Though telemedicine has been around for about 15 years, it is just now starting to gain some traction. With rising medical costs and increased insurance premiums, this might be the next great wave of health care — medical advice and care given by an actual doctor through devices nearly everyone can access — a phone or computer.
Teladoc is a company that provides these services. Back in 2002, it devised a system that connected doctors with patients in real time, over the phone and via Internet. By bringing together doctors with free time from canceled appointments or days off and patients needing help even after regular clinic hours, Teladoc provided a way to solve a significant need in the healthcare industry by providing care in real time.
Plus, (and this is a big plus), telemedicine is a lot cheaper than a regular doctor's visit.
Right now, telemedicine, (also called 'telehealth) is typically available as a supplement to company-sponsored healthcare plans. But, there are options for those who do not have access to telemedicine through their company-sponsored plan.
Services to the general consumer such as Call a Doctor Plus or Doc on Call 24-7 cost around $20 a month, while MD Live offers a per-session visit for a cost of $49.
Teladoc added nearly 1,000 clients in the first quarter of this year, including Southwest Airlines, Dell and Lockheed Martin. It's part of 26 health plans, including Aetna, Oscar and Blue Shield of California. Several hospitals, such as Memorial Hermann in Houston, have added the service. But, even though telemedicine is huge when it comes to decreasing costs for businesses, costing an average of $.48 per member per month, the biggest hurdle for more companies adopting telemedicine is an overworked HR department, according to more Teladoc CEO Jason Gorevic.
This year, Mr. Gorevic says Teladoc expects to handle 1 million patient visits. In addition, according to Willis Towers Watson, more than 80% of large companies are expected to offer telemedicine by 2018.
Though telemedicine is not a substitute for emergency care, it can be a great way to increase convenience and significantly reduce healthcare costs.


There's one problem that drives both new and seasoned knitters crazy: a messy edge stitch. Edge stitches, aka selvedge, are a way to finish off a piece neatly. You never want loose, sloppy stitches, and that's specially true for those first and last ones in your rows.
If this happens to you (we've all been there!), here are four sure-fire fixes.
Get into the habit of giving your first and last stitches in each row an extra tug before moving on.
After you knit that very first stitch, give that yarn a tug and hang on to it while you're knitting the second stitch. When you reach the end of the row, check the last stitch before and after turning to make sure it didn't loosen. Pull the yarn tightly before beginning the next row.
This is one of the simplest solutions: Just slip the first stitch of each row. Slipping will stretch the edge stitches out over two rows, getting rid of any loose ends.
For right-side rows, slip the first stitch with the yarn in front. For wrong-side rows, slip the first stitch with the yarn in back. Always slip the stitch purl-wise so you don't twist the stitches. This way, you end up with a tidy border that looks the same on the front and the back.
A chained edge gives you a neat braid that runs up and down each side of your knitting. It's a great technique to use on scarves and other flat knitting projects so the edges are even.
Right side rows: Slip the first and last stitch purl-wise with the yarn in front.
Wrong side rows: Knit the first stitch of the row through the back loop. Knit the last stitch of the row.
The garter stitch is a knitting basic, and usually the first stitch you learn to knit. If you're using the garter stitch , the super simple two-stitch I-cord can give your piece a really polished look.
Put the different Continental holds into practice as you begin knitting. You'll also practice Grace's clasped hold.


text:
Site last updated on December 27th, 2019
Jesus Christians.com
Preferred Language: English | Espanol | Deutsch | Francois | Po Polsku | Easy English
jExtensions
Forgot password? Forgot username? Create an account!
Only registered users can use the forum and earn points to unlock restricted articles.
Former Kidney Transplant Patient Fights Israeli Reluctance to Donate Organs
Created on Friday, 25 December 2009 11:00
Written by Raphael Ahren, Haaretz
For four years, Judith Nusbaum struggled with a failing kidney, sometimes fainting from a dangerously low blood count. Reluctantly, she started giving herself renal hormone injections and eventually had to undergo regular dialysis. Tired of the bothersome procedures, she decided to look for a new kidney. But after her doctors said it might take five years to find a suitable transplant, the retiree went online to find [her] own donor.
Within a few months of sending e-mails to everyone she knew, Nusbaum, who moved from New Jersey to Israel in 1973, was contacted by Martin Filla, a 36-year-old Australian who was willing to fly to Israel to donate his kidney. This week, Nusbaum and Filla celebrated the fourth anniversary of the successful transplantation.
"Because of this gift that I received - I call it my Hanukkah miracle - I feel this tremendous need to give back," said Nusbaum, now 71, who spends her free time lecturing about the many complicated legal and religious issue of organ donation in Israel.
"I'm not pushing everyone to give a live organ, but I'm trying to convince people to sign an organ donor card because Israel is one of the lowest countries in the world [in terms of people] agreeing to give their organs after death - I think we're up to 11 percent [of the population] and when I came on the scene it was only about four percent." Most Western countries achieve organ-donor membership of up to 30 percent, according to the U.S.-based Halachic Organ Donor Society.
Donor society officials and Nusbaum - who says some 100 Israelis die each year waiting for an organ transplant, assert that Israel's low donation rate is rooted in a widespread misinterpretation of Jewish law. "People think that you must be buried whole, otherwise you're not going to be resurrected, but that is incorrect," the Rishon Letzion resident says. "Even totally non-religious people, when the time for death comes, say to themselves that they have to be buried whole."
Biblical law indeed forbids needlessly mutilating a body, delaying its burial and deriving benefit from a body, such as selling it for medical research. However, "most rabbis agree that pikuach nefesh, saving a life, is more important than these prohibitions," Nusbaum said.
Yet there remains some opposition to organ donations, mainly from within the Haredi community. The bone of contention is the definition of death. According to the Chief Rabbinate and many other leading Orthodox rabbis, a person dies when his brain-stem ceases to function, even if the heart continues to beat with the help of a ventilator. A minority opinion, however, holds that as long as the heart beats, a person is considered alive and it is forbidden to harvest his or her organs.
"There are some countries where your organs are harvested automatically after you die, unless you have declined previously," Nusbaum explained. Although Israel last year passed a law recognizing brain-stem death and encouraging organ donations, organs of people who haven't signed a donor card are still not allowed to be touched. "It's a shame," she says, "because once you die your organs decay immediately and what good are they in the ground?"
Nusbaum's next lecture about organ donation in Israel will take place this Sunday at 7:00 P.M. at AACI's Tel Aviv Center, 76 Ibn Gvirol Street.
SHARE THIS ARTICLE ON SOCIAL MEDIA!
Home > Media > Kidneys > Other Kidney Stories > Former Kidney Transplant Patient Fights Israeli Reluctance to Donate Organs
Mail us at: info@jesuschristians.com, OR write to: Jesus Christians, P.O.Box A678, Sydney South, Australia 1235

redpajama_set_name: RedPajamaCommonCrawl


text:
\section{Introduction}
We consider the following  one-dimensional   isentropic Navier-Stokes system  for polytropic gas in the Lagrangian coordinate,
\begin{equation}\label{1.1}
\left\{ \begin{array}{ll}
&v_t-u_x=0,\quad \quad \quad\quad \quad \quad t>0, x\in \mathbb{R},\\
&u_t+p_x=(\mu(v)\frac{u_x}{v^{ }})_x,    \quad \quad  \, \,t>0, x\in \mathbb{R},
\end{array} \right.
\end{equation}
with the initial data:
\begin{equation}\label{1.2}
(v, u)(x, 0) = (v_0,u_0) (x)\longrightarrow (v_{\pm},u_{\pm}),\quad \text{as} \quad  x\rightarrow \infty.
\end{equation}
Here $v(x,t)=\frac{1}{\rho(x,t)}$ is the specific volume, $u(x,t)$   the fluid velocity, $p=a v^{-\gamma}$  the pressure with constant $a>0$, $\gamma> 1$  the adiabatic constant, and $\mu(v)=\mu_{0}v^{-\alpha}$   the viscosity coefficient with $\alpha\geq 0$. Without loss of generality, we assume $\mu_0=1$ in the rest of this article.
When the viscosity $\mu(v)\equiv 0$, the system (\ref{1.1}) becomes  the  Euler system
\begin{equation}
\left\{ \begin{array}{ll}\label{1.3}
&v_t-u_x=0,\\
&u_t+p_x=0.
\end{array} \right.
\end{equation}

It is known that the equation (\ref{1.3}) has rich  wave phenomena, such as shock and rarefaction.   The shock  is mollified  as the so-called viscous shock wave  when $\mu(v)>0$. The    time asymptotic  stability   of  single wave pattern   has been extensively studied in a large amount of literature since the pioneer works of \cite{g1986,mn1985}, see   \cite{fs1998,  hlz2017,km1985,l1997,lz2009,lz2015,m,mn1994,sx1993} and the reference therein, see other interesting works on the composite wave \cite{hm2009,hlm2010}.
However, most of above works require the strength of shock wave is   small, that is, the shock is weak. The stability of large amplitude shock (strong shock) is more interesting and challenging in both mathematics and physics.

Matsumura-Nishihara \cite{mn1985} showed that the viscous shock wave is stable if $ |v_+-v_-|<C(\gamma - 1)^{-1}$, that is, when $ \gamma  $ tends   to  $1  $, the strength of shock wave could be large. The condition is later relaxed to the condition that $ |v_+-v_-|<C(\gamma - 1)^{-2}$ in \cite{km1985}. The restriction on the strength of shock  was removed in  \cite{mw2010}   by a wonderful weighted energy method as $\alpha >\frac{\gamma-1} {2} $. Vasseur-Yao  \cite{vy2016} removed the condition $\alpha >\frac{\gamma-1} {2}$ by introducing an elegant variable transformation.  Moreover,  He-Huang  \cite{hh2020} extended the result of \cite{vy2016} to general pressure $p(v)$ and  viscosity $\mu(v)$, where $\mu(v)$ could be any positive smooth function.

It is important to study the stability of   composite wave consisting of at least two waves.  From \cite{hm2009},  it is not difficult to show the asymptotic stability of a composite wave consisting of 1-viscous shock wave and 2-viscous shock wave, provided that the strengths of the two shocks   satisfy  the condition ``small with same order".

In this paper, we study the asymptotic stability of this kind of composite wave with two large amplitude shock waves. More precisely, let $(V_1, U_1 )(x, t) $ be the 1-viscous shock wave connecting the left state $(v_-, u_- ) $ with an intermediate state $(v_m, u_m  ) $ and $(V_2, U_2 ) (x, t)$  be the 2-viscous shock wave connecting  $(v_m, u_m ) $ with the right state $(v_+, u_+ ) $ where the viscous shock waves are given in (\ref{2.2}) and (\ref{2.3}). The  intermediate state  $(v_m, u_m ) $  is determined by the RH condition, i.e.,
\begin{equation}\label{1.4}
\left\{\begin{array}{ll}
-s_{2}(v_+-v_m)-(u_+-u_m)=0, \\
-s_{2}(u_+-u_m)+(p(v_+)-p(v_m))=0,
\end{array}
\right.
\end{equation}
and
\begin{equation}\label{1.5}
\left\{\begin{array}{ll}
-s_{1}(v_m-v_-)-(u_m-u_-)=0, \\
-s_{1}(u_m-u_-)+(p(v_m)-p(v_-))=0.
\end{array}
\right.
\end{equation}
We denote the composite wave consisting of the two viscous shock waves $(V_{i}  ,U_{i}  ),$    $i = 1, 2$  by  $( V, U)(x, t) = (V_{1}  + V_{2} - v_{m},U_{1 }+U_{2}-u_{m} )$.

We outline the strategy as follows. In order to remove the condition ``small with same order", motivated by \cite{vy2016} and \cite{hh2020}, we introduce a new variable ${}{h}$, and formulate a new equation $\eqref{3.2}_2$ for ${}{h}$ in which the viscous term is moved to the mass equation $\eqref{3.2}_1$ such that the two nonlinear terms ${}{p}_x$ and $(\frac{{}{v}_x}{{}{v}^{\alpha+1}})_x $ are decoupled, so the interaction between nonlinear terms is weaken, and  the    low order   estimates are obtained. We then turn to the original system \eqref{1.1} to derive the higher order energy estimates, and finally complete the a priori estimates. On the other hand, since  the strengths of 1-shock wave and 2-shock  wave are arbitrarily large, the interaction between the two shocks is strong. We have to assume that 1-shock  wave is initially far away from 2-shock wave so that the interaction is weak.

The rest of the paper will be arranged as follows. In section \ref{section2}, the composite wave is formulated and the main result is stated.   In section \ref{section3}, the problem is reformulated by the anti-derivatives of the perturbations around the  composite wave. In section \ref{section4}, the a priori estimates are established. In section \ref{section5}, the main theorem is proved.

\noindent \textbf { Notation.}
The functional $\|\cdot\|_{L^p(\Omega)}$ is defined by $\| f\|_{L^p(\Omega)} =  (\int_{\Omega}|f|^{p}(\xi )\operatorname{ d }\xi )^{\frac{1}{p}}$. The symbol $\Omega$ is often omitted  when $\Omega=(-\infty,\infty)$. We denote for simplicity
\begin{equation*}
\| f\| =  \left(\int_{ -\infty}^{ \infty}f^{2}(\xi )\operatorname{ d }\xi \right)^{\frac{1}{2}}
\end{equation*}
as $p=2$. In addition, $H^m$ denotes the  $m$-th  order Sobolev space of functions defined by
 \begin{equation*}
\|f\|_{m} =  \left( \sum_{k=0}^{m}  \|\partial^{k}_{\xi}f\|^2 \right)^{\frac{1}{2}}.
\end{equation*}{}

\section{Preliminaries and Main Theorem }\label{section2}
\subsection{ Viscous Shock Profile}
Before stating the main results, we recall the Riemann problem for the   Euler equation (\ref{1.3}) with the Riemann initial data
\begin{equation}\label{Riemann}
(v,u)(x,0)=\left\{ \begin{array}{ll}
&(v_-,u_-),x<0,\\
&(v_+,u_+),x>0.\\
\end{array} \right.
\end{equation}
It is known that the system (\ref{1.3}) has two eigenvalues: $\lambda_{1}=-\sqrt{- p'  (v)}<0 $, $\lambda_{2}=-\lambda_{1}>0 $.  By the standard arguments (e.g. \cite{s1983}),     we define the shock curve  $S_{1}$ (resp $S_2$)\\
\begin{equation*}
 \left\{ \begin{array}{ll}
u=u_--\sqrt{(v_--v)(v^{-\gamma}-v_{-}^{-\gamma})}  ,u<u_{-} ,v<v_{-}  ,S_1,\\
u=u_--\sqrt{(v_--v)(v^{-\gamma}-v_{-}^{-\gamma})}  ,u<u_{-} ,v>v_{-}  ,S_2,\\
\end{array} \right.
\end{equation*}\\
and $SS(v_-,u_-)$:
\begin{eqnarray*}
SS(v_-,u_-)=     \{ (v,u)|  u \leq  u_{-} ;  S_{1}(u) < v <  S_{2}(u)  \}.
\end{eqnarray*}
In this paper, we assume that $(v_+,u_+)\in SS (v_{-},u_{-})$.    Thus the Riemann solution of (\ref{1.3}),(\ref{Riemann}) consists of two shock waves (and three constant states), that is,  there exists an intermediate state $\left(v_{m}, u_{m}{}\right)$, such that $(v_m,u_m)\in S_1(v_{-},u_{-})$ with the shock speed $s_{1}<0$, and $(v_{ {+}},u_{ {+}})\in S_2(v_{m},u_{m})$ with the shock speed $s_{2}>0.$ Here the shock speeds $s_{1}$ and $s_{2}$ are constants determined by the $\mathrm{RH}$ condition and satisfy entropy conditions
\begin{eqnarray}
\lambda_{1}\left(v_{-} {}\right)>s_{1}>\lambda_{1}\left(v_{m} {}\right), \lambda_{2}\left(v_{m} \right)>s_{2}>\lambda_{2}\left(v_{+} \right).
\end{eqnarray}
In what follows, we define $( \chi_{1}, \chi_{2} )$ below
\begin{eqnarray*}
\chi_{1}: = v_{-}-v_{m},\qquad \chi_{2}:= v_{+}-v_{m}.
\end{eqnarray*}
  We see that the   1-shock wave is a traveling wave solution of (\ref{1.1}) with the formula $(V_{1},U_{1} )(x-s_{1}t)$, satisfying
\begin{equation}\label{2.2}
\left\{ \begin{array}{ll}
&{-s_1}{V_1}'-{U_1}'=0,\\
&{-s_1}U_1'+p(V_1)'=(\frac{U_1'}{V_1^{\alpha+1}})',\\
&(V_{1},U_{1})(+\infty)=(v_m,u_{m}), \\
&(V_{1},U_{1})(-\infty)=(v_-,u_-),
\end{array} \right.
\end{equation}
where $'= {\operatorname{d}}/{\operatorname{d}\xi_{1}}, \quad \xi_1=x-s_1t .$ Similarly, the 2-viscous shock wave $(V_{2},U_{2} )(x -s_{2}t)$  satisfies
\begin{equation}\label{2.3}
\left\{ \begin{array}{ll}
&{-s_2}{V_2}'-{U_2}'=0,\\
&{-s_2}U_2'+p(V_2)'=(\frac{U_2'}{V_2^{\alpha+1}})',\\
&(V_{2},U_{2})(+\infty)=(v_{+},u_{+}),\\
&(V_{2},U_{2})(-\infty)=(v_m,u_m),
\end{array} \right.
\end{equation}
where $'= {\operatorname{d}}/{\operatorname{d}\xi_{2}}, \quad \xi_2=x-s_2t .$

\begin{lma}\label{lemma2.1} (\cite{km1985}) There are positive constants $C  $ and  $c_{1,2} ,$  such that
\begin{flalign*}
\begin{split}
&  (U_{i})_{x}\leq 0, \quad i= 1,2,   \\
&\left| V_{1}-v_{m}  \right|\leqslant C \chi_{1} \mathrm{e}^{-c_{1}\left|x-s_{1} t\right|}, \quad x>s_{1} t, \quad t \geqslant 0, \\
&\left| V_{2}-v_{m}  \right|\leqslant C  \chi_{2} \mathrm{e}^{-c_{2}\left|x-s_{2} t\right|}, \quad x<s_{2} t, \quad t \geqslant 0.
\end{split}
\end{flalign*}
\end{lma}

\subsection{Location of the Shift $\beta_{1}$ and $\beta_{2}$ }
As mentioned before, we assume that the 2-viscous shock wave is initially far away from the 1-viscous shock profile, that is, the shock profile is  $(V_2,U_2)(x-\beta)$ with some constant $\beta>0$ as $t=0$. The two shocks formulate a composite wave by $V(x)=V_{1}(x )+V_{2}(x -\beta_{ })-v_{m}, U(x)=U_{1}(x )+U_{2}(x  -\beta_{ })-u_{m}$. We
consider the situation where the initial data $({}{v}_0,{}{ u}_0)(x)$ is given in a neighborhood of $(V,U)(x)$. The solution is expected to tend to the composite wave
 \begin{align}\label{2.4}
\begin{split}
&V(x,t;\beta_1,\beta_2;\beta)=V_{1}(x-s_{1}t+ \beta_{1})+V_{2}(x -s_{2}t-\beta_{ }+\beta_{2})-v_{m},   \\ &U(x,t;\beta_1,\beta_2;\beta)=U_{1}(x-s_{1}t+ \beta_{1})+U_{2}(x -s_{2}t-\beta_{ }+\beta_{2})-u_{m},
\end{split}
 \end{align}
where the shifts $\beta_1$ and $\beta_2$ are supposed to satisfy
\begin{align*}
\begin{split}
0=&\int_{-\infty}^{\infty}\left(
\begin{array}{cccc}
{}{v}_0(x) -    V(x,0;\beta_{1}, \beta_{2};\beta)  \\
{}{u}_0(x) -    U(x,0;\beta_{1}, \beta_{2};\beta)
\end{array}
\right )
\operatorname{d}x:=\left(\begin{array}{cccc}
I_1(\beta_1,\beta_2;\beta)  \\
I_2(\beta_1,\beta_2;\beta)
\end{array}
\right ).
\end{split}&
\end{align*}
We shall find unique $\beta_1$ and $\beta_2$ such that $I_i(\beta_1,\beta_2;\beta)=0, i=1,2.$
Note that
\begin{align}\label{2.5}
\begin{split}
&I_1(\beta_1,\beta_2;\beta)\\
=&\int_{-\infty}^{\infty}
{}{v}_0(x) -    V(x,0;0,0;\beta)+ V(x,0;0,0;\beta) -   V(x,0;\beta_{1}, \beta_{2};\beta)  \operatorname{d}x\\
=&I_{01}+\int_{-\infty}^{\infty} V_1(x ) -   V_1(x +\beta_1)  \operatorname{d}x\\
&+\int_{-\infty}^{\infty} V_2(x-\beta) -   V_2(x-\beta+\beta_2) \operatorname{d}x\\
=&I_{01}-\beta_1(v_m-v_-)-\beta_2(v_+-v_m),
\end{split}
\end{align}
where
\begin{equation}\label{2.6}
I_{01}=\int_{-\infty}^{\infty}
{}{v}_0(x) -    V(x,0;0,0;\beta)    \operatorname{d}x.
\end{equation}
Similarly one can get
\begin{align}
I_2(\beta_1,\beta_2;\beta)=I_{02}-\beta_1(u_m-u_-)-\beta_2(u_+-u_m),
\end{align}
where
\begin{equation}\label{2.8}
I_{02}=\int_{-\infty}^{\infty}
{}{u}_0(x) -    U(x,0;0,0;\beta)   \operatorname{d}x.
\end{equation}
Utilizing (\ref{2.5})-(\ref{2.8}), R-H condition (\ref{1.4})-(\ref{1.5}),  we have
\begin{align*}
\begin{split}
\left(
\begin{array}{cccc}
I_{01}  \\
I_{02}
\end{array}
\right )=  -\beta_{1}\left(
\begin{array}{cccc}
v_--v_{m}   \\
u_{-}-u_{m} \\
\end{array}
\right )-
\beta_{2}\left(
\begin{array}{cccc}
v_m-v_{+}   \\
u_m-u_{+} \\
\end{array}
\right ).\\
\end{split}&
\end{align*}
Thus, one gets
\begin{eqnarray}\label{2.9}
\beta_{1}    =\frac{I_{01}s_{2}+I_{02}}{\chi_{1}(s_{1}-s_2)  }, \quad \beta_{2} =\frac{I_{01}s_{1}+I_{02}}{\chi_{2}(s_{1}-s_2) }.
\end{eqnarray}

\subsection{Main Theorem }
To state the main theorem, we assume
\begin{flalign}\label{2.10}
\begin{split}
&v_{0}(x)-V(x,0;0,0;\beta)\in \mathbb{H}^1   \cap \mathbb{L}^1 \quad u_{0}(x)-U(x,0;0,0;\beta)\in \mathbb{H}^1    \cap \mathbb{L}^1.
\end{split}
 \end{flalign}
 Then we can define
\begin{eqnarray}
(\phi_{0},\psi_0)(x)= \int_{-\infty}^{x} [ v_{0}(y )-V(y,0;\beta_{1},\beta_{2};\beta)  ,  u_{0}(y )-U(y,0;\beta_{1},\beta_{2};\beta)    ] \operatorname{d}y.
\end{eqnarray}
In view of $I_i(\beta_1,\beta_2;\beta)=0, i=1,2$,  we  further assume that
\begin{eqnarray}\label{2.12}
(\phi_{0},\psi_0) \in \mathbb{L}^2.
\end{eqnarray}
We abbreviate $(V(x,t;\beta_{1},\beta_{2};\beta),U(x,t;\beta_{1},\beta_{2};\beta)) \ \text{as}\  (V ,U )$  in the rest part of this paper.
We are ready to state the main result.
\begin{thm}\label{theorem}
Suppose    (\ref{2.10})-(\ref{2.12}) hold and  {$(v_+,u_+)\in SS (v_{-},u_{-})$}.  There exists a positive constant   $\delta_0$, such that if $$\|\phi_{0}\|_{2}+\|\psi_{0}\|_{2}+\beta^{-1}\leq\delta_{0},$$ then the Cauchy problem (\ref{1.1}),(\ref{1.2})   has a unique global solution $(v,u)(x,t) $ satisfying
\begin{align}
\begin{split}
&( {v}-V,{u}-U)\in C^0([0,+\infty);\mathbb{H}^2), {v}-V \in \mathbb{L}^2( 0,+\infty ;\mathbb{H}^3),\\
&{u}-U\in \mathbb{L}^2( 0,+\infty ;\mathbb{H}^2).
\end{split}\label{2.13}
\end{align}
Moreover,
\begin{eqnarray}
\sup_{x\in \mathbb{R}_{ }}                       | {v }-V  |     \rightarrow 0 , \quad \sup_{x\in \mathbb{R}_{ }}                       | {u}-U  |     \rightarrow 0,    \text{   as } t\rightarrow +\infty.
\label{2.14}\end{eqnarray}
\end{thm}
\section{Reformulation of the Original Problem }\label{section3}
Set
 \begin{align}\label{3.1}
 \begin{split}
\phi&( x,t):=\int^x_ {-\infty}{}{(v-V)}(y,t)  \operatorname{d}y,  \\
  \psi&( x,t):=\int^x_{-\infty} {}{(u-U)}(y,t)  \operatorname{d}y,
\end{split}
 \end{align}
which means that we look for the solution $(v,u)(x,t)$ in the form
\begin{align}\label{t3.2}
v&( x,t)=\phi_x (x,t)+  V(x,t;\beta_{1},\beta_{2};\beta), \nonumber\\
u&( x,t)=\psi_x (x,t)+  U(x,t;\beta_{1},\beta_{2};\beta).
\end{align}
From (\ref{2.2})-(\ref{2.4}), we know the shock profile $(V,U)$ satisfies
\begin{equation}
\left\{ \begin{array}{ll}
&{V}_{t}-{U}_{x}=0,\\
&U_{t}+p(V)_{x}-\left(\frac{U_{x}}{V^{\alpha+1}}\right)_{x}={}{W}_{x},\\
&(V,U)(\pm \infty,t;\beta_{1},\beta_{2};\beta)=(v_{\pm}, u_{\pm}),
\end{array} \right.\label{3.2}
\end{equation}
where
\begin{equation*}
W=  \frac{U_{2x}}{V_2^{\alpha+1}}  + \frac{U_{1x}}{V_{1}^{\alpha+1}}  - \frac{U_{x}}{V^{\alpha+1}}+p(V)+p(v_m)-p(V_{1})-p(V_2).
\end{equation*}
Motivated by  \cite{mm1999}, substitute (\ref{t3.2}) into (\ref{1.1}) and integrate the resulting system with respect to $x$,  we have
\begin{equation}
\left\{ \begin{array}{ll}
&\phi_{t}-\psi_{x}  =0, \\
&\psi_{t}-f(V,U_x) \phi_{x}-\frac{{\psi_{x x}}}{V^{\alpha+1}} =F-W ,
\end{array} \right.  \label{3.3}
\end{equation}
 with the initial condition:
\begin{align}\label{3.4}
\left(\phi_{0}, \psi_{0}\right)&(x) \in \mathbb{H}^{2}, \quad x \in \mathbb{R},
\end{align}
where
\begin{align}\label{3.5}
f(V,U_x)= -p^{\prime}(V)    - (\alpha+1)\frac{{} U_{x}}{V^{\alpha+2}} >0,
\end{align}
\begin{align}\label{3.6}
F&= \frac{{}{u}_{x}}{{}{v}^{\alpha+1}}-\frac{U_{x}}{V^{\alpha+1}} - \frac{\psi_{xx}}{V^{\alpha+1}}+(\alpha+1)\frac{U_x \phi_x }{V^{\alpha+2}}-\left[p({}{v})-p(V)-p'(V)\phi_x\right].
\end{align}
We will seek the solution in the functional space $\mathbb{X}_{\delta}(0,T)$ for any $0\leq T < +\infty $,
\begin{align*}
\begin{split}
\mathbb{X}_{\delta}(0,T):=&\left\{ (\phi,\psi)\in C ([0,T];\mathbb{H}^2)|\phi_{x} \in  \mathbb{L}^2(0,T;\mathbb{H}^1) ,\psi_{x} \in  \mathbb{L}^2(0,T;\mathbb{H}^2)\right. \\
&  \sup_{0\leq t\leq T}\|(\phi, \psi)(t)\|_2\leq\delta    \},
\end{split}&
\end{align*}
 where ${ \delta} \ll 1$ is small.
\begin{pro}\label{prposition3.1} (A priori estimate)
Suppose  that $(\phi,\psi) \in \mathbb{X}_{\delta}(0,T)$ is the solution of  (\ref{3.3}), (\ref{3.4})  for some time $T>0$. There exists a positive constant $\delta_0  $ independent of  $T$, such that if
$$ \sup_{0\leq t\leq T}\|(\phi, \psi)(t)\|_{{2}} \leq \delta_{ }\leq \delta_{0},$$   for $t \in [0,T]$,
then
\begin{eqnarray*}
\|(\phi, \psi)(t)\|_{{2}}^{2}+    \int_{0}^t     (  \|  \phi_{x}(t)  \|^2_{1}  +   \|\psi_{x}(t)\|_{2}^2   )    \operatorname{d}t       \leq C_{0} ( \|(\phi_{0},\psi_{0})\|_{{2}}^2+   e^{-C_-\beta}),
\end{eqnarray*}
where $C_{0}  >1$ and $C_{-} $ are two positive constants independent of $T$.
\end{pro}

As long as  Proposition \ref{prposition3.1} is proved,   the local solution $(\phi,\psi)$   can be extend to $T =+\infty. $ We have the following Lemma.

\begin{lma}\label{lemma3.1}
  If $(\phi_{0},\psi_{0})\in \mathbb{H}^2$, there exists a positive constant $\delta_{1}=\frac{\delta_{0}}{\sqrt{C_{0}}}$, such that if
$$\|(\phi_{0},\psi_{0})\|_{{2}}^2+   e^{-C_-\beta} \leq \delta_{1}^{2},$$ then  the Cauchy problem  (\ref{3.3}), (\ref{3.4}) has a unique global solution
$(\phi,\psi)\in \mathbb{X}_{\delta_{0}}(0,\infty)$  satisfying
\begin{align*}
\sup_{t\geq0}\|(\phi, \psi)(t)\|_{{2}}^{2}+    \int_{0}^\infty   (  \|  \phi_{x}(t)  \|^2_{1}  +   \|\psi_{x}(t)\|_{2}^2   )    \operatorname{d}t       \leq C_{0}  ( \|(\phi_{0},\psi_{0})\|_{{2}}^2+   e^{-C_-\beta}).
\end{align*}
\end{lma}

{}

\section{a Priori Estimate  }\label{section4}
Throughout this section, we assume that the problem $(\ref{3.3}), (\ref{3.4})$ has a solution $(\phi,\psi)\in \mathbb{X}_{\delta}(0,T), $ for some $T>0$,
\begin{eqnarray}\label{4.1}
\sup_{0\leq t\leq T}\|(\phi, \psi)(t)\|_{2}\leq \delta.
\end{eqnarray}
It follows from the Sobolev inequality that $\frac{1}{2}v_{m}\leq v \leq \frac{3}{2} \max\{v_{
-},v_{+}\}$, and
\begin{align*}
\sup_{0\leq t\leq T}  \{  \|(\phi, \psi)(t)\|_{\mathbb{L}^{\infty}}    +   \|(\phi_{x}, \psi_{x})(t)\|_{\mathbb{L}^{\infty}}   \}  \leq  {\delta} .
\end{align*}

\subsection{  Low Order Estimate.}In order to  remove  the condition  ``small with same order", we introduce  a new perturbation $(\phi,\Psi)$ instead of $(\phi,\psi)$, where $\Psi$ will be  defined below. Motivated by \cite{vy2016} and \cite{hh2020}, we introduce a new effective velocity   ${}{h}={}{u}-{}{v}^{-(\alpha+1)}{}{v}_{x}$. Setting $ h_0 (x)=:h(x,0) $, the equations (\ref{1.1}), (\ref{1.2}) become
\begin{equation}
\left\{ \begin{array}{ll}
&{}{v}_t-{}{h}_x=(\frac{{}{v}_{x}}{{}{v}^{\alpha+1}})_{x},\\
&{}{h}_t+{}{p}_x=0,
\end{array} \right.\label{4.2}
\end{equation}
and
\begin{equation*}
(v_{0}, h_{0})(x) = (v_0,u_0-v_{0}^{-(\alpha+1)}{v}_{0x}) (x)\longrightarrow (v_{\pm},u_{\pm}),\quad \text{as} \quad  x\rightarrow \pm\infty.
\end{equation*}
Let $H=U-V^{-(\alpha+1)}V_{x}$. Then (\ref{3.2}) is equivalent to
\begin{equation}
\left\{ \begin{array}{ll}
&V_{t}-H_{x}=\left(\frac{V_{x}}{V^{\alpha+1}}\right)_{x},\\
&H_{t}+p(V)_{x}= {W}_{x},\\
&(V,H)(\pm \infty,t)=(v_{\pm},u_{\pm}).
\end{array} \right.\label{4.4}
\end{equation}\\
We define
\begin{eqnarray}
 \int_{-\infty}^x({}{h}-H)\operatorname{d}x:=\Psi.
\label{4.5}\end{eqnarray}
Substituting (\ref{4.4}) from (\ref{4.2}) and integrating the resulting system with respect to $x$, we have from  (\ref{4.5}), $(\ref{3.1})_{1}$ that
\begin{equation}
\left\{ \begin{array}{ll}
&\phi_t- \Psi_x-\frac{\phi_{xx}}{V^{\alpha+1}}+(\alpha+1)\frac{V_x \phi_x }{V^{\alpha+2}}=G\\
&\Psi_t+p'(V)\phi_x=-p({v}|V)-W,
\end{array} \right.  \label{4.6}
\end{equation}
where
\begin{eqnarray*}
G=\frac{{}{v}_{x}}{{}{v}^{\alpha+1}}-\frac{V_{x}}{V^{\alpha+1}} - \frac{\phi_{xx}}{V^{\alpha+1}}+(\alpha+1)\frac{V_x \phi_x }{V^{\alpha+2}},
\end{eqnarray*}
\begin{eqnarray*}
p({}{v}|V)=\left(p({}{v})-p(V)\right)-p'(V)\phi_x,
\end{eqnarray*}
with the  initial data
\begin{eqnarray*}
 \phi  (x,0) \in \mathbb{H}^{2}, \quad \Psi (x,0) \in \mathbb{H}^{1}.
\end{eqnarray*}
\begin{lma}\label{lemma4.1}
Under the assumption of (\ref{4.1}), it holds that
\begin{flalign}\label{s4.07}
\begin{split}
&|p({}{v}|V)|\leq C \phi_{x}^{2},\\
&|p({}{v}|V)_{x}|\leq C (|\phi_{xx}\phi_{x}|+|V_x|\phi_{x}^{2}),\\
&|G|\leq C (|\phi_{xx}\phi_{x}|+|V_x|\phi^{2}_{x}),
\end{split}
\end{flalign}
\begin{flalign}\label{s4.08}
\begin{split}
&|F|\leq C( \phi_{x} ^{2}+|\phi_{x}\psi_{xx}|),\\
&|F_{x}|\leq C(\phi_{x}^{2}+|\phi_{x}^{ } \phi_{x x}^{ }|+|\psi_{x x}^{ } \phi_{x x}^{ }|+|\psi_{x x x}^{ } \phi_{x}^{ }|+|\phi_{x}^{ } \psi_{x x}^{ } |,
\end{split}
\end{flalign}

and
\begin{eqnarray}\label{s4.09} \begin{split}
\|    {\Psi}_{0}  \|_{1}^{2}    \leq&  \|    {\psi}_{0}  \|_{1}^{2}+    C  \|    {\phi}_{0}   \|_{2}^{2},\\
 \| \psi \|^{2}  \leq &     \| \Psi \| ^2+ C\|\phi \|_{ 1}^2,      \\
 \| \psi_{x} \|^{2} \leq &     \| \Psi_{x} \| ^2+ C\|\phi_{x} \|_{ 1}^2.
\end{split}\end{eqnarray}
Here $C$ is a constant depends only on $  v_\pm $ and $  u_\pm $.
\end{lma}

\begin{proof}
Note that
\begin{eqnarray}\label{s4.10}
\begin{split}
   \Psi (x,t)=&\int_{-\infty}^{x}           [ {(u-U )  } (y,t)  ]  \operatorname{ d }y\\
   &-\int_{-\infty}^{x} \left( v^{- \alpha  } v_y-{}{V}^{- \alpha  }V_y\right) (y,t)\operatorname{ d }y \\
    :=& \psi (x,t)  +q(x,t )\leq \psi (x,t)  + C_{ } |\phi_{ x} (x,t)|,\\
     \psi (x,t)=& \Psi (x,t)  -q(x,t )\leq \Psi (x,t)  + C_{ }| \phi_{ x} (x,t)|.
     \end{split}
\end{eqnarray}
one have (\ref{s4.09}) from  (\ref{s4.10}) immediately.   The  estimates (\ref{s4.07}) and (\ref{s4.08}) can  be found in  \cite{hh2020} and   \cite{mm1999}  respectively. Thus the proof is completed.
\end{proof}
It is worth  to point out that the initial data $ (v_0, h_0)(x)   $  should satisfy the following equation
\begin{align}\label{4.8}
\begin{split}
0=&\int_{-\infty}^{\infty}\left(
\begin{array}{cccc}
{}{v}_0(x) -    V(x,0;\beta_{1}, \beta_{2};\beta)  \\
{}{h}_0(x) -    H(x,0;\beta_{1}, \beta_{2};\beta)
\end{array}
\right)
\operatorname{d}x.
\end{split}&
\end{align}
Here $H(x,0;\beta_{1}, \beta_{2};\beta)=U(x,0;\beta_{1}, \beta_{2};\beta)-[V(x,0;\beta_{1}, \beta_{2};\beta)]^{-(\alpha+1)}[V(x,0;\beta_{1}, \beta_{2};\beta)]_{x}$.   By directly calculate,   we know $({\ref{4.8}})$ is equivalent to   $I_i(\beta_1,\beta_2;\beta)=0, i=1,2.$

\begin{lma}\label{lemma4.2}
Under the same conditions of     Proposition \ref{prposition3.1}, it holds that
\begin{flalign}
 \|W\|_{2}\leq C_{ }  e^{-C_-\beta}e^{-c' t},
\end{flalign}
where $ C_{ } ,C_-,c' $ are constants independent of t.
 \end{lma}
\begin{proof}
 \begin{align}
\begin{split}
|W|=&\left|\frac{U_{1x}}{V_1^{\alpha+1}}+\frac{U_{2x}}{V_2^{\alpha+1}}-\frac{U_{x}}{V^{\alpha+1}}+p(V)+p(v_m)-p(V_{1})-p(V_2) \right|\\
=& \left|\left(\frac{U_{1x}}{V_1^{\alpha+1}}-\frac{U_{1x}}{V^{\alpha+1}}\right)+\left(\frac{U_{2x}}{V_2^{\alpha+1}}-\frac{U_{2x}}{V^{\alpha+1}}\right)\right|\\
&+\left|\left(p(V)-p(V_{1})\right)+\left(p(v_m)-p(V_2)\right)\right|\\
=&\left| U_{1x}\left(\frac{1}{V_1^{\alpha+1}}-\frac{1}{V^{\alpha+1}}\right)+    U_{2x}  \left(\frac{1}{V_2^{\alpha+1}}-\frac{1}{V^{\alpha+1}}\right)\right|\\
&+\left|\left(p(V_{1}+V_{2}-v_{m})-p(V_{1})\right)+\left(p(v_m)-p(V_2)\right)\right|\\
\leq&C\{ |(V_2-v_m)|+|U_{2x}|\}.
\end{split}&
\end{align}
By $(\ref{2.3}) $,  we get
\begin{equation}\label{4.11}
 \left|\frac{\partial^{j}U_{2}}{\partial x^{j}}\right| ,\left|\frac{\partial^{j}(V_{2}-v_m)}{\partial x^{j}}\right|    \leq C  |V_2-v_m|, \forall j\in \mathbb{N}.
\end{equation}
On the other hand,  in the same way,   it is still true to replace ($V_2,U_2$) with ($V_1,U_1$) in (\ref{4.11}).  We get $\left|\frac{\partial^{n}W}{\partial x^{n}}\right| \leq C  |V_i-v_m|, i=1,2; \forall n\in \mathbb{N}.$
By (\ref{2.9}) and (\ref{2.10}), we know   $ {\beta}_{1},{\beta}_{2} $  are bounded. {If we choose $\beta> 3 \max\{|\beta_{1}|,|\beta_{2}| \}$, for $n=0,1 $, it follows that:}
\begin{align*}
\begin{split}
\int_{-\infty}^{\infty} \left|\frac{\partial^{n} W}{\partial{x}^{n}}\right|^{2}  \operatorname{d}x=& \int_{-\infty}^{  \frac{\beta}{2}}\left|\frac{\partial^{n} W}{\partial{x}^{n}}\right|^{2}  \operatorname{d} x+ \int_{  \frac{\beta}{2}}^ { \infty}\left|\frac{\partial^{n} W}{\partial{x}^{n}}\right|^{2} \operatorname{d}x\\
 \leq &C \int_{-\infty }^{ \frac{\beta}{2}}   |V_{2}( x-s_{2}t+\beta_{2}-\beta)-v_{m}|^{2} \operatorname{d}x\\
 &+C \int_{ \frac{\beta}{2}}^ { \infty }  |V_{1}( x-s_{1}t+\beta_{1} )-v_{m}|^{2} \operatorname{d}x\\
 \leq &C \chi_{2}^{2} \int_{-\infty }^{ \frac{\beta}{2}}    \exp[ 2c_{2}( x-s_{2}t+\beta_{2}-\beta)]  ^{} \operatorname{d}x\\
 &+C \chi_{1}^{2} \int_{ \frac{\beta}{2}}^ { \infty }   \exp[ -2c_{1}  ( x-s_{1}t+\beta_{1} )]  ^{} \operatorname{d}x\\
=&  C \chi_{2}^{2} e^{- 2c_{2} s_{2} t}      \quad \frac{e^{c_{2}\left( 2\beta_{2}- \beta\right) }}{2c_{2}} + C   \chi_{1}^{2}   e^{2c_{1} s_{1} t}  \quad \frac{e^{-c_{1}\left(  {\beta} +2\beta_{1}\right)}}{ 2c_{1}} \\
\leq&C   e^{- 2c_{2} s_{2} t}        {e^{ - \frac{c_{2} }{3}\beta }} + C   e^{2c_{1} s_{1} t}    {e^{  \frac{- c_{1} }{3}{\beta}   }}.  \\
\end{split}&
\end{align*}
We have used Lemma \ref{lemma2.1} in the second inequality. Setting $c':=\min (-c_{1} s_{1},  c_{2} s_{2}     ); C_{-} := \frac{1}{6}\min (c_{1}  ,  c_{2}       ),         $ we get the proof of the Lemma.
\end{proof}
\begin{lma}\label{lemma4.3}
Under the same assumptions of Proposition \ref{prposition3.1}, it holds that
\begin{align*}
\begin{split}
&\|(\phi,\Psi)\|_{ }^2(t)+ \int_0^t\int_{-\infty}^{\infty}   \left(\frac{1}{p'(V)}\right)_t \Psi^2\operatorname{d} x\operatorname{ d} t+\int_0^t \| \phi_x\|^2\operatorname{ d} t\\
\leq& C_{}\|(\phi_0,\Psi_0)\|_{ }^2+C{\delta}  \int_0^t \| \phi_{xx}\|^{2}\operatorname{  d}t + C_{} e^{-C_-\beta}.
\end{split}
\end{align*}
\end{lma}
\begin{proof}
Multiply $(\ref{4.6})_1 $ and $(\ref{4.6})_2$ by $\phi$ and $\frac{\Psi}{-p'(V)}$, respectively, sum them up, and  integrate result with  respect to $t$ and $x$ over $ [0,t]\times \mathbb{R} $. We have
\begin{align}
\begin{split}
&\frac{1}{2}\int_{-\infty}^{\infty}      \left(\phi^2-\frac{\Psi^2}{p'(V)}\right)   \operatorname{d}x
+\int_0^t\int_{-\infty}^{\infty}\left\{\frac{1}{2}\left(\frac{1}{p'(V)}\right)_t \Psi^2
+       \frac{\phi_{x}^2}{V^{\alpha+1}}\right\}   \operatorname{d} x \operatorname{ d} t \\
=&\int_0^t\int_{-\infty}^{\infty}       G_{ }\phi  \operatorname{d}x \operatorname{ d} t
+ \int_0^t\int_{-\infty}^{\infty}          \frac{p({v}|V)\Psi}{p'(V)}  \operatorname{d}x \operatorname{ d} t
\\
&+ \int_0^t\int_{-\infty}^{\infty}        W\frac{\Psi}{p'(V)}  \operatorname{d }x \operatorname{ d} t+\frac{1}{2}    \int_{-\infty}^{\infty}      \left(\phi^2-\frac{\Psi^2}{p'(V)}\right)\Big|_{t=0}   \operatorname{d }x =: \sum_{i=1}^4 A_i.
\label{4.12}\end{split}&
\end{align}
Utilize to Lemma \ref{lemma4.1}, we can get
\begin{align}
\begin{split}
&|A_1+A_2|\\
\leq& C \left(\int_0^t\int_{-\infty}^{\infty}   \left|  \phi_{xx}^{2} \phi \right| +  \left|    \phi_x \phi_{xx}  \phi\right|  +     \left| \Psi \phi_x^2 \right|  \operatorname{d}x \operatorname{d}t\right)\\
\leq& C \int_0^t    \|\phi\|_{\mathbb{L}^\infty}    \int_{-\infty}^{\infty}   \left|\phi_x^{2}+ \phi_{xx}^{2}  \right| \operatorname{d}x \operatorname{d}t+ C \int_0^t      \|\Psi\|_{\mathbb{L}^\infty}   \int_{-\infty}^{\infty}   \phi_x^2  \operatorname{d}x \operatorname{d}t\\
\leq&   C (\|\phi\|_{2}+  \|\psi\|_{1}   ) \int_0^t        \|\phi_x\|^2 +\|\phi_{xx}\|^2  \operatorname{  d}t\\
\leq & C \delta \int_0^t        \|\phi_x\|^2 +\|\phi_{xx}\|^2  \operatorname{  d}t.
\end{split}&
\end{align}
With the help of Lemma \ref{lemma4.2}, one has
\begin{align}
\begin{split}
|A_3|\leq& C  \int_0^t\int_{-\infty}^{\infty}      \left| W \Psi \right|  \operatorname{d}x\operatorname{d}t\leq C  \int_0^t     \|W\|   \|\Psi\|        \operatorname{d}t\leq  C  \delta     e^{-C_- \beta}.
\end{split}&
\label{4.14}\end{align}
Taking $\delta$  sufficient small, using (\ref{4.12})-(\ref{4.14}), we get Lemma \ref{lemma4.3}.
\end{proof}
\begin{lma}\label{lemma4.4}
Under the same assumptions of Proposition \ref{prposition3.1}, it holds that
\begin{eqnarray*}
\|(\phi,\Psi)(t)\|_{ 1}^2+\int_0^t\|  \phi_x  \|_{ 1}^2\operatorname{d}t\leq C_{ }\|(\phi_0,\Psi_0)\|_{ 1}^2 + C_{ } e^{-C_-\beta}.
\end{eqnarray*}
\end{lma}
\begin{proof}
Multiply $ (\ref{4.6})_1 $ and $  (\ref{4.6})_2 $ by $-\phi_{xx}$  and $\frac{\Psi_{xx}}{p'(V)}$, respectively and sum over the result, intergrade the result with  respect to $t$ and $x$ over $ [0,t]\times \mathbb{R}$. We have
\begin{align}
\begin{split}
& \frac{1}{2}  \int_{-\infty}^{\infty}  \left(\phi_x^2-\frac{\Psi_x^2}{p'(V)}\right)    \operatorname{d}x    + \int_0^t\int_{-\infty}^{\infty} \left\{ \frac{1}{2}  \left(\frac{1}{p'(V)}\right)_t\Psi_x^2    + \frac{\phi^2_{xx}}{V^{\alpha+1}} \right\}\operatorname{d}x\operatorname{d}t \\
=&\frac{1}{2}  \int_{-\infty}^{\infty}  \left(\phi_x^2-\frac{\Psi_x^2}{p'(V)}\right)\Big|_{t=0}    \operatorname{d}x  \\
&-\int_0^t\int_{-\infty}^{\infty}  \left[ G -(\alpha+1)\frac{V_x }{V^{\alpha+2}}  \phi_x \right]\phi_{xx}   \operatorname{d}x\operatorname{d}t  \\
 &-  \int_0^t\int_{-\infty}^{\infty}     \left(\frac{1}{p'(V)}\right)_{x}  p'(V) \Psi_{x} \phi_{x}  \operatorname{d}x\operatorname{d}t + \int_0^t\int_{-\infty}^{\infty}  \frac{\Psi_{x}W_{  x}}{p'(V)}  \operatorname{d}x\operatorname{d}t\\
  &+  \int_0^t\int_{-\infty}^{\infty}      \frac{1}{p'(V)} p(v|V)_{x}\Psi_{x} \operatorname{d}x\operatorname{d}t\\
   =:& \frac{1}{2}  \int_{-\infty}^{\infty}  \left(\phi_x^2-\frac{\Psi_x^2}{p'(V)}\right)\Big|_{t=0}    \operatorname{d}x +\sum_{i=1}^{4} B_i.
\end{split}&
\label{4.15}\end{align}{}
Now we estimate $B_i$ term by term. The Cauchy inequality indicates that
\begin{align}
\begin{split}
|B_1|&    \leq     C  \int_0^t\int_{-\infty}^{\infty}   (|\phi_{xx}\phi_x|+| \phi^{2}_x|)|{ \phi_{xx}}| +      | \phi_x     \phi_{xx} |               \operatorname{d}x\operatorname{d}t .\\
  &\leq (C \delta + \varepsilon )\int_0^t  \|\phi_{xx}\|^{2}  \operatorname{d}t  + C_{\varepsilon}   \int_0^t   \|\phi_{x}\|^2\operatorname{d}t,\\
\end{split}&
\end{align}
and
\begin{align}
\begin{split}
B_2  \leq&  \min(-s_1;s_2) \int_0^t \int_{-\infty}^{\infty}\left|\left(\frac{1}{4 p'(V)}\right)_x\right|\Psi_x ^2\operatorname{d}x\operatorname{d}t \\
&+ C\int_0^t\int_{-\infty}^{\infty}\left| \left(\frac{1}{ p'(V)}\right)_x [p'(V)]^2\right|\phi_x ^2\operatorname{d}x\operatorname{d}t\\
\leq& \int_0^t\int_{-\infty}^{\infty}\left(\frac{1}{4 p'(V)}\right)_t \Psi_x ^2\operatorname{d}x\operatorname{d}t +C \int_{0}^{t}   \|\phi_x\| ^2  \operatorname{d}t\\
\end{split}&
\label{4.17}\end{align}
The last inequality is base on the following inequality
\begin{align*}
\begin{split}
 \left(\frac{1}{p'({}{V})}\right)_t =& \left(p'({}{V})\right)^{-2} p''({}{V}) (-{}{V}_{1}'(-s_1)+{}{V}'_{2}( s_2))  \\
\geq&  \left(p'({}{V})\right)^{-2} p''({}{V}) |{}{V}_{x} | \min(-s_1; s_2) \\
=&\min(-s_1; s_2) \left|\left(\frac{1}{p'({}{V})}\right)_x\right|.
\end{split}&
\end{align*}
Making use of Lemma \ref{lemma4.2}, it follows that
\begin{align}
\begin{split}
|B_3|\leq \int_0^t\int_{-\infty}^{\infty}  \left| \frac{\Psi_{x}W_{  x}}{p'(V)}  \right|   \operatorname{d}x\operatorname{d}t \leq C  \int_0^t  \|W_{x}\|  \|\Psi_{x}\|   \operatorname{d}t \leq C \delta e^{-C_-\beta} .
\end{split}&
\end{align}
By $(\ref{s4.10})_{1}$ and the Sobolev inequality, we obtain
\begin{align}\label{4.19}
\begin{split}
|B_4|\leq & C\int_0^t\int_{0}^{\infty}     \left| (\phi_{x}\phi_{xx}+V_x\phi_{x}^{2}) \Psi_{x}       \right| \operatorname{d}x \operatorname{d} t    \\
\leq&   C\int_0^t\int_{0}^{\infty}     \left| (\phi_{x}\phi_{xx}+V_x\phi_{x}^{2}) \psi_{x}       \right|   \operatorname{d}x\operatorname{d} t   \\
& + C\int_0^t\int_{0}^{\infty}          \left| (\phi_{xx}\phi_{xx}+V_x\phi_{x}\phi_{xx} ) \phi_{x}       \right| \operatorname{d}x\operatorname{d} t \\
\leq&   C (\|\phi\|_{2}+  \|\psi\|_{2}   ) \int_0^t        \|\phi_x\|^2 +\|\phi_{xx}\|^2  \operatorname{  d}t \\
\leq&   C\delta \int_0^t    (\|\phi_{xx}\|^2+\|\phi_{x}\|^2 )    \operatorname{ d} t.
\end{split}
\end{align}
From (\ref{4.15})-(\ref{4.19}), we get
\begin{align*}
\begin{split}
& \frac{1}{2} \int_{-\infty}^{\infty}  \left(\phi_x^2-\frac{\Psi_x^2}{p'(V)}\right)    \operatorname{d}x+ \frac{1}{4}\int_0^t\int_{-\infty}^{\infty}    \left(\frac{1}{p'(V)}\right)_t\Psi_x^2\operatorname{d}x\operatorname{d}t  +\int_0^t\int_{-\infty}^{\infty}  \frac{\phi^2_{xx}}{V^{\alpha+1}} \operatorname{d}x\operatorname{d}t \\
\leq&  (C +C\delta+C_{\varepsilon} )\int_0^t   \|\phi_{x}\|^2 \operatorname{d}t
 +(C\delta+\varepsilon )\int_0^t     \|\phi_{xx}\|^2  \operatorname{d}t\\
& +  C_{ } e^{-C_-\beta}+C_{ }    \left(   \|\phi_{0x}\|^2   +\|\Psi_{0x}\|^2 \right)   .
\end{split}&
\end{align*}
Choosing  $\varepsilon$  appropriately small and $\delta$ sufficient small,   together with Lemma \ref{lemma4.3}, we get  the proof of Lemma \ref{lemma4.4}.
\end{proof}{}
\begin{lma}\label{lemma4.5}
Under the same assumptions of Proposition \ref{prposition3.1}, it holds that
\begin{eqnarray*}
\int_0^t    \|\Psi_{x}(t)\|_{  }^2   \operatorname{d}t  \leq   C  \|(\phi_0,\Psi_0)\|_{ 1}^2 +    C e^{-C_-\beta}.
\end{eqnarray*}
\end{lma}
\begin{proof}
Multiplying $(\ref{4.6})_1 $  by $\Psi_{x}$  and make use of $(\ref{4.6})_2$, we get
\begin{align}
\begin{split}
\Psi_{x}^{2}=&(\phi\Psi_{x})_{t}+\{\phi[ p(v)-p(V)+W]\}_{x}-\phi_{x} (p( v)-p({V}{}))\\
&-\frac{\Psi_{x}\phi_{xx}}{V^{\alpha+1}}-\phi_x W -\Psi_{x} G +(\alpha+1) \frac{V_x}{V^{\alpha+2}}\phi_x\Psi_{x} .
\label{4.20}
\end{split}&
\end{align}
Integrating $ (\ref{4.20})$ with  respect to $t$ and $x$ over $ [0,t]\times \mathbb{R} $, we obtain that
\begin{align}
\begin{split}
& \int_{0}^{t}\int_{-\infty}^{\infty}  \Psi_{x}^{2}  \operatorname{d}x\operatorname{d}t\\
=&-\int_{-\infty}^{\infty} \phi\Psi_{x}|_{t=0}\operatorname{d}x-\int_{0}^{t}\int_{-\infty}^{\infty} \Psi_{x} G  \operatorname{d}x\operatorname{d}t\\
&+    \int_{0}^{t}\int_{-\infty}^{\infty} (\alpha+1)\frac{V_x}{V^{\alpha+2}} \Psi_{x} \phi_x\operatorname{d}x\operatorname{d}t
+\int_{-\infty}^{\infty}\phi\Psi_{x}\operatorname{d}x\\
&-\int_{0}^{t}\int_{-\infty}^{\infty} \frac{\Psi_{x}\phi_{xx}}{V^{\alpha+1}}\operatorname{d}x\operatorname{d}t-\int_{0}^{t}\int_{-\infty}^{\infty}\phi_{x}\left(p(v)-p(V)\right)       \operatorname{d}x\operatorname{d}t\\
&-\int_{0}^{t}\int_{-\infty}^{\infty} \phi_{x}W       \operatorname{d}x\operatorname{d}t\\
=&-\int_{-\infty}^{\infty} \phi\Psi_{x}|_{t=0}\operatorname{d}x+\sum_{i=1}^6 H_i.
\end{split}&
\label{4.21}\end{align}
We estimate $H_i$ term by term. By the Cauchy inequality, it follows that
\begin{align}
\begin{split}
H_1&\leq C \int_{0}^{t}  \|\phi_{x}\|_{L^{\infty}}  \int_{-\infty}^{\infty}    \Psi_{x}(|\phi_{xx}|+  |\phi_{x}|)         \operatorname{d}x\operatorname{d}t\\
&\leq  \varepsilon \int_{0}^{t}  \|\Psi_{x}\|^{2}  \operatorname{d}t+ C_{\varepsilon} \int_{0}^{t}   ( \|\phi_{xx}\|^{2} + \|\phi_{x} \|^{2}   )      \operatorname{d}t,
\end{split}&
\end{align}
In addition, it is straightforward to imply that
\begin{align}
\begin{split}
&H_2+H_3+H_4+H_5\\
\leq &  \| (\phi^{}, \Psi_{x}) \|^{2}+\varepsilon\int_{0}^{t} \|\Psi_{x}\|^{2}\operatorname{  d}t+C_{\varepsilon}\int_{0}^{t}( \|\phi_{xx}\|^2       + \|\phi_{x}\|^2 )\operatorname{  d}t.
\label{c4}\end{split}&
\end{align}
Making use of Lemma \ref{lemma4.2}, we have
\begin{align}
\begin{split}
H_6&=\int_{0}^{t}\int_{-\infty}^{\infty}\phi_{x}W       \operatorname{d}x\operatorname{d}t \leq  \int_{0}^{t}  \| W\|       \|\phi_{x}\|      \operatorname{d}t
\leq C \delta e^{- C_-\beta}.
\label{4.24}
\end{split}&
\end{align}
Collecting   (\ref{4.21})-(\ref{4.24}) and using Lemma \ref{lemma4.4}, we get the Lemma \ref{lemma4.5}.
\end{proof}
Combining Lemma \ref{lemma4.3}-Lemma \ref{lemma4.5}, we  obtain the following low order estimates
\begin{align*}
\|(\phi,\Psi)\|_{ 1}^2(t)+ \int_0^t  \| \Psi_x\|^2  \operatorname{d}t+\int_0^t \| \phi_x\|_{1}^2 \operatorname{d}t\leq C_{}\|(\phi_0,\Psi_0)\|_{ 1}^2 + C_{} e^{-C_-\beta},
\end{align*}
with the help of $(\ref{s4.09})$, which can be rewritten by the variables $\phi$ and $\psi$ as
\begin{lma}\label{lemma4.6}
Under the same assumptions of Proposition \ref{prposition3.1}, it holds that
\begin{align*}
\begin{split}
&(\| \phi \|_{ 1}^2 + \| \psi \| ^2)(t)+\int_0^t  \| \psi_x\|^2  \operatorname{d}t+\int_0^t \| \phi_x\|_{1}^2 \operatorname{d}t\leq C_{}\|     \phi_0 \|_{2}^2 +C_{}\| \psi_0 \|_{ 1}^2 + C_{} e^{-C_-\beta}.
\end{split}
\end{align*}
\end{lma}
\subsection{High Order Estimate.}
We turn to the original equation \eqref{3.3} to study the higher order estimates.
\begin{lma}\label{lemma4.7}
Under the same assumptions of Proposition \ref{prposition3.1}, it holds that
\begin{align}\label{4.25}
\begin{split}
&  \| \psi_{x} \|  ^2 (t)  +\int_0^t  \| \psi_{xx}\| ^2  \operatorname{d}t\leq C_{}\|     \phi_0 \|_{2}^2 +C_{}\| \psi_0 \|_{ 1}^2 + C_{} e^{-C_-\beta}.
\end{split}
\end{align}
\end{lma}
\begin{proof}  Multiplying   $(\ref{3.3})_{2}$ by $-\psi_{x x}$,  integrating the result with  respect to $t$ and $x$ over $ [0,t]\times \mathbb{R} $ gives
\begin{align}\label{4.26}
\begin{split}
&   \frac{1}{2}\| \psi_{x}\|^{2}  (t)
+\int_{0}^{t}\int_{-\infty}^{\infty} \frac{{\psi_{x x}^{2}}}{V^{\alpha+1}} \operatorname{d}x \operatorname{d}t \\
=&\frac{1}{2}\| \psi_{0x}\|^{2} +\int_{0}^{t}\int_{-\infty}^{\infty} W \psi_{x x} \operatorname{d}x \operatorname{d}t\\
&-\int_{0}^{t}\int_{-\infty}^{\infty} f(V,U_x) \phi_{x} \psi_{x x} \operatorname{d}x \operatorname{d}t   -\int_{0}^{t}\int_{-\infty}^{\infty} F \psi_{x x} \operatorname{d}x \operatorname{d}t
   \\
=:&\frac{1}{2}\| \psi_{0x}\|^{2} +\sum_{i=1}^3 M_i.
\end{split}
\end{align}
Making use of Lemma \ref{lemma4.2}, we have
\begin{align} \label{4.27}
\begin{split}
M_{1}  &\leq \varepsilon \int_{0}^{t} \|\psi_{x x}\|^{2}\operatorname{  d}t+ C_{\varepsilon}\int_{0}^{t}  \|W\|^{2}\operatorname{  d}t. \\
 &\leq \varepsilon \int_{0}^{t} \|\psi_{x x}\|^{2}\operatorname{  d}t+  C_{} e^{-C_-\beta}.
\end{split}
\end{align}
The Cauchy inequality implies that
\begin{align}\label{4.28}
M_{2}  \leq \varepsilon \int_{0}^{t} \|\psi_{x x}\|^{2}\operatorname{  d}t+ C_{\varepsilon}\int_{0}^{t}  \|\phi_{x}\|^{2}\operatorname{  d}t.
\end{align}
By $(\ref{s4.08})_{1}$ and the Sobolev inequality, yields
\begin{align} \label{4.29}
\begin{split}
M_{3} &\leq C \int_{0}^{t}\int_{-\infty}^{\infty}\left(\left|\phi_{x}\right|^{2}  +\left|\phi_{x}\right|\left|\psi_{x x}\right|\right)\left|\psi_{x x}\right| \operatorname{d} x \operatorname{d}t \\
&\leq C \int_{0}^{t}\int_{-\infty}^{\infty}\left|\phi_{x}\right|\left(\left|\phi_{x}\right|^{2}+\left|\psi_{x x}\right|^{2}\right) \operatorname{d}x\operatorname{d}t   \\
&\leq C   \delta \int_{0}^{t} \left(\left\|\phi_{x}\right\|^{2}+\left\|\psi_{x x}\right\|^{2}\right) \operatorname{  d}t.
\end{split}
\end{align}
Substituting (\ref{4.27})-(\ref{4.29})  into $(\ref{4.26}) $ and using Lemma \ref{lemma4.6}, we obtain (\ref{4.25}).
\end{proof}
\begin{lma}\label{lemma4.8}
Under the same assumptions of Proposition \ref{prposition3.1}, it holds that
\begin{align}\label{4.30}
\begin{split}
&\| \phi_{xx} \| ^2   +\int_0^t  \| \phi_{xx}\|_{}^2  \operatorname{d}t \leq C_{}\|     \phi_0 \|_{2}^2 +C_{}\| \psi_0 \|_{ 1}^2 + C_{} e^{-C_-\beta}+ C\delta \int_{0}^{t}\left\|\psi_{xx x} \right\|^2  \operatorname{d}t.
\end{split}
\end{align}
\end{lma}

\begin{proof}
 Differentiating    $(\ref{3.3})_{1}$ with  respect to $x$,  using  $(\ref{3.3})_{2}, $ we have
\begin{align}\label{4.31}
\begin{split}
\frac{  \phi_{x t}}{V^{\alpha+1}}+f(V,U_x) \phi_{x}=\psi_{t}-F+W.
\end{split}
 \end{align}
Differentiating    $(\ref{4.31})$ in respect of $x$ and multiplying  the derivative  by $\phi_{x x}$,  integrating the result in respect of $t$ and $x$ over $ [0,t]\times \mathbb{R} $, using (\ref{2.3}), one has
\begin{align} \label{4.32}
\begin{split}
 &\frac{1}{2} \int_{-\infty}^{\infty}  \frac{ \phi_{x x}^{2}}{  V^{  \alpha+1  }}  \operatorname{d  }x
 +\int_{0}^{t}\int_{-\infty}^{\infty}\left(f(V,U_x)+  \frac{\alpha+1}{2} \frac{  U_x  }{ V^{\alpha+2}}\right) \phi_{x x}^{2}\operatorname{d}x \operatorname{d}t  \\
 =& \frac{1}{2} \int_{-\infty}^{\infty}  \frac{ \phi_{x x}^{2}}{  V^{  \alpha+1  }}  \Big|_{t=0}\operatorname{d  }x-\int_{-\infty}^{\infty}   \psi_{x } \phi_{x x}    \Big|_{t=0}\operatorname{d  }x+\int_{-\infty}^{\infty}   \psi_{x } \phi_{x x}   \operatorname{d  }x  \\
&+\int_{0}^{t}\int_{-\infty}^{\infty}W_{x}\phi_{x x}\operatorname{d}x\operatorname{d}t
+\int_{0}^{t}        \| \psi_{x x}\|^{2}\operatorname{    d}t-\int_{0}^{t}\int_{-\infty}^{\infty}F_{x} \phi_{x x}\operatorname{d}x\operatorname{d}t
  \\
&+(\alpha+1)\int_{0}^{t}\int_{-\infty}^{\infty}\frac{{} V_{x}}{V^{\alpha+2}} \psi_{x x} \phi_{x x}\operatorname{d}x\operatorname{d}t-\int_{0}^{t}\int_{-\infty}^{\infty}f(V,U_x)_{x} \phi_{x} \phi_{x x}\operatorname{d}x\operatorname{d}t   \\
=:&\frac{1}{2} \int_{-\infty}^{\infty}  \frac{ \phi_{x x}^{2}}{  V^{  \alpha+1  }}  \Big|_{t=0}\operatorname{d }x-\int_{-\infty}^{\infty}   \psi_{x } \phi_{x x}    \Big|_{t=0}\operatorname{d  }x+\sum_{i=1}^6 N_i.
\end{split}
\end{align}
By $U_x<0$ and (\ref{3.5}), one has
\begin{align} \label{4.33}
\begin{split}
&f(V,U_x)+  \frac{\alpha+1}{2} \frac{  U_x  }{ V^{\alpha+2}}\\
=&-p'(V )-  \frac{\alpha+1}{2} \frac{  U_x  }{ V^{\alpha+2}}\geq - \max \{p'(v_-),p'(v_+)\}>0.
\end{split}
\end{align}
The Cauchy inequality yields
\begin{align}
N_{1}\leq  \varepsilon  \|\phi_{x x}\|^{2}   +C_\varepsilon    \|\psi_{x }\|  ^{2}.
\end{align}
 Similar to (\ref{4.27}), we get
\begin{align}
N_{2}  \leq \varepsilon       \int_{0}^{t} \|\phi_{x x}\|^{2} \operatorname{  d}t    +C_\varepsilon   e^{-C_-\beta}.
\end{align}
$ N_{3}  $ can be controlled by (\ref{4.25}). Using  $(\ref{s4.08})_{2}$, and Cauchy inequality,   we have
\begin{align*}
\begin{split}
|N_{4}| \leq &  \varepsilon \int_{0}^{t}  \|\phi_{x x}\|^{2} \operatorname{  d}t  +    C_{\varepsilon}   \int_{0}^{t}\left\|F_{ x}\right\|^{2} \operatorname{  d}t. \\
\leq &  \varepsilon \int_{0}^{t}  \|\phi_{x x}\|^{2} \operatorname{  d}t  +  C_{\varepsilon}  \delta     \int_{0}^{t}  \left(\left\|\phi_{x}\right\|_{1}^{2}+\left\|\psi_{x}\right\|_{2}^{2}\right)\operatorname{  d}t.
\end{split}
\end{align*}
The Cauchy inequality yields
\begin{align}
\begin{split}
|N_{5}| \leq C & \int_{0}^{t}\int_{-\infty}^{\infty} \left|\frac{{} V_{x}}{V^{\alpha+2}} \psi_{x x} \phi_{x x}\right| \operatorname{d}x \operatorname{d}t\leq \varepsilon \int_{0}^{t}  \|\phi_{x x}\|^{2} \operatorname{  d}t  +    C_{\varepsilon}   \int_{0}^{t}\left\|\psi_{x x}\right\|^{2} \operatorname{  d}t.
\end{split}
\end{align}
With the help of
$$f(V,U_x)_{x}= -p^{\prime\prime}(V)V_{x}    - (\alpha+1)\frac{{} U_{xx}}{V^{\alpha+2}}   + (\alpha+1)(\alpha+2)\frac{{} U_{x}}{V^{\alpha+3}}V_{x}   < C, $$
one gets
\begin{align} \label{4.38}
\begin{split}
|N_{6}| \leq &  \varepsilon \int_{0}^{t}  \|\phi_{x x}\|^{2} \operatorname{  d}t  +    C_{\varepsilon}   \int_{0}^{t}\left\|\phi_{ x}\right\|^{2} \operatorname{  d}t. \\
\end{split}
\end{align}
Choosing  $\varepsilon$  small,  substituting  (\ref{4.33})-(\ref{4.38})  into (\ref{4.32})   and  using  Lemma \ref{lemma4.6}, Lemma \ref{lemma4.7},    we have (\ref{4.30}).
\end{proof}

On the other hand, differentiating the second equation of (\ref{3.3}) with respect to $x$, multiplying the derivative by $-\psi_{x x x}$, integrating the resulting equality over $[0, \infty)  \mathbb{\times}[0, t]$, using Lemma \ref{lemma4.6}-Lemma \ref{lemma4.8}, we can get the highest order estimate in the same way, which is listed as follows  and the proof is omitted.

\begin{lma}\label{lemma4.9}
Under the same assumptions of Proposition \ref{prposition3.1}, it holds that
\begin{align}\label{4.39}
\begin{split}
&  \| \psi_{xx} (t)\| ^2+\int_0^t  \| \psi_{xxx}\| ^2  \operatorname{d}t \leq   C_{}\|   (  \phi_0 , \psi_0 )\|_{ 2}^2 + C_{} e^{-C_-\beta} .
\end{split}
\end{align}
\end{lma}
Finally, Proposition \ref{prposition3.1} is obtained by Lemma \ref{lemma4.5}-Lemma \ref{lemma4.9}.
\section{Proof of Theorem \ref{theorem}}\label{section5}
It is straightforward to imply   (\ref{2.13}) from  Lemma  \ref{lemma3.1}. It remains to show (\ref{2.14}). The following useful lemma will be used.
\begin{lma}(\cite{mn1985})\label{lemma5.1}
Assume that the function $f(t) \geq 0\in \mathbb{L}^1(0, +\infty) \cap  \mathbb{BV}(0, +\infty) $, then it holds that $f(t) \rightarrow0$ as $t \rightarrow \infty$.
\end{lma}
Let us turn to the system   (\ref{3.3}). Differentiating  (\ref{3.3})$_1$   with respect to $x$, multiplying the
resulting equation by $\phi_{  x}$ and integrating it with respect to $ { x}$ on $(-\infty,\infty)$, we have
\begin{equation*}
 \left|\frac{\operatorname{d}}{\operatorname{d}t}\left(\|\phi_{ x}\|^{2}\right)\right|\leq C(\|\phi_{x}\|^{2} +\|\psi_{xx}\|^{2})  .
\end{equation*}
With the aid of Lemma  {\ref{lemma3.1}}, we have
\begin{equation*}
\int_{-\infty}^{\infty} \left|\frac{\operatorname{d}}{\operatorname{d}t}\left(\|\phi_{xx}\|^{2}\right)\right| \operatorname{d}t \leq C,
\end{equation*}
which implies $\|\phi_{ x}\|^{2}\in \mathbb{L}^1(0, +\infty) \cap  \mathbb{BV}(0, +\infty)$. By Lemma \ref{lemma5.1}, we have
 \begin{equation*}
    \|\phi_{ x}\|\rightarrow0 \quad   \text{as} \quad   t\rightarrow+\infty.
 \end{equation*}
Since $\|\phi_{xx}\|$ is bounded, the Sobolev inequality implies that
 \begin{eqnarray*}
 \|{}{v}-V\|_{\infty}^{2}=\|\phi_{x}\|_{\infty}^{2} \leq 2\| \phi_{x}(t)\|_{}   \| \phi_{xx}(t)\|_{} \rightarrow  0.
\end{eqnarray*}
 Similarly, we have
 \begin{eqnarray*}
 \|{}{u}-U\|_{\infty}^{2}=\|\psi_{x}\|_{\infty}^{2} \leq 2\| \psi_{x}(t)\|_{}   \| \psi_{xx}(t)\|_{} \rightarrow  0.
\end{eqnarray*}
Therefore, the proof of Theorem \ref{theorem} is completed.

redpajama_set_name: RedPajamaArXiv


text:
Fifa 22 With License Key Product Key Full
The power of the HyperMotion-enabled engine has been developed to provide the most accurate and immersive football experience. It also allows you to take a peek behind the scenes at how ball and body mechanics drive the player's decisions at every level of the game.
Fifa 22 Product Key delivers the best-in-class gameplay on the market and is available on Xbox One, PlayStation 4 and PC.// (C) Copyright John Maddock 2015.
// Use, modification and distribution are subject to the
// Boost Software License, Version 1.0. (See accompanying file
// LICENSE_1_0.txt or copy at
#ifndef BOOST_MATH_COMPLEX_ACOSH_INCLUDED
#define BOOST_MATH_COMPLEX_ACOSH_INCLUDED
#ifndef BOOST_MATH_COMPLEX_DETAILS_INCLUDED
# include
#ifndef BOOST_MATH_COMPLEX_ASINH_INCLUDED
#ifndef BOOST_MATH_COMPLEX_ATANH_INCLUDED
#ifndef BOOST_MATH_COMPLEX_ACOTH_INCLUDED
#endif // BOOST_MATH_COMPLEX_ACOSH_INCLUDED
How to make a git alias to manage a submodule and not checkout to submodule dir
I have a git repo with many submodules which is generated by an Ant script. This is the content of my.gitmodules file:
[submodule "test"] path = test
This is the content of my.git/config file (let's call it myproj, test is a submodule of mypro
Fifa 22 Features Key:
Authentic Real Players – Authentic teams from across the globe become realities as you collect, create, and progress with 22 of the world's best football clubs, packed with new and returning superstars, legends and club greats from across the history of the game. Whether you play as a club or build your squad from the world's most talented players, you'll always feel like you are playing as who you know.
Master Your Gameplay – New ways to play on and off the pitch through Immersive Commentary, All-New Kicking System, Full Touch Revamp, and Tactical Defending. The highly enhanced gameplay is powered by new prototypes that will change the way the ball moves on the pitch, react to your every touch, and adjust to every move you make as you take on the tactics of the world's finest.
New Career Mode – A more immersive experience that connects you with your clubs, gives you tools to build and shape your identity, and makes every off-the-pitch action as impactful as it is on the pitch, with more options to catch every key development stage of a club's life.
New Formation System – No longer are the formations set in stone. Create a formation and assign where players should line up as you design your tactics off the pitch. Play to your strengths and counter-balance an on-ball midfielder or a striker as on defense to capitalize on a dangerous winger.
New Player Ratings – Player ratings provide a more true-to-life estimation of a player's performance. Every skill, attribute, and overall performance rating is directly calculated from game data at the time of performance.
FIFA TV Enhanced – Watch live matches, access content across all platforms, and see how coaches do things in-game. FIFA TV also significantly reduces loading times.
Dynamic Ultimate Team Carousel – Invite new friends to join your squad, then keep the squad together with a broad range of options that support both the legendary collectables and fan-favorite superstars.
International Team of The Year – Choose from all the stars of the top leagues including Brazil, Mexico, Germany, France, Italy, Spain and more, and play three different games to prove yourself one of the best Soccer teams in the world.
Fifa 22 License Key
#FIFA
FIFA (from "FOOTBALL") is a series of sports video games that was developed by EA Canada, published by Electronic Arts and distributed by EA Sports. The series centers on the sport of association football and its amateur and professional versions.
Originally released in September of 1993 on the Nintendo Entertainment System (NES), the game eventually spread to other systems, including the Sega Genesis, Mega Drive, the Sega CD, Nintendo GameCube, the PlayStation, PlayStation 2, Xbox and Xbox 360, and the Nintendo 3DS and PlayStation Vita. There have also been numerous mobile versions released.
The series would eventually mature to adapt the sport in a more realistic manner, with greater attention paid to the tactics and strategy of the game. The latest entry is FIFA 19. The FIFA series of video games was originally developed by EA Canada, and is published by Electronic Arts. The FIFA series of video games was originally developed by EA Canada, and is published by Electronic Arts. The original series introduced players to the sport of association football in the mid-1980s. It was primarily available for home consoles and the PC by 1995. The series would eventually mature to adapt the sport in a more realistic manner, with greater attention paid to the tactics and strategy of the game. The latest entry is FIFA 19.
At the very beginning
The very first edition, titled simply FIFA, was released on the Nintendo Entertainment System (NES) in North America on September 26, 1993. In Europe, it was released on the same day as an official rival to Nintendo's Super Mario Bros. The game was developed by EA Canada and published by Electronic Arts.
The very first edition, titled simply FIFA, was released on the Nintendo Entertainment System (NES) in North America on September 26, 1993. In Europe, it was released on the same day as an official rival to Nintendo's Super Mario Bros. The game was developed by EA Canada and published by Electronic Arts. The very first edition, titled simply FIFA, was released on the Nintendo Entertainment System (NES) in North America on September 26, 1993. In Europe, it was released on the same day as an official rival to Nintendo's Super Mario Bros. The game was developed by EA Canada and published by Electronic Arts.
The very first edition, titled simply FIFA, was released on the Nintendo Entertainment System (NES) in North America on September 26, 1993. In Europe, it was released on the
bc9d6d6daa
Fifa 22 Crack + Download [32|64bit] [Latest-2022]
The #1 FIFA videogame franchise is back in FIFA 22 with numerous new features and improvements to enhance your experience from club selection, customisation, and visual upgrades. Ultimate Team is back and better than ever! Now you can construct your Ultimate Team from scratch and customise unique items and set up builds that put you in the best position to win any match. The new Quick Bar gives you the most relevant settings and options in seconds, including the new contextual loadouts.
Collect and build your Ultimate Team to form an unstoppable force for either the CPU or your friends in Live Leagues, and compete online in the all-new International Friendly Leagues. Play with your friends in Skirmish Matches against the CPU or your friends, or jump into Quick Matches at any time.
FIFA 22 is the most realistic football experience on consoles. Enjoy authentic gameplay that combines everything you love about the beautiful game, with improved skill moves, contextual loadouts, and Dynamic Trajectory Control. Match the control you are used to in FIFA with an all-new control scheme that brings the ball to you with more accuracy and control.
Discover a smarter AI in new areas of the pitch, and improved technology for goalkeepers. Enjoy the most detailed and immersive gameplay on consoles.
• A smarter AI. Highly responsive AI brings the ball to you with intelligence, control, and accuracy.
• Brand new Free Kick system. Choose where to strike from, the angle, and when to strike through the run of play and set-up. Free Kicks are the most challenging skill moves in FIFA.
• An all-new control scheme. Enjoy the most accurate, responsive ball control in football on consoles.
• Improved team and player intelligence. An all-new real-time physics engine and new transfer system give you more freedom to play as you want.
• A brand-new game world. An all-new mesh deformation engine delivers a more balanced, realistic, and responsive game experience.
• Beautiful new visuals. Enjoy the most detailed, authentic, and beautiful game world on consoles.
• New player animations. Enjoy more movement and improved facial expressions.
• Enhanced player animations. Enjoy more realistic player emotions as they learn, and react to the situation.
• Improved ball physics. Enjoy more natural ball behaviour, which reacts to the changing dynamics of play.
• More player faces. Enjoy more facial expression to add to the authenticity of every player.
• New player animations.
FIFA 22 introduces "HyperMotion Technology," which uses motion capture data collected from 22 real-life players playing a complete, high-intensity football match in motion capture suits. The data collected from player movements, tackles, aerial duels and on-ball actions is used to power FIFA 22 gameplay.
Career Mode – Live out your dreams as both a manager and a player in FIFA 22. Create the newest club in FIFA, design your kits, style your stadium, and choose whether to compete with the elite or rise up from the lower divisions as you manage your club to glory. Or test your skills as a player, with a more immersive Player Career mode that gives you more ways to progress, achieve, and immerse yourself in your Pro's journey through the game.
Tackling has been reworked in a number of areas: the ability to slide tackles now allows you to knock the ball out of the flight path and into the path of your man; while the 'personal foul' system has been improved to encourage more aggressive, rucking and foul-mauling gameplay.
Recent match engine improvements feature a more dynamic camera motion; closer and more organic camera movements; and match officials responding more intelligently to the game situation via crowd noise, referee report, and referees' view.
Carriers and one-twos have been overhauled and more emphasis has been placed on skillful, compact passing.
FIFA World Cup™ re-spawns have been reworked to make them feel more authentic, responding to the new ball, certain tactics and the changing playing conditions; while dressing rooms, semi-transparent crowd levels, sun-glare effects and 360-degree stadium views were added to FIFA's re-spawn re-working.
See yourself as an amateur and a young pro on new versions of the clubs section; and walk in your former managers' shoes to experience their experiences and emotions on the touchline, on the sidelines, and in the dugout.
Introducing the first player ratings system to be seen in any major football game. Each of the more than 260 FIFA classifications has a new numerical rating between 0 and 100, making every player more unique than ever and driving endless debate. Revisit the stats pages
Free Fifa 22 With Key
FIFA is one of the most influential sports games of all time, winning countless awards over the past 30 years and leading the sports gaming revolution on the PS2, Xbox, PC and now PS4.
The reveal trailer for FIFA 25 was just released by EA, watch it here.
With the most sweeping changes in the series' history, FIFA 25 introduces a deeper, more authentic, more interconnected story mode. All 25 FIFA World Cups – from 1930 to 2030 – are included. Players will build their careers by stepping into the shoes of the biggest legends in the game.
FIFA 25 is the first title in EA SPORTS' FIFA franchise to support cross-platform play, allowing players to take their games on the road or play online with friends. FIFA 25 also includes Career Mode, a new Ultimate Team™ mode, and new ways to play online with friends through co-op and online multiplayer.
In Career Mode, players will take control of their own player journey through the chronologically ordered history of the FIFA World Cup™. Players can now edit their profile and select their nationality, goalscoring system and goalkeepers.
From new stadiums to the introduction of substitutes, to adjustments to how players create and execute skill moves – FIFA 25 changes the way players can play and compete.
The World Cup is a global experience unlike any other, with all 35 hosts – from Argentina to Uruguay – receiving FIFA World Cup Points. FIFA 25 is the first title in the history of the series to be broadcast to over 1.4 billion television viewers.
Live tournaments will be even more important than ever as players compete in a new Overtime system. Overtime will be activated when there is still time on the clock and is played over multiple minutes and ends when a team scores. Overtime will be seen on the pitch during the match, and live commentators will call the action.
The World Cup app is live and updated for iOS and Android. As part of the game, players can receive World Cup updates and World Cup news on social media.
The Three Lions – The most famous on-field play
The Three Lions, the English national team, is making its return to the FIFA World Cup™ after four years, and fans will play in iconic stadiums across the globe in FIFA 25.
A new World Cup Experience will take place in all 20 selected host stadiums. Fan experiences will be further enhanced with new access points
How To Crack:
Unzip it to your hard drive
Go to the directory and run the game
OS: Windows 7 or above
Processor: Any Processor 1.5 GHz or greater (2.5 GHz recommended)
Hard Drive: 1GB free space
Graphics Card: DirectX9
OS: Windows 10 or above
Processor: Any Processor 2.5 GHz or greater (4 GHz recommended)
https://buycoffeemugs.com/fifa-22-keygen-crack-serial-key-with-product-key-download/
https://over-the-blues.com/advert/fifa-22-keygen-x64/
http://hoverboardndrones.com/?p=27352
http://mysteriesoftheunknown.com/wp-content/uploads/2022/07/Fifa_22_Crack_File_Only__Free_Final_2022.pdf
https://rosaedu.com/fifa-22-crack-exe-file-keygen-free-download/
https://progressivehealthcareindia.com/2022/07/05/fifa-22-keygen-only-registration-code-free-download/
https://survivalistprepping.com/diet/fifa-22-keygen-exe-serial-number-full-torrent/
https://biodashofficial.com/fifa-22-keygenerator/
https://earthoceanandairtravel.com/2022/07/05/fifa-22-hacked-free-download-2/
https://ibipti.com/fifa-22-keygen-crack-setup-win-mac/
https://towntexas.com/wp-content/uploads/2022/07/Fifa_22-23.pdf
https://lutce.ru/wp-content/uploads/2022/07/fifa_22-22.pdf
https://kintarocapital.com/wp-content/uploads/2022/07/Fifa_22_Keygen__With_Product_Key_Download_Updated2022-1.pdf
https://loutechperu.com/wp-content/uploads/2022/07/Fifa_22_Hacked___Keygen_For_LifeTime_PCWindows_April2022.pdf
http://gobigup.com/?p=16776
https://in-loving-memory.online/fifa-22-registration-code-x64-march-2022/
https://versiis.com/41259/fifa-22-free-3264bit-2022-latest/
https://guaraparadise.com/2022/07/05/fifa-22-crack-keygen-serial-number-full-torrent-mac-win-updated-2022/
https://nelsonescobar.site/fifa-22-product-key-and-xforce-keygen-3264bit-2022/
https://silkfromvietnam.com/fifa-22-serial-key-incl-product-key-x64/
This entry was posted in Uncategorized and tagged Fifa 22.
Fifa 22 Nulled Full Product Key PC/Windows 🔆
Fifa 22 Crack Mega License Code & Keygen Free Download [April-2022]


text:
Q: Threading with subprocess I am using python 2.7 and new to Threading. I got a class file and run method. But I don't see the run method invoked when I create instances of thread. I am also planning to use subprocess.Popen inside the run method and get stdout of the process for each filename and print the output.
Please tell me what I am missing here for run method to be called.
class FileScanThread(threading.Thread):
    def __init__(self, myFileName):
        print("In File Scan Thread")
        self.mapFile = myFileName
        #myjar=myFileName
        self.start()

    def run(self):
        print self.mapFile

  x= FileScanThread("myfile.txt")

A: you're forgetting to call the mother class constructor to specify target. It's not java, and run has no particular meaning. By default, target is None and the thread does nothing.
import threading

class FileScanThread(threading.Thread):
    def __init__(self, myFileName):
        threading.Thread.__init__(self,target=self.run)
        # another syntax uses "super", which is simpler in python 3
        # super().__init__(target=self.run)

        print("In File Scan Thread")
        self.mapFile = myFileName
        #myjar=myFileName
        self.start()

    def run(self):
        print(self.mapFile)

x= FileScanThread("myfile.txt")

x.join()  # when you're done

A: This will do what you want. You aren't calling __init__ from the class Thread.
class FileScanThread(threading.Thread):
    def __init__(self, myFileName):
        threading.Thread.__init__(self)
        print("In File Scan Thread")
        self.mapFile = myFileName
        #myjar=myFileName
        self.start()

    def run(self):
        print self.mapFile

x = FileScanThread("myfile.txt")

I don't think you have to pass target argument to it. At least that's not usually how I do it.
Output:
In File Scan Thread
myfile.txt

redpajama_set_name: RedPajamaStackExchange


text: <manifest package="com.commonsense.android.kotlin.views" />

redpajama_set_name: RedPajamaGithub


text:
// Copyright (c) 2011-present, Facebook, Inc.  All rights reserved.
//  This source code is licensed under both the GPLv2 (found in the
//  COPYING file in the root directory) and Apache 2.0 License
//  (found in the LICENSE.Apache file in the root directory).

package org.rocksdb;

/**
 * Options for Compression
 */
public class CompressionOptions extends RocksObject {

  public CompressionOptions() {
    super(newCompressionOptions());
  }

  public CompressionOptions setWindowBits(final int windowBits) {
    setWindowBits(nativeHandle_, windowBits);
    return this;
  }

  public int windowBits() {
    return windowBits(nativeHandle_);
  }

  public CompressionOptions setLevel(final int level) {
    setLevel(nativeHandle_, level);
    return this;
  }

  public int level() {
    return level(nativeHandle_);
  }

  public CompressionOptions setStrategy(final int strategy) {
    setStrategy(nativeHandle_, strategy);
    return this;
  }

  public int strategy() {
    return strategy(nativeHandle_);
  }

  /**
   * Maximum size of dictionary used to prime the compression library. Currently
   * this dictionary will be constructed by sampling the first output file in a
   * subcompaction when the target level is bottommost. This dictionary will be
   * loaded into the compression library before compressing/uncompressing each
   * data block of subsequent files in the subcompaction. Effectively, this
   * improves compression ratios when there are repetitions across data blocks.
   *
   * A value of 0 indicates the feature is disabled.
   *
   * Default: 0.
   *
   * @param maxDictBytes Maximum bytes to use for the dictionary
   *
   * @return the reference to the current options
   */
  public CompressionOptions setMaxDictBytes(final int maxDictBytes) {
    setMaxDictBytes(nativeHandle_, maxDictBytes);
    return this;
  }

  /**
   * Maximum size of dictionary used to prime the compression library.
   *
   * @return The maximum bytes to use for the dictionary
   */
  public int maxDictBytes() {
    return maxDictBytes(nativeHandle_);
  }

  /**
   * Maximum size of training data passed to zstd's dictionary trainer. Using
   * zstd's dictionary trainer can achieve even better compression ratio
   * improvements than using {@link #setMaxDictBytes(int)} alone.
   *
   * The training data will be used to generate a dictionary
   * of {@link #maxDictBytes()}.
   *
   * Default: 0.
   *
   * @param zstdMaxTrainBytes Maximum bytes to use for training ZStd.
   *
   * @return the reference to the current options
   */
  public CompressionOptions setZStdMaxTrainBytes(final int zstdMaxTrainBytes) {
    setZstdMaxTrainBytes(nativeHandle_, zstdMaxTrainBytes);
    return this;
  }

  /**
   * Maximum size of training data passed to zstd's dictionary trainer.
   *
   * @return Maximum bytes to use for training ZStd
   */
  public int zstdMaxTrainBytes() {
    return zstdMaxTrainBytes(nativeHandle_);
  }

  /**
   * When the compression options are set by the user, it will be set to "true".
   * For bottommost_compression_opts, to enable it, user must set enabled=true.
   * Otherwise, bottommost compression will use compression_opts as default
   * compression options.
   *
   * For compression_opts, if compression_opts.enabled=false, it is still
   * used as compression options for compression process.
   *
   * Default: false.
   *
   * @param enabled true to use these compression options
   *     for the bottommost_compression_opts, false otherwise
   *
   * @return the reference to the current options
   */
  public CompressionOptions setEnabled(final boolean enabled) {
    setEnabled(nativeHandle_, enabled);
    return this;
  }

  /**
   * Determine whether these compression options
   * are used for the bottommost_compression_opts.
   *
   * @return true if these compression options are used
   *     for the bottommost_compression_opts, false otherwise
   */
  public boolean enabled() {
    return enabled(nativeHandle_);
  }

  private native static long newCompressionOptions();
  @Override protected final native void disposeInternal(final long handle);

  private native void setWindowBits(final long handle, final int windowBits);
  private native int windowBits(final long handle);
  private native void setLevel(final long handle, final int level);
  private native int level(final long handle);
  private native void setStrategy(final long handle, final int strategy);
  private native int strategy(final long handle);
  private native void setMaxDictBytes(final long handle, final int maxDictBytes);
  private native int maxDictBytes(final long handle);
  private native void setZstdMaxTrainBytes(final long handle,
      final int zstdMaxTrainBytes);
  private native int zstdMaxTrainBytes(final long handle);
  private native void setEnabled(final long handle, final boolean enabled);
  private native boolean enabled(final long handle);
}


We provide cost-effective, satellite-based voice communication and data transfer services for the commercial fishing and related marine industries.
STS SeaMail is the most efficient way to access your email account and Internet data while on the water or in remote locations. STS SeaMail is based on the original, proven compression algorithm. It is simply the fastest, easiest-to-use and most reliable satellite phone email available, saving you time, money and frustration.
STS SeaMail + the OPTIMIZER is the best solution available for Internet connectivity. Sophisticated data compression saves you expensive connect time. OPTIMIZER transfers data via local Wi-Fi enabled devices - instantly!
You can't always be next to your radio. The compact CallerId unit keeps a record of calls - number & time of call - while you're away from your radio.
DialPad Plus is a direct replacement for Hughes G2 mic systems. Adds ease of use plus other features over a regular mic.
We offer enhanced Iridium and Inmarsat satellite services thru Pivotel. Sign up with Pivotel for special promotions.
View video of STS/Satellite West products and services in action in Alaska.


Got a new laptop? Windows 10 includes some wonderful features along with a revamped interface for Microsoft's operating system. No matter how experienced you are with Windows, you still may need help getting used to this, so let's get you started.
If something goes wrong with your laptop, you can save a lot of time and hassle if you have a "restore point," which is like a backup of your entire operating system. To set up a restore point, search for "restore" from the taskbar and click Create a restore point. You'll be taken to the System Protection tab of the System Properties window.
From there you can choose what you want to be included in the back and then click the Configure button. Select the radio dial to Turn on system protection if it's not already on. And then you can choose how much disk space to reserve, usually no more than 2 or 3 percent.
If you want to prolong your laptop's battery life, one of the best things you can do is switch the Power Saver, High Performance, and Balanced power plans based on your needs. To choose a plan, right click the battery icon in the lower-right corner of your screen and click Power settings. Next, click Additional power settings to select a power plan.
To restrict which apps can be installed on your laptop, you can disallow anything that isn't in the Windows Store. Go to Settings > Apps > Apps & features and you can choose whether to permit installations from only the Windows Store, any app installations (with a warning), or unrestricted app installations.
Windows 10 offers an easy way to see which apps are installed on your new laptop and a quick way to uninstall those you don't want. Head to Settings > Apps > Apps & features and peruse the list. If you don't want an app and are 100% certain your computer doesn't need it, click the Uninstall button.
Ransomware is a form of malicious software (or malware) that makes all your data inaccessible until you pay a fee to hackers.
To combat it, type 'Windows Defender Security Center' into the search bar at the bottom of your screen, click it and go to Virus & threat protection > Virus & threat protection settings. Here, you'll be able to enable a new option called Controlled folder access, which protects you against ransomware attacks. By default, the Desktop, Documents, Music, Pictures, and Videos folders are protected, but you can add others too.
Do you know what settings to change and update to optimize your laptop? This article barely scratches the surface of Window 10's security and efficiency settings. Call us today for quick chat with one of our Microsoft experts about taking yours to the next level.


text:
Telugu Hungama
భక్తి పాటల లిరిక్స్
క్రిస్టియన్ పాటల లిరిక్స్
సరికొత్త సినిమాలు
సినిమా అప్డేట్స్
Wiki & Biography
Facts & Beliefs
డైలీ న్యూస్
Best Places To Visit in Hyderabad – Tour Guide
May 16, 2020 May 15, 2020 by Telugu Hungama Staff
Best Places To Visit in Hyderabad: Hyderabad, City of nizam, and a well-known center for IT industry alongside with Bangalore in India. Many people don't know that Hyderabad is a historic city with many Tourist places and also must-visit places. This is the reason why Hyderabad is one of the top cities in the world and attracts more tourists every year. Now in this post, we are here to help you with the best places to be visited in Hyderabad.
These are the Best Places To Visit in Hyderabad
1. Charminar
Whenever you hear the name of Hyderabad the ideal symbol which gets stuck in mind is that Beautiful Charminar. Yes, Charminar has been marked as a landmark for the Hyderabad city and one of the most visited places in Hyderabad. Believe it or not, Every tourist Who is visiting Hyderabad must go to Charminar, Admire its beauty and then Have a Cup of Authentic Irani Chai.
Charminar is also surrounded by those Bright Bangle markets and traditional ornaments for ladies. These shops actually resemble the old culture and bring us the beauty of Nizam's Time Ornaments, Bangles.
Best Places to Visit in Hyderabad
2. Hussain Sagar
Hussain Sagar Lake is a man mad lake Located at the center of the City. Hussain Sagar is Very Close to Secunderabad Railway Station. Hussain Sagar is another beautiful piece of Nizam rulers, and it's actually made to complete the needs of water for the People of Hyderabad. Then gradually it became so famous and Government also started developing the surroundings of Hussain Sagar.
There is a Buddha statue situated at the center of Hussain Sagar lake which adds more beauty to the Hussain Sagar Lake. You can also enjoy and admire the beauty of the lake by boating in the Lake and there is also Lumbini park next to Hussain Sagar which is a family picnic hotspot.
3. Golconda
Golconda Fort is built by the Nizam rulers and its totally made of rocks. You can have a clear view of Hyderabad City from Golconda Fort. People who love architecture and admires it should visit Golconda Fort for sure. If they are in Hyderabad. You can have busses always running to Golconda fort from corners of the city, So you can reach the Golconda Fort easily.
Golconda fort resembles the history, culture, Architecture of Hyderabad in the 16th century. Golconda Fort also has some special facilities like water supply through wells and Then the Signaling system of Qutub Shahi time. Golconda Fort is a must and should for people who love to visit historic monuments and Architecture.
4. Ramoji Film City
Now we Move on to Entertainment related places from traditional historic monuments. Yes, you heard it right, its Ramoji Film City. Worlds largest film studio which is Ramoji Film city is situated in Hyderabad and you can have a visit to Ramoji film city and return within one day.
Ramoji Film city has different locations and sets built for Film shootings and it really surprises visitors. Even some locations are designed in such a way that it looks like Foreign Country. Ramoji Film city also has an Airport Set, Railway station, high Court, and many more. So, If you are visiting Hyderabad hen make sure that Ramoji Film City is there in your Visiting Places list.
5. Birla Mandir
We know that the best tourist places guide will not be completed without including any Devotional Site. Yes, our Famous nizams Hyderabad also has one famous devotional tourist place. Birla Mandir is a temple situated on a hill near Hussain Sagar Lake and also at the city center.
This temple was built by Birla Trust in the 1970s and the marble work for this temple took almost 10 years. Here people can visit the temple in timings and can seek the blessings of Lord Venkateshwara Swamy.
With this, we are completing the list of Best places to visit Hyderabad guide. If you feel we missed any place, Comment on this post by mentioning that place Name.
Categories Other, Fun Tags Best Places To Visit in Hyderabad Post navigation
8movierulz Plz Telugu Movies 2020 – Free Download Full HD 1080P
Tamilrockers Telugu Movies 2020 Download – A New Free Movie Site
Alludu Adhurs Movie Leaked on Tamilrockers
Top 10 Evergreen Romantic Telugu Films Of All Time
Happy Makar Sankranthi Wishes 2021 | Wishes | Greetings | Status
Sankranthi Wishes in Telugu 2021
Sankranti Rangoli Designs 2021
© 2021 TeluguHungama • All Rights Reserved • TeluguAce


Ixtapan de la Sal is a town and municipality located in the State of Mexico, Mexico. Escape the urban bustle at Nexpa Beach and Las Estacas Natural River. You'll discover tucked-away gems like Mercado Central and Skydiving. Explore Ixtapan de la Sal's surroundings by going to Taxco (Teleferico de Taxco, Silver Museum (Museo de la Plateria), & more), Museo Luis Mario Schneider (in Malinalco) and Zoofari (in Amacuzac). Spend the 7th (Tue) exploring nature at Iztaccihuatl and Popocatepetl National Park. The adventure continues: take your sightseeing to a higher altitude at The Pena of Bernal, get outside with Grutas La Estrella, don't miss a visit to Plaza Maclovia, and cool off at Parque Acuatico.
To find maps, ratings, photos, and other tourist information, go to the Ixtapan de la Sal vacation trip planner.
If you are flying in from Canada, the closest major airports are Licenciado Benito Juarez International Airport, Licenciado Adolfo Lopez Mateos International Airport and General Francisco J. Mujica International Airport. In February in Ixtapan de la Sal, expect temperatures between 34°C during the day and 17°C at night. Finish up your sightseeing early on the 11th (Sat) so you can travel back home.