text:
\section{Introduction}

Analysis of the distance-redshift relation using high redshift Type Ia
supernovae has led to the discovery that the expansion of the Universe
is currently accelerating \citep{riess98,perlmutter99}. This suggests
that the dominant contribution to the present-day energy budget is a
component with equation of state $w<-1/3$, called
``dark-energy''. Combining measurements of CMB fluctuations
\citep{debernardis00,lee01,halverson02,pearson03,scott03,hinshaw03}
with measurements of the clustering of present day galaxies
\citep{percival01,tegmark04a,cole05} has confirmed this requirement
for dark energy
(e.g. \citealt{efstathiou02,percival02,spergel03,tegmark04b}). These
studies favour a flat Universe with $\Omega_M\simeq0.3$, with the
remaining contribution made up of dark energy.

The nature of the dark energy is the source of much debate. Perhaps
the most straightforward candidate is a positive cosmological constant
$\Lambda$ with equation of state parameter $w=-1$. This simple picture
forms a special case in a broader class of models where the dark
energy is the manifestation of a scalar field slowly rolling down its
potential. In the limit of a completely flat potential, these models
lead to $w=-1$ \citep{wetterich88,peebles88,ratra88}. A subclass of
quintessence models with constant $-1<w<-1/3$ was proposed by
\citet{caldwell98a,caldwell98b}. Many other forms have been proposed
for the shape of this potential, leading to an equation of state
parameter that is dependent on the scale factor (see
\citealt{peebles03} for a review).

Given the plethora of models, many parameterisations have been
introduced in order to observationally constrain $w(a)$ (see
\citealt{johri04} for a review). However, there is obviously a
limitation imposed by any parameterisation \citep{bassett04}
and, in the present paper, we have tried to be as general as possible
in the equations presented and discussed. In order to demonstrate the
effects of the dark energy equation of state in numerical examples, we
pay particular attention to the parameterisation of \citet{jassal04}
\begin{equation}
  w(a)=w_0+w_1a(1-a).
    \label{eq:wparam}
\end{equation}
The present day value of $w|_{a=1}=w_0$, and its derivative
$dw(a)/da|_{a=1}=-w_1$ will serve to demonstrate the possible
cosmological signatures of a wider class of models. We also consider
models that assume $w(a)=w$ is constant.  Qualitatively, many of the
effects of general $w(a)$ models can be predicted by interpolating
between models with constant $w$. In fact, for many models, by the
lookback time by which $w(a)$ has evolved significantly from its
present day value, the cosmological significance of $w(a)$ is greatly
reduced (although see, for example, \citealt{maor02}). Obviously, this
also signifies that an evolving $w(a)$ is harder to
observationally constrain than constant $w$ \citep{kujat02}. If the
dark energy equation of state only varies slowly with time, then
observational predictions are well approximated by treating $w(a)=w$
as a constant \citep{wang00}, with
\begin{equation}
  w \simeq \frac{\int\,da\, \Omega_X(a)w(a)}{\int\,da\, \Omega_X(a)},
\end{equation}
where $\Omega_X$ is the dark energy density relative to the critical
density (see also \citealt{dave02}).

The equation of state for the dark energy does not uniquely define the
behaviour of this component. The formation of structure is also
dependent on the sound speed of the dark energy which limits its
clustering properties. In the original formalism for quintessence
\citep{caldwell98a,caldwell98b}, the dark energy component has a high
sound speed which means that it can cluster on the largest scales, but
does not cluster on the scales of galaxy clusters and below.

Consequently, the dark energy only affects the matter power
spectrum \citep{ma99}, and the CMB anisotropies \citep{caldwell98b} on
very large scales. For the special case of a cosmological constant,
$w=-1$, the clustering of the dark energy is not an issue as the
energy density in perturbations always remains at the background
level. Obviously, for $w\ne-1$, the clustering properties of the dark
energy strongly affect the build-up of structure in the Universe. In
particular for spherical perturbations, the linear growth rate,
critical overdensity for collapse, and details of subsequent behaviour
and virialisation are all dependent on this property. In this paper we
follow the majority of current literature and only consider a
non-clustering dark energy component. However, we do note that models
in which the dark energy clusters on small scales are being discussed
with increasing frequency
\citep{hu04a,nunes04,hannestad05,manera05,maor05}.

In general, for the variables used in this paper, if no dependence is
quoted for a given quantity (e.g. $\Omega_M$), it should be assumed to
be calculated at present day. If instead explicit dependence is given
(e.g. $\Omega_M(a)$), the quantity is assumed to vary with epoch. The
exception to this rule is $w(a)$, where if no dependence on $a$ is
given, we additionally assume that $w(a)=w$ is constant in time.

We start by reviewing the behaviour of different cosmological models,
and the critical parameters that separate models with different
properties (Section~\ref{sec:dynamics}) as this can be related to the
behaviour of spherical perturbations. We then calculate the linear
growth factor (Section~\ref{sec:linear}), the critical overdensity for
collapse at present day (Section~\ref{sec:dc}), and as a function of
time (Section~\ref{sec:dc_evol}). This critical overdensity is then
used to determine the mass function (Section~\ref{sec:mass_func}) and
the rate of structure growth (Section~\ref{sec:rate_grow}). Finally we
consider the virialisation of perturbations, and the difficulties
associated with these calculations in dark energy cosmologies
(Section~\ref{sec:virial}).

\section{dynamics of cosmological models}  \label{sec:dynamics}

It is assumed that the dark energy has an equation of state relating
its pressure $p_X$ and density $\rho_X$ given by
$p_X=w(a)\rho_X$. For general $w(a)$, the dynamical expansion of the
Universe is specified by the Friedmann equation
\begin{equation}
  E^2(a) = \frac{H^2(a)}{H_0^2}
         = \Omega_Ma^{-3}+\Omega_Ka^{-2}+\Omega_Xa^{f(a)},
  \label{eq:friedmann_eq1}
\end{equation}
where $\Omega_K\equiv(1-\Omega_M-\Omega_X)$ is the curvature constant,
$H(a)\equiv\dot{a}/a$ is the Hubble parameter with present day value
$H_0$. $f(a)$ is calculated by solving the conservation of energy
equation for the dark energy $d(\rho_Xa^3)/da = -3p_Xa^2$ \citep{caldwell98b},
giving $\rho_X\propto a^{f(a)}$, where
\begin{equation}
  f(a) = \frac{-3}{\ln a}\int_0^{\ln a}[1+w(a')]d\ln a'.
   \label{eq:rho_X}
\end{equation}
For constant $w$, $f(a)=-3(1+w)$. For the parameterisation
$w(a)=w_0+w_1a(1-a)$ of \citet{jassal04},
\begin{equation}
  f(a)=-3(1+w_0)+\frac{3w_1}{2\ln a}(1-a)^2.
  \label{eq:faw_jassal}
\end{equation}

The evolution of the matter density $\Omega_M(a)$ and dark energy
density $\Omega_X(a)$ are given by
\begin{equation}
  \Omega_M(a)=\frac{\Omega_M a^{-3}}{E^2(a)},\,\,\,
  \Omega_X(a)=\frac{\Omega_X a^{f(a)}}{E^2(a)}.
  \label{eq:omega_evol}
\end{equation}

It is immediately apparent that the equation of state of the dark
energy has a strong affect on the behaviour of these equations, even
for models where $w(a)$ is constant. For example, for $w=-1/3$, the
dark energy terms in Eq.~\ref{eq:friedmann_eq1} cancel, leaving a
cosmological model with an expansion time history that behaves exactly
as an open Universe with matter density $\Omega_M$, although the
space-time geometry differs (e.g. review by \citealt{peebles03}).  For
$w<-1/3$, at late times the dark energy will dominate the dynamics of
the expansion, with the epoch of transition from matter to dark energy
domination dependent on $w$. Decreasing the equation of state $w$ from
$-1/3$ smoothly interpolates between the open Universe model,
cosmological constant ($\Lambda$ model) and extrapolates beyond.

The asymptotic behaviour (either forwards or backwards in time) of
different cosmological models is delineated by models with so-called
critical parameters. These separate cosmologies that predict future
recollapse, expansion forever and models that do not start at a
big-bang, but instead ``loiter'' at early times, asymptotically
tending towards a stable solution such as Einstein's static model for
$\Lambda$ cosmologies. For these critical models, the zero points of
$(da/dt)^2=E^2(a)a^2=0$ should occur at turning points of this
equation. For constant $w$, differentiating
Eq.~\ref{eq:friedmann_eq1}, we see that the critical cosmologies
should have $E^2(a)a^2=0$ when \citep{chiba05}
\begin{equation}
  a_{\rm turn} = \left[\frac{\Omega_M}{-(1+3w)\Omega_X}
    \right]^{\frac{-1}{3w}}.
    \label{eq:a_turn}
\end{equation}
Substituting this value of the scale factor back into
Eq.~\ref{eq:friedmann_eq1} gives an equation for the critical
parameters.

For $w=-1$, this reduces to the well known cubic equation
\citep{glanfield66}
\begin{equation}
  (\Omega_M+\Omega_\Lambda-1)^3 = \frac{27}{4}\Omega_M^2\Omega_\Lambda
  \label{eq:omega_critical}
\end{equation}
that can be solved analytically \citep{felten86}. A detailed
discussion of the behaviour of $\Lambda$ models is given by
\citet{moles91}.

\begin{figure*}
  \resizebox{5.8cm}{!}{\includegraphics{3637f1a.ps}}
  \resizebox{5.8cm}{!}{\includegraphics{3637f1b.ps}}
  \resizebox{5.8cm}{!}{\includegraphics{3637f1c.ps}}\\
  \resizebox{5.8cm}{!}{\includegraphics{3637f1d.ps}}
  \resizebox{5.8cm}{!}{\includegraphics{3637f1e.ps}}
  \resizebox{5.8cm}{!}{\includegraphics{3637f1f.ps}}\\
  \resizebox{5.8cm}{!}{\includegraphics{3637f1g.ps}}
  \resizebox{5.8cm}{!}{\includegraphics{3637f1h.ps}}
  \resizebox{5.8cm}{!}{\includegraphics{3637f1i.ps}}\\
  \caption{Plots showing the evolution of the matter and vacuum energy
  densities for a selection of cosmologies with different dark energy
  equation of state (grey lines). For cosmologies with $\Omega_X>0$,
  $a=1$ was fixed when the matter density and vacuum density were
  equal. The critical models that border the different types of
  evolution are shown by the black lines. Dashed lines in all plots
  show the critical models for $\Lambda$ cosmologies. The dotted line
  for $w_1\ge0$ shows $\Omega_X=0$, to emphasis that recollapse can
  occur if $\Omega_X>0$ provided that $\Omega_M>>\Omega_X$.
  \label{fig:critical_cosmology_models}}
\end{figure*}

For general $w(a)$, it is straightforward to numerically determine the
critical parameters from Eq.~\ref{eq:friedmann_eq1} and its
derivative. The different regions in ($\Omega_M$,$\Omega_X$) space are
shown in Fig.~\ref{fig:critical_cosmology_models} for $w_0=-4/3,-1,
-2/3$ and $w_1=-1/3,0,1/3$ using the parameterisation of
Eq.~\ref{eq:wparam}. Critical values of $\Omega_M$ and $\Omega_X$ at
$a=1$ are shown by the solid black lines.

For comparison, in Fig.~\ref{fig:critical_cosmology_models} we also
plot various cosmological tracks (grey lines). For general $w(a)$
models, the cosmology is not uniquely specified by $\Omega_M(a)$ and
$\Omega_X(a)$, as we also need to specify $a$. The cosmological tracks
in Fig.~\ref{fig:critical_cosmology_models} for $\Omega_X>0$ have
$a=1$ when $\Omega_M=\Omega_X$. For general models, the tracks can
therefore cross, and can move into regions of
($\Omega_M(a)$,$\Omega_X(a)$) space that would have been excluded at
$a=1$. For the panels where $w_1\ne0$, the cosmological tracks should
simply be though of as examples of possible tracks that go through
particular $\Omega_M(a)$ and $\Omega_X(a)$.

For $w_1=0$, $w_0<-1$ models favour a larger region of parameter space
for which there is no big-bang, while $w_0>-1$ leads to recollapse for
models in a larger region in ($\Omega_M$, $\Omega_X$) space,
reflecting the fact that a smaller amount of matter is required to
collapse the Universe before the dark energy dominates. For $w_0>-1$
cosmologies, a future singularity is predicted where the scale factor
and Hubble parameter diverge, leading to a ``big-rip'' rather than
expansion forever \citep{caldwell03a}. For further discussion of the
behaviour of $w_1=0$ cosmologies, see \citet{dearaujo05,chiba05}.

If we allow $w_1\ne0$, the behaviour becomes even more
complicated. From Eq.~\ref{eq:faw_jassal}, for $w_1<0$,
$lim_{a\to\infty}\rho_X=0$, and the dark energy term in
Eq.~\ref{eq:friedmann_eq1} tends to zero. This means that all closed
cosmologies ($\Omega_K<0$) will eventually recollapse as $da/dt=0$ for
some finite $a>1$. Open cosmologies expand forever, with
$lim_{a\to\infty}da/dt=\sqrt{\Omega_K}$. When $\Omega_X>0$, open
models become matter dominated at late times, and can go through a
phase where $\Omega_M(a)$ increases (although obviously $\rho_M$ does
not). For $w_1>0$ and $\Omega_X>0$, the dark energy increases
monotonically with the scale factor, and it is increasingly unlikely
that the matter can cause recollapse before the dark energy takes hold
and accelerates the expansion of the Universe. The region of models
which have $\Omega_X>0$, but that recollapse therefore becomes
smaller.

Solutions that recollapse are of particular importance for the
spherical top-hat collapse model: for $\Lambda$ cosmologies, overdense
regions that recollapse exactly follow the behaviour of these
models. As we will see later on, for general $w(a)$ cosmologies we
cannot link spherical perturbations directly to one of these
cosmological models if the dark energy does not cluster on the scales
of interest.

Given present observational constraints, the region of
$(\Omega_M,\Omega_X)$ space probed in
Fig.~\ref{fig:critical_cosmology_models} is only of academic interest,
and in the remainder of this paper we focus on the subset of models
with $0<\Omega_M<1$ and $0<\Omega_X<1$.

\section{linear growth of fluctuations}  \label{sec:linear}

Considering the behaviour of homogeneous spherical perturbations
provides one of the most simple models for the formation of structure
in the Universe. The ease with which the behaviour can be modelled
follows from Birkhoff's theorem, which states that a spherically
symmetric gravitational field in empty space is static and is always
described by the Schwarzchild metric \citep{birkhoff23}. This gives
that the behaviour of an homogeneous sphere of uniform density can
itself be modelled using the same equations of
Section~\ref{sec:dynamics}. One of the important applications of the
spherical perturbation model is the derivation of the linear growth
rate (pioneered by \citealt{zel58, peebles_lss}, section~10). The
application proceeds as follows: We consider two spheres containing
equal amounts of material, one of background material with radius $a$,
and one of radius $a_p$ with a homogeneous change in
overdensity. Henceforth quantities with a subscript $p$ refer to the
perturbation, while no subscript relates to the background. The
densities within the spheres are related to their radii, with
\begin{equation}
  \rho_p a_p^3=\rho a^3, \,\,\, \delta\equiv\rho_p/\rho-1,
  \label{eq:arel1}
\end{equation}
giving, to first order in in $\delta$,
\begin{equation}
  a_p=a(1-\delta/3).
  \label{eq:arel2}
\end{equation}
The cosmological equation for both the spherical perturbation and the
background is
\begin{equation}
  \frac{1}{a}\frac{d^2a}{dt^2}=-\frac{H_0^2}{2}
    \left[\Omega_Ma^{-3}+[1+3w(a)]\Omega_Xa^{f(a)}\right],
    \label{eq:cosmo}
\end{equation}
where $a$ should be replaced by $a_p$ in the matter density term for
the perturbation. The dark energy density $\rho_X\propto a^{f(a)}$,
is the same for both the perturbation and the background if the dark
energy does not cluster. Because of this, substituting
Eqns~\ref{eq:arel1} \&~\ref{eq:arel2} into this equation gives, to
first order in $\delta$,
\begin{equation}
  \frac{3}{2}\Omega_MH_0^2a^{-3} \delta =
  \frac{d^2\delta}{dt^2}+\frac{2}{a}\frac{da}{dt}\frac{d\delta}{dt}.
\end{equation}
Changing variables from $t$ to $a$ gives
\begin{displaymath}
  \frac{3}{2}\Omega_Ma^{-3}\delta = \frac{d^2\delta}{da^2}E^2(a)a^2
    + \frac{d\delta}{da}\left\{2aE^2(a)\right.
\end{displaymath}
\begin{equation}
  \hspace{1.0cm}
    \left.-\frac{a}{2}\left[\Omega_Ma^{-3}
    +[3w(a)+1]\Omega_Xa^{f(a)}\right]\right\},
  \label{eq:ddda2}
\end{equation}
which can be further simplified to give
\begin{displaymath}
  \frac{3}{2}\Omega_M(a) =   \frac{d^2\ln\delta}{d\ln a^2}
    + \left(\frac{d\ln\delta}{d\ln a}\right)^2
    + \frac{d\ln\delta}{d\ln a}\left\{1\right.
\end{displaymath}
\begin{equation}
  \hspace{2cm}
    \left.-\frac{1}{2}\left[\Omega_M(a)+[3w(a)+1]\Omega_X(a)\right]\right\}.
  \label{eq:dlndda2}
\end{equation}
This is the generalisation of Equation B7 in \citet{wang98}
to non-flat cosmologies, and is valid for general $w(a)$.

\begin{figure}
  \centering
  \resizebox{5.8cm}{!}{\includegraphics{3637f2a.ps}}
  \resizebox{5.8cm}{!}{\includegraphics{3637f2b.ps}}
  \resizebox{5.8cm}{!}{\includegraphics{3637f2c.ps}}
  \caption{Plots showing contours of constant linear growth factor to
  present day for a selection of cosmologies (grey and black
  lines). The growth factor is normalised to unity for $\Omega_M=1$,
  $\Omega_X=0$. Increasing $w$ from $-4/3$ to $-2/3$, decreases the
  growth factor leading to behaviour more like that of an open
  Universe. Dotted contours are for the fitting formula of
  Eq.~\ref{eq:Dapprox_quin}, together with
  Eqns.~\ref{eq:Dlin_alpha_fit} \&~\ref{eq:Dlin_A_fit}. The dashed
  line highlights flat cosmological models. \label{fig:lin_grow_w}}
\end{figure}

Eq.~\ref{eq:dlndda2} can easily be solved by numerical integration,
and we show contours of different linear growth factor to present day
in ($\Omega_M$,$\Omega_X$) space in Fig.~\ref{fig:lin_grow_w} for
constant $w=-2/3,-1, -4/3$. The linear growth factor is strongly
dependent on $w$, with $w>-1$ models behaving more like open Universes
than $w<-1$ models as the effect of the dark energy diminishes. For
the linear growth factor in a variety of cosmological models with time
dependent $w(a)$ see, for example, \citet{doran01,linder03}.

For $\Lambda$ cosmologies, the growing mode solution to this equation
is \citep{heath77}
\begin{equation}
  D(a) = \frac{5\Omega_M}{2} E(a) \int^{a}_0\frac{da'}{[a'E(a')]^3},
    \label{eq:lin_growth_factor}
\end{equation}
where $E(a)$ is given by Eq.~\ref{eq:friedmann_eq1}. Although this
integral can be easily solved numerically, it is common to use the
approximation of \citet{carroll}, which follows from work in
\citet{lightman90} and \citet{lahav91}
\begin{eqnarray}
  \nonumber
  \lefteqn{D(a) \simeq \frac{5\Omega_M(a)a}{2}
    \left[\Omega_M(a)^{4/7}-\Omega_\Lambda(a)\right.}\\
  & & \hspace{2.0cm} \left.+\left(1+\frac{\Omega_M(a)}{2}\right)
    \left(1+\frac{\Omega_\Lambda(a)}{70}\right) \right]^{-1}.
    \label{eq:Dapprox}
\end{eqnarray}

A general solution for the growing mode solution in dark energy
cosmologies, equivalent to Eq.~\ref{eq:lin_growth_factor}, has yet to
be found. However, for flat cosmological models, with constant $w$,
the solution can be written in terms of the hypergeometric function
$_2F_1$ \citep{silveira94}
\begin{equation}
  D(a) = a\,_2F_1\left[-\frac{1}{3w},\frac{w-1}{2w},1-\frac{5}{6w},
	              -a^{-3w}\frac{1-\Omega_M}{\Omega_M}\right].
    \label{eq:Dhyp}
\end{equation}

Writing the growth index as
\begin{equation}
  \frac{d\ln\delta}{d\ln a} = \Omega_M^\alpha(a),
\end{equation}
\citet{wang98} use Eq.~\ref{eq:dlndda2} for the special case of flat
cosmologies to give
\begin{displaymath}
  \alpha \simeq \frac{3}{5-w/(1-w)}
\end{displaymath}
\begin{equation}
  \hspace{0.5cm}
    +\frac{3}{125}
    \frac{(1-w)(1-3w/2)}{(1-6w/5)^3}\left[1-\Omega_M(a)\right].
  \label{eq:Dlin_alpha_fit}
\end{equation}
This led \citet{basilakos03} to extend the approximation of
\citet{carroll} given by Eq.~\ref{eq:Dapprox} to the case of $w\ne-1$
\begin{eqnarray}
  \nonumber
  \lefteqn{D(a) \simeq \frac{5\Omega_M(a)a}{2}
    \left[\Omega_M(a)^\alpha-\Omega_X(a)\right.}\\
  & & \hspace{2.0cm} \left.+\left(1+\frac{\Omega_M(a)}{2}\right)
    \left(1+\mathcal{A}\Omega_X(a)\right) \right]^{-1},
    \label{eq:Dapprox_quin}
\end{eqnarray}

with $\alpha$ given by Eq.~\ref{eq:Dlin_alpha_fit}, and
$\mathcal{A}\simeq1.742+3.343w+1.615w^2$. In Fig.~\ref{fig:Dlin_A_fit}
we plot the $\mathcal{A}$ values required to match
Eq.~\ref{eq:Dapprox_quin} to the true linear growth factor (given by
Eq.~\ref{eq:Dhyp}), for flat cosmological models with
$0.1<\Omega_M<0.9$ as a function of $w$ (grey lines). The fit of
\citet{basilakos03} is shown by the dashed line. This is a poor fit for
$w<-1$, so instead, we propose
\begin{equation}
  \mathcal{A} = \frac{-0.28}{w+0.08}-0.3,
    \label{eq:Dlin_A_fit}
\end{equation}
shown by the black line in Fig.~\ref{fig:Dlin_A_fit}.

\begin{figure}
  \centering
  \resizebox{6.5cm}{!}{\includegraphics{3637f3.ps}}
  \caption{Plot showing the true value of $\mathcal{A}$ in
  Eq.~\ref{eq:Dapprox_quin} as a function of $w$ for 9 flat
  cosmologies with $\Omega_M$ evenly spread between $0.1$ and $0.9$
  (grey lines). For comparison we plot the fitting formula of
  \citet{basilakos03} (dashed line) and for Eq.~\ref{eq:Dlin_A_fit} (black
  line). \label{fig:Dlin_A_fit}}
\end{figure}

Eq.~\ref{eq:Dlin_A_fit} has been determined by fitting to flat
cosmological models with $0.1<\Omega_M<0.9$. For non-flat models, the
approximation of Eq.~\ref{eq:Dapprox_quin} remains a good fit. In
Fig.~\ref{fig:lin_grow_w}, the dotted contours are for the fitting
formula of Eq.~\ref{eq:Dapprox_quin}, together with
Eqns.~\ref{eq:Dlin_alpha_fit} \&~\ref{eq:Dlin_A_fit}, compared with
the true value of $D_0$ given by the solid contours. The fitting
formula fails for $\Omega_M<<0.1$, but for $\Omega_M>0.1$, the maximum
error (with $0<\Omega_X<1$) is 3.8\% for $w=-4/3$, 2.6\% for $w=-1$
and 5.1\% for $w=-2/3$. For comparison, the fitting formula of
\citet{carroll} given by Eq.~\ref{eq:Dapprox} is accurate to 2.1\% for
$w=-1$ over this range of $\Omega_M$.

\section{the critical density for collapse of spherical perturbations}
  \label{sec:dc}

We now calculate the critical overdensity for collapse of homogeneous
spherical perturbations at present day in a homogeneous dark energy
background. The method adopted is a development of that in
\citet{percival00}, where the critical overdensity in $\Lambda$
cosmologies was calculated. Solution schemes for an Einstein-de Sitter
cosmology \citep{gunn72}, for open cosmologies \citet{lacey93} and for
flat $\Lambda$ cosmologies \citep{eke96} were summarised in
\citet{kitayama96}. See also the solution scheme for $\Lambda$
cosmologies used by \citet{barrow84,barrow93}.

As in Section ~\ref{sec:linear}, we consider two spheres containing
equal amounts of material: one of background material with radius $a$,
and one of radius $a_p$ with a homogeneous change in overdensity. If
the dark energy component is negligible, as at early times for
$lim_{a\to0}w(a)<-1/3$,
\begin{equation}
  \left(\frac{da}{d(H_0t)}\right)^2=\frac{\Omega_M}{a}+\epsilon,
  \label{eq:friedmann1}
\end{equation}
where $\epsilon$ is allowed to take any real value. For the
background, $\epsilon=\Omega_K\equiv(1-\Omega_M-\Omega_X)$ is the
standard curvature constant. The matter density $\Omega_M$ is the same
for both the perturbation and the background as the two spherical
regions contain the same mass. Following \citet{percival00}, a series
solution for $a(H_0t)$ in the limit $H_0t\to0$ can be obtained given
by $a=\alpha (H_0t)^{2/3}+\beta (H_0t)^{4/3}+O[(H_0t)^{6/3}]$, where
\begin{equation}
  \alpha = \left(\frac{9\Omega_M}{4}\right)^{1/3}, \,\,\,
  \beta  = \frac{3\epsilon}{20}\left(\frac{12}{\Omega_M}\right)^{1/3}.
    \label{eq:ab}
\end{equation}
Using the fact that the spheres contain equal mass,
\begin{equation}
  \lim_{H_0t\to0}\delta(H_0t)=
    \frac{3}{\alpha}(\beta-\beta_p)(H_0t)^{2/3}+O[(H_0t)^{4/3}].
  \label{eq:limits}
\end{equation}
Substituting Eq.~\ref{eq:ab} into Eq.~\ref{eq:limits} gives that
\begin{displaymath}
  \lim_{H_0t\to0}\delta(H_0t)=
\end{displaymath}
\begin{equation}
  \hspace{1cm}
    \frac{3}{5}\left(\frac{3}{2\Omega_M}\right)^{2/3}
    \left[(1-\Omega_M-\Omega_X)-\epsilon_p\right]
    (H_0t)^{2/3}.
  \label{eq:ktolimd}
\end{equation}

We now extrapolate this limiting behaviour to present day, using the
linear growth factor to extrapolate the normalisation of the density
field from early times. This gives
\begin{equation}
  \delta_c = D_0\lim_{H_0t\to0}\left[\frac{\delta(t)}{D(t)}\right],
  \label{eq:delta_c_extrap}
\end{equation}
where $D_0$ is the linear growth factor to present day. Given the
normalisation of $D(t)$ adopted in Section~\ref{sec:linear},
$\lim_{H_0t\to0}D(H_0t)=\alpha(H_0t)^{2/3}$, where $\alpha$ is given
by Eq.~\ref{eq:ab}. We can therefore write $\delta_c$ as
\begin{equation}
  \frac{\delta_c}{D_0}= \frac{3}{5\Omega_M}
    \left[(1-\Omega_M-\Omega_X)-\epsilon_p\right].
  \label{eq:delta_c1}
\end{equation}

This formula relates the linearly extrapolated overdensity $\delta_c$
to the initial curvature of the perturbation for cosmological models
in which the dark energy becomes negligible as $H_0t\to0$.

\begin{figure}
  \centering
  \resizebox{5.6cm}{!}{\includegraphics{3637f4a.ps}}
  \resizebox{5.6cm}{!}{\includegraphics{3637f4b.ps}}
  \resizebox{5.6cm}{!}{\includegraphics{3637f4c.ps}}
  \caption{Plots showing contours of constant critical overdensity for
  a selection of cosmologies (grey and black lines) with
  constant $w$. Contours are plotted as a ratio of $\delta_{\rm EdS}$
  as given by Eq.~\ref{eq:delta_eds} from $0.96\delta_{\rm EdS}$ to
  $1.02\delta_{\rm EdS}$ at intervals of $0.005\delta_{\rm EdS}$. For
  the $w=-1$ cosmology we also plot the values determined by
  accurately solving Eq.~\ref{eq:friedmann2} using standard Elliptical
  integrals (dotted lines). The difference between solid and dotted
  lines are caused by the numerical integration of
  Eqns~\ref{eq:num_int1}, \ref{eq:num_int2} \& \ref{eq:num_int3}. The
  dashed line highlights flat cosmological models (as in
  Fig.~\ref{fig:lin_grow_w}). \label{fig:dc_w}}
\end{figure}

\subsection{case 1: cosmological constant} \label{sec:delc_lambda}

For $\Lambda$ cosmologies, the curvature of the perturbation (and
energy) is conserved through the Friedmann equation
\begin{equation}
  \left(\frac{da_p}{d(H_0t)}\right)^2=\frac{\Omega_M}{a_p}+\epsilon_p
    + \Omega_\Lambda a_p^2.
  \label{eq:friedmann2}
\end{equation}

This equation defines a mini-cosmology, so using the methodology of
Section~\ref{sec:dynamics}, the requirement for collapse can be seen
to be $-\epsilon_p^3>27\Omega_\Lambda\Omega_M^2/4$ (compare with
Eq.~\ref{eq:omega_critical}). Given a perturbation that collapses, the
time taken can be found by integrating Eq.~\ref{eq:friedmann2}, which
can be reduced to a function of standard Elliptical integrals.

If $\Omega_\Lambda=0$, Eq.~\ref{eq:friedmann2} can be solved
analytically and, for an Einstein-de Sitter cosmology, the critical
overdensity for collapse at present day reduces to
\begin{equation}
  \delta_{\rm EdS} \equiv \frac{3}{20}(12\pi)^{2/3} \simeq 1.686,
    \label{eq:delta_eds}
\end{equation}
which was first derived by \citet{gunn72}.

\subsection{case 2: general $w(a)$ cosmologies} \label{sec:delc_quinn}

When the dark energy does not cluster, the energy within a spherical
perturbation is not conserved (a comprehensive discussion of this is
given in \citealt{weinberg03}). Although this means that we cannot use
Eq.~\ref{eq:friedmann2} to determine the behaviour of the
perturbation, we can still use the cosmology equation
(Eq.~\ref{eq:cosmo}). \citet{wang98} provide a boundary value problem
for solving this second order differential equation, setting the
boundary at the turn-around time. However, given the relatively
straightforward initial evolution considered above, it is far simpler
to set up an initial value problem (in either $a_p$ or $\delta$) to
determine the subsequent behaviour. In a recent paper, \citet{chiba05}
have also determined the limiting initial conditions for the
differential equations, working directly from the cosmology
equation. However, it is perhaps more intuitive to link the critical
overdensity to the initial curvature of the perturbation
(Eq.~\ref{eq:delta_c1}).

To see how this proceeds from the derivation above, suppose that we
know $\delta_c$. Then Eq.~\ref{eq:delta_c1} can be used to find the
initial curvature $\epsilon_p$. The initial conditions, $a_p$,
$\delta$, and $da_p/dt$ at some small, but finite $a$ can be obtained
by substituting $\epsilon_p$ into Eqns~\ref{eq:friedmann1}
\&~\ref{eq:ktolimd}.

Given these initial conditions, the evolution of the perturbation is
uniquely specified by three equations: the cosmology equation for the
perturbation and the background, and the Friedmann equation for the
background. For completeness we repeat these equations here.
\begin{equation}
  \frac{1}{a_p}\frac{d^2a_p}{d(H_0t)^2}=-\frac{1}{2}
  \left[\Omega_Ma_p^{-3}+(3w(a)+1)\Omega_Xa^{f(a)}\right],
  \label{eq:num_int1}
\end{equation}
\begin{equation}
  \frac{1}{a}\frac{d^2a}{d(H_0t)^2}=-\frac{1}{2}
  \left[\Omega_Ma^{-3}+(3w(a)+1)\Omega_Xa^{f(a)}\right],
  \label{eq:num_int2}
\end{equation}
\begin{equation}
  \frac{1}{a^2}\left[\frac{da}{d(H_0t)}\right]^2=
    \Omega_Ma^{-3}+\Omega_Ka^{-2}+\Omega_Xa^{f(a)}.
  \label{eq:num_int3}
\end{equation}

By setting the initial value for the solution of these equations, we
avoid any issues to do with symmetry: for general $w(a)$ cosmologies,
not only is Eq.~\ref{eq:friedmann2} invalid, but additionally the
evolution of $a_p$ in time is no longer symmetric about the point of
maximum expansion, because the effect of the dark energy is not
symmetric about this point. This asymmetry is automatically accounted
for by solving these equations from an initial value. In fact, this
asymmetry leads to potentially interesting behaviour for the spherical
perturbations: given the right initial conditions, perturbations can
start to recollapse (turn-around), but then the repulsive force of the
dark energy can cause re-expansion \citep{chiba05}.

In Fig.~\ref{fig:dc_w}, we show contours of constant $\delta_c$ as a
function of $\Omega_M$ and $\Omega_X$ for constant $w=-4/3,-1,
-2/3$. Contours are plotted as a function of $\delta_{\rm EdS}$ as
given by Eq.~\ref{eq:delta_eds}. As $\Omega_X\to0$, the solutions
asymptote towards the open Universe values calculated by
\citet{lacey93}. For $\Omega_X>0$, we see that decreasing $w$ from
$-2/3$ to $-4/3$ increases the effect of the dark energy. As for the
linear growth factor, $w>-1$ cosmologies behave more like open
cosmologies than those with $w<-1$: decreasing $w$ increases the
importance of the dark energy for calculating $\delta_c$. The critical
overdensities for collapse in a variety of cosmologies with varying
$w(a)$ are compared in \citet{mota04}.

\section{the evolution of the critical overdensity}  \label{sec:dc_evol}

The evolution of the critical overdensity for collapse $\delta_c(a)$,
is usually defined as follows: for a cosmological model with
parameters $\Omega_M$ \& $\Omega_X$, $\delta_c(a)$ gives the
overdensity for a perturbation that collapses at scale factor $a$,
normalised at present day. For example if we had a density field (and
associated power spectrum) normalised at present day, then
$\delta_c(a)$ (where $a$ does not necessarily equal 1) relates to
spherical perturbations in this density field that collapse at scale
factor $a$. $\delta_c$ is the particular case for perturbations that
collapse at present day: perturbations that collapse earlier obviously
have to be significantly more overdense. To calculate $\delta_c(a)$,
when integrating the Friedmann equation (Eq.~\ref{eq:friedmann2}) for
$\Lambda$ cosmologies, or numerically integrating
Eqns.~\ref{eq:num_int1}, \ref{eq:num_int2} \& \ref{eq:num_int3} we
would look for collapse at scale factor $a$ rather than $a=1$.

The rather weak evolution of the critical overdensity as a function of
cosmological model (Fig.~\ref{fig:dc_w}), means that the linear growth
factor can be used to approximate $\delta_c(a)$: If $\delta_c$ is
constant along a particular cosmological track then the evolution of
$\delta_c(a)$ is purely driven by $D(a)^{-1}$. The only change in
$\delta_c(a)$ between two collapse times is caused by the change in
overall normalisation of the field, which can be seen by considering
Eq.~\ref{eq:delta_c_extrap} for two cosmologies along a single
cosmological track. The most obvious choice for the normalisation is
$\delta_{\rm EdS}$, so the approximation will be correct in the limit
as $a\to0$,
\begin{equation}
  \delta_c(a) \simeq \frac{D_0}{D(a)} \delta_{\rm EdS}.
  \label{eq:dc_approx}
\end{equation}

\begin{figure}
  \centering
  \resizebox{6.5cm}{!}{\includegraphics{3637f5.ps}}

  \caption{Plot showing the ratio between the critical overdensity for
  collapse $\delta_c(a)$ and the approximation given by
  Eq.~\ref{eq:dc_approx}, as a function of redshift for three
  different cosmological models (black lines). $\Omega_M=0.3$ and
  $\Omega_X=0.7$ are assumed, while $w$ is assumed to be constant with
  $w=-2/3,-1$, or $-4/3$. The grey lines shows the ratio between the
  true critical overdensity for collapse and the approximation, where
  the linear growth factor has itself been approximated by
  Eq.~\ref{eq:Dapprox_quin}. The error in using the Einstein-de Sitter
  critical overdensity is of the same order as the error in the
  approximation of using the fitting formula of
  Eq.~\ref{eq:Dapprox_quin}. \label{fig:dc_approx}}
\end{figure}

In order to demonstrate this approximation, in
Fig.~\ref{fig:dc_approx}, we plot the ratio between the true critical
overdensity $\delta_c(a)$ to the approximation given by
Eq.~\ref{eq:dc_approx} for three cosmological models with
$\Omega_M=0.3$, $\Omega_X=0.7$, but with constant $w=-2/3,-1,-4/3$. As
$a\to0$, the approximation becomes more accurate. At $a=1$ (redshift
$0$), the ratio is the same as the value of the surface contoured in
Fig.~\ref{fig:dc_w}. We also plot the approximate value of
$\delta_c(a)$ calculated from Eq.~\ref{eq:dc_approx}, but with $D(a)$
and $D_0$ calculated using the approximation given by
Eq.~\ref{eq:Dapprox_quin}, Eq.~\ref{eq:Dlin_A_fit}
\&~Eq.~\ref{eq:Dlin_alpha_fit} (grey lines). The error from using the
approximation of Eq.~\ref{eq:dc_approx} is of the same order as that
from assuming the approximation to the linear growth factor for these
cosmologies.

\section{the mass function}  \label{sec:mass_func}

The usefulness of the spherical model was emphasised when Press \&
Schechter considered smoothing the initial density field to determine
the relative abundances of perturbations on different scales
(\citealt{ps}: PS). When combined with the critical overdensity for
collapse this provided a statistical model for the formation of
structure in the Universe: smoothing the fluctuations leads to the
masses of collapsed objects, while the spherical perturbation model
gives the epoch of collapse for those perturbations that are
sufficiently dense. Obviously such a simple model will fail in detail,
particularly given the known complexities of asymmetrical
gravitational collapse, and numerical simulations have now quantified
these problems \citep{st99, jenkins2001}. However PS theory has been
incredibly successful and arguably still provides key insight into the
processes at work in structure formation.

Two alternative formalisms are often considered for the collapse of
perturbations in PS theory
\begin{enumerate}
  \item The overdensity field is assumed to grow with the linear
  growth factor, and when perturbations reach the critical overdensity
  they are said to have collapsed.
  \item Each overdense region is considered to be spherical and its
  collapse time is calculated as in Section~\ref{sec:delc_lambda}.
\end{enumerate}
Given the discussion in Section~\ref{sec:dc_evol}, it is easy to see
that the first formalism, corresponding to a growing field, matches
the approximation to $\delta_c(a)$ using the linear growth factor
given by Eq.~\ref{eq:dc_approx}. The second formalism, which is
adopted in the following analysis, corresponds to using the correct
$\delta_c(a)$ for the spherical model.

\citet{ma99} considered the effect of quintessence on the mass
transfer function. They provided fitting formulae for the ratio
between the quintessence and $\Lambda$ cosmologies. However, if the
dark energy only clusters on very large scales, the transfer function
is only altered on these scales. If the power spectrum is normalised
to $\sigma_8$ (the rms density fluctuation on scales of $8\,h\,{\rm Mpc}^{-1}$),
then the scales usually of interest are not affected \citep{lokas04}.

\begin{figure}
  \centering
  \resizebox{6.5cm}{!}{\includegraphics{3637f6.ps}}

  \caption{Plot showing the predicted mass function calculated using
the fitting formula of \citet{st99} calculated for $\Omega_M=0.3$,
$\Omega_X=0.7$ for three different values of $w$, and at three epochs
corresponding to $a=1/3, 1/2, 1$. Because the power spectrum is
normalised at present day, and $\delta_c$ is only weakly dependent on
cosmology, then there is little difference between the predicted mass
functions for $a=1$. As we go further back in time the difference
becomes more severe because of the differing linear growth
factors. \label{fig:mass_function_w}}
\end{figure}

To demonstrate the effect of the dark energy equation of state on the
mass function, we plot the cumulative mass function $N(>M)$,
calculated using the numerical fit of \citet{st99} for 3 different
cosmologies and 3 different epochs in
Fig.~\ref{fig:mass_function_w}. To determine the power spectrum we
have used the fitting formulae of \citet{eh98} with $\Omega_M=0.3$,
$\Omega_b/\Omega_M=0.15$, $\sigma_8=0.9$, $n_s=1$. The critical
overdensity for collapse for $w=-2/3,-1$ \& $-4/3$ and $\Omega_X=0.7$
was then calculated for $a=1/3,1/2,1$, corresponding to redshifts
$z=2,1,0$. As expected, because the critical overdensity for collapse
is only weakly dependent on cosmological parameters
(Fig.~\ref{fig:dc_w}), at $a=1$ (the epoch at which the power spectrum
is normalised) we see very little difference in the predicted mass
functions for different cosmologies. If the normalisation of the power
spectrum had been constrained at a different epoch (for example by CMB
fluctuations), then this would not be correct. The evolution of the
mass function is strongly dependent on $w$ because of the effect on
the evolution of $\delta_c(a)$ (Section~\ref{sec:dc_evol}) through the
linear growth factor (Fig.~\ref{fig:lin_grow_w}). Consequently,
determining the mass function at redshifts other than that used to
normalise the power spectrum offers a stronger possibility of
measuring $w(a)$. We will discuss the evolution of structure growth
further in the next Section.

In order to compare with the observed cluster counts, we must convert
from comoving position to observed angular position and redshift. The
number of sources with mass $>M$ per unit solid angle in a redshift
slice $dz$ is given by
\begin{equation}
  N(>M, \Delta z) = \int_z^{z+\Delta z}\,dz\, N(>M) d_{\rm prop}^2
    \frac{dd_{\rm prop}}{dz},
\end{equation}
where the proper distance $d_{\rm prop}$ is given by
\begin{equation}
  d_{\rm prop}= \frac{c}{H_0}\int_a^1\,\frac{da}{a^2E(a)}.
\end{equation}
This correction to the mass function reduces the significance of $w$
at low redshifts for masses of order $10^{14}{\rm\,M_\odot}$ \citep{solevi05}.

\section{rate of structure growth}  \label{sec:rate_grow}

As discussed in the previous Section, the present day mass function
does not provide a good test of $w$, although its evolution in time
does. The Press-Schechter mass function (and the fitting formula of
\citealt{st99}) is independent of epoch when written as a function of
$\nu=\delta_c/\sigma_M$, where $\sigma_M$ is the rms fluctuation in
the initial overdensity field on a scale corresponding to mass
$M$. Consequently, it is easy to see that the evolution of the mass
function is dependent on the rate at which $\delta_c$ changes,
$d\delta_c(a)/da$. It is this quantity that we are testing by
comparing mass functions at different epochs.

Extended Press-Schechter theory uses the smoothed initial overdensity
field to create an analytic model for the build-up of structure
\citep{bond91,bower91,lacey93}, in addition to providing a statistical
model for the mass function. Within this extension to the theory, the
rate at which structures grow is again driven by $d\delta_c(a)/da$
\citep{percival99,percival00,cole00,miller05}. Appendix~A of
\citet{miller05} showed that the approximation of
Eq.~\ref{eq:dc_approx} can be easily extended to $d\delta_c(a)/da$ for
$\Lambda$ cosmologies.

\begin{figure}
  \centering
  \resizebox{6.5cm}{!}{\includegraphics{3637f7.ps}}

  \caption{Plot showing the derivative of the critical overdensity for
  collapse with respect to the scale factor $d\delta_c(a)/da$ (black
  lines) and the approximation calculated from Eq.~\ref{eq:dc_approx}
  (grey lines), as a function of redshift for three different
  cosmological models. $\Omega_M=0.3$ and $\Omega_X=0.7$ are assumed,
  while $w=-4/3,-1$, or $-2/3$. The approximation is so good that
  the grey lines are almost completely hidden behind the black lines.
  \label{fig:ddcda}}
\end{figure}

Here, we extend this analysis to consider $d\delta_c(a)/da$ for
$w\ne-1$ cosmologies. In Fig.~\ref{fig:ddcda} we show
$d\delta_c(a)/da$ for three flat cosmological models with
$\Omega_M=0.3$, and $w=-4/3,-1$, or $-2/3$ calculated using the
derivation of Section~\ref{sec:delc_quinn} (black lines) and the fit
of Eq.~\ref{eq:dc_approx} (grey lines). In fact, the fit is so good
that the grey lines are hardly visible in this plot. As expected
$d\delta_c(a)/da$ is strongly dependent on the dark energy equation of
state.

\section{virialisation}  \label{sec:virial}

The inhomogeneous nature of true perturbations means that they do not
collapse to singularities, but instead stabilise at finite size. For
$\Lambda$ cosmologies it is possible to use energy considerations to
determine the final radius and density of the virialised perturbation
\citep{lahav91}. The extension of this analysis to more general dark
energy cosmologies has been considered by a number of authors
\citep{wang98,horellou05,maor05}.

Within a perturbation, the potential energy due to the matter $U_G$ and
dark energy $U_X$ are given by \citep{horellou05,maor05}
\begin{equation}
  U_G = -\frac{3GM^2}{5R},\,\,\,
  U_X = [1+3w(a)]\frac{4\pi GM}{10}\rho_X R^2.
  \label{eq:energy}
\end{equation}
These can be calculated from the Poisson Equation with pressure
term. Note that there is some confusion in the literature about the
exact form of $U_X$ and the $[1+3w(a)]$ term has sometimes been
neglected in the past, although it is included in more recent work
\citep{battye03,horellou05}. Even without this term, the discussion
below about the lack of energy conservation within the perturbation
remains valid, although the numerical results will obviously change.

For dark energy cosmologies the virial theorem, that a system with
potential energy $U\propto R^p$ virialises with temperature $T=pU/2$,
holds and $T=-\frac{1}{2}U_G+U_X$ at the epoch of
virialisation. Assuming conservation of total energy between
turn-around at $a_{\rm ta}$ and virialisation $a_{\rm vir}$ gives
\begin{equation}
  U_G(a_{\rm ta}) + U_X(a_{\rm ta}) = \frac{1}{2}U_G(a_{\rm vir}) +
    2U_X(a_{\rm vir}).
  \label{eq:totenergy}
\end{equation}
Substituting the definitions given by Eq.~\ref{eq:energy} leads to
\citep{wang98,horellou05,maor05}
\begin{equation}
 \left(1-[1+3w(a_{\rm ta})]\frac{q}{2}\right)x
    + [1+3w(a_{\rm vir})]\frac{qx^3}{y}
    =\frac{1}{2},
  \label{eq:r_ratio_const_energy_ta}
\end{equation}
where
\begin{eqnarray}
\nonumber
 x & = & \frac{R_{\rm vir}}{R_{\rm ta}},\\
\nonumber
 q & = & \frac{\Omega_X(a_{\rm ta})}
              {[1+\delta(a_{\rm ta})]\Omega_M(a_{\rm ta})},\\
 y & = & \frac{\rho_X(a_{\rm ta})}{\rho_X(a_{\rm vir})}
     = \frac{a_{\rm ta}^{\,\,f(a_{\rm ta})}}{a_{\rm vir}^{\,\,f(a_{\rm vir})}}.
\end{eqnarray}
Here $q$ gives the ratio of the dark energy density to the matter
density in the perturbation at turn-around. For $w=-1$, $y=1$ and
Eq.~\ref{eq:r_ratio_const_energy_ta} reduces to the formula of
\citet{lahav91}. For $w=-1/3$ or $\Omega_X=0$, we find $x=1/2$.

The above derivation was based on the assumption that total energy is
conserved for the perturbation between turn-around and
virialisation. This is a common assumption in the literature for
cosmologies in which the dark energy remains homogeneous on the scales
of the perturbations
(e.g. \citealt{wang98,weinberg03,battye03,horellou05}). Even in work
that considers possible dark energy clustering, energy conservation
has previously been assumed in the homogeneous case (see the
discussion leading to equation 26 of \citealt{maor05}). However, the
potential energy of the matter due to the presence of the dark energy
$U_X$ ($U_{12}$ in the notation of \citealt{maor05}) is dependent on
the dark energy density in the perturbation $\rho_X(a)$. The evolution
of this density lies with the background, rather than the
perturbation, so the total energy is not expected to be conserved:
this is why we could not write down a Friedmann equation for the
perturbation in Section~\ref{sec:dc}. Obviously, if the total energy
of the perturbation between turn-around and virialisation is not
conserved, then Equation~\ref{eq:totenergy} does not hold.

\begin{figure}
  \centering
  \resizebox{6.5cm}{!}{\includegraphics{3637f8.ps}}

  \caption{The total energy in an ideal homogeneous spherical
  perturbation (as modelled in Section~\ref{sec:dc}), undergoing
  collapse to a singularity at $a=1$, relative to the energy at
  turn-around (black lines). $\Omega_M=0.3$ and $\Omega_X=0.7$ are
  assumed, with constant $w$ at the values shown. For general $w$, the
  total energy is not conserved. If the perturbations had remained at
  the turn-around size throughout their evolution, then the total
  energies would have evolved along the grey lines. The actual
  evolution in total energy lies between the line of constant total
  energy and the line of constant size for each
  cosmology. \label{fig:tot_energy_evol_w}}
\end{figure}

In fact, we can consider two extreme situations. In the first, as
above, the total energy at $a_{\rm vir}$ is the same as at $a_{\rm
ta}$. In the second, we assume that the perturbation did not change
size between the two epochs. Following the second assumption, the
total energy in the system at $a_{\rm vir}$ would have been altered
from that at $a_{\rm ta}$ by the change in the dark energy potential
$U_{X,1}-U_{X,2}$, where
\begin{eqnarray}
  U_{X,1} & = &
    [1+3w(a_{\rm ta})]\frac{4\pi GM}{10}\rho_X(a_{\rm ta}) R_{\rm ta}^2,\\
  U_{X,2} & = &
    [1+3w(a_{\rm vir})]\frac{4\pi GM}{10}\rho_X(a_{\rm vir}) R_{\rm ta}^2.
\end{eqnarray}
We call using the dark energy potential $U_{X,1}$ to calculate the
total energy in the perturbation at virialisation ``fixing the energy
at turn-around'', and using $U_{X,2}$ ``fixing the energy at
virialisation''. This is demonstrated in
Fig.~\ref{fig:tot_energy_evol_w}, where we plot the total energy in an
ideal homogeneous perturbation undergoing collapse to a singularity at
$a=1$ relative to the energy at turn-around (black lines), for a
number of cosmologies. The total energy was calculated by combining
the analysis of Section~\ref{sec:dc} with the definitions of potential
energy of Eq.~\ref{eq:energy}. Obviously if the total energy were constant
we would find a horizontal line, as is the case when $w=-1$. If the
perturbation did not evolve in size, with the radius fixed at the
turn-around value, then the evolution of the total energy is shown by
the grey lines. The actual total energy within the perturbation lies
between these two extreme cases for each value of $w$ assumed.

For a more realistic perturbation that underwent virialisation rather
than collapsing to a singularity, provided that the dark energy
potential varies monotonically between $a_{\rm ta}$ and $a_{\rm vir}$,
then the change in total energy in the system between turn-around and
virialisation should still lie between these two cases: some of the
change in total energy due to the dark energy remaining homogeneous
will be converted into kinetic energy, and some will be ``lost'' to
the background.

The second scenario, using $U_{X,2}$ to ``fix'' the energy at
virialisation alters Eq.~\ref{eq:r_ratio_const_energy_ta} to give
\begin{equation}
  \left(1-[1+3w(a_{\rm vir})]\frac{q}{2y}\right)x
    + [1+3w(a_{\rm vir})]\frac{qx^3}{y}
    =\frac{1}{2},
  \label{eq:r_ratio_const_energy_vir}
\end{equation}
with $x$, $y$, \& $q$ defined as before. For $w=-1$ this equation again
reduces to the formula of \citet{lahav91}.

\begin{figure}
  \centering
  \resizebox{6.5cm}{!}{\includegraphics{3637f9.ps}}

  \caption{Upper panel: the ratio between the virialisation radius and
   maximum turn-around radius for a spherical perturbation that
   virialises at $a=1$ (black lines) or $a=1/2$ (grey lines), assumed
   to be the same as the epoch predicted for collapse of a homogeneous
   perturbation. We assume that $\Omega_M=0.3$, $\Omega_X=0.7$, and
   plot results as a function of constant $w$. The dashed and solid
   lines show two different calculations assuming conservation of
   energy based on the dark energy density either at turn-around, or
   at virialisation. Lower panel: as upper panel, but now showing the
   overdensity of the virialised system. \label{fig:Rvir_over_Rta}}
\end{figure}

In the upper panel of Fig.~\ref{fig:Rvir_over_Rta} we plot $R_{\rm
vir}/R_{\rm ta}$ in these two cases in a cosmology with
$\Omega_M=0.3$, $\Omega_X=0.7$, as a function of constant $w$. We
assume that virialisation occurs at the collapse epoch, set to be
either the present day or $a=1/2$, for the homogeneous spherical
model. For constant $w=-1/3$ we find $R_{\rm vir}/R_{\rm ta}=1/2$ as
expected. For constant $w=-1$, the two solutions converge to the
result of \citet{lahav91}. For $-1<w<-1/3$, the component of the
energy of the perturbation in the form of dark energy changes from
turn-around to virialisation, and both energy conservation arguments
predict different values of $R_{\rm vir}/R_{\rm ta}$, although the
trend with $w$ is the same for both. However, for $w<-1$, the
solutions diverge. It is easy to see why: for $w<<-1$, the dark energy
becomes increasingly important at late times in the evolution of the
Universe. For a solution that collapses at present day (for example),
turn-around must happen at an epoch where the dark energy has yet to
be cosmologically important. It is only between turn-around and
virialisation that the dark energy becomes important. Setting the
energy to be constant based on the dark energy density at
virialisation simply continues the trend from $-1/3>w>-1$, with
$\rho_X$ increasing as $w$ decreases, leading to a decrease in the
potential due to the dark energy $U_X$, and a smaller $R_{\rm
vir}/R_{\rm ta}$ ratio. However, setting the dark energy density at
turn-around has the opposite effect: $\rho_X$ decreases, leading to
$U_X$ and $R_{\rm vir}/R_{\rm ta}$ increasing. For perturbations that
turn-around, but do not collapse, the dark energy density increases so
rapidly between turn-around and virialisation that the predicted
$R_{\rm vir}/R_{\rm ta}$ keeps increasing (although virialisation is
never reached because the perturbation can never stabilise).

In the lower panel of Fig.~\ref{fig:Rvir_over_Rta} we plot the
overdensity at virialisation $\Delta_{\rm vir}$, calculated for the
two values of the total energy. As can be seen, the result has a
very similar dependence on $w$ as described above for $R_{\rm
vir}/R_{\rm ta}$. It is clear that further analysis is required before
measurements that depend on $\Delta_{\rm vir}$ can be used to
constrain $w$. The answer may lie in numerical simulations of the time
evolution of the perturbation leading to virialisation, possibly of
the form of \citet{engineer00}, or possibly standard N-body
simulations \citep{meneghetti05,bartelmann05}. Such simulations will
need to consider the evolution of total energy with time as well as
the changing epoch of virialisation: given the possible strong effect
of the dark energy, it seems clear that the assumption that
virialisation of the perturbation occurs at the collapse time
predicted in the homogeneous case will also break down in addition to
the conservation of total energy.

\section{conclusions}

The presence of dark energy alters the way in which cosmological
structures grow, thus providing an observational signature that is
complementary to geometrical effects.  The structure growth is
dependent on the normalisation of the dark energy density $\Omega_X$,
its equation of state, and sound speed, which determines how this
component clusters. In this paper we have only considered the effect
of the first two of these properties, assuming that the dark energy
remains homogeneous on the scales of interest due to a high sound
speed. The spherical top-hat model has been used to determine the
linear growth rate and non-linear collapse overdensity threshold. The
equations provided have allowed for general $w(a)$. We have also
considered the statistics of observed structures through the mass
function and its evolution. Finally, the virialisation of
perturbations has been considered and a new argument has been
presented demonstrating the importance of the lack of energy
conservation within a perturbation. It is clear that more work is
required before observations that use arguments based on the energy in
perturbations can be used to constrain the dark energy. However, there
is clearly tremendous potential for future observations to detect the
cosmological effects of dark energy in sufficient detail to pin down
its properties.  Proving that $w\ne-1$, or indeed that $w=-1$ would be
an exciting result, and remains one of the goals of modern cosmology.

\section*{Acknowledgements}
WJP is grateful for support from PPARC.

\setlength{\bibhang}{2.0em}

redpajama_set_name: RedPajamaArXiv


Go to the appropriate website and if necessary, select your choice country/region.
Follow all the given on-screen instructions to work with a new supplies or just have a check on cartridge compatibility with the printer.
Click on "No" button, "OK" icon or just tap "Continue" icon to dismiss the message. The printer will continue to go ahead with the print job.
As suggested by Printer Support team, users need to dismiss the message every time they are printing.
Related blog: How To Fix Printer PCL XL Error ?
If still users are unable to print or they are not able to dismiss this error message then, printer should be reset.
Turn on the printer device and if it is not switched on then, do it now.
Wait until the printer device is in idle state before you continue.
With your printer switched on, just disconnect the power cord from the rear section of the printer.
Unplug the device's power cord from the wall outlet section.
Wait for at-least 60 seconds.
Plug your device power cord into the wall outlet and then, re-connect the power cord to the rear of the printer.
Switch on the printer device where printer will go through a warm-up phase. The printer lights will now start flashing while the carriage will start moving at the same time.
Wait for a while to let the warm-up period finishes and the printer will move into idle state before proceeding further.


When the General Assembly adjourned "sine die" near midnight on July 1st, it was the end to one of the most contentious biennium sessions in recent memory. The 2015 "long" session was the longest in a decade, lasting almost into October, and featured several high-profile battles between the House, Senate and Governor. While the 2016 "short" session (second year of the biennium) adjourned earlier than any in recent memory and did not feature the same kind of drawn out battles we witnessed last year, it was not without moments of significant drama. Despite an insistence from leaders in both chambers that major, controversial issues would have to wait until the next long session (a pledge which was upheld much more than insiders expected back in April), conflicts still managed to erupt and derail major priorities for each chamber. As we detailed in the previous report, bills that were important to two Senate leaders were shot down by the House on the final day of session, and the resulting breakdown between the chambers stranded several high-profile pieces of legislation – including a regulatory reform package that had taken weeks to negotiate; an anti-immigration measure opposed by law enforcement but seemingly destined to pass; and a trio of Constitutional amendments that would have appeared on the November ballot, including one to cap state income tax levels. Read the full report here.


Hello, everyone, welcome to Quan Rong Gallery. We guarantee each piece of art crafts in our store is unique, and is made by hand with authentic materials.
The bidder cards may be charged 4 days after an invoice has been sent.
Payment is due in 7 days after the ending of sale. We reserve the right to hold merchandise until payment clears. We only accept the bank wire transfer for any payment of more than $2,000.
The responsibility of import duty or other extra oversea custom charges goes to the international bidder.
The following Conditions of Sale and Terms of Guarantee are Quan Rong Gallery's entire agreement with the purchaser relative to the property listed in our store. By participating in any sale, you acknowledge that you are bound by these terms and conditions.?
We have exercised reasonable care to describe correctly the property to be sold, but we do not warrant the correctness of authorship, period, source, origin, authenticity, measurement, or condition of said property. No statements shall be deemed such a warranty or representation or an assumption of liability with respect thereto, but are to be construed as opinions only. Buyers are encouraged to personally examine all property to be sold and to determine its condition, size, and whether or not it has been repaired or restored. As a service to prospective purchasers, we may note the physical condition of certain items. However, the fact that damages, repairs, restorations or other defects are described for certain items, does not mean that all defects to such items are described or that similar conditions do not exist with respect to other items although not noted. Such descriptions are not intended to negate the conditions of sale included in our store.
We reserves the right to withdraw any property before the sale and shall have no liability whatsoever for such withdrawal.
We reserve the right to reject any bid. The highest bidder shall be the purchaser. Your bid is a legally binding contract. We require the purchaser to remit the purchase price.
All purchases are subject to the New Jersey sales tax (currently 7%) unless the purchaser possesses a New Jersey sales tax exemption or resale number and registers that number with the company or has purchases shipped out of state.
Our store only accept return from the domestic buyers in the United States. We accept no return from the international buyers. After receiving this item, the purchaser has 7 days for inspection. The purchaser pays for all shipping fees and will be charged 10% processing fee. After receiving the returned item and making sure it is still intact and salable, we will refund the purchaser the reasonable amount of money.


These cookies are used to collect information about how visitors use our website. We use the information to compile reports and to help us improve the website. The cookies collect information in an anonymous form, including the number of visitors to the website, where visitors have come to the website from and the pages they visited. Read Google's overview of privacy and safeguarding data.


MUST READ: Their Grass Is Greener Than Ours!
Home Beware Of Marriage Destroyers Love and Marriage Marriage Marriage Advice Marriage Counselling MUST READ: Their Grass Is Greener Than Ours!
Have you ever found that we all gravitate towards the successful people. We want to be associated with those who are doing well, which is good because it means we appreciate the good taste of their pudding.
I have also seen that at times we are tempted to move over the areas where things look better i.e greener pastures / grass. When your business is not performing you are tempted to move to the line of business of a friend who seems to be doing well.
If you are an employee you will want to change jobs and for a citizen you may consider immigrating to a "better" country. If it is relationship you may consider leaving your partner for another but for marriage "God forbid" in Nigerian tone but in the mind or on talk you may hear people say things like "I wish I married or was married to ..."
Why? Because grass is or looks greener on the other side. That is when people say I am looking for greener pastures. But what can you do when the grass is greener on the other side. Grass can only be greener when you put attention and focus on it. If you ignore it, never expect it to be greener and better. During a dry season take time to water it and fertilize it. Remember it does not just turn green as you start but you need to be consistent and patient and you will see it getting better.
In a wet season you have to deal with the weeds. Work on your ground, feed it just be responsible and your grass will be greener. Visit the person on the other side and learn how they keep grass green and do the same. Don't abandon you marriage, business, ministry or career just because someone is doing better somewhere else. Also don't be quick to jump ship. Work on it, feed it and cultivate it.
When grass is greener on the other side, go there learn how they made it greener and go to your side cultivate it, fertilise it, remove weeds and follow the ways of the other side.
Great day and Stay Blessed.


One of a pack of six "Wild Dingos" in the McNamara household. He always accepted new shelter dog members in the home with the attitude, "What's one more?," which was quickly followed up by, "Are you going to eat that?" A good buddy, he will be missed.


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text:
You are here: Home > Discover our Way > On the Water
Kennet & Avon Canal Trust Interview
We spoke to Robert Dean, President of the Kennet & Avon Canal Trust, about this incredible waterway and its place on the Great West Way.
on Aug 25 2020
Our Great West Way: Richard Jones
Richard Jones currently works as a Waterways Operative along the Kennet and Avon Canal for the Canal and River Trust. He says everyday is unique with the role and location being both different and challenging but that doesn't stop him on the day to day grind.
on Apr 05 2019
Our Great West Way: Jonathan Hobbs
Jonathan Hobbs is managing director of boating firm Hobbs of Henley. He is the fifth generation of his family to run the firm, which was founded by Harry Hobbs in 1870. Jonathan has just been appointed as a Queen's Waterman, following in the footsteps of his dad, Tony.
on Jul 03 2018
Follow The Great West Way
#GreatWestWay
Share The Great West Way
Keep up to date with all the latest news and offers on the Great West Way

redpajama_set_name: RedPajamaCommonCrawl


text:
Red Riding: The Year of Our Lord 1974
2009 | 102 minutes | Thriller | Mystery | Crime | Drama
It's Yorkshire in 1974, and fear, mistrust and institutionalised police corruption are running riot. Rookie journalist Eddie Dunford is determined to search for the truth in an increasingly complex maze of lies and deceit surrounding the police investigation into a series of child abductions. When young Clare Kemplay goes missing, Eddie and his colleague, Barry, persuade their editor to let them investigate links with two similar abductions in the last decade. But after a mutilated body is found on a construction site owned by a local property magnate, Eddie and Barry are drawn into a deadly world of secrecy, intimidation, shocking revelations and police brutality.


I just want to drop in and say that we're sorry that we haven't made much update over the past month. My days are spent with helping other companies complete their games and working on paid development contracts and nights / weekends are spent working on Project Phoenix.
The cause of radio silence during the past month has been the result of many meetings and studio time to create a story concept for Project Phoenix, which would really set a better understanding to the world of Azuregard.
Here's a sneak peek at what new artwork / character design we've been working on. The work is created out of my own personal funds (don't tell my wife and kids) and I've asked someone very very famous animator to animate it in a very awesome way. This animation will be used in a special place in the game and also, will give you hidden information about the people of Azuregard.
Also here's a shout out to my very good friend, Hiroki Kikuta. He is currently working on Unraveled which is "An indie 16-bit-style RPG drawing inspiration from Chrono Trigger and Tomb Raider focusing on the real world plight of workers in the shipbreaking industry in India, with music by Secret of Mana's Hiroki Kikuta and Dragon Fantasy Book II's Dale North."
Expect a "proper" update from our PR staff soon, and my apologies for holding everything up my end.
PS I'll be at E3 this year, I was wondering if people nearby would like to go drinking (ie pub crawl) with me on the 16th of June to make up for our poor updates?
Otoshigami No. 40723, Maxime, and 36 more people like this update.
*Raises hand* but I'm not an E3 attendant so I'll meet you all at whichever bar you go to first if you could please post it up when you know. No reason to pay for their parking & deal with the traffic there otherwise hehe, it's going to be a mess tonight.
So I'm thinking of meeting at one of the E3 gates tomorrow at around 1800. I have an interview till then so might run a few mins late. Who's still in for a pubcrawl?
What time will the pub crawl begin? After the hour meetup for E3 attendees?
"Otherwise, I didn't word it correctly but the story is done for Project Phoenix, we're just working on side quest stories that would touch on the history and the world of Azuregard.
In regards to myself funding part of the project, well, firstly the scope we're aiming for is a bit more than what Kickstarter gave us in funds. And the sidequests and history lessons within Project Phoenix is purely my own will to add this content and in no way should 'raise a red flag'."
So the 'story concept' that he's working on is entirely flavor texts, side content, etc. The main story is done and his funding is purely to flesh out the history and atmosphere of the world. He's a passionate creator. Thanks for the hard work and personal commitment to the project, sir.
It'll be good if Project Phoenix at least have 80% completion from this year onwards. Otherwise, everyone would love to have their pledged funds back even though they aren't willing too. Good luck!
@Timotheus - To quote "The work is created out of my own personal funds" where does this say the project is at a lack of funds. I read that as he paid out of his own pocket, meaning he deviated from the funding. Their are project managers or coordinators that will often pay out of their own pocket for the reason of a gamble without using expenditures.
I can appreciate where you might be concerned - and for someone who just found out they were burned on another Kickstarter project, I'm not going to lose faith in this.
Take a look at some other project - ZeBoyd are currently behind on Cosmic Star, then there's the River City Ransom game. Like them, Hiro's been doing his best to update.
@Joshua totally agree, however this lack of funds appearing during creating the story concept (?!) of Project Phoenix is worrisome.
Also, date for deliverables was Nov 2014, and that they are barely getting a story concept in place as of May 2015 is definitely worrisome.
E3 meet-up session sounds great.
@Timotheus - Because in a perfect world, even $1 million USD alone is not enough to fund a project of this one's intended scale. Often the case in this scenario is to "prove out" the interest in a concept in order to seek out the actual required funding via investors or other means.
And that's in a perfect world. A project that drags on longer that is expected (fairly normal), or encounters delays or team member churn (also fairly normal) can find themselves in dire straits financially.
You should read the answer to the first question of the FAQ section.
As Timotheus said, I was slightly worried when I read this as well. Where did all the money go? And I thought this WAS a paid development? How come it's been shafted as a side project? Definitely confused!
I am unclear why you needed to use your personal funds for this after the project has raised over $1 million USD.
Seriously, at least show us a higher resolution image.
Thanks for the update. Would definitely join you if I was going, but I hope you have fun. Glad to see you guys are still workinground on the game, and look forward to more updates soon.
Oh and P.S. the art is really beautiful!!
Thank you for this Hiro, really means a lot you putting this extra effort forward despite time constraints & needing to pump out work on the project itself.
Any Alpha updates? I remember reading that Alpha will cover act 1 and that it is scheduled for June. How many acts are there?
I would love to! If you can help me get my hands on some tickets, I'll help be your assistant for as long as you need me to. Either way, I live in the LA area, so it would be a pleasure to share some drinks with you!
Maybe one day I might come to a bar near you!


text:
Police raids lead to thirteen arrests for drug and modern slavery offences
Thirteen people were arrested yesterday in police raids across Greater Manchester and North Yorkshire. The nine men and four women,
GMP's 'brave' agency bonds will break chains of modern slavery and human trafficking
In the fight to end modern slavery and human trafficking Greater Manchester Police must 'be brave' in their partnerships with other agencies, according to the Independent Anti-Slavery Commissioner.
Manchester Fringe Festival show sheds light on the dark world of human trafficking
Shocking short stories of human trafficking from around the world are brought together in one educational and inspiring theatrical performance set to hit the stage at the Greater Manchester Fringe Festival.
Manchester must unify to tackle sex crime shame, warns first female bishop
The Right Reverend Libby Lane, the first female Bishop, made one of her first official public appearances in her new role to launch Manchester Airport's Travel Safe Week.
European 'slaves' on less than £2 per hour rescued in police raid on Rochdale factory
A Rochdale factory raid has rescued 20 Eastern European immigrants who were getting paid paid less than two pound per hour for working more than 80 hours per week.
Sick Eccles pair forced to pay £100,000 to deaf girl kept as slave in nine-year ordeal
A deaf and mute girl – who was trafficked into the country aged ten and was repeatedly raped and forced to do domestic chores by her Eccles-based captors – has been awarded more than £100,000 in compensation.
Rise in reported human trafficking victims in UK means eye is on issue, claims Manchester charity
Hope for Justice believe the increase in reports shows that more people are now being identified and rescused from desperate conditions.
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In August 2017, the Fashion Institute of Technology (FIT) will become the second State University of New York (SUNY) institution to offer degree programs at SUNY Korea in Songdo. SUNY is the first American university in Korea and is also SUNY's first global campus outside of the United States.
The FIT programs being offered in Korea are Fashion Design and Fashion Business Management — two signature curricula of the college — leading to the Associate in Applied Science (AAS) degree. These programs reflect the college's historical commitment to providing industry-ready graduates for the fashion industry and its related businesses.
Fashion Design is one of the earliest programs ever offered by the college; the Fashion Business Management program is the oldest and largest program of its kind in the United States, providing students a comprehensive business curriculum focused on the fashion industry.
FIT's location in Korea makes it the college's third location abroad, along with Milan and Florence, and extends the institution's global reach.
The application deadline is June 30 and, after that, admission is on a rolling basis. Admitted students will earn their AAS degree at FIT at SUNY Korea and may then apply to FIT's bachelor's degree programs in New York or in Milan for Fashion Design.
Classes begin on August 25, 2017, at the Incheon Global Campus in Songdo, Korea's only "smart city," which is becoming Northeast Asia's economic hub. The campus features state-of-the-art facilities, classrooms, a library, research labs, a sports center, auditorium, multicultural activity center, dining hall, dormitory, and guest house, among other amenities. The Incheon Global Campus is a national project established by the Korean government and Incheon Metropolitan City. SUNY Korea is the first campus to locate there.
SUNY Korea was established in 2012 as the first American university in Korea through the combined effort and investment of the South Korean and U.S. governments and SUNY at Stony Brook University.
The State University of New York is the largest comprehensive university system in the United States. Its impact in New York State and across the globe begins with 64 institutions, including research universities, academic medical centers, liberal arts colleges, community colleges, colleges of technology, and an online learning network. SUNY serves nearly 1.3 million students, including nearly 600,000 in credit-bearing courses and programs and more than 700,000 through continuing education and community outreach programs. SUNY's nearly 3 million alumni are located around the globe, each making their own unique impact.
The Fashion Institute of Technology, a part of the State University of New York, has been a leader in career education in art, design, business, and technology for more than 70 years. With a curriculum that provides a singular blend of hands-on, practical experience, classroom study, and a firm grounding in the liberal arts, FIT offers a wide range of outstanding programs that are affordable and relevant to today's rapidly changing industries.
Internationally renowned, FIT draws on its New York City location to provide a vibrant, creative community in which to learn. The college offers nearly 50 majors and grants AAS, BFA, BS, MA, MFA, and MPS degrees, preparing students for professional success and leadership in the global marketplace. Among notable alumni in fashion are Calvin Klein, Michael Kors, Amsale Aberra, Reem Acra, Brian Atwood, Dennis Basso, Francisco Costa, Norma Kamali, Nanette Lepore, Bibhu Mohapatra, Ralph Rucci, John Bartlett, and Michelle Smith.
Other prominent graduates include Leslie Blodgett, creator of bareMinerals; international restaurant designer Tony Chi; Nina Garcia, creative director, Marie Claire; Essie Weingarten, founder of Essie Cosmetics; and Joe Zee, executive creative officer, Yahoo Style. Visit fitnyc.edu for more information.


text:
Q: How to insert text from textview according to checkbox? I am making shopping list app in Kotlin. Main screen has 4 tabs, each for one store. On page for inserting new items I have 2 textview's, for product name and quantity. Also, on that page I have 4 checkboxes for 4 stores. I want to insert texts from textviews on specific tab when checkbox with same name as tab is checked. Didn't find any examples online. I would much appreciate everyones help.
<?xml version="1.0" encoding="utf-8"?>
<FrameLayout
    xmlns:android="http://schemas.android.com/apk/res/android"
    android:layout_width="match_parent"
    android:layout_height="match_parent"
    xmlns:tools="http://schemas.android.com/tools"
    xmlns:app="http://schemas.android.com/apk/res-auto" >

<androidx.constraintlayout.widget.ConstraintLayout
        android:layout_width="match_parent"
        android:layout_height="match_parent"
        android:paddingTop="30sp"
        tools:context=".ItemInputActivity" >

    <EditText
            android:id="@+id/productId"
            android:layout_width="0dp"
            android:layout_height="wrap_content"
            android:visibility="gone"
            tools:ignore="MissingConstraints"
    />

    <EditText
            android:id="@+id/inputItem"
            android:layout_width="0dp"
            android:layout_height="50dp"
            android:layout_marginStart="22dp"
            android:layout_marginTop="26dp"
            android:layout_marginEnd="22dp"
            android:ems="10"
            android:hint="@string/naziv_proizvoda"
            android:background="@drawable/bg_form"
            android:paddingStart="10dp"
            android:paddingEnd="10dp"
            android:inputType="textPersonName"
            android:textSize="16sp"
            app:layout_constraintEnd_toEndOf="parent"
            app:layout_constraintHorizontal_bias="0.0"
            app:layout_constraintStart_toStartOf="parent"
            app:layout_constraintTop_toTopOf="parent"
            android:importantForAutofill="no" />

    <EditText
        android:id="@+id/inputNumber"
        android:layout_width="0dp"
        android:layout_height="50dp"
        android:layout_marginStart="22dp"
        android:layout_marginTop="20sp"
        android:layout_marginEnd="22dp"
        android:background="@drawable/bg_form"
        android:ems="10"
        android:hint="@string/kolicina_proizvoda"
        android:importantForAutofill="no"
        android:inputType="number"
        android:paddingStart="10dp"
        android:paddingEnd="10dp"
        android:textSize="16sp"
        app:layout_constraintEnd_toEndOf="parent"
        app:layout_constraintHorizontal_bias="0.0"
        app:layout_constraintStart_toStartOf="parent"
        app:layout_constraintTop_toBottomOf="@id/inputItem" />

    <CheckBox
        android:id="@+id/konzumCheck"
        android:layout_width="0dp"
        android:layout_height="wrap_content"
        android:layout_marginStart="22sp"
        android:layout_marginEnd="22sp"
        android:minHeight="48dp"
        android:text="@string/konzum"
        app:layout_constraintBottom_toTopOf="@+id/lidlCheck"
        app:layout_constraintEnd_toEndOf="parent"
        app:layout_constraintStart_toStartOf="parent"
        app:layout_constraintTop_toBottomOf="@id/inputNumber" />

    <CheckBox
            android:id="@+id/lidlCheck"
            android:layout_width="0dp"
            android:layout_height="wrap_content"
            android:layout_marginStart="22sp"
            android:layout_marginEnd="22sp"
            android:text="@string/lidl"
            android:minHeight="48dp"
            app:layout_constraintTop_toBottomOf="@id/konzumCheck"
            app:layout_constraintStart_toStartOf="parent"
            app:layout_constraintEnd_toEndOf="parent"
            app:layout_constraintBottom_toTopOf="@+id/kauflandCheck"

    />

    <CheckBox
            android:id="@+id/kauflandCheck"
            android:layout_width="0dp"
            android:layout_height="wrap_content"
            android:layout_marginStart="22sp"
            android:layout_marginEnd="22sp"
            android:text="@string/kaufland"
            android:minHeight="48dp"
            app:layout_constraintTop_toBottomOf="@id/lidlCheck"
            app:layout_constraintStart_toStartOf="parent"
            app:layout_constraintEnd_toEndOf="parent"
            app:layout_constraintBottom_toTopOf="@+id/sparCheck"

    />

    <CheckBox
            android:id="@+id/sparCheck"
            android:layout_width="0dp"
            android:layout_height="wrap_content"
            android:layout_marginStart="22sp"
            android:layout_marginEnd="22sp"
            android:text="@string/spar"
            android:minHeight="48dp"
            app:layout_constraintTop_toBottomOf="@id/kauflandCheck"
            app:layout_constraintStart_toStartOf="parent"
            app:layout_constraintEnd_toEndOf="parent"
            app:layout_constraintBottom_toTopOf="@+id/inputButton"

    />

    <Button
        android:id="@+id/inputButton"
        android:layout_width="wrap_content"
        android:layout_height="wrap_content"
        android:layout_marginTop="35sp"
        android:text="@string/spremi"
        android:textSize="12sp"
        app:layout_constraintEnd_toStartOf="@id/itemListActivity"
        app:layout_constraintStart_toStartOf="parent"
        app:layout_constraintTop_toBottomOf="@id/sparCheck" />

    <Button
        android:id="@+id/itemListActivity"
        android:layout_width="wrap_content"
        android:layout_height="wrap_content"
        android:layout_marginTop="35sp"
        android:text="@string/lista_proizvoda"
        android:textSize="12sp"
        app:layout_constraintEnd_toEndOf="parent"
        app:layout_constraintStart_toEndOf="@id/inputButton"
        app:layout_constraintTop_toBottomOf="@id/sparCheck"

        />

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The workshop will take place in Washington DC, Nov. 19-21 in conjunction with the annual meeting of the Middle East Studies Association. Fellows will attend roundtable discussions led by faculty experts on topics including Syrian refugees, Islam in America, and ISIS recruitment in the United States.
Fellows will develop a deeper understanding of Middle East politics especially as they impinge on, or are connected with issues facing American society. They will build a network of contacts with expertise on the region and gain exposure to cutting edge insights on the Middle East. Fellows will also receive lists (and personal introductions where possible) of local scholars available for background interviews on future stories. All expenses (airfare, local transport, lodging and meals) will be covered.
To apply submit a resume; a recently published article; and a short paragraph (200-300 words) outlining why the workshop would be beneficial to you as a writer. Send materials to: imesnrc@gwu.edu with the subject heading "Journalist Workshop Application" no later than September 8.
For information regarding eligibility, email Weiner at sweiner@gwu.edu.


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Lisa Ann And Amy Fisher
August 4, 2022 by selectografix.com
Lisa Ann is a famous pornstar, who has received many accolades for her career. She is a top-rated porn actress in the world. She achieved mainstream fame after parodying US politician Sarah Palin in the video "Sarah Palin's Political Career." Among her other achievements, she has been inducted into the AVN Hall of Fame, XRCO Hall of Fame, and Urban X Hall of Fame. She hosts a talk show on Sirius satellite radio called "Strippertown".
Lisa Ann is not only a star in porn movies, but she also has many interracial projects. These include "When Lisa Met Kortney", (2011) and "Summer Love", (2013). She is also known for her solo sex scenes, which include "The Hundreds Girl" and "Tasty Taylor" (2014). Her latest releases include "Lisa Ann Chronicles" for Brazzers, and "Evil Angels" for Naughty America.
Lisa Ann is a porn industry veteran who has been an inspiration to younger performers. As a talent agent at LA Direct Models she saw that older performers weren't represented well. To remedy this, she launched her own talent management company in 2006, which she later renamed "Lisa Ann's Talent Management" and merged with Adam Glasser's Lighthouse Agency in 2007.
Lisa Ann Pornstar, a high school-stripper, started acting in pornographic movies at the age of 16. At that time, she was a teenager, but she got involved with erotic dancing to help pay for college. She became a full-time actress in 1994. However, her career ended in 1997 due to the AIDS scare. She worked for several years at strip clubs as a featured dancer. She set up Lisa Ann's Talent Management in 2006 as her own talent agency. It merged with Lighthouse Agency in 2007, which is managed by Adam Glasser. This move allowed her to represent a wider range of young porn stars.
She started her career as a stripper in high school, and then moved to California. She starred in a parody of Vice Presidential candidate Sarah Palin, which helped propel her career. She is considered to be one of the greatest porn actors ever. In addition to acting, she has also produced several popular porn parodies and comedy DVD titles.
Lisa Ann, despite leaving the adult film industry over five years ago is still the most sought-after pornstar on Pornhub. But she's no longer just a pornstar; she's now an avid sports enthusiast. The Life is her memoir that details her journey from pornstar into a sports enthusiast.
She once revealed that she enjoys watching basketball, and loves to watch NBA games on TV. When the NBA draft rolls around, she often makes a list of athletes that she would like to sleep with. Although it may seem odd that Lisa Ann is interested in athletes, she explains that her only concern is the best.
Although she started her career in the pornographic world, she now works in sports radio. She is also a passionate sports fan, and she enjoys 50 to 60 games every year.
Former porn star Lisa Ann has revealed that she prefers to have sex with athletes. The former porn star has been rumored to date NBA players, although she has not said which ones. Lisa Ann is a huge fan of the sport and enjoys watching NBA games live on TV. She has also admitted that she prefers athletes over other people, but that safety is always her number one priority.
Athletes are often contacted by Lisa Ann, and it's believed that she has up to 100 athletes communicating with her at any given time. Despite the large number of requests, she only meets about a quarter of them. However, she says that she is happy to do so.
Georgia Jones And Lisa Ann
Lisa Ann Standing


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MAN ROBS DAVIE BANK
Staff reportsSUN-SENTINEL
DAVIE -- A man claiming to have a gun walked into a bank on Monday and stole an undetermined amount of cash, police said.
The man walked into the First Union National Bank, 4601 S. University Drive, about 1:30 p.m. and demanded money from a teller, police spokeswoman Christine Murray said.
Police described the suspect as a white male, about 40 years old, 5 feet 8 inches tall with a medium build and thick brown hair. The gunman's face was pockmarked and he wore prescription sunglasses, a tan cap and tan knit shirt with a collar, Murray said.
Anyone with information is urged to call Detective Kelly Woodroof at 797-1176.


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6 Best Practices for Managing the Identity Lifecycle
Every time organizations hire a new employee, he or she needs access to essential information, apps and processes to successfully perform daily tasks. With the cost of data breaches at $4 million per incident and businesses losing an average of $158 for every stolen record, it's crucial that organizations grant and manage access with the utmost care.
Employee identities and the information to which associated credentials allow access must be carefully managed throughout each team member's time at your organization. Defined by Techopedia as "the full life cycle of identity and access for a user on a given system," identity lifecycle covers every aspect of identity and access management (IAM) from the moment a person is hired to the moment they leave the company.
With constant changes in technology and the dynamic nature of employees' access needs in the modern workplace, it's essential to follow these 6 IAM best practices throughout the employee lifecycle.
IAM should begin with the most straightforward steps for better security:
Enable multifactor authentication,
Create and enforce a Bring Your Own Device (BYOD) policy, or consider a Corporate-Owned, Personally Enabled (COPE) policy as an alternative,
Update all tools, platforms and apps regularly, and
Encrypt all data during sending and receiving.
Proper employee training also ensures all staff members understand policies and procedures, thereby minimizing the risk of error and reducing vulnerabilities resulting from ignorance.
Start with Smart Provisioning
Role- and attribute-based access control methods assign employee access based on the minimum levels necessary to complete tasks. This makes it easier to allocate privileges to new employees. Instead of guessing what access they'll require and running the risk of being too liberal, your system can be set to automatically assign the right level of access at the time of hiring. Real-time provisioning ensures access is available to all employees from day one. Adding a single sign-on (SSO) process streamlines the procedure, allowing staff members to use multiple apps using just one set of credentials.
Use Automatic Updating
SSO also eases the burden on your IT department when paired with automatic updating. An increasing number of apps are required to manage modern businesses, and your IT team doesn't have the time to update provisions across apps or create new rules every time you adopt another platform.
Look for a solution designed for adding apps centrally and creating the proper provisions across all of them at the same time. As the apps you use change, employees gain instant access based on existing permissions, preventing bottlenecks in essential workflows.
Prevent Privileges from Piling Up
Privileged accounts give specific employees access to the most sensitive data and processes within your system. However, employee responsibilities change over time, and it may not always be necessary for high-level permissions to remain in place. Privilege levels must be adjusted accordingly as part of regular automatic updates. By revoking access as soon as it's no longer needed, you minimize vulnerabilities and shut the door on hackers who target these types of accounts.
Put Up a (Geo) Fence
If your company has a team of remote employees or otherwise allows remote access to data, geo-fencing can cut down on the risk of sensitive information being accessed from the wrong places. Many employees still use public Wi-Fi connections to perform business tasks, and logging into your system while sipping a latte at Starbucks can throw the door wide open for hackers.
Geo-fencing adds another layer of protection by preventing access outside of specific locations. If you choose to implement a "fence," make sure your access rules don't create situations so restrictive your remote staff members can't do their jobs.
Have a Plan for Deprovisioning
Around 49 percent of former employees log into their accounts after leaving a job or being let go. Deprovisioning prevents this type of unauthorized access by completely revoking privileges as soon as a person no longer works for your company. Like provisioning and continuous certification, deprovisioning can be automated to offload your IT department from the tedious task of revoking permissions and removing roles. This is especially important in cases where an employee's exit was less than cordial and your company could be at risk for a malicious attack if the account remains open.
Adopting a framework for proper identity lifecycle management gives you more control over the information to which you employees have access and decreases the likelihood your company will suffer a data breach. Even in a world where BYOD and remote work have become everyday realities, following best practices for managing identity and access keeps your company safe and ensures no accounts are left open to enterprising hackers. Working with a professional can make it easier to identify weaknesses in your current systems and implement the best fixes for your business model.
Learn about audit and certification of your IAM program.
Identity Management Institute
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IMI services help its members advance in their careers, and, gain the trust of the business community to hire certified members for managing their identity and access risks.
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Q: Does logging in with a Skype alias grant access to other Microsoft Account-authenticated services, such as Onedrive? I have recently been subjected to an automated, successful attack from India that managed to gain access to my Skype alias to spam a few links. I have taken the necessary steps to re-ensure the security of my account.

Note: My Skype login-alias is from before the Microsoft-Skype era, when you could log-in with a username-password combination instead of an email-password combination.

Is it possible that such a login gained access to my OneDrive account as well, or was it constrained to interaction with Skype only? (such as sending messages)


The town of Jorhat has a number of religious places like temples, namghars, satras, mosques, churches and gurudwaras where both local devotess and devotees from all over Assam come to offer their prayers. The Dhekiakhowa Bornamghar in Jorhat is amongst the most popular temples here. Let us discover more about the religious spots in Jorhat.
This is a namghar of Jorhat established by Vaishnavite saint Madhabdeva for preaching Vaishnavite culture and teachings. It was established in the year 1528 more than 485 years back. It is located in Dhekiakhowa village of Jorhat town. It is situated at a distance of 15 kms east of Jorhat and around 3.5 kms from the National Highway 37. Due to its large campus and the historical essence related to it, the namghar is called a Bornamghar. The namghar is located in a beautiful complex with the entrance decorated with two elephant structures holding an umbrella. The namhar has large rooms with structures of Krishna and His avatars built across the rooms. There is also a room nearby where earthen lamps and incense sticks are lit. The namghar every year hosts prayer meetings and also celebrates 'Raas' utsav and the birth and death anniversaries of Vaishnavite saints Shrimanta Shankardeva and Madhavdeva. The namghar also contributes for the social as well as the cultural welfare of the people in addition to preaching the Eka sarana religion.
The Buragosain Devalaya or Buragosain Thaan is located in Jorhat town and is a popular Shakta shrine. The temple deity is Burigosain and there is also an idol of a priest which were brought from Jayantiya. They were established first in Rangpur and later were shifted to the present location in Jorhat.
The Bilvesvar Shiva temple is located on the South trunk road in Jorhat towards the northern part of the Jorhat district. The Bilvesvar Shiva temple has a holy tank near it which was built by Ruchinath Buragohain. The temple is located at a distance of 35 kms from Jorhat town on the NH 37. Tourists can reach the temple by state operated buses and taxis available from Jorhat town.
Jorhat has a number of mosques situated across the town. Bhogdoi Mosque, Garali Mosque, Bura Masjid, Tarajan Mosque, Station Chariali Masjid are famous mosques located across Jorhat which are visited frequently by devotees.
Jorhat town has a number of churches like the Jorhat Baptist Church, St. Mary Mother of Church and Believers Church in Jorhat. The Jorhat Baptist Church was established in the year 1906 and is located in the Rajabari mission compound area in Jorhat town. The St Mary Mother of Church is located in Lichubari area of Jorhat district.
Dakhinpat Satra: The Dakhinpat Satra was found by Vaishnavite saint Banamalidev and the center regularly holds the important Rasleela festival.
Garamurh Satra: This Satra, which was founded by Saint Lakshmikanta Deva, houses ancient weapons of Ahom rule which are known as 'Bartop' or cannons.
Auniati Satra: The Auniati Satra was founded by Niranjan Pthakdeva and is popular for 'Paalnaam' and Apsara dances held here. There are also many ancient Assamese artifacts, utensils and other commodities in the Satra. There are around hundred and twenty five disciples in the satra.
Kamalabari Satra: This Satra was found by Bedulapadma Ata and it also has a branch Uttar Kamalabari Satra which regularly hosts cultural programmes of popular Satria Art across India and also abroad.
Benegenaati Satra: This Satra has many cultural and historically significant antiques. The Satra is a center of performing arts and houses the royal raiment belonging to Ahom King Swargadeo Gadadhar Singha. This raiment is made of pure gold and there is a golden royal umbrella in the Satra.
Shamaguri Satra: The Shamaguri Satra of Majuli is popular for mask making in India.