,
\label{5.1}
\end{eqnarray}
where $n$ is the multiplicity in a bin of size $\delta$,  the
average is performed over all events for the $k$th bin, and the summation
is  over all bins of the same $\delta$, $M$ being the total number of bins
$(2Y/\delta)$. Data on
$F_q$ for soft interaction have been obtained by NA22 \cite{na2}.  In
recent years Bose-Einstein correlation between identical particles has been
recognized as having an important effect on the intermittency
data at very  small $\delta$ \cite{ddk}.  However,
at this stage of our development of ECOMB, we have  not
 included BE correlation, since it is unrelated to the color
dynamics that we attempt to tune. We therefore limit our scope in this
first attempt and  focus here on $F_q$, for which we fit  the  data  of
\cite{na2} as functions of bin width, rather than on correlation functions at
very small momentum-difference squared.

The parameters that we have varied to give the best fit of the
intermittency data at ${\sqrt s}=22$ GeV are:
\begin{eqnarray}
\hat \nu(s) = 9.1, \qquad a(s) = 0.63, \\
\eta_{\rm max}=5,\qquad \eta_c=3.5,\qquad \eta_0=1.9, \\
\beta=0.0015,\qquad \gamma_1=0.077, \qquad \gamma_2=5.
\label{5.2}
\end{eqnarray}
Note that $\gamma_1\gamma_2=0.385$, implying that it is roughly twice
as likely for a link to contract than to expand. To explain why the first four
parameters listed above are different from the ones used previously for the
ISR data (in Sec.\ 3 and Table I), we remark that we have not been
able to derive from the values of
$F_q$ given by the data of NA22
\cite{na2} the values of $C_q$ that can agree with those of ISR
\cite{dat}. Thus while
the parameters in Table I are adequate for the  ISR data that
range up to 63 GeV, we must use a slightly different set of parameters at
$\sqrt s = 22$ GeV for the NA22 data that provide the only information on
intermittency.

	In Fig.\ 11 we show the intermittency data of \cite{na2}, which to our
knowledge have not been reproduced by any model, except ECCO
\cite{hp,ddk}.  The lines shown
 in Fig.\ 11 are the result of our present calculation in ECOMB.
 Evidently, the agreement between our results and the data  are
satisfactory for all values of
$\delta y$ and $q$.
It should be noted that to achieve the fits attained is highly nontrivial. If
any part of the dynamical process in generating the hadrons is altered,
one would not be able to obtain the rising factorial moments, no matter
how many parameters are used.  By working with the many parts of our
model, all of which affect the determination of $F_q$, we have
gained confidence in regarding the dynamics of color mutation  and
branching as having captured the essential properties of soft interaction.

\section{Conclusion}

It is rather satisfying that we have been able to reproduce the
intermittency data in Fig.\ 11. Scaling behavior of that type
implies self-similarity in the dynamics of particle production.
The branching process of color-neutral clusters, successively
partitioning into small clusters, is self-similar, since the same
algorithm is used at every step. Thus from the outset ECOMB has a
chance of generating a scaling behavior, in contrast to the string
model or dual parton model, which have been shown by NA22 not to
fit the intermittency data \cite{na2}.  However, to have
self-similar dynamics does not guarantee that the observed scaling
behavior can be obtained. An appropriate balance of contraction
and expansion of the clusters during the evolution is necessary to
capture the essence of the color dynamics of a complex system.
Furthermore, the initial state of the parton system at the start
of the evolution process is also important, since it can dictate
the bin size from which the scaling behavior commences. These
physical aspects of the model must be incorporated properly in
order to produce the result shown in Fig.\ 11.

We have not considered the intermittency data of UA1 \cite{ua1}
because they contain minijets. If one is willing to adopt the
point of view that such semihard subprocesses are not dominant
enough to alter the nature of intermittency, one could attempt to
apply ECOMB to the UA1 data. However, it is well known that
geometrical scaling and KNO scaling are violated at the SPS
energies, so some modification is necessary.

The most important omission in this paper is Bose-Einstein
correlation, without which our model is not completely realistic.
That defect must be corrected in an improved version. At this
stage we can only offer this version as a first step in the right
direction. Whereas the details of our parametrization here may
alter after the BE correlation is incorporated, the branching
dynamics of color mutation will hold as the basic framework of the
model. Since the power-law behavior of $F_q$ has been observed for
nonidentical particles \cite{aga}, we know that self-similarity is
necessary in the absence of BE correlation. After the
symmetrization of identical-particle states is performed, the
strength of intermittency may be enhanced. The parameters may
therefore have to be readjusted, but the main features of the
dynamics need no modification.

We have amalgamated many concepts that form various elements of
the conventional wisdom about soft interaction. They include: (a)
hadrons having sizes, (b) eikonalism, (c) parton model, (d)
interaction of quarks via gluons, (e) statistical properties of a
many-body system, (f) spatial contraction and expansion of a color system,
 and (g) resonance production.  They are interlaced by intricate connections
described in this paper. One may regard the approximation of
nonperturbative QCD  by color mutation as a gross simplification. We
conjecture that the final realistic result will be insensitive to the
details of how well many-body QCD is approximated, since the model is
constrained by so many other aspects of soft interaction.  This work
demonstrates the importance of how each and every one of those
separate components of the overall structure must work together in
order to achieve the scaling behavior of local fluctuations that is observed.

\begin{center}
\subsubsection*{Acknowledgment}
\end{center}

We are grateful to Prof.\ W.\ Kittel for supplying us with the NA22 data and
valuable answers to our questions.  This work was supported in part by U.S.
Department of Energy under Grant No. DE-FG03-96ER40972.

\vspace*{2cm}

redpajama_set_name: RedPajamaArXiv


Latest post Wed, Nov 7 2018 6:47 AM by luca.mg. 2 replies.
Hello all, when trying to add simple motion to a still image in MC, I hit the effect editor button and the window pops up, but it does not display any clips or effects. What is happening?
If you want to edit a motion effect, you need to open the motion effect editor (it's under the Tools menu).
It might help to know what you're trying to accomplish, as you seem to have applied a freeze frame effect to a still image.
Hi abrownstein8087 and welcome to the forums. Not sure what You want to accomplish. That's the effect editor, if by simple motion You mean adjusting speed, as in a motion effect clip, You need to open the motion effect editor instead. If You want to move the still frame You have to apply an effect (resize, PnP, 3d warp) before opening the effect editor. Not in front of a system to double check right now, but You may need to ALT-drag the effect on top of a motion effect clip.


text:
Постальська волость — історична адміністративно-територіальна одиниця Аккерманського повіту Бессарабської губернії з центром у поселенні Посталь.

Населення (на 1886 рік) — 3089 осіб (1590 чоловічої статі та 1499 — жіночої).

Поселення волості:
 Посталь — поселення за 25 верст від повітового міста, 376 осіб; волосне правління; 2 молитовних будинки, паровий млин. За 5 верст — молитовний будинок. За 12 верст — молитовний будинок. За 15 верст — 2 молитовних будинки. За 17 верст - школа. За 18 верст - молитовний будинок.

Примітки

Волості Бессарабської губернії
Історія Білгород-Дністровського району
Колишні німецькі колонії Одеської області

redpajama_set_name: RedPajamaWikipedia


text:
package com.abewy.android.apps.klyph.adapter.holder;

import android.view.ViewGroup;

public class AdvertisingHolder
{
	private ViewGroup	adContainer;

	public AdvertisingHolder(ViewGroup adContainer)
	{
		this.adContainer = adContainer;
	}

	public ViewGroup getAdContainer()
	{
		return adContainer;
	}
}

redpajama_set_name: RedPajamaGithub


Siyu Duan is a London based fashion menswear designer, inspired by zoom in science, human energy and daily objects. Exploring and building the possibilities of shape, lines, colour and print. Duan will introduce more tailored pieces after creating a couple collections. Duan believes clothes are something that can wrap around the human body in three dimensional way and protect the body nicely, without the necessity of adding specific details or following rules. Trying to fill the gap between clothes and art he uses tailoring technic with the combination of art to let people change the way they think about menswear and ultimately push fashion forward into a new dimension.
Siyu Duan will be showcasing his exclusive SS15 collection at the Zeitgeist Show on Friday 10th October.


Should a denominational affiliated church leave that connection out of its name? Some churches have opted to leave their denominational connection out of the name feeling that it can be a hindrance to attracting new people. Others have left the name in preferring the "trusted brand" approach. New research suggests that it is a double-edged sword. On the one hand, denominational churches are perceived as more formal and rigid and old-fashioned. On the other hand, churches not connected to a long-established denomination or denominational churches that hide their affiliation are perceived as less honest and give a feeling of uncertainty as to what they may believe.
The bottom line for me is that this is nothing more than a red herring. Church communities will thrive when they are actively making and maturing disciples, and centrally focused on the mission Jesus gave to it, whether that church is part of a denomination or not-- making disciples and getting outside the walls of the church building is the ticket to vitality. The problem is not the name on the sign in front of the building; the problem is inwardly focused congregations that see discipleship as a one hour a week endeavor and that function more like a country club than God's people who are called to be a light to the nations in word and deed.
Tuesday, February 26th is National Pistachio Day. Even nuts have their own special interest lobby.
Let us then not be ashamed to confess our sins unto the Lord. Shame indeed there is when each makes known his sins, but that shame, as it were, ploughs his land, removes the ever-recurring brambles, prunes the thorns, and gives life to the fruits which he believed were dead. Follow him who, by diligently ploughing his field, sought for eternal fruit.
Confession is indeed good for the soul.
Some interesting links on the Genesis death sandwich, ten weird ways we deal with the dead, and some alleged relics of Jesus (emphasis on "alleged").
Spring training has begun! It won't be long until the boys of summer are back on the diamond. There are few things in life more pleasurable than sitting in the stands on a balmy summer evening watching a baseball game!
One ton of water is required to make one pound of refined sugar.
February 22, 1980: The U.S. hockey team upsets the Soviet Union in the Winter games of the XIII Olympiad.


text:
The slightly sordid melodrama and para-psychological philosophizing lean uncomfortably against a sappy romance.
THE HOUSE OF VELVET AND GLASS
by Katherine Howe ‧ RELEASE DATE: April 10, 2012
Howe (The Physick Book of Deliverance Dane, 2009) sets her second novel among early-20th-century Bostonians fascinated by the power of both spiritualism and the new science of psychology.
Twenty-seven-year-old spinster Sibyl Allston lives a quiet life with her father Lan, a successful businessman who talks little about his youth as a sailor in the Far East. In 1915 both are still mourning the deaths of Sibyl's mother, Helen, and younger sister Eulah, who drowned on the Titanic three years before. Except for her regular visits to the medium, Mrs. Dee, in hopes of making contact with her mother and sister, Sibyl is a retiring, conventional young woman. Then her younger brother Harlan is thrown out of Harvard, ends up in the hospital after a fight he will not discuss, and moves back into the family home along with a young woman named Dovie, whose background remains as murky as her relationship to Harlan. Dovie introduces Sibyl to a potentially dangerous habit in Boston's Chinatown, but at the same time Sibyl's former beau re-enters her life. Benton is now a psychology professor at Harvard who tries to help Sibyl by exposing Mrs. Dee as a fraud. But as the country drifts toward World War I, Sibyl begins to realize she may possess an unexpected gift as a seer, one that she unknowingly inherited from her father along with a taste for opium. Is knowing the future a gift or a curse, or does it depend on the angle through which it is viewed? Ultimately Sibyl learns that even within a world ruled by fate, choices can be made.
Publisher: Voice/Hyperion
Review Posted Online: March 19, 2012
Kirkus Reviews Issue: April 1, 2012
Categories: LITERARY FICTION
More by Anderson Cooper
by Anderson Cooper & Katherine Howe
THE DAUGHTERS OF TEMPERANCE HOBBS
by Katherine Howe
Miller makes Homer pertinent to women facing 21st-century monsters.
Reader Votes
Kirkus Reviews'
by Madeline Miller ‧ RELEASE DATE: April 10, 2018
A retelling of ancient Greek lore gives exhilarating voice to a witch.
"Monsters are a boon for gods. Imagine all the prayers." So says Circe, a sly, petulant, and finally commanding voice that narrates the entirety of Miller's dazzling second novel. The writer returns to Homer, the wellspring that led her to an Orange Prize for The Song of Achilles (2012). This time, she dips into The Odyssey for the legend of Circe, a nymph who turns Odysseus' crew of men into pigs. The novel, with its distinctive feminist tang, starts with the sentence: "When I was born, the name for what I was did not exist." Readers will relish following the puzzle of this unpromising daughter of the sun god Helios and his wife, Perse, who had negligible use for their child. It takes banishment to the island Aeaea for Circe to sense her calling as a sorceress: "I will not be like a bird bred in a cage, I thought, too dull to fly even when the door stands open. I stepped into those woods and my life began." This lonely, scorned figure learns herbs and potions, surrounds herself with lions, and, in a heart-stopping chapter, outwits the monster Scylla to propel Daedalus and his boat to safety. She makes lovers of Hermes and then two mortal men. She midwifes the birth of the Minotaur on Crete and performs her own C-section. And as she grows in power, she muses that "not even Odysseus could talk his way past [her] witchcraft. He had talked his way past the witch instead." Circe's fascination with mortals becomes the book's marrow and delivers its thrilling ending. All the while, the supernatural sits intriguingly alongside "the tonic of ordinary things." A few passages coil toward melodrama, and one inelegant line after a rape seems jarringly modern, but the spell holds fast. Expect Miller's readership to mushroom like one of Circe's spells.
Publisher: Little, Brown
Kirkus Reviews Issue: Feb. 1, 2018
Categories: LITERARY FICTION | HISTORICAL FICTION
More About This Book
Madeline Miller's Circe is Selection of Now Read This Book Club
THE SECRET HISTORY
by Donna Tartt ‧ RELEASE DATE: Sept. 16, 1992
The Brat Pack meets The Bacchae in this precious, way-too-long, and utterly unsuspenseful town-and-gown murder tale. A bunch of ever-so-mandarin college kids in a small Vermont school are the eager epigones of an aloof classics professor, and in their exclusivity and snobbishness and eagerness to please their teacher, they are moved to try to enact Dionysian frenzies in the woods. During the only one that actually comes off, a local farmer happens upon them—and they kill him. But the death isn't ruled a murder—and might never have been if one of the gang—a cadging sybarite named Bunny Corcoran—hadn't shown signs of cracking under the secret's weight. And so he too is dispatched. The narrator, a blank-slate Californian named Richard Pepen chronicles the coverup. But if you're thinking remorse-drama, conscience masque, or even semi-trashy who'll-break-first? page-turner, forget it: This is a straight gee-whiz, first-to-have-ever-noticed college novel—"Hampden College, as a body, was always strangely prone to hysteria. Whether from isolation, malice, or simple boredom, people there were far more credulous and excitable than educated people are generally thought to be, and this hermetic, overheated atmosphere made it a thriving black petri dish of melodrama and distortion." First-novelist Tartt goes muzzy when she has to describe human confrontations (the murder, or sex, or even the ping-ponging of fear), and is much more comfortable in transcribing aimless dorm-room paranoia or the TV shows that the malefactors anesthetize themselves with as fate ticks down. By telegraphing the murders, Tartt wants us to be continually horrified at these kids—while inviting us to semi-enjoy their manneristic fetishes and refined tastes. This ersatz-Fitzgerald mix of moralizing and mirror-looking (Jay McInerney shook and poured the shaker first) is very 80's—and in Tartt's strenuous version already seems dated, formulaic. Les Nerds du Mal—and about as deep (if not nearly as involving) as a TV movie.
Pub Date: Sept. 16, 1992
Review Posted Online: May 20, 2010
Kirkus Reviews Issue: July 1, 1992
More by Donna Tartt
by Donna Tartt
THE LITTLE FRIEND
Podcast Will Explore Bennington College Lit Trio
'The Secret History' Is New 'Today' Book Club Pick

redpajama_set_name: RedPajamaCommonCrawl


Check out the top workout room paint colors from Benjamin Moore.Find Benjamin Moore Paint Color 465 Antique Jade in a sample size, gallons or quarts of paint shipped directly to your door.
Find the revere pewter paint color ideas for various rooms such as bedroom, kitchen, living room, dining room.For Retailers Mybenjaminmoore.com - A Portal Developed Exclusively.
Update: Benjamin Moore has selected Simply White OC-117 as their 2016 Color Of the Year.The Decorologist tells you the color names and tips for using them.
Painting over wallpaper is easy when you use the right techniques. Our experts help you navigate color families and collections to find the right colors for your home.
Learn how to use color to pump up or zen out your home gym or fitness room.
Get fresh home paint ideas from the experts at Benjamin Moore.
Experience Century, a small batch interior paint featuring a soft touch finish and unparalleled depth of color made for designers, by designers.
My favorite Benjamin Moore warm gray paint colors or sometimes we call the color, greige.
Resources and information for authorized Benjamin Moore retailers.Top 2016 Benjamin Moore paint colors with simple design ideas, photo gallery, color wheel samples swatch and decorating tips.
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From traditional to modern, our ideas for exterior paint color combinations will inspire your imagination.Alligatoring is patterned cracking in the surface of the paint film that.Seems like a lot of Benjamin Moore users here - but have seen very little reference to their Color Stories full spectrum paint colors.
From business hours to a phone number, find the information you.Valspar Saffron Ivory is a soft and elegant yellow paint color that is. One of over 3,500 exclusive Benjamin Moore colours. Antique Jade.
These hues are the most favored by interior designers and home decor bloggers.
Search Colors. On-screen and printer colour representations may vary from actual paint. Best Benjamin Moore paint color reviews for your home design ideas with most popular 2015 colors for kitchens, bathrooms, bedrooms and living rooms.


text:
Berger and Green Attorneys at Law Award Heart Disease Scholarship to Meredith Labuda, Ballwin, Mo.
Berger and Green is excited to announce the Heart Disease Scholarship winner
PITTSBURGH, PA, August 12, 2020 /24-7PressRelease/ — Berger and Green Attorneys at Law, a Pittsburgh-based personal injury law firm, has awarded its annual Heart Disease Scholarship to Meredith Labuda, 18, of Ballwin, Mo. Miss Labuda recently graduated from Parkway South High School in Manchester, Mo., and will attend St. Louis University this fall.
Berger and Green has been helping people with medical disabilities for more than 40 years. Heart disease is still the number one cause of death in the U.S., according to the Centers for Disease Control and Prevention (CDC), and children who have heart conditions or congenital defects must forge a difficult path. That's one of the reasons why the firm established its annual $1,000 scholarship for one deserving student per year in 2017.
Miss Labuda was born with Hypoplastic Left Heart Syndrome, a condition in which the left side of her heart cannot pump blood into the body. She required several surgeries to mitigate the defect. Miss Labuda's moving essay was centered around her last surgery. She described her emotions and observations, which moved from self-concern and worry to compassion for other pediatric patients and ultimately gratitude for the nursing staff.
"When my nurses walked into my room, it was like the sun coming out after a rainy day," she wrote.
The nurses were so inspiring that Miss Labuda has decided to pursue a pediatric nursing career at St. Louis University.
Like many of the scholarship applicants, Miss Labuda is a high-achieving student. She graduated summa cum laude and is a member of both the National Honor Society and Key Club. She was a Vacation Bible School leader and served as a counselor or leader for various hospital pediatric camps.
She was also selected to attend the Parkway 2016 Presidential Inauguration Trip to Washington D.C. as well as a two-week trip through Rome, Normandy, and Paris celebrating the U.S. World War II military forces on the 75th anniversary of D-Day.
She is the daughter of Brian and Christine Labuda.
The Heart Disease Scholarship is only one of many Berger and Green community commitments. The firm is involved in many Pittsburgh charities, including Take Steps for Crohn's and Colitis Walk, the holiday toy drive called Stuff a Bus and the Neighborhood Legal Services Association's Equal Justice Campaign.
For more information on the Berger and Green scholarship, visit our website.
PreviousPatricia Parker Selected For "2020 America's Best Real Estate Professionals: New York Individuals"
NextStylist Carmen Rojas Opens New Salon, Jojma & Esencia Beauti, at Salon and Spa Galleria in Lake Worth TX
Washington Wheat Growers Welcome Balanced Environmental Impact Statement; Debate On The Value Of The Lower Snake River Dams Settled
Alsco Uniforms returns to Las Vegas Motor Speedway for a second time in 2021 with the NASCAR Xfinity Series Alsco Uniforms 302
US Navy Veterans Mesothelioma Advocate Recommends Attorney Erik Karst of the Law Firm of Karst von Oiste For A Navy Veteran NCO or Officer Who Has Mesothelioma-Compensation Might Be Millions
A Lifetime of Advocacy Leads to Huge Impact


text:
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<Root xmlns="http://15below.com/Substitutions.xsd">
  <Namespaces/>
  <Files>
    <File Filename="TestUpdateFiles\TestConfig1.xml">
      <Changes>
        <Change>
          <XPath>/root/value</XPath>
          <AppendAfter>
            <![CDATA[<NewTag/>]]>
          </AppendAfter>
        </Change>
      </Changes>
    </File>
  </Files>
</Root>


I would just like to thank all of you again for either visiting or participating in my 23rd "Themed Blog & Shop Hop" - I had so much fun and I hope that you did also!
"What I've Been Up to Lately" by Karen from "Masquerading Crafter"
Please join us tomorrow for the 24th Themed Blog & Shop Hop!
Oh, my! I never even imagined I would even have placed at all.
I am so happy even if it was just the clicks I won.


(PRESS RELEASE) -- Working closely with one of the leading regulated online casinos in New Jersey, Vegas Kings have been managing all Resorts Digital Gaming's online and offline creatives for the last two and a half years, and have recently secured a further 12–month retainer contract to continue providing a full tiered service to both Resorts Casino and Mohegan Sun Casino.
"We are very excited and proud to continue our close working relationship with the Resorts Digital Gaming team. Both brands are gaining great share within the New Jersey online market and the additional value that VK brings to the table is helping pave the way for both services to be at the forefront of the industry," says Ashley Adir, CEO of Vegas Kings.
Vegas Kings handles all the daily creative and web development requests ranging from online acquisition banner creatives, social media adverts, HTML mailers, video production promoting new games to full HD TV adverts, billboards and website back-end development.
"We love working with Vegas Kings and were so excited and thrilled to sign another year with them. Without them, being one of the leading operators in New Jersey would not be possible," says Ed Andrewes, CEO of Resorts Digital Gaming, LLC.


text:
cd "`dirname $0`"

$PYTHON_EXECUTABLE $BIGDL_HOME/pyspark/example/tf_example.py


text:
La perdición de los hombres és una pel·lícula còmica mexicana de 2000 dirigida per Arturo Ripstein.

Argument
Dos homes salten darrere d'uns cactus i colpegen a un home al cap amb una pedra. Després porten el cos a la cabanya del mort i se sentin amb el seu cos durant la nit mentre parlen, es queixen i ballen. Més tard, en l'estació de policia, dues dones venen a reclamar el cos: una esposa amargada i verinosa i una dona més jove i bonica. Lluiten i barallen fins que un d'ells es fa càrrec del cos. Més tard esbrinem per què va ser assassinat l'homònim "Rei del beisbol".

Repartiment
 Patricia Reyes Spíndola com Axe Face
 Rafael Inclán com l'altre home
 Luis Felipe Tovar com l'home
 Carlos Chávez com un que ve
 Leticia Valenzuela com l'altra dona
 Marco Zapata com el fill de l'altra dona
 Alejandra Montoya com Moon face

Premis i distincions
Festival Internacional de Cinema de Sant Sebastià

Festival de Gramado

Referències

Enllaços externs

 La perdición de los hombres a Versión española, rtve.es

Pel·lícules en castellà
Pel·lícules de Mèxic del 2000
Pel·lícules de comèdia del 2000
Pel·lícules de comèdia de Mèxic


text:
Q: What's the difference between Settings and *.config? I've worked a little with *.config files in the past, but I've not uses Settings files at all.  Simply put, what's the difference between a project's Settings file and *.config file?  Are there conventions as to what information goes in which?  When should one be used over the other?  How are Settings files built - are they embedded into the assembly, or kept external like *.config files?

A: Not much when you look at where the data is stored..
Settings gives you

*

*a GUI (In the Project Properties window) to create key-value pairs as opposed to manually tweaking the app.config

*a designer generated type safe class to access key-value pairs.

*It also makes a distinction between application-level and user-level settings.

Internally the key-value pairs are stored in a section in the app.config itself. Settings gives you a better API to deal with this problem and hence should be preferred to read-write to the app.config file.
Create a settings file in your project and then double click the corresponding app.config file. You should see your settings within an applicationSettings/userSettings node.

A: A project's settings file drives part the .config. Kind of.
If you add settings you will see that a custom configuration section is created in your configuration file. Instead of specifying ConfigurationSettings.Application("myKey") the settings file is used to autogenerate a strongly typed class which exposes your settings as properties, but the actual settings are still held in the configuration file.
However one difference is user settings (for certain project types). These you can set as well as get and persist them into the user's local profile directory without having to write those bits yourself.

redpajama_set_name: RedPajamaStackExchange


Get me up to speed Reved.George and Vera went to BRP some years ago.Did they go back to Yamaha and what about Cat?
Ya your right. I thought they were Yamaha sled dealer but I was a little out of date. On the Yamaha site it's either Markham Mower or DT in Uxbridge way.
Alternatively I am also on the board of our local pc support group so if you need anything please do not hesitate to contact me.
You can pm me here or email me from the website listed above.
I am humbled by your support for me. I might have met you at the Snow Crest Pancake Breakfast ride this year. I'm the other guy who rides behind Blake G without a Orange Flag I hear it's to locate Blake when he's lost ... Hehe We're trying to get 02Sled a red flag same purpose but also to tell them apart.
On a serious note, I am feeling much better but fighting constipation from Codene. I never thought having a bowel movement meant so much to me. I was almost in tears from stomach pain. It happened about 1hr ago and life is good.
Steve for sure I will take part in PC Rides again this coming winter.
I cannot stress enough that everyone should establish a PSA baseline, get checked regularly and stay away from Codene.
I see your sense of humour hasn't suffered. Guess what. Someone who used to be a good friend and has been demoted to friend saw the videos Blake did and got me a flag for my sled for my birthday. He would have ever thought Blake would be a trend setter. Before you know it there will be a sea of orange flags on the sleds on the trails. We just need to get one for you as well.
Try downing a bottle of prune juice. After an operation I returned home pretty stuck up and this is what was recommended. It worked really well. Try to align the TV so you can see out the bathroom door from where you are sitting and operate the remote from there.
My best wishes for a speedy recovery and a long snowy winter.
Thanks for the info. The doctor put me on Euro Lac and boy does it work.
Hopeto ride with you guys again this winter.
Great advice and its one of the things that we constatly promote!
Please don't hesitate to contact us that's what we are here for, see ya on the snow very soon!!


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Careers360 Ranking -
Top MBA Colleges in Bishnupur accepting MAT score in 2016
Each year Careers360 ranks and rates the Top MBA Colleges in Bishnupur accepting MAT score. The ranking is based on factors like quality of students, research output, industry interface, publications, academic productivity and so on. Read more here - Ranking Methodology.
State West Bengal (1)
City Bangalore (17) Pune (10) Mumbai (6) Coimbatore (6) New Delhi (5) Hyderabad (5) Chennai (4) Jaipur (4) Bhubaneshwar (4) Greater Noida (4) Noida (3) Ranchi (3) Dehradun (3) Lucknow (3) Kochi (2) Navi Mumbai (2) Pimpri-Chinchwad (2) Secunderabad (2) Warangal (2) Ahmedabad (2) Indore (2) Kolkata (2) Gurgaon (2) Raipur (1) Salem (1) Anand (1) Roorkee (1) Rourkela (1) Sengipatti (1) Siruseri (1) Thiruparankundram (1) Thane (1) Tumakuru (1) Visakhapatnam (1) Ballari (1) Bishnupur (1) Belgaum (1) Idukki (1) Harihar (1) Kanchipuram (1) Chandigarh (1) Kattankulathur (1) Mathura (1) Durg (1) Faridabad (1) Ghaziabad (1) Udupi (1) Vellore (1) Gwalior (1) Gajapati (1) Itanagar (1) Jorhat (1) Gram Baroli (1) Nerhe (1) Mysuru (1) Nashik (1)
Ownership Private (1)
Exam CAT (1) GMAT (1) CMAT (1) XAT (1) JEMAT (1) MAT (1) ATMA (1)
Year: Year 2020 2017 2016
Bishnupur MAT
College Name
Calcutta Business School, Bishnupur
You cannot compare more than 2 colleges at a time


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Home»Golf»Fifteen-time USGA champion Alexa Pano turns professional, will make pro debut on Epson Tour
Fifteen-time USGA champion Alexa Pano turns professional, will make pro debut on Epson Tour
April 12, 2022 3 Mins Read
Alexa Pano had one final goal to reach before turning professional: Play a competitive round at Augusta National.
To do that, she had to qualify for the final round of the recent Augusta National Women's Amateur, doubling the pressure on the 17-year-old.
"It was definitely a massive deal to get it done this year," Pano said Tuesday. "Everything revolved around that being my last event. I was so happy I could get it done this year. It was everything I dreamed of."
Few knew when Pano walked off the hallowed course on April 2 after shooting a 74 and tying for 12th, that it would be her final round as an amateur. On Tuesday, Pano announced on social media she is turning professional, saying the decision "has been a long time coming."
"This is her life decision," said Rick Pano, Alexa's dad and caddie. "I'm extremely happy she is doing this."
Rick said it didn't hit him until the practice round at Augusta National, the day before the ANWA final.
"She's walking down the fairway … it just popped into my head and I said, 'Tomorrow's it.' "
Pano's amateur career has been legendary. Her list of accomplishments stacks up with the best: Three appearances in the AWNA and that top 12 finish this year, a member of the winning United States Junior Ryder Cup team in 2016, 15 USGA championships, tied for the most U.S. Kids Golf World Championships with five and 19 LPGA/Epson tournaments.
2022 Augusta National Women's Amateur
Alexa Pano of the United States plays her stroke from the No. 1 tee during a practice round for the Augusta National Women's Amateur at Augusta National Golf Club, Friday, April 1, 2022. (Photo: Augusta National Women's Amateur)
In 2019, she was the youngest golfer to qualify for the U.S. Women's Open and to play in the inaugural ANWA. At 11, she was the youngest golfer to play an LPGA of Japan Tour event.
Pano said one of her coaches texted her Tuesday and asked if she felt any different.
"I kind of feel exactly the same," she told him.
Pano's maturity and ability to not be overwhelmed by the moment have defined her career. That will come in handy next week when she plays her first tournament on the Epson Tour as a professional, the Copper Rock Championship in Hurricane, Utah.
"I don't think there will be any nerves," said Pano, who is being homeschooled and will receive her high school diploma this year. "It's kind of just like another golf tournament for me. I've always gone into every event I was playing in to try and win it, even when I've had good weeks and bad weeks. I don't think anything changes as far as golf mindset."
Pano has full status on the Epson Tour – the qualifying tour of the LPGA – after finishing in the top 10 of Stage II of the LPGA Q-School in October. She is planning to play in 16 Epson events. She has been invited to play in an LPGA Tour event in Japan in the fall and may play in two or three others.
Pano also will attempt to qualify for the June 2-5 U.S. Women's Open next month.
"It's my belief that she did it for two reasons, both competitive," Rick said. "Since she was 8, she always wanted to play against the best players in the world, the highest level she could. And she's driven by seeing how good she can get.
"It's a different mentality, it's a different emotion, and it's different maturity level. I think we're prepared for it, but you never know until you get there."
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Nusra Front military leadership KIA'd by Syrian Arab Air Force
File photo: Syrian Arab Air Force Mikoyan MiG-29SM multirole fighter aircraft
According to Aljazeera:
An air strike by Syrian government forces has killed a senior commander of the Syrian branch of al-Qaeda, al-Nusra Front, Syrian state media has reported.
SANA state news agency said Abu Hammam al-Shami, also known as al-Farouq al-Suri, was killed in a special army operation in Idlib province on Thursday.
Al-Shami, a veteran al-Qaeda leader from Damascus, held the title of general military commander for al-Nusra Front.
Pentagon spokesman, Colonel Steve Warren, said: "We cannot confirm press reports of the deaths of senior al-Nusra leaders near the province of Idlib."
However, he added: "Neither the US or the coalition have conducted air strikes near that location in recent days."
COMMENTARY: According to Nusra Front, three other military leaders were KIA in the airstrike, including Abu Musab Falastini, Abu Omar Kurdi, and Abu Baraa Ansari.
If the airstrike was indeed carried out by SyAAF (Syrian Arab Air Force), it would serve to provide a boost to Syrian Arab Republic armed forces, as well as the Iran-led coaltion against ISIL and Al-Qaeda linked forces that includes Nusra Front.
Some social media sources claim the airstrike was carried out by SyAAF Mikoyan MiG-29 aircraft. If true, it may have been the SyAAF Mikoyan MiG-29SM, a type known to carry an expanded arsenal of air-to-ground weaponry, including Kh-29T/TE (AS-14 'Kedge') and Kh-31A/P (AS-17 'Krypton') missiles and KAB-500KR guided bombs. [source: IHS Jane's]
Below: situation map for forces at Idlib Governate, dated 05MAR15 [source: Peto Lucem]
Posted by Mark Pyruz at 12:38 AM
Labels: al-Nusra, Iran-led coalition, Syria, Syrian conflict
good für Syria
Brig. Gen. Basrawi (IQAF.ret) said...
The air support provided by the Western coalition has cast shadows over Syrian Air Force's constant efforts in combating ISIS, which unfortunately have largely been un-recognized in the West.
interested party said...
Over shadowed by barrel bombs perhaps? Still, it maybe a good sign that the SAF has been able to regroup its assets and act on good intelligence. This country needs peace. Where is the FSA? Thanks for nothing USA and Turkey!. Lets hope this mess's end game is not a final show down between Al-Nusra and IS. Both of those travesty's destroyed and an accommodation between FSA and the Syrian government would better.
https://medium.com/war-is-boring/america-dropped-deadly-barrel-bombs-in-vietnam-f006f1ce77cf
why all talk about barrel bombs like its something catastrophic?
guys tell me what is different between barrel-bombs & normal bomb?
1) both are bomb with explosive material.
2) both drop from planes.
3) both unguided weapons.
4) both made by military facility.
5) both kills peoples.