text:
\section{Introduction}

AdS/CFT correspondence \cite{Mal} has thought us to think of a gravitational theory
on an asymptotically locally AdS geometry as a dual description of a strongly coupled field theory
with a UV fixed point. It is dual in the sense that there is a one to one
correspondence between objects in the gravitational theory and those in the dual field theory
\cite{{GKP}, {Witten}}. Having an AdS geometry guarantees that the dual field theory has
conformal symmetry.

It is always challenging to see in what extend the gauge/gravity correspondence can be generalized
to geometries which are not asymptotically AdS. In particular one may consider the case where
the theory is not conformally invariant, though it may still  be invariant under a certain scaling. Indeed
such a generalization,  has been made in literature in the context of the application of the  AdS/CFT correspondence in the condensed matter physics (for a review see for example\cite{Hartnoll:2009sz}).
A prototype example  of such a model is a theory with the Lifshitz fixed point where the theory
has a spatial isotropic scale invariance  which is characterized by a dynamical exponent, $ z$, as follows
\begin{equation}
t\rightarrow \lambda^z t,\;\;\;\;\;\;\;\;\;\;x_i\rightarrow \lambda x_i,
\end{equation}
where $t$ is time and $x_i$'s are spatial directions of the space-time.

The holographic description of a $(d+1)$-dimensional theory with the Lifshitz fixed point has been considered
in\cite{KLM}\footnote{See also \cite{Koroteev:2007yp} for an earlier work on a geometry with the Lifshitz scaling.} where it was proposed  that the corresponding gravitational dual can be defined by a gravity
on the following metric (see also \cite{Taylor})\footnote{Geometries with non-relativistic conformal
symmetry have also been considered in \cite{{Son},{BMc}}. For earlier work on geometry
with Schr\"odinger symmetry see \cite{Alishahiha:2003ru}.}
\begin{equation}\label{metric0}
ds^2_{d+2}=R^2\left(-\frac{dt^2}{r^{2z}}+\frac{dr^2}{r^2}+\frac{\sum_{i=1}^ddx_i^2}{r^2} \right),
\end{equation}
where $R$ is the radius of curvature\footnote{Through out this paper we set $R=1$.}.

It is worth to mention that a metric with Lifshitz isometry is not a solution of a pure cosmological Einstein gravity. This is simply because in the pure Einstein gravity there is nothing to produce an anisotropic in
the space-time. In fact to
obtain  such a solution one needs to couple the Einstein gravity  to other fields. In the minimal case
the extra field could be a massive gauge field \cite{Taylor} which can, indeed, produce an anisotropic in
the space-time leading to Lifshitz geometry.

More naturally the Lifshitz metric may be found in an Einstein-Maxwell-Dilaton theory\cite{{Eric}, {Peet}, {BBPZ}, {GKPTIW}, {Sandip}, {Berglund}}. Actually by including both dilaton (in general a scalar with non-trivial
potential) and an abelian gauge field, one can find even more interesting metrics. In particular one may
obtain a metric with the following form \cite{Kiritsis}
\begin{equation}
\label{metric1}
ds_{d+2}^2=r^{\frac{2\theta}{d}} \left(-\frac{dt^2}{r^{2z}}+\frac{dr^2}{r^2}+\frac{\sum_{i=1}^ddx_i^2}{r^2} \right),
\end{equation}
where the constants $z$ and $\theta$ are  dynamical and  hyperscaling violation exponents, respectively. This is the most general geometry which is spatially homogeneous and covariant under the following scale transformations
\begin{equation}
t\rightarrow \lambda^z t, \quad r\rightarrow \lambda r, \quad x_i\rightarrow \lambda x_i, \quad
ds_{d+2} \rightarrow \lambda^{\frac{\theta}{d}} ds_{d+2}.
\end{equation}
Note that the metric \eqref{metric1} is conformally  a Lifshitz geometry which is the
scale invariant limit $\theta=0$ of \eqref{metric1}.  Indeed with a non-zero $\theta$, the distance is not
invariant under the scaling which in the context of AdS/CFT indicates  violations of
hyperscaling in the dual field theory. More precisely, while in $(d+1)$-dimensional theories
without  hyperscaling (dual to background\eqref{metric0})  the entropy
scales as $T^{d/z}$ with temperature, in the present case (dual to background \eqref{metric1}) it scales
as $T^{(d-\theta)/z}$ \cite{{Gouteraux:2011ce},{Huijse:2011ef}}.

Holographic aspects of theories with  hyperscaling violation have been studied in\cite{Dong:2012se}
where the authors have shown that  in order to have a physically sensible dual field theory one should
assume
\begin{equation}
 (d-\theta)(dz-\theta-d) \geq 0,\quad      (z-1)(d+z-\theta) \geq 0.
\end{equation}
which is a necessary condition  for the null energy condition to be satisfied, {\it i.e.}  $T_{\mu\nu} N^{\mu}N^{\nu}\geq 0$. In particular it was shown that for $\theta=d-1$ the holographic entanglement
entropy shows a logarithmic violation of the area law indicating that the dual theory exhibits an
${\cal O}(N^2)$
Fermi surface \cite{{Ogawa:2011bz},{Huijse:2011ef}}. Therefore the geometry \eqref{metric1}
with specific values of its parameters could provide a gravitational dual for a system with
Fermi surface in any dimensions.

However, we note that due to hyperscaling violation as well as the behavior of dilaton field
at large distances, the background \eqref{metric1} cannot provide a dual description
of a theory in all range of energies from UV to IR \cite{{Bhattacharya:2012zu},{Kundu:2012jn}}
(see also\cite{Dong:2012se}) .  In fact gravity on the background \eqref{metric1} may be considered
as an effective theory valid over an intermediate energy scale.

One of the aim of the  present paper is to further  explore certain features of hyperscaling
violation theories by
making use of the gravity dual given by \eqref{metric1}.  More precisely we will probe the background
by an open string which in turns can be used to study the response of the theory to an
external object. In particular we shall study potential between external objects, drag force as well
as a rotating object. We will also make a comment on a closed string probing the background.

Following \cite{deBoer:2011wk} we will also consider a geometry with an  anisotropic scaling
in a spatial direction. The corresponding geometry can be obtained  by
a double Wick rotation from  the metric \eqref{metric1}.
To be more concrete,  consider a double Wick rotation as follows
\begin{equation}
t\rightarrow i y,\;\;\;\;\;\;\;\;\;\;\;x_{d}\rightarrow i t,
\end{equation}
then the metric \eqref{metric1} becomes
\begin{equation}
\label{metric2}
ds_{d+2}^2=r^{\frac{2\theta}{d}} \left(\frac{dy^2}{r^{2z}}+\frac{dr^2}{r^2}+\frac{\sum_{i=1}^{d-1}dx_i^2
}{r^2}-\frac{dt^2}{r^2} \right).
\end{equation}
The above metric is covariant under the following scale transformations
\begin{equation}
y\rightarrow \lambda^z y,\;\;\;\;\;\;r\rightarrow \lambda r,\;\;\;\;\;\;ds_{d+2}\rightarrow
\lambda^{\frac{\theta}{d}} ds_{d+2},\;\;\;\;\;\;(t,x_i)\rightarrow \lambda (t,x_i),
\end{equation}
for $i=1,\cdots,d-1$.

In the present paper we will also intend to study holographic aspects a theory whose dual
gravitational theory is given by  a
gravity on the background \eqref{metric2}. In particular, we study holographic entanglement
entropy in this background. We show that for $\theta=d-1$ for any $z$, the  entanglement
entropy exhibits a  logarithmic violation of the area law showing that the geometry may also
provide a suitable gravitational description for theories with ${\cal O}(N^2)$ Fermi surface.
We will also probe this geometry by an open string.

The paper is organized as follows. In the next section we study holographic entanglement
entropy using the metric \eqref{metric2}. In section three we will consider an open string probing
the metrics \eqref{metric1} and \eqref{metric2}. For completeness of our study we will consider
a closed string probe in section four. The last section is devoted to discussions.
In what follows we only consider the case with $\theta\leq d$.

\section{Holographic entanglement entropy}

In this section we will study the entanglement entropy by making use of the AdS/CFT correspondence. To compute the entanglement entropy via AdS/CFT correspondence
one needs to minimize a surface in the bulk gravity.  More precisely, given a gravitational  theory with
 the  bulk Newton's constant $G_N$, the holographic entanglement entropy
is given by \cite{RT:2006PRL,RT:2006}
\begin{equation}\label{EE}
S_A=\frac{\mathrm{Area}(\gamma_A)}{4G_N},
\end{equation}
where $\gamma_A$ is the  minimal surface in the bulk whose boundary coincides with the boundary of the entangling region.

 It is important to note that in order to compute the holographic entropy, since we are dealing
with a spatial surface,  one needs to work  at  constant time. In other words, the $g_{tt}$ component
of the metric does not, directly,  contribute to the holographic entanglement entropy. On the other hand,
for the hyperscaling violating geometry \eqref{metric1}, there are non-trivial effects due to
non-relativistic nature of the metric which in turn comes from the $g_{tt}$ component.

Holographic entanglement entropy of the background \eqref{metric1} has been
studied in \cite{Dong:2012se} where it was shown that the entanglement entropy exhibits interesting behaviors
for $d-1\leq \theta\leq d$. Indeed while the theory has extension entropy for $\theta=d$ it shows
logarithmic violation of area law for $\theta=d-1$.

In this section following \cite{deBoer:2011wk}  we would like to study holographic entanglement
entropy for the background \eqref{metric2}. For this metric even at constant time slices the metric
has an anisotropic scaling.

To proceed,  we will calculate entanglement entropy for a strip subsystem in the dual theory.
From gravity point of view  one needs to minimize a surface in the geometry \eqref{metric2}  whose intersection with the boundary
coincides to the strip.  In course to do so, we recognize two possible ways to
embed the strip in the theory depending on the directions we choose for the strip.
In the first  case the width of the strip is along $y$ direction while in the second case one may pick up one
of the isotropic directions  $x_i$'s for the width of the strip. In what follows we consider both of them.

\subsection*{Case A}

For the first case, where the width of strip is along the anisotropic scaling direction, consider the following strip
\begin{equation}\label{stripA}
\frac{\ell}{2}\leq y\leq \frac{\ell}{2}, \;\;\;\;\;\;\;\;\;\;\;\;\;0\leq x_i\leq L,\;\;{\rm for}\;i=1,\cdots,d-1.
\end{equation}
Now the aim is to  minimize a surface on the bulk whose boundary is the above strip and its profile
in the bulk is given by $y=y(r)$. From the geometry \eqref{metric2} the induced metric on this surface reads
\begin{equation}
ds_{ind}^2=r^{2\frac{\theta}{d}}\left[ \left(\frac{y'^2}{r^{2z}}+\frac{1}{r^2}\right)dr^2+\frac{\sum_{i=1}^{d-1}dx_i^2
}{r^2} \right].
\end{equation}
Therefore the area of the surface is
\begin{equation}
A=L^{d-1}\int_\epsilon dr\; \frac{\sqrt{r^{2(z-1)}+y'^2}}{r^{d+z-\theta-1}}.
\end{equation}
where prime represents derivative with respect to $r$.
Note that since we are considering $\theta\leq d$, one  has $d+z-\theta-1\geq 0$.
Therefore the area always diverges at UV where $r\rightarrow 0$, and thus we had to introduce
a UV cut off $\epsilon$ in the above expression.

To minimize the area one may consider the above expression as an action of  a one dimensional mechanical
 system whose momentum is a constant of motion
\begin{equation}
\frac{1}{r^{d+z-\theta-1}}
\frac{y'}{\sqrt{r^{2(z-1)}+y'^2}}=\frac{1}{r_0^{d+z-\theta-1}}={\rm constant}.
\end{equation}
Here $r_0$ is the turning point where $y'|_{r_0}\rightarrow\infty$. The above constraint can be solved
to find the  width of the strip  as a function of turning point $r_0$,
\begin{equation}
l=2r_0^z\int_0^1d\xi\;\frac{\xi^{d+2z-\theta-2}}{\sqrt{1-\xi^{2(d+z-\theta-1)}}}.
\end{equation}
Finally for the area we arrive at
\begin{equation}
A=\frac{L^{d-1}}{r_0^{d-\theta-1}}\int_{\frac{\epsilon}{r_0}}^1d\xi \;
\frac{\xi^{\theta-d}}{\sqrt{1-\xi^{2(d+z-\theta-1)}}},
\end{equation}
It is now possible to preform the above integrals and eliminate
$r_0$ between them to find the  entanglement entropy as a function of width $\ell$.
For $\theta\neq d-1$,  one finds
\begin{equation}
\ell=c_0 r_0^z,\;\;\;\;\;\;\;\;\;A=\frac{L^{d-1}}{d-\theta-1}\left(\frac{1}{\epsilon^{d-\theta-1}}-
\frac{b_0}{r_0^{d-\theta-1}}\right),
\end{equation}
with
\begin{equation}
c_0=\frac{2\sqrt{\pi}}{z}\;\frac{\Gamma\left(\frac{d+2z-\theta-1}{2(d+z-\theta-1)}\right)}
{\Gamma\left(\frac{z}{2(d+z-\theta-1)}\right)},\;\;\;\;\;\;\;\;\;\;\;
b_0=\sqrt{\pi}\;\frac{\Gamma\left(\frac{-d+\theta+1}{2(d+z-\theta-1)}\right)}
{\Gamma\left(\frac{z}{2(d+z-\theta-1)}\right)}.
\end{equation}
Plugging the obtained minimized area in the equation \eqref{EE}, one can find  the entanglement
entropy as follows
\begin{equation}
S=\frac{L^{d-1}}{4(d-\theta-1)G_N}\left(\frac{1}{\epsilon^{d-\theta-1}}-b_0
\frac{c_0^{(d-\theta-1)/z}}{\ell^{(d-\theta-1)/z}}\right).
\end{equation}
As we already mentioned,  one  would not expect that the metric provides the gravitational dual
for whole range of the energies. In fact above a given dynamical scale, $r_F$, one would expect that
the UV theory will be described by a UV completion geometry\cite{Dong:2012se}\footnote{
With the dynamical scale $r_F$ the metric \eqref{metric1} should be read$$
ds_{d+2}^2=\left(\frac{r}{r_F}\right)^{\frac{2\theta}{d}} \left(-\frac{dt^2}{r^{2z}}+\frac{dr^2}{r^2}+\frac{\sum_{i=1}^ddx_i^2}{r^2} \right)$$.}.
 Taking into account
the dynamical scale $r_F$, the entanglement entropy reads
\begin{equation}
S=\frac{L^{d-1}}{4(d-\theta-1)G_N}\left[\left(\frac{\epsilon}{r_F}\right)^\theta\;\frac{1}{\epsilon^{d-1}}-
\left(\frac{\ell^{1/z}}{r_F}\right)^\theta\;
\frac{b_0c_0^{(d-\theta-1)/z}}{\ell^{(d-1)/z}}\right].
\end{equation}

On the other hand for  $\theta=d-1$ and any $z$, one gets $z\ell =2r_0^z$ while for the area one finds
$A=-L^{d-1}\ln\frac{\epsilon}{2^{1/z}r_0}$. Therefore in this case, considering the
scaling $r_F$,   one arrives at
\begin{equation}
S=\frac{1}{4z\pi G_N}\;\frac{L^{d-1}}{r_F^{d-1}}\;\ln\frac{z\ell}{\epsilon^z},
\end{equation}
showing that the dual theory exhibits logarithmic violation for the area law which could be an
indicator of having a Fermi surface in the model. Note also that  for $d=\theta$, the expression for $A$ is finite and indeed for the entropy we find
\begin{equation}
S\sim L^{d-1}\ell^{1/z}.
\end{equation}

It is interesting to note that, even though in the present case where the anisotropic scaling
was along a spatial direction, the system exhibits similar behaviors as that in \cite{Dong:2012se}
where the anisotropic scaling was along the time direction. Actually the results are almost
identical up to a $1/z$ factor in the power which can be understood from the fact that
the scaling of the width of the strip  in these two cases are related by factor of $z$. Therefore
from the results of  \cite{Dong:2012se} one can find our results by just replacing
$r_0\rightarrow r_0^{z}$, or $\ell\rightarrow \ell^{1/z}$.

\subsection*{Case B}

Let us consider  a case where the width of strip is along one of $x_i$'s directions. The corresponding
strip subsystem may be given by
\begin{equation}\label{stripB}
\frac{\ell}{2}\leq x_{d-1}\leq \frac{\ell}{2},\;\;\;\;\;\;0\leq y\leq L,\;\;\;\;\;\;0\leq x_i\leq L,\;\;\;\;
{\rm for}\;i=1,\cdots, d-2.
\end{equation}
The holographic entanglement entropy is given by a minimal surface whose shape at the boundary coincides
to the above stripe and  has a profile in the bulk given by $x_1=x(r)$.  The induced
metric on the surface is
\begin{equation}
ds^2_{ind}=r^{2\frac{\theta}{d}}\left[\frac{dy^2}{r^{z}}+(1+x'^2)\frac{dr^2}{r^2}+
\frac{\sum_{i=1}^{d-2}dx_i^2}{r^2}\right].
\end{equation}
Thus the area reads
\begin{equation}
A=L^{d-1}\int dr\;\frac{\sqrt{1+x'^2}}{r^{d+z-\theta-1}}.
\end{equation}
One can  go through the well known procedure to minimize the surface, as we did in the previous
case. Doing so, one arrives at the following expressions for the width $\ell$ and area $A$
\begin{equation}
\ell=2r_0\int_0^1d\xi\;\frac{\xi^{d+z-\theta-1}}{\sqrt{1-\xi^{2(d+z-\theta-1)}}},\;\;\;
A=\frac{L^{d-1}}{r^{d+z-\theta-2}}\int_{\frac{\epsilon}{r_0}}^1d\xi\;
\frac{\xi^{-(d+z-\theta-1)}}{\sqrt{1-\xi^{2(d+z-\theta-1)}}}
\end{equation}
Then it is easy to calculate  the above integrals to find the width,$\ell$,  and area $A$ as functions of turning
point $r_0$. By eliminating $r_0$ between these two functions, we will find the holographic
 entanglement entropy as a function of  width $\ell$. In fact for $\theta\neq d+z-2$ one finds
\begin{equation}
\ell=c_0 r_0,\;\;\;\;\;\;\;\;\;\;\;A=\frac{L^{d-1}}{d+z-\theta-2}\;\left(\frac{1}{\epsilon^{d+z-\theta-2}}-
\frac{b_0}{r^{d+z-\theta-2}}\right),
\end{equation}
where
\begin{equation}
c_0=\sqrt{\pi }\;\frac{{\Gamma}\left(\frac{d+z-\theta }{2 (d+z-\theta-1 )}\right)}{{\Gamma}\left(\frac{1}{2 (d+z-\theta-1 )}\right)} ,\;\;\;\;\;\;b_0=\sqrt{\pi }\;\frac{ {\Gamma}\left(\frac{d+z-\theta }{2 (d+z-\theta-1 )}\right)}{ {\Gamma}\left(\frac{1}{2 (d+z-\theta-1 )}\right)}.
\end{equation}
Therefore, taking into account the dynamical scale $r_F$, the entanglement entropy is
\begin{equation}
S=\frac{L^{d-1}}{4(d+z-\theta-2)G_N}\;\left[\left(\frac{\epsilon}{r_F}\right)^\theta
\frac{1}{\epsilon^{d+z-2}}-\left(\frac{l}{r_F}\right)^\theta
\frac{b_0c_0^{d+z-\theta-2}}{\ell^{d+z-2}}\right].
\end{equation}

On the other hand for $\theta= d+z-2$ one gets $\ell=2r_0$, while the area exhibits a logarithmic
behavior, $A=L^{d-1}\ln\frac{2r_0}{\epsilon}$. Thus the entanglement entropy is found to be
\begin{equation}
S=\frac{1}{4G_N}\;\frac{L^{d-1}}{r_F^{d+z-2}}\;\ln\frac{\ell}{\epsilon},
\end{equation}
that  violates the area law. Here we have also restored the dynamical scale $r_F$. If we restrict
ourselves to the case of $z\geq 2$ we get the above logarithmic violation of area law just
for $d=\theta$. Thus, taking into account that we are  interested in $\theta\leq d$, the subsystem defined by \eqref{stripB},  unlike the case of \eqref{stripA}, can never have an extensive entropy.

However we note that, if we let the dynamical exponent to be one, $z=1$, then the
entanglement entropy of the subsystem \eqref{stripB} exhibits  logarithmic violation of area
for $\theta=d-1$. Moreover for $z=1$ one may have  $\theta=d+z-1$  which means
$\theta=d$. In this case the area turns out to  be a constant leading to
an extensive  entanglement entropy as follows
\begin{equation}
 S\sim L^{d-1}\ell.
\end{equation}
Of course it is worth mentioning that in this case the metric \eqref{metric1} is, actually, flat space
(more precisely, it is a metric of upper half space) and it is not clear what the
holographic entanglement entropy means!

\section{Open string probe}

In this section we would like to probe the background \eqref{metric1} and \eqref{metric2} by an
open string. As we already mentioned these geometries are expected to provide gravitational
dual for theories with hyperscaling violation in a specific range of energies. Indeed these
geometries may be though of as an effective holographic description of the dual theories with
a UV cut off set by the dynamical scale $r_F$ over which the geometries may not provide
a good description.

Therefore by probing these geometries with an open string one can explore the interaction of an
external object in an effective theory exhibiting hyperscaling violation. In particular
we will consider a static or moving open string which in turn can be used to find the effective
potential between two external point like objects  or the drag force the external object may experience.

\subsection{Wilson loop}

The effective potential between external point like objects may be obtained by computing
the Wilson loop in the model. Actually AdS/CFT correspondence has provided a simple
prescription to compute the Wilson loop in a strongly coupled field theory by making use
of its gravitational dual\cite{{Rey:1998ik},{Maldacena:1998im}}. In this
context the Wilson loop can be computed by minimizing a world sheet of an open string whose ends
on the boundary are, indeed, representing the external objects.

To proceed consider the following ansatz for the open string
\begin{equation}
t=\tau,\;\;\;\;\;\;\;r=\sigma,\;\;\;\;\;\; x_1=x(r),
\end{equation}
one the background \eqref{metric1}.  For this ansatz the Nambu-Goto  action reads
\begin{equation}
I=-\frac{1}{2\pi \alpha'}\int dt dr\;{r^{-\frac{d(z+1)-2\theta}{d}}} {\sqrt{1+{x'}^2}}.
\end{equation}
This action can be thought of as a one dimensional mechanical system for $x$ whose momentum is a
constant of motion. With this interpretation, denoting the turning  point by $r_0$  where $x'\rightarrow \infty$, one finds
\begin{equation}
\ell=2\int_0^{r_0} dr \;\frac{\left(\frac{r}{r_0}\right)^{\frac{d(z+1)-2\theta}{d}}}{\sqrt{1- \left(\frac{r^2}{r_0^2}\right)^{\frac{d(z+1)-2\theta}{d}}}},
\end{equation}
where $\ell$ is the distance between two external objects.  Note that in the cases we are
interested in one has $d(z+1)-2\theta\geq 0$. It is, then, easy to perform the integral yielding to
 \begin{equation}
\ell=c_0 r_0, \;\;\;\;\;\;\;{\rm  with}\; c_0=\sqrt{\pi}\frac{ {\Gamma}\left(\frac{d (2+z)-2 \theta }{2 (d(z+1) -2 \theta )}\right)}{{\Gamma}\left(\frac{d}{2( d( z+1)-2 \theta) }\right)}
\end{equation}
On the other hand  the on shell action of the string reads
\begin{equation}
I=-\frac{T}{2\pi\alpha'}\int_\epsilon^{r_0}dr \; \frac{ r^{-\frac{d(z+1)-2\theta}{d}}}{\sqrt{1- \left(\frac{r^2}{r_0^2}\right)^{\frac{d(z+1)-2\theta}{d}}}}=-\frac{Td}{2\pi(zd-2{\theta})\alpha'}
\left(\frac{1}{\epsilon^{z-\frac{2 \theta }{d}}}
+\frac{I_0}{ r_0^{z-\frac{2 \theta }{d}}}\right),
\end{equation}
where $T$ is the time interval over which the Wilson loop is calculated, and
\begin{equation}
I_0=\frac{\sqrt{\pi }}{1+2  z-4\frac{ \theta}{d} }\;
\frac{ {\Gamma}\left(\frac{-d z+2 \theta }{2 (d( z+1)-2 \theta )}\right)}
{ {\Gamma}\left(\frac{-d(1+2z)+4\theta}{2( d( z+1)-2 \theta) }\right)}
\end{equation}
Therefore for $zd\neq 2\theta$, restoring the dynamical scale $r_F$, the effective potential reads
\begin{equation}
V_{\rm eff}= -\frac{d}{2\pi(zd-2{\theta})\alpha'}
\left[\left(\frac{\epsilon}{r_F}\right)^{\frac{2 \theta }{d}}\frac{1}{\epsilon^{z}}
+\left(\frac{\ell}{r_F}\right)^{\frac{2 \theta }{d}}
\frac{I_0c_0^{z-\frac{2 \theta }{d}}}{ \ell^{z}}\right].
\end{equation}
While for $zd=2\theta$ one has $\ell=2r_0$ and  for the action one gets
\begin{equation}
I=-\frac{T}{2\pi\alpha'}\int_{\frac{\epsilon}{r_0}}^1\frac{d\xi}{\xi\sqrt{1-\xi^2}}=-\frac{T}{2\pi\alpha'}
\ln\frac{2r_0}{\epsilon}.
\end{equation}
Thus in this case the effective potential has a logarithmic behavior  as follows
\begin{equation}
V_{\rm eff}=-\frac{1}{2\pi r_F^z\alpha'}\ln\frac{\ell}{\epsilon}.
\end{equation}

So far we have considered an open string probing the metric \eqref{metric1}. We would like to
extend our study for the metric \eqref{metric2} too. In this case we recognize two distinctive cases
depending on whether the distance between the external objects is along the
anisotropic scaling direction, $y$, or along one of  $x_i$'s directions. Actually for both of cases
one may go through the similar computations as presented above to calculate the
effective potential between two point like external objects. Doing so one arrives at
\begin{eqnarray}
{\rm Along}\;y \;\;{\rm direction}\;&& V_{\rm eff}\sim \left\{\begin{array}{ll} -\ell^{\frac{2\theta-d}{zd}}& \theta\neq \frac{d}{2},\cr &\cr -\frac{1}{z}\ln\frac{\ell}{\epsilon} &\theta=\frac{d}{2},\end{array}\right.\cr &&\cr
{\rm Along}\;x_1\; {\rm direction}\;&& V_{\rm eff}\sim\left\{\begin{array}{ll} -\ell^{\frac{2\theta-d}{d}}& \theta\neq \frac{d}{2},\cr &\cr -\ln\frac{\ell}{\epsilon}&\theta= \frac{d}{2}.\end{array}\right.
\end{eqnarray}
It is worth to note that since $\theta\leq d$, it is possible (for example for $\theta=d$) to get linear or
fractional power law  effective potential. In fact due to the anisotropic in the spatial directions, it
is possible to get a power law effective potential in  one direction while
a confining potential in other directions.

\subsection{Drag force}

Let us consider an open string moving in the background \eqref{metric1}
 which
could represent an external  point like  moving source in an effective theory with hyperscaling
violation. This can be used to study the drag force that the external object
might feel\cite{Gubser:2006bz}\footnote{ After we submitted our paper we were aware that the
drag force in the background \eqref{metric1} has also been, recently, sudied in \cite{Kiritsis:2012ta}.} .
Drag force  for non-relativistic theories with Schr\"odinger or Lifshitz symmetries have
been studied in \cite{Akhavan:2008ep} and \cite{Fadafan:2009an}, respectively, where it was
shown that even at zero  temperature the drag force is non-zero. It is indeed the aim of this
subsection to study the drag force for theories with hyperscaling violation.

Consider  the following  ansatz for the moving string
\begin{equation}
t=\tau,\;\;\;\;\;\;r=\sigma,\;\;\;\;\;\;x_1=vt+x(r),
\end{equation}
and all other coordinates are set to zero.
Then the Nambu-Goto action for this string reads
\begin{equation}
I=-\frac{1}{2\pi\alpha'}\int dt dr\; r^{2\frac{\theta}{d}-2}\sqrt{r^{2(1-z)}(1+{x'}^2)-v^2},
\end{equation}
 Since the metric components
are $t$ independent, the above action may be treated as a one dimensional mechanical
system whose momentum is the constant of motion
\begin{equation}
 r^{2\frac{\theta}{d}-2}\;\frac{r^{2(1-z)}{x'}}{\sqrt{r^{2(1-z)}(1+{x'}^2)-v^2}}=-2\pi\alpha' \Pi_x=
{\rm constant},
\end{equation}
which can be solved to find $x'$ as follows
\begin{equation}\label{cons}
{x'}^2=4\pi^2{\alpha'}^2\Pi_x^2\;\frac{1-r^{2(z-1)}v^2}{r^{4\frac{\theta}{d}-2(z+1)}-
4\pi{\alpha'}^2\Pi_x^2}.
\end{equation}
In terms of the constant $\Pi_x$,  energy, $E$, and  momentum, $P$, that the  open string gains from
through its end point are given by
\begin{equation}
\frac{dE}{dt}=\Pi_x v.\;\;\;\;\;\;\;\;\;\;\;\frac{dP}{dt}=\Pi_x.
\end{equation}
The constant $\Pi_x$ can be obtained by requiring
that the numerator and denominator of \eqref{cons} vanish at the same point,
imposed by the fact that $x'$ should be real. Setting the numerator  to zero one finds $v=r_0^{1-z}$.
From this solution we  observe
that as we are varying $r_0$ from infinity to zero (flowing from IR to UV), the velocity takes its value from
 zero to infinity.
This is, in fact, due to the non-relativistic property of the dual field
theory. Moreover by  plugging the solution $r_0$ into the denominator one arrives at
\begin{equation}
\Pi_x=-\frac{v}{2\pi {\alpha'}}\; v^{\frac{2(d-\theta)}{d(z-1)}}.
\end{equation}
Now consider a single non-relativistic particle with momentum $P$ and mass $M$,
then we have $P = Mv$. It is useful to formally rewrite the above expression for the
drag force in terms of $P$. Then we can perform the integral which for $d\neq \theta$ yielding
to
\begin{equation}
P=\left(P_0^{-\frac{2(d-\theta)}{d(z-1)}}+\frac{d-\theta}{d(z-1)\pi\alpha'}\;
\frac{t}{M^{\frac{d(z-3)+2\theta)}{d(z-1)}}}\right)^{-\frac{d(z-1)}{2(d-\theta)}},
\end{equation}
while for $d=\theta$ one finds
\begin{equation}
P=P_0e^{-\frac{t}{2\pi\alpha' M}}.
\end{equation}
Here $P_0$ is the initial momentum.

We note that even though  the theory we considered here was at zero
temperature the drag force is non-zero. In other words, as the open string moves on the metric \eqref{metric1} it experiences a non-zero
friction. Therefore if we let the open string (external point like object) moves with an initial velocity (initial momentum $p_0$)  after some time it will stop unless one compensates the losing energies by an
external force.

Actually having a non-zero drag force even at zero temperature appears when there is  an
anisotropic scaling between time and the direction the string moves. This is of course a typical
feature of non-relativistic
field theories whose gravitational duals have metrics with an anisotropic scaling.

In fact it is straightforward to compute the induced metric on the string  worldsheet and  argue
that there is an event. For example for an open string moving in the geometry \eqref{metric1} the induced metric on its worldsheet is
\begin{equation}
ds^2=r^{\frac{2\theta}{2}-2}\left[-(r^{2(1-z)}-v^2)dt^2+(1+{x'}^2)dr^2+2vx'dr dt\right],
\end{equation}
which can be diagonalized by the following change of coordinates\cite{Gursoy:2010aa}
\begin{equation}
t=\tau+\eta(r),\;\;\;\;\;\;{\rm with}\;\;\eta'(r)=\frac{v x'}{r^{2(1-z)}-v^2},
\end{equation}
by which the induced metric reads
\begin{equation}
ds^2=r^{\frac{2\theta}{2}-2}\left[-(r^{2(1-z)}-v^2)d\tau^2+\frac{r^{\frac{4\theta}{d}-2(z+1)}}{r^{\frac{4\theta}{d}-2(z+1)}-4\pi^2\alpha'^2\Pi_x^2} dr^2\right].
\end{equation}
As we see the induced metric develops an event horizon whose location is given by $r_0^{2(1-z)}-v^2=0$, and the Hawking temperature is
\begin{equation}
T=\frac{\sqrt{(z-1)(z+1-\frac{2\theta}{d})}}{2\pi r_0^z}.
\end{equation}
On observes that even the bulk is at zero temperature, the worldsheet is thermal which should be
responsible of having energy loss in this case. Note that for  $z=1$ the temperature is zero and
indeed for this the energy loss is zero too.

Let us now study an open string  moving  in the metric \eqref{metric2}. In this case we
could consider a situation where either the string moves in $x_1$ or $y$ directions. In the first case,
actually, due to the rotational symmetry in $x_1$ and $t$ directions when the string moves in $x_1$ direction, one gets nothing new, except
that of the pure AdS case\cite{Gubser:2006bz}. Namely there is no drag force.

On the other hand when the open string moves in $y$ direction, the induced metric on its
worldvolume is
\begin{equation}
ds^2=r^{\frac{2\theta}{2}-2}\left[-(1-v^2r^{2(1-z)})dt^2+(1+{x'}^2r^{2(1-z)})dr^2+2vx'r^{2(1-z)}dr dt\right],
\end{equation}
which, by making use of the equation of motion of $\phi$, can be recast to the following form
\begin{equation}
ds^2=r^{\frac{2\theta}{2}-2}\left[-(1-v^2r^{2(1-z)})d\tau^2+\frac{r^{\frac{4\theta}{d}-2(z+1)}}{r^{\frac{4\theta}{d}-2(z+1)}-4\pi^2\alpha'^2\Pi_x^2} dr^2\right].
\end{equation}
It seems that the resultant world-volume metric has an event horizon and the situation could be the
same as before. We note, however, that if we went through the standard procedure, as we did in the
previous case, the Hawking temperature turns out to be imaginary which could mean that the
ansatz we considered for the  open string is not a consistent solution. Therefore it seems that even in this
case where the string moves along a direction with an anisotrpoic scaling, the drag force is zero.

\subsection{Rotating open string}

As a final example of open strings probing the geometries \eqref{metric1} and \eqref{metric2},  in this subsection we will consider a rotating open string in the bulk that describes, holographically, an
external point like object in the strongly coupled theories with hyperscaling violation undergoes
circular motion. Such a study  has been first done for a rotating quark in strongly coupled
${\cal N}=4$ SYM theory in\cite{{Fadafan:2008bq},{Athanasiou:2010pv}} where the authors ``have  computed the energy
density and angular distribution of the power radiated by a rotating quark in this theory.''\footnote{
Rotating massive quark in an anisotropic strongly coupled plasma has also
been studied\cite{Fadafan:2012qu}.
For rotating strings on  non-conformal holography see \cite{AliAkbari:2011ue}.}
To start let us  consider the following change of coordinates in the metrics \eqref{metric1} and \eqref{metric2}
\begin{equation}
(x_1,x_2)\rightarrow (\rho,\phi);\;\;\;\;\;\;{\rm such\; that}\;\;\;dx_1^2+dx_2^2=d\rho^2+\rho^2d\phi^2,
\end{equation}
by which the metrics \eqref{metric1} and \eqref{metric2} may be recast to the following forms
\begin{eqnarray}\label{met1}
&&ds^2_{d+2}=r^{\frac{2\theta}{d}}\left(-\frac{dt^2}{r^{2z}}+\frac{dr^2}{r^2}+\frac{d\rho^2}{r^2}+\frac{\rho^2 d\phi^2}{r^2}+\frac{\sum_{i=3}^ddx_i^2}{r^2} \right),\\
&&ds_{d+2}^2=r^{\frac{2\theta}{d}} \left(\frac{dy^2}{r^{2z}}+\frac{dr^2}{r^2}+
\frac{d\rho^2}{r^2}+\frac{\rho^2d\phi^2}{r^2}+\frac{\sum_{i=3}^{d-1}dx_i^2
}{r^2}-\frac{dt^2}{r^2} \right).\label{met2}
\end{eqnarray}
Let us now consider the following ansatz for a rotating open string in these backgrounds
\begin{equation}
t=\tau,\;\;\;\;\;r=\sigma,\;\;\;\;\;\;\rho=\rho(r),\;\;\;\;\;\;\;\phi=\omega t+\phi(r),
\end{equation}
and all other coordinates are set to zero. From dual field theory point of view this corresponds to an extremal point like object undergoes a circular motion  around the center $\rho=0$ with frequency $\omega$.

The Nambu-Goto action for this open string in the background \eqref{met1} is
\begin{equation}\label{act1}
I=-\frac{1}{2\pi\alpha'}\int dt dr \; r^{2\frac{\theta}{d}-1-z}\sqrt{(1-\rho^2\omega^2r^{2(z-1)})(1+{\rho'}^2)+\rho^2{\phi'}^2},
\end{equation}
whereas for the metric \eqref{met2} it becomes
\begin{equation}\label{act2}
I=-\frac{1}{2\pi\alpha'}\int dt dr \; r^{2\frac{\theta}{d}-2}\sqrt{(1-\rho^2\omega^2)(1+{\rho'}^2)+\rho^2{\phi'}^2}.
\end{equation}
Note that the action \eqref{act2} up to a factor of $r^{2\frac{\theta}{d}}$ is the same as that
for pure AdS case studied in \cite{Athanasiou:2010pv} .

In both cases the actions are  independent of $\phi(r)$, and therefore the corresponding angular momentum,
$\Pi_\phi=-\frac{\partial{\cal L}}{\partial\phi'}$,  is an integral of motion. In other words for the action \eqref{act1}, setting $p=2\frac{\theta}{d}-1-z$ and $q=2(z-1)$ one has
\begin{equation}
\Pi_\phi =\frac{-r^p\rho^2 \phi'}{\sqrt{(1-\rho^2\omega^2r^q)(1+{\rho'}^2)+\rho^2{\phi'}^2}} ={\rm constant },
\end{equation}
while for action \eqref{act2}, setting $\tilde{p}=2\frac{\theta}{d}-2$ one gets
\begin{equation}
\Pi_\phi =\frac{-r^{\tilde{p}}\rho^2 \phi'}{\sqrt{(1-\rho^2\omega^2)(1+{\rho'}^2)+\rho^2{\phi'}^2}} ={\rm constant }.
\end{equation}
Using these expressions one can find the  equation of motion for $\phi(r)$ as follows
\begin{eqnarray}\label{phi1}
{\rm for\; action\; \eqref{act1}} &&\phi'^2=\frac{\Pi_\phi^2 (1-\omega^2 \rho^2r^q) (1+\rho'^2)}{\rho^2(r^{2p}\rho^2-\Pi_\phi^2)},\\
{\rm for\; action\; \eqref{act2}} &&\phi'^2=\frac{\Pi_\phi^2 (1-\omega^2 \rho^2) (1+\rho'^2)}{\rho^2(r^{2\tilde{p}}\rho^2-\Pi_\phi^2)}.\label{phi2}
\end{eqnarray}
Finally, utilizing the above expressions,  the equation of  motion for $\rho(r)$,  is then given by
\begin{eqnarray}
{\rm for\; action\; \eqref{act1}} &&\rho''+\left(\frac{\rho (r-p\rho\rho')}{r(r^{-2p}\Pi_\phi^2-\rho^2)}+
\frac{(2-qr^{q-1}\omega^2\rho^3\rho')}{2\rho(1-\rho^2\omega^2r^q)}
\right)(1+\rho'^2)=0,\cr &&\cr
{\rm for\; action\; \eqref{act2}} &&\rho''+\left(\frac{\rho (r-\tilde{p}\rho\rho')}{r(r^{-2\tilde{p}}\Pi_\phi^2-\rho^2)}+\frac{1}{\rho(1-\rho^2\omega^2)}
\right)(1+\rho'^2)=0.
\end{eqnarray}
We have now all equations to study the rotating strings. To proceed, in what follows we will only  consider
the first case which is based on the action \eqref{act1}.  Actually the results for the second case  can be obtained from the first one by replacing $p\rightarrow \tilde{p}$ and $q\rightarrow 0$.

In general to find a solution for the rotating string we have to solve the equations of motion of $\rho$ and $\phi$
with a given initial data\cite{Athanasiou:2010pv}. Actually to solve the equation of motion for $\rho$ we find that it is
singular when $\Pi_\phi^2-\rho^2r^{2p}=0$ or  $1-\rho^2\omega^2r^q=0$. On the
other hand in order to impose the reality condition on $\phi'$ one has to assume that
these two expressions should vanish at the same point. Let us denote by $r_0$ the point where
both of the expressions vanish. Then one gets
\begin{equation}\label{rho0}
\rho_0=\frac{(\Pi_\phi\omega)^{\frac{-q}{2p-q}}}{\omega},\;\;\;\;\;\;\;\;\;\;r_0=(\Pi_\phi\omega)^{\frac{2}{2p-q}},
\end{equation}
where $\rho_0=\rho(r_0)$. On the other hand $\rho'(r_0)$ may also be fixed by $\omega$ and $\Pi_\phi$
as follows. Following \cite{Athanasiou:2010pv} let us expand $\rho$ around $r_0$,
\begin{equation}
\rho=\rho_0+\rho_1(r-r_0)+\frac{1}{2}\rho_2(r-r_0)^2+\cdots.
\end{equation}
Plugging this expansion in the equation of motion for $\rho$ and requiring all terms in the expansion vanish identically we can read the coefficients $\rho_i$.  At the first order, for $2p+q\neq 0$, one finds
\begin{equation}
\rho_1^2 - \frac{2\left(2\omega^2-pq(\Pi_\phi \omega)^{\frac{2q+4}{q-2p}}\right)}{(q+2p)\omega (\Pi_\phi \omega)^{\frac{q+2}{q-2p}} } \rho_1-1=0,
\end{equation}
which can be solved to find $\rho_1$ in terms of $\omega$ and $\Pi_\phi$.

 Therefore with $\omega$ and $\Pi_\phi$ as the initial data one should be able to find a unique solution
for the rotating open string. Indeed, by making use of a numerical method we have solved the equation of motion for $\rho$ with specific
 values of $p$ and $q$. In particular in the figure (1) we have plotted
$\rho$ as a function of $r$ for the cases of $q=2$ and $p=-3/2,-2,-3$ which correspond to
the cases where $z=2$ and $\theta= \frac{3d}{4},\frac{d}{2},0$.
In order to compare the results with that in the pure AdS case\cite{Athanasiou:2010pv}, we have also plotted $\rho$ as a function of
$r$ for the case of $z=1,\theta=0$.
\begin{figure}
\begin{center}
\includegraphics[scale=0.16]{rho3}
\caption{$\rho$ as a function of $r$ for the cases of  $z=2$ and $\theta=\frac{3d}{4},\frac{d}{2},0$ which
are shown by  dashed, dotted and thin curves, respectively. In order to compare our
results with that of  AdS case ($z=1, \theta=0$), we have also plotted this case which is shown by a
thick curve.   Note that to solve the equation we
have set the initial date as $\omega=\Pi_\phi=1$.}
\end{center}\label{fig1}
\end{figure}

The function of  $\rho(r)$ shows how the string spreads as a function depth\cite{Athanasiou:2010pv}.
Actually as we can see from the figure (1) for the rotating string in the AdS case, the string spreads linearly, $\rho\sim r$, as we approach the IR region (see also the exact solution given in \cite{Athanasiou:2010pv}). On the other hand although in the present  case the string still
spreads  as a function of depth, the rate of spreading is slower than that in the AdS case. In fact in our
case, as one can see from our numerical solution, the asymptotic behavior is $\rho\sim r^\alpha$
for $r\gg 1$ with $\alpha< 1$. Of course for $r<1$ the string on the hyperscaling violation
metrics spreads faster than that on the pure AdS (see figure 1). Pictorially, these
behaviors can be visualized by projecting the function $\rho(\phi)$ to a $r={\rm constant}$ (boundary) surface as we have depicted in figure (2).
\begin{figure}
\begin{center}
\includegraphics[scale=.05]{q2}
\caption{Here we have plotted $\rho$ as a function of $\phi$ for the cases of  $z=1, \theta=0$ (left), $z=2, \theta=0$ (middle) and $z=2, \theta=
\frac{d}{2}$ (right). The function is projected in to $x_1-x_2$ plane, where $\rho$ and $\phi$ are polar coordinates of this place. Here we have set
$\omega=\Pi_\phi=1$.}
\end{center}
\end{figure}

On the other hand looking at the behavior of the function $\phi$ which describes how the string
 winds in azimuthal angle as a function of depth\cite{Athanasiou:2010pv}, one finds that
in the present case where we have the hyperscaling violation, it grows faster that that in AdS as we move
toward the core of  the space-time.

For $2p+q=0$, expanding $\rho$ around $\rho_0$ we find that all $\rho_i=0$. Indeed it is easy to show that in this case $\rho={\rm constant}$ is an exact
solution of the equation of motion where the constant is found to be
$\rho=\sqrt{\Pi_\phi/\omega}$ which is consistent with \eqref{rho0}. Moreover,
in this case the equation of motion of $\phi$ can also be solved exactly.  In fact for $2p+q=0$, which corresponds to $\theta=d$ for all values of $z$, one finds\footnote{Note that
this solution is not valid for $z=1$. Actually for $\theta=d$ and $z=1$ the geometry reduces to
the flat space-time where we do not have a well defined holography.}
\begin{equation}
\phi=\omega\left(t+\frac{r^z}{z}\right),\;\;\;\;\;\;\;\;\;\;\;\rho=\rho_0=\sqrt{\frac{\Pi_\phi}{\omega}},\;\;\;\;\;\;\;\;\;\;r_0=(\Pi_\phi\omega)^{\frac{1}{2(1-z)}}.
\end{equation}

To wrap up this section we note that  looking at the induced metric of the string worldsheet one
 observes that it has an even horizon. More precisely, with a proper change of coordinates,  the
induced metric of the string worldsheet is found
\begin{equation}
ds^2=r^{\frac{2\theta}{d}-2-q}\left[-(1-\omega^2\rho^2r^q)d\tau^2+\frac{r^{2p+q}\rho^2(1+\rho'^2)}
{r^{2p}\rho^2-\Pi_\phi^2}dr^2\right],
\end{equation}
which has an even horizon at $r=r_0$. The corresponding  Hawking temperature is
\begin{equation}
T=\frac{1}{4\pi \rho_0 r_0^z}\sqrt{-\frac{2(q\rho_0+2\rho_1r0)(p\rho_0+\rho_1r_0)}{ 1+\rho_1^2}}.
\end{equation}
It is crucial to note that to have a solution for $\rho(r)$ in the vicinity of $r_0$, the positivity condition of the right hand side of the equation (\ref{phi1}) reduces to the following inequality
\begin{equation}
(q\rho_0+2\rho_1r0)(p\rho_0+\rho_1r_0)<0,
\end{equation}
which is necessary to have a well defined real Hawking temperature.

Having found the shape of the rotating  string, it is then possible to compute the radiation power
of the string. From the Nambu-Goto action one can obtain the  energy density and energy flux
of string from which  the energy loss rate of the  string is found\cite{Athanasiou:2010pv}
\begin{equation}
\frac{dE}{dt}=\frac{\Pi_\phi \omega}{2\pi\alpha'}.
\end{equation}
Of course the goal is to compute the energy loss rate in terms of the parameters of the dual field
theory which is frequency and the radius of circle the external object moves around, {\it i.e.} $\rho_*=\rho(r\rightarrow 0)$. With the numerical solution we have obtained, it is easy to find $L=\Pi_\phi\omega$
as a function of $\rho_*$ which is indeed the energy loss rate up to factor of $1/2\pi\alpha'$.
In the figure (3) we have drown the function of $L$ in terms of $\rho_*$ for the case of $z=2,\theta=0$.
\begin{figure}
\begin{center}
\includegraphics[scale=.2]{L2}
\caption{Here we have plotted $\rho_{*}$ as a function of $L=\Pi_\phi\omega$ for the case of  $z=2, \theta=0$. Essentially this is the energy loss rate in terms of the radius of circle the external object moves.}
\end{center}
\end{figure}
Form our numerical solution, for large $\rho_*$, one finds $L\sim \rho_*^4$.

As a final remark we note that  $r_0$ fixes the local velocity of string. Since
$r_0$ can change from zero to infinity, it means that the local velocity could be infinity, indicating
the non-relativistic nature  of the dual theory.

\section{Closed string probe}

Since it is possible to find a geometry with non-trivial hyperscaling exponent from string theory
(see for example \cite{{Dong:2012se},{Narayan},{AMK}}) it is natural to study a closed string propagating in this background
which could be dual to an operator in the dual field theory with n hyperscaling violation. In fact
in this section, for completeness of our study, we will  probe the geometry \eqref{metric1} by a closed string. Via AdS/CFT correspondence a closed string moving in the
bulk should correspond to a field (operator) configuration with specific energy and probably some other quantum numbers. Therefore it could be possible to study certain
properties of the dual theory by making use of a semi-classical closed string on the bulk.
In what follows we will  consider a folded rotating closed\cite{Gubser:2002} and circular pulsating\cite{Minahan:2002rc}
 strings in the background \eqref{metric1}.\footnote{Circular pulsating closed string on the
confining geometry has also been studied in \cite{mosaffa}.}

\subsection{Folded closed string}

In this subsection we study a solution representing a rotating
closed string configuration which is stretched along the
radial coordinate. In order to study this system one needs
to write an action for this closed string.
Let us parameterize the string worldsheet by $\sigma $ and $\tau$. We can fix the reparameterization
invariance by a parameterization such that the time coordinate of space-time,
$t$ to be equal to worldsheet time, i.e. $t=\tau$.
In this gauge a closed string configuration
representing a rotating string with angular velocity
$\omega$ on geometry (\ref{metric1}) stretched along the radial
coordinate is given by
\begin{eqnarray}
&& t=\tau,\qquad  \phi_{d-1}=\phi=\omega \tau,\qquad r(\sigma)=r(\sigma+2\pi),\cr\cr
&&  \phi_i=\frac{\pi}{2} \;\;({\mathrm for} \; i=1\cdots d-2)  ,\quad  \rho=\rho_0 ={\rm constant.}
\label{CL}
\end{eqnarray}
where $\sigma$ and $\tau$ are coordinates of the string world sheet. Moreover we parametrize the $d$-dimensional Euclidean space in the metric (\ref{metric1}) as follows
\begin{equation}
\sum_{i=1}^d dx_i^2=d\rho^2+\rho^2 (d\phi_1^2+\sin^2\phi_1d\phi_2^2+\cdots+\sin^2\phi_1...\sin^2\phi_{d-2}d\phi_{d-1}^2).
\end{equation}
For this  ansatz  the Nambu-Goto action,
reads
\begin{equation}
I=-4\frac{T}{2\pi\alpha' }\int_{0}^{r_0} r^{\frac{2\theta}{d}-2}\sqrt{r^{2-2z}\dot{t}^2-\rho_0^2\dot{\phi}^2}\; dr
\end{equation}
where $dot$ represents derivative with respect to $\tau$ and $r_0=(\rho_0\omega)^{1/(1-z)}$. The factor of 4 comes from the fact that we are dealing with a
folded closed string. Working with one fold string, the string can be divided to four
segments. Using the periodicity condition we just need to perform the integral for
one quarter of string multiplied by factor 4.  When the periodicity condition is satisfied, using the above Nambu-Goto action the conserved quantities are given by
\begin{eqnarray}
 E=\frac{2T}{\pi\alpha'}\int_{0}^{r_{0}}   dr \frac{ r^{\frac{2\theta}{d}-2z}}{     \sqrt{r^{2-2z}-\rho_0^2\omega^2}}, \;\;\;\;\;\;\;\;S=\frac{2T\rho_0^2\omega}{\pi\alpha' }
\int_{0}^{r_{0}}   dr \frac{ r^{\frac{2\theta}{d}-2}}{     \sqrt{r^{2-2z}-\rho_0^2\omega^2}},
\end{eqnarray}
From these expressions we could find a relation between $E$ and $S$. Actually the above integrals can be performed exactly, though generically they
diverge and need to be regularized.  Indeed
setting $x=r/r_0$, one has
\begin{eqnarray}\label{En-Sp}
&&{ \cal E}=\frac{\pi\alpha'}{2T}E=r_0^{\frac{2\theta}{d} -z}   \int_0^{1}\frac{ x^{\frac{2\theta}{d}-z-1}}{\sqrt{1-x^{2z-2}}}\; dx ={\cal E}_0  r_0^{\frac{2\theta}{d} -z}\\
&& {\cal S}= \frac{\pi\alpha'}{2T\rho_0}S=r_0^{\frac{2\theta}{d} -1} \int_0^{1}\frac{ x^{\frac{2\theta}{d}+z-3}}{\sqrt{1-x^{2z-2}}}\; dx= {\cal S}_0 r_0^{\frac{2\theta}{d} -1} \end{eqnarray}
where constants ${\cal E}_0$ and ${\cal S}_0$ are given by
\begin{equation}
{\cal E}_0=\frac{\sqrt{\pi}}{2(z-1)}\frac{\Gamma\left(\frac{2\theta-zd}{2d(z-1)} \right)}{\Gamma\left(\frac{2\theta-1}{2d(z-1)} \right)},\quad   {\cal S}_0=\frac{\sqrt{\pi}}{2(z-1)}\frac{\Gamma\left(\frac{2\theta+zd-2d}{2d(z-1)} \right)}{\Gamma\left(\frac{2\theta+2zd-3d}{2d(z-1)} \right)}.
\end{equation}
Therefore with a proper regularization one finds
\begin{equation}\label{ES}
{\cal E}={\cal E}_0{\cal S}_0^{\frac{zd-2\theta}{2\theta-d}}\; {\cal S}^{\frac{2\theta-zd}{2\theta-d}}.
\end{equation}

Looking at the explicit form of the energy and spin,  depending on the nature of the divergences  we recognize two distinct cases. Actually although in a typical case we get
power law divergence, there are cases where we get logarithmic divergences that correspond to the cases where
either $2\theta= zd$, or $\theta=0,\;z=2$. Note that the latter case is indeed Lifshitz geometry with scaling exponent $z=2$.

For  $2\theta= zd$ the energy diverges  due to UV divergence of the integral. Therefore we need to regularize it by performing the integral with a
UV cut off $\epsilon$. Doing so, one arrives at
\begin{equation}
{\cal E}=\int_\epsilon^{r_0}\frac{dr}{r\sqrt{1-(\frac{r}{r_0})^{2(z-1)}}}=\ln \frac{r_0}{\epsilon}+\frac{1}{z-1}\ln2.
\end{equation}
On the other hand in this case one has ${\cal S}=\frac{r^{z-1}}{z-1}$. Therefore one finds
\begin{equation}
{\cal E}=\frac{1}{z-1}\ln \frac{2(z-1)\cal S}{\epsilon^{z-1}}.
\end{equation}

In the case of  $\theta=0,\;z=2$, although the energy and spin both diverge
logarithmically, the relation between energy and spin  is still given by the equation \eqref{ES} for
$\theta=0$ and $z=2$.

It is also obvious  from the equation \eqref{ES} that the expression becomes ill-defined for
$\theta=\frac{d}{2}$. In fact in this case  starting from the  original expression for the energy and spin
in the equation \eqref{En-Sp} one finds that the spin is a constant for any turning point, {\it i.e.}
${\cal S}=\frac{\pi}{2(z-1)}$, while the energy is zero.

It is interesting to note that although the closed string, depending on $\omega$  could be short or long, the relation between energy and spin remains unchanged in all
cases discussed above. It is
in contrast to the AdS case where for short string ($\omega\rightarrow  \infty$) we find  the
flat space Regge trajectory, while for long string ($\omega\rightarrow 0$)  the energy in terms
of spin has logarithmic  behavior\cite{Gubser:2002}.

\subsection{Circular pulsating string}

In this subsection we will consider a pulsating string which wrapped $m$ times around $\phi_{d-1}$
direction. In other words we study a circular string that expand and contract in
the radial direction. The corresponding ansatz for the circular pulsating string is
\begin{equation}
t=\tau,\;\;\;\;\;\;\;r=r(t),\;\;\;\;\;\;\;\phi_{d-1}=m\sigma,\;\;\;\;\;\;\;\;\phi_i=\frac{\pi}{2},\;\;\;\;\;\;\;\;\;\rho=\rho_0={\rm constant}.
\end{equation}
 For this configuration the string action reads
\begin{equation}
I=-\frac{m\rho_0}{\alpha'}\int dt\; r^{2\frac{\theta}{d}-z-1}\sqrt{1-r^{2(z-1)}\dot{r}^2}.
\end{equation}
Setting $\xi=r^z/z$ the above action can be recast to the following form
\begin{equation}
I=-\frac{m\rho_0}{\alpha'}\int dt\; f(\xi) \sqrt{1-\dot{\xi}^2},\;\;\;\;\;\;\;{\rm with}\;f(\xi)=(z\xi)^{\frac{2\theta-zd-d}{zd}}.
\end{equation}
This action can be treated as a one-dimensional quantum mechanical system whose Hamiltonian is
\begin{equation}
H=\sqrt{\Pi^2+(\frac{m\rho_0}{\alpha'})^2f^2(\xi)}
\end{equation}
 where $\Pi$ is the canonical momentum  given by
\begin{equation}
\Pi=\frac{m\rho_0}{\alpha'}f(\xi)\;\frac{\dot{\xi}}{\sqrt{1-\dot{\xi}^2}}.
\end{equation}
Following \cite{Minahan:2002rc} $H^2$ can be considered as a one dimensional quantum mechanical system with the potential $(\frac{m\rho_0}{\alpha'})^2f^2(\xi)$. Therefore
using  the Bohr-Sommerfeld quantization we have
\begin{equation}
(n+\frac{1}{2})\pi=E\int_{\xi_0}^\infty d\xi\;\sqrt{1-\left(\frac{ f(\xi)}{f(\xi_0)}\right)^2},
\end{equation}
where $\xi_0$ defined by the root of $f(\xi_0)=\frac{\alpha' E}{m\rho_0}$. Performing the integral, with a proper regularization, one finds
\begin{equation}
(n+\frac{1}{2})\pi=-\frac{\sqrt{\pi}}{2z}\;\frac{\Gamma\left(\frac{d-2\theta}{d(z+1)-2\theta}\right)}
{\Gamma\left(\frac{1}{2}+\frac{d-2\theta}{d(z+1)-2\theta}\right)} \;
\left(\frac{\alpha' E}{m\rho_0}\right)^{\frac{zd}{2\theta-zd-d}}E.
\end{equation}

It is worth to note that, unlike the AdS case,  in the present  case due to the non-trivial IR geometry, the string while pulsating cannot approach $r=0$. Indeed there is a low bound for the string in the
radial direction fixed by
\begin{equation}
r\ge \left(\frac{m\rho_0}{E\alpha'}\right)^{\frac{d}{d+dz-2\theta}}.
\end{equation}

\section{Discussions   }

In this paper we have studied certain features of strongly coupled theories with hyperscaling violation by making use of AdS/CFT correspondence. More precisely we have considered a gravitational model
on a background which is conformally a metric with the Lifshitz isometry. The metric has two
parameters corresponding to dynamical and hyperscaling violation exponents. This geometry may be found
from  an Einstein-Maxwell-Dilaton theory.

By making use of a double Wick rotation it is possible to have a situation where the anisotropic scaling
could be  along either  time or one of spatial directions.  In both cases, using AdS/CFT correspondence,
 we have computed
several quantities including holographic entanglement entropy,
Wilson loop, drag force as well as energy loss of a rotating string.

 Although we have studied the different quantities for a generic dynamical and hyperscaling violation exponents in arbitrary dimensions, we have found that for  particular values  of the parameters
the theory exhibits interesting behavior.

To compute the entanglement entropy for a strip in a theory with an anisotropic scaling
along a spatial direction we considered two distinctive cases depending  on
whether the width of the strip is along the anisotropic direction. When
the width of the strip is along the anisotropic direction we have found that when
$\theta=d-1$ for any $z$, the entanglement entropy exhibits a logarithmic violation of area
law while for $\theta=d$, the system has an extensive entropy. Indeed the situation is very
similar to the case where the anisotropic scaling is along the time direction\cite{Dong:2012se}.
On the other hand for the case where the width of strip is along a spatial direction with a normal
scaling, the entanglement entropy shows logarithmic behavior for $\theta=d$ and $z=2$, while in
this case the subsystem never has an extensive  entropy. Having found the logarithmic behavior
might  indicate that the model has a Fermi surface.

For an open string probing the geometry one can read several interesting quantities, such as Wilson loop
which in turn can be used to read the effective potential between two external point like
objects in the system. We have shown that typically the effective potential is power low, though
for special cases it could be logarithmic.

For a moving or rotating open string we have observed  that even though the geometry are at
zero temperature, the induced metric on the worldvolume of the open string has an event
horizon leading to a non-zero Hawking termperature for worldvoulme theory. This might be
the reason we are getting non-zero drag force for the string. Again in this case we find that
$\theta=d$ is an special case where the string shows an anomalous behavior.

We have also probed the background with different closed strings. The closed strings we have
considered include rotating folded and circular pulsating strings. From the gravity point of view
it is possible to find the energy of the strings in terms of the quantum numbers the strings may have.
This may be used to find  the dispersion relation of a possible field configuration in the dual strongly
coupled hyperscaling violation field theory. The anomalous behavior can also been seen for
closed string too. In particular for $zd=2\theta$ ( which includes $\theta=d,z=2$) the
dispersion relation is logarithmic.

In this paper we have only considered a zero temperature background, though it could be generalized
to the finite temperature too. In fact the finite temperature metric has the following form\cite{Dong:2012se}
\begin{equation}
ds_{d+2}^2=\left( \frac{r}{r_F}\right)^{\frac{2\theta}{d}}\left(-r^{-2(z-1)}f(r)dt^2+\frac{dr^2}{f(r)} + dx_i^2\right),
\end{equation}
where
\begin{equation}
f(r)=1-\frac{r^{d+z-\theta}}{r_h^{d+z-\theta}}
\end{equation}
It would be interesting to study the quantities we have considered in this paper at  finite temperature.

\vspace*{1cm}

{\bf Acknowledgments}

We would like to thank Eoin \'O Colg\'ain, Mohammad  Mohammadi Mozaffar, Ali Mollabashi, Amir E. Mosaffa and Ali Vahedi for discussions on
different aspects of holographic entanglement entropy and hyperscaling violation theories.
 The research of M.A. is supported by Iran National Science Foundation (INSF). The work of H.Y.  is supported by the National Research Foundation of Korea Grant funded by the Korean Government (NRF-2011- 0023230)

redpajama_set_name: RedPajamaArXiv


With an Open Skies agreement between the U.S. and Brazil on the horizon, Brazil's most prominent air carriers are preparing to receive a big boost in travel between the two countries.
RIO DE JANEIRO, BRAZIL – Despite the political and economic uncertainty swirling around Brazil at the moment, the country's biggest airlines, Gol, Azul, as well as Chilean-based LATAM, are jockeying for position to prepare for the much-anticipated ratification of the U.S.-Brazil Open Skies agreement.
With an Open Skies agreement between the U.S. and Brazil on the horizon, Brazil's most prominent air carriers are hoping for a big boost in travel between the two countries, photo internet recreation.
In March, Brazil's Senate approved the agreement, which dates back to 2010, but, as of this writing, the bill still awaits the signature of Brazil President Michel Temer. The agreement is expected to pave the way for more flights between the two countries and greater competition among airlines.
"Within two years of Open Skies, the airlines in Brazil will have joint ventures with U.S. airlines," exclaimed Paulo Sergio Kakinoff, CEO of Gol, Brazil's most popular domestic airline, in a recent interview with Bloomberg.
Kakinoff added that with the U.S.-Brazil Open Skies agreement on the horizon the company would soon be adding flights from Fortaleza and Brasilia to Orlando and Miami.
Brazilian airline, Azul, has also strengthened its ties with the U.S. in recent weeks. Earlier this month, United Airlines purchased additional shares in the carrier from China's Hainan Airlines, doubling United's stake in Azul from 3.7 percent to 8 percent.
"Following our initial investment [in Azul] in 2015, connecting traffic between our airlines is at an all-time high, significantly benefiting our customers traveling between the US and Brazil," explained United Airlines Vice President, Andrew Levy.
"Azul's strong network in Brazil, unique business model and exceptional customer service make this transaction a good long-term investment," he added.
Despite the enthusiasm among Brazil's airlines, the Open Skies agreement has yet to receive presidential endorsement and is still not officially ratified. LATAM Airlines, Brazil's largest international carrier, remains optimistic despite the delay.
According the Brazilian airline association, ABEAR, among Brazilian airlines, Gol tops the domestic market with 34 percent market share, with LATAM a close second at 33 percent.
For international travel, LATAM leads the way with a 68 percent market share, followed by Azul at fifteen percent, and Gol at twelve percent.
Can we expect the same for European carriers and the reinstatement of direct flights from London to North East brazil?
Gol tops the domestic market by regularly having the lowest price, but not in service. It is not "Brazil's most popular domestic airline" as stated in the article. It is considered by me and all my Brazilian friends that have expressed an opinion that it is the worst, most unpleasant Brazilian airline, and also unethical. I flew from CNF to GRU on Gol recently. Scheduled to leave at 10:00 am and arrive at 11:20 am, the announcement from the cockpit was that it would be a 50-minute flight. When they landed at 11:08, they announced that again they had arrived before the stated time. This is misleading at a minimum. The return was on Latam, where they only served water, with no other options and no snack. Azul, often considered to be the best, had great service, all you can eat snacks and a good assortment of beverages. Azul also has screens on the back of the seats in front of you, which Gol and Latam do not, at least on the domestic flights. As Einstein said "Not everything that counts can be counted, and not everything that can be counted counts".


Feed aggregator | Haji Abdullah Alireza & Co., Ltd.
Philip Falcone, founder of hedge fund Harbinger Capital Management, told investors Monday that he would soon cede control of wannabe wireless carrier LightSquared.
Small business lending could take a major hit if a federal program that insures small business accounts ends later this year.
NYSE Euronext shares fell 5% on Monday after the stock exchange operator reported a sharp decline in quarterly profits on weak trading volume and merger break-up costs.
U.S. stocks were in the red Monday, on track to end the last day of what's been a mostly sour month on a weak note.


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text:
Two years' 'hard work' spurs cross-border shared services deal
admin 8 June 2012
Cotswold councils hope for £675,000 back-office savings as Socitm suggests best practice principles
The launch of a cross-border shared service involving local authorities across Gloucestershire and Oxfordshire has demonstrated how long it can take to get council partners working closely together to drive back-office savings.
Go Shared Services will provide finance, procurement, HR and payroll services to Cotswold district council, Cheltenham borough council, Forest of Dean district council and West Oxfordshire district council while cutting £675,000 per year off the cost of back office functions.
But getting to the launch of the shared service took almost two years of work across the local authority partners, including procuring the ERP software; purchasing the hardware; designing the way the ERP system functions; establishing a robust IT link across the partners; determining which local authority partner would become the employing authority for the shared service; and testing and implementing the new system.
Three local authorities and the two non-local authority clients have successfully implemented the ERP system and preparations are underway for the remaining partner Cotswold district council to go live this summer. In the autumn, the shared service will be reshaped to deliver both the financial and non-financial benefits which were forecast in the business case for the project.
Currently, the shared service is also providing services to two clients: Cheltenham Borough Homes (Cheltenham borough council's arm's-length management organisation); and Ubico (a local authority company owned by Cheltenham borough council and Cotswold district council) – which are using the ERP system for their back-office functions.
The cross-borough shared service is the latest example of how the sharing of services, including ICT and other functions, is becoming a necessity for local public services, according to public sector IT group Socitm.
In a new briefing paper,Shared services: time for a re-think?Socitm argues that under current financial pressures, shared services are likely to grow rather than fade away. The briefing sets out to provide some key principles for ensuring that a shared service venture will meet its objectives, and not fall by the wayside.
In its first principle, Socitm argues that sharing should be one of the first options to consider and much more than an optional extra to turn to in desperation, but should become a way of life. It also argues that any strategy should cover a range of sharing approaches for services, networks, data centres, applications, procurements, policies, specialist skills and ICT managers.
Its third principle says that whether shared ICT services support frontline or back-office services, for example, finance, HR and procurement, successful sharing depends largely on the willingness to standardise business processes.
Its remaining principles say that benchmarking is critical to indicate the scale of possible savings and the levels of service provided; that each council should share its plans for future major procurements in order to avoid perpetuating the current fragmented approach and to spot opportunities for significant sharing; and finally that organisations adopt a governance framework that ensures that the right objectives are set, achieved and measured.
Michael Larner, senior analyst at public sector market intelligence firm Kable, said: "Go Services' announcement shows how hard – and long – negotiations have to be between council partners to drive real savings. The fact that the partnership is across county lines rather than within the county adds a layer of complexity which appears to have been worked on from the outset.
"What this tells us in light of the Socitm's latest shared services guidelines is that working on the framework and governance is the most important success factor for shared services. Kable research from last year showed a slow down in the numbers of new shared service projects coming to market, however with austerity set to continue suppliers should expect more back office shared service arrangements.
"Councillors and IT departments can potentially reach across borders but if cost savings are the sole focus the arrangement is not likely to last."

redpajama_set_name: RedPajamaCommonCrawl


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He has been moved to the Oklahoma City FTC. Don't know if it is a permenant placement or just for a medical evaluation. Looks like he got a ride on CONAIR.
CONAIR. You heard it here first.
Yep, sure did . . .
Anyone making book on where they are going to place him permanently?
How about in the nose of a rocket on a deep space probe?
Now he is in Atlanta Prison. Gone 'big time' at a 'big house.' Forget that North Carolina rumor.
Now he is at Butner FCI in N.C. for that physical. They are moving him pretty quickly around the system.
"They are whisking Cunningham around faster than they did Bush on 9/11. "
There is some great material being written about this matter. Pretty funny!


The commander of the Iranian Revolutionary Guards Corps (IRGC) Quds Force is in Iraq as an adviser at the request of the government in Baghdad, Iraq's foreign minister said on June 6.
Maj. Gen. Qassem Soleimani is assisting Iraqi forces in the fight against Islamic State of Iraq and Levant (ISIL), according to Iraqi Foreign Minister Ibrahim al-Jaafari.
Image of Maj. Gen. Qassem Suleimani, grey hair and beard, purportedly shows him on an Iraqi battlefield. /IRINN state television.
"The presence of Iran's military advisers under the command of Maj. Gen. Qassem Soleimani in Iraq comes at the request of the legitimate government of Iraq for confronting the terrorists and extremists causing instability and insecurity in the Arab country and the region," Foreign Ministry spokesman Hossein Jaberi Ansari added.
The comments were in response to Saudi Foreign Minister Adel al-Jubeir's recent accusations that Iran's military leaders are interfering in the internal affairs of other countries in the Middle East.
"In order to recognize its own interests, friends and enemies, the Iraqi nation does not need statements by the foreign minister of a country that has been the biggest factor of instability and a sponsor of terrorism in Iraq, the region and the world in the past decade and a half," Ansari said.
A Wall Street Journal report said that Soleimani is in close contact with the anti-American commander of the Iran-backed Shi'ite militia movement taking part in the offensive to retake Fallujah from ISIL.
Jamal Jaafar Ibrahimi, primarily known as Abu Mahdi al-Mohandes, commands the Popular Mobilization Forces (PMF) and is said to be Soleimani's right-hand man in Iraq.


Mayfair is a modern collabarative range of wide and thin stripes combined with a geometric tone on tone design. It mimicks a cut velvet and is co-ordinated with Cushion, a soft velvet like fabric and Trojan II , a linen like base cloth which has also been re-coloured for this season. The colour pallete is modern with cool grey's, earthy taupe's ,soft blue's, a hint of chartuese, black, charcoal grey, and a pop of mulberry.


text:
Home › Corgi VA04120 Ford Cortina Mk2 Lotus, Anchor Blue
Corgi VA04120 Ford Cortina Mk2 Lotus, Anchor Blue
Ford Cortina Mk2 Twin Cam (Lotus) Anchor BlueThe Mk2 Cortina was heavier and wider than the Mk1 but a Lotus version was developed and used successfully in competition. The Mk2, however, was builtentirely in house by Ford who fitted engines and other components supplied by Lotus who were at this time moving from Cheshunt, Hertfordshire, to Hethel,Norfolk. It was launched in 1967 as the Ford Cortina-Lotus (rather than Lotus -Cortina) and in 1968 was renamed the Cortina Twin Cam to bring it into linewith the Escort Twin Cam, which used the same Lotus engine. Production ceased in July 1970 by which time 4032 examples had been built


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text:
#ifndef _SOURCE_PARSER_H
#define _SOURCE_PARSER_H

#include <stddef.h>
#include "../common/error.h"
#include "../common/utils.h"

bc_trie_t* blogc_source_parse(const char *src, size_t src_len, int toctree_maxdepth,
    bc_error_t **err);

#endif /* _SOURCE_PARSER_H */

redpajama_set_name: RedPajamaGithub


text:
Corethrella albicoxa är en tvåvingeart som beskrevs av Art Borkent 2008. Corethrella albicoxa ingår i släktet Corethrella och familjen Corethrellidae. Inga underarter finns listade i Catalogue of Life.

Källor

Tvåvingar
albicoxa

redpajama_set_name: RedPajamaWikipedia


text:
#ifndef PLAYGROUND_FLENS_DFT_DFT_H
#define PLAYGROUND_FLENS_DFT_DFT_H 1

#include<playground/flens/dft/matrix.h>
#include<playground/flens/dft/vector.h>

#endif // PLAYGROUND_FLENS_DFT_DFT_H


text:
Media Release by Senator the Hon Ursula Stephens
Celebrating Governance Best Practice in the Third Sector
Best practice governance is vital to a strong respected third sector, said Parliamentary Secretary for Social Inclusion and the Voluntary Sector, Senator Stephens at tonight's Transparency Awards ceremony.
The Transparency Awards were initiated by PricewaterhouseCoopers to recognise the quality and transparency of reporting in the third sector.
"The awards play a significant and valuable role in not only recognising excellence in the sector but also promoting best practice reporting by the role model of the winner and the learnings that are achieved through the intensive judging process," said Senator Stephens.
Senator Stephens said that there is currently much activity, both Government and sector-led which is coalescing around third sector regulation issues.
"The government has been looking at how best to regulate and support the sector in a way that balances the need for good governance with a lean regulatory system. The focus is on enabling better regulation, not additional or burdensome regulation," Senator Stephens said.
Dr Stephens outlined the government's work on third sector regulatory reform, including commissioning the Productivity Commission to undertake a study into the contribution of the sector to the nation's economy, funding the ABS to update its statistical information on the sector and securing the agreement of a working group of the Council of Australian Governments to start work on harmonising commonwealth, state and territory third sector regulation.
Senator Stephens presented the award to Oxfam for its outstanding reporting practices and the runner-up award to World Vision. She congratulated all participants for entering the awards, PricewaterhouseCoopers for initiating and hosting the awards each year and the other sponsors of the event: the Institute of Chartered Accountants in Australia and the Centre for Social Impact.


text:
Q: Kivy Color Wheel I understand Kivy ships with a color picker (kivy.uix.colorpicker), which is great and all, but I just want the wheel - the color wheel. That's all I want to have show in a certain space. The entire other half of the layout I don't need. At all.
Using kivy's KV, ColorWheel as a widget shows absolutely nothing, but doesn't throw any errors. I'm really confused because it seems as though the wheel itself is a pretty standalone widget (looking at the documentation) and I have no idea why I can't see it.
Help?

A: The ColorWheel object needs to trigger its "init_wheel" method to display something. And this is not done in its "init" method.
You also need to edit the "on_hsv" method to listen at the color selection.
This class inherits from the ColorWheel object and changes it to make it autonomous:
from kivy.uix.colorpicker import ColorWheel

class AutonomousColorWheel(ColorWheel):
    def __init__(self, **kwarg):
        super(AutonomousColorWheel, self).__init__(**kwarg)
        self.init_wheel(dt = 0)

    def on__hsv(self, instance, value):
        super(AutonomousColorWheel, self).on__hsv(instance, value)
        print(self.rgba)     #Or any method you want to trigger

Hope it helps.

redpajama_set_name: RedPajamaStackExchange


text:
New Orleans (59)
El Paso (19)
DEA Eases Requirements For FDA-Approved Clinical Trials On Cannabidiol
WASHINGTON - The United States Drug Enforcement (DEA) recently eased some of the regulatory requirements imposed by the Controlled Substances (CSA) for those who are conducting FDA-approved clinical trials on (CBD), an extract of the marijuana plant. These modifications will streamline the research process regarding CBD's possible medicinal value and...
Federal Indictment Charges Eight With Participating In Taos County Heroin Trafficking And Money Laundering Ring
ALBUQUERQUE, N.M. - Last week, a federal grand jury indicted eight individuals on heroin trafficking and money laundering charges based on a DEA-led investigation into an organization that allegedly distributed heroin in Taos County, N.M., announced U.S. Attorney Damon P. Martinez and Special Agent in Charge Will R. Glaspy of...
Federal Jury Finds Career Offender From Albuquerque Guilty Of Crack Trafficking And Firearms Charges
ALBUQUERQUE, N.M. - A federal jury sitting in Albuquerque, N.M., returned a verdict late yesterday afternoon finding Gabriel Mirabal guilty on narcotics trafficking and firearms charges after a six-day trial. The guilty verdict was announced by U.S. Attorney Damon P. Martinez, Special Agent in Charge Will R. Glaspy of DEA's...
Thirty-Four Facing Federal And Tribal Charges Arising Out Of Methamphetamine Trafficking On Mescalero Apache Reservation
LAS CRUCES, N.M. - Thirty-four individuals are facing federal and tribal drug charges as the result of an 18-month multi-agency investigation spearheaded by the Drug Enforcement (DEA) and Bureau of Indian (BIA) into methamphetamine trafficking on the Mescalero Apache Reservation. Eighteen defendants, including five members of the Mescalero Apache Tribe...
Pharmacy Robber Sentenced To 141 Months For Conviction On Federal Hobbs Act, Drug Trafficking And Firearms Charges
ALBUQUERQUE, N.M. - Victor Hurtado, 21, of Albuquerque, N.M., was sentenced today in federal court to 141 months in federal prison for his conviction on Hobbs Act, drug trafficking and firearms charges arising out of a pharmacy robbery in Jan. 2015, and a traffic stop in March 2015. Hurtado will...
Narcotics Task Force Announces Marijuana Seizures
SAN DIEGO - This morning, the DEA San Diego Field Division's Narcotics Task (NTF) along with the San Diego County Sheriff's Department and Health Advocates Rejecting Marijuana, (HARM) announce the total amount of illegal marijuana plants seized in San Diego County in 2015. During calendar year 2015, NTF and our...
Federal Grand Jury Indicts Davon Lymon On Narcotics Trafficking And Firearms Charges
ALBUQUERQUE, N.M. - U.S. Attorney Damon P. Martinez, Special Agent in Charge Thomas G. Atteberry, ATF Phoenix Field Division, and Special Agent in Charge Will R. Glaspy, DEA El Paso Division announced today that a federal grand jury has returned a three-count indictment charging Albuquerque resident Davon Lymon, 34, with...
San Diego Pharmacy Owners Pay $750,000 To Resolve Drug Diversion Allegations
SAN DIEGO - Drug Enforcement (DEA) San Diego Special Agent in Charge William R. Sherman and United States Attorney Laura E. Duffy announced that a group of San Diego pharmacies and their owners have paid $750,000 to the federal government to resolve allegations that they mishandled significant amounts of highly...
DEA Announces "360 Strategy" To Address Heroin, Prescription Drugs And Violent Crime
PITTSBURGH - The United States Drug Enforcement Administration today announced Pittsburgh as the pilot city for a comprehensive law enforcement and prevention "360 Strategy" to help cities dealing with a heroin and prescription drug abuse epidemic, and its associated violent crime. DEA Special Agent in Charge for the Philadelphia Division...
DEA Releases 2015 Drug Threat Assessment: Heroin And Painkiller Abuse Continue To Concern
WASHINGTON - DEA Acting Administrator Chuck Rosenberg today announced results from the 2015 National Drug Threat (NDTA), which found that drug overdose deaths are the leading cause of injury death in the United States, ahead of deaths from motor vehicle accidents and firearms. In 2013, more than 46,000 people in...


Dr. Stanley Workman, Shawnee State University (SSU) professor and local pianist and vocalist, is preparing to leave the country once again to showcase his voice across seas. His upcoming trip has him leaving for China to perform with two of his colleagues in a tribute to World War II.
Workman has traveled the country, as well as the globe, to present his powerful, classically trained voice and looks forward to showing the people of China his talent for a third time.
A friend of Workman's, James Huang, is the Chinese composer who stages these international concerts.
Workman said he is always excited to travel and perform for different people of the world. He explained that he is always interested in seeing just how similar people of other cultures are to the people at home.
The major difference he notices between China and America is that there are many more people in China. He also stated they are often more expressive of their delight in his voice.
Workman said that he has had various peers join him for these performances. The guests he will be bringing on this trip include SSU's John Huston and Mariah Minter Ginn.
Workman said he will be singing "The Longest Day," a song referring to D-Day; "Bella Ciao," which is a swell-known political piece; "A Life of Love," which he will be singing with Ginn; "A Call for Peace," an original by Huang that discusses the topic of loss from World War II and how it is still felt today; and more.
Workman said that each culture of the allied forces has a tribute in the show, so songs will include many languages, including English, Spanish, French, Italian, and Chinese.
Reach Joseph Pratt at 740-353-3101, ext. 1932, or by Twitter @JosephPratt03.


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How smart to take the cellmass in the middle of the training?
ARE BCAA powder and AMINO TABLETS SAME? Or whats the difference between them?
Is Animal PAK enough for your daily vitamin needs?
taking test supps and cutting???
Do you have to cycle protein w/ creatine in it?
M Drol For Sale !!!
holy crap 3ad at half the price!!!
cycle i will be starting soon. thoughts?
How often should you consume BCAA's??
nutrex lipo 6 and still gain muscle???
Does Superpump250 retain water ?
Glycer Grow question! CL reps... any one?
Here's my stack - Let me know what you think.
universal animal pak doesnt ship to canada? why is that?
Just want to clear something up with ActX and Stoked.
hows this pre during and post workout set up sound?
Guys. Started this supplement stack today.
New Formadrol Formula, any thoughts?
Stoked = makes me pass out.
Should I be taking Animal Pak every day?
mass caps vs. mass tabs?
unfamiliar with ON (optimal nutrition) cheaper and better? body used to white flood..
do any sites have hyperdrol in stock?
1 or 2 bottles reversitol necessary for use as pct for Havoc on a 4 week cycle?
What to do about back pumps??
Would you take WF with Inatrbolic or is there no need?
How does chocolate nitro tech taste??
whats the best natty test booster?
Controlled Labs Stack + Alcohol?
White Flood AND white blood?
should thier be a big value tub of bold 200???
Recommended flavors for SP250 and SizeOn?
Best way to get testosterone?
short cycles vs pulse cycles?
day 3 of havoc - concern?
Does O-3 fish oil elevate ALT level?
Should I just start on MASS XF?
Best bang for my buck.
How much Man Scorch & Lean Xtreme to take?
Could taking something like Activate Xtreme get rid of gyno?
what happen to all the American Whey hype?
Shoul i take 1 or 2 pak of animal pak every day?
Does brand matter when it comes to beta alanine?
SAMe vs Milk Thistle for liver problem?
Holy crap...MAN Clout can't be THIS strong, can it?
L-Tyrosine + Sea Kelp to boost T3 thyroid hormone?
What to add to this Stack?
H-Drol w/ 11-oxo Bridge - What PCT?
Shouldnt i take pre-workout protein and pre-work out supplement no xplode together?
can i take SizeOn at 15?
Need a supplement to help me with strength/size at 15.
going to place this bb.com order for libido...thoughts?
PM Supplement for Fat Burning?
What does GPLC (Glycine Propionyl-L-Carnitine) do?
Which ON Casein tastes best?
Are the Satur8 Tabs Any Good?
if someone who didn't work out took creatine..
any over the counter PH that doesn't show up as juice?
what's your opinion on the new MAN CLOUT?
Has anyone recovered from liver problem (elevated ALT)?
why is bb.com more expensive than other sites?
Something similar to the old Stimulant X?
what fats to eat with 3-AD?
Is it still beneficial to take 1/2 the serving recommended of w/e protein you use?
Anybody interested in Jungle warfare Part 1 ?
Serioes Mass for a skinny friend?
Mass Fx after Stoked and AX cycle???
Vanilla Whey - Scivation and ON comparable?
Lean Xtreme on a bulk?
can someone tell me what PH this is?
Does anybody know how whey/casein proteins are harvested for various supplements?
stupid question...but what is BSN's whey protein product?


text:
You have come to the ESPN Africa edition, for other ESPN editions, click above.
Olympic SportsOlympic Sports
HomeOlympic Sports
Moscow and WADA discuss date for lab visit
201dReuters
Farabee hat trick keys U.S. rout at world juniors
SafeSport CEO Pfohl will step down next month
Russia working with WADA on lab data - Kremlin
Paris, Innerhofer finish 1-2 in Bormio downhill
Kosi airlifted off downhill course after crash
Canada, Russia notch victories at world juniors
RUSADA asks for Putin's help to get doping data
Msocow and WADA discuss date for next lab visit
A sign at an entrance to the Russian Anti-Doping Agency (RUSADA); the executive committee of the World Anti-Doping Agency (WADA) previously lifted Russia's suspension over the doping scandal. Valery Sharifulin\TASS via Getty Images
Moscow and the World Anti-Doping Agency are discussing a date for WADA experts to visit and receive laboratory data, Russia's sports minister said on Saturday.
Russia's anti-doping agency, RUSADA, stands on the verge of suspension after being stripped of its accreditation in 2015 when a WADA-commissioned report found evidence of widespread state-sponsored doping in Russian athletics.
Rusada was conditionally - and controversially - reinstated in September but if judicial authorities fail to hand over laboratory data by the end of the year, it will again lose its status, raising the prospect of Russia being banned from a second consecutive Olympics and remaining shut out of international athletics.
The minister, Pavel Kolobkov, said his ministry had received a letter from WADA president Craig Reedie outlining "the options for organising the process of copying the data from the Moscow anti-doping laboratory" and specifying the equipment to be used.
A WADA team returned from Moscow empty-handed this month after Russian authorities said their equipment was not certified under Russian law.
WADA has said its Compliance Review Committee will look at a report by the team when it meets on Jan. 14-15 in Montreal.
"In parallel we continue to make efforts to retrieve the lab data and as such we remain in contact with the Russian authorities in that regard," it said in an e-mail on Saturday.
Kolobkov said that Russia's Investigative Committee, which is holding the data for its own probe, had approved the equipment to be used.
He said WADA and Russia had a "mutual understanding" on the issue, adding: "We are currently discussing a date for the next visit."
Russia was barred from competing at this year's Pyeongchang Olympics by the International Olympic Committee (IOC) after it was found to have run a state-sponsored doping cover-up scheme at the 2014 Games in the Russian city of Sochi.
Some Russians with no history of doping were invited to compete as neutrals, however. The world athletics federation, the IAAF, has also cleared some Russians to compete internationally as neutrals.
Moscow has denied any involvement in state-sponsored doping but has acknowledged some issues in its enforcement of anti-doping regulations.
RUSADA head Yuri Ganus urged President Vladimir Putin this week to ensure the laboratory data were handed over to prevent Russia being further isolated on the global sports stage.


text:
#ifndef SHD_UTILITY_H_
#define SHD_UTILITY_H_

#include "shadow.h"

#define utility_assert(expr) \
do { \
	if G_LIKELY (expr) { \
		; \
	} else { \
		utility_handleError(__FILE__, __LINE__, G_STRFUNC, #expr); \
	} \
} while (0)

guint utility_ipPortHash(in_addr_t ip, in_port_t port);
guint utility_int16Hash(gconstpointer value);
gboolean utility_int16Equal(gconstpointer value1, gconstpointer value2);
gint utility_doubleCompare(const gdouble* value1, const gdouble* value2, gpointer userData);
gint utility_simulationTimeCompare(const SimulationTime* value1, const SimulationTime* value2,
		gpointer userData);
gchar* utility_getHomePath(const gchar* path);
guint utility_getRawCPUFrequency(const gchar* freqFilename);

void utility_handleError(const gchar* file, gint line, const gchar* funtcion, const gchar* message);

#endif /* SHD_UTILITY_H_ */


Could we use SBO 2007A in the Virtualization solutions like as VMWare ESXi, VMWare Server or Citrix XenSource ?
I have read http://service.sap.com/smb/sbo/platforms and I only fnd VMWare ESXi and there are no VMWare Server, or Citrix XenSource .
Recovery virtual machines in VMware ESX.
I've got the above statement from the platform link. What does it means ?
SBO 2007A could be supported by VMWare ESX3.5 as of PL47. Citrix XenApp 4.0 and 4.5 support 2005 version and limited version for 2007A.
One question per one thread please. This is the forum rule.


text:
Liberty Christian's Tyler Rose, No. 7, runs down the field after hauling in a pass against Turner Ashby in Lynchburg on November 15, 2019.
Taylor Irby/The News & Advance/
Region roundup: Staunton River inducts new Hall of Fame class, local athletes sign, UVa's Trent enters transfer portal
Three Liberty Christian athletes locked in their college destinations Friday, when they participated in a signing day at the school.
Tyler Rose (football) and Naomi Jones (softball) will continue their playing careers at Division I schools William & Mary and Liberty, respectively, while Lexi Hawkins (softball) will make the short trek over to Division III Randolph.
During his career on the gridiron, Rose, a receiver, routinely wowed fans with impressive grabs. He consistently was one of the area's leaders in receiving yards, finishing his senior season with 730 yards receiving on 51 catches (14.3 yards per reception). The 6-foot-2, 196-pound athlete, who chose the Tribe over offers from Army, Air Force, Campbell, Western Illinois and VMI, also was an all-Region 3C selection this year.
Jones, who was a standout infielder/pitcher at E.C. Glass before transferring to LCA ahead of the current school year, posted a .561 batting average during her junior season. Her performance at the plate also included five home runs and 19 RBIs. In the circle, she struck out 186 batters and posted a 3.61 ERA. Jones was a first-team all-Seminole District and all-Region 4D honoree at utility.
Hawkins, a catcher, was an all-Seminole District second-team selection last season to go with her Region 4D honorable mention accolade.
SRHS inducts new Hall of Fame class
Staunton River High School inducted a new class into its athletic Hall of Fame on Friday evening, a group that includes longtime baseball coach Brian Divers, who also took over a struggling football team with little notice for eight games in 2018.
Divers, who has served as varsity baseball coach since 1999 and is a 1990 SRHS graduate, was an all-district and all-region baseball and football selection during his career. While attending SRHS, he lettered in baseball, basketball and football.
The class also includes all-state basketball star Allen Wainwright (1969), who scored 830 career points; state track champ and football player Kevin Martin ('97), who rushed for 1,695 yards and scored 26 touchdowns one season; and golfer Kylen Johnson ('04), a three-time all-district and all-region selection.
SRHS also inducted track standout Candace Nelms ('05), a triple jump state champ who went on to a successful track career at JMU; Jennifer Martin ('88), who played volleyball and indoor and outdoor track and who was inducted into the Christopher Newport Hall of Fame in 1999; Bill Leatherman, who coached the school's boys basketball team for nine seasons beginning in 1966; and the Woodford family (as contributors), who have participated in athletic programs in Moneta throughout three generations.
UVa's Trent enters transfer portal
Former Jefferson Forest High School offensive lineman Ben Trent, who played in a total of 13 games during the past two seasons at Virginia, has entered the transfer portal.
Trent is a graduate transfer and has one season of eligibility remaining.
Ben Cates covers high school sports for The News & Advance. Reach him at (434) 385-5527.
Naomi Jones
Ben Trent
Staunton River High School
Brian Divers
Tyler Rose
Lexi Hawkins