text:
\section{Introduction}
The geometrical structures as throat like, called wormholes, which interface two isolated and different areas of space-times and have no singularity or horizon. As a bridge model of a particle, the wormholes solutions  were firstly found in 1935 by Einstein and Rosen \cite{ref1}. The investigation of Lorentzian wormholes with regards to General Relativity (GR) was invigorated by the remarkable work of Morris and Thorne in 1988 \cite{ref2,ref3}. The flaring-out state of the throat is the basic component in wormhole physics, which in general relativity involves the infringement of the null energy condition (NEC). The violation of null energy condition represents the presence of exotic matter. A significant issue in wormhole solutions is the setting up of energy conditions. In such manner, different techniques have been suggested in the previous works that manage the scenarios of energy conditions with in wormhole background. Along this line, work on thin-shell wormholes has been done in \cite{ref4} and dynamical wormholes \cite{ref5,ref6,ref7}, where the supporting matter is focused on the wormholes throat.\\

Different autonomous high-precision observational information have acknowledged with alarming proof that the Universe is experiencing a period of accelerating expansion \cite{ref8}. Many proposals have been suggested in the published work to clarify this idea, varying from modified gravity theory to dark energy models. In modified gravity theory, one may suppose that the Einstein's hypothesis of general relativity (GR) does not work at large scales, and a more generalized action depicts the gravitational field. Hilbert derived the Einstein field equation of GR from the action principle, by embracing the scalar curvature as a linear function, $R$, in the Lagrangian gravitational density. Although, there are no presumptive basis to limit the gravitational Lagrangian to this structure, and naturally a few speculations have been proposed. In the context of modified theories of gravity, the presence of higher order terms in curvature would allow for building thin-shell wormholes supported by ordinary matter \cite{ref9}. Recently, many people try to build and study wormhole solutions within the framework of modified theories of gravity in various context \cite{ref10}.\\

  The modified $f(R)$ gravity, a popular gravity theory, which modifies the Einstein GR  gravitational action $R$ by an arbitrary function $f(R)$, where $R$ is a well- known Ricci scalar. The accelerated expansion of the Universe  may be  demonstrated by these models  \cite{ref11}. It is observed that, in  $f(R)$ gravity,  the energy conditions can be satisfy by the  higher-order curvature invariants \cite{ref12}. The wormhole solutions in modified $f(R)$ gravity with non constant Ricci scalar are obtained  in \cite{ref13}. Lately, the junction conditions applied to the development of pure double layer bubbles and thin-shell wormholes in $f(R)$ gravity \cite{ref14}. Using the non-commutative geometry, the new static wormholes are built in $f(R)$ gravity \cite{ref15} and the wormhole solutions cosmological evolution is explored in \cite{ref16}.  Wormhole solutions (Lorentzian), which are consistent with the cosmological evolution and solar system observations  were also investigated in viable modified $f(R)$ theories of gravity \cite{ref17}. These wormholes were observed in explicit $f(R)$ models which are considered to repeat sensible situations of cosmological behavior dependent on the accelerated expansion of the Universe. It was demonstrated that the weak energy conditions (WEC) holds at the region of the throat for specific scopes of the free parameters of the hypothesis. The  weak energy condition is fulfilled at a particular point in space with the simple choices of shape function for the asymptotically flat wormhole solutions. A hybrid and exponential shape function in modified gravity are introduced in \cite{ref18,ref19}. Recently, two different shape function for wormhole structure in $f(R)$ gravity were proposed in \cite{ref20,ref21}.\\

 Because of the absence of wormholes observations at present, in spite of the considerable number of endeavors and proposition \cite{ref22}, some material and geometrical  highlights of wormholes, for example, the equation of state (EoS) and the shape function, are as yet not exactly known. Especially, a few structures for the shape function $b(r)$ have been suggested and investigated so far, as one may check, for example, \cite{ref23}. As the shape function $b(r)$  have to obey several conditions and not arbitrary. We propose a new shape function for modified $f(R)$ gravity and GR in this work, which must be, normally as per the shape function conditions.\\

This paper is composed in the accompanying way: In Sec. II, the field equations and the wormhole metric is presented in reference to $f(R)$ gravity. In Sec. III, energy conditions are defined.  In Sec. IV, wormholes models are described.  In Sec. V, results and discussions are explored. Finally, conclusions are given in Sec. VI.

\section{Field Equations and Wormhole Metric}
The theory of  $f(R)$ gravity starts from the generalization of the Einstein's theory of relativity. The action in $f(R)$ theory is defined as

\begin{equation}\label{eq1}
S = \frac{1}{2\kappa} \int  \sqrt{-g} \left[f(R)+ \mathcal{L}_m\right]  d^4 x,
\end{equation}
where $\kappa= 2 \pi G$, $g$ is the metric determinant and $\mathcal{L}_m $ is matter Lagrangian density of the metric $g_{\upsilon\mu}$. For mathematical simplicity $\kappa$ is considered to be unity.

Varying Eq. (\ref{eq1}) with respect to  $g_{\upsilon\mu}$, the fourth-order non-linear field equations are obtained as
\begin{equation}\label{eq2}
F_{R} R_{\upsilon\mu} -\frac{1}{2} f g_{\upsilon\mu} - \bigtriangledown_{\upsilon} \bigtriangledown_{\mu} F_{R} + \Box F_{R} \,g_{\upsilon\mu} = T^m _{\upsilon\mu},
\end{equation}
where $\Box= \bigtriangledown_{\upsilon} \bigtriangledown^{\upsilon}$, $\bigtriangledown_{\upsilon}$ denotes, covariant derivative operator. $R$ and $R_{\upsilon\mu}$ denote curvature scalar and Ricci tensor respectively.  $T^m _{\upsilon\mu}$ denotes energy momentum tensor and $F_{R}=\frac{d f}{d R}$.

The effective field equation can be obtained by using Eq. (\ref{eq2}) as

\begin{equation}\label{eq3}
G_{\upsilon \mu} = T^{eff} _{\upsilon\mu}=R_{\upsilon \mu} -\frac{1}{2}R g_{\upsilon\mu} = T^{g}_{\upsilon\mu} + \frac{8 \pi}{F_{R}} T^{m}_{\upsilon\mu},
\end{equation}
where $G_{\upsilon \mu}$ denotes the Einstein tensor, $T^{eff} _{\upsilon\mu}$ denotes effective energy momentum tensor and $T^{g}_{\upsilon\mu} = \frac{1}{F_{R}}\left[\bigtriangledown_{\upsilon}\bigtriangledown_{\mu}F_{R}-\left(\Box F_{R}+\frac{1}{2}RF_{R}-\frac{1}{2}f\right)g_{\upsilon\mu}\right]$. The energy momentum tensor for the matter source of the wormholes is $T_{\upsilon\mu}=\frac{\partial\mathcal{L}_m}{\partial g^{\upsilon\mu}}$, which can be written as

\begin{equation}\label{eq4}
T_{\upsilon\mu}=\left(\rho + p_{l}\right)u_{\upsilon}u_{\mu} -p_{l}g_{\upsilon\mu} + \left(p_{r}-p_{l}\right)X_{\upsilon}X_{\mu},
\end{equation}
such that $u^{\upsilon}u_{\upsilon}=-1$ and $X^{\upsilon}X_{\upsilon}=1$. Here $rho$, $p_r$ and $p_l$ denote energy density, radial pressure and tangential pressure respectively.

We explore static and spherically symmetric wormhole geometries in $f(R)$ in gravity, so we take metric describing wormhole geometry as
\begin{equation}\label{eq5}
ds^{2}= -e^{2\chi(r)}dt^{2}+e^{\psi(r)}dr^{2} +r^{2}\left(d\theta^{2}+ sin^{2}\theta^{2}\phi^{2}\right),
\end{equation}
where $\chi(r)$ is arbitrary function of $r$, indicates gravitational redshift (called redshift function). $\psi(r) = \left(1-\frac{b(r)}{r}\right)^{-1}$ and $r_{0}<r<\infty$. The minimum value $r_{0}$ denotes throat radius of wormhole, $b(r)$ describes geometry of the wormhole and is known as the shape function. This shape function  is responsible for shape of the wormhole and it must have the following properties:$\, (i)\, b(r_{0})=r_{0}, (ii)\, b'(r_0)<1, (iii)\, \frac{b(r)-b'(r)r}{b(r)^{2}}>0, (iv)\, \frac{b(r)}{r}\rightarrow 0\,\, as\,\, r\rightarrow\infty, (v)\,\frac{b(r)}{r}<1\,\, for\,\, r>r_{0}$.  Moreover, to avoid event horizon (non-traversable condition) $\chi(r)$ should be every where finite. However, In this article, we consider constant redshift function for mathematical simplicity.

Here $R$ (Ricci scalar tensor) is  given by $R=\frac{2b'(r)}{r^{2}}$.
This yields Einstein's fields equations for the action Eq.(\ref{eq1}) in $f(R)$ gravity as:

 \begin{equation}\label{eq6}
 \rho = \frac{ b'(r) F_{R}}{r^{2}}- H,
 \end{equation}

\begin{equation}\label{eq67}
p_{r} = -\frac{ b(r) F_{R}}{r^{3}} - \left(1- \frac{b(r)}{r}\right)\left[F_{R}'' + \frac{F_{R}'\left(r b'
	(r)-b(r)\right)}{2r^{2}\left(1-\frac{b(r)}{r}\right)}\right]+ H,
\end{equation}

\begin{equation}\label{eq8}
p_{l} = \frac{ \left(b(r)-rb'(r)\right) F_{R}}{2r^{3}}-\frac{F_{R}'}{r}\left(1-\frac{b(r)}{r}\right)+ H,
\end{equation}
where $H = \frac{1}{4} \left(R F_{R} + \Box F_{R} + T\right)$  and prime upon the function indicates derivative with respect to radial coordinate $r$.

The radial state parameter i.e EOS parameter in terms of radial pressure is defined as
\begin{equation}\label{eq9}
\omega = \frac{p_{r}}{\rho}.
\end{equation}

The anisotropy parameter $\Delta$ in terms of radial pressure $p_{r}$ and tangential pressure $p_{l}$ is defined as

\begin{equation}\label{eq10}
\Delta = p_{l}-p_{r}.
\end{equation}
 The negative and positive sign of $\delta$ indicate that geometry is attractive or repulsive, $\delta = 0$ indicates geometry has an isotropic pressure.

\section{Energy Conditions}
The energy conditions play important roll to analyze physical existence of wormhole geometry. The important energy conditions are NEC (null energy condition), WEC (weak energy condition), SEC (strong energy condition), and DEC (dominant energy condition). NEC for any null vector is defined as $T_{\upsilon\mu} k^{\upsilon}k^{\mu} \geq 0\Leftrightarrow NEC$. Alternatively, NEC can also be defined in terms of principal pressures as $\forall i, \rho + p_{i}\geq 0 \Leftrightarrow NEC$. WEC for a timelike vector is defined as $T_{\upsilon\mu} V^{\upsilon}V^{\mu} \geq 0\Leftrightarrow WEC$. This WEC in terms of principal pressures can also be defined as $\rho\geq 0$ and $\forall i, \rho + p_{i}\geq 0 \Leftrightarrow WEC $. For a time-like vector, SEC is defined as $(T_{\upsilon\mu}-\frac{T}{2}g_{\upsilon\mu}) V^{\upsilon}V^{\mu} \geq 0\Leftrightarrow SEC$, where $T$ denotes trace of energy momentum tensor. SEC in terms of principal pressures is defined as $T = -\rho + \sum_{j} p_{j}$ and  $\forall j, \rho + p_{j}\geq 0,  \rho +\sum_{j} p_{j}\geq 0  \Leftrightarrow SEC$. DEC for a time-like vector is defined as $DEC \Leftrightarrow T_{\upsilon\mu} V^{\upsilon}V^{\mu} \geq 0$ and $T_{\upsilon\mu}$ is not space like.
Alternately, DEC is also defined in terms of principal pressures $\rho \geq 0$ and $\forall i, p_{i}\in \left[-\rho, +\rho\right] \Leftrightarrow DEC$.

In the present article, These energy conditions are investigated in terms of radial pressure $p_{r}$ and tangential pressure $p_{l}$ as follows:
\begin{itemize}
	\item $\rho + p_{r}\geq 0, \rho + p_{l}\geq 0$ (NEC),
	\item $\rho\geq0, \rho + p_{r}\geq 0, \rho + p_{l}\geq 0$ (WEC),
	\item $ \rho + p_{r}\geq 0, \rho + p_{l}\geq 0,\rho+p_{r}+2p_{l}\geq 0$ (SEC),
	\item $\rho \geq 0, \rho -|p_{r}| \geq 0, \rho -|p_{l}| \geq 0 $ (DEC).
\end{itemize}

  \begin{figure}
	\centering
	(a)\includegraphics[width=12cm, height=8cm, angle=0]{fig1}
	\caption {Nature of $b(r)$, throat condition $b(r)<r$, flaring out condition $b'(r)<1$ and asymptotically flatness $\lim\limits_{r\rightarrow \infty} \frac{b(r)}{r}=0$ for $r_0 = 1$.}
\end{figure}

\section{Models of Wormholes}

In the present paper, $f(R)$ model is taken, which is defined by Nojiri and Odintsov \cite{Nojiri2003} as
\begin{equation}\label{eq11}
f(R)= R + \alpha R^{m}-\beta R^{-n},
\end{equation}
where $\alpha, \beta, m $ and $n$ are taken as positive constants. The term $R^{m}$ dominates when $R^{-n}$ vanishes in the case of curvature increases and it represent evolution of inflation at early times. Similarly when curvature decrease the term   $R^{-n}$ dominates and $R^{m}$  vanishes that shows the production of present acceleration. In the framework of $FRW$ universe such forms of $f(R)$ are considered by Cao $ et\, al.$ \cite{Cao2017} for exploration of the probabilities of late time acceleration. Moradpour \cite{Moradpour2017} investigated traversable wormholes in the background of Lyra manifold and general relativity. He studies energy conditions by using hyperbolic shape function. Godani and Samanta \cite{Godani2019} investigated non violation of energy conditions in $f(R)$ gravity by using the same hyperbolic shape function.

In this section, we will obtain wormhole models that for their matter content are constructed from different hypotheses in viable $f(R)$ gravity. Here, a new shape function is defined as

\begin{equation}\label{eq12}
b(r)= {r_{{0}}}\left(\frac {{a}^{r}}{{a}^{r_{0}}}\right),
\end{equation}
where $a$ is base and  $0<a<1$. We can see directly in Fig.1 that the proposed shape function satisfies all the conditions i.e. basic requirements of shape functions, such as throat condition, flaring out condition and typical asymptotically flatness condition for WH geometry.

This new shape function  is taken into account to investigate the wormhole solutions. The energy density $\left(\rho\right)$, radial pressure $\left(p_{r}\right)$, tangential pressure  $\left(p_{l}\right)$ can be obtained by using field equations (\ref{eq6})- (\ref{eq8}) as

\begin{eqnarray}
\rho &=&\frac{1}{r^{2}} \left[ r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) +{2}^{-1+m}\alpha\, \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}} \right) ^{m}m{r}^{2}\right.\nonumber\\
&+&
\left.{2}^{-1-n}\beta\, \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}} \right) ^{-n}n{r}^{2}\right],
 \end{eqnarray}

 \begin{eqnarray}
p_{r}&=& -\frac{1}{4  {r}^{3}{r_{{0}}}\left(\ln \left( a \right)\right)}\left[ 4\,{r_{{0}}}^{2}{a}^{r-r_{{0}}}\ln  \left( a \right) +4\,\alpha\,{2}^{m} \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a\right) }{{r}^{2}}} \right)^{m}m{a}^{r_{{0}}-r}{r}^{3}\right. \nonumber\\
&-&
\left.12\,\alpha\,{	m}^{2} \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}} \right)^{m}{2}^{m}{a}^{r_{{0}}-r}{r}^{3}+12\,\beta\,{n}^{2}\left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}
} \right) ^{-n}{2}^{-n}{a}^{r_{{0}}-r}{r}^{3}\right. \nonumber\\
&+&
\left.4\,\beta\,{2}^{-n}\left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}} \right)^{-n}n{a}^{r_{{0}}-r}{r}^{3}+4\,{2}^{1+m}\alpha\, \left( {
	\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}}
\right) ^{m}{m}^{3}{a}^{r_{{0}}-r}{r}^{3}\right. \nonumber\\
&+&
\left.4\,{2}^{1-n}\beta\, \left(
{\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}}
\right) ^{-n}{n}^{3}{a}^{r_{{0}}-r}{r}^{3}-4\,{2}^{1-n}\beta\,
\left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}
} \right) ^{-n}{n}^{3}{r}^{2}r_{{0}}\right. \nonumber\\
&-&
\left.4\,{2}^{1+m}\alpha\, \left({\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}}\right)^{m}{m}^{3}{r}^{2}r_{{0}}-13\,\alpha\,{m}^{2} \left( {\frac {	r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}} \right) ^{m}{2}^{m}{r}^{3}r_{{0}}\ln  \left( a \right) \right. \nonumber\\
&+&
\left.13\,\beta\,{n}^{2} \left({\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}}\right) ^{-n}{2}^{-n}{r}^{3}r_{{0}}\ln  \left( a \right) +4\,{2}^{1-n}\beta\, \left( {\frac{r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}} \right) ^{-n}{n}^{3}{r}^{3}r_{{0}}\ln  \left( a \right)\right. \nonumber\\
&+&
\left.4\,{2}^{1+m}\alpha\, \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a\right) }{{r}^{2}}} \right) ^{m}{m}^{3}{r}^{3}r_{{0}}\ln  \left( a\right) -4\,{2}^{-1-n}\beta\, \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}	\ln  \left( a \right) }{{r}^{2}}} \right) ^{-n}{n}^{3} \left( \ln \left( a \right)  \right) ^{2}{r}^{4}r_{{0}}\right. \nonumber\\
&-&
\left.3\,\beta\,{n}^{2}{r}^{4}\left( \ln  \left( a \right)  \right) ^{2} \left( {\frac {r_{{0}}{a}^	{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}} \right) ^{-n}{2}^{-n}r_{{0}}-4\,{2}^{-1+m}\alpha\, \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln \left( a \right) }{{r}^{2}}} \right) ^{m}{m}^{3} \left( \ln  \left( a\right)  \right) ^{2}{r}^{4}r_{{0}}\right. \nonumber
\end{eqnarray}

\begin{eqnarray}
&+&
\left.3\,\alpha\,{m}^{2}{r}^{4} \left(\ln  \left( a \right)  \right) ^{2} \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}} \right) ^{m}{2}^{m}r_{{0}}-4\,{2}^{1+m}\alpha\, \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a	\right) }{{r}^{2}}} \right) ^{m}m{a}^{r_{{0}}-r}{r}^{4}\ln  \left( a\right)\right. \nonumber\\
&-&
\left.4\,{2}^{1-n}\beta\, \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}
\ln  \left( a \right) }{{r}^{2}}} \right) ^{-n}n{a}^{r_{{0}}-r}{r}^{4}
\ln  \left( a \right) -4\,{2}^{1-n}\beta\, \left( {\frac {r_{{0}}{a}^{
r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}} \right) ^{-n}{n}^{3}{a}^{r
_{{0}}-r}{r}^{4}\ln  \left( a \right)\right. \nonumber\\
&-&
\left.4\,{2}^{1+m}\alpha\, \left({\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left(a\right)}{{r}^{2}}}\right)^{m}{m}^{3}{a}^{r_{{0}}-r}{r}^{4}\ln  \left( a \right) +16\,\alpha\,{m}^{2}{r}^{4} \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln	\left( a \right) }{{r}^{2}}} \right) ^{m}{2}^{m}{a}^{r_{{0}}-r}\ln \left( a \right)\right. \nonumber\\
 &-&
\left.16\,\beta\,{n}^{2}{r}^{4} \left( {\frac {r_{{0}}{a}
^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}} \right) ^{-n}{2}^{-n}{a}
^{r_{{0}}-r}\ln  \left( a \right) -4\,\alpha\,{m}^{2}{r}^{5} \left(
\ln  \left( a \right)  \right) ^{2} \left( {\frac {r_{{0}}{a}^{r-r_{{0
}}}\ln  \left( a \right) }{{r}^{2}}} \right) ^{m}{2}^{m}{a}^{r_{{0}}-r
}\right. \nonumber\\
&+&
\left.4\,{2}^{-1+m}\alpha\, \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln
\left( a \right) }{{r}^{2}}} \right) ^{m}m{a}^{r_{{0}}-r}{r}^{5}
\left( \ln  \left( a \right)  \right) ^{2}+4\,{2}^{-1-n}\beta\,
\left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}
} \right) ^{-n}n{a}^{r_{{0}}-r}{r}^{5} \left( \ln  \left( a \right)
\right) ^{2}\right. \nonumber\\
&+&
\left.4\,{2}^{-1+m}\alpha\, \left( {\frac {r_{{0}}{a}^{r-r_{{0
}}}\ln  \left( a \right) }{{r}^{2}}} \right) ^{m}{m}^{3}{a}^{r_{{0}}-r
} \left( \ln  \left( a \right)  \right) ^{2}{r}^{5}+4\,{2}^{-1-n}\beta
\, \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2
}}} \right) ^{-n}{n}^{3}{a}^{r_{{0}}-r} \left( \ln  \left( a \right)
\right) ^{2}{r}^{5}\right. \nonumber\\
&+&
\left.4\,\beta\,{n}^{2}{r}^{5} \left( \ln  \left( a\right)  \right) ^{2} \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln \left( a \right) }{{r}^{2}}}\right)^{-n}{2}^{-n}{a}^{r_{{0}}-r}-20\,{2}^{-1-n}\beta\,{n}^{2} \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln	\left( a \right) }{{r}^{2}}} \right) ^{-n}{r}^{2}r_{{0}}\right. \nonumber\\
&+&
\left.20\,{2}^{-1+m}\alpha\,{m}^{2} \left( {\frac{r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a\right) }{{r}^{2}}} \right) ^{m}{r}^{2}r_{{0}}+5\,{2}^{m}{r}^{3}r_{{0}}\alpha\, \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right)}{{r}^{2}}} \right) ^{m}m\ln  \left( a \right) \right. \nonumber\\
&-&
\left.{2}^{m}\alpha\,\left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}} \right) ^{m}m{r}^{4} \left( \ln  \left( a \right)  \right) ^{2}r_{{0}}+5\,{2}^{-n}{r}^{3}r_{{0}}\beta\, \left( {\frac {r_{{0}}{a}^{r-r_{{0	}}}\ln  \left( a \right) }{{r}^{2}}} \right) ^{-n}n\ln  \left( a\right) \right. \nonumber\\
&-&
\left.{2}^{-n}\beta\, \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln\left( a \right) }{{r}^{2}}} \right) ^{-n}n{r}^{4} \left( \ln \left( a \right)  \right) ^{2}r_{{0}} \right],
  \end{eqnarray}

 \begin{eqnarray}
p_{l}&=& -\frac{1}{4 {r}^{3}{r_{{0}}}	\left( \ln  \left( a \right)  \right)} \left[ 4\,{r}^{4}{2}^{-1+m}\alpha\,{m}^{2} \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}} \right) ^{m}{a}^{r_	{{0}}-r}\ln  \left( a \right)\right. \nonumber\\
&-&
\left.4\,{r}^{3}r_{{0}}{2}^{-1+m}\alpha\,{m}^{2} \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}} \right) ^{m}\ln  \left( a \right) -4\,\alpha\,{m}^{2} \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}}
\right) ^{m}{2}^{m}{a}^{r_{{0}}-r}{r}^{3}\right. \nonumber\\
&+&
\left.4\,\alpha\,{m}^{2} \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}}\right) ^{m}{2}^{m}{r}^{2}r_{{0}}-4\,{r}^{4}{2}^{-1+m}\alpha\,
\left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}
} \right) ^{m}m{a}^{r_{{0}}-r}\ln  \left( a \right)\right. \nonumber\\
&+&
\left.3\,{2}^{m}{r}^{3}r_{{0}}\alpha\, \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a\right) }{{r}^{2}}} \right) ^{m}m\ln  \left( a \right) +4\,\alpha\,{2}^{m} \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}} \right) ^{m}m{a}^{r_{{0}}-r}{r}^{3}\right. \nonumber\\
&-&
\left.5\,\alpha\,{2}^{m} \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left(a\right)}{{r}^{2}}}\right)^{m}m{r}^{2}r_{{0}}-4\,{r}^{4}{2}^{-1-n}\beta\,{n}^{2}\left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}} \right) ^{-n}{a}^{r_{{0}}-r}\ln  \left( a \right)\right. \nonumber\\
&+&
\left.4\,{r}^{3}r_{{0}}{2}^{-1-n}\beta\,{n}^{2} \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln 	\left( a \right) }{{r}^{2}}} \right) ^{-n}\ln  \left( a \right) +4\,\beta\,{n}^{2} \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a\right) }{{r}^{2}}} \right) ^{-n}{2}^{-n}{a}^{r_{{0}}-r}{r}^{3}\right. \nonumber\\
&-&
\left.4\,\beta\,{n}^{2} \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left(a\right)}{{r}^{2}}}\right)^{-n}{2}^{-n}{r}^{2}r_{{0}}-4\,{r}^{4}{2}^{-1-n}\beta\, \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a
\right) }{{r}^{2}}} \right) ^{-n}n{a}^{r_{{0}}-r}\ln  \left( a
\right)\right. \nonumber\\
&+&
\left.3\,{2}^{-n}{r}^{3}r_{{0}}\beta\, \left( {\frac {r_{{0}}{a}^{
r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}} \right) ^{-n}n\ln  \left(
a \right) +4\,\beta\,{2}^{-n} \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}
\ln  \left( a \right) }{{r}^{2}}} \right) ^{-n}n{a}^{r_{{0}}-r}{r}^{3}
\right. \nonumber\\
&-&
\left.5\,\beta\,{2}^{-n} \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left(a\right)}{{r}^{2}}}\right)^{-n}n{r}^{2}r_{{0}}-2\,{r_{{0}}}^{2}{a}^{r-r_{{0}}}\ln  \left( a \right) +2\,{r_{{0}}}^{2} \left( \ln  \left( a \right)  \right) ^{2}r{a}^{r-r_{{0}}} \right],
\end{eqnarray}

\begin{eqnarray}
\rho + p_{r}&=& \frac{1}{4 {r}^{3}{r_{{0}}}	\left( \ln \left( a \right) \right)} \left[ 4\,{r_{{0}}}^{2} \left( \ln  \left( a \right)  \right)^{2}r{a}^{r-r_{{0}}}-4\,{r_{{0}}}^{2}{a}^{r-r_{{0}}}\ln  \left( a\right)\right.\nonumber\\
&-&
\left.4\,\alpha\,{2}^{m} \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln
\left( a \right) }{{r}^{2}}} \right) ^{m}m{a}^{r_{{0}}-r}{r}^{3}+12\,
\alpha\,{m}^{2} \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a
\right) }{{r}^{2}}} \right) ^{m}{2}^{m}{a}^{r_{{0}}-r}{r}^{3}\right.\nonumber\\
&-&
\left. 12\,\beta\,{n}^{2} \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left(a\right)}{{r}^{2}}}\right)^{-n}{2}^{-n}{a}^{r_{{0}}-r}{r}^{3}-4\,\beta\,{2}^{-n} \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a
\right) }{{r}^{2}}} \right) ^{-n}n{a}^{r_{{0}}-r}{r}^{3}\right.\nonumber\\
&-&
\left.4\,{2}^{1+m}\alpha\, \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left(a\right)}{{r}^{2}}}\right)^{m}{m}^{3}{a}^{r_{{0}}-r}{r}^{3}-4\,{2}^{1-n}\beta\, \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}} \right) ^{-n}{n}^{3}{a}^{r_{{0}}-r}{r}^{3}\right.\nonumber\\
&+&
\left.4\,{2}^{1-n}\beta\,\left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}} \right) ^{-n}{n}^{3}{r}^{2}r_{{0}}+4\,{2}^{1+m}\alpha\, \left( {
\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}}
\right) ^{m}{m}^{3}{r}^{2}r_{{0}}\right.\nonumber\\
&+&
\left.13\,\alpha\,{m}^{2} \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln
 \left( a \right) }{{r}^{2}}} \right) ^{m}{2}^{m}{r}^{3}r_{{0}}\ln  \left( a \right) -13\,\beta\,{n}^{2} \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}}
\right) ^{-n}{2}^{-n}{r}^{3}r_{{0}}\ln  \left( a \right)\right.\nonumber\\
&-&
\left.4\,{2}^{1-n}\beta\, \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{	{r}^{2}}} \right) ^{-n}{n}^{3}{r}^{3}r_{{0}}\ln  \left( a \right) -4\,{2}^{1+m}\alpha\, \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a\right) }{{r}^{2}}} \right) ^{m}{m}^{3}{r}^{3}r_{{0}}\ln  \left( a\right)\right.\nonumber\\
&+&
\left.4\,{2}^{-1-n}\beta\, \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}
\ln  \left( a \right) }{{r}^{2}}} \right) ^{-n}{n}^{3} \left( \ln
\left( a \right)  \right) ^{2}{r}^{4}r_{{0}}+3\,\beta\,{n}^{2}{r}^{4}
\left( \ln  \left( a \right)  \right) ^{2} \left( {\frac {r_{{0}}{a}^
{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}} \right) ^{-n}{2}^{-n}r_{{0}}\right.\nonumber\\
&+&
\left.4\,{2}^{-1+m}\alpha\, \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln
\left( a \right) }{{r}^{2}}} \right) ^{m}{m}^{3} \left( \ln  \left( a
\right) \right) ^{2}{r}^{4}r_{{0}}-3\,\alpha\,{m}^{2}{r}^{4} \left(
\ln  \left( a \right)  \right) ^{2} \left( {\frac {r_{{0}}{a}^{r-r_{{0
}}}\ln  \left( a \right) }{{r}^{2}}} \right) ^{m}{2}^{m}r_{{0}}\right.\nonumber\\
&+&
\left.4\,{2}^{1+m}\alpha\, \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a\right) }{{r}^{2}}} \right) ^{m}m{a}^{r_{{0}}-r}{r}^{4}\ln  \left( a\right)+4\,{2}^{1-n}\beta\,\left({\frac{r_{{0}}{a}^{r-r_{{0}}}
\ln  \left( a \right) }{{r}^{2}}} \right) ^{-n}n{a}^{r_{{0}}-r}{r}^{4}
\ln  \left( a \right)\right.\nonumber\\
&+&
\left.4\,{2}^{1-n}\beta\, \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}} \right) ^{-n}{n}^{3}{a}^{r	_{{0}}-r}{r}^{4}\ln  \left( a \right) +4\,{2}^{1+m}\alpha\, \left( {
\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}}
\right) ^{m}{m}^{3}{a}^{r_{{0}}-r}{r}^{4}\ln  \left( a \right)\right.\nonumber\\
&-&
\left.16\,\alpha\,{m}^{2}{r}^{4} \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln 	\left( a \right) }{{r}^{2}}} \right) ^{m}{2}^{m}{a}^{r_{{0}}-r}\ln\left(a\right)+16\,\beta\,{n}^{2}{r}^{4} \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}} \right) ^{-n}{2}^{-n}{a}^{r_{{0}}-r}\ln  \left( a \right)\right.\nonumber\\
&+&
\left.4\,\alpha\,{m}^{2}{r}^{5} \left( \ln  \left( a \right)  \right) ^{2} \left( {\frac {r_{{0}}{a}^{r-r_{{0	}}}\ln  \left( a \right) }{{r}^{2}}} \right) ^{m}{2}^{m}{a}^{r_{{0}}-r}-4\,{2}^{-1+m}\alpha\, \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln\left( a \right) }{{r}^{2}}} \right) ^{m}\right.\nonumber\\
&\times&
\left.m{a}^{r_{{0}}-r}{r}^{5}
\left( \ln  \left( a \right)  \right) ^{2}-4\,{2}^{-1-n}\beta\,
\left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}
} \right) ^{-n}n{a}^{r_{{0}}-r}{r}^{5} \left( \ln  \left( a \right)
\right) ^{2}\right.\nonumber\\
&-&
\left.4\,{2}^{-1+m}\alpha\, \left( {\frac {r_{{0}}{a}^{r-r_{{0
}}}\ln  \left( a \right) }{{r}^{2}}} \right) ^{m}{m}^{3}{a}^{r_{{0}}-r
} \left( \ln  \left( a \right)  \right) ^{2}{r}^{5}\right.\nonumber\\
&-&
\left.4\,{2}^{-1-n}\beta
\, \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2
}}} \right) ^{-n}{n}^{3}{a}^{r_{{0}}-r} \left( \ln  \left( a \right)
\right) ^{2}{r}^{5} \right.\nonumber\\
&-&
\left.4\,\beta\,{n}^{2}{r}^{5} \left( \ln  \left( a
\right)  \right) ^{2} \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln
\left( a \right) }{{r}^{2}}} \right) ^{-n}{2}^{-n}{a}^{r_{{0}}-r}+20
\,{2}^{-1-n}\beta\,{n}^{2} \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln
\left( a \right) }{{r}^{2}}} \right) ^{-n}{r}^{2}r_{{0}}\right.\nonumber\\
&-&
\left.20\,{2}^{-1+m}\alpha\,{m}^{2} \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a\right) }{{r}^{2}}} \right) ^{m}{r}^{2}r_{{0}}-3\,{2}^{m}{r}^{3}r_{{0}}\alpha\, \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right)}{{r}^{2}}} \right) ^{m}m\ln  \left( a \right) \right.\nonumber\\
&+&
\left.{2}^{m}\alpha\,
\left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}
} \right) ^{m}m{r}^{4} \left( \ln  \left( a \right)  \right) ^{2}r_{{0
}}-3\,{2}^{-n}{r}^{3}r_{{0}}\beta\, \left( {\frac {r_{{0}}{a}^{r-r_{{0
}}}\ln  \left( a \right) }{{r}^{2}}} \right) ^{-n}n\ln  \left( a
\right)\right.\nonumber\\
&+&
\left.{2}^{-n}\beta\, \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln
\left( a \right) }{{r}^{2}}} \right) ^{-n}n{r}^{4} \left( \ln
\left( a \right)  \right) ^{2}r_{{0}} \right],
\end{eqnarray}

\begin{eqnarray}
\rho + p_{l}&=&\frac{1}{4 {r}^{3}{r_{{0}}} \left( \ln
\left( a \right)  \right)}\, \left[ 2\,{r_{{0}}}^{2} \left( \ln  \left(a\right)\right)^{2}r{a}^{r-r_{{0}}}+4\,{r}^{3}r_{{0}}{2}^{-1+m}\alpha\,{m}^{2} \left( {	\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}}\right) ^{m}\ln  \left( a \right)\right. \nonumber\\
 &-&
\left.{2}^{m}{r}^{3}r_{{0}}\alpha\,\left({\frac{r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}} \right) ^{m}m\ln  \left( a \right) -4\,{r}^{3}r_{{0}}{2}^{-1-n}\beta\,{n}^{2} \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}} \right) ^{-n}\ln  \left( a \right)\right. \nonumber\\
&-&
\left.{2}^{-n}{r}^{3}r_{{0}}\beta\,\left({\frac{r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}} \right) ^{-n}n\ln  \left( a \right) +2\,{r_{{0}}}^{2}{a}^{r-r_{{0}}}\ln  \left( a \right)\right. \nonumber\\
 &+&
\left.5\,\beta\,{2}^{-n} \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left(a\right)}{{r}^{2}}}\right)^{-n}n{r}^{2}r_{{0}}+5\,\alpha\,{2}^{m} \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln \left( a \right) }{{r}^{2}}} \right) ^{m}m{r}^{2}r_{{0}}\right. \nonumber\\
&-&
\left.4\,\alpha\,{2}^{m} \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left(a\right)}{{r}^{2}}}\right)^{m}m{a}^{r_{{0}}-r}{r}^{3}+4\,\alpha\,{m}^{2} \left({\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}}\right)^{m}{2}^{m}{a}^{r_{{0}}-r}{r}^{3}\right. \nonumber\\
&-&
\left.4\,\beta\,{n}^{2} \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left(a\right)}{{r}^{2}}}\right)^{-n}{2}^{-n}{a}^{r_{{0}}-r}{r}^{3}-4\,\beta\,{2}^{-n}\left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}} \right) ^{-n}n{a}^{r_{{0}}-r}{r}^{3}\right. \nonumber\\
&+&
\left.4\,\beta\,{n}^{2} \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}}\right) ^{-n}{2}^{-n}{r}^{2}r_{{0}}-4\,\alpha\,{m}^{2} \left( {\frac
{r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}} \right) ^{m}{
2}^{m}{r}^{2}r_{{0}}\right. \nonumber\\
&-&
\left.4\,{r}^{4}{2}^{-1+m}\alpha\,{m}^{2} \left({\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}}
\right) ^{m}{a}^{r_{{0}}-r}\ln  \left( a \right) \right. \nonumber\\
&+&
\left.4\,{r}^{4}{2}^{-1+m}\alpha\, \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}} \right) ^{m}m{a}^{r_{{0}}-r}\ln  \left( a \right) \right. \nonumber\\
&+&
\left.4\,{r}^{4}{2}^{-1-n}\beta\,{n}^{2} \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln\left( a \right) }{{r}^{2}}} \right) ^{-n}{a}^{r_{{0}}-r}\ln  \left( a \right)\right. \nonumber\\
&+&
\left.4\,{r}^{4}{2}^{-1-n}\beta\, \left( {\frac {r_{{0}}{a}^{r-r_
{{0}}}\ln  \left( a \right) }{{r}^{2}}} \right) ^{-n}n{a}^{r_{{0}}-r}
\ln  \left( a \right)  \right],
\end{eqnarray}

\begin{eqnarray}
\rho + p_{r}+ 2\,p_{l}&=&-\frac{1}{4 {r}{r_{{0}}} \left( \ln  \left( a
\right)  \right)}\, \left[ -20\,\alpha\,{m}^{2}r \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}} \right) ^{m}{2}^{m}{a}^{r_{{0}}-r}\right. \nonumber\\
&+&
\left.4\,{2}^{1-n}\beta\, \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln
\left( a \right) }{{r}^{2}}} \right) ^{-n}{n}^{3}{a}^{r_{{0}}-r}r+20
\,\beta\,{n}^{2}r \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a
\right) }{{r}^{2}}} \right) ^{-n}{2}^{-n}{a}^{r_{{0}}-r}\right. \nonumber\\
&+&
\left.4\,{2}^{1+m}\alpha\, \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left(a\right)}{{r}^{2}}}\right)^{m}{m}^{3}{a}^{r_{{0}}-r}r+12\,\alpha\,{2}^{m}\left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}} \right) ^{m}m{a}^{r_{{0}}-r}r\right. \nonumber\\
&+&
\left.12\,\beta\,{2}^{-n} \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left(a\right)}{{r}^{2}}}\right)^{-n}n{a}^{r_{{0}}-r}r-
4\,{2}^{1-n}\beta\, \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}} \right) ^{-n}{n}^{3}r_{{0}}\right. \nonumber\\
&-&
\left. 4\,{2}^{1+m}\alpha\, \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a\right) }{{r}^{2}}} \right)^{m}{m}^{3}r_{{0}}+36\,{2}^{-1+m}\alpha\,{m}^{2} \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}} \right) ^{m}r_{{0}}\right. \nonumber\\
&-&
\left.20\,{2}^{-1+m}\alpha\, \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}} \right) ^{m}mr_{{0}}-36\,{2}^{-1-n}\beta\,{n}^{2} \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}	\ln  \left( a \right) }{{r}^{2}}} \right) ^{-n}r_{{0}}\right. \nonumber
\end{eqnarray}

\begin{eqnarray}
&-&
\left.20\,{2}^{-1-n}\beta\, \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}} \right) ^{-n}nr_{{0}}-{2}^{m}\alpha\, \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}} \right) ^{m}m{r}^{2}\left( \ln  \left( a \right)  \right) ^{2}r_{{0}}\right. \nonumber\\
&-&
\left.{2}^{-n}\beta\,
\left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}
} \right) ^{-n}n{r}^{2} \left( \ln  \left( a \right)  \right) ^{2}r_{{0}}+20\,\alpha\,{m}^{2}{r}^{2}\ln  \left( a \right)  \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}} \right) ^{m}{2}^{m}{a}^{r_{{0}}-r}\right. \nonumber\\
&-&
\left.20\,\beta\,{n}^{2}{r}^{2}\ln  \left( a \right)
\left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}
} \right) ^{-n}{2}^{-n}{a}^{r_{{0}}-r}-17\,\alpha\,{m}^{2} \left( {
\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}}
\right) ^{m}{2}^{m}rr_{{0}}\ln  \left( a \right)\right. \nonumber\\
& +&
\left.17\,\beta\,{n}^{2}\left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}} \right) ^{-n}{2}^{-n}rr_{{0}}\ln  \left( a \right) +4\,{2}^{1-n}\beta\, \left( {\frac{r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{
r}^{2}}} \right) ^{-n}{n}^{3}rr_{{0}}\ln  \left( a \right)\right. \nonumber\\
&+&
\left.4\,{2}^{1+m}\alpha\, \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}} \right) ^{m}{m}^{3}rr_{{0}}\ln  \left( a \right) -4\,{2}^{-1-n}\beta\, \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a\right) }{{r}^{2}}} \right) ^{-n}\right. \nonumber\\
&\times&
\left.{n}^{3} \left( \ln  \left( a\right)  \right)^{2}{r}^{2}r_{{0}}-3\,\beta\,{n}^{2}{r}^{2} \left(\ln  \left( a \right)  \right) ^{2} \left( {\frac {r_{{0}}{a}^{r-r_{{0
}}}\ln  \left( a \right) }{{r}^{2}}} \right) ^{-n}{2}^{-n}r_{{0}}\right. \nonumber\\
&-&
\left.4\,{
2}^{-1+m}\alpha\, \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a
\right) }{{r}^{2}}} \right) ^{m}{m}^{3} \left( \ln  \left( a \right)
\right) ^{2}{r}^{2}r_{{0}}\right. \nonumber\\
&+&
\left.3\,\alpha\,{m}^{2}{r}^{2} \left( \ln \left( a \right)  \right) ^{2} \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}} \right) ^{m}{2}^{m}r_{{0}}-4\,{2}^{1
-n}\beta\, \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right)
	}{{r}^{2}}} \right) ^{-n}\right. \nonumber\\
&\times&
\left.{n}^{3}{a}^{r_{{0}}-r}{r}^{2}\ln  \left( a\right) -4\,{2}^{1+m}\alpha\, \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}
\ln  \left( a \right) }{{r}^{2}}} \right) ^{m}{m}^{3}{a}^{r_{{0}}-r}{r
}^{2}\ln  \left( a \right)\right. \nonumber\\
&-&
\left.4\,\alpha\,{m}^{2}{r}^{3} \left( \ln\left( a \right)  \right) ^{2} \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}} \right) ^{m}{2}^{m}{a}^{r_{{0}}-r}+4\,{2}^{-1+m}\alpha\, \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left(a \right) }{{r}^{2}}} \right) ^{m}\right. \nonumber\\
&\times&
\left.m{a}^{r_{{0}}-r}{r}^{3} \left( \ln \left( a \right)  \right) ^{2}+\,{2}^{-1-n}\beta\, \left( {\frac {r_	{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}} \right) ^{-n}n{a}^{r_{{0}}-r}{r}^{3} \left( \ln  \left( a \right)  \right) ^{2}\right. \nonumber\\
&+&
\left.4\,{2}^{-1+m}\alpha\, \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a\right) }{{r}^{2}}} \right) ^{m}{m}^{3}{a}^{r_{{0}}-r} \left( \ln \left( a \right)  \right) ^{2}{r}^{3}+\,{2}^{-1-n}\beta\, \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}}\right) ^{-n}\right. \nonumber\\
&\times&
\left.{n}^{3}{a}^{r_{{0}}-r} \left( \ln  \left( a \right) \right) ^{2}{r}^{3}+ 4\,\beta\,{n}^{2}{r}^{3} \left( \ln  \left( a
\right)  \right) ^{2} \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln
\left( a \right) }{{r}^{2}}} \right) ^{-n}{2}^{-n}{a}^{r_{{0}}-r}\right. \nonumber
\end{eqnarray}
\begin{eqnarray}
&-&
\left.12\,{2}^{m}\alpha\, \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a\right) }{{r}^{2}}} \right) ^{m}m{a}^{r_{{0}}-r}{r}^{2}\ln  \left( a\right) -12\,{2}^{-n}\beta\, \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}	\ln  \left( a \right) }{{r}^{2}}} \right) ^{-n}n{a}^{r_{{0}}-r}{r}^{2}\ln  \left( a \right) \right. \nonumber\\
&+&
\left.9\,{2}^{m}\alpha\, \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}} \right) ^{m}mrr_{{0}}\ln
\left( a \right) +9\,{2}^{-n}\beta\, \left( {\frac {r_{{0}}{a}^{r-r_{
{0}}}\ln  \left( a \right) }{{r}^{2}}} \right) ^{-n}nrr_{{0}}\ln
\left( a \right)  \right],
\end{eqnarray}

\begin{eqnarray}
\rho-\left|p_{r}\right|&=&\frac{1}{4 r^{2}}\, \left[4\,r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) +4\,{2}^{-
1+m}\alpha\, \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a
\right) }{{r}^{2}}} \right) ^{m}m{r}^{2}\right. \nonumber\\
&+&
\left.4\,{2}^{-1-n}\beta\, \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}}\right) ^{-n}n{r}^{2}- \left|  \left( -{2}^{m}\alpha\, \left( {\frac 	{r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}} \right) ^{m}m
{r}^{4} \left( \ln  \left( a \right)  \right) ^{2}r_{{0}}\right.\right.\right. \nonumber\\
&-&
\left.\left.\left.{2}^{-n}\beta\, \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{
r}^{2}}} \right) ^{-n}n{r}^{4} \left( \ln  \left( a \right)  \right) ^
{2}r_{{0}}-{2}^{1+m}\alpha\, \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln
\left( a \right) }{{r}^{2}}} \right) ^{m}{m}^{3} \left( \ln  \left( a
\right)  \right) ^{2}{r}^{4}r_{{0}}\right.\right.\right. \nonumber\\
&-&
\left.\left.\left.{2}^{1-n}\beta\, \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}} \right) ^{-n}{n}^{3} \left( \ln  \left( a \right)  \right) ^{2}{r}^{4}r_{{0}}\right. \right.\right.\nonumber\\
&+&
\left.\left.\left.{2}^{1+m}\alpha\,m{a}^{r_{{0}}-r}{r}^{5} \left( \ln  \left( a \right) \right) ^{2} \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a\right) }{{r}^{2}}} \right) ^{m}+{2}^{1+m}\alpha\,{m}^{3}{a}^{r_{{0}}-r} \left( \ln  \left( a \right)  \right) ^{2}{r}^{5} \left( {\frac {r	_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}} \right) ^{m}\right. \right.\right.\nonumber\\
&+&
\left.\left.\left.{2}^{1-n}\beta\,n{a}^{r_{{0}}-r}{r}^{5} \left( \ln  \left( a \right)\right) ^{2} \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a\right) }{{r}^{2}}} \right) ^{-n}+{2}^{1-n}\beta\,{n}^{3}{a}^{r_{{0}}-r} \left( \ln  \left( a \right)  \right) ^{2}{r}^{5} \left( {\frac {r
_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}} \right) ^{-n}\right. \right.\right.\nonumber\\
&-&
\left.\left.\left.13\,\alpha\,{m}^{2} \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a\right) }{{r}^{2}}} \right) ^{m}{2}^{m}{r}^{3}r_{{0}}\ln  \left( a\right) +13\,\beta\,{n}^{2} \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln
\left( a \right) }{{r}^{2}}} \right) ^{-n}{2}^{-n}{r}^{3}r_{{0}}\ln
\left( a \right) \right. \right.\right.\nonumber\\
&-&
\left.\left.\left.3\,\beta\,{n}^{2}{r}^{4} \left( \ln  \left( a
\right)  \right) ^{2} \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln
\left( a \right) }{{r}^{2}}} \right) ^{-n}{2}^{-n}r_{{0}}+3\,\alpha\,
{m}^{2}{r}^{4} \left( \ln  \left( a \right)  \right) ^{2} \left( {
\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}}
\right) ^{m}{2}^{m}r_{{0}}\right. \right.\right.\nonumber\\
&+&
\left.\left.\left.16\,\alpha\,{m}^{2}{r}^{4} \left( {\frac {
r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}} \right) ^{m}{2
}^{m}{a}^{r_{{0}}-r}\ln  \left( a \right)-16\,\beta\,{n}^{2}{r}^{4}
\left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}
} \right) ^{-n}{2}^{-n}{a}^{r_{{0}}-r}\ln  \left( a \right)\right. \right.\right.\nonumber\\
& -&
\left.\left.\left.4\,\alpha\,{m}^{2}{r}^{5} \left( \ln  \left( a \right)  \right) ^{2} \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}}\right)^{m}{2}^{m}{a}^{r_{{0}}-r}+4\,\beta\,{n}^{2}{r}^{5} \left(\ln  \left( a \right)  \right) ^{2} \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}} \right) ^{-n}{2}^{-n}{a}^{r_{{0}}-r}\right. \right.\right.\nonumber\\
&+&
\left.\left.\left.8\,{2}^{m}\alpha\, \left( {\frac{r_{{0}}{a}^{r-r_{{0}}}\ln \left( a \right) }{{r}^{2}}} \right) ^{m}{m}^{3}{r}^{3}r_{{0}}\ln\left( a \right) -8\,{2}^{m}\alpha\, \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}} \right) ^{m}m{a}^{r_{{0}}-r}{r}^{4}\ln  \left( a \right)\right. \right.\right.\nonumber\\
&-&
\left.\left.\left.8\,{2}^{m}\alpha\, \left( {\frac {r_{{0}}{a
}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}} \right) ^{m}{m}^{3}{a}^
{r_{{0}}-r}{r}^{4}\ln  \left( a \right) +8\,{2}^{-n}\beta\, \left( {
	\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}}
\right) ^{-n}{n}^{3}{r}^{3}r_{{0}}\ln  \left( a \right)\right. \right.\right.\nonumber\\
&-&
\left.\left.\left.8\,{2}^{-n}\beta\, \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}} \right) ^{-n}n{a}^{r_{{0}}-r}{r}^{4}\ln  \left( a \right) -8
\,{2}^{-n}\beta\, \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a
\right) }{{r}^{2}}} \right) ^{-n}{n}^{3}{a}^{r_{{0}}-r}{r}^{4}\ln
\left( a \right) \right. \right.\right.\nonumber\\
&+&
\left.\left.\left.8\,{2}^{m}\alpha\, \left( {\frac {r_{{0}}{a}^{r-r_{
{0}}}\ln  \left( a \right) }{{r}^{2}}} \right) ^{m}{m}^{3}{a}^{r_{{0}}
-r}{r}^{3}-8\,{2}^{m}\alpha\, \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}
\ln  \left( a \right) }{{r}^{2}}} \right) ^{m}{m}^{3}{r}^{2}r_{{0}}\right. \right.\right.\nonumber\\
&+&
\left.\left.\left.8\,{2}^{-n}\beta\, \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a\right) }{{r}^{2}}} \right) ^{-n}{n}^{3}{a}^{r_{{0}}-r}{r}^{3}-8\,{2}^{-n}\beta\, \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a\right) }{{r}^{2}}} \right) ^{-n}{n}^{3}{r}^{2}r_{{0}}\right. \right.\right.\nonumber\\
&+&
\left.\left.\left.5\,{2}^{-n}{r}^{3}r_{{0}}\beta\, \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a\right) }{{r}^{2}}} \right) ^{-n}n\ln  \left( a \right) +5\,{2}^{m}{r}^{3}r_{{0}}\alpha\, \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left(a \right) }{{r}^{2}}} \right) ^{m}m\ln  \left( a \right) \right. \right.\right.\nonumber\\
&+&
\left.\left.\left.4\,\alpha\,{2}^{m} \left( {\frac{r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r
}^{2}}} \right) ^{m}m{a}^{r_{{0}}-r}{r}^{3}-12\,\alpha\,{m}^{2}
\left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}
} \right) ^{m}{2}^{m}{a}^{r_{{0}}-r}{r}^{3}\right. \right.\right.\nonumber\\
&+&
\left.\left.\left.12\,\beta\,{n}^{2} \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}}
\right) ^{-n}{2}^{-n}{a}^{r_{{0}}-r}{r}^{3}+4\,\beta\,{2}^{-n}
\left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}
} \right) ^{-n}n{a}^{r_{{0}}-r}{r}^{3}\right. \right.\right.\nonumber\\
&-&
\left.\left.\left.10\,\beta\,{n}^{2} \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}}
\right) ^{-n}{2}^{-n}{r}^{2}r_{{0}}+10\,\alpha\,{m}^{2} \left( {
\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}}
\right) ^{m}{2}^{m}{r}^{2}r_{{0}}\right. \right.\right.\nonumber\\
&+&
\left.\left.\left.4\,{r_{{0}}}^{2}{a}^{r-r_{{0}}}\ln
\left( a \right)  \right) {r}^{-3}{r_{{0}}}^{-1} \left( \ln  \left( a
\right)  \right) ^{-1} \right| {r}^{2} \right],
\end{eqnarray}
\begin{eqnarray}
\rho-\left|p_{l}\right|&=&\frac{1}{4}r^{2}\, \left[ 4\,r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) +4\,{2}^{-
1+m}\alpha\, \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a
\right) }{{r}^{2}}} \right) ^{m}m{r}^{2}\right.\nonumber\\
&+&
\left.4\,{2}^{-1-n}\beta\, \left({\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}}\right) ^{-n}n{r}^{2}- \left|  \left( {2}^{1+m}\alpha\,{m}^{2}{r}^{4}{a}^{r_{{0}}-r}\ln  \left( a \right)  \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}} \right) ^{m}\right. \right.\right.\nonumber\\
&-&
\left.\left.\left.{2}^{1+m}\alpha\,{	m}^{2} \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}} \right) ^{m}{r}^{3}r_{{0}}\ln  \left( a \right) -4\,\alpha\,{m
}^{2} \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}
^{2}}} \right) ^{m}{2}^{m}{a}^{r_{{0}}-r}{r}^{3}\right. \right.\right.\nonumber\\
&+&
\left.\left.\left.4\,\alpha\,{m}^{2}\left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}
} \right) ^{m}{2}^{m}{r}^{2}r_{{0}}-{2}^{1+m}\alpha\, \left( {\frac {r
_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}} \right) ^{m}m{a
}^{r_{{0}}-r}{r}^{4}\ln  \left( a \right) \right. \right.\right.\nonumber\\
&+&
\left.\left.\left.3\,{2}^{m}{r}^{3}r_{{0}}\alpha\, \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}} \right) ^{m}m\ln  \left( a \right) +4\,\alpha\,{2}^{m}\left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}
} \right) ^{m}m{a}^{r_{{0}}-r}{r}^{3}\right. \right.\right.\nonumber\\
&-&
\left.\left.\left.5\,\alpha\,{2}^{m} \left( {
\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}}
\right) ^{m}m{r}^{2}r_{{0}}-{2}^{1-n}\beta\,{n}^{2}{r}^{4}{a}^{r_{{0}
}-r}\ln  \left( a \right)  \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln
\left( a \right) }{{r}^{2}}} \right) ^{-n}\right. \right.\right.\nonumber\\
&+&
\left.\left.\left.{2}^{1-n}\beta\,{n}^{2}
\left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}
} \right) ^{-n}{r}^{3}r_{{0}}\ln  \left( a \right) +4\,\beta\,{n}^{2}
\left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}
} \right) ^{-n}{2}^{-n}{a}^{r_{{0}}-r}{r}^{3}\right. \right.\right.\nonumber\\
&-&
\left.\left.\left.4\,\beta\,{n}^{2}
\left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}
} \right) ^{-n}{2}^{-n}{r}^{2}r_{{0}}-{2}^{1-n}\beta\, \left( {\frac {
r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}} \right) ^{-n}n
{a}^{r_{{0}}-r}{r}^{4}\ln  \left( a \right)\right. \right.\right.\nonumber\\
&+&
\left.\left.\left.3\,{2}^{-n}{r}^{3}r_{{0}}
\beta\, \left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{
r}^{2}}} \right) ^{-n}n\ln  \left( a \right) +4\,\beta\,{2}^{-n}
\left( {\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}
} \right) ^{-n}n{a}^{r_{{0}}-r}{r}^{3}\right. \right.\right.\nonumber\\
&-&
\left.\left.\left.5\,\beta\,{2}^{-n} \left( {
\frac {r_{{0}}{a}^{r-r_{{0}}}\ln  \left( a \right) }{{r}^{2}}}
\right) ^{-n}n{r}^{2}r_{{0}}-2\,{r_{{0}}}^{2}{a}^{r-r_{{0}}}\ln
\left( a \right)\right. \right.\right.\nonumber\\
&+&
\left.\left.\left.2\,{r_{{0}}}^{2} \left( \ln  \left( a \right)
\right) ^{2}r{a}^{r-r_{{0}}} \right) {r}^{-3}{r_{{0}}}^{-1} \left(
\ln  \left( a \right)  \right) ^{-1} \right| {r}^{2} \right].
\end{eqnarray}

 \begin{figure}
 	\centering
  	(a)\includegraphics[width=4cm, height=4cm, angle=0]{fig2}
  	(b)\includegraphics[width=4cm, height=4cm, angle=0]{fig3}
  	(c)\includegraphics[width=4cm, height=4cm, angle=0]{fig4}
  	\caption {(a) NEC, $\rho + p_r$ for $\alpha=0, \beta=0$, (b) NEC, $\rho + p_l$ for $\alpha=0, \beta=0$,(c) SEC, $\rho + p_r + 2p_l$ for for $\alpha=0, \beta=0$ .}
\end{figure}

  \begin{figure}
  (a)\includegraphics[width=3.5cm, height=4cm, angle=0]{fig5}
  (b)\includegraphics[width=3.5cm, height=4cm, angle=0]{fig6}
  (c)\includegraphics[width=3.5cm, height=4cm, angle=0]{fig7}
  (d)\includegraphics[width=3.5cm, height=4cm, angle=0]{fig8}
  \caption {(a) DEC, $\rho - p_r$ for $\alpha=0, \beta=0$, (b) DEC, $\rho - p_l$ for $\alpha=0, \beta=0$, (c) EOS,for $\alpha=0,\beta=0$ (d)$\bigtriangleup =p_l-p_r$ for $\alpha=0,\beta=0$ .}
  \end{figure}

 \begin{figure}
 \centering
 (a)\includegraphics[width=3.5cm, height=4cm, angle=0]{fig9}
 (b)\includegraphics[width=3.5cm, height=4cm, angle=0]{fig10}
 (c)\includegraphics[width=3.5cm, height=4cm, angle=0]{fig11}
 (d)\includegraphics[width=3.5cm, height=4cm, angle=0]{fig12}
 \caption {(a) WEC, $\rho$ for $\beta=0, a=0.5, m=2$ (b) NEC, $\rho + p_r$ for $\beta=0, a=0.5, m=2$, (c) NEC, $\rho + p_l$ for$\beta=0, a=0.5, m=2$,(d) SEC, $\rho + p_r + 2p_l$ for$\beta=0, a=0.5, m=2$.}
\end{figure}

  \begin{figure}
   \centering
  (a)\includegraphics[width=3.5cm, height=4cm, angle=0]{fig13}
  (b)\includegraphics[width=3.5cm, height=4cm, angle=0]{fig14}
  (c)\includegraphics[width=3.5cm, height=4cm, angle=0]{fig15}
  (d)\includegraphics[width=3.5cm, height=4cm, angle=0]{fig16}
  \caption {(a) DEC, $\rho - p_r$ for $\beta=0, a=0.5, m=2$, (b) DEC, $\rho - p_l$ for$\beta=0, a=0.5, m=2$, (c) EOS,for $\beta=0, a=0.5, m=2$ (d)$\bigtriangleup=p_l-p_r$ or $\beta=0, a=0.5, m=2$.}
\end{figure}

  \begin{figure}
 	\centering
 	(a)\includegraphics[width=3.5cm, height=4cm, angle=0]{fig17}
 	(b)\includegraphics[width=3.5cm, height=4cm, angle=0]{fig18}
 	(c)\includegraphics[width=3.5cm, height=4cm, angle=0]{fig19}
 	(d)\includegraphics[width=3.5cm, height=4cm, angle=0]{fig20}
 	\caption {(a) WEC, $\rho$ for $\alpha=0, a=0.5, n=4$ (b) NEC, $\rho + p_r$ for $\alpha=0, a=0.5, n=4$, (c) NEC, $\rho + p_l$ for$\alpha=0, a=0.5, n=4$,(d) SEC, $\rho + p_r + 2p_l$ for$\alpha=0, a=0.5, n=4$.}
 \end{figure}
 \begin{figure}
	\centering
	(a)\includegraphics[width=3.5cm, height=4cm, angle=0]{fig21}
	(b)\includegraphics[width=3.5cm, height=4cm, angle=0]{fig22}
	(c)\includegraphics[width=3.5cm, height=4cm, angle=0]{fig23}
	(d)\includegraphics[width=3.5cm, height=4cm, angle=0]{fig24}
	\caption {(a) DEC, $\rho - p_r$ for $\alpha=0, a=0.5, n=4$, (b) DEC, $\rho - p_l$ for$\beta=0, a=0.5, n=4$, (c) EOS,for $\alpha=0, a=0.5, n=4$ (d)$\bigtriangleup=p_l-p_r$ for $\alpha=0, a=0.5, n=4$.}
 \end{figure}
  \begin{figure}
 	\centering
 	(a)\includegraphics[width=3.5cm, height=4cm, angle=0]{fig25}
 	(b)\includegraphics[width=3.5cm, height=4cm, angle=0]{fig26}
 	(c)\includegraphics[width=3.5cm, height=4cm, angle=0]{fig27}
 	(d)\includegraphics[width=3.5cm, height=4cm, angle=0]{fig28}
 	\caption {(a) WEC, $\rho$ for $\alpha=5, a=0.5, m=2, n=4$ (b) NEC, $\rho + p_r$ for $\alpha=5, a=0.5, m=2, n=4$, (c) NEC, $\rho + p_l$ for$\alpha=5, a=0.5, m=2, n=4$,(d) SEC, $\rho + p_r + 2p_l$ for$\alpha=5, a=0.5, m=2, n=4$.}
 \end{figure}
 \begin{figure}
 	\centering
 	(a)\includegraphics[width=3.5cm, height=4cm, angle=0]{fig29}
 	(b)\includegraphics[width=3.5cm, height=4cm, angle=0]{fig30}
 	(c)\includegraphics[width=3.5cm, height=4cm, angle=0]{fig31}
 	(d)\includegraphics[width=3.5cm, height=4cm, angle=0]{fig32}
 	\caption {(a) DEC, $\rho - p_r$ for $\alpha=5, a=0.5, m=2, n=4$, (b) DEC, $\rho - p_l$ for$\alpha=5, a=0.5, m=2, n=4$, (c) EOS,for $\alpha=5, a=0.5, m=2, n=4$ (d)$\bigtriangleup=p_l-p_r$ for $\alpha=5, a=0.5, m=2, n=4$.}
 \end{figure}

  \begin{figure}
 	\centering
 	(a)\includegraphics[width=3.5cm, height=4cm, angle=0]{fig33}
 	(b)\includegraphics[width=3.5cm, height=4cm, angle=0]{fig34}
 	(c)\includegraphics[width=3.5cm, height=4cm, angle=0]{fig35}
 	(d)\includegraphics[width=3.5cm, height=4cm, angle=0]{fig36}
 	\caption {(a) WEC, $\rho$ for $\beta=5, a=0.5, m=2, n=4$ (b) NEC, $\rho + p_r$ for $\beta=5, a=0.5, m=2, n=4$, (c) NEC, $\rho + p_l$ for$\beta=5, a=0.5, m=2, n=4$,(d) SEC, $\rho + p_r + 2p_l$ for$\beta=5, a=0.5, m=2, n=4$.}
 \end{figure}
   \begin{figure}
   	\centering
   	(a)\includegraphics[width=3.5cm, height=4cm, angle=0]{fig37}
   	(b)\includegraphics[width=3.5cm, height=4cm, angle=0]{fig38}
   	(c)\includegraphics[width=3.5cm, height=4cm, angle=0]{fig39}
   	(d)\includegraphics[width=3.5cm, height=4cm, angle=0]{fig40}
   	\caption {(a) DEC, $\rho - p_r$ for $\beta=5, a=0.5, m=2, n=4$, (b) DEC, $\rho - p_l$ for$\beta=5, a=0.5, m=2, n=4$, (c) EOS,for $\beta=5, a=0.5, m=2, n=4$ (d)$\bigtriangleup=p_l-p_r$ for $\beta=5, a=0.5, m=2, n=4$.}
   \end{figure}
 \section{Results and Discussion}

The wormhole geometries are very much affected on shape function $b(r)$, so in literature various shape functions are defined and wormhole solutions are investigated. Several researchers explored violation or non-violation of energy conditions in the context of wormhole solutions. In the present investigation, the shape function $b(r)= {r_{{0}}}\left(\frac {{a}^{r}}{{a}^{r_{0}}}\right)$ is taken into account and explored the wormhole solutions in the framework of $f(R)$ gravity with $f(R)= R + \alpha R^{m}-\beta R^{-n}$, where $\alpha, \beta, m $ and $n$ are positive real numbers. Here different cases are analyzed for various values of parameters in function $f(R)$ and NEC, WEC, SEC, DEC, EOS (equation of state) and anisotropy parameter are examined.

\subsection{Case 1: General Relativity Case}

For general relativity case the parameters $\alpha$ and $\beta$ is considered to be zero i.e. $f(R)= R$. The energy density $\rho$ is found to be a negative function of radial coordinate, which indicate the presence of exotic matter in wormhole geometry. In Fig. 2(a) and 2(b), NEC is plotted in terms of radial coordinate and tangential coordinate.  $\rho + p_{r}$ is found to be negative and   $\rho + p_{l}$ is found to be positive. In Fig.2(c), SEC is plotted. It is observed that SEC is also violating in this case. DEC in terms of $\rho-\left| p_{r}\right|$ and $\rho-\left| p_{l}\right|$ is also plotted in Fig.3(a) and 3(b). Both are obtained to be negative. Therefore, for present model NEC, SEC, and DEC are violated. Hence, in general relativity this model strongly support that the wormhole is filled with exotic matter. In Fig.3(c), EOS parameter $\omega$ is plotted, which comes out to be positive. This shows the role of matter in the universe. From Fig.3(d), it is found that anisotropy parameter $\bigtriangleup$ is positive, that supports  the repulsive geometry of universe.

\subsection{Case 2: $f(R)= R + \alpha R^{m}$}

For this case energy density is plotted in Fig.4(a), which comes out to be positive function of $r$. We also found NEC in term of $\rho +p_{r}$ is violating at the throat. The first NEC is plotted in Fig.4(b). The second NEC in term of $\rho + p_{l}$ is plotted in Fig.4(c). It is observed that second NEC is violating for $\alpha > 125$. In Fig.4(d), it is analyzed that SEC is also violating for $ r> r_{0}=1$. The DEC in terms of $\rho - |p_{r}|$ and $\rho - |p_{l}|$ is plotted in Figs.5(a) and 5(b), which are observed to be negative. Therefore, in this model violation of energy conditions confirmed  the presence of exotic matter in wormhole geometry. EOS parameter $\omega$ is plotted in Fig.5(c). It is analyzed that phantom fluid is dominant in wormhole. The anisotropy parameter $\bigtriangleup$ is shown in Fig.5(d), which is found to be positive at throat $r_{0}= 1$. Also anisotropy parameter is observed positive for $r > 2$, that indicate the repulsive nature of the geometry of Universe.

\subsection{Case 3: $f(R)= R - \beta R^{-n}$}

In this model $\beta$ and $n$ are positive real numbers. In Fig.6(a), energy density is plotted for $a = 0.5$, $n=4$ and $\beta > 20$, which is found to be positive. For the same values of parameters the first and second NEC are plotted in Figs.6(b)and 6(c), which are observed to be positive. The SEC is also analyzed as positive function of $r$, which can be seen in Fig.6(d). However, first and second DEC are violating as both are observed to be negative in Figs.7(a)and 7(b). In Fig.7(c), EOS parameter is plotted, which is found to be positive and anisotropy parameter is found to be negative in Fig.7(d). Therefore, in the present model validation of NEC and SEC indicates presence of non-exotic matter and $w>0$ shows role of non-phantom fluid, $\bigtriangleup <0$ indicated attractive geometry. Thus in this model we conclude that wormhole solution with attractive geometry could exists without violating NEC and SEC with presence of non-phantom fluid.

\subsection{Case 4: $f(R)= R + \alpha R^{m} - \beta R^{-n}$}

In this model $\alpha \neq 0, \beta \neq 0$, $m$ and $n$ are positive real numbers. In the first sub-case energy density is plotted in Fig.8(a) for $a=0.5, \alpha = 5, m = 2, n=4$ and $\beta > 10$. Energy density is found to be positive. For the same values of parameters first and second NEC are analyzed, which are observed positive in Figs.8(b) and 8(c). The SEC is also found to be positive in Fig.8(d). However, both DEC are observed to be negative in Figs.9(a) and 9(b). The EOS parameter is found to be positive function of radial coordinate $r$ in Fig.9(c). However, $\bigtriangleup$ is observed to be negative.

In the second sub-case the parameters are taken as $a=0.5, \beta =5, m=2, n=4$ and $\alpha >1$. The energy density is plotted in Fig.10(a), which is found to be positive function of radial coordinate. The first and second NEC are observed to be positive in Figs.10(b) and 10(c). The SEC is also found to be positive in Fig.10(d). However, first and second DECs are analyzed to be negative in Figs. 11(a)and 11(b). The EOS parameter is observed as positive and anisotropy parameter is negative in Figs.11(c) and 11(d).
Therefore, in both the sub-cases this model indicated the existence of wormhole without violating NECs and SEC. However, DECs are violating. The anisotropy parameter and EOS parameter indicates attractive geometry with non-phantom fluid.

 Thus, we observed that results obtained in viable modified theories of gravity in cases (2-4) are completely different from general relativity case.

\section{Conclusion}
Modified gravitational theories have received considerable attention over the last few decades as a possible alternative to GR. Obviously, this incorporates two stages of universe expansion: rapid expansion (early inflation) and present cosmic acceleration. The present paper is focused on wormhole models using the framework of $f(R)$ gravity by considering a new shape function $b(r)= {r_{{0}}}\left(\frac {{a}^{r}}{{a}^{r_{0}}}\right), \,\,0<a<1.$ The lower bound of radial coordinate $r=r_{0}=1$ defines the throat radius, also there are no black holes/horizons i.e wormhole regions are valid everywhere for $r>r_{0}$. The shape function satisfies all desired condition for wormhole structure like $b'(r_{0})<1$ etc. Here, the function $f(R)$ is taken in well known form as $f(R)= R + \alpha R^{m}-\beta R^{-n}$ (see in \cite{Nojiri2003}) and exact solutions are obtained. On varying the parameters ($\alpha, \beta, m $ and $n$), energy conditions (NEC, SEC, DEC), equation of state parameter and anisotropic parameter are analyzed in four different cases. It is observed that in the case of GR, wormhole is filled with exotic matter, geometry is repulsive, while in other cases of $f(R) = R + R^{m}$, wormhole is found filled with exotic matter with phantom fluid whose geometry is repulsive. In other two case of $f(R)$, it is analyzed that wormhole solutions may exists without violation of NEC and SEC, moreover role of non-phantom fluid is observed in these cases with attractive geometry. In this case wormhole satisfies energy conditions (NEC and SEC) due to matter threading and gravitational fluid is also interpreted by its higher order curvature derivative terms. Therefore, framework of modified gravity found  significant while discussing the existence of wormhole solutions. Thus, $f(R)$ gravity can be a useful framework in wormhole physics in addition to its applications in cosmology.

\section*{Acknowledgments}
The authors are thankful to GLA University, Mathura, India for providing help and support to do this research work. The authors are also appreciative to A. Pradhan for his fruitful suggestions which improved the paper in present form.

redpajama_set_name: RedPajamaArXiv


Tunis, 9 March 2011 - The Board of Directors of the African Development Bank (AfDB) approved on Wednesday, 9 March 2011 in Tunis, a UA 21.8-million (USD 34.3 million) loan to Nigeria to finance capacity building for Public-Private Partnerships (PPP) in infrastructure sectors, particularly in power and transport. The Federal Government of Nigeria (FGN) has identified these sectors as key to the country's overall development, and seeks to expand growth by involving the private sector through PPP projects.
PPPs are seen as part of the solution for Nigeria's infrastructure deficit because of their ability to attract finance, share risks, mobilize technical and managerial know-how, avoid the usual cost escalation associated with conventional construction contracts, and change the project focus from short- to long-term.
The success of PPP projects lies in creating an enabling environment for both the public and the private sectors. The public sector must prepare well-structured and bankable PPP projects to attract private investment while safeguarding the public interest. This is best achieved by building appropriate capacity in the public sector.
The loan will fund activities to build capacity for PPP projects in the ministries, departments and agencies (MDAs) at the federal and state levels. The project will contribute to increased institutional capacity to prepare and successfully implement PPP projects in the power and transport sectors and will strengthen cooperation between federal and state government institutions in charge of infrastructure delivery.
Over the next three years, the project will be implemented on three levels: 1) providing general awareness on PPP projects to all Nigerian states, including civil society, private sector, NGOs, media and MDAs at federal level; 2) providing training on the fundamentals of PPP; and 3) providing specialized capacity building support to selected states and MDAs on transactions and related issues.
The loan is aligned with Nigeria's development agenda and the Bank's current Country Strategy Paper for Nigeria. It aims to create conditions to develop private sector activities in the non-oil sector and to make rapid progress in MDG targets, such as increased energy access, poverty reduction, increased access to education, increased access to health services and better global partnerships.


text:
Rating : 2.4 out of 5
By : Viyannakkaran On 25/09/2008
In : Computer related
A woman had been married three times and was still a virgin...
A woman had been married three times and was still a virgin. Somebody asked her how that could be possible.
"Well," she said. "The first time I married an octogenarian and he died before we could consummate the marriage."
"The second time I married a naval officer and war broke out on our wedding day."
"The third time I married a Microsoft Windows programmer and he just sat on the edge of the bed and kept telling me how good it was going to be."
Added By Viyannakkaran
Copy Below & paste to Forum :
[url=http://www.openjokes.com][b]A woman had been married three times and was still a virgin...[/b][br]A woman had been married three times and was still a virgin. Somebody asked her how that could be possible.[br] [br] "Well," she said. "The first time I married an octogenarian and he died before we could consummate the marriage."[br] [br] "The second time I married a naval officer and war broke out on our wedding day."[br] [br] "The third time I married a Microsoft Windows programmer and he just sat on the edge of the bed and kept telling me how good it was going to be."[br] [br] [br]Added By Viyannakkaran[br]More Pictures & Videos Visit [url=http://www.openjokes.com]OpenJokes.com[/url][/url]
Related Jokes
A man and a woman were .....
A man and a woman were having...
A Blonde suspects her boyfriend of cheating on her...
A Blonde suspects her boyfriend...
Never before had Sue looked...
Best of the best \"Out of Office\" automatic email replies
;) I am currently out of the...
Darling ...
Husband [:D] arling, my sweet...
A woman had been married three times and was still a virgin...\n A woman had been married three times and was still a virgin. Somebody asked her how that could be possible.
Added By Viyannakkaran	\n See more funny pictures and videos at OpenJokes.Com

redpajama_set_name: RedPajamaCommonCrawl


text:
Canada News Today
News of Canada
Globalization Partners Announces Major Revenue Launch in Asia Pacific
BOSTON, July 20, 2020 /PRNewswire/ — Globalization Partners, which simplifies global business by enabling companies to hire and retain team members in…
BOSTON, July 20, 2020 /PRNewswire/ — Globalization Partners, which simplifies global business by enabling companies to hire and retain team members in 180+ countries without the complexity of setting up international branch offices or subsidiaries, today announced the launch of its new Asia Pacific revenue team and the appointment of Charles Ferguson as General Manager in the region. With significant business momentum across North America and EMEA over the last 12 months, Asia Pacific is the next key piece of the company's global growth trajectory. The company has maintained back-office operations in Asia since 2014. This new stage of growth is focused on replicating the revenue generating machine it has already created in North America and leveraging the potential growth seen out of Asia.
This expansion comes on the back of the company's $150 million funding round, and at a time of considerable demand for Globalization Partners' solution. The new Asia Pacific operations will support companies based in Asia who are looking to expand both within and outside the region. It will also support the company's growing Asia Pacific customer base.
«Globalization Partners provided us with exceptional insight into employment standards and regulations in Australia, enabling us to quickly and easily hire our director of services to facilitate our expansion into that region,» said Robert DeSteno, Co-Founder and Chief Executive Officer of Archive360. «As the emerging global standard for intelligent enterprise information management, their solution made it easy for us to continue to concentrate on our business while avoiding the need to invest heavily in time or infrastructure that would typically be associated with expanding our team in Asia Pacific.»
«Our intention is to take our solution that enables any company to hire anyone, anywhere, in as little as twelve hours into every market around the globe,» said Nicole Sahin, Chief Executive Officer and Founder of Globalization Partners. «The Asia Pacific region represents a significant opportunity and Charles Ferguson's exceptional entrepreneurial and executive experience in Human Capital Management solutions will be key in enabling us to meet our growth goals.»
Reporting to Diane Albano, Chief Revenue Officer, Ferguson will be responsible for the scaling and efficiency of the Asia Pacific revenue-generation team, managing the company's partner strategy and ultimately replicating the phenomenal success of Globalization Partners in North America, by capturing the market need for Asian companies looking for a simple and easy way to go global.
«We anticipate that APAC will be one of our fastest-growing regions and Charles will be instrumental in executing our on-the-ground strategy,» said Diane Albano, Globalization Partners. His strong leadership and unparalleled expertise in leading business expansion initiatives in Asia is ideally suited as we grow our presence there.»
Charles was most recently Group Chief Commercial Officer for Tricor Group, a leading business expansion specialist in Asia where he was responsible for designing and executing the global sales, marketing, and product innovation strategy. Prior to this role, Charles was President and General Manager for the Asia Pacific region at ADP, where he brought his experience and technology passion to the fore as the driver for delivering ADP's employee engagement and Human Capital Management solutions to firms of every size in Asia. Charles also co-founded management consulting and advisory services firm ReedHamilton where he led the technology and innovation practice. Prior to that he held positions at SAP, Salesforce, Microsoft and Intel.
«Asia Pacific is one of the most dynamic markets in the world and I am looking forward to working with the team to build out our presence and drive opportunities in the region,» said Charles Ferguson, General Manager, APAC, Globalization Partners.
About Globalization Partners
Globalization Partners enables companies to quickly and easily expand internationally across six continents and 187 countries. Our solution allows companies to hire employees in as little as 12 hours without having to navigate complex international legal, tax, and HR issues. When companies find top talent, that team member is put on our locally compliant payroll. We are the most trustworthy solution in the market and offer 24/7/365 premium support services. We have teams and offices worldwide with global headquarters located in Boston and California and regional headquarters in London, Ireland, Singapore and Dubai.
Globalization Partners' innovative platform is Privacy Shield certified for HR Data, and has consistently attained 97% customer satisfaction ratings by making it easy for companies to go global. To find out more, please visit: globalization-partners.com or connect with us via Twitter, LinkedIn, Facebook, or check out our Blog.
Karen Pantinas
Kpantinas@globalization-partners.com
View original content to download multimedia:http://www.prnewswire.com/news-releases/globalization-partners-announces-major-revenue-launch-in-asia-pacific-301096533.html
SOURCE Globalization Partners
IDB Invest and IFC Co-lead a $1.1 billion Financing to LD Celulose to Promote Growth and Strengthen Competitiveness of the Brazilian Pulp Industry
Care and Cleanliness Commitment
Consolidated Water Declares Third Quarter Cash Dividend
Konstantin Chaykin: New Mars Conqueror Mk3 Fighter Watch Is Launched


Scientists have discovered that the tips of your chromosomes, your telomeres are affected by chronic stress. Simply put, the healthier your telomeres, the easier it is for your cells to divide and replenish every area of your body, from bones to brain.
Think of a telomere as a Q-tip with a protective cotton end. Over time the cotton tip naturally wears away depending on how often and vigorously it is used - whether it's used to clean a delicate inner ear or a hard-to-reach greasy spot on your stove top.
When you are psychologically stressed, the body's stress response is activated. Your supply of stem cells divide and rush to fix the problem. Each time the cells divide, the telomeres get shorter. Chronic stress destroys those telomeres, shortening them and making it harder for stem cells to produce. Eventually, the cells cease to function and you age faster.
There are two hormones in your body that have a big influence on your waistline: leptin and ghrelin. When there is plenty of leptin in your system, you feel full and are less likely to overeat. But when ghrelin takes over, you get that hard to beat, "got to eat" impulse that can lead to a stop at the closest fast-food restaurant.
The goal is to romance leptin and repel ghrelin. That means getting plenty of sleep because ghrelin thrives while leptin suffers from too little sleep.
Fat on the hips and arms may be unfashionable, but belly fat - the kind that accumulates around internal organs - has been linked to many modern diseases. Having a big belly is even more closely correlated with health problems than obesity in general. Scientists have several explanations. A large waist (over 40 inches for men and 35 inches for women) may be a sign of psychological stress and related health problems, since the stress hormone, cortisol, seems to prefer to send fat to the abdomen. The solution: lose weight.
Psychological stress creates biochemical changes in the body that affect the immune system. Cortisol, a harmone released when stressed, inhibits chemicals that strengthen disease fighting defenses. That means making it harder to fight a flu virus or bacterial infection, or aggravating your allegies, asthma and eczema.
Stress has also been shown to raise the level of inflammation in the body, which is associated with heart disease. A recent study by the journal Psychosomatic Medicine found that stressful conditions can raise the amount of C-reactive protein, a marker for inflammation associated with cadiovascular problems later in life.
There are plenty of ways to counteract the negatives of stress. As you probably know, exercise is particularly good because it uses up excess levels of cortisol and adrenaline while elevating feel-good endorphins. Another powerful defense is meditation.
In a recent column, Angela Lunde of the Mayo Clinic wrote that many people confuse Alzheimer's disease and dementia; that while Alzheimer's accounts for 60-70 percent of dementia cases, other conditions can cause the symptoms of dementia such as poor memory. This includes chronic stress.
Stress causes headaches, moodiness, and anxiety. That's because the stress response floods the body with chemicals that increase tension, and inhibit calm, clear thinking.
Negative thinking is increasingly recognized as a source of many stress related problems. Cognitive behavioral therapy or CBT, which coaches stressed people to examine and challenge negative thinking, can be very effective in improving cognitive functioning.
They call it beauty sleep for a reason and most women will agree that nothing kills the complexion like too little of it. But for reasons that are still unclear, poor sleep habits appear to make women more vulnerable to heart disease than men.
A study by Dr. Edward Suarez at Duke University recorded the levels of cholesterol, insulin, glucose, the clotting agent fibrinogen, inflammatory proteins that contribute to heart disease and insuline resistance (a marker for diabetes). Because emotional factors affect sleep as well, he assessed his patients' levels of depression, hostility and anger. Dr. Suarezmen found a consistent link between poor sleep and higher risk levels for heart disease and diabetes - but only among women.
Dr. Suarez believes higher testosterone levels in men make a difference. Testosterone is known to reduce heart-damaging inflammatory proteins. And while sleep is not the only factor when weighing risks, too little slumber can raise the risks. Bottom line: a good night's rest is about more than beauty.
One of the coping hormones released when you are under stress is Corticotropin-releasing Hormone or CRH. While CRH fights stress, it also interacts with other chemicals that affect reproduction and sexual behavior (the body is temporarily shutting down all nonessential functions).
Stress can also lead to depression, which diminishes sexual desire as will excess weight. Extra belly fat tends to convert testosterone (the hormone that which triggers the libido) to estrogen.
Feeling stressed about stress? There is one more thing to say: laughter is some of the best medicine around and it's free!
So if you are feeling blue, perhaps this video will cheer you up.


This was my first time renting a property with my partner (who had problems with every letting agent prior). Staff at Nicola Kennedy Letting were nothing but outstanding in the service they provided. With a busy schedule, I appreciated texts now and again highlighting any future inspections or even them checking to see if we had any issues with our tenancy.
I have reccomend them to all friends and family looking for letting agencys in the area and should I move back to their catchment area then I will know who to approach.
The fees were very reasonable within the overall price of the rent.


text:
(Photo collage: Tablet Magazine; original photos: Wikipedia, Alex Wong/Getty Images, Flickr, Issouf Sanogo/AFP/Getty Images, Flickr/Tiffany Von Arnim, Wikipedia, Flickr/Nick Solari, Drew Angerer/Getty Images )
Straight Outta Brooklyn, by Way of Vermont: The Bernie Sanders Story
Tracing the Jewish roots of the presidential hopeful, from Burlington to the kibbutz and back
By Jas Chana
August 20, 2015 • 12:00 AM
In the 24 hours after Bernie Sanders launched his presidential bid on May 26, the No. 2 most frequently Googled question about America's newest potential president was: Is Bernie Sanders Jewish? As always, the particulars are much more interesting than the question of is he or isn't he. For one NPR host, the idea that Sanders was Jewish and had spent time on a kibbutz meant that he probably held an Israeli passport, an instinctive conflation of Jewishness and foreign loyalties that might have once been more common on the right. Others were simply puzzled by how a socialist Jew wound up as a senator from Vermont.
Bernie Sanders is a typical American Jew of his generation in that his story doesn't hew to any preconceived narratives or stereotypes, except for the fact that it begins in Brooklyn, where he and his brother Larry grew up in a modest apartment located off Kings Highway. Like many Brooklyn families, the Sanderses aspired to become middle-class Americans while living in the shadow of the Holocaust.
In 1921, Larry and Bernie's father, Eli, left his family in Slopnice, a rural village in the South of Poland, and immigrated to the United States. During the Nazi occupation of Poland, Slopnice's wide-open fields were used for airdrops before the businesses and goods of the town's local Jews were closed and confiscated. Most of Eli's family was sent to concentration camps where they were killed.
"Politics was not an aside [for us]," Larry Sanders has said. "It was life or death."
On Aug. 29, 2013, the U.S. senator, his brother, and their wives returned to Slopnice, where the mayor, Adam Soltys, greeted them as dignitaries and showed them around the sleepy village. The group was taken to the town's war memorial, two of the local schools, and even the place where the Sanders family home once stood. They were shown the official documents and photographs of the house, preserved in Slopnice's archives, which the visitors kept as souvenirs. A statement from the municipality of Slopnice described Bernie as being "warm, cordial, and friendly" during his visit to reconnect with his father's place of birth. It explained that he wanted to know exactly how daily life in the village had changed in the hundred years since his father left.
During a discussion, Larry said Bernie pressed Soltys for any information he might have about his father's family. Soltys recalled that his own father had gone to school with the daughter of Eli Sanders' half-brother. His name was Romek, he said, but he was called Romek of the Abraham. Soltys told them that at the time the Nazis invaded Poland, Romek was the leader of Slopnice's Jewish community.
"Which of course," Larry said, "meant he was one of the first to be killed."
Larry, who is seven years older than Bernie, explained that for him and his younger brother, the two political figures who held the greatest influence were Adolf Hitler and Franklin Roosevelt. "Politics could go desperately wrong," Larry said, "but it could also have a positive impact." Although the Sanders family did not directly benefit from Roosevelt's New Deal, the program remained an important symbol. In the lingering shadow of Nazi oppression, the American ideals of hope, justice, and of prosperity for all was a beacon.
Bernie and Larry both attended James Madison High School and Hebrew school on the weekends. There they studied Torah, learned about the prophets, Egypt, and the Jewish history of slavery. Larry told me that for him and his brother the stories did not hold great religious significance per se. Rather, in them, justice, and the way humans must distinguish right from wrong were plainly evident. "[Scripture] was encountered on an unintellectual level, but nonetheless it went very deep," Larry explained. "We did not distinguish Jewishness from being American."
In his 1998 memoir Outsider in the House, Bernie Sanders credits his older brother with introducing him to "political ideas." Larry was the president of the Young Democrats club at Brooklyn College and, in "fulfilling his sibling duties," he would "drag" his kid brother along to their meetings. The group's first campaign was the halting of an urban renewal project in New York's Lower East Side that would result in the eviction of low-income residents. Larry went door to door around Kings Highway, with Bernie in tow, requesting signatures from people in support of overturning the project. Unfortunately, despite racking up a considerable amount of local support, for one reason or another (to this day Larry suspects fraud), their efforts were unsuccessful. Like Bernie, Larry has pursued a career in politics: in the United Kingdom, where he currently represents the Green Party in Oxford West and Abingdon. Also like Bernie, Larry espouses the importance of universal health care and free college tuition.
Bernie and Larry Sanders', together with their wives, visit a World War II war memorial with Adam Soltys, the mayor of Slopnice. (Photo courtesy Municipality of Slopnice)
Although Eli Sanders' job as a paint salesman put food on the table for his wife Dorothy and their two boys, the family had to budget meticulously to get through each month. In the book The Jews of Capitol Hill: A Compendium of Jewish Congressional Members, by Kurt Stone, Bernie Sanders is quoted as saying about his childhood: "It's not that we were poor, but [there was always] the constant pressure of never having enough money. … The money question to me has always been very deep and emotional."
Alan Abbey, a reporter for the Burlington Free Press in the 1980s, described the milieu of post-Holocaust Jewish Brooklyn as having an acknowledged "outsiderness" combined with a strong sense of social conscience and a brute determination to survive. Abbey's parents were of the same ilk as Sanders', and he says the prevailing belief was that "[we are] here now" and "goddammit if [we] aren't going to survive and prosper."
Left-leaning, progressive, political thought was "in the air," said Walter Block, a leading libertarian economist and a contemporary at James Madison, where he also ran on the track team with Sanders. "Most of our grandparents and parents had escaped either from Hitler or the Soviet Union," Block said. "Everyone just took that view."
At James Madison, Bernie Sanders was a talented athlete and a natural leader. Block recalled how the high school's freshmen would look up to him during their senior year track sessions. A man named Nathan Crinsky, whom Sanders dubbed "Nate the Nose," coached them, and the nickname stuck. In that same year, Sanders ran for student-body president. His campaign promise was to get James Madison to "adopt" a Korean orphan, by providing scholarships for children whose families had been torn apart by the Korean war of 1950-53. Of the three candidates running for the position, Sanders received the fewest votes. However, despite his loss, the high school decided to follow through with his proposal and did in fact set up the scholarship fund.
After Sanders graduated from James Madison in 1959 he enrolled at Brooklyn College, where he was miserable. Block, who went with Sanders to Brooklyn College, told me that Sanders "was constantly complaining about the teachers and that the school wasn't academically rigorous enough." That same year his mother, Dorothy, died. Sanders decided to leave the city. He transferred to the University of Chicago where he eventually received a political science degree. The Chicago years were crucially formative for the man the New York Times would later call the "Socialist Senator." In the predominantly black areas surrounding the university, Bernie was "thrown right in the middle of the civil rights movement," Larry said. At the university he joined student organizations like the Young People's Socialist League and the Congress of Racial Equality.
Sanders writes in Outsider in the House that at the University of Chicago he largely neglected his formal studies, instead opting to spend hours in the library's stacks poring over the works of Jefferson, Lincoln, Marx, Engels, Debs, and Trotsky. "I read everything I could get my hands on—except what I was required to read for class," he writes. Outside the library, Sanders was involved in a sit-in protest against the University of Chicago's policy of racial segregation in off-campus housing. He was also part of a march on Washington, D.C., to protest the proliferation of nuclear weapons. Sanders' student jobs included working briefly for a trade union, the United Packinghouse Workers, as well as in a California mental hospital as a volunteer for the American Friends Service Committee. After scraping through to his graduation in 1964, he briefly returned to New York where, according to the National Journal, he started teaching children from low-income families for the new Head Start Program.
But in that same year, filled with a post-graduate thirst for adventure, Sanders decided to leave the city once again to travel abroad. Larry, who was also overseas at the time, said that they both made plans to spend the longest period of their trip in Israel. Larry told me that the decision was an unreflective one. "It never occurred to us not to visit Israel," he said. "It was quite natural." Neither he nor Bernie were Zionists in a "deep sense," Larry explained, but he mentioned that they were impressed by their cousin, who lived in Israel, and who stressed the fundamental importance of equality to the Zionist vision.
'The kibbutz was marvelous. People could do things in which they had no background whatsoever.'
Both brothers decided to spend their time in Israel living and working on kibbutzim. Bernie arrived in Israel first and was there for six months total; Larry showed up four months after Bernie's arrival and didn't leave until 1967. In that time, Larry met his first wife and lived on two kibbutzim: Matsuva in the north and Yotvata in the south. Unfortunately, no one I spoke to for the purpose of this article had any idea or recollection of the name of Bernie's kibbutz. However, Professor Richard Sugarman, a religious-studies professor at the University of Vermont, one of Sanders' closest friends, and the man who encouraged him to run for mayor of Burlington in 1980, told me it was one of the "oldest kibbutzim." (Requests for the information from Sanders' press office went unanswered.)
The Sanders brothers' time in Israel overlapped by only two months and because they lived on separate kibbutzim they have only been able to exchange stories from their experiences as kibbutzniks later in their lives. Larry recalled being impressed with his younger brother's tales of leadership on his kibbutz. While Larry was more interested in the day-to-day activity of kibbutz life, Bernie relished the "planning elements:" He loved the idea of people working together to complete every required task. Bernie would hurl questions at his fellow kibbutzniks, asking them, "What are you doing? What are your economic plans?"
"The kibbutz was marvelous in that sense," Larry recalled. "People could do things in which they had no background whatsoever."
Sugarman described Sanders as having a "prophetic sensibility of issues surrounding the connection between morality and economics." For this reason, during his time on the kibbutz, Sanders was inspired by how willing people were to take up any kind of work. Sanders described the egalitarian, agrarian nature of kibbutz life as a "less alienating form of labor," Sugarman said, and went as far to say it was "a utopian form of existence."
"Bernie's socialism was about trying to give people a better society," Sugarman commented, and this was at the "heart of his thinking about Israel" at the time. According to Larry, Bernie also described the routine of 1960s kibbutz life as "a very good way to raise children" because parents, men in particular, were given much more free time than they ever could have had in the city.
Larry said the kibbutz experience was valuable for him and his brother simply because it showed them that "you didn't need big bosses, you didn't need massive wealth" to live a decent life. Socialism was something "that could work."
But for Sanders, the kibbutz experience wasn't just about politics. "[Bernie] wanted to see Israelis growing vegetables!" Sugarman said. Because they grew up in the city, both brothers felt a deep fascination with rural life and the ability to grow things. As a Boy Scout, Bernie would cry as the bus departed the campsite in upstate New York to travel back to Brooklyn. And in fact, it was Bernie's synergy with nature, Larry said, not any political ambition, that inspired his eventual move to Vermont in 1967. According to Larry, Bernie saw the Green Mountain State as simply "a much more pleasant place to be" than the city.
On Oct. 23, 1980, Alan Abbey, then a 26-year-old City Hall reporter for the Burlington Free Press, broke the news about Sanders' entry into the race for the mayoral seat in Vermont's largest city. "Historian and film-strip maker Bernie Sanders," the article reads, "the Liberty Union gubernatorial candidate in 1976, said he is testing whether he can build a coalition of poor people, blue collar workers, and university students for the March 1981 election."
During his time in Vermont in the late '60s and throughout the '70s, Sanders lived something of an impoverished existence. When he first moved to the state, Sanders initially lived in a converted sugar mill with dirt floors. He scraped a living together by working a series of odd jobs ranging from carpentry to freelance writing. But it was during these transitional years that he discovered the Liberty Union Party, a small coalition of left-leaning Vermonters that offered local voters an alternative to the two-party system. According to Outsider in the House, Sanders became a representative for the party after going to a small Liberty Union meeting. Once there, Sanders writes, "full of enthusiasm for what I believed was right and just, I offered my views on education, the economy, and the war in Vietnam." Sanders was chosen on the spot as Liberty Union's candidate for the then-open seat on the U.S. Senate. Sanders had launched his political career.
Alan Abbey's article announcing Sanders' decision to run for the mayoral seat. (Burlington Free Press, October 1980)
Over the next decade, Sanders earned a reputation around Vermont for his tireless campaigning. He ran twice for a seat in the senate and twice for the position of governor—unsuccessfully each time. "He was always a fringe player," said Abbey, "as much an outsider as he is now in his presidential campaign." Sanders put his political career on hold in 1977 because he felt Liberty Union had reached a point of stasis. Sanders writes in Outsider in the House that, at the time, Liberty Union was not "attracting new members, new energy, or new leadership."
During this break, Sanders founded a company he named the American People's Historical Society. It produced educational filmstrips intended to expose college-age youth to "extraordinary Americans" they wouldn't have otherwise heard of. Of the films he made, his greatest work was a half-hour biopic of the "life and ideas" of Eugene Victor Debs, founder of the American Socialist Party. The film was distributed around American colleges and was even broadcast on Vermont public television.
Abbey described the city of Burlington at this time as a "standard blue collar," declining industrial city, with a population made up primarily of Irish and French Catholics. He said that, at this point, the city could have gone either way: "upscale and hipster," as it is today, or further into decline.
In 1980, Sanders decided to resurrect his political career and run for mayor of Burlington after Sugarman, whom he shared an apartment with, "dragged" him to the city's clerk office to rifle through the breakdown of results of the 1976 gubernatorial election. Sugarman revealed that although Sanders' popularity waned across the state, it was fairly strong in Burlington itself. Sanders writes in Outsider: "Richard reasoned that if all our efforts were concentrated on our hometown, we might win the upcoming mayoral election."
The incumbent government of Burlington immediately dismissed Sanders' chances. Abbey said that this is because it was a "very creaky democratic machine" that had not had a truly contested race in years.
In that first article Abbey wrote on Sanders, he quotes the new mayoral candidate as stating: "The goal must be to take political power away from the handful of millionaires who currently control it through Mayor [Gordon] Paquette and place that power in the hands of the working people of the city who are the vast majority of the Burlington population." The Sanders of the 1980s, Abbey comments, mayoral hopeful, and the Sanders of today, presidential hopeful, are saying "word for word" the same thing. "The only difference is he's changed the word millionaire to billionaire."
Throughout the bitterly cold Vermont winter of 1980, Sanders' campaign strategy was to knock on as many doors as he could, telling people—according to Outsider in the House—that "[he] would do [his] best to represent those in the city who had long been locked out of City Hall." Abbey would sometimes accompany Sanders as he campaigned. Together they would go from "the bluest of the blue" neighborhood in Burlington, the Old North End, characterized by its rickety houses, walking up through the increasingly affluent neighborhoods to eventually reach Burlington's wealthy New North End. Abbey would stand behind Sanders as he knocked on each door, furiously scribbling into his notebook as the disheveled candidate, dressed in a "frumpy winter coat," discussed gritty issues, like the state of the sewage network and garbage pickup schedule, on the door steps of Burlington's residents. Abbey said Sanders did not try to present any "grand socialist ideas"—rather, as Sanders puts it in Outsider: "I listened to their concerns and supported their grievances … as I stood in kitchens and stood on front stoops in low-income houses, I heard the bitterness in their voices." According to Abbey, the message Sanders conveyed was a simple one: that "this is your city and it's time to take it back."
The Sanders campaign began to pick up momentum. In the newsroom of the Burlington Free Press, Sanders' became known as "Total"—said in a thick Brooklyn accent—because of his grouchy, "full tilted" way of delivering his attacks against the current state of the city: "This is total travesty that … !" And the locals started to listen. "It was clear to me he was connecting to people," Abbey said. "He was a newcomer and an outsider, but I saw people's eyes and I saw them responding."
In response, the seemingly entrenched democratic governance in Burlington started to become unsettled. Burlington's Oasis Diner was made famous locally because it was a pit stop for even highly placed Democratic politicians hoping to curry favor with local voters. Photographs of these numerous diplomatic visits lined the Oasis' walls. Shortly before the mayoral election, Abbey, who because of his reporting had become closely associated with the Sanders campaign, visited the diner and found himself being berated by its Greek owner. The man, whom Abbey refused to name, was a staunch Democrat who was known to be a "behind the scenes player" in the local politics. Abbey told me that the owner lamented Sanders' growing popularity and interrogated the young reporter, delineating exactly how and why Sanders would be "terrible" for the future of the city.
"The issue of [Sanders] being Jewish did not emerge at all" during his campaign, Abbey commented, "except toward the end and only in a negative sense."
A week before the mayoral election, a series of mimeographed fliers began appearing around town. "The big story," the flier read, is that "Bernie Sanders and the parents of Alan Abbey attended the same high school in Brooklyn." The information on the flier was factually incorrect, Abbey told me. His parents attended Midwood High School, not James Madison. But the point was "to tar [Sanders] with the 'New Yorker' brush," i.e., to highlight the fact that Sanders and Abbey were Jews. The Jewish community in Burlington was small, and Sanders was not a part of it. Sanders was, and still is, notoriously private about his personal life, wanting the focus to always be on the political issues at stake. But the flier disturbed Abbey in a way he'll never forget. He described it as an underhanded attempt by local Democrats to tarnish Sanders' reputation and discredit Abbey's coverage of the election by appealing to the "latent anti-Semitism" in working-class "rural America." However, "Bernie," Abbey stressed, "never rose to the bait."
Sanders ignored the flier as well as the resulting stir it caused. He won the election, beating the incumbent democratic Mayor Paquette by just 10 votes. Abbey said that what followed—Sander's tenure as Burlington's "Socialist" mayor coupled with copious media attention to "the red mayor in the Green Mountains" (as Rolling Stone termed him at the time)—was "really a revolution" for the city.
Abbey mentioned that the current commentary on Sanders' presidential campaign is comparable to that of his mayoral campaign over 30 years ago. The common refrain being: "Of course he won't win, but … "
"The conditions are right," Abbey said. Sanders' authenticity, his "bedrock sincerity," is currently resonating with the same sorts of disaffected groups as it did in the past. He added, "Don't underestimate Bernie."
Like this article? Sign up for our Daily Digest to get Tablet Magazine's new content in your inbox each morning.
Jas Chana is a former intern at Tablet.
unblocked games 76 says:
Go with these games and play each game from this list and be a
veteran player of these greatest games.
europe coach says:
Thank you, I've just been searching for information about this subject for a while and yours is the best I've found out till now.
But, what about the bottom line? Are you positive in regards
to the source?
celtic Wedding ring tattoo says:
February 5, 2017 - 7:40 pm
The primary that you must consider is thee budget.
Love is among thhe most incredible things which take
place in everyone's life after we grow up. The pricing is often inflated in line with markjet demand. http://colbyjzpe592blog.blogocial.com
Harlan says:
March 9, 2017 - 6:15 am
Nesse artigo, revelarei verdades que ninguém nunca contou a você sobre ganhar dinheiro online.