It took me 2 days to complete the backend interface translation. I would like to share the Chinese language pack with the community. The .po file has been uploaded to https://translate.phplist.com.
Last edited by Zhong on 2:24pm, Sun 22 Mar, 2015, edited 1 time in total.
The updated .po file is attached.
The files has been updated again. see attached.


text:
Timex Ironman Move X20 Review
The Timex Ironman Move X20 does some things right but its inaccuracy and a high price tag bring it down. Timex will have to strike the correct balance in the next iteration because right now, we can't recommend the Move X20.
When it comes to wristwatches, Timex is a popular brand. The company which was founded in 1854 has numerous sub brands under its name, one of which comprises of rugged and reliable watches, made in collaboration with the Ironman brand. Can the Timex Ironman Move X20 live up to the legacy of the brand? Let's find out.
Build and design
The Timex Ironman Move X20's build is very similar to what you get from a normal Ironman watch, that is to say a good quality resin case and silicone belt. On the other hand, the design of the Timex Move X20 is rather unimpressive. The plastic shell which hold the sensors and the display sits rigidly on the wrist and makes the whole device feel awkward because it never really takes the shape of your wrist unlike traditional watches. As a result, you'll often find yourself fidgeting with the tracker during the day or just be annoyed by the way it wobbles when you move your arm. The charging port for the wearable is on the back with two conductive points which connect to the charging dock, which is then locked into place via a clasp; plus, the charging cable is really short adding to the unituitive design.
Features: covering all the basics
There are many fitness trackers available in the market which offer a lot more than a step counter and activity tracker but the Move X20 has covered only the basics. There is an activity tracker, workout tracker, sleep tracker and it tells time as well. When tethered to a smartphone, it also displays call and text message notifications which is quite handy. While the notifications work as intended, I had trouble with the activity tracker. Normal walking and workout sessions are recorded with an error margin of around 50-100 steps, normal for today's fitness trackers. The deal breaker for me however was that it also recorded my daily commute as part of my activity session, because it mistook me riding slowly on my scooter through Delhi traffic as me running. This meant at the end of the day according to the Partner app I was running 8-10 kilometers everyday and burning like 2,000 to 3,000 calories. I had to switch off the device during my commute to overcome this problem.
The illuminated LED display on the X20 is easily visible. By pressing the play button, you can toggle through time, step counter, distance counter, calorie counter, day & date and weather information as well if you have it tethered to a phone. As far as sleep tracking is concerned, the Timex Ironman Move X20 is quite accurate. I am a light sleeper and the device analysis did show that. However, some people may find it annoying that you have to push buttons to let it know that you are going to sleep or start a workout and repeat the ritual when you wake up or finish your workout.
A sloppy app
The Move X20 syncs with its partner app on a smartphone via Bluetooth. Like the wearable itself, the app also covers the basics and looks like a work in progress. You can monitor your activity and your sleep patterns but nothing else. A good partner app should give you tips regarding what to eat, what not eat or how to get the most out of your sleep. Fitness enthusiasts would love to have an app which would let them set goals according to what they have achieved or what they want to achieve. To put it in easy terms, all this activity data should translate into something which will let you optimize your lifestyle and fitness in the real world rather than just being some numbers in an app.
Battery: A week full of running around
In a week of use, the Timex Ironman Move X20's battery went from 100 percent to 10 percent which is average at best. There are plenty of fitness trackers in the market which offer much more 'on time' between charges. For example, an equally featured Garmin Vivofit claims a battery-life of one whole year.
Bottomline
The Timex Ironman Move X20 does some things right but its inaccuracy and a high price tag bring it down. And with competition like the Garmin Vivofit and Xiaomi Mi Band which offer a similar set of features for much less, it's not a sensible buy either. Timex will have to strike the correct balance in the next iteration because right now, we can't recommend the Move X20.
Tags: Timex Ironman Move X20
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redpajama_set_name: RedPajamaCommonCrawl


Irish Ferries operate the ferry crossings between Rosslare and Cherbourg, and Rosslare and Roscoff in France. Irish Ferries are signed up to the Pet Passport Scheme which allows you to take your pet between Ireland and France provided you have visited the vet and obtained the necessary papers.
The good news for pet owners is that Irish Ferries has extended the scheme to cover the Rosslare to Roscoff ferry route, whereas previously it was only available on the Rosslare Cherbourg crossing.
Irish Ferries also provide a dedicated walking area (by arrangement on board) on the deck of the Oscar Wilde cruise ferry, so even your pet can enjoy the sea air.
More information about ferry routes between Ireland, France and the UK from Irish Ferries.


• These binders are the eco-consious alternative to a vinyl binder.
• Printed with low VOC-emitting, renewable vegetable-based inks by request.
• The Eco Binders are a cost-effective solution.
• The Eco-Binders are a perfect way to "green up" your presentations.
• Flexible 26pt. chipboard or rigid options are all durable, lasting longer, thus reducing costs for replacement.
• These binders will appeal to your "green-minded" clients.
• Inside Pockets: Flexible option has two, 4" high, open center pockets. Rigid do not come with pockets.


In a form application defined as Editable Grid View Orientation, I want to be able to set certain fields as readonly based on the content of one of the fields in the record. So the first row/record in the grid might have columns 3 and 5 set to readonly, then the second row/record might have columns 3 and 5 not readonly, but columns 7 and 8, and so on. How can this be done?
Just to be clear, I tried to sc_field_readonly() in the onLoadRecord event. The problem is that all the rows in the grid end up having the readonly attribute set to what the last record loaded is set to.
Now when accessing each record the field Name is NOT readonly. It seems that the sc_field_readonly is applying to the entire field Name column and not each individual Cell of the table.
That is how the macro works, you either set the whole field as readonly or you don't. It is not possible to set to each individual registry (cell) of the table.
You can send this as a suggestion to us at suggestion@scriptcase.net.
This feature is very important. I have needed it several times. Has it been taken into account?


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text:
Super Bowl Predictions: Writers explain their NFL Championship picks
The Philadelphia Eagles and the New England Patriots compete for the Super Bowl LII title on Feb. 4. Photo Courtesy of Wikimedia Commons
AJ Traub
Henry Schweber: New England Patriots
While we have both number 1 seeds in the Super Bowl, there is still a clear underdog. The Philadelphia Eagles lost star quarterback Carson Wentz to a season ending ACL tear towards the end of the regular season, but journeyman quarterback Nick Foles has more than held his own in his stead. On the other side, the powerhouse New England Patriots are continuing their dominant ramp through the rest of the league. After an impressive comeback win against the vaunted Jacksonville defense, Tom Brady remains one of the premier quarterbacks in the league, even at his advanced age. It's fair to question if the Eagles are the Patriots' toughest test yet, but when I delve into the completeness of the teams, I'm unsure if that's the case. Jacksonville was very well-rounded, but ultimately had some shortcomings at the quarterback position. I see the Eagles as the same sort of team, and while Nick Foles has excelled up to this point, I don't believe that it will continue. The Patriots' coaching excellence and experience will propel them to another Super Bowl victory, one that will come with less resistance than commonly thought.
Final Score: 31-17 Patriots
AJ Traub: New England Patriots
I predicted the Patriots would win the Super Bowl at the beginning of the season, and the team has done nothing to make me want to change my pick. Amendola has seriously stepped up for the injured Julian Edelman when it comes to clutch playoff receptions. The Patriots showed that they are still very capable of making improbable comebacks with the AFC Championship victory over Jacksonville. Eagles fans and even team members have been shown no love in Minnesota after Philadelphia defended their home field in the NFC Championship against the Vikings. It's an experienced dynasty versus a streaky backup quarterback-led team of underdogs. Philly has defied their expectations on the way to a Super Bowl run, but their opponents include 5-time championship winning coach and quarterback duo Bill Belichick and Tom Brady. The Eagles may very well put up some points on the Patriots in the first half, but New England has all the tools and experience to make their victory less dramatic than the last two.
Lindsey Quigley: Philadelphia Eagles
The Philadelphia Eagles were plagued by injuries this season, losing key players such as Jordan Hicks, Jason Peters and star quarterback Carson Wentz to a devastating ACL injury. While losing Carson was heartbreaking for Eagles fans, there was still a team who had work left to finish. As soon as his injury sidelined him, everyone deemed that the Eagles would be a "one and done" team in the playoffs, despite having the best record in the league. In both games against the Atlanta Falcons and Minnesota Vikings, the Eagles were the underdogs, despite having home field advantage. The Eagles defense dominated those two games, letting up just 17 points total over the two, and Nick Foles stunned the talented Minnesota defense throwing for 3 touchdowns and 352 passing yards. From Doug Pederson's dynamic offensive play calling to the stellar Eagles defense, I think Bill Belichick and Tom Brady will not be feeling the same as they did after Super Bowl XXXIX against the Eagles. The Eagles are coming off of two electric home games at Lincoln Financial Field, and are headed to Minnesota with confidence, energy and the entire City of Brotherly Love behind them. I predict the Philadelphia Eagles will defy the odds once again, and Philadelphia will get their parade down Broad Street for the first time since 2008 when the Phillies won the World Series.
Final Score: 31-20 Eagles
Senior Brendan Cronin becomes first Lafayette golfer to be named Patriot League Scholar-Athlete of the Year
Golf team picks up speed with fourth place finish
Lafayette welcomes Lehigh to Fisher Stadium for 156th Rivalry game
Track and field teams blown out at Lehigh Easter Races
Recent TikTok video highlights gender-based inequities in the NCAA
Track and field teams slow out of the gate to start spring season
Women's basketball sweeps Loyola to close out regular season
A plan months in the making: How the college is keeping athletes safe from illness and injury


This is my local home-page at Comenius-University, Bratislava.
These pages are written in english.
These pages are mostly written in german; in the literature- and URL-lists you will find many references to english texts.


text:
Roger Lorang (born 22 November 1930) was a Luxembourgian footballer. He played in one match for the Luxembourg national football team in 1953. He was also part of Luxembourg's team for their qualification matches for the 1954 FIFA World Cup.

References

External links

1930 births
Possibly living people
Luxembourgian footballers
Luxembourg international footballers
Place of birth missing (living people)
Association footballers not categorized by position

redpajama_set_name: RedPajamaWikipedia


text:
\section{Introduction}
Boltzmann pondered on how to understand thermodynamics with the Newton's equations;
his answer to this question along with Gibbs' theory have become the foundation of classical
statistical mechanics ~\cite{huang_huang_1987,landau}. After quantum mechanics been
fully formulated, many giants in physics discussed a similar issue:  how to understand
thermodynamics with the  Schr\"odinger equation~\cite{eS,eV}.
In a 1929 paper, von Neumann provided an answer to this question by proving
two inequalities  ``in full rigor and without disorder assumptions"~\cite{eV}.
These two inequalities, which he called the quantum ergordic theorem and
the quantum H-theorem,  respectively,   laid down
a foundation for quantum statistical mechanics. However, this work has been largely
forgotten and apparently have never been mentioned in any modern textbook
on quantum statistical mechanics~\cite{huang_huang_1987,landau}.
There are discussions on why this work had almost been forgotten~\cite{goldstein}. In our opinion, one of the likely reasons is that  von Neumann introduced a
rather unfamiliar concept, {\it macroscopic operators},
to prove his theorems.   It appears very hard to compute  these commuting
macroscopic operators, and related variables such as an entropy defined for a pure quantum
state~\cite{eV}.

Recently there have been renewed interests on the foundation of quantum statistical mechanics~\cite{zhuang_equilibration_2012,gemmer_quantum_2009,rigol_thermalization_2008,biroli_effect_2010,cassidy_generalized_2011,deutsch_quantum_1991,srednicki_chaos_1994,rigol_alternatives_2012,short_equilibration_2011,short_quantum_2012,popescu_entanglement_2006,popescu_foundations_2005,
linden_quantum_2009,cho_emergence_2010,ikeda_eigenstate_2011,rigol_relaxation_2007,reimann_foundation_2008,
reimann_equilibration_2012,xiong_universal_2011,goldstein_canonical_2006,suncp,wang,santos_weak_2012,reimann_typicality_2007,yukav_equilibration_2011, yukav_decoherence_2012, yukav_nonequilibrium_2011,riera_thermalization_2012,gogolin_absence_2011,christian_pure_2010,Emerson2013,Fine1,Fine2,Fine3,borgonovi_chaos_1998,flambaum_towards_1996} perhaps due to the remarkable progress in experimental realization of coherent quantum systems~\cite{Davis_BEC_1995,shin_distillation_2004,yao_prb_2006,zhao_anomalous_2011,huang_observation_2011,yao_nature}. An important result achieved is an inequality proved by
Reimann~\cite{reimann_foundation_2008,reimann_equilibration_2012} and later modified
by Short \it {et al.}\rm \cite{short_equilibration_2011,short_quantum_2012}. This
inequality can be regarded as a different version of von Neumann's quantum ergodic theorem.
The advantage of this new inequality is that every variable involved is well known and
can be computed.  For this reason, when we discuss quantum ergodic theorem, we refer to
the inequality proved by Reimann unless stated otherwise.

According to the quantum ergodic theorem, an isolated quantum system starting
with a far-from-equilibrium state will relax dynamically to an equilibrium state and
stay there with very small fluctuations for almost all the time.  To be more specific,
for an isolated quantum system described by the wave function $\ket{\psi(t)}$,
it will relax to the following equilibrium state
\begin{equation}
\rho_\infty=\sum_k |c_k|^2\ket{E_k}\bra{E_k}\,,
\end{equation}
where $\ket{E_k}$ is the energy eigenstate of the system and $c_k$'s are the
expansion coefficients of $\ket{\psi(t)}$ in term of these eigenstates.  The density matrix
$\rho_\infty$ is regarded as the micro-canonical ensemble by von Neumann~\cite{eV}.
It is different from the usual micro-canonical ensemble found in textbooks
~\cite{huang_huang_1987,landau}, where the coefficients $c_k$'s take
an identical value within a narrow energy shell.  As $|c_k|$'s
do not change with time, the micro-canonical density matrix $\rho_\infty$ is completely
determined by the initial condition. By utilizing this fact and the supposition principle,
we were able to predict a new quantum state which is at equilibrium with
multiple temperatures, challenging the conventional
wisdom that an equilibrium state has only one temperature~\cite{zhuang_equilibration_2012}.

The quantum ergodic theorem holds only for quantum systems with no degenerate
energy gaps. Mathematically, this condition   is
expressed as~\cite{eV,reimann_foundation_2008,reimann_equilibration_2012}
\begin{equation}
E_k-E_l=E_m-E_n\Rightarrow\left\{
\begin{array}{c}
E_k=E_l~{\rm and}~E_m=E_n\\
{\rm or}\\
E_k=E_m~{\rm and}~E_l=E_n
\end{array}\right.\,.
\label{condition}
\end{equation}
However, it is not clear at all how this condition of non-degenerate energy gap is related to
the familiar classification of quantum systems by their integrability. For a general integrable system, this condition is not satisfied as  quantum integrable systems  have the Poisson distribution of energy level spacing~\cite{introduction}, which imply
the existence of many degenerate
eigen-energies.  However, there are plenty of examples of integrable systems, which have no
energy degeneracy at all. In fact, there are already reports of dynamical relaxation in integrable
systems~\cite{Santos,Santos2}.

The case for quantum chaotic systems is more complicated. As is well known,  quantum chaotic systems have the Wigner distribution of energy level spacing~\cite{introduction}. The Wigner distribution has two prominent features: zero probability at zero energy level spacing and a peak at a finite energy level spacing. The former feature means that there is little degeneracy,
which is favorite for the condition (\ref{condition}) being satisfied.
The latter implies that there are large number of energy level spacings
around the peak value, which is clearly unfavorite for the condition (\ref{condition})
being satisfied. As a result,  it is not clear at all in the sense of mathematical
rigor  whether the quantum ergodic theorem and H-theorem hold for
quantum chaotic systems or not.  We led by intuition tend  to  believe
that  the quantum ergodic theorem and  H-theorem should hold for quantum
chaotic systems. Von Neumann believed
that his theorems should hold when the condition (\ref{condition}) is violated by
``infrequent exceptions"~\cite{eV}. This belief is now confirmed by
Short and Farrelly~\cite{short_quantum_2012}.  Despite this progress, it is still not clear
how these mathematical conditions are related to the integrability of a system.
The main purpose of this paper is to demonstrate
that the quantum ergordic theorem applies to quantum chaotic systems
numerically with examples.

In this paper we study two quantum chaotic systems,
the ripple billiard~\cite{li_quantum_2002,xiong_universal_2011} and  the
Henon-Heiles system~\cite{henon,zhuang_equilibration_2012}.
Our numerical simulation shows that both systems will indeed dynamically relax to
an equilibrium state where the overall features of the wave function no longer change.
For the ripple billiard system, where the successive energy-eigenstates can be computed,
the quantum ergodic inequality can be verified directly. In addition, we define entropies
for pure quantum states in the spirit of von Neumann as it is not clear  how to compute
the entropy defined for a pure quantum state by him. We find that these entropies will
approach maximized values,  offering another indication  that the system is indeed
equilibrating dynamically.

We have also analyzed  the properties of the equilibrium state reached after the dynamical relaxation in quantum chaotic systems. We  find an interesting correspondence between the quantum equilibrium state and the classical micro-canonical ensemble. We discuss
the underlying mechanism with the correspondence between the quantum and the
classical Liouville equations. At the end, we consider the statistical properties of
fluctuations in quantum chaotic systems and find a distinction between the
distributions of quantum fluctuations and the classical fluctuations.

This paper is organized as follows.   In Section \uppercase\expandafter{\romannumeral2} we introduce
the two  quantum chaotic systems, ripple billiard and Henon-Heiles system. In Section \uppercase\expandafter{\romannumeral3} we study the dynamical equilibration of quantum chaotic systems. In Section \uppercase\expandafter{\romannumeral4} we numerically verify the quantum ergodic theorem  in the ripple billiard system. In Section \uppercase\expandafter{\romannumeral5} we discuss the quantum-classical correspondence for the equilibrium states in detail. In Section \uppercase\expandafter{\romannumeral6} we discuss the fluctuation properties of the quantum systems and their corresponding classical systems. Finally in Section \uppercase\expandafter{\romannumeral7} we discuss the implications for many-body cases and summarize our results.

\begin{figure}
\centering
\subfigure[]{
\label{contourH}
\includegraphics[width=0.21\textwidth ]{Contour_HH.eps}}
\centering
\subfigure[]{
\label{contourR}
\includegraphics[width=0.23\textwidth]{ripple_billiard_demo.eps}}
\caption{(a) Energy contours of the Henon-Heiles potential $V(x,y)$. The thick
solid lines are the contours  for $V/V_c=1/2,1,2$ from inside to outside.
The unit of axis is $r_c$. $A$, $B$ and $C$ are three saddle points and $O$ is the stable point.
(b) The shape of ripple billiard.
}
\end{figure}
\section{Models}

We focus on single particle quantum chaotic systems. There are two main reasons
for this choice.  First, single particle quantum systems are much less challenging numerically
and easier to analyze.  Second, according to random matrix theory,
the statistics of energy level spacings of quantum chaotic systems only depends on the type of
matrix of the system when its Hamiltonian is expressed in  an orthonormal basis~\cite{introduction}.
This property has nothing to do with whether the system is single particle or many body.
According to the condition (\ref{condition}),  the property of the eigen-energy spectrum
is the most important factor determining whether the quantum system will equilibrate or not.
There are properties that exist only in many-body systems, for example, the correlations~\cite{Flambaum}.
So far, no one has shown that the correlation plays any essential role in the equilibration process.
We also emphasize that we here consider isolated quantum systems and do not
consider the dynamics of quantum systems under external driving~\cite{Wilkinson}.
It is well known that a classical system will behave very differently under different drivings.
This feature seems to be shared by quantum systems~\cite{Wilkinson}.

A single particle in a two-dimensional chaotic potential is described by the Hamiltonian
\begin{equation}
H={p^2}/{2m}+V(x,y)\,.
\end{equation}
We choose the Henon-Heiles potential~\cite{henon} and the ripple billiard~\cite{li_quantum_2002}
as two examples for our study.
The Henon-Heiles potential is given by $V(x,y)= \frac{U}{2}(x^2+y^2)+\lambda (x^2y-\frac{y^3}{3})$. The energy contour of Henon-Heiles potential is shown in Fig. \ref{contourH}; it has four special points: one stable point O$(0,0)$, three saddle points A$(0,r_c)$, B$(-\frac{\sqrt{3}}{2}r_c,-\frac{1}{2}r_c)$, C$(\frac{\sqrt{3}}{2}r_c,-\frac{1}{2}r_c)$, where  $r_c\equiv\frac{U}{\lambda}$.
The classical orbits in the Henon-Heiles potential are chaotic when the energy is above $V_c/2$
and approach fully chaotic when the energy is close to $V_c$ with
$V_c\equiv\frac{U^3}{6\lambda^2}$. For later use, we set  $p_0=\sqrt{2mV_c}$.

Billiard systems are a two dimensional area surrounded by infinite potential walls at the edges.
For the ripple billiard~\cite{li_quantum_2002},  as shown in Fig. \ref{contourR}, the left and right edges are described by functions $x=\mp[b-a\cos(\pi y/b)]$ and the up and down edges are
two straight lines at $y=2b$ and $y=0$. The two geometrical parameters $a$, $b$ control the shape of
the billiard .  When $a=0$ the ripple billiard is a square with width $2b$.  As $a$ increases from zero, it changes from an integrable system to a mixed, then to a fully chaotic system. It becomes mixed again when $a$ becomes very large. We have chosen for our computation $a=6,~b=15$, which corresponds to a fully chaotic case.

The two systems are chosen because each of them has its own advantages. For
the ripple billiard system, its successive eigenstates from the ground state up to the
3000th excited state can be computed numerically with great  precision~\cite{li_quantum_2002}.
To the best of our knowledge, for all other studied quantum chaotic systems, the high-energy eigenstates can
only be computed selectively~\cite{li_statistical_1994}.
The famous Henon-Heiles system is chosen to bring our study beyond billiards where $|p|$
is a constant of motion,  allowing us to gain more insights into general systems.
In addition, we note that the Henon-Heiles system is beyond what is considered by
von Neumann and others as it  has no bound eigenstates mathematically. However,
its resonant states can be regarded as bound states in our numerically studies, where
the dynamical evolution lasts for a finite time and
hard-wall boundaries are imposed at distance~\cite{hh_bound}.

\section{Dynamical equilibration}
We numerically study the wave packet dynamics with the Schr\"odinger equation for
these two systems. In our numerical simulation we set $m=\frac{1}{2}$, $\hbar=1$.
The initial states are highly localized moving Gaussian wave packet for both systems,
\begin{equation}
\psi(\vec{r},t=0)=\frac{\alpha}{\sqrt{\pi}}\exp(-\frac{1}{2}\alpha^2(\vec{r}-\vec{r_{i}})^2)\exp(i\vec{p_{i}}\cdot \vec{r}/\hbar)
\label{initial_condition}
\end{equation}
with $1/\alpha=3r_c/40 $, $\vec{r}_{i}=(0.3,0)r_c$, and $\vec{p}_{i}=
\sqrt{7/10}(\cos10^\circ, \sin10^\circ)\,p_0$
for the Henon-Heiles system; $1/\alpha=a/6$, $\vec{r}_{i}=(0,0)$, and $\vec{p}_{i}=
(5,0)$ for the ripple billiard system. In both systems, a classical particle
with the above initial position
$\vec{r}_{i}$ and momentum $\vec{p}_{i}$
has a fully chaotic orbit, which we confirmed  by computing  the Poincare section.
\begin{figure}
\includegraphics[width=0.48\textwidth ]{evolution_p.eps}
\caption{Time evolution of (a) $\bra{\psi}P_x\ket{\psi}$ and (b) $\bra{\psi}P_y\ket{\psi}$
in the ripple billiard. The red lines are $\mbox{tr}(\rho_\infty p_x)$ and $\mbox{tr}(\rho_\infty p_x)$. The initial condition of $\vec{P}$ is (5,0). $T_s\equiv\frac{2(a+b)}{|p_i|/m}$.}
\label{momentum}
\end{figure}

The subsequent dynamical evolutions of these two Gaussian wave packets are computed.
For the ripple billiard, the dynamical evolution can be found in Ref.~\cite{xiong_universal_2011}; for
the Henon-Heiles system, the evolution is illustrated  in Ref.~\cite{zhuang_equilibration_2012}.
Both evolutions are very similar to each other. Here is a brief description: the smooth Gaussian
wave packet starts to spread out and gets diffracted by the potentials; the interference between
diffracted waves begins to make the wave packet appear more and more irregular; eventually the
wave packet spreads out over the classically allowed region rather uniformly with small speckles.
 This overall feature will no longer change, signaling that the system has dynamically equilibrated.

To illustrate this dynamical equilibration process, we compute how
the expectation of momentum changes with time for the ripple billiard system.
The results for both $p_x$ and $p_y$ are shown in Fig. \ref{momentum}, where
the momenta are seen to relax to equilibrium values after a
short period of large fluctuations.

Equilibration should be accompanied by a maximizing entropy. Von Neumann was able to
define an entropy for a pure quantum state and proved that this entropy
will stay very close to its ensemble entropy almost all the time (the quantum H-theorem)~\cite{eV}. However, there appears no viable  procedure which one can use to compute this version of von Neumann entropy.  As an alternative, we define an entropy in the spirit of von Neumann,
\begin{equation}
S_r=-\int \frac{|\psi(x,y,t)|^2}{|\psi_\infty(x,y)|^2}\ln \frac{|\psi(x,y,t)|^2}{|\psi_\infty(x,y)|^2} dxdy\,,
\end{equation}
where $|\psi_\infty(x,y)|$ is the long time average of $|\psi(x,y,t)|^2$~\cite{zhuang_equilibration_2012}.
As shown in Fig.~\ref{entropy},  the entropy will increase  with time with small fluctuations and eventually saturate to a maximized value.  The increasing entropies in Fig.~\ref{entropy} can be regarded
as a ``spiritual" illustration of von Neumann's quantum H-theorem.
\begin{figure}
\includegraphics[width=0.49\textwidth ]{Sr_t_all.eps}
\caption{Time evolutions of entropy in (a)  Henon-Heiles system;
(b) ripple billiard.}
\label{entropy}
\end{figure}

In summary, we have observed numerically that dynamical equilibration indeed occurs in
both the Henon-Heiles system and the ripple billiard: an initially localized Gaussian wave packet
with low entropy will dynamically evolve into a quantum state with a maximized
entropy, where the wave packet spreads out and looks irregular with speckles.
This is clearly consistent with both the quantum ergodic theorem and quantum H-theorem.
It is reasonable to expect that this kind of dynamical equilibration occurs in any quantum
chaotic system. Meanwhile we note that the equilibration process for the Henon-Heiles system
deserves more detailed study in the future. As noted before, the Henon-Heiles system
has no bound states. As a result, a Gaussian wave packet will eventually leak out
and spread out in the whole space, not confined to just the triangle area, beyond the tunneling time.
In our numerical simulation, the equilibration time is clearly much shorter than the tunneling time.
It would be very interesting to investigate in which situations where the equilibration time becomes shorter
than the tunneling time. It might also be worthwhile  to formulate mathematically the ergordic theorem for this kind of systems.

\section{Verification of quantum ergodic theorem}
The mathematical expression of the quantum ergodic theorem is an inequality.
For an arbitrary operator $A$, this inequality reads~\cite{reimann_foundation_2008,short_equilibration_2011,short_quantum_2012}
\begin{equation}
\sigma^2_A\equiv \frac{\braket{| \mbox{tr}\{A\ket{\psi(t)}\bra{\psi(t)}\}- \mbox{tr}(A\rho_\infty)|^2}_t}{\|A\|^2}\le \frac{1}{d_{\mbox{eff}}}\,,
\label{ineq}
\end{equation}
where  $d_{\rm eff}\equiv1/\sum_k |a_k|^4$ measures effectively how many energy eigenstates
are occupied in the state $\ket{\psi}$.  The subscript $t$ in $\braket{}_t$ indicates a long time averaging. We emphasize that this inequality is much stronger than the following approximation
\begin{equation}
\braket{\mbox{tr}\{A\ket{\psi(t)}\bra{\psi(t)}\}}_t\approx \mbox{tr}(A\rho_\infty)\,,
\label{ergodic}
\end{equation}
which can be readily proved for any quantum systems with no energy degeneracy.  The above
approximation can still be true even when $\mbox{tr}\{A\ket{\psi(t)}\bra{\psi(t)}\}$ fluctuate
greatly from $\mbox{tr}(A\rho_\infty)$ as long as the positive large fluctuations cancel out
the negative large fluctuations. However, the fluctuations can not cancel each other in
the inequality (\ref{ineq}); this means that the inequality (\ref{ineq}) dictates that the fluctuations are very small most of the time when $d_{\mbox{eff}}\gg 1$. So, the approximation relation (\ref{ergodic}) coupled with the inequality (\ref{ineq}) shows
that the long time averaging is equivalent to ensemble averaging, essence of
ergodicity, in all quantum systems that satisfy the condition (\ref{condition}).

To test  numerically the inequality (\ref{ineq}), one needs to compute the energy eigenstates
$\ket{E_k}$ successively up to a high energy value and find the expansion coefficients
$c_k$. We are able to
do it for the ripple billiard system. The expansion coefficients of the initial state Eq. (\ref{initial_condition}) are computed and shown in Fig. \ref{decomposition}, where $c_k$'s are grouped
according the symmetry of the eigenstates.  Both groups peak around 500th eigenstates and have a width
around 300. With the computed $c_k$'s, we find that the  effective dimension $d_{\rm eff}$
is around 300, satisfying the condition $d_{\rm eff}\gg 1$.

Without loss of generality, we choose to compute the left hand side (l.h.s.) of the
inequality Eq. (\ref{ineq}) for momentum operator $\vec{P}=(p_x,p_y)$. By using the symmetry
of the eigenstates, one can readily show exactly that $\mbox{tr}(\rho_\infty p_x)=0$ and
$\mbox{tr}(\rho_\infty p_y)=0$. The time evolution of momentum is already shown in Fig.~\ref{momentum}. We calculate the long time average
between $t=10T_s$ and $t=14T_s$.  The time unit $T_s\equiv\frac{2(a+b)}{|p_i|/m}$ is the period of
the motion of a classical particle with the same initial momentum and position.
We find that $\braket{\mbox{tr}\{\ket{\psi(t)}\bra{\psi(t)}p_x\}}_t\simeq0.0021$ and $\braket{\mbox{tr}\{\ket{\psi(t)}\bra{\psi(t)}p_y\}}_t\simeq-0.0033$, very close to the ensemble average $\mbox{tr}(\rho_\infty p_x)=0$ and  $\mbox{tr}(\rho_\infty p_y)=0$, respectively.  At the same time,  we find that
\begin{eqnarray}
&&\braket{| \mbox{tr}\{\vec{P}\ket{\psi(t)}\bra{\psi(t)}\}- \mbox{tr}(\vec{P}\rho_\infty)|^2}_t\nonumber\\
&&=\braket{| \mbox{tr}\{\vec{P}\ket{\psi(t)}\bra{\psi(t)}|^2}_t \simeq0.0039\,.
\end{eqnarray}

\begin{figure}
\includegraphics[width=0.45\textwidth ]{even_even_odd_even.eps}
\caption{The distribution of expansion coefficients $c_k$  in the ripple billiard system for (a) even-even eigenstates and (b) odd-even eigenstates.}
\label{decomposition}
\end{figure}

\begin{figure*}
\centering
\subfigure[]{
\label{correspondence}
\includegraphics[width=0.45\textwidth]{rp_qc_no_fit_pr.eps}}
\centering
\subfigure[]{
\label{husimiplot}
\includegraphics[width=0.4\textwidth ]{sigma_20_2.eps}}
\caption{
(a) Comparison between   quantum and classical  equilibrium distributions
in the Henon-Heiles system.  $P(x)$ is for the real space and $f(p)$ for momentum space.
The unit for $x$ is $r_c$ and the unit for $p$ is $p_0$.
(b) Section of the Husimi function $H_{r.p}\equiv \braket{\vec{r},\vec{p}|\hat{\rho}(t) |\vec{r},\vec{p}}$ in the Henon-Heiles system at $t=0.2126$. The red circle is the section of the classical phase space density $\rho_c(\vec{r},\vec{p})$. The section is at $y=0, p_y=0$. The unit for $x$ is $r_c$ and the unit for $p_x$ is $p_0$.  The coarse-graining parameter for the Husimi function $\sigma\simeq0.11r_c$;
}
\end{figure*}

For operator $\vec{P}$, the maximum value $\|\vec{P}\|^2=\sup\{\braket{\psi|P^\dagger P|\psi}\}$.
Since we have chosen $m=1/2$ and the wave function is only none zero inside the billiard, we have
 $\|\vec{P}\|^2=\sup\{\braket{\psi|H|\psi}\}$, that is, $\|\vec{P}\|^2$ is effectively
 the largest energy in the occupied Hilbert space. According to Fig. \ref{decomposition}, the ocuppied Hilbert space is roughly spanned by the eigenstates  between the100th even-even(odd-even) eigenstates and the 1000th even-even(odd-even) eigenstates. The upper bound can be estimated as the eigenvalue of the 1000th even-even(odd-even) eigenstates, i.e. $\|\vec{P}\|^2\simeq 55.64$. So, the relative fluctuation or the l.h.s. of Eq. (\ref{ineq}) is $\sigma_{\vec{P}}^2\simeq 7\times 10^{-5}$.  As $1/d_{\mbox{eff}}\simeq 3\times10^{-3}$,  we see that
the inequality (\ref{ineq}) is clearly satisfied. Moreover, our computation in fact shows
that the right hand side (r.h.s.) of the inequality is  about 30 times larger than the l.h.s. This indicates that it is possible to improve the inequality, for example, replacing $\|A\|^2$ with the averaged value.

Before we proceed further,  we want to mention that the inequality for quantum ergodicity
proved by von Neumann ~\cite{eV} has a different
upper bound on the r.h.s.. However,  his theoretical formalism relies
on the introduction of macroscopic operators (such as macroscopic position and momentum) that commute with each other.  It appears not be a straightforward task to construct these macroscopic operators and compute them numerically. As a result, we did
not compute von Neumann's upper bound.

\section{Quantum-classical correspondence at equilibrium}
According to the quantum ergodic theorem,  the equilibrium state is described by
the density matrix $\rho_\infty$, which can be regarded as the quantum  micro-canonical ensemble.
We analyze  this quantum equilibrium state
and find that it possesses many features that resemble the classical  micro-canonical ensemble.
This kind of quantum-classical correspondence has been studied and found in a spin
system~\cite{Emerson,Guarneri}.  To illustrate  this  quantum-classical correspondence, we compare $\rho_\infty$ in both the real space and the momentum space with the classical micro-canonical ensemble
\begin{equation}
\rho_c= \frac{1}{\Omega}\delta(H(\vec{p},\vec{r})-E)
\end{equation}
where $\Omega$ is the normalization factor and $H(\vec{p},\vec{r})$ is the corresponding classical Hamiltonian of the fully chaotic system. Here we choose the Henon-Heiles system to analyze because its probability distribution in phase space is more general than the billiard system where $|\vec{p}|$ is a constant of motion. For the quantum results, we calculate $n_\infty(\vec{r})=\braket{\vec{r}|\rho_\infty|\vec{r}}$ and $n_\infty(\vec{p})=\braket{\vec{p}|\rho_\infty|\vec{p}}$ by long-time averaging; For the classical results, we calculate the probability distribution in real space and momentum space $n_c(\vec{r})$ and $n_c(\vec{p})$ from the micro-canonical ensemble $\rho_c(r,p)$ by integration over $\vec{p}$ and $\vec{r}$ separately.

For better comparison, we choose the following marginal distribution without loss of generality: for the real space,
we integrate out  the $y$ dimension to obtain the density distribution $P(x)$;
for the momentum space,  we integrate out  the angle variable to find the momentum distribution $f(p)$. The  results are shown in Fig. \ref{correspondence}, where we see the quantum and classical distributions are consistent, except for some quantum tunneling effect indicated by the non-zero value of the quantum distribution in the classically forbidden region.

This correspondence also exists in phase space. In quantum mechanics, the
uncertainty relation does not allow the construction of a phase space in principle.
However, a kind of quasi-quantum distribution  in phase space can be constructed
with the  Husimi function $H_{r.p}$ ~\cite{lee_signatures_1993,toscano_husimiwigner_2008}.
This is to calculate the projection of the density operator on a Gaussian wave packet $\braket{\vec{r^\prime}|\vec{r}, \vec{p}}=C\exp(-\frac{(\vec{r^\prime}-\vec{r})^2}{2\sigma^2}+\frac{i\vec{p}\cdot(\vec{r^\prime}-\vec{r})}{\hbar})$ centered around position $\vec{r}$ and momentum $\vec{p}$
\begin{equation}
H_{r.p}\equiv \braket{\vec{r},\vec{p}|\rho|\vec{r},\vec{p}}\,.
\end{equation}
The  Husimi function can be understood as coarse grained phase space density with parameter $\sigma$ controlling the coarse graining.  We have computed the Husimi function $H_{r,p}$ for
a density matrix $\rho\equiv \ket{\psi}\bra{\psi}$ at $t=0.2126$ (which is after equilibration) and compared
it to the classical ensemble $\rho_c$. For easy illustration, we use a 2-dimensional section
in the 4-dimensional phase space of the Henon-Heiles system. Without loss of generality, we choose the section at $y=0, p_y=0$ and the results are
plotted in Fig. \ref{husimiplot}.  We can see that the Husimi function centers around the phase space where the classical density is non-zero, indicating the quantum-classical correspondence.  Note
that the quantum fluctuations in the phase space are much larger than the ones seen in Fig. \ref{correspondence}. The reason is that the results in Fig. \ref{correspondence} are obtained after being
averaged over time and integrated over a given dimension.

One possible  understanding for this correspondence is through the quantum and classical Liouville equations. Intuitively, one can think of the quantum wave-packet as an ensemble of particles with equivalent classical probability density in the phase space~\cite{ballentine_inadequacy_1994,ballentine_moment_1998}.  The time evolution of quantum density matrix operator $\rho(t)$ is governed by the quantum Liouville equation,  $\partial_t\rho(t)=\frac{1}{i\hbar}[{H},{\rho(t)}]$; the time evolution of the classical probability density $\rho_c(t)$ is governed by the classical Liouville equation,  $\partial_t\rho_c(t)=[H,\rho_c(t)]_{\rm PB}$. These two time evolution equations have an identical algebraic structure, implying a possible quantum-classical correspondence in the equilibrium states. Moreover, there are numerical evidences for this correspondence in the studying of
the time evolution of the ensemble average and quantum expectation value~\cite{ballentine_inadequacy_1994,ballentine_moment_1998}. Note that
this quantum-classical correspondence is not implied in  the quantum ergodic theorem~\cite{eV,short_equilibration_2011,short_quantum_2012,reimann_foundation_2008,reimann_equilibration_2012}.

\begin{figure}
\centering
\subfigure[]{
\label{finalstate}
\includegraphics[width=0.22\textwidth ]{final_state.eps}}
\centering
\subfigure[]{
\label{finalstaten}
\includegraphics[width=0.24\textwidth ]{final_state_n.eps}}
\centering\\
\subfigure[]{
\label{eigenfy}
\includegraphics[width=0.22\textwidth ]{eigen1.eps}}
\centering
\subfigure[]{
\label{eigen}
\includegraphics[width=0.24\textwidth ]{eigen2.eps}}
\caption{(a) Marginal distributions $f(y)\int n(\vec{r}) dx$ for the equilibrium state  in the ripple billiard system. The black line is for the quantum result while the red line is for the classical result.
(b) The density distribution $n(r)$ of the equilibration state in the ripple billiard system.
(c) Marginal distribution $f(y)$ for the 493rd even-even eigenstate  in ripple billiard system.
(d) Density distribution $n(x,y)$ of the 493rd even-even eigenstate. For this eigenstate,  the expansion  coefficient $|c_i|^2=0.0086$ in the initial Gaussian wave packet (\ref{initial_condition}).
}
\end{figure}

We emphasize here that the quantum-classical correspondence discussed so far needs to be
understood in the sense of typicality~\cite{Lebowitz_pt,popescu_entanglement_2006,popescu_foundations_2005,
goldstein_canonical_2006,reimann_typicality_2007}. As dictated by the quantum ergodic theorem,
the equilibrium state is completely determined by the initial expansion coefficient $|c_k|^2$.
For a typical initial state, $|c_k|^2$ should have a distribution similar to what is shown in
Fig. \ref{decomposition} with a large effective dimension $d_{\rm eff}$. For these states,
we expect that the quantum-classical correspondence hold. However, for many atypical states,
this quantum-classical correspondence may not hold. For example, the ergodic inequality (\ref{ineq})
holds for an energy eigenstate; but energy eigenstate does not belong to the typicality class.
Here we use the ripple billiard to illustrate this point as the energy eigenstates in this system
can be computed successively~\cite{li_quantum_2002,xiong_universal_2011}.
We study the position space marginal distribution $f(y)=\int \braket{\vec{r}|\rho|\vec{r}} dx$, and compare it with the classical result $(b-a\cos(2\pi y/L))/bL$. We compute $f(y)$ first for the equilibrium state $\rho(t\gg T_s)$. We see in Fig. \ref{finalstate} that  the quantum result (black line) are in good agreement with the classical result (red line).   For completeness,  we also show the density $\braket{\vec{r}|\rho|\vec{r}}$ in Fig. \ref{finalstaten}.

For eigenstates, we choose to study the eigenstates that have relatively large expansion coefficients
$|c_k|^2$ in the initial wave packet (\ref{initial_condition}). We find that the results
for them are similar. Without loss of generality, we choose
the 493rd even-even eigenstates with  coefficient $|c_k|^2=0.0086$ as the example.
The marginal distribution $f(y)$ for this eigenstate is shown in Fig. \ref{eigenfy}. Compared with the result for the equilibrium state in Fig. \ref{finalstate}, we see a clear distinction: the eigenstate has larger fluctuations and bigger deviation from the classical distribution. In fact,  this
distinction is also seen in the density plot.  As seen in Fig. \ref{eigen}, the density distribution
for the eigenstate has certain uneven patterns, similar to  what have been found in ``scar"
states~\cite{heller_bound-state_1984}; these patterns are absent in  the distribution of the equilibrium state ( Fig. \ref{finalstaten}). Although eigenstates appear to be too special, their difference
from a typical quantum state  does indicate that  not all quantum states that
satisfy the inequality (\ref{ineq}) can relax to an equilibrium state which has the quantum-classical correspondence. In other words, all quantum states in a chaotic system may be classified into
two groups: one has the quantum-classical correspondence and the other does not have. It is not
yet clear whether there are simple ways to separate them other than using direct computation as we did. In Ref.\cite{Guarneri},  a remarkable correspondence between eigenstates and their
classical counterparts is found for the shape of eigenfunctions and
 the local spectral density of states. This seems to indicates that when the
 properties not related to the complexity of a wave function is considered,
 the quantum-classical correspondence can still be found for eigenstates.

\section{Fluctuation property}
\begin{figure}
\centering
\subfigure[]{
\label{fig:subfig:b}
\includegraphics[width=0.23\textwidth ]{exponential_r.eps}}
\centering
\subfigure[]{
\label{fig:subfig:b}
\includegraphics[width=0.23\textwidth]{exponential_p.eps}}
\centering \\
\subfigure[]{
\label{fig:subfig:b}
\includegraphics[width=0.23\textwidth ]{phase.eps}}
\centering
\subfigure[]{
\label{fig:subfig:b}
\includegraphics[width=0.23\textwidth]{correlation_r.eps}}
\caption{
(a) Log plot of the distribution function $P(n(r_i)/n_\infty(r_i))$ of the relative {\it quantum} fluctuation $n(r_i)/n_\infty(r_i)$.
(b)log plot of the distribution function $P(n(p_i)/n_\infty(p_i))$ of the relative {\it quantum} fluctuation $n(p_i)/n_\infty(p_i)$.
(c) The phase of the equilibrated wave function in the real space for the Henon-Heiles system.
(d) The normalized spatial correlation function $C(r)=\frac{1}{\braket{\Delta n^2}}\braket{(n(0)-\bar{n})(n(r)-\bar{n})}$ of density in the real space at equilibrium for the Henon-Heiles system.
}
\label{exponential}
\end{figure}

While the equilibrium density operator $\rho_\infty$ shares a good correspondence with the classical microcanonical ensemble $\rho_c$, the operator $\rho(t)$ does fluctuate around the equilibrium density operator, as shown in Fig. \ref{finalstaten}. This fluctuation has been shown to obey the exponential distribution in the ripple billiard system~\cite{xiong_universal_2011}. Here we focus on the Henon-Heiles system to bring this exponential distribution beyond billiard systems. To quantitatively show the fluctuation, we compare the probability density in both the real space and the momentum space, i.e. we compare $n(\xi)\equiv \braket{\xi|\rho(t)|\xi}$ with $n_\infty(\xi)$, $\xi=\vec{r},\vec{p}$.

Numerically this is realized by calculating the density $n(\xi_i) \mbox{ and }n_\infty(\xi_i) (i=1,\cdots, N)$ of $N$ small discrete region and calculate the distribution of the relative fluctuation $n(\xi_i)/n_\infty(\xi_i)$. Due to limited numerical precision, we choose different $N$ in the real space and momentum space and the results are shown in Fig. \ref{exponential}(a,b). Both distributions are found to be well fitted by exponential distribution. Due to the different $N$, the coefficients of the fitted exponential distributions are different in the real space and the momentum space.

\begin{figure}
\centering
\subfigure[]{
\label{fig:subfig:b}
\includegraphics[width=0.23\textwidth]{classical_r.eps}}
\centering
\subfigure[]{
\label{fig:subfig:b}
\includegraphics[width=0.23\textwidth]{classical_p.eps}}
\caption{
(a) The distribution function $P(n(r_i)/n_\infty(r_i))$ of the relative {\it classical} fluctuation $n(r_i)/n_\infty(r_i)$.
(b) The distribution function $P(n(p_i)/n_\infty(p_i))$ of the relative {\it  classical} fluctuation $n(p_i)/n_\infty(p_i)$.
}
\label{classical}
\end{figure}

This exponential distribution results from the randomness of wave function in a quantum chaotic system. Though the system is deterministic and evolves strictly with the Schr\"{o}dinger equation, the  scattering by
the potential wall bring the wave function to a state where the probability density and phases behave like random numbers.  Here we demonstrate the randomness by computing the phase of the wave function and the normalized probability density  correlation function $C(r)=\frac{1}{\braket{\Delta n^2}}\braket{(n(0)-\bar{n})(n(r)-\bar{n})}$ in the real space after equilibrium in the Henon-Heiles system. The results are shown in Fig. \ref{exponential}(c, d). We see that the phases vary rapidly in real space and the spatial correlation in real space decreases exponentially to zero within small distance compared to the
characteristic length scale $r_c$. These features  indicate certain randomness in the behavior of wave function in quantum chaotic systems. With this established randomness, the proof in Ref.~\cite{xiong_universal_2011} with slight modification, can explain this exponential distribution (see also the Appendix). Note that this randomness of wave function in quantum chaotic system is consistent with the idea of typicality~\cite{goldstein_canonical_2006}. It also supports, though not directly, the assumption we made in Eq. (2) and Eq. (3) in our previously work~\cite{zhuang_equilibration_2012}.

This exponential fluctuation is a pure quantum phenomenon. To show the quantum nature we consider the classical correspondence of an ensemble of particles obeying the same initial Gaussian
distribution of position and momentum and calculate their time evolution. Their phase space  distribution $\rho_c(t)$ approaches the microcanonical distribution $\rho_c$ due to the ergodicity in the Henon-Heiles system with certain fluctuation. Following the quantum case, we calculate the relative fluctuations $n_c(\xi,t)/n_c(\xi), \xi=\vec{r},\vec{p}$ and study their distributions. The classical relative fluctuations is Gaussian  as indicated in Fig. \ref{classical}. This shows that the exponential distribution of relative fluctuations is of quantum nature and absent in the classical system.

Besides the difference from classical case, we note that this exponential distribution is also different from the Porter-Thomas distribution in eigenstates~\cite{porter_fluctuations_1956} and the result now known
as the Berry's conjecture~\cite{Berry}. These results are only for eigenstates, which are real up to
an overall phase for systems with time reversal symmetry.
 The exponential distribution only exists for a complex wave function, For a generic quantum system,
 even if its all energy-eigenstates are real, its dynamical wave function is in general complex.
This distinction again shows that the general equilibrium statistical properties cannot be understood simply by properties of single eigenstates.   Superposition of numerous eigenstates is crucial.
We feel it very helpful to compare directly
the exponential distribution and the the Port-Thomas distribution~\cite{porter_fluctuations_1956}. We have re-derived these two  distributions
within the same mathematical framework in the Appendix.

\section{Discussion and Summary}
In summary, we have studied equilibration of quantum chaotic systems in the framework
suggested by von Neumann in 1929. Our study has examined various aspects of this issue,
such as dynamical equilibration,  quantum-classical correspondence between quantum equilibrium density operator $\rho_\infty$ and classical microcanonical ensemble $\rho_c$,  and the relative fluctuations around the equilibrium state.  All the results are illustrated with two single particle
quantum chaotic systems. We  expect most of the results  to hold in many-body quantum chaotic systems.

The dynamical equilibration should hold in many-body quantum chaotic systems because
it is completely determined by the energy gap statistics, which is universal
for all quantum chaotic systems. The quantum-classical correspondence should also hold
as it apparently originates from the similarity between quantum and classical Liouville equations.

However, the fluctuation properties in a many-body system will generally have Gaussian form, different from the single-particle case. The only except might be a Bose-Einstein condensate or a superconductor
where the many-body system can be described by a single-variable wave function. In all other cases,
the probability density at a given point $\xi=\vec{r},\vec{p}$ can be expressed by
\begin{equation}
n(\xi_1)=\int d\xi_2\cdots d\xi_N\, n(\xi_1,\xi_2\cdots,\xi_N)\,,
\end{equation}
where $N$ is the number of particles in this system. The fluctuation in $n(\xi_1,\xi_2\cdots,\xi_N)$ should have the exponential distribution due to the quantum chaotic nature of the many-body system. The integration over $N-1$ variables will produce a Gaussian distribution
due to the central limit theorem.

We note that one has to use many-body systems to discuss
the canonical statistics for a subsystem of the large isolated system. However, one
can use  the correspondence between $\rho_\infty$ and $\rho_c$ illustrated here with single-particle
systems to show that a subsystem of the many-body system will behave in canonical ensemble statistics. The derivation is similar to the work by Srednicki~\cite{srednicki_chaos_1994} and here we do not discuss further.

Although von Neumann has laid down the basic theoretical framework for the dynamical
equilibration in quantum systems in 1929~\cite{eV}, we believe that the study of this
fundamental issue has just started and many basic questions are still await to be answered.
Our study here and other related studies~\cite{Santos,Santos2} have indicated that
the quantum ergodic theorem hold for a class of quantum systems larger than
what is specified by the condition (\ref{condition}).  It is imperative to know how
to relax the condition (\ref{condition}) mathematically. We are also not clear about
the properties of the entropy  defined for a pure state by von Neumann.
We believe that these studies will not only lead to a better perspective on the foundation of quantum statistical
mechanics but also produce new physics such as the quantum multi-temperature equilibrium
state predicted in Ref.~\cite{zhuang_equilibration_2012} by us.

\begin{acknowledgments}
This work is supported by the NBRP of China (2012CB921300,2013CB921900) and
the NSF of China (11274024,11128407) and the RFDP of China (20110001110091).
\end{acknowledgments}

redpajama_set_name: RedPajamaArXiv


text:
Home » Tales of Crestoria : A Detailed Outlook (Everything You Need to Know)
Tales of Crestoria : A Detailed Outlook (Everything You Need to Know)
Shahbaaz
Tales of Crestoria is the latest game of the Tales franchise, exclusively for mobile devices. Developed by Bandai Namco entertainment inc and Klab, the game us all set for global release in the coming months.
Although initially a Japanese franchise, the tales series has managed to gain significant fanbase throughout the world since its first game in 1995. Now with the latest title Tales of Crestoria, the franchise is finally ready to enter into mobile gaming. With its global release only mere weeks away, specific details have started surfacing. Here is everything you should know.
Tales of Crestoria Announcement and Global Release Date
The developers first announced that they were working on their new game back in September 2018 via its Japanese twitter. Tales of Crestoria was initially scheduled for global release in the last quarter of 2019. However, due to development issues, the game was delayed.
Bandai Namco has not made any official statement about the release dates yet, but most sources suggest that the new launch date for the game is in June 2020.
Read Also | Tales of Crestoria is Expected to Release in June for iOS and Android
Tales of Crestoria Story
The game Tales of Crestoria takes place in a yet unnamed world. This world mandates that each of its residents carry special devices known as vision orbs. These devices record and report everything that an individual sees. When a crime happens, the vision orb data is used to judge the person. People thus found guilty of a crime are marked with a "strain" and an "enforcer" assigned to execute the sentence. The "strains" are symbols that appear on the body of a convict, branding them as "sinners"(the game calls criminals "sinners") to be hunted down by enforcers.
See also Dragon Raja Review: The New Gold Standard For Mobile MMORPGs
The game starts with placing the players in the shoes of Kanata Hjuger, the son of a monk who does his best to protect the weak. However, Kanata finds himself convicted guilty and exiled from society in his effort to protect someone very significant to him.
Video Credit: MaryVer Gamer Youtube Channel
The Home screen will act as the main navigation menu for the game. From there, players can access character rooms to personalize the characters. Tales of Crestoria offers a vast range of customization for characters, including various attachments.
Apart from the main storyline of the game, there are "side story," "episodes," and "face chat" that players can access during the game. While the main storyline is about Kanata and his friends, the side story takes place around the characters that they come across.
Episodes tell the backstory of each character outside of the main storyline. And face chats are fun conversations and interactions among the characters happening between jobs.
Memoria Stones are crystals of mana formed by strong emotions or memories. Players can use these stones to make a new character for their squad. Memoria Stones can also boost a character's stats when equipped.
Battle System
Tales of Crestoria will use a turn-based system for battles. That is surprising because the choice is very uncommon for the Tales series. We will have to wait and see how well the developers implement it.
Characters have regular attacks, combos, and special attacks that are unique to the characters. A certain number of normal attacks and combos enables the character to use special attacks. Characters also have unique abilities that players can use during battle.
See also Sorry Castle Cats, It's Time for Dungeon Dogs
Read |Spyjinx: Epic Games Reveals Their New Mobile Game for iOS
Main Playable Characters
There are six playable characters in Tales of Crestoria. Each of them has its back story., which unfolds as players progress through the game. They are
Kanata Hjuger
Kanata is the son of a monk who is also a village leader. He is protective of the weak and goes to any lengths to ensure that, which often puts him in trouble. Kanata has a deep fascination with the vision orbs and the way that they work. His crime is that he protected someone very close to him.
Misella
A young orphan raised in the monastery of Kanata's father. She is strong, and unlike Kanata, never loses herself in the heat of the moment. She is very protective of Kanata and will do everything in her power to keep him from harm. Her crime is an attempt to save a person close to her from punishment.
Known as the "Great transgressor," Vicious is a frightening character hated by almost everyone. He seems to withhold mystical powers within him and lives his life without a care for others. His crime is being born in the world. Vicious comes across Kanata and Misella while they were on the run just after becoming sinners, and joins them.
Aegis Alver
He is a young knight and a captain of the kingdom of Medagal. He is a sincere and honorable person, always doing the right thing, which often makes him look like a hardheaded person. Aegis is hell-bent on hunting down Kanata and his group of "sinners."
See also Taxi Sim 2020 Game Review: is this Game Worth Your Time?
Yuna Azetta
Yuna is a skilled journalist with a very bright personality. She is talkative and almost like a sister figure in the group. Yuna may not seem like it, but she will take any risk in her pursuit of truth. She runs a black market information store with vicious.
Orwin Granberg
Orwin is a tired old man. Despite having a wife Naya and a 10-year-old daughter Aura with her, he does not want to continue living. He does not earn anything and lives off his wife's money.
The developers have unveiled that the theme of Tales of Crestoria is "crime and betrayal." That is why almost all the main characters have a sin or crime that they carry with them.
As of now, Tales Of Crestoria is available for pre-register in Playstore and Appstore for Android and IOS devices, respectively. Since last week the game is available for open beta testing in Canada and few other countries.
Dragon Raja Review: This Is The New Gold Standard For Mobile MMORPGs
Legends of Runeterra Is Now Available on iOS and Android Worldwide
Soul of Eden: Rayark Inc's Upcoming Clash Royale Strategy Game
I don't need to "get a life". I'm a gamer. I have lots of lives.


"Every Soul Has a Purpose and Every Purpose Has a Story"
Paul Ernest began his career in advertising design in 1993 after receiving his BFA at the University of North Texas. Having been brought up in a family of fine artists and writers, Paul decided to pursue his love of photography and storytelling imagery. He began to experiment with a style combining composite photography with visually tactile elements and a warm color palette. Combining his passion for storytelling, Paul released his first image entitled "Chasing Butterflies" in 2009. Since then Paul has gone on to create numerous collections telling stories of healing, growth and inspiration.


text:
Home/White Sox Prospects
White Sox AA Pitcher of July: SP Frankie Montas
By James Poellnitz
A couple of weeks ago, the Chicago White Sox called up Frankie Montas from Double-A Birmingham to the majors to be the team's 26th man in a double-header against the Kansas City Royals.
Though the circumstances didn't give Montas the chance to get into either game, the opportunity shows how highly the team feels about him.
The hard-throwing right-hander has come alive over the last two months in Birmingham.
In July, Montas went 2-1 with a 1.96 ERA and a 1.00 WHIP in five starts. He had 28 strikeouts in 23 innings and opponents hit just .202 against him.
He has not allowed more than three runs in any start this season and you have to go back to May 19th to find the last time he allowed more than two runs in a game.
His best start last month came on July 19th against the Pensacola Blue Wahoos (Reds AA affiliate). Montas picked up his third win of the season behind two hits, one walk and eight strikeouts in five innings.
Watch him work for his eighth strikeout of the night in the video below.
For the year, Montas is 3-2 with 2.43 ERA (which ranks third among Southern League pitchers) in 18 starts. In 89 innings, he has 82 strikeouts and opponents are hitting .212 against him.
Myles Jaye started the season as one of the best pitchers on the Barons. After hitting a speed bump in May to the tune of a 5.64 ERA, he has put himself back on track and overall is putting together a strong body of work.
More from White Sox Prospects
Tyler Schweitzer could become a great White Sox pitcher
The Chicago White Sox drafted well on days two and three
This White Sox prospect is absolutely on fire right now in AAA
Yoelqui Cespedes has been red-hot for the White Sox
Looking at the potential of White Sox prospect Oscar Colas
In July, Jaye went 4-1 with a 1.93 ERA in five starts. Opponents hit .202 against him and he had 20 strikeouts in 28 innings. At one point he had a 32-inning scoreless streak that stretched from June 17th to July 13th.
Jaye's best start last month came on July 8th against the Tennessee Smokies (Cubs AA affiliate). He allowed no runs on six hits while striking out eight over seven innings. He also picked up his eighth win of the season in that outing.
Overall, Jaye is 11-4 with a 2.66 ERA in 19 starts. Those 11 wins lead the Southern League and his ERA is good for fifth. He has 80 strikeouts in 111.2 innings and opponents are hitting .228 against him.
AA notes
Mark Blackmar went 3-0 with 3.10 ERA in five July starts. His 113 innings leads the Barons…. Kyle Hansen has gone 14 straight relief appearances without allowing a run. You have to go all the way back to June 5th to find the last time he allowed a run….. Zach Isler went 4-4 in save opportunities in July and posted a 1.46 ERA in his nine appearances.
More from Southside Showdown
The Chicago White Sox might have had a season ending loss
The Chicago White Sox are expecting Tim Anderson back soon
Miguel Cairo's words spark life into the Chicago White Sox
Dylan Cease should be the favorite for the AL Cy Young Award
Ozzie Guillen speaks the whole truth about Tony La Russa


text:
"""Internal network layer helper methods."""

import select
import struct

_HAS_POLL = True
_poller = None
_EVENT_MASK = 0
try:
    from select import poll
    _poller = poll()
    _EVENT_MASK = (select.POLLIN | select.POLLPRI | select.POLLERR |
                   select.POLLHUP | select.POLLNVAL)
except ImportError:
    _HAS_POLL = False

from pymongo import helpers, message
from pymongo.errors import AutoReconnect

_UNPACK_INT = struct.Struct("<i").unpack

def command(sock, dbname, spec, slave_ok, is_mongos, read_preference,
            codec_options, check=True, allowable_errors=None):
    """Execute a command over the socket, or raise socket.error.

    :Parameters:
      - `sock`: a raw socket instance
      - `dbname`: name of the database on which to run the command
      - `spec`: a command document as a dict, SON, or mapping object
      - `slave_ok`: whether to set the SlaveOkay wire protocol bit
      - `is_mongos`: are we connected to a mongos?
      - `read_preference`: a read preference
      - `codec_options`: a CodecOptions instance
      - `check`: raise OperationFailure if there are errors
      - `allowable_errors`: errors to ignore if `check` is True
    """
    ns = dbname + '.$cmd'
    flags = 4 if slave_ok else 0
    if is_mongos:
        spec = message._maybe_add_read_preference(spec, read_preference)
    request_id, msg, _ = message.query(flags, ns, 0, -1, spec,
                                       None, codec_options)
    sock.sendall(msg)
    response = receive_message(sock, 1, request_id)
    unpacked = helpers._unpack_response(response, codec_options=codec_options)
    response_doc = unpacked['data'][0]
    msg = "command %s on namespace %s failed: %%s" % (
        repr(spec).replace("%", "%%"), ns)
    if check:
        helpers._check_command_response(response_doc, msg, allowable_errors)
    return response_doc

def receive_message(sock, operation, request_id):
    """Receive a raw BSON message or raise socket.error."""
    header = _receive_data_on_socket(sock, 16)
    length = _UNPACK_INT(header[:4])[0]

    actual_op = _UNPACK_INT(header[12:])[0]
    assert operation == actual_op, ("wire protocol error: "
                                    "unknown opcode %r" % (actual_op,))
    # No request_id for exhaust cursor "getMore".
    if request_id is not None:
        response_id = _UNPACK_INT(header[8:12])[0]
        assert request_id == response_id, (
            "wire protocol error: got response id %r but expected %r"
            % (response_id, request_id))

    assert length > 16, ("wire protocol error: message length is shorter"
                         " than standard message header: %r" % (length,))

    return _receive_data_on_socket(sock, length - 16)

def _receive_data_on_socket(sock, length):
    msg = b""
    while length:
        chunk = sock.recv(length)
        if chunk == b"":
            raise AutoReconnect("connection closed")

        length -= len(chunk)
        msg += chunk

    return msg

def socket_closed(sock):
    """Return True if we know socket has been closed, False otherwise.
    """
    try:
        if _HAS_POLL:
            _poller.register(sock, _EVENT_MASK)
            rd = _poller.poll(0)
            _poller.unregister(sock)
        else:
            rd, _, _ = select.select([sock], [], [], 0)
    # Any exception here is equally bad (select.error, ValueError, etc.).
    except:
        return True
    return len(rd) > 0

redpajama_set_name: RedPajamaGithub


Payment plans are available and will cost more; talk to Katherine.
If you were referred by someone, who may we thank for your referral?
I will review it personally, and get back to you within 48 hours (after July 10th), to set up a phone conversation.
Together, we'll determine whether or not this Training is a good fit, for where you're heading in your practice, as well as for the needs of Entering the Healing Temple™.
If it's not, we'll either step away or we'll map out what needs to happen, in order for "the fit" to emerge.
If it IS a fit, you'll pay the $500 non-refundable deposit, and you'll choose either the Full Pay or the Payment Plan.


text:
CPA6 () – білок, який кодується однойменним геном, розташованим у людей на короткому плечі 8-ї хромосоми. Довжина поліпептидного ланцюга білка становить 437 амінокислот, а молекулярна маса — 51 008.

Кодований геном білок за функціями належить до гідролаз, протеаз, металопротеаз, карбоксипептидаз.
Задіяний у такому біологічному процесі, як альтернативний сплайсинг.
Білок має сайт для зв'язування з іонами металів, іоном цинку.
Локалізований у позаклітинному матриксі.
Також секретований назовні.

Література

Примітки

Див. також
 Хромосома 8

Протеази
Некатегоризовані білки


This content is password protected. Please enter your user name and password. If you wish to gain access to this area of the site, please submit the form below or call 800-657-0793 to inquire about access.
Please completely fill out the form below if you wish to have access to our to our sell sheets, product images or to add your dealership address to the locator. We will process your request within 48 business hours.
Please make sure you click the box at the very bottom if you wish to included in our dealer locator.
Please include me in your dealer locator.


text:
Interim Content
Affidavit from Daniel Avery, 28 December 1843
1 July 1797–16 Oct. 1851. Farmer, carpenter. Born in Oswego Co., New York. Son of Daniel Avery and Sarah. Moved to Franklin Co., Ohio, by 1821. Married Margaret Adams, 4 Jan. 1821, in Franklin Co. Moved to Worthington, Franklin Co., by Sept. 1825; to Perry...
, Affidavit, before JS,
, IL, 28 Dec. 1843; handwriting of
; docket in handwriting of
Thomas Bullock
23 Dec. 1816–10 Feb. 1885. Farmer, excise officer, secretary, clerk. Born in Leek, Staffordshire, England. Son of Thomas Bullock and Mary Hall. Married Henrietta Rushton, 25 June 1838. Moved to Ardee, Co. Louth, Ireland, Nov. 1839; to Isle of Anglesey, Aug...
; nine pages; JS Office Papers, CHL.
State of Illinois) ss
On the 28th day of Decr— 1843, came
before me Joseph Smith Mayor of the
aforesaid, and after being duly sworn, deposeth and saith that on the 2d day of December 1843, he was unlawfully arrested by force and arms, and Kidnapped And Kidnapped at Doty's Mill in
bear Creek precinct
Named after stream that rises near Carthage, Illinois, and flows southwest into Mississippi River. JS arrested in area, 5 June 1841, by Adams Co., Illinois, sheriff Thomas King, acting on warrant from Illinois governor Thomas Carlin, who planned to deliver...
Formed from Pike Co., 1825. Described in 1837 as predominantly prairie and "deficient in timber." Early settlers came mainly from mid-Atlantic and southern states. Population in 1835 about 3,200; in 1840 about 9,900; and in 1844 at least 15,000. Carthage ...
Became part of Northwest Territory of U.S., 1787. Admitted as state, 1818. Population in 1840 about 480,000. Population in 1845 about 660,000. Plentiful, inexpensive land attracted settlers from northern and southern states. Following expulsion from Missouri...
aforesaid by Col.
Levi Williams
18 Apr. 1794–27 Nov. 1860. Postmaster, farmer, military officer. Born in Madison Co., Kentucky. Married Mary (Polly) Reid. Moved to Hancock Co., Illinois, ca. 1831, eventually settling in Green Plains. Served in Black Hawk War, 1832. Served as captain in ...
, his Son John Williams, <of
Hancock Co.
>
John Elliot[t]
Ca. 1820–3 Oct. 1862. Schoolmaster, deputy sheriff, constable, clerk, marshal. Born in Butler Co., Ohio. Lived four miles south of Warsaw, Hancock Co., Illinois, 1843, where he worked as a schoolmaster. Arrested for and later acquitted of kidnapping Daniel...
, a school master from 4½ miles below
Located at foot of Des Moines rapids of Mississippi River at site of three military forts: Fort Johnson (1814), Cantonment Davis (1815–1818), and Fort Edwards (1816–1824). First settlers participated in fur trade. Important trade and shipping center. Post...
, William Middleton and Joseph McCoy of Clark County Missouri and four others.
Col Williams
held his bowie knife to his breast. Six of the other stood with their pistols cocked and th[e]ir fingers upon the triggers, muzzels presented at his body, ready to fire, and two stood with clubs, and, amid the most horrid oaths and imprecations, took and bound me with silk handerchiefs, your said
affiant
and led him away between two men, one holding a savage bowie knife on one side and the other a cocked pistol on the other side, (having taking taken away your said
s weapons [p. 1]
aforesaid, and after being duly sworn, deposeth and saith that on the 2d day of December 1843, he was unlawfully arrested by force and arms, And Kidnapped at Doty's Mill in
, his Son John Williams, of
held his bowie knife to his breast. Six of the other stood with their pistols cocked and their fingers upon the triggers, muzzels presented at his body, ready to fire, and two stood with clubs, and, amid the most horrid oaths and imprecations, took and bound with silk handerchiefs, your said
and led him away between two men, one holding a savage bowie knife on one side and the other a cocked pistol on the other side, (having taken away your said


FELIX Austria finished 2008 in a survey conducted by Hewitt Associates study on an employer an excellent second place.
Employees feel comfortable. Appreciation and promotion of employees is a top priority. Combined with strong brand and know-how in food employees are the most important asset of the company.
FELIX employees have their own canteen, where they can start their day with healthy breakfast. At Lunch they can choose between two menus and an enormous salad buffet. They can purchase these wide range of products for a employee price.
In a regular period of time FELIX Austria organizes company outings. Our employees take this time to get to know each other and learn new experiences. FELIX company outings are always a real highlight!


text:
COASTER-net TV
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Mad Mouse
Specific Type: Wild Mouse
Seating: Single Cars, 2 x 2
Length: 1,268 feet
Manufacturer: Arrow Dynamics
Official Debut: 1999
Michigan's Adventure got back into the steel coaster market in 1999 with the addition of two steel coasters. Both were family oriented, with one of them being the kiddie coaster Big Dipper and the other being Mad Mouse. As its name would suggest, Mad Mouse is a fairly standard wild mouse type coaster. One unique feature of it though is the fact that it is one of only three currently operating Arrow Dynamics wild mouse coasters in the world. These coasters aren't the most impressive with their height or speed, but their unbanked lateral turns and overall smooth ride make these rides fun for the whole family. The train setup of Mad Mouse consists of several single-car trains which seat four people each. To make up for the capacity issues posed by having four person trains Mad Mouse has several block breaks so a large number of trains can run on the track at the same time. At the cost of $2 million, Mad Mouse has proven to be a great investment for Michigan's Adventure.
The journey on Mad Mouse begins as you take a right turn out of the boarding area, Mad Mouse lacks a traditional station, and begin heading up the 68' tall lift hill. As the train crests the lift it doesn't take a dive back down towards the ground like a traditional coaster. Instead the train takes a gentle drop of only a few feet while turning right. After the turn is completed the track levels out and begins heading in a straight line. The track then suddenly takes an unbanked turn to the right leaving riders feeling like they are about to fly out into the midway. After turning 180 degrees the train slides through some brakes and gets ready for another unbanked turn, this time to the left while riders feel like they will fly out into the parking lot. The train continues this pattern while slightly descending so the train keeps up its speed. After the train gets done doing its zig-zag routine riders will have gone through six 180 degree turns, three to the right and three to the left. After its last turn it slides through some brakes once again and takes a right hand turn. This time instead of heading back in the direction it came from the train dives towards the ground while turning right and heads underneath the track which it just traveled over. After reaching the ground the train heads right back up for a little airtime. After cresting the airtime hill the car slides through more brakes and makes a wide 180 degree right hand turn. Upon completing the turn the car dives back towards the ground and then goes right back uphill for a small hill and more brakes. Up next is another wide right hand turn followed by a small drop and a small airtime hill that gives riders a nice pop of air. Up next is a small hill with brakes on top followed by a gentle right hand turn into the final brakes. Here the riders wait until it is their turn to get off the ride and enjoy the rest of Michigan's Adventure.
©1998-2016 COASTER-net.com, All Rights Reserved.
© COPYRIGHT COASTER-net.com 1998-2016. ALL RIGHTS RESERVED.


text:
Saint-Julien-sur-Calonne
French Version : http://www.cartesfrance.fr/carte-france-ville/14601_Saint-Julien-sur-Calonne.html
Calvados >
Town of Saint-Julien-sur-Calonne
The village of Saint-Julien-sur-Calonne is a small village located north west of France. The town of Saint-Julien-sur-Calonne is located in the department of Calvados of the french region Basse-Normandie.	The town of Saint-Julien-sur-Calonne is located in the township of Pont-l'Évêque part of the district of Lisieux. The area code for Saint-Julien-sur-Calonne is 14601 (also known as code INSEE), and the Saint-Julien-sur-Calonne zip code is 14130.
Geography and map of Saint-Julien-sur-Calonne :
The altitude of the city hall of Saint-Julien-sur-Calonne is approximately 50 meters. The Saint-Julien-sur-Calonne surface is 8.54 km ². The latitude and longitude of Saint-Julien-sur-Calonne are 49.289 degrees North and 0.228 degrees East. Nearby cities and towns of Saint-Julien-sur-Calonne are : Surville (14130) at 1.86 km, Vieux-Bourg (14130) at 2.95 km, Manneville-la-Pipard (14130) at 3.39 km, Pont-l'Évêque (14130) at 3.39 km, Pierrefitte-en-Auge (14130) at 3.93 km, Le Mesnil-sur-Blangy (14130) at 4.19 km, Tourville-en-Auge (14130) at 4.22 km, Les Authieux-sur-Calonne (14130) at 4.23 km.
(The distances to these nearby towns of Saint-Julien-sur-Calonne are calculated as the crow flies)
Population and housing of Saint-Julien-sur-Calonne :
The population of Saint-Julien-sur-Calonne was 189 in 1999, 194 in 2006 and 193 in 2007. The population density of Saint-Julien-sur-Calonne is 22.60 inhabitants per km². The number of housing of Saint-Julien-sur-Calonne was 124 in 2007. These homes of Saint-Julien-sur-Calonne consist of 78 main residences, 43 second or occasional homes and 3 vacant homes.
I like Saint-Julien-sur-Calonne !
Administrative Information of Saint-Julien-sur-Calonne
Region : Basse-Normandie (25)
Departement : Calvados (14)
District : Lisieux
Township : Pont-l'Évêque
Nearby towns of Saint-Julien-sur-Calonne
Here are maps and information of the close municipalities near Saint-Julien-sur-Calonne.
See all the towns of Calvados (Distances are calculated as the crow flies)
Surville (14) at 1.86 km Vieux-Bourg (14) at 2.95 km
Manneville-la-Pipard (14) at 3.39 km Pont-l'Évêque (14) at 3.39 km
Pierrefitte-en-Auge (14) at 3.93 km Le Mesnil-sur-Blangy (14) at 4.19 km
Tourville-en-Auge (14) at 4.22 km Les Authieux-sur-Calonne (14) at 4.23 km
Saint-Benoît-d'Hébertot (14) at 4.25 km Coudray-Rabut (14) at 4.25 km
Saint-André-d'Hébertot (14) at 4.55 km Fierville-les-Parcs (14) at 5.46 km
Saint-Hymer (14) at 5.64 km Saint-Martin-aux-Chartrains (14) at 5.80 km
Reux (14) at 5.85 km Blangy-le-Château (14) at 6.11 km
Le Theil-en-Auge (14) at 6.53 km Le Breuil-en-Auge (14) at 7.01 km
Saint-Gatien-des-Bois (14) at 7.04 km Canapville (14) at 7.23 km
Geography of Saint-Julien-sur-Calonne
Population and housings of Saint-Julien-sur-Calonne
Population data : Population Saint-Julien-sur-Calonne
Population density : 22.60 hab/km²
Housings data : Housing Saint-Julien-sur-Calonne
Hotel Saint-Julien-sur-Calonne
Search hotels near Saint-Julien-sur-Calonne : Book your hotel now !
Find all hotels of Saint-Julien-sur-Calonne :
Hotel : Auberge Saint Martin
Situated in the heart of the Normandy countryside, Auberge Saint Martin offers comfortable rooms and serves regional cuisine in its traditional restaurant. All the rooms at the...
Address : route de Rouen 14130 Surville
Distance Hotel - Saint-Julien-sur-Calonne : 1.74 km
Bed and Breakfast : Le Prieuré Boutefol
Offering an outdoor pool, this B&B is set in a 17th-centry priory and it is located in Surville. Surrounded by the countryside, it provides free parking and free WiFi access. ...
Contact : Le Prieuré Boutefol 313 route de Rouen 14130 Surville
Distance Bed and Breakfast - Saint-Julien-sur-Calonne : 2.05 km
Bed and Breakfast : Le Vieux Pressoir
Offering a heated, covered pool in the tree-lined garden, Le Vieux Pressoir B&B is located in Pont-l'Évêque. It has fitness equipment, a relaxation area and a continental breakf...
Contact : 379 route de Rouen 14130 Pont-l'Évêque
Hotel : Hotel et Spa Le Lion d'Or
Located in Pont-l'Évêque, a 15-minute drive from Deauville, this fully remodelled former coaching inn offers 3-star accommodation and a 200 m² spa with a swimming pool, steam ro...
Contact : 8, Place Saint Mélaine 14130 Pont-l'Évêque
Apartment : La Villa Bottentuit
Located in Pont-l'Évêque, 2.4 km from Pont-L'Evêque Lake, La Villa Bottentuit offers a living room with a flat-screen TV. Guests staying at this apartment have access to a fully...
Address : Place Vaucquelin 14130 Pont-l'Évêque
Distance Apartment - Saint-Julien-sur-Calonne : 2.70 km
Bed and Breakfast : Les Fruitiers
Les Fruitiers is situated in Les Authieux-sur-Calonne, 16 km from Deauville. Free WiFi is offered and free private parking is available on site. Certain units include views of ...
Contact : 1482 Route de Blangy 14130 Les Authieux-sur-Calonne
Hotel : Eden Park
Eden Park is located in the heart of the Auge region, 15 minutes away from Deauville, Trouville and Honfleur. The hotel Eden Park features 50 fully-equipped rooms accessed by s...
Contact : Avenue de la Libération RD48 14130 Pont-l'Évêque
Guest accommodation : Manoir du Poirier de Chio
Located in Pont-l'Évêque, just a 20-minute drive from Deauville, Manoir du Poirier de Chio dates back to the 17th-Century and offers a large garden. Honfleur is 17 km away. Ind...
Contact : 40 avenue de la Libération 14130 Pont-l'Évêque
Distance Guest accommodation - Saint-Julien-sur-Calonne : 3.13 km
Bed and Breakfast : Maison d'hôtes Les Vikings
Located 800 metres from Pont-l'Évêque city centre, Maison d'hôtes Les Vikings is set in the Normandy countryside. This guest house features a floral garden, a wooden caravan and...
Address : 15 Avenue De La Libération 14130 Pont-l'Évêque
Guest accommodation : Maison Normande
Maison Normande is set in Saint-André-d'Hébertot, 15 km from Deauville and 12 km from Honfleur. Free private parking is available on site. This room feature a private bathroom ...
Contact : 97 route de Saint Benoit 14130 Saint-André-d'Hébertot
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La grande demeure
Photo taken : 10 Août 2010
Photographer : fvexler
Photo of the town of Saint-Julien-sur-Calonne or neighboring municipalities	 A 13
Taken by : marc76640
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14-Surville monument aux morts
By : jefrpy
Pic of the town of Saint-Julien-sur-Calonne or neighboring towns	 Camping du Lac
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Saint-Julien-sur-Calonne, Fransa
Photo taken : 22 Mars 2010
Photographer : savunma
Photo of the town of Saint-Julien-sur-Calonne or neighboring municipalities	 Golf Saint-Julien
Picture taken : 01 Juin 2012
Taken by : picavet.be
Chateau du Mont Saint léger
Pic taken : 13 Mars 2013
By : Pierre PAGNIEZ
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The latest weather data for Saint-Julien-sur-Calonne were collected Saturday, 18 January 2020 at 14:48 from the nearest observation station of Lisieux.
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text:
"You Oughta' Been There When the Lord Saved Me!" She said, "I was a prostitute"… Another was a Catholic priest destine for hell
[An Excerpt] source
"October 18, 1985 will be a date that I will remember until I take my dying breath. I was involved in a head-on collision with a truck… …the scalp on the right side of my head was ripped from my skull. "
"Gang members shot him 8 times; an angel saved his life"
"I was like 'God help me."
Police suspect the attempted murder was a random case of initiates … He played piano with R&B singer Chris Brown. He traveled with gospel musicians like Donnie McClurkin, but he didn't really pay attention to the gospel. He was drawn by the money and extravagant lifestyle. Read full testimony at source.
"How Did I Get Like This? – A Prostitute Says" "I just remember going, 'How did I get to this point? This is my life?" Tina Hoffman never intended to become a prostitute. But eventually, she lived up to her step-father's words. "I remember my step-dad telling me when I was little, 'Oh, You're just going to grow up to be a whore like your mother,'" Tina recalls. "My mom wasn't of course. She was an extremely hardworking, you know, beautiful, wonderful mother."
https:/youtu.be/FZvJGxXbCRM
1 800-759-0700 (Prayer Line)
Tags: miracle from heavenCategories: media dialogue
32 thoughts on ""You Oughta' Been There When the Lord Saved Me!" She said, "I was a prostitute"… Another was a Catholic priest destine for hell"
Simply Splendid Food says:
07, 08, at 0:00
By the grace of God..what a story!😏🏆😍
Those are heart-warming stories of redemption. Thank you.
Americaoncoffee says:
They are amazing. Thank you for visiting and commenting. With every saved soul m, the stronger is our battle against Satan. 🙏
PRAPTI GUPTA says:
Thank you Prapti! ♥
Amazing stories.
Agree. Thank you for comment and for your visit today.
Great story 💜💜💜
Thank you.✝
Quite a poignant account of raw reality. I must say it makes you count your own blessings, yet saddened for others.
We all have a major cross in our lives. We all come to crossroads and we all have stories about our life's journey. Peace and blessings. 🛐
Yes..it reminds me of the old Nietzsche saying. "If it doesn't kill you… it makes you stronger.". He actually wrote it about a lady that broke his heart…It does have a universal ring to it though. Cheers! 😍
Those who endure to testify are a blessed 🙏
Amen!🤩
Commander Sandeep Dhawan (Veteran) says:
Blessings to you!
Lashaan Balasingam @ Bookidote says:
It's amazing when people get ahold of themselves and change for the better. Thanks for sharing! Take care! :)
Amen! I hope there will be a plethora of spiritual awakenings that will better our relationship with the Lord and kindreds. Many blessings to you and thank you for your visit.
apoet'svisionKrissy says:
Amazing !!! Miracle
More of God's Grace will come with more spreading of the gospel.
Kirt D Tisdale says:
Inspirational stories!! Thanks for sharing!
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