text:
\section{Introduction}
The measurement problem is always the fundamental problem in quantum related discussion. In the history of quantum mechanics, kinds of theories
typically differ from the interpretation of the measurement process. The orthodox quantum mechanics also known as Copenhagen interpretation explained
the measurement process by the collapse of the wave function as an independent law which is considered to be unprofessional by Bell . The many-worlds
interpretation developed by Hugh Everett described the measurement by ``branching'' which had to face qualitative problem and quantitative problem
about probability \cite{saunders2010many}\cite{vaidman2014quantum}. The Bohmian mechanics as a deterministic theory viewed measurement process as the
evolution of wave function determined by Schr\"{o}dinger equation and the evolution of trajectory determined by guidence equation
\cite{pladevall2019applied}\cite{sebens2015quantum}, but controversial for ``hidden variables''. Other interpretations were mentioned in
\cite{ringbauer2017reality}\cite{dewitt2015many} and several locally deterministic interpretations were reviewed in \cite{waegell2017locally}. All
ontic and epistemic interpretations argue about what the reality of wave function is, in other words, what object the quantum state is
\cite{ringbauer2017reality}. Measurement is the key to connect the reality and wave function or probability \cite{merali2015really}. The acceptance of the measurement as a
special behavior in the evolution of quantum system like Copenhagen interpretation may bring the discussion into philosophy about ontology and
epistemology \cite{ringbauer2017reality}. We will not argue about these opinions like Einstein and Bohr but using another method to show the
connection between reality and probability. \par
Hall, Deckert, and Wiseman proposed a many-interacting-worlds (MIW) method through  a huge, but finite, number of classical ``worlds'' and quantum
effects arise from the interaction between these worlds \cite{hall2014quantum}. The worlds in MIW are definitely different from the many-worlds
interpretation since classical worlds mean determinism in every world and never branch out. If all equally weighted worlds represent reality, then
the probabilities come from the ignorance of which world the observers actually occupy. The reality or ontology in MIW method is the macroscopic
properties of worlds like world configurations and velocities described by probability density while more detailed discussion in
\cite{sebens2015quantum} called Prodigal QM which is an early idea blending many-world and Bohmian mechanics. We could say that the observers will
not specialize the measurement process in MIW since it's involved in the evolution of entire system according to Bohmian mechanics while MIW method
interpreted the evolution classic-like by introducing interaction potential. \par
The physical part of this method mainly constructed on de Broglie-Bohm mechanics but represented with respect to probability density function instead
of wave function, which made it easy to discuss the transformation from continuous density to discrete empirical density. According to the quantum potential in Bohm mechanics\cite{bohm1952suggested} and the discussion in \cite{hall2014quantum}, since we mainly work on the average of energy in the following sections, the interworld potential for $N$ countable ``worlds'' can be replaced b
\begin{equation}
U_{N}(\mathbf{X})=\sum^{N}_{n=1}\sum^{K}_{k=1}\left.\frac{\hslash^{2}}{8m^{k}P(\mathbf{q})^{2}}\left(\frac{\partial P(\mathbf{q})}{\partial
q^{k}}\right)^{2}\right|_{\mathbf{q}=\mathbf{x}_{n}},
\end{equation}
where $\mathbf{X}=\{\mathbf{x}_{1},\dots ,\mathbf{x}_{N}\}$  denotes the world configurations,  $\mathbf{x}_{n}=\{x^{1}_{n}(t),\dots ,x^{K}_{n}(t)\}$
denotes the world-particle position, $m^{k}$ is the mass of the $k$th particle, $P(\mathbf{q})$ is the probability density of system. Our purpose is
to find
some proper empirical distribution
\begin{equation}
\mathbb{P}_{N}(A)=\frac{\#\{n:x_{n}\in A\}}{N},\label{empirical distribution}
\end{equation}
for any Borel set $A\subset\mathbb{R}$, whose density $P^{*}_{N}(A)$ can approximate the probability density $P(\mathbf{X})$, where $\# A$ denotes
the number of elements in the set $A$.
We expect that the quantum effects would improve as $N\to\infty$. A toy model related to ground state of harmonic oscillator was simulated using MIW
method in \cite{hall2014quantum}.
In this article we will not use dynamical MIW algorithm \cite{sturniolo2018computational}\cite{cruz2018quantum}\cite{goldstein2014quantum} to evolve
the world-particle and the classical mechanics in per ``world'' is also built on the interworld interaction potential, so we can pay little attention
on time variable $t$.\par
Mathematically, ones can interpret this method  from probability theory  since the approximation of probability is an important part in MIW method.
The intelligent idea in this method is countable classical ``worlds'' reflected in the $N$ of empirical distribution. How to find the proper
empirical density is the key point when we apply MIW method to a given system. Stein's method is a good choice for density approximation. Actually
the relation between MIW method and stein's method has been studied deeply in
\cite{mckeague2016stein}\cite{chen2020optimal}\cite{mckeague2016convergence}.\par
The higher excited states \cite{mckeague2016stein}\cite{ghadimi2018nonlocality} and higher dimensional models \cite{herrmann2017ground} of harmonic oscillator have been
simulated. All of these show the succeed of MIW method as an approach to standard quantum mechanics at least in harmonic oscillator model. \par
However all of these discussion about harmonic oscillator rely on the close relation between the solution of harmonic oscillator and standard
Gaussian \cite{herrmann2017ground}. The framework and foundation of stein's method on normal approximation is also more detailed than other
distribution. When it comes to other models such as hydrogen atom which was also a perfectly solved problem in quantum history, we need to consider
the applicability of MIW method. Mathematically saying, we need to consider the approximation of non-gaussian distribution. In this article we will
test the one-dimensional Coulomb potential model in the first excited state using MIW method. As a necessary part in approximation of density, we
also provide a proof of the convergency when the number of ``worlds'' $N\rightarrow\infty$. Nevertheless, we try to discuss the generality when apply
MIW method to different cases.\par
Before we list our results, we should explain why we focus on the one-dimension case and the first excited state of Coulomb potential model. Our
purpose is to test MIW method with hydrogen model and the results will be reflected in the approximation of empirical distribution to hydrogen atom's
probability
density. The one dimensional case is the most intuitive and mathematically simplified. Higher dimension will not only greatly increase the complexity
of analytical calculation but also be difficult to graph the comparison of simulated results.
For choosing the first excited state, it's easy to derive that the ground state of one dimensional hydrogen atom is trivial \cite{loudon1959one}.
The node problem in the first excited state of one dimensional hydrogen atom case is different from non-ground states of one dimensional harmonic oscillator, since there is an infinity potential barrier at $x=0$. This constraint will turn to a special boundary condition at $x=0$ which forces us to discuss interworld potential in half in the following sections.
\section{Interworld interaction potential}
According to MIW method, the Hamiltonian of a given system is given by
\begin{equation}
H_{N}(\mathbf{X},\mathbf{P}):=\sum_{n=1}^{N}\sum_{k=1}^{K}\frac{(p_{n}^{k})^{2}}{2m^{k}}+\sum_{n=1}^{N}V\left(\mathbf{x}_{n}\right)+U_{N}(\mathbf{X}),
\end{equation}
where the first term is the kinetic energy with the definition of momentum $\mathbf{P}=\{\mathbf{p}_{1},\dots,\mathbf{p}_{N}\}$ and
$\mathbf{p}_{n}=\{p_{n}^{1},\dots,p_{n}^{K}\}$, the second term is the potential energy of given system. In our case we default $K=1$ which means
only one particle per ``world''
and totally $N$ ``worlds'' in 1d Coulomb potential of the form (Gaussian units)
\begin{equation}
V\left(x_{n}\right)=-\frac{e^2}{\vert x_{n}\vert}.
\end{equation}\par
Not like 3d hydrogen atom, it turns out more difficult to completely discuss the solutions of 1d Coulomb potential \cite{loudon1959one}. Here we
display the 1st excited state solution of the form
\begin{equation}
\Psi_{1}(x)=B_{1}xe^{-\vert x\vert},
\end{equation}
where we use dimensionless unit $me^{2}/\hslash^{2}=1$ and $B_{1}=\sqrt{2}$ is determined by normalization. In the following we will focus on the
distribution density of the form
\begin{equation}
P(x)=\vert\Psi_{1}(x)\vert^{2}=2x^{2}e^{-2\vert x\vert},
\end{equation
called weighted Laplace distribution, which is the target function we try to approximate with some empirical distribution. But there is a singularity
problem at $z=0$, and by easily derivation its third order derivative is discontinue which makes it not smooth enough. In \cite{pike2012stein} John
Pike had developed a framework of Laplace distribution using stein's method. We will begin with the stein's equation of Laplace distribution
in Lemma 2.2 of \cite{pike2012stein} ($b=1$ in our case),
\begin{equation}
g'(x)-\text{sgn}(x)g(x)=\widetilde{h}(x),\  g(0)=0,
\end{equation}
where $h\in \mathcal{H}=\{h:\mathbb{R}\to\mathbb{R}\text{ Lipschitz with }\Vert h\Vert_{\infty}\leq1\}$ and $W\sim\text{Laplace}(0,1)$,
$\widetilde{h}(x)=h(x)-\mathbb{E}[h(W)]$. The solution is given by
\begin{equation}
g_{h}(x)=\left\{
\begin{aligned}
&-e^{x}\int_{x}^{\infty}\widetilde{h}(y)e^{-y}dy\ &\textrm{$x>0$},\\
&e^{-x}\int^{x}_{-\infty}\widetilde{h}(y)e^{y}dy\ &\textrm{$x<0$}.
\end{aligned}\right.
\end{equation}\par
Different from other smooth continue distribution such as standard Gaussian, the form of Laplace distribution especially the absolute value makes the
solution a piecewise function.
similar to
the process of solving 1d hydrogen atom.
Thus without loss of generality, we can treat $P(x)$ in the same way. Once we discuss (weighted) Laplace distribution in part, it will degenerate to
two independent but essentially same (weighted) Exponential distribution. So we can turn to the stein's equation of weighted Exponential distribution
$P_{\pm}(x)=2x^{2}e^{\mp 2x}$ (subscript ``$+$'' means $z>0$, ``$-$'' means $z<0$)
\begin{equation}
g'(x)+\frac{P'_{\pm}(x)}{P_{\pm}(x)}g(x)=\widetilde{h}(x).
\end{equation}\par
If we want to perform the zero-bias transformation based on the stein's equation to construct another distribution, we must deal with the singularity
at $z=0$ which is excluded by stein's equation but continue where actually $P_{\pm}(0)=0$. \cite{mckeague2016stein} provided a generalized zero-bias
transformations that solved the singularity in higher excited states of 1d harmonic oscillator or called two-sided Maxwell case. We will try to apply
this method to our case. Follow the Definition 3.1 in \cite{mckeague2016stein}, we say that a random variable $W^{*}$ has
definition
\emph{b-generalized-zero-bias distribution} of $W$ if
\begin{equation}
\sigma^{2}\mathbb{E}\left[\frac{g'(W^{*})}{b(W^{*})}\right]=\mathbb{E}\left[\frac{\text{sgn}(W)g(W)}{b(W)}\right]
\end{equation}
for $\sigma^{2}=\mathbb{E}[W^{2}/b(W)]<\infty$, where $W$ is a symmetric random variable with density $P(x)=b(x)e^{-2\vert x\vert}$ and
$b:\mathbb{R}\to\mathbb{R}$ a non-negative function. The density of $W^{*}$ is
\begin{equation}
P^{*}(z)=\frac{1}{\sigma^{2}}b(z)\mathbb{E}\left[\frac{\text{sgn}(W)}{b(W)}1_{\vert W\vert\geq \vert z\vert}\right].
\end{equation}
In fact $z\leq0$ or $z\geq0$ makes no difference when we discuss the process of construction so that we will only focus on $z\geq0$ while $z\leq0$
just need adjust the sign. The proof is similar to the Proposition 2.1 in \cite{chen2011normal}
\begin{equation}
\begin{aligned}
\sigma^{2}\int_{0}^{\infty}\frac{g'(z)}{b(z)}\frac{1}{\sigma^{2}}b(z)\int_{z}^{\infty}\frac{1}{b(w)}b(w)e^{-2w}dwdz
&=\int_{0}^{\infty}g'(z)\int_{z}^{\infty}e^{-2w}dwdz\\
&=\int_{0}^{\infty}\int_{0}^{w}g'(z)e^{-2w}dzdw\\
&=\int_{0}^{\infty}\frac{g(w)}{b(w)}b(w)e^{-2w}dw.\nonumber
\end{aligned}
\end{equation}\par
Following the Proposition 3.5 in \cite{mckeague2016stein}, we can also construct a empirical density function using the \emph{b-generalized-zero-bias
distribution} method. Given a empirical distribution $\mathbb{P}_{N}(A)$ defined in Eq.(\ref{empirical distribution}), and let
$x_{1}>x_{2}>\dots>x_{N}>0$, $x_{0}=\infty$, $x_{N+1}=0$. The corresponding density function $\mathbb{P}^{*}_{N}$ is given by
\begin{equation}
P^{*}_{N}(x)\propto b(x)\sum_{i=1}^{n}\frac{1}{b(x_{n})}
\end{equation}
for $x_{n+1}<x\leq x_{n}$ ($n=1,\dots,N-1$). \par
Next we aim at the interworld interaction potential. We begin with 1d Coulomb potential and notice that
\begin{equation}
\begin{aligned}
\left(\sum_{n=1}^{N}\frac{1}{x_{n}}\right)^{2}
&=\left[\sum_{n=1}^{N}\frac{x_{n}^{2}-x_{n+1}^{2}}{x_{n}(x_{n}^{2}-x_{n+1}^{2})}\right]^{2}\\
&=\left[\sum_{n=1}^{N}\left(\frac{1}{x_{n}(x_{n}^{2}-x_{n+1}^{2})}-\frac{1}{x_{n-1}(x_{n-1}^{2}-x_{n}^{2})}\right)x_{n}^{2}\right]^{2}\\
&\leq\left[\sum_{n=1}^{N}1^{2}\right]\left[\sum_{n=1}^{N}\left(\frac{1}{x_{n}(x_{n}^{2}-x_{n+1}^{2})}-\frac{1}{x_{n-1}(x_{n-1}^{2}-x_{n}^{2})}\right)^{2}\frac{x_{n}^{4}}{1^{2}}\right]\\
&=N\sum_{n=1}^{N}\left(\frac{1}{x_{n}(x_{n}^{2}-x_{n+1}^{2})}-\frac{1}{x_{n-1}(x_{n-1}^{2}-x_{n}^{2})}\right)^{2}x_{n}^{4}\nonumber
\end{aligned}
\end{equation}
with equality if and only if
\begin{equation}
\frac{1}{x_{n}^{2}}=\alpha\left(\frac{1}{x_{n}(x_{n}^{2}-x_{n+1}^{2})}-\frac{1}{x_{n-1}(x_{n-1}^{2}-x_{n}^{2})}\right)\label{condition1}
\end{equation}
for some constant $\alpha$. Let's rewrite $P^{*}_{N}(x_{n})$ as
\begin{equation}
P^{*}_{N}(x_{n})=\frac{\alpha}{N+1}\frac{x_{n}}{x_{n}^{2}-x_{n+1}^{2}}
\end{equation}
since $x_{N+1}$ is counted in the interaction which means we have $N+1$ worlds here.\par
Using $\frac{P^{*'}_{N}(x_{n})}{P^{*}_{N}(x_{n})}=\frac{P^{*}_{N}(x_{n-1})-P^{*}_{N}(x_{n})}{(x_{n-1}-x_{n})P^{*}_{N}(x_{n})}$, the $U_{N}(\mathbf{X})$ is approximated by
\begin{equation}
U_{N}(\mathbf{X})\approx4\sum_{n=1}^{N}\frac{\hslash^{2}}{8m}\left(\frac{1}{x_{n}(x_{n}^{2}-x_{n+1}^{2})}-\frac{1}{x_{n-1}(x_{n-1}^{2}-x_{n}^{2})}\right)^{2}x_{n}^{4}\geq\frac{1}{N}\frac{\hslash^{2}}{2m}\left(\sum_{n=1}^{N}\frac{1}{x_{n}}\right)^{2}.\label{UN}
\end{equation}\par
Then we put $U_{N}(\mathbf{X})$ and $V_{N}(\mathbf{X})$ together to display the average Hamiltonian of $N+1$ worlds at 1st excited state
\begin{equation}
\begin{aligned}
H_{N}(\mathbf{X})&=\frac{1}{N+1}\left(U_{N}(\mathbf{X})+V_{N}(\mathbf{X})\right)\\
&\geq\frac{1}{N+1}\left[\frac{1}{N}\frac{\hslash^{2}}{2m}\left(\sum_{n=1}^{N}\frac{1}{x_{n}}\right)^{2}-\sum_{n=1}^{N}\frac{e^{2}}{x_{n}}\right]\\
&=\frac{1}{N(N+1)}\frac{\hslash^{2}}{2m}\left[\sum_{n=1}^{N}\frac{1}{x_{n}}-\frac{me^{2}N}{\hslash^{2}}\right]^{2}-\frac{me^{4}N}{2\hslash^{2}(N+1)}\\
&\geq-\frac{me^{4}N}{2\hslash^{2}(N+1)}\nonumber
\end{aligned}
\end{equation}
with the second equality if and only if
\begin{equation}
\sum_{n=1}^{N}\frac{1}{x_{n}}=\frac{me^{2}N}{\hslash^{2}}=N,\label{condition2}
\end{equation}
where the second equality deu to dimensionless unit.\par
Now the minimun of $H_{N}$ is the energy of 1d hydrogen atom at 1st excited state as expected when $N\to\infty$. In next section we will show that
the conditions Eq.(\ref{condition1}) and Eq.(\ref{condition2}) can both be satisfied and will derive the recursion for simulation. In order to
determine $\alpha$,
we substitute the conditions for equality to holds into Eq.(\ref{UN}) and obtain $\alpha=1$.\par
Though the discussion above is only half of the whole system, the symmetry ensure the same process can work in $(-\infty,0)$. The total number of worlds is $2N+1$ since we fix the world $x_{N+1}$ at $x=0$ as a boundary condition.
\section{Simulation of 1d 1st excited state}
In this section we will focus on the comparison between $P^{*}_{N}(\mathbf{X})$ and $P(x)$.
using dimensionless units for convinience which means we will set $me^{2}/\hslash=1$. Under these preconditions we have $P(x)=2x^{2}e^{-2x}$ for
$x\geq0$.
To solve the world configurations, we take the sum of both side of Eq.(\ref{condition1}) and obtain the recursion
\begin{equation}
x_{n+1}^{2}=x_{n}^{2}-\left(x_{n}\sum_{i=1}^{n}\frac{1}{x_{i}^{2}}\right)^{-1}.\label{recursion1}
\end{equation}
Using the boundary condition $x_{N+1}=0$ we can theoretically solve a complex equation with respect to $x_{1}$
\begin{equation}
x_{N}(x_{1})^{3}\left(\sum_{i=1}^{N}\frac{1}{x_{i}(x_{1})^{2}}\right)-1=0,\label{recursion2}
\end{equation}
which means we obtain all world configurations.\par

\begin{figure}[ht]
\centering
\includegraphics[width=8.6cm]{12}
\caption{Half of 1d Coulomb potential model for $N=11$ ($x\geq0$) at 1st excited state. The stepped curve is
$P^{*}_{N}(x_{n})=x_{n}(N+1)^{-1}(x_{n}^{2}-x_{n+1}^{2})^{-1}$ with respect to dimensionless world configurations $x_{1},\dots,x_{N}$ solved by
Eq.(\ref{recursion2}) and
$\sum_{n=1}^{N}P^{*}_{N}(x_{n})(x_{n}-x_{n+1})\approx0.54$. The smooth curve is $P(x)=2x^{2}e^{-2x}$ which is the dimensionless solution of 1d 1st
excited state hydrogen atom in $x\geq0$.}\label{fig1}
\end{figure}\par
For small values of $N$, Eq.(\ref{recursion2}) can be solved analytically as shown in Fig.\ref{fig1} when $N=11$, where $P(x)$ is plotted by smooth
curve. Though it seems that the approximation to $P(x)$ is not perfect before the local maximum when $N$ is small, the probability
$\mathbb{P}_{N,+}=\sum_{n=1}^{N}P^{*}_{N}(x_{n})(x_{n}-x_{n+1})$ is approaching to $0.5$ which is exactly $\int_{0}^{\infty}P(x)dx$ with increaing
$N$ and we will prove the convergency in next section. With the convergency, it's predictable that $x_{1}$ is increasing with $N$ which means the
area
$\int_{x_{1}}^{\infty}P(x)dx$ is decreasing and so is the difference area before local maximum.\par

\begin{figure}[ht]
\centering
\includegraphics[width=8.6cm]{21}
\caption{Half of 1d Coulomb potential model for $N=21$ ($x\geq0$) at 1st excited state. The stepped curve is
$P^{*}_{N}(x_{n})=x_{n}(N+1)^{-1}(x_{n}^{2}-x_{n+1}^{2})^{-1}$ with respect to dimensionless world configurations $x_{1},\dots,x_{N}$ solved by
Eq.(\ref{recursion2}) and
$\sum_{n=1}^{N}P^{*}_{N}(x_{n})(x_{n}-x_{n+1})\approx0.526$. The smooth curve is $P(x)=2x^{2}e^{-2x}$ which is the dimensionless solution of 1d 1st
excited state hydrogen atom in $x\geq0$.}\label{fig2}
\end{figure}\par
Larger values of $N$ is shown in Fig.\ref{fig2} with numerical solution. The approximation is better as expected but it took 2 weeks to calculate on
personal computer. The symmetry of the solution ensure the results in $x<0$.
\section{Proof of convergency}
As shown in previous section, it's natural to expect that $P(x)=\lim_{N\to\infty}P^{*}_{N}(x)$. Before the proof we need to bound $x_{N}$ using
condition Eq.(\ref{condition2}) and Eq.(\ref{recursion2}).
\begin{equation}
x_{N}^{3}N=x_{N}^{3}\frac{1}{N}\left(\sum_{n=1}^{N}\frac{1}{x_{n}}\right)^{2}\leq1=x_{N}^{3}\sum_{n=1}^{N}\frac{1}{x_{n}^{2}}\leq
x_{N}^{3}\frac{1}{x_{N}}\sum_{n=1}^{N}\frac{1}{x_{n}}=x_{N}^{2}N
\end{equation}
which means
\begin{equation}
\frac{1}{\sqrt{N}}\leq x_{N}\leq\frac{1}{\sqrt[3]{N}}.
\end{equation}
The inequality become equality if and only if $N=1$. Thus we can assume that $x_{N}=O(1/\sqrt[a]{N})$ where $2<a<3$. We begin with the differential
equation
\begin{equation}
\begin{aligned}
\frac{P^{*}_{N}(x_{n})-P^{*}_{N}(x_{n+1})}{x_{n}-x_{n+1}}
&=\frac{x_{n}^{2}\displaystyle\sum_{i=1}^{n}\frac{1}{x_{i}^{2}}-x_{n+1}^{2}\sum_{i=1}^{n+1}\frac{1}{x_{i}^{2}}}{(N+1)(x_{n}-x_{n+1})}\\
&=\frac{1}{N+1}\left[\frac{1-x_{n}}{x_{n}(x_{n}-x_{n+1})}\right]\\
&=\frac{1}{N+1}\left[\frac{x_{n}+x_{n+1}-x_{n}x_{n+1}-x_{n}^{2}}{x_{n}(x_{n}^{2}-x_{n+1}^{2})}\right]\\
&=\frac{1}{N+1}\left[\frac{x_{n}-1}{x_{n}(x_{n}+x_{n+1})}\right]+2\left(\frac{1}{x_{n}}-1\right)P^{*}_{N}(x_{n}).\label{ode}
\end{aligned}
\end{equation}
Now let's discuss the first term in last equality. We focus on the function
\begin{equation}
f(x_{n})=\frac{x_{n}-1}{x_{n}(x_{n}+x_{n+1})}
\end{equation}
Since the sequence $x_{n}>0$ and $\lim_{N\to\infty}x_{N}=0$, we have $\text{max}\vert f(x_{n})\vert=\vert f(x_{N})\vert$. The order can be determined
by
\begin{equation}
\frac{1}{N+1}\left\vert\frac{x_{n}-1}{x_{n}(x_{n}+x_{n+1})}\right\vert\leq\frac{1}{N+1}\left\vert\frac{1}{x_{N}^{2}}\right\vert=O(N^{\frac{2}{a}-1})
\end{equation}
which means if we take $N\to\infty$, Eq.(\ref{ode}) tends to first-order ODE $P'(x)-2(1/x-1)P(x)=0$ with general solution $P(x)=Cx^{2}e^{-2x}$. To
determine $C$, we notice that
\begin{equation}
\sum_{n=0}^{N}P^{*}_{N}(x_{n})(x_{n}-x_{n+1})=\frac{1}{N+1}\sum_{n=0}^{N}\frac{x_{n}}{x_{n}+x_{n+1}}\geq\frac{1}{N+1}\sum_{n=0}^{N}\frac{x_{n}}{2x_{n}}=\frac{1}{2},
\end{equation}
and
\begin{equation}
\begin{aligned}
\int_{0}^{\infty}P^{*}_{N}(x)dx=&\frac{1}{3(N+1)}\sum_{n=0}^{N}\frac{1}{x_{n}(x_{n}^{2}-x_{n+1}^{2})}\left(x_{n}^{3}-x_{n+1}^{3}\right)\\
=&\frac{1}{3(N+1)}\sum_{n=0}^{N}\left[1+\frac{x_{n+1}^{2}}{x_{n}(x_{n}+x_{n+1})}\right]\leq\frac{1}{2}.
\end{aligned}
\end{equation}
Then we have
\begin{equation}
\frac{1}{4}C=\int_{0}^{\infty}P(x)dx=\lim_{N\to\infty}\sum_{n=0}^{N}P^{*}_{N}(x_{n})(x_{n}-x_{n+1})\geq\frac{1}{2},
\end{equation}
and by the bounded convergence theorem
\begin{equation}
\frac{1}{4}C=\int_{0}^{\infty}P(x)dx=\lim_{N\to\infty}\int_{0}^{\infty}P^{*}_{N}(x)dx\leq\frac{1}{2},
\end{equation}
which means $C=2$. Now we have shown that $P^{*}_{N}(x)$ with respect to solution of recursion Eq.(\ref{recursion1}) and Eq.(\ref{recursion2})
converges to $P(x)$ which is the solution of 1d Coulomb potential, but the rate of convergence remains uncertain. Using stein's method following
\cite{mckeague2016stein} will be an good approach to bound the rate of convergence which is not our main purpose in this article.
\section{Discussion}
As an extension of many-interacting-worlds method to non-Gaussian model, our work follows the similar process in Gaussian model by using stein's
method via the density approach to construct an proper empirical density without using wave function when the classical worlds is countable finite.
With some mathematical techniques we obtained the interaction potential, and also calculated the world configurations and energy described by
density. We have analytically proved the availability of MIW method on one dimensional Coulomb potential. But what we have done is the framework of
the Coulomb model which does not include the whole MIW method since the determinism of worlds need to be discussed in future work especially the
velocity and dynamic. Yet we still ignore the spin and entanglement problem (discussed in \cite{elsayed2018entangled} using Bohmian trajectories) for
the unclear reality of wave function. \par
With the application of MIW method in several potential systems, we should consider the generality of this method. Here we propose a question: if MIW
method works for any given potentials? If we simplify this question, till now the $x^{2}$ potential and $x^{-1}$ potential have been simulated, but
how about
$x^{r}$ potential when $-1<r<2$. The intuitive idea is to follow the process before. Firstly to obtain the solution of Schr\"{o}dinger equation with
$x^{r}$ potential. Then we can approximate the probability and try to construct the interaction potential to test the availability of MIW method.\par
If we follow the original idea in \cite{hall2014quantum}, it just needs \emph{a suitably smoothed version of the empirical density} to approximate
$P(x)$ and its derivatives. In our case the singularity of $P(x)$ at $x=0$ makes it not smooth but we find a suitably smoothed empirical density
$P_{N}(x)$ to approximate it piecewise. It seems remain lots of option about the empirical density but when it comes to a specific potential system
it's not easy to figure out the proper density. Especially when the form of $P(x)$ is not common with singularity or piecewise even discontinuous,
the smooth of corresponding empirical density will be hard to guarantee that means for some strange potential system MIW method may fail. Obviously
we need to consider the framework of MIW method about whether it is available in the system that can be solved by standard quantum mechanics at
least. \par
Since most research show the connection between MIW method in stationary state problem and stein's method , we can focus on the approximation of
$P(x)$ by stein's method via density approach. The Condition 13.1 in \cite{chen2011normal} provides the constraint of $P(x)$. If for the systems that
can be solved by quantum mechanics, the corresponding $P(x)$ satisfies or piecewise satisfies the condition, we may at least conclude that MIW method
works as an approach to quantum mechanics. \par
Another crucial topic is the ability independent from standard quantum mechanics to solve the quantum systems, in other words the ability to obtain
the density independent from approximation. Since no wave function is involved in MIW method and dynamic is also based on density, it seems we cannot
internally
complete this method which means it might be regarded as an approach to quantum mechanics rather than a quantum theory. Though the ontology has been
determined, the dependence of MIW on density approach makes it controversial to be a quantum theory. We still need more framework on MIW method about
the
solution of  quantum systems. In the future we look forward to find the supplement to MIW method about the wave function or probability.
potential system independently since we can not come out an empirical density without $P(x)$ which is the solution from quantum mechanics.
\section*{Acknowledgements}
The research was supported by National Key R\&D Program of China under Grant No.2018YFB1601402-2.

redpajama_set_name: RedPajamaArXiv


We're ramping up for another school year! The boys are starting third and sixth grade. Hold on for a sec while I wipe away the tears. We've had a fun-filled summer, but it's time to change gears and start our back to school checklist. Because my husband is an elementary school principal, we look for ways to help as many students as possible. Today, I'm sharing a super simple way you can help raise money for your school. I promise it won't take much effort at all, but the benefits of this wonderful program can really make a difference! Read on for more details.
I received monetary compensation from General Mills and SC Johnson in exchange for my endorsement of Box Tops For Education.
Box Tops for Education offers schools across America the opportunity to earn free money! All you have to do is shop your favorite Box Tops products. There are hundreds of eligible items! With brands from Cheerios to Ziploc® brand bags, there are so many ways to help your child's school. You don't even need a child at the school of your choice. It can be your own childhood elementary or middle school!
In addition to shopping for participating products from your favorite brands (some are featured below), you can also earn sign up for a FREE Box Tops account and earn entries into online sweepstakes, or use the Box Tops Bonus App to scan everyday receipts and earn cash for your school. Isn't that amazing? I told you it would be easy! Through September 30th they have a special promotion where you can upload up to 10 receipts with participating purchases and earn entries into a 1 million box tops sweepstakes! Every Box Top equals 10 cents so that could be life changing for a school to win.
When you sign up for a free Box Tops account, you can also clip coupons to save money while you shop. It's truly a win-win for everyone!
Get the kids involved too!
Make it a family affair by gathering the kids to help clip the Box Tops. Believe me – anything that feels like a craft is fun to them. With the printable collection sheets, they can use glue or tape the clipped Box Tops to the sheets too. My boys won't turn down a snack either, and many of the participating products like Nature Valley Biscuit Sandwiches or Yoplait Go-Gurt make great snacks!
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Head in-stores to load up on your favorite participating brands and you'll be set for back to school lunches and after-school snacks too. Right now Sam's Club has an abundance of products with Bonus Box Tops on the outside and inside of the packages. Just look for the specially marked boxes!
Don't forget to download the App and sign up for a free account to snap photos of your receipts for bonus entries and sweepstakes opportunities!


text:
Sidney Thomas "Tommy" Boyce (nacido el 29 de septiembre de 1939 – fallecido el 23 de noviembre de 1994) y Bobby Hart (nacido con el nombre de Robert Luke Harshman;18 de febrero de 1939) fueron un dúo de compositores estadounidenses muy exitoso en los años sesenta. Son conocidos por escribir canciones para The Monkees.

Discografía
Álbumes:
 Test Patterns (A&M LP 126 (Mono)/SP 4126 (Stereo), 1967)
 I Wonder What She's Doing Tonite? (A&M LP 143/SP 4143, 1968)
 It's All Happening On The Inside* (A&M SP 4162, 1969)
 Dolenz, Jones, Boyce & Hart (Capitol ST-11513, 1976)
 Dolenz, Jones, Boyce & Hart – Live in Japan (Capitol/Toshiba-EMI ECS-91018, 1981)
 16 Rarities (SG Records, 1981 – This is a bootleg of B-sides and oddities)
 The Anthology (A&M Records Australia/Polygram 525 193–2, 1995)

Álbum Notas
 It's All Happening On The Inside lanzado en Canadá como Which One's Boyce & Which One's Hart?

Sencillos

Referencias

Enlaces externos
 Forgotten Hits feature on Boyce and Hart
 [ AMG]
 Interview with Bobby Hart discussing his career and partnership with Tommy Boyce

Dúos de música de Estados Unidos
Música en los años 1970

redpajama_set_name: RedPajamaWikipedia


text:
New Bestseller? Insiders Say 10 Million OPPO R11s Bound for Sale
Oct 28, 2017, 10:32am 2018/05/07 08:10:30 IThome
OPPO will release its fullscreen mobile phone, the OPPO R11s, at a press conference on November 2. The company has gone through several rounds of promotion, unveiling the handset's appearance, features and more. The biggest remaining mystery is its price.
Days ago, an industry insider whose Weibo is @KevinWangDiary, wrote, "Going by the supply chain, there have been 10 million OPPO R11s ordered by suppliers and the official photos are released. We just need to wait for OPPO to publish the price at its press conference. I expect it will be 2,999 yuan." The inventory status suggests OPPO expects promising sales of the OPPO R11s.
Sanoo Statistics said the OPPO R11, the phone's last generation, has been the most popular mobile phone in the 2,500 to 3,000 yuan price range since its launch in June. It could be considered a bestseller. The number of R11 phones available in the first batch may have been as few as 2 million. OPPO R11s is expected to replace the OPPO R11 as OPPO's top selling mobile phone.
IT Home reported the OPPO R11s will have a 6.01 inch screen in the 18:9 aspect ratio. It also has a more interactive design and comfortable feel. The red OPPO R11s also features a special fullscreen design – its "star-like screen"(星幕屏).
The OPPO R11s has new 20 megapixel and 16 megapixel cameras, which offer a double f/1.7 aperture. The software can automatically identify lighting conditions and switch the main camera. The front 20 megapixel camera supports AI smart beautifying and can recognize gender, age, skin color, and skin condition by reading 254 facial features.
The OPPO R11s will come in three colors: red, black, and champagne. The OPPO R11s will be released on November 2, and IT Home will have a new report after the event.
This article originally appeared in IT Home and was translated by Pandaily.
Tags oppo | oppo r11s
OPPO Launches Full-Screen R11s at 2999 Yuan
OPPO launched its first full-screen mobile R11s on November 2, joining other major brands in providing full-screen products.
Industry Nov 04 May 7, 2018
OnePlus Founder: The Differences Between OnePlus and Xiaomi
Yesterday OnePlus launched their new flagship device OnePlus 5. Here is an interview almost 3 years ago with OnePlus founder Peter Lau, at that moment their first generation product OnePlus One just made its debut. Recently, the British magazine "Connect" published the following: "What the Moto G did for the budget end of the market, […]
Industry Jun 22 August 1, 2018
Geekpark
Beijing Metro Offers Swipe to Ride: Is NFC Going Mainstream ?
Beijing Metro announced a partnership with the Beijing Municipal Administration Traffic Card to launch mobile swipe-to-ride service on June 26. The first phase will will see NFC subway payment available on the subway's Fangshan Line. Some 160 NFC-capable mobile phones by brands such as Xiaomi, Huawei, Samsung, Nubia, OnePlus and Meizu will support the new […]
Industry Jul 04 August 1, 2018
Kevin Zhou
Lei Jun announces Xiaomi sales reached a historical high
This was the first good news that came across after Xiaomi CEO Lei Jun was, once again, in control of the supply chain. On July 7th, Lei sent out an internal e-mail, announcing the sale of Xiaomi mobile phones during the second quarter of 2017 reached 23.16 million units, ranking this number a historical high […]

redpajama_set_name: RedPajamaCommonCrawl


Kuwait – Kuwait voters turned out in large numbers at the poll stations to elect new representatives for the National Assembly, the 15th since Kuwait's independence in 1961.
Kuwaiti sources told Asharq Al-Awsat newspaper that the turnout was between 69% and 72% compared to 2013, where it was 51.9%.
Political observers attributed the huge participation among both genders to two main reasons. They believe that economic challenges and the expected laws to be passed drove citizens to elect for their representatives. The second reason is the return of the abstainers who sat out in 2013 elections.
Kuwaiti political analysts believe that the return of opposition is the reason for the huge turnout. Resources close to the regime believe that brings back the national unity and unites all parties in the National Assembly.
The current government, led by Sheikh Jaber Mubarak al-Hamad al-Subah, is expected to resign on Monday.
Turnout was high with some polling stations reporting that 80 percent of eligible voters had cast their ballots by the time polls closed, state-run Kuwait Television reported.
The elections witnessed huge participation of the elderly since the government provided wheel chairs and transportation. A voter was sick, and used an ambulance to take him on his hospital bed to the polling station to cast his vote.
Friday was electoral silence day, one day before the actual elections day. The law provides that the media, even electronic media, is not allowed to practice any activities regarding the candidates' electoral campaigns.
Nominees themselves will have to bring their campaigning to a complete halt. Anyone, including the media, caught breaking the mandated silence will be subject to a KD 5,000 fine.
Pre-election silence aims to give voters a chance to carefully consider their choice for the election day. The media can only offer messages to educate the voters on elections, or urge them to positively take part in the vote.
According to the Ministry of Information's relevant decree, broadcasting, re-broadcasting or publishing any interviews, programs or reports with candidates for the National Assembly elections or the Municipal Council, is prohibited on the polling day, and the day before it.
Asharq al-Awsat newspaper toured the polling stations in some schools and saw candidates among their supporters. They were in their designated tents with their pictures hung inside and with food everywhere. It was like a celebration.
According to Kuwaiti law, candidates are allowed to enter the polls stations. Former Speaker Marzouk al-Ghanem told the press that Kuwait is facing many challenges that should be addressed.
Meanwhile, Ministry of Interior warned voters not to take photos of the ballots after casting their votes, saying this is prohibited by the election law. According to the law, a violator can spend five years behind bars, and pay a fine of KD 5,000, the ministry's statement added.
Article 44 of Kuwait's Election Law provides for punishing violators in the case of using force or threatening to prevent voters from practicing their rights, or to vote for certain candidates, or refraining from balloting.
The same article provides for a penalty in case of vote buying, promoting false news about a candidate's behavior among voters, or going to the polling station with a device with the intention of taking photos of ballots to prove one has voted for a certain nominee. Also, one will be punished if he goes to the polling centers carrying a fire arm, according to Article 30 of the law.
Kuwait- Authorities in Kuwait are tracking down details extracted from an arrested group of residents suspected of plotting and leading terror attacks against U.S. soldiers assigned to the country.
A collision between a truck driven by an Egyptian and a vehicle carrying three U.S. soldiers in Kuwait was a "terrorist attack," not an accident as first thought, the U.S. embassy said.
"U.S. Embassy in Kuwait confirms that what at first appeared to be a routine traffic accident involving three deployed U.S. military personnel… was in fact an attempted terrorist attack," the mission said in a statement posted on its website.
The statement said the attack took place on Thursday and that the U.S. soldiers escaped unhurt.
The soldiers also rescued the Egyptian driver when his truck caught fire, it said.
The Kuwaiti interior ministry said on Saturday that authorities arrested the Egyptian driver and found with him a hand-written note in which he had pledged allegiance to ISIS.
It also said that the driver, identified as Ibrahim Sulaiman, 28, also carried a belt and material suspected of being explosives.
Sulaiman told investigators that he supported the group and believed that its leader Abu Bakr Al Baghdadi should be the head of all Muslims.
Sulaiman said that his attempts to learn how to make an explosive belt from the internet had failed as he did not have the required items.
Kuwaiti authorities announced in July they had dismantled three ISIS cells plotting attacks, including a suicide bombing against a Shi'ite mosque and against an interior ministry target.
An ISIS-linked suicide bomber had killed 26 worshippers in June last year when he blew himself up in a mosque.
The U.S. embassy said it was not aware of specific, credible threats against private U.S. citizens in Kuwait at this time.
But it warned that the attack serves as a reminder to maintain a high level of attentiveness, advising U.S. citizens to review their personal security plans and remain alert.
Kuwait yesterday reiterated its vision to have a nuclear weapon free Middle East. The Gulf state's foreign ministry representative, Talal Al-Fasam, called for the International Atomic Energy Agency (IAEA) to apply its mandate to implement nuclear safeguards in the region. He made his comments at the 60th General Conference of the agency.
Al-Fasam also addressed the Israeli standpoint on non-proliferation. He asserted that Israel must sign the Non-Proliferation Treaty.
The Kuwaiti official noted that that all countries in the region are signatories to and abide by the treaty while Israel persists in its refusal to do so. Indeed, he pointed out, Israel even refuses to open its nuclear installations to IAEA inspectors.
– If BDS compels G4S to follow through with its announcement by ending all forms of complicity in Israel's violations of international law, G4S would become the fourth multinational to abandon the Israeli market, in less than a year, due to heavy losses and/or reputational risk.
– In September 2015, French corporate giant Veolia set the trend by selling off all of its businesses in Israel after losing tenders and contracts worth billions of dollars following a seven-year BDS campaign against its role in illegal Israeli settlement projects.
– Irish building materials corporation CRH has more recently exited the Israeli market, selling off its 25% stake in the Israeli occupation-profiteer Nesher Cement.
– French telecommunications giant Orange announced earlier this year the termination of its franchise relationship with Israeli Partner Communications, after intense BDS pressure in France and Egypt.
– In a related major development, the $20-billion pension fund of the United Methodist Churchdeclared in January 2016 the five largest Israeli banks off limits for investment and divested from the two that it held in its portfolios.
– The Israel Export Institute has revealed that Israel's exports in 2015 have dropped by 7% over 2014.
– Foreign direct investment in Israel dropped by 46% in 2014 as compared to 2013, according to a UN report. One of the report's authors admitted that BDS played a key role in this sharp drop.
– In addition to abandoning its Israeli contracts, G4S announced in March it was selling its mass incarceration businesses that operate youth detention centers in the UK and the US. It is accused by campaigners of involvement in racist and abusive practices.
CAIRO: President Abdel Fatah al-Sisi met with Kuwaiti Justice Minister Yacoub Al Sanea to discuss counter-terrorism efforts that will be on the agenda of the Justice Arab Ministers meeting facilitated by the Arab League Wednesday, the Presidential office said in a statement.
"President Sisi stressed the necessity of enhancing judiciary cooperation to face the current challenges and organized crimes that face the Arab nation," the statement said.
Both sides tackled the necessity of combating the terrorists who use online sites and social media for disseminating their extremist ideologies, the statement continued.
President Sisi had paid Kuwait a one-day visit to enhance bilateral relations.
In March 2015, Kuwait pledged $4 billion dollars in investments to Egyptian, followed by an $8B pledge by Saudi Arabia and UAE during the Sharm el-Sheikh Economic Development Conference.
Kuwait is one of the Gulf States that supported the mass protests which called for the end of the former President Mohamed Morsi's regime. Between July 2013, when Morsi was removed from office, and January 2015 Kuwait granted Egypt $4 billion in aid.
Kuwait will send ground troops to Saudi Arabia as part of their involvement in the ground offensive in Yemen against the Ansarullah rebels, known as Houthis, a local newspaper reported Tuesday citing an unnamed government source.
Sending the troops was approved by the country's cabinet and will be sent to Saudi Arabia as early as next week. No information was provided about the size of the force. Kuwait is part of the Saudi-led coalition in Yemen which kicked off late March and involves more than 10 Saudi regional allies.
However, Kuwait has only been providing air support and if the report is true, Kuwait would become the latest country to provide ground troops to the coalition alongside the United Arab Emirates, Qatar, Bahrain and Sudan.
Saudi Arabia launched the operation in a bid to reinstate their Yemeni ally, exiled President Abd-Rabbu Mansour Hadi,l after the rebels took control of the capital Sanaa and other parts of the country ousting the Saudi-backed government and forcing Hadi to flee to Riyadh.
The Islamic State in Iraq and Syria (ISIS) has claimed responsibility for the bloody explosion that rocked a Shia mosque in Kuwait's capital.
The fatal attack took place during Friday's prayers at the Shiite-affiliated Imam Al-Sadeq mosque, killing at least 27 people and wounding 227 others.
A group calling itself "Najd Province" [believed to be affiliated with ISIS]claimed responsibility of the attack. The same group said it had carried out two bombing attacks on Shi mosques in Saudi Arabi late on May where more than two dozen were killed.
A statement posted by pro-ISIS social media accounts boasted the offensive against what they called 'Temple of the Rejectionists", a derogatory term used by the extremist Sunni group to describe Shia Muslims.
The perpetrator of the massacre was identified as Abu Suleiman Al-Muwahed.
"The worshippers were on Sujood [kneeling]when the suicide bomber walked in the detonated his explosive belt. He looked in his 20s, I saw him with my own eyes", said MP Khalil Al-Salih who happened to be at the Imam Sadiq mosque during the attack.
That a suicide bomber blows himself up among a congregation of worshippers during Friday prayers in the Holy month of Ramadan has been denounced by the majority of Muslims worldwide.
Immediately after the fatal blast, Kuwaiti Emir Sheikh Sabah Al-Ahmad Al-Jaber Al-Sabah visited the damaged mosque, along with the speaker of Kuwaiti parliament who called the cabinet for an urgent meeting.
The cabinet declared Saturday an official day of mourning for the victims.
The government of Kuwait has announced that it will not deal with 50 companies due to their role in illegal Israeli settlements in the occupied Palestinian territory in a move being welcomed by campaigners as a landmark success for the Boycott, Divestment and Sanctions (BDS) movement.
The blacklisted companies include some of the top corporate targets of the BDS movement, such as Volvo, Heidelberg Cement, Dexia, Pizzarotti, Alstom as well as Veolia. Veolia was recently excluded from a $750m contract, and "all future contracts," by Kuwaiti authorities over its role in the illegal Jerusalem Light Rail project and other projects that serve illegal Israeli settlements.
The blacklisted companies are expected to be excluded from contracts worth billions of dollars, especially if other Arab countries take similar steps.
According to media reports, the Kuwaiti Ministry of Commerce and Industry is also investigating the Kuwaiti operations of G4S, the British security company that secures Israeli military checkpoints and colonies and helps Israel run prisons at which Palestinian political prisoners are tortured, with a view to cancelling its license to operate if it does not terminate its participation in Israeli violations of international law.
"This landmark decision means that international companies will now pay an even heavier price for participating in Israeli violations of international law.
"As European banks and pension funds continue to divest from Israel's occupation and companies such as Veolia and G4S lose billions of dollars as a result of sustained, effective grassroots campaigning, many firms will now be wondering whether supporting Israel's regime of occupation, colonialism and apartheid is good for business," said Shuaibi.
Many European governments have taken steps to discourage firms from having economic links to the Israeli occupation of Gaza and the West Bank, including East Jerusalem, but this is the first time a government has decided to boycott international companies over their role in illegal Israeli settlements.
The Arab Summit of 2006 in Khartoum unanimously called for punitive measures against the companies, including Veolia and Alstom, involved in Israel's colonization of Jerusalem.
The BNC has been working closely with BDS Kuwait since 2010 on advocating for accountability measures against international corporations that are complicit in Israel's violations of international law and Palestinian rights.
"In the wake of Israel's massacre in Gaza, which was only made possible with the support of international governments and companies, we urge all governments, especially Arab League and OIC members, to impose sanctions on Israel and take action against the complicit corporations that profit from Israel's occupation and crimes," added Barghouti.
International companies that participate in Israel's violations of international law have faced increasing pressure as a result of BDS campaigning in recent years.
Veolia recently announced that it intends to sell off large parts of its business in Israel after boycott campaigns cost the company more than $23bn – not counting Veolia's latest losses in Kuwait — in lost potential contracts, although the French multinational will still remain involved in the illegal Jerusalem Light Rail Project.
British security giant G4S has pledged to end some aspects of its involvement in torture-ridden Israel's prison system and checkpoints after trade unions, NGOs, universities and other public bodies cancelled contracts with the company.
The Presbyterian Church (USA) voted in June to divest from Caterpillar, Motorola Solutions, and Hewlett Packard over their role in Israel's occupation of Palestinian territory.
In January, Dutch pension giant PGGM announced it was divesting from five Israeli banks due to their support for illegal Israeli settlements. In February, it emerged that the sovereign fund of Luxembourg had taken a similar step, excluding nine Israeli banks and firms from its portfolio. In the months that followed, banks and pension funds in Norway, the Netherlands, the US and Denmark made similar announcements.
According to reliable sources in Kuwait, following this humiliating defeat, Veolia was compelled to withdraw from a tender for a project to expand the "Um Al-Haiman" waste water treatment station after qualifying for it. The project is valued at about $1.5 billion.
Even before this total loss of contracts worth $2.25B, Veolia had already lost or had to pull out of tenders worth approximately $24 billion, mainly in the UK, Sweden, Ireland and the U.S.
Veolia has been forced to admit that the campaign against it is having a major impact and recently announced that it intends to sell off its Israeli water, waste, and energy businesses, having already sold off its share in companies that operate bus lines through illegal Israeli settlements. The campaign against Veolia shall continue until it ends all aspects of its participation in Israeli violations of international law, including by withdrawing from the Jerusalem Light Rail and the Tovlan landfill, two infrastructure projects for illegal Israeli settlements.
The BNC appealed a few months ago to Kuwait's Government and parliament to exclude Veolia because of its involvement in a number of Israeli projects that blatantly violate international law and the Palestinian human rights, including the "Jerusalem Light Rail" that connects the illegal settlements in and around occupied Jerusalem with the city.
This latest BDS victory against Veolia in Kuwait is seen by observers as "the tip of the BDS iceberg" in the Arab world.


text:
Capital Wins Defensive Battle with Well-Timed Strike
Capital (5-1) 0 1 1
Wooster (3-3-1) 0 0 0
Pictured: Chewy Gordon (photo credit: Spencer Dilyard)
2nd - 79:12 - Spirk, Sam (Capital)
G: Sam Spirk - 1
A: Chewy Gordon - 1
Sh: Daniel Bundschuh - 4
Sv: Logan Wiedman - 6
Sh: Bennett Anderson - 5
Sv: Will Collis - 2
By: Sean Neidig, sports information graduate assistant
WOOSTER, Ohio – Capital University Men's Soccer played 90 minutes of regulation without a goal from either side on Saturday and looked to be heading that way on Wednesday against the College of Wooster. Thankfully for the Crusaders, one of the team's newcomers came on to score the deciding goal late in the match to defeat the Fighting Scots 1-0.
With less than 10 minutes to play in the contest, Capital had been building attacking momentum throughout the second half and wearing down the Wooster defense. After getting outshot in the first half and the beginning stages of the second, Capital's attack-minded players showed their strength and endurance by continuing to push forward while the Crusader defense prevented Wooster from getting as many shots away.
The strategy paid off with 10:48 left on the clock as freshman Sam Spirk netted the winning goal. With the Crusaders probing forward on the far side of the pitch, Spirk was able to slip through the defense and receive a perfectly placed ball from Chewy Gordon. Spirk then directed his shot past Wooster's keeper for what ended up as the game-winning goal. The strike was Spirk's second goal of the year and gave Gordon, more known for scoring himself, his first assist of the season.
The Scots were not able to get another shot off as the Capital defense clamped down in the final 10 minutes to preserve the one-goal lead.
The first half produced a goalless 45 minutes and only three total shots on goal, all belonging to Wooster. Capital jumped out to a 6-1 lead in shots taken early but the Scots quickly caught up and ended up with a 10-8 advantage in first-half shots. By the end of the match though, the Crusaders took a 17-15 lead in shots during the second-half flurry that led to the goal.
Fresh off of being named Ohio Athletic Conference Defensive Player of the Week, senior keeper Logan Wiedman made six saves in another clean sheet, his third of the season and third shutout in the past four matches.
With the win, Capital improves to 5-1 overall. The Crusaders will play in Bernlohr Stadium for the first time in two weeks on Saturday, Sept. 22 when they host Thomas More College (Ky.) for their next match. Kickoff under the lights is scheduled for 7 p.m.


This new patch series is built on top of the above previous work.
- Patches 1/94 to 47/94 are here from the RFC patch series.
refactor the code around a bit.
and function parameters that have been renamed.
- Patches 48/94 to 84/94 were new in v1.
- Lockfile management changes as suggested by Junio.
- Many memory leaks were fixed as suggested by Eric.
- A patch was splitted into two as suggested by Duy.
- Some file descriptors have been closed as suggested by Dscho.
- Some early return were moved up as suggested by Eric.
- Many commit messages were improved.
were done before returning from some functions.
- Patches 85/94 to 94/94 are new and can be considered RFC.
feature in the libified apply functionality.
unfortunately this makes some reviewers unhappy.
The last patch 94/94 adds a --silent command line option to git apply.
could make it easier to test the new silent feature.
patches. That's why this part of the series can be considered RFC.
series if it is prefered.
test on other platforms especially Windows and perhaps OSX too.
Ævar used his Debian laptop with SSD.
command launched by the rebase command taking 3.705677431 s.
gitdiff_verify_name() change the variable itself.
-1 instead of die()ing in case of error.
'state->p_value' in a following patch.
it safer to later move global variables into a "state" struct.
"git diff header lacks filename information when removing "
'state->linenr' in a following patch.
* file (and how) we're patching right now.. The "is_xxxx"
* things are flags, where -1 means "don't know yet".
die("git diff header lacks filename information "
to make it safer to later move global variables into a "state" struct.
algorithm in a separate line_by_line_fuzzy_match() function.
+	* Ok, the preimage matches with whitespace fuzz.
+	* matches the preimage before the end of the file.
+	* lines to use the same whitespace as the target.
+	* If whitespace is missing in the target (i.e.
+	* use the whitespace from the preimage.
* we need it to adjust whitespace if we match.
-	* Ok, the preimage matches with whitespace fuzz.
-	* matches the preimage before the end of the file.
-	* lines to use the same whitespace as the target.
-	* If whitespace is missing in the target (i.e.
-	* use the whitespace from the preimage.
file. It can be local to cmd_apply(), so let's move it there.
This will make it easier to libify the apply functionality.
a "git apply" process which can be bad for performance.
to get rid of the global variables in "builtin/apply.c".
helper functions that need it and will be passed around the call chain.
* --index updates the cache as well.
* --cached updates only the cache without ever touching the working tree.
* p_value for the given patch.
* very likely to apply to our directory.
* new file we should try to match whatever "patch" does. I have no idea.
* again for the next patch.
will be used by different pieces of code.
and easy to use init_apply_state() function.
* replace the part of "img" with "postimage" text.
* without leading context must match at the beginning.
* A hunk without trailing lines must match at the end.
* with unidiff without any context.
* for the caller to write it out to the final destination.
* --index-info shows the old and new index info for paths if available.
* empty to us here.
- * --index updates the cache as well.
* we read from the result of a previous diff.
* this function will be called.
* the path the patch creates does not exist in the current tree.
* the next patch is to look at the line counts..
* by the caller, not a copy, when we return.
return error("cannot reverse-apply a binary patch "
* or in the helper function apply_binary_fragment() this calls.
* apply at applied_pos (counts in line numbers) in "img".
* Update "img" to remove "preimage" and replace it with "postimage".
fprintf_ln(stderr, _("Context reduced to (%ld/%ld)"
- * --cached updates only the cache without ever touching the working tree.
* we create them and try again.


text:
Q: Pandas fill NaN using prior value corresponding to some other pandas column I have a very large dataframe that looks like the following:
    fraction     id
0   0.729797       0
1   0.141084       1
2   0.226900       2
3   0.960937       3
4   0.452835       4
5   NaN            1
6   0.352142       2
7   0.104814       3
8   0.345633       4
9   0.498004       1
10   0.131665       2
11   NaN            3
12   0.886092       4
13   0.839767       1
14   0.257997       2
15   0.526350       3

Currently I am just filling NaN data with 0s using the following line of code:
df.fillna(0,inplace=True)

Is there a way to fill all NaN data using the prior "fraction" value using corresponding "id"s?
For example, the row at index #5 has a NaN value for "fraction", and has an "id" value of 1. The prior "fraction" value for id #1 was 0.141084.
Is there a way to replace with this value, and do this operation for the entire dataframe?
Thank You

A: Perform a groupby on 'id' and then forward fill with ffill:
df['fraction'] = df.groupby('id')['fraction'].ffill()

Note that you can do the same process on all columns in your DataFrame at once by omitting the ['fraction'].  In the case of your example data the output is the same:
df = df.groupby('id').ffill()

The resulting output:
    fraction  id
0   0.729797   0
1   0.141084   1
2   0.226900   2
3   0.960937   3
4   0.452835   4
5   0.141084   1
6   0.352142   2
7   0.104814   3
8   0.345633   4
9   0.498004   1
10  0.131665   2
11  0.104814   3
12  0.886092   4
13  0.839767   1
14  0.257997   2
15  0.526350   3

redpajama_set_name: RedPajamaStackExchange


text:
12/14/2012 06:30 pm ET Updated Dec 17, 2012
25 Statistics That Reveal Everything You Need To Know About The U.S. Firearms Industry
By Harry Bradford
A row of different AR-15 style rifles are displayed for sale at the Firing-Line indoor range and gun shop, Thursday, July 26, 2012 in Aurora, Colo. The Friday, July 20, 2012 massacre inside a crowded Colorado movie theater has prompted a sudden increase in gun sales and firearms training. Police said suspect James Holmes donned body armor and was armed with an AR-15 rifle, a shotgun and handguns during the attack. (AP Photo/Alex Brandon)
On Friday, December 14, a gunman entered an elementary school in Newtown, Conn., and shot and killed 26 people including 20 children. Earlier that same week, an Oregon man shot three people at a shopping mall before taking his own life. A few months before that, a gunman entered a movie theater in Aurora, Colo., and left having taken 12 lives.
Tragedies such as these have raised serious questions about a firearms industry growing larger and more powerful everyday. Today, it's easier for most Americans to access guns than it is to find mental health treatment. Such realities have set in motion a conversation about the nation's gun control laws, and the powerful industry such rules would regulate. So how big is the gun economy really?
Here is everything you need to know about the U.S. firearms industry:
31 billion - Economic impact of the firearms industry in 2011 in dollars.
4 billion - The number of dollars spent in annual commercial gun and ammunitions sales -- a 20-year high.
270 to 300 million - Estimated number of guns owned by Americans. That's about one for every American citizen.
158 million - Number of background checks conducted since the FBI was mandated to do so by Congress in 1993.
70 to 80 million - Number of Americans who own guns.
45 million - Number of Americans estimated to own handguns.
16.8 million - Number of background checks for gun sales in 2012.
8.5 million - Number of background checks for gun sales in 2002.
154,873 - The record number of background check calls the FBI reported receiving on Black Friday this year.
700 to 2000 - Cost of a .223-caliber semi-automatic rifle, which some reports indicate was the type of firearm used in the attack in Newtown, CT.
200 - Percent profit boost for gunmakers since Obama was elected in 2008.
96 - Percent of the $3 million that gun lobbyists donated during the 2012 election that went to Republicans.
87 - Percent of children killed in the 23 wealthiest nations who are American.
80 - Percent of gun deaths from the 23 wealthiest countries that are American deaths.
78 - Percent of Americans who favored making the sale of firearms "more strict" in 1990.
62.8 - Percent of people who own guns in Wyoming, the state with the highest rate of gun ownership in the U.S.
62 - Percent of 125 online sellers who said they "probably couldn't pass a background check."
47 - Percent of Americans who report owning a gun.
40 - 45 - Percent of U.S. households that own a gun.
33 - Percent increase in Winchester's ammunition sales since 2007.
16.2 - Percent of people who own guns in Connecticut.
4.44 - Percent that gun manufacturer Sturm, Ruger & Company's stock fell on the day of the Newtown school shooting.
1 - U.S.'s ranking in guns owned per 100 people.
Sandy Hook Elementary School Shooting
Harry Bradford
Former Associate Business Editor, The Huffington Post
Business Firearms Newtown School Shooting Gun Sales Guns
Connecticut State Police Release Sandy Hook Report
NEWTOWN, CT - UNSPECIFED DATE: In this handout crime scene evidence photo provided by the Connecticut State Police, shows the Newtown Tehcnology Team ID of Adam Lanza in the bathroom at the suspect's house on Yogananda St. following the December 14, 2012 shooting rampage at Sandy Hook Elementary School, taken on an unspecified date in Newtown, Connecticut . A report was released November 25, 2013 by Connecticut State Attorney Stephen Sedensky III summarizing the Newtown school shooting that left 20 children and six women dead inside Sandy Hook Elementary School. According to the report, a motive behind the shooting by gunman Adam Lanza is still unknown. (Photo by Connecticut State Police via Getty Images)


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Tue, 30 November 2021
Episode 462 - Edward Sorel
Legendary artist, illustrator, cartoonist, & author Ed Sorel joins the show to celebrate the publication of his memoir, Profusely Illustrated (Knopf). We get into his remarkable career (and "unremarkable life"), the rage that drove his political cartooning for more than a half-century, the illustrations that made him realize he had come into his own as an artist, the origins of Push Pin Studios & his stories of working with Seymour Chwast and Milton Glaser, the terrible lessons in abstractionism that beat figurative drawing out of him for years, and his need to look at his past work to remind himself that he does know how to draw. We talk about whether political cartooning is intended to change minds or provide comfort, how writing is like a pastel drawing, how he balanced art, commentary, and commerce over his career, why he refused to sell his drawings to certain hated people, how he learned to harness the nervous energy of his line to create a unique style (and why he hates tracing), why this (secular) patron saint of late starters got around to a memoir at 92, and more! Follow Ed on Instagram • More info at our site • Support The Virtual Memories Show via Patreon or Paypal
Direct download: Episode_462_-_Edward_Sorel.mp3


Abstract: The CLASS model is a top-down capital stress testing framework that uses public data, simple econometric models and auxiliary assumptions to project the effect of macroeconomic scenarios on U.S. banking firms. Through the lens of the model, we find that the total banking system capital shortfall under stressful macroeconomic conditions began to rise 4years before the financial crisis, peaking in the fourth quarter of 2008. The capital gap has since fallen sharply, and is now significantly below pre-crisis levels. In the cross-section, banking firms estimated to be most sensitive to macroeconomic conditions also have higher capital ratios, consistent with a "precautionary" view of bank capital, though this behavior is evident only since the crisis. We interpret our results as evidence that the resiliency of the U.S. banking system has improved since the financial crisis, and also as an illustration of the value of stress testing as a macroprudential policy tool.


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Home Kids He Started Singing 'You Raise Me Up', Then the Crowd Erupts When...
He Started Singing 'You Raise Me Up', Then the Crowd Erupts When the Little Girl Joins in
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I have heard "You Raise Me Up" a countless number of times. But when these two tiny kids got on the stage and started singing it, I couldn't believe my own ears.
These children are really small in age, but the way they sing this epic masterpiece is definitely going to get you hooked! Their rendition is simply unbelievable!
At first, I really didn't know what to expect, but as they finished their performance, I had a tear in my eye. Such powerful voices at such a young age! "You Raise Me Up" was originally composed by the duo Secret Garden. But it gained popularity when Josh Groban covered it in 2003. This song is usually sung as a contemporary hymn in church services.
Watch this incredible performance by these two little kids in the video below! Let us know if you enjoyed it via your comments!
Don't forget to SHARE this with your friends and families!
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Dance Couple's Love Story is as Good as Their Performance – I Love This!
Deaf Baby Hears Mom's 'I Love You' for First Time –...
Young Boy Nails this Dance Challenge With Impressively Smooth Moves


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Omicron Likely to Be Dominant Strain Globally in 2022, May Lead to More Hospitalisations: Singapore Experts
The new and highly transmissible Omicron variant of the deadly coronavirus has increased immune escape compared with the Delta variant and appears likely to become the dominant SARS-CoV-2 strain globally in 2022, according to Singapore-based experts. The World Health Organization (WHO) has called for the world to pull together to end the COVID-19 pandemic next year.
"2022 must be the year we end the pandemic," WHO Director-General Tedros Adhanom Ghebreyesus told reporters in Geneva on Monday. But Singapore-based experts said much depends on how potent the Omicron variant is and asserted that it was futile to try and predict when the pandemic will end.
It appears likely that Omicron will become the dominant SARS-CoV-2 strain globally in 2022, Public health expert Associate Professor Natasha Howard said, adding that the Omicron variant is more transmissible and has increased immune escape compared with the Delta strain. The rise of the more transmissible variant, increased case numbers and hospitalisations are likely, said Howard, the interdisciplinary health policy and systems researcher from the Saw Swee Hock School of Public Health in Singapore.
The implications of this are still unclear, but it shows that the pandemic is not controlled yet and until initial and booster COVID-19 vaccine doses are accessible to everyone eligible globally, we can expect new variants to emerge, she warned. For the Singapore population, it is clear that two COVID-19 vaccine doses are not enough to provide reasonable protection against Omicron and people should get booster shots as soon as they are eligible, she said.
Citing Imperial College modelling data, she said that the risk of reinfection with the Omicron variant is more than five times higher and it does not appear milder than the Delta variant. Omicron will likely be the cause of a significant wave of COVID-19, said Associate Professor Ashley St John from the Duke-NUS Medical School's Emerging Infectious Diseases Programme. "But while the Omicron variant is more transmissible than most we have seen, it is still SARS-CoV-2," she said.
The genetic backbone of Omicron is very, very different However, we don't yet have consistent data whether those genetic differences result in increased severity, the professor explained. Public health experts are thus monitoring the data on severity for Omicron and are waiting for more concrete numbers to bolster the initial assessment that vaccines are efficacious against it, she said.
Dr Lim Wee Kiat, associate director at the Singapore Management University's Centre for Management Practice, said it was futile to try and predict when the pandemic will end. After all, the 1918 flu pandemic never really ended, according to the US CDC (Centre of Disease Control and Prevention), descendants of the influenza virus from more than a century ago still circulate today, Lim Wee said.
The path to normalcy is going to be punctuated by twists and dead ends, even reversals, as we have seen here in Singapore and elsewhere, the Channel quoted Dr Lim, a disaster sociologist by training, as saying. And while Omicron may further delay the roll-out of the Singapore government's COVID-19 endemic roadmap, the city state's experience in managing the pandemic over the past two years is a plus.
Our experience in managing the pandemic over the past two years means that we are unlikely to revert to a circuit-breaker' type situation, which will only serve as a last resort given Singapore's endemic goal, especially since most of the population has been vaccinated, said Nydia Ngiow, Singapore managing director of strategic advisory firm Bowyer Group Asia. Meanwhile, Singapore reported 322 new COVID-19 cases on Thursday, of which 89 are imported or those who arrived here. There are also two fatalities, taking the country's death toll from coronavirus complications to 820 deaths.
As of Thursday, Singapore has recorded 277,042 COVID-19 cases since the start of the pandemic.