text:
\section{Introduction}

The development of stability analysis for stochastic dynamical systems reveals some characteristic features of the systems against deterministic dynamical systems. The features basically arise due to the system formulation being stochastic differential equations. Roughly speaking, functionals of the solutions have dynamics influenced by their Hessian terms, hence the stability analysis based on Lyapunov's sense requires results different from the original Lyapunov stability theory for dynamical systems represented by ordinary differential equations \cite{khasminskii2012,kozin1969,mao2007}.

The most popular stability analysis for equilibria of stochastic systems is based on {\it asymptotic stability in probability (ASiP)}, and a way to ensure the property is to prove the existence of (strict) {\it stochastic Lyapunov functions (SLFs)} \cite{khasminskii2012,mao2007}. The ASiP property and SLFs are respectively considered as stochastic versions of asymptotic stability and (strict) Lyapunov functions for equilibria of ordinary differential equations.

A characteristic feature of stochastic stability analysis appears in the discussion on ASiP at Remark 5.5 in \cite{khasminskii2012}, which implies that a stochastic system having smooth vector fields sometimes requires SLFs with non-smoothness at the equilibria. The situation does not occur for any deterministic system having smooth vector fields because of the necessary condition for the existence of Lyapunov functions \cite{khalil}. This motivates us to relax a sufficient condition for SLFs to have non-smoothness at the target equilibria \cite{nishimura2018automatica}.

At the same time, the permission of non-smooth SLFs causes another issue of ensuring some stability for non-equilibria. For example, a stochastic system having a constant diffusion coefficient has possibility to have an SLF without smoothness at a target point, while the system has no equilibrium because of the property of the diffusion coefficient. This requires new stability definitions for the justification of the non-smoothness of an SLF \cite{nishimura2018automatica}. The extension enables considering ``asymptotic stability'' for stochastic systems with additive noises such as Linear-Quadratic-Gaussian (LQG)-controlled systems. Therefore, the development of stochastic stability by non-smooth SLFs may provide fruitful discussions on characteristic features of stochastic dynamical systems.

To develop the stability analysis based on non-smooth SLFs, they should be discussed with the notions of {\it viscosity solutions} for partial differential equations \cite{crandall1992} as with deterministic stability analysis \cite{camilli2008,rifford2000}. For stochastic systems, viscosity solutions are considered for stochastic optimal control problems \cite{fleming2006} and uniform almost sure asymptotic stability (UASAS) \cite{bardi2005}. However, the connection between non-smooth SLFs and viscosity solutions is still under construction. The works for UASAS does not achieve ASiP properties directly because the analysis is based on the (weak) invariant sets. The UASAS property requires the sublevel sets of SLFs to be invariant sets; however, the ASiP allow the sets being non-invariant sets. This implies that the construction of the bridge between viscosity solutions and our non-smooth SLFs needs another way without passing through the notion of invariant sets.

Recently, the authors provide a discussion on the relationship between viscosity solutions and a specific form of a non-smooth SLF \cite{nishimura2017ascc} via the way of \cite{nishimura2018automatica}, which does not use the notion of invariant sets. The non-smooth SLF is firstly transformed into a $C^2$ function for guaranteeing the existence of a global solution to the target stochastic differential equation; and then, the solution is confirmed to satisfy the property of ASiP or the stability for additive noises. After that, the $C^2$ function is considered as a {\it test function} for a viscosity supersolution, however, the analysis concludes that the related Lyapunov equation does not achieve a viscosity supersolution due to the existence of a test function not satisfying the inequality for the supersolution. Therefore, in \cite{nishimura2017ascc}, the notion of {\it viscosity weak supersolution} is proposed for clarifying the relationship between the notion of viscosity solutions and non-smooth SLFs.

In this paper, we generalize the analysis in \cite{nishimura2017ascc} by considering SLFs in the class of lower semicontinuous functions as with the usual sense of viscosity solutions \cite{bardi2005}. In the procedure, we also claim that LQG-controlled systems have the origins being ``asymptotically stable'' by transforming quadratic Lyapunov functions for deterministic LQ-controlled systems into lower semicontinuous SLFs.

{\it Notations.} $\Rset^d$ is the $d$-dimensional Euclidean space, especially $\Rset:=\Rset^1$. $|x|$ denotes the Euclidean norm of $x \in \Rset^n$. For $a, b\in\Rset$, let $a\wedge b$ denote the minimum of $a$ and $b$. Let ${\mathcal{P}} :=(\Omega,\mathcal{F}, \{\mathcal{F}_t\}_{t \ge 0}, \mathbb{P})$ be a filtered probability space, where $\Omega$ is the sample space, $\mathcal{F}$ is the $\sigma$-algebra that is a collection of all the events, $\{\mathcal{F}_t\}_{t \ge 0}$ is a filtration of $\mathcal{F}$, and $\mathbb{P}$ is a probability measure. The probability of some event $A$ and the expectation of some random variable $X$ are written as $\mathbb{P} [ A ]$ and $\mathbb{E}[X]$, respectively. The function $w :=[w_1,w_2,\ldots,w_d]^T \in \Rset^d$ is a $d$-dimensional standard Wiener process defined on $\mathcal{P}$. The differential form of It\^o integral of a function $\sigma_\alpha: \Rset^n \rightarrow \Rset^n$ in $w_\alpha(t)$ is denoted by $\sigma_\alpha(x) dw_\alpha(t)$ for $\alpha=1,2,...$

\section{Preliminary Discussions}

In this section, we provide preliminary discussions on stochastic systems, viscosity solutions, target points and stochastic stability based on \cite{bardi2005,fleming2006,khasminskii2012,nishimura2018automatica}.

\subsection{System Representation and Basic Definitions}

In this paper, we consider the following stochastic system:
\begin{align}\label{eq:sys-sto}
dx(t) = f(x(t)) dt + \sum_{\alpha=1}^d \sigma_\alpha(x(t)) dw_\alpha(t),
\end{align}
where $x \in \Rset^n$ is a state vector, $f: \Rset^n \to \Rset^n$ is a drift coefficient and $\sigma_1,\ldots,\sigma_d: \Rset^n \to \Rset^n$ are diffusion coefficients; we also assume that all the coefficients $f(x),\sigma_1(x),\ldots,\sigma_d(x)$ of \eqref{eq:sys-sto} are locally Lipschitz.

For a function $v:\Rset^n \to \Rset$ with $n =1,2,\ldots$, we define an {\it infinitesimal operator} $\mathcal{L}$ such that
\begin{align}
(\mathcal{L}v)(x,v,p,X) := &p f(x) + \frac12 \sum_{\alpha=1}^d \sigma_\alpha^T X \sigma_\alpha,
\end{align}
where $(p,X)$ is an element of a semijet:
\begin{align}
&\mathcal{J}^{-,2}v(x) := \left\{ (p,X) \in \Rset^n \times S(n) \right| \mathrm{for}\  y \to x, v(y) \ge  \nonumber \\
    &v(x) +p (y-x) + \frac12 (y-x)^T X (y-x) \left.+ o(|y-x|^2) \right\},   \label{eq:semijet}
\end{align}
where $S(n)$ is the set of symmetric $n \times n$ matrices. The semijet is, roughly, a set of generalized notions of the first and the second sub-derivatives of $v(x)$ in $x$. For $x \in M(v) := \{ x \in \Rset^n | v(x)$ is $C^2\}$ with choosing $p = (\partial v/\partial x)^T$ and $X = \partial p / \partial x$, we employ an abridged notation: $(\mathcal{L}v)(x) = (\mathcal{L}v)(x,v,p,X)$.

\subsection{Viscosity Supersolutions and Lyapunov Equations}

In this subsection, we consider the basic definition of Lyapunov equations based on viscosity supersolutions for stochastic systems \cite{crandall1992,fleming2006}.

Let $x \in \Rset^n$, $v: \Rset^n \to \Rset$, $p \in \Rset^n$, $X \in \Rset^n \times \Rset^n$, and
\begin{align}\label{eq:viscosity}
F(x,v,p,X) = 0
\end{align}
be degenerate elliptic; that is, for any $Y \in \Rset^n \times \Rset^n$ satisfying $Y-X$ being positive definite, $F(x,v,p,X) \ge F(x,v,p,Y)$.

Here, we define the notion of a viscosity supersolution.
\begin{defn}[viscosity supersolution \cite{bardi2005,crandall1992}]\label{def:viscosity2}
A lower semicontinuous function $v(x)$ is said to be a viscosity supersolution for \eqref{eq:viscosity} if
\begin{align}\label{ineq:viscosity2}
F(x, v, p, X) \ge 0
\end{align}
holds for any $x \in \Rset^n$ and for any $(p,X) \in \mathcal{J}^{-,2}v(x)$.  $\hspace*{\fill}\square$
\end{defn}

For our convenience, we put another notion of viscosity supersolution without semijet directly:
\begin{defn}[viscosity supersolution \cite{fleming2006}]\label{def:viscosity1}
A lower semicontinuous function $v: \Rset^n \to \Rset$ is said to be a {\it viscosity supersolution} for \eqref{eq:viscosity} on an open subspace $\mathcal{O} \subset \Rset^n$ if for any $\phi: \mathcal{O} \to \Rset$ being smooth,
\begin{align}\label{ineq:viscosity1}
F\left( x_0,\phi(x_0),\frac{\partial \phi}{\partial x}(x_0), \frac{\partial^2 \phi}{\partial x^2}(x_0) \right) \ge 0
\end{align}
holds for any $x_0 \in \mathcal{O}$ satisfying $v(x_0) = \phi(x_0)$ and $\phi(x) \le v(x)$ for a neighborhood of $x_0$. $\hspace*{\fill}\square$
\end{defn}

The above function $\phi(x)$ is said to be a {\it test function}. Definition~\ref{def:viscosity2} and Definition~\ref{def:viscosity1} are the same notions \cite{fleming2006}.

A viscosity supersolution is a key notion for building a bridge between viscosity solution theory and Lyapunov stability theory. Supposing $v(x)$ being $C^2$ and setting $x_0=0$ and $F=-\mathcal{L}v$, we obtain $(\mathcal{L}v)(x) \le 0$ for any $x \in \mathcal{O}$ via \eqref{ineq:viscosity1}; that is, $v(x)$ is an SLF \cite{khasminskii2012,mao2007}. Thus,
\begin{align}\label{eq:lyapunov}
-(\mathcal{L}v)(x,v,p,X) -l(x) = 0
\end{align}
is said to be a {\it Lyapunov equation}, where $l:\Rset^n \to \Rset$ is assumed to be continuous and positive semi-definite.

\subsection{Target Points}
For considering non-smooth SLFs, we should consider the case of the origin of \eqref{eq:sys-sto} being an non-equilibrium. In \cite{nishimura2018automatica}, the origin is categorized as an {\it instantaneous point} or an {\it almost sure equilibrium} as long as $f(0) = 0$. This classification is meaningful because the two notions are mutually independent; at the same time, they are somewhat awkward because sufficient conditions for stability notions for instantaneous points include the ones for almost sure equilibria. To make the discussion on stability properties simpler, we define a new notion for covering both the instantaneous point and the almost sure equilibrium:

\begin{defn}[equilibrium]\label{defn:asequi}
The origin of \eqref{eq:sys-sto} is said to be a {\it noisy equilibrium} if $f(0)=0$. It is also said to be an
{\it almost sure equilibrium} if  $f(0)=0$ and $\sigma(0)=0$. $\hspace*{\fill}\square$
\end{defn}

This paper mainly considers stability for noisy equilibria, and then almost sure equilibria as a special case for noisy equilibria.

\subsection{Global Solutions}
In this subsection, we summarize the results of global solutions.

The target system \eqref{eq:sys-sto} has at least a solution in local time because all the coefficients are locally Lipschitz. The existence of a solution in global time is not ensured obviously because a linear growth condition or global boundedness of the coefficients are not guaranteed. In the basic analysis of stochastic stability \cite{khasminskii2012,mao2007}, a global solution is ensured by the existence of a smooth SLF. However, a non-smooth SLF $V(x)$ are impossible to guarantee a global solution directly because the dynamical analysis for $V(x)$ is broken when sample paths leaves $M(V)$. This implies that, we need a $C^2$ function implicitly to derive a sufficient condition for the existence of a global solution.

\begin{defn}[FCiP \cite{nishimura2018automatica}]
The system \eqref{eq:sys-sto} is said to be {\it forward complete in probability (FCiP)} if for each $x_0\in\Rset^n$, there exists a continuous function $\psi: [0,\infty)\times(0,1)\to[0,\infty)$ such that
\begin{align}
\label{eq:FCiP}
\mathbb{P}\left[\forall t\in[0,\infty), \ |x(t)|\le
\psi(t,\epsilon)
\right]\ge 1-\epsilon
\end{align}
holds for all $\epsilon\in (0,1)$. $\hspace*{\fill}\square$
\end{defn}

Roughly, FCiP ensures the existence of a solution to \eqref{eq:sys-sto} for $t \in [0,\infty)$. This implies that, the sentence ``the system is FCiP'' can be translated into ``the system has a global solution (in forward time in probability)''. In the previous work \cite{nishimura2018automatica}, a sufficient condition for FCiP via $C^2$ function as follows:
\begin{lem}[\cite{nishimura2018automatica}]\label{lem:FCiP}
Let the system \eqref{eq:sys-sto} be considered. If there exists a positive definite, proper and $C^2$ function $y: \Rset^n \rightarrow \Rset$ such that
\begin{align}
\label{eq:suf-fcip}
(\mathcal{L}y)(x) \leq c y(x) + g
\end{align}
for all $x \in \Rset^n$ and for some constants $c, g\in[0,\infty)$, then system \eqref{eq:sys-sto} is FCiP. $\hspace*{\fill}\blacklozenge$
\end{lem}

\subsection{Basic Stability Analysis}
In this subsection, we provide stability notions for noisy equilibria by making a small change of the definitions in \cite{nishimura2018automatica}.

Let a stopping time be defined by
$\tau_0 := \inf \{ t > 0 \,|\, x(t)=0 \}$, where $\infty=\inf\emptyset$.

\begin{defn}[stability]\label{def:stability}
The system \eqref{eq:sys-sto} and the origin are respectively assumed to be FCiP and a noisy equilibrium. The origin is said to be {\it noisily stable (NS)} if $x(t)$ satisfies
\begin{align}\label{eq:def-is}
\forall \eta>0,\ \forall \epsilon > 0,\  \exists \delta=\delta(\eta,\epsilon)>0,\  {\mathrm{s.t.}} \nonumber \\
\sup_{|x_0| \le \delta} \mathbb{P} \left[ \sup_{0 \le t} |x(t\wedge \tau_0)|> \eta \right]  < \epsilon;
\end{align}
and furthermore, the origin is an almost sure equilibrium, then the origin is said to be {\it stable in probability (SiP)}. $\hspace*{\fill}\blacklozenge$
\end{defn}

\begin{defn}[asymptotic stability]\label{def:as}
The system \eqref{eq:sys-sto} and the origin are respectively assumed to be FCiP and a noisy equilibrium. The origin is said to be {\it noisily asymptotically stable (NAS)}
if it is NS and satisfies
\begin{align}\label{eq:ias}
\forall \eta' > 0, \
\forall x_o \in \Rset^n, \
\mathbb{P} \left[ \limsup_{t \to \infty}  |x(t\wedge \tau_0)| > \eta'  \right] = 0;
\end{align}
and furthermore, the origin is an almost sure equilibrium, then the origin is said to be {\it asymptotically stable in probability (ASiP)}. $\hspace*{\fill}\blacklozenge$
\end{defn}

The above definitions are the same as the ones in the previous work \cite{nishimura2018automatica} except the two changes: one is assuming the FCiP properties, and the other is the classification of the origin. Therefore, the following sufficient conditions for the stability properties are directly obtained by the proofs for the main results in \cite{nishimura2018automatica}:

\begin{thm}\label{the:stable}
The system \eqref{eq:sys-sto} and the origin are respectively assumed to be FCiP and a noisy equilibrium. If there exists a function $V: \Rset^n \rightarrow \Rset$ such that it is continuous, positive definite, proper, $C^2$ except at the origin and $(\mathcal{L}V)(x) \le 0$ holds for all $x \in \Rset^n \setminus \{0\}$, the origin is NS. In addition, if it is an almost sure equilibrium, it is SiP. $\hspace*{\fill}\blacklozenge$
\end{thm}

\begin{thm}\label{the:as}
The system \eqref{eq:sys-sto} and the origin are respectively assumed to be FCiP and a noisy equilibrium. If there exists a function $V: \Rset^n \rightarrow \Rset$ such that it is continuous, positive definite, proper, $C^2$ except at the origin and $(\mathcal{L}V)(x) < 0$ holds for all $x \in \Rset^n \setminus \{0\}$, the origin is NAS. In addition, if it is an almost sure equilibrium, it is ASiP. $\hspace*{\fill}\blacklozenge$
\end{thm}

Roughly, the function $V(x)$ is said to be a {\it stochastic Lyapunov function (SLF)} if it satisfies the conditions for Theorem~\ref{the:stable}, and a {\it strict SLF} if it satisfies the conditions for Theorem~\ref{the:as}. Note, however, that, this paper considers more relaxed versions of SLFs and strict SLFs; the concrete definitions of them are provided in Subsection~\ref{subsec:stability} below.

\begin{rem}
In the previous works \cite{khasminskii2012,nishimura2018automatica}, the origin is said to be SiP if the origin is an almost sure equilibrium and $x(t)$ satisfies
\begin{align}\label{eq:def-sip}
\forall \eta>0,\ \forall \epsilon > 0,\  \exists \delta=\delta(\eta,\epsilon)>0,\  {\mathrm{s.t.}} \nonumber \\
\sup_{|x_0| \le \delta} \mathbb{P} \left[ \sup_{0 \le t} |x(t)|>\eta \right]  < \epsilon,
\end{align}
which is the same conditions for the SiP in Definition~\ref{def:stability} because of the assumption of the FCiP property. The ASiP property in Definition~\ref{def:as} is also the same in the previous works. $\hspace*{\fill}\blacklozenge$
\end{rem}

\section{Stability Analysis via Viscosity Weak Supersolution}

This section provides the main results of this paper. It shows our non-smooth SLFs being not included in the notion of viscosity supersolutions via a simple example, followed by a new definition of {\it viscosity weak supersolution}, and then, our sufficient conditions with the construction of the bridge between stochastic Lyapunov stability analysis and viscosity solution theory.

\subsection{Non-Smooth SLFs vs. Viscosity Supersolutions}\label{subsec:example1}

Firstly, we provide a simple example that an SLF does not a viscosity supersolution. Consider
\begin{align}
dx(t) = -x(t) dt + dw(t),\ x,w \in \Rset.
\end{align}
The origin is NAS because it has a function $V_1(x)=|x|$ satisfying $(\mathcal{L}V_1)(x) = - |x|$ except the origin. Here we calculate elements of the semijet of the function; that is, considering \eqref{eq:semijet} with $v=V_1$, we obtain
\begin{align}\label{eq:ex1}
(p,X) = \left\{ \begin{array}{ll}
    (1,X) \ \mathrm{with}\ X \le 0, & x>0;\\
    (p_0,X_0), & x=0;\\
    (-1,X)\ \mathrm{with}\ X\le 0, & x<0;
    \end{array}\right.
\end{align}
where $p_0 \in [-1,1]$ and
\begin{align}\label{eq:ex1-X0}
X_0 = \left\{ \begin{array}{ll}
    X \ \mathrm{with}\ X \le 0 & \mathrm{if}\ p_0 = \pm 1;\\
    X \ \mathrm{with}\ X \in \Rset & \mathrm{if}\ p_0 \in (-1,1).
    \end{array}\right.
\end{align}

Therefore, $V_1(x)$ satisfies
\begin{align}\label{ineq:ex1}
-(\mathcal{L}V_1)(x,V_1,p,X) = p x - \frac12 X \ge 0
\end{align}
for any $x \neq 0$, while the inequality does not hold for some combination of $(p_0,X_0)$ for $x = 0$. This simply implies that $V_1(x)$ is not a viscosity supersolution to $-(\mathcal{L}V_1)(x,V_1,p,X)=0$ despite satisfying all the conditions for Theorem~\ref{the:as}.

The above observation is also confirmed via Definition~\ref{def:viscosity1}. Considering $\phi(x)=x^2$ as a test function in $x=0$, we obtain
\begin{align}
-(\mathcal{L}\phi)(x) = 2x^2 - 1;
\end{align}
this does not imply \eqref{ineq:viscosity1} because $-(\mathcal{L}\phi)(0)=-1 \ngeq 0$. Noticing the word ``for any $\phi$'' in Definition~\ref{def:viscosity1}, we conclude that $V_1(x)$ is not a viscosity supersolution.

Consequently, to build a bridge between stochastic Lyapunov stability theory and viscosity solution theory, we need a relaxed notion of viscosity supersolutions.

\subsection{Viscosity Weak Supersolutions}
Reconsider the simple example in the previous subsection. While \eqref{eq:ex1-X0} includes elements banishing $V_1(x)$ from being a viscosity supersolution, it also has elements making $V_1(x)$ being an SLF. For example, we choose $(p_0,X_0)=(0,0)$ or $\phi(x)=x^4$, then we obtain $-(\mathcal{L}V_1)(0,V_1,p_0,X_0)=0$ or $-(\mathcal{L}\phi)(0)=0$. That is, we can consider the possibility for our SLFs to have ``some'' element in the semijet satisfying \eqref{ineq:viscosity2} or \eqref{ineq:viscosity1}. This motivates us to consider the following relaxed version of viscosity supersolution:

\begin{defn}[viscosity weak supersolution]\label{def:weakviscosity2}
A lower semicontinuous function $v(x)$ is said to be a {\it viscosity weak supersolution} for \eqref{eq:viscosity} if {\it there exists} $(p,X) \in \mathcal{J}^{-,2}V_0(x)$ such that \eqref{ineq:viscosity2} holds for any $x \in \Rset^n$.  $\hspace*{\fill}\square$
\end{defn}

Of course, another version is defined as follows:
\begin{defn}[viscosity weak supersolution]\label{def:weakviscosity1}
A lower semicontinuous function $v: \Rset^n \to \Rset$ is said to be a {\it viscosity weak supersolution} for \eqref{eq:viscosity} on an open subspace $\mathcal{O} \subset \Rset^n$ if for some $\phi: \mathcal{O} \to \Rset$ being smooth, \eqref{ineq:viscosity1} holds for any $x_0 \in \mathcal{O}$ satisfying $v(x_0) = \phi(x_0)$ and $\phi(x) \le v(x)$ for a neighborhood of $x_0$. $\hspace*{\fill}\square$
\end{defn}

The main claim of this paper is to show that the notion of viscosity weak supersolutions is useful for stability analysis of stochastic systems using non-smooth SLFs.

\subsection{Stability Conditions via Viscosity Weak Supersolution}\label{subsec:stability}

Here we derive sufficient conditions for stability properties using viscosity weak supersolutions. First, we define our SLFs:
\begin{defn}[SLF]
Consider the system \eqref{eq:sys-sto}. A continuous, positive definite and proper function $V: \Rset^n \rightarrow \Rset$ is said to be a {\it stochastic Lyapunov function (SLF)} if it is a viscosity weak supersolution to the Lyapunov equation \eqref{eq:lyapunov}. Furthermore, $V(x)$ is said to be a {\it strict stochastic Lyapunov function (strict SLF)} if there exists a continuous and positive definite function $l:\Rset^n \to \Rset$ such that $V(x)$ is a viscosity weak supersolution to \eqref{eq:lyapunov}. $\hspace*{\fill}\square$
\end{defn}

Then, we claim the following sufficient conditions for stability properties:
\begin{thm}\label{the:stable-main}
The system \eqref{eq:sys-sto} and the origin are respectively assumed to be FCiP and a noisy equilibrium. If there exists an SLF, the origin is NS. In addition, if it is an almost sure equilibrium, it is SiP. $\hspace*{\fill}\blacklozenge$
\end{thm}

The proof is shown in Appendix~\ref{app:stable}. Then, we also derive sufficient conditions for asymptotic stability properties:
\begin{thm}\label{the:as-main}
The system \eqref{eq:sys-sto} and the origin are respectively assumed to be FCiP and a noisy equilibrium. If there exists a strict SLF, the origin is NAS. In addition, if it is an almost sure equilibrium, it is ASiP. $\hspace*{\fill}\blacklozenge$
\end{thm}
The proof is also shown in Appendix~\ref{app:as}.

\section{Case Study}

This section provides some discussions on the benefits of allowing non-smooth SLFs: the validity of the notion of viscosity weak supersolutions under the assumption of the origins being almost sure equilibria, showing a particular shape of SLFs ensuring the FCiP property, and proving the LQG-controlled systems always have the origins being NAS.

\subsection{ASiP vs. Viscosity Supersolutions}

The simple example of NAS in Subsection~\ref{subsec:example1} simply states the necessity of considering viscosity weak supersolutions. However, we may suspect that the notion is no need for ASiP properties. For example, another simple example of
\begin{align}
dx(t) = - \frac12 x(t) dt + x(t)dw(t),\ x,w \in \Rset,
\end{align}
has the origin being ASiP because $V_1(x)=|x|$ implies $(\mathcal{L}V_1)(x) =  - (1/2) |x| < 0$ except the origin. Because the strict SLF $V_1(x)$ has the same semijet as \eqref{eq:ex1} and \eqref{eq:ex1-X0}, we obtain
\begin{align}
-(\mathcal{L}V_1)(x,V,p,X) &= \frac12 p x - \frac12 X x^2 \left\{ \begin{array}{ll}
	> 0 & x \neq 0, \\
	= 0 & x = 0.
	\end{array}\right.
\end{align}
Therefore, $V_1(x)$ is a viscosity supersolution to \eqref{eq:lyapunov} with $l=0$.

The above result states that the requirement of viscosity weak supersolutions may not be indispensable for the ASiP property. However, we claim that the employment of the notion simplifies the discovery of SLFs; let us confirm it by the following example:
\begin{align}\label{eq:ex-chained}
dx = -x dt + g_1(x) dw_1 + g_2(x) dw_2,\  x \in \Rset^3,
\end{align}
where $g_1=(1,0,x_2)^T$ and $g_2=(0,1,0)^T$. Let a candidate of a strict SLF is designed by $V_c(x)=|x_1| + |x_2| + |x_3|$.

Letting $p=(p_i)$ and $X=(X_{ij})$ with $i,j \in 1,2,\ldots,d$, the elements of the semijet $\mathcal{J}^{-,2}V_0$ are derived as follows: for all $x \in M(V_c)$,
\begin{align}\label{eq:jet1}
p_i = \mathrm{sgn}(x_i) \ \mathrm{and}\ X \le 0,
\end{align}
where $X \le 0$ denotes that X is negative semidefinite. For a point $x$ satisfying $x_k=0$ for some $k =1,2,\ldots,d$ and $x_i \neq 0$ for $i \neq k$,
\begin{align}\label{eq:jet2}
p_i=\left\{ \begin{array}{ll}
	\mathrm{sgn}(x_i), & i \neq k \\
	-1 \ \mathrm{or}\ 1, & i = k
\end{array}\right\},\ \mathrm{and}\
X \le 0
\end{align}
or
\begin{align}\label{eq:jet3}
\left\{ \begin{array}{lll}
	p_i = \mathrm{sgn}(x_i),\ \mathrm{and} & (X_{ij}) \le 0, &i,j \neq k \\
	p_k \in (-1,1),\ \mathrm{and} & X_{ik} \in \Rset.
\end{array}\right\}.
\end{align}

This calculation implies that, $X$ is capable of having positively-large values at $x \in \Rset^n \setminus M(V_c)$. Therefore, $\mathcal{J}^{-,2}V_c$ generally has elements such that \eqref{ineq:viscosity2} is not satisfied.

In this way, $V_c(x)$ is confirmed to be out of the notion of a viscosity supersolution; however, the semijets $\mathcal{J}^{-,2}V_c$ always has an element $(p,X)$ making $-(\mathcal{L}V_c)(x,V_c,p,X)-l(x) \ge 0$ with some positive definite function $l(x)$; that is, $V_c(x)$ is a viscosity weak supersolution. Therefore, $V_c(x)$ is a strict SLF.

\subsection{Non-Smooth SLF Ensuring FCiP Property}

The SLF $V_c(x)=|x_1|+|x_2|+|x_3|$ in the previous subsection does not ensure the target system being FCiP directly because, before confirming the property, the dynamical analysis is stopped at the first exit time from $M(V_c)$. However, it has a shape ensuring the FCiP property implicitly. The following result shows that an SLF formed
\begin{align}\label{eq:slf}
V_0(x) = \sum_{i=1}^n \frac{1}{p_i} |x_i|^{p_i},\quad p_1,\ldots,p_n > 0,
\end{align}
ensures the target system \eqref{eq:sys-sto} being FCiP:
\begin{thm}\label{the:special}
If $V_0(x)$ is an SLF for \eqref{eq:sys-sto}, the system is FCiP and the origin is NS. $\hspace*{\fill}\blacklozenge$
\end{thm}
The proof is shown in Appendix~\ref{app:special}, provided that the proof for NS property is abbreviated because it is obviously ensured by the combination of the existence of an SLF and the confirmation of the FCiP property.

\subsection{Stability for LQG-Controlled Systems}
Here we consider the benefit of non-smooth SLFs for stability analysis of controlled systems. Let
\begin{align}\label{eq:sys-lqg}
dx(t) = \{ Ax(t) + Bu(t) \} dt + \sum_{k=1}^d G_k dw_k,
\end{align}
where $x \in \Rset^n$, $u \in \Rset^m$, $w \in \Rset^d$, and $A$, $B$ and $G=(G_1,\ldots,G_d)$ are $n \times n$, $n \times m$ and $n \times d$-dimensional matrices, respectively. The function $u(t)$ is a control input vector, and is designed here by
\begin{align}\label{eq:lqg}
u(t)=-R^{-1}B^T Px(t),
\end{align}
where $R$ and $P$ are positive definite $n \times n$ matrices satisfying a Riccati equation
\begin{align}
A^T P + P A - PBR^{-1}B^TP + Q = 0,
\end{align}
where $Q$ is also a positive definite $n \times n$ matrix. Then, the control input is said to be an LQG regulator because it minimizes the related cost function
\begin{align}
J(x,u) = \int_0^\infty \left( x(s)^T Q x(s) + u^T(s) R u(s) \right) ds,
\end{align}
and $V_{LQ}(x)=\inf_{u \in \Rset^m} J(x,u)$ results in $V_{LQ}(x)=x^T P x$ \cite{athans1971}. If $G=0$, $V_{LQ}(x)$ is a Lyapunov function because $\dot{V}_{LQ}(x(t))= -x^T (Q+PBR^{-1}B^TP) x$ being negative definite. However, If $G \neq 0$, it is generally not an SLF because
\begin{align}
(\mathcal{L}V_{LQ})(x)=-x^T (Q+PBR^{-1}B^TP) x + \sum_{k=1}^d G_k^T P G_k;
\end{align}
that is, the value is positive for sufficiently near the origin.

Nevertheless, we claim the following:
\begin{thm}\label{the:lqg}
The origin of \eqref{eq:sys-lqg} with \eqref{eq:lqg} is NAS. $\hspace*{\fill}\blacklozenge$
\end{thm}
The theorem is proven by designing a non-smooth strict SLF by transforming $V_{LQ}(x)$; the detail is provided in Appendix~\ref{app:lqg}.

Here we consider a benefit of the above theorem to control theory. An availability of LQG controllers is that they are obtained from Riccati equations for linear-quadratic (LQ) control systems without any noise \cite{athans1971}; that is, the additive noises for state equations are not obstacles for optimality. As with the optimality, the above discussions imply that ``for linear systems, asymptotic stability preserves against the addition of additive noises'' if we recognize NAS as stochastic stability of just the counterpart for asymptotic stability of deterministic systems.

Thus, we conclude that the notion of NAS has a theoretical contribution in connecting asymptotic stability properties for deterministic and stochastic systems, and the connection is supported by non-smooth SLFs those are also viscosity weak supersolutions.

\section{Conclusion}

In this paper, we developed stability analysis for stochastic systems via non-smooth stochastic Lyapunov functions. In the procedure, we redefined the notions of stability properties including the situation of the origins losing the equilibrium states, confirmed that the notion of viscosity supersolutions is insufficient to describe our non-smooth stochastic Lyapunov functions, proposed a new notion of viscosity weak supersolutions for building a bridge between stochastic Lyapunov stability theory and viscosity solution theory, and showed the contribution of our stability analysis to stochastic control theory.

redpajama_set_name: RedPajamaArXiv


The Pension Benefit Guaranty Corporation (PBGC) has issued a final regulation revising the annual financial and actuarial reporting requirements under Section 4010 of the Employee Retirement Income Security Act (ERISA) for sponsors of defined benefit pension plans with funding percentages of less than 80 percent. The revisions adopt some but not all of the changes proposed by the PBGC on July 27, 2015.
The PBGC's previous §4010 regulation included a reporting waiver for plan sponsors in any controlled group where aggregate underfunding was $15 million or less. After pension funding relief was enacted, this aggregate underfunding was determined using the same "stabilized interest rates" that are used to determine the minimum funding requirements. Under the final regulation, the aggregate funding must be determined without the use of stabilized interest rates.
The final regulation also provides a reporting waiver for all controlled groups with fewer than 500 defined benefit pension participants. The PBGC determined that controlled groups that sponsor defined benefit pension plans with few participants (in the aggregate) pose minimal risk to the pension insurance system and, thus, the PBGC did not need the reports.
The new rules apply for the 2016 reporting year, generally affecting reporting that is due April 17, 2017 and later.


One of my fondest memories of DJ AM (RIP) is the night I became a fan of DJ A-Trak. I had the pleasure of seeing DJ AM, Steve Aoki, [[[zuper blahq]]] aka Will.I.am and DJ A-Trak all spin in one night. Up until that point I had only seen A-Trak once. Well, let's just say I had not realized AM stopped spinning… A-Trak was incredible that night and I have been a fan every since. With the release of the official video for "Barbra Streisand" by Duck Sauce (DJ A-Trak and Armand Van Helden collaboration), I think I am falling in love all over again with A-Trak. I have always been a fan of Armand Van Helden. If you have not checked out the So ME directed video make sure to take a look now.


Charismatic couple Alia Bhatt and Ranbir Kapoor walked in together at Umang 2019. They looked charming together and posed for the paparazzi.
While Ranbir Kapoor looked dapper in a deep blue suit paired up with the white shirt, Alia Bhatt looked gorgeous in a highly embellished anarkali. The actress's hair is nicely done and she donned a huge pair of earrings. She kept her neck bare. Her make-up was perfectly done and she donned a million dollar smile on her face.
Alia and Ranbir are speculated to get married soon but the 'Raazi' actor said that she is not getting married so soon and currently she is totally focused on her acting career. However, her father Mahesh Bhatt said that he has no any issue of Alia getting married anytime.


text:
Early & Transitional
Fowler/Fusil
Antiques Originals for Sale
Contemporary Guns for Sale
The gun was built for use by Leonardo DiCaprio in the movie, "The Revenant".
The gun was built on a moderately figured piece of curly maple in the classic Bucks County style. The build is based on an original which was handled and photographed by the builder. The hardware is copied from an original John Shuler, Sr. rifle. The barrel is a 44″ Colerain B weight 50 cal. While many original Bucks Co. rifles had English import locks, the original had somewhat larger than normal Germanic lock. I found that a Jim Chambers Golden age lock was a near match for the original. The carving of this rifle is somewhat atypical for a Bucks Co. gun in that it is a blend of both raised and incised carving, showing a decided Lehigh Co. influence.
In July 2014, the order for the guns came in. Two were ordered in case one was damaged during the filming. The two guns had to be in British Columbia by the end of August. There was some burning of the midnight oil to fill the order, but it was a thrilling once-in-a-lifetime opportunity. I have completed another copy of the gun and it will be on display and available for purchase at the 18th Century Artisan show (2016). www.18thcenturyartisanshow.com

redpajama_set_name: RedPajamaCommonCrawl


That you now have additional options to help manage your business taxes through our My Business Account service?
access a variety of business tax information and services, including account balances and activities.
Starting in November 2008, you will be able to transfer payments and credits within your GST/HST,* corporation income tax, or other levies account. This service will allow you to transfer amounts not yet applied to an assessed period and view the results immediately, including updated interest amounts and account balances. If the amount you wish to transfer has already been applied to an assessed period, you can request a transfer through our Make online requests service in My Business Account.
Business owners can authorize their employees and representatives to view or change their tax information online. Once authorized, the employees and representatives would access the services through Represent a client at www.cra.gc.ca/representatives.


Newport is a new city, granted in 2001.
It has a great many listed buildings, and places of note, that might go unnoticed. There are a good many beautiful walks around, and contains most City attractions without many of the downsides of other Cities.
Newport is in easy reach of lots of places elsewhere in South Wales, South West England, along the M4 and up to Birmingham too. Below is a particularly beautiful map showing Newport. Notice the blue River Usk, Llanwern Steel works large rectangle on the right-hand side, and the M4, a grey belt across the north of the City.
In the centre, the remains of Newport Castle are highly visible and contrast against road and rail links, plus attractions of the Newport Wave, and the New Arts Centre.
See CastleWales.com for more information about our Castle.


text:
Q: How do I plot loglikelihood functions of the Cauchy distribution in R? I need to determine whether or not there is always a unique root of the log-likelihood equation l'(x,0)=0 for different samples sizes of the Cauchy distribution.
But I am unsure about how to actually define the log-likelihood function R and about actually being able to plot these graphs. Any advice would be appreciated!

A: "The" Cauchy distribution is a misnomer: it is intended to refer to a family of distributions.
As an example, let's consider the location-scale family of distributions whose PDFs are given by
$$f(x; \mu, \sigma) = \frac{1}{\pi \sigma}\left(1 + \left(\frac{x-\mu}{\sigma}\right)^2\right)^{-1}.$$
(The special case $\mu=0, \sigma=1$ is the Cauchy distribution.)
By definition, the log likelihood $\Lambda$ of a batch of $n$ data $(x_i)$, $i=1, 2, \ldots, n$, is the logarithm of their probability, assuming the data are independently and identically distributed according to $f(x;\mu,\sigma)$.  The independence assumption implies the probability is the product of individual probabilities, whence
$$\Lambda(\mu,\sigma; x) = \log \prod_{i=1}^n f(x_i;\mu,\sigma) = -\sum_{i=1}^n\log\left(1 + \left(\frac{x_i-\mu}{\sigma}\right)^2\right) -n \log(\pi \sigma).$$
This must be plotted as the parameters $\mu$ and $\sigma$ vary.
In R, use contour or filled.contour to make such a plot.  As with many scale families, it will be clearer to plot $\sigma$ on a logarithmic scale.  So, we estimate a reasonable range for $\mu$, a reasonable range for $\log(\sigma)$, divide those ranges into little pieces, evaluate  $\Lambda$ at each possible combination of those pieces, and contour the results:
logLikelihood <- function(median, scale, x) {
  -sum(log(1 + ((x-median)/scale)^2)) - length(x)*log(pi*scale)
}

set.seed(17)
data <- rnorm(3) # Sample data (not drawn from a Cauchy distribution!)

medians <- seq(-3, 3, 1/50)                       # Range of medians to plot
scales <- seq(-1.5, 2, 1/50)                      # Range of (log) scales to plot
u <- as.matrix(expand.grid(medians, exp(scales))) # Points to evaluate
z <- matrix(apply(u, 1, function(v) logLikelihood(v[1], v[2], data)),
       nrow = length(medians))                    # Values of Lambda on the grid
filled.contour(medians, scales, z, color.palette=terrain.colors,
               xlab="Median", ylab="Log(scale)",
               main="Cauchy Log Likelihood")

redpajama_set_name: RedPajamaStackExchange


This is my little room in Muswell Hill. When I moved to London I knew that I'd be staying in temporary accommodation for the first few months. It has been very strange to move from one furnished room to the next, knowing that I won't be staying long, when I lived in the same room for the first 24 years of my life (a room that I miss terribly). It has made settling in much harder - especially because flathunting is a gruesome, stressful experience. In a couple of days, however, I'll be moving into my first real flat. 'Real' because it's unfurnished, because I'll be living with a friend, because I didn't grow up there, because we have a tiny garden. Saying goodbye to Muswell Hill won't be easy - I've fallen hard for the neighbourhood, its houses and trees, the proximity to Alexandra Palace, seeing familiar friendly faces at the bus stop every day, the ridiculous Planet Organic with its comedy food, the ice cream parlour, the curving hilly streets, and, above all, the quietness. But I look forward to exploring a new neighbourhood, settling in, making myself at home, hunting for charity shop furniture. Walthamstow, here we come. Send me postcards, prints, embroideries and chairs!


text:
HomeCampusPolice find no evidence of hate crime in fight at Fairfax High
Police find no evidence of hate crime in fight at Fairfax High
By Kawah Wahidi via Wikimedia Creative Commons
Posted By Randall
Despite objections from a civil rights group, police say they don't plan to file hate crime charges after a fight at Fairfax High in Fairfax, VA.
ABC13 reports that the student told police that several postings made on social media that racial comments were made during the attack were false.
However, she did say that her hijab became undone during the altercation, exposing her hair.
WTOP reported that hundreds of students walked out of class Thursday to show their support for the student and to speak out against Islamphobia. 27,000 people signed a change.org petition demanding the school district do more in response to the attack.
Abed Ayoub of the American-Arab Anti-Discrimination Committee condemned the conclusion by the Fairfax Police Department.
"We strongly disagree with the decision by the City of Fairfax Police Department. Many witnesses have attested that the victim's hijab was forcibly removed during the altercation. Witnesses also corroborated the victim's statement that students in the classroom engaged in racist and Islamophobic drawings, and that the perpetrator made racist comments prior to the attack. This was shared multiple times with law enforcement."
The attacking student has since returned to class.
CampusSouth Asian AmericanSoutheast Asian American
bias attack
Fairfax Police Department
Islamphobic
religious bigotry


text:
NBA Rumors: Kyrie Irving's Former Coach Predicts All-Star Point Guard's Next Landing Spot
Maddie Meyer / Getty Images
JB Baruelo
Boston Celtics point guard Kyrie Irving is expected to be one of the most sought-after superstars in the 2019 NBA free agency. After committing to re-sign with the Celtics before the start of the 2018-19 NBA season, Irving had a change of heart and already wants to keep all his options open next summer. In the past months, Irving has been linked to several NBA teams who could open up enough salary cap space for a max contract in the 2019 NBA offseason.
These include the New York Knicks, Los Angeles Clippers, Los Angeles Lakers, and the Brooklyn Nets. Like the majority of rumors and speculations, Kyrie Irving's high school coach, Kevin Boyle, said in a recent interview with Ian Begley of SportsNet New York that the All-Star point guard will be heading to the Knicks next July.
"I think there's a good chance in my opinion that Kyrie ends up there," Boyle said, stressing that he was speaking as a fan and not as someone who had inside information on Irving's plans. "In my gut, I would think that would work best for him and I would think that (the Knicks) have a really strong chance of that happening. But I have not spoken directly to him and I don't know that to be a fact."
Morning sports update: NBA insider thinks Kyrie Irving will return to the Celtics and is 'playing all of you guys right now' https://t.co/cCbKJzS8aQ pic.twitter.com/e2GwZrza8z
— Boston.com Celtics News (@BDCCeltics) May 17, 2019
It may only be an opinion of Coach Kevin Boyle, but it is definitely not a surprise if Kyrie Irving really decides to leave the Celtics for the Knicks in the 2019 NBA free agency. The Knicks are not in any way a better team than the Celtics right now, but they have the opportunity to build a roster that can legitimately contend for the NBA championship title next summer. After giving Irving a max contract, the Knicks will still have enough salary cap space to chase another big name on the open market. Aside from Irving, Golden State Warriors small forward Kevin Durant is also on the top of the list of the Knicks' free-agent targets.
The successful acquisition of Kevin Durant and Kyrie Irving will undeniably turn the Knicks from one of the worst teams in the league to a legitimate playoff contender in the Eastern Conference. However, the Knicks' offseason won't only focus on targeting superstars on the free agency market. The Knicks have a plethora of trade assets to engage in a blockbuster deal and could target Anthony Davis of the New Orleans Pelicans next summer.


HTML is the language of the web. It is now becoming the language of everything you do online – from email to news to e-books and more. And, although most of us never "touch" the actual code, it's behind many of the things you see and do online.
Right now we're watching an HTML revolution in the making. But, like many revolutions, things can get a little messy at times. The online world is in the process of moving to an updated version of HTML called HTML5. It offers a lot of great things for those of us who create content and we are excited about these new opportunities. BUT! We're not all there yet. And, it will be a while before we do get there. In the meantime, here are some things you can do to insure you enjoy the best browsing experience you can.
Make sure you're using the latest version of your web browser. In order to take advantage of these new HTML capabilities, you need to use a browser that supports them. Older browsers don't. Even some of the newer browsers don't support all of the new capabilities – yet. Opera [Win & Mac] and Chrome [Win & Mac] have the best support with Firefox [Win & Mac] and Safari [Mac] close behind. The latest version of Internet Explorer [Win] supports a majority of HTML5 capabilities, but still lags far behind the rest of the field.
Remember that you and your browser are in charge. You can override font style and sizes shown on a site by changing settings in your browser. Press CTRL/+ (CMD/+ for Mac) to increase the font size and CTRL/- (CMD/-) to decrease. To change the font style, look in your browser's options panel. If things look really weird, you might check your "text encoding" settings. The "default" setting is probably the best, but you might also try the Western or Unicode options. This setting defines which alphabet is used to present content.
HTML5 makes its biggest impact with media, simplifying the way audio and video are added to a web page. Most sites can identify the browser you are using to visit their site and then display their media using a method supported by your browser. If you visit a site displaying media only in HTML5 and your browser doesn't support it, you won't be able to view that media. You might try using another browser that does support HTML5.
Most web developers are doing everything they can to insure you enjoy the best experience possible when you visit their site. At the same time, they are working hard to learn HTML5 while building sites that cover all these constantly changing possibilities. It means an awful lot of work for them and sometimes it doesn't always work just right. It's a challenge but one that's well worth the effort.
Every day we're seeing new and amazing views of our world thanks to HTML and these hard-working developers, designers, writers, photographers and artists that bring it to us.


text:
Is There a Better Way for the Left to Talk About American Christianity?
Marie Mutsuki Mockett on the Intersection of Justice and Faith
By Marie Mutsuki Mockett
"This is the anthropologists' answer to the question, why are people almost always, almost everywhere, religious. Another answer, favored by those who claim to be defenders of science, is that religion formed around the desire to explain what prescientific humankind could not account for. Again, this notion does not bear scrutiny. The literatures of antiquity are clearly about other business."
–Marilynne Robinson, from When I Was a Child I Read Books
English is my third language. I learned it after Japanese and German once I started nursery school in California, and I still remember the physical discomfort of being unable to tell the adults who offered me milk that I had an allergy; I understood them, but they could not understand me. With time, each language I acquired clarified my world and had the effect of clarifying me; I became a person who could participate in a story.
The first two books I wrote required Japanese—a lot of it—and the effort stretched my mental capabilities. Whatever I did next, I wanted to stick to English, the language with which I am now most comfortable. Starting in 2016, I lived in a trailer beside a harvesting crew, and followed them as they worked the fields, and went to church every Sunday. Never mind that I did not grow up going to church and that I am not a Christian; at least everything would be in English.
At one of the first services I attended, the pastor spoke of the need for "restoration," a curious turn of phrase, I thought, considering that the building had been freshly painted chocolate brown and the pews were filled with multigenerational families. The way the pastor had leaned into the term—restoration—implied a concept that was fraught in this environment.
On the road, I became close to a 23-year-old harvester named Juston, and I asked him what was meant by "restoration."
"There are certain key phrases," he said, "that mean things to us, but won't mean anything to you. 'Restoration' is one of them."
Maybe this was the moment when I decided, consciously, to at least in part treat the world of Christian America as a foreign country with a foreign language.
A few weeks later, when we attended a mega church in Oklahoma City, the language was much more accessible. Pastor Craig wanted me to know that he understood I might be in pain, and that there was a way out of the hurt. I left that church a little teary, though I acknowledge it probably helped that he had a killer band and a great sound system.
"That's called a seeker sermon," Juston told me. "It was specifically designed for someone like you."
Maybe this was the moment when I decided, consciously, to at least in part treat the world of Christian America as a foreign country with a foreign language. I could enter into it, as I had Californian English, and try to learn the movements, the nuances, the in-group cues.
I also had to acknowledge that a pre-programmed soundtrack had played in my head each time I had engaged in conversation with someone about God or church. It didn't matter if I was talking to an atheist, recovering Catholic, or Jew; a disembodied voice told me that science was the real deal and taking religion seriously bordered on superstition. "Religion," said the voice, "is stupid." God, by association, is stupid too.
The loudest exponent of the "religion is stupid" earworm is probably the evolutionary scientist Richard Dawkins, whom I had read obsessively at one point in my twenties and thirties. In The Selfish Gene, Dawkins writes, "The God of the Old Testament is arguably the most unpleasant character in all fiction: jealous and proud of it; a petty, unjust, unforgiving control-freak; a vindictive, bloodthirsty, homophobic, racist, infanticidal, genocidal, filicidal, pestilential, megalomaniacal, sadomasochistic, capriciously malevolent bully." Milder variations of this mindset run through mainstream, popular culture. I'm thinking of a New Yorker cartoon in which Noah and his wife stand in the open doorway to the ark, now resting on dry land thickly carpeted with skulls and bones. "No, you were right—this is much better than how it was before," Noah yells, as two donkeys peer over his shoulder and a rainbow floats in the upper left corner.
In Colson Whitehead's novel The Underground Railroad, his heroine, Cora, says "Poems were too close to prayer, rousing regrettable passions. Waiting for God to rescue you when it was up to you. Poetry and prayer put ideas in people's heads that got them killed, distracting them from the ruthless mechanism of the world." Religion, so important on the actual Underground Railroad, plays almost no part in this story; it is a kind of liberal-educated person's fantasy of what abolition could have been.
Visualize the indulgent way adults regard three-year-olds peering up the chimney on Christmas Eve: that's the other way I've seen my peers refer to God and to religion. God is like some kind of therapy pet, a defanged harmless thing that doesn't kill its own children but that makes everything from work stress to derailed travel plans bearable without inspiring any of the awe that might prompt the building of a cathedral. God is also rarely called to as "God."
I've come to believe that "Religion is stupid" is an inherently hazardous way to think.
In her book Help, Thanks, Wow, Anne Lamott refers to God as "the Good" in case the name God is "too triggering." Variations of this cute, and almost ingratiating tone appear in uplifting social media memes, or in the watered down religious paraphernalia of the belief system known as "New Age," both of which feature flowers and balloons accompanied by terms like "inner light" and "goodness," but never God, and drawn in a font resembling a childish scrawl.
Something about both these viewpoints has never sat quite right with me. I'm old enough to remember when "Made in Japan" elicited titters. The experience of watching "Made in Japan" go from meaning "cheap" to meaning "cool" has bordered on a kind of gaslighting for me. Things are not always what they seem and people can switch sides quickly. A part of me found the "God is stupid" or "God isn't really God but is cute" narrative to similarly be too easy and glib.
As adults, when we pick up a language class from Babbel, do we automatically weaken ourselves? I know from childhood that some part of me has remained consistent each time I learned a new language. Why would Christianity be any different?
I've come to believe that "Religion is stupid" is an inherently hazardous way to think. The most obvious reason why it is dangerous is that Donald Trump is our president, and that he feels free to sprinkle Evangelical code words into his Tweets that tell his base he is speaking to them. It doesn't matter if, in using these code words, he sounds like the evangelical equivalent to a first semester French student trying to ask about the hour of the day, but inadvertently commenting about the weather. At least, it seems, he is trying. Meanwhile, we, the liberal and educated, are left with "God is stupid" or "God is cute."
There are other problems with both of these scripted ways of talking about God. First, they depend on the assumption that religion is solely an outmoded and superstitious way of thinking that we, the modern and educated, have outgrown. Second, both stances have the effect of making us blind to certain realities about our actual history. And third, they block secular people from connecting in any deeper way with Christians—a dangerous proposition for a politician, or anyone hoping to have conversations across our fractured country.
Frances Fitzgerald, in her in her award-winning book, The Evangelicals, writes that the "black church did not impact the white church until the mid-20th century when the Civil Rights movement began in earnest." Fitzgerald is primarily concerned with the history of the Evangelicals as a voting block in the United States; for a long time, this was also my general interest in and grasp of how religion, race and history intersected in America. But this view doesn't capture the complex manner in which white evangelical Christianity developed—and remains—in the United States, nor does it address the experience of Christianity.
When we reduce Christianity to either "stupid" or "triggering," we aid those who have hijacked this religion and warped it into a form of cruelty.
Albert Raboteau, in his classic book Slave Religion, is one scholar who has carefully traced the interplay between the white churches of the colonies, and the establishment of the black church in America. Once enslaved and free men and women understood that true Christianity involved tolerance and love, the Christianity of the slaveholders was revealed as hypocritical. Colonial theologians had distorted the essential meaning of the golden rule in order to justify not only the practice of slavery in the colonies clear back to the 17th century, but also the segregated black church, which became so popular after the Civil War ended in 1863. In intellectual circles, this drama tends to be flattened, or sometimes dismissed, since considering Christianity seriously runs the risk of making one seem "stupid." But in fact, the argument could be made that the black church was and is doing extraordinary work in restoring church in America to what church is supposed to be.
The great writer and activist Frederick Douglass—who escaped enslavement and traversed the actual Underground Railroad—said of Christianity: "I love the pure, peaceable, and impartial Christianity of Christ: I therefore hate the corrupt, slaveholding, women-whipping, cradle-plundering, partial and hypocritical Christianity of this land." This is in pretty stark contrast to the viewpoint of a figure like Ta-Nehisi Coates, an unabashed atheist, whose own views are closer to Cora's in the fictional Underground Railroad. "I don't believe the arc of the universe bends towards justice. I don't even believe in an arc. I believe in chaos. I believe powerful people who think they can make Utopia out of chaos should be watched closely. I don't know that it all ends badly. But I think it probably does."
The difference between Douglass and Coates might be explained by some as the difference between a "believer" and a "nonbeliever"; certainly this is how I would once have simplified the distinction between these two men. But I now think that these two labels are misleading. I don't think the difference between these two men is primarily about belief or the decades separating them, but about what Christianity is.
When you learn another language, and travel to another country, it is possible that you will be introduced to a new perspective you have not previously considered. On the road with the harvesters, this is what happened to me. I had for so long accepted, without thinking, that Christianity was an outmoded way of explaining how the world worked and that while this might be fine for the Amish and their devotion to the horse and buggy, no forward-thinking person could really think seriously about God. This has changed. While I did not become a Christian, I did begin to ask: what is Christianity?
Juston, my guide into evangelical America, would sometimes speak of "materialism"—the idea that we are no more than atoms and that our notions of fairness and love are accidents of brain chemistry absent of any meaning. Coates's position reflects the current extreme end of the "God is stupid" narrative. If there is no meaning—if we are all simply physical bodies in possession of that strange thing called consciousness—then why be good, and good to each other? But for Juston and his likeminded friends, the path to undoing the injustice of slavery and the racialization of the United States lies in Christianity and depends on an understanding of what Christianity actually is. The role of Martin Luther King, Jr., a pastor, is often a source of discomfort for secular intellectuals who want to believe the Civil Rights movement could have happened without the language of Christ and God. (See Yale scholar Martin Hägglund's This Life as a recent example.) But many historians argue that Christianity was necessary to push the Civil Rights agenda as far as it has come.
The idea that Christianity was the best humans could do before science showed up, is a fairly new way to think about religion. While hard-core fundamentalists are responsible for this interpretation of the gospel, intellectuals have not helped matters by enforcing this position. Not everyone holds this viewpoint, however. Marilynne Robinson writes: "I suppose it was in the 18th century of our era that the notion became solidly fixed in the Western mind that all this narrative was an attempt at explaining what science would one day explain truly and finally." What if, in fact, Christianity is about something else entirely?
What do we on the left mean when we say we value intelligence and truth? When we reduce Christianity to either "stupid" or "triggering," we aid those who have hijacked this religion and warped it into a form of cruelty. It ought to be possible to talk about Christianity—as a non Christian—using the words and phrases that have meaning within the world of religion and which restore Christianity to its essential message: care for the poor, the sick and a reconciliation with each other. Anyone can speak this language. Communication between the secular world and the religious world should not be in the hands of Donald Trump; it should be in the hands of people who stand for what is true.
Marie Mutsuki Mockett is the author of AMERICAN HARVEST: God, Country, and Farming in the Heartland, published by Graywolf Press in April 2020.
atheismChristianitycivil rightsDonald TrumpevangelicalsMarie Mutsuki MockettreligionRichard DawkinsTa-Nehisi Coates
Marie Mutsuki Mockett
Marie Mutsuki Mockett, author of American Harvest, is also the author of a novel, Picking Bones from Ash, a memoir, Where the Dead Pause, and the Japanese Say Goodbye, which was a finalist for the PEN Open Book Award. She has written for The New York Times, Salon, National Geographic, Glamour, Ploughshares, and other publications and has been a guest on The World, Talk of the Nation and All Things Considered on NPR. She is a core faculty member of the Rainier Writing Workshop and a Visiting Writer in the MFA program Saint Mary's College in Moraga, California. She lives in San Francisco.
Looking for Middle-Earth? Go to the Middle of England
America Wasn't a Nation At Its Founding, It Was a Means
to an End
For Tolkien, England was a land of revelation. Though he had English parents, he was actually born in the African veldt,...


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Rehanging The Great Bell of Tong.
In 1892 Taylor's was commissioned to cast a 46 cwt Bourdon Bell for the village of Tong in Shropshire. This bell was hung with full ringing fittings in a new cast iron and steel bell frame independent of the 12cwt ring of six that also hang in the tower. In 1952 Taylor's rehung the ring […]
Gospel Oak's New Bells
London's All Hallows, Gospel Oak has had three new bells dedicated to complete a chime of nine bells ( an octave and one semi-tone). We supplied six of the bells in the 1950's, together with a frame to accommodate the nine bells, so the completion of the scheme has taken some time. It is traditional […]
Restoring Cast Iron & Steel Bell Frames.
Over the past century and a quarter the use of cast iron and steel for bell frames has become the norm. If designed with sufficient strength these materials give the absolute rigidity that it is so important to the smooth handling of change ringing bells. Taylor's has produced hundreds of such frames, and we are […]
Casting Bells in a Pit
Traditionally all bell founders dug a pit and buried their bell moulds before casting – this was primarily to protect themselves from the molten metal when casting should the bell case split. With the introduction of much stronger cast iron bell copes in the mid 19th century the risk of the cases splitting was virtually […]
Conserving Ancient Church Bells
Restoring and conserving old bells forms an important part of our business, and with generations of experience we can claim to be experts in this field. Removing cast-in iron crown staples from the crowns of these bells lessens the risk of them becoming cracked in their heads, and designing and manufacturing headstocks that allow original […]
The Denison Mears Bequest
Denison Mears was the son of Gwendoline, the daughter of John William Taylor Junior. Denison died in 2018 and left a bequest in his will of £55,500 which will be used towards the £1 million matched funding needed to release the major grant from The Heritage Lottery Fund for the restoration and development of the […]
We Welcome Foundry Apprentice Sam Armistead!
It's good to bring in young blood so that the craft skills of generations can be handed on. Sam Armistead has joined our team as a Foundry Apprentice and he's making a very good impression. We hope Sam will be with us for many years – he and our other young people are the face […]
Restoring Zennor's Bells
The 12cwt ring of six at this church was last rehung by Gillett & Johnston in 1926, when four of the bells were recast and all new fittings and a cast iron and steel bell frame was installed. Steel is very susceptible to rusting in the salty air of the coast if it is not […]
Foundry Restoration


The first one was good, the second one was amazing!!! The 22nd edition of the Montecarlo Storico Rally concluded in the evening saw this year as a participant, but above all as a protagonist, the Stancheris crew composed by father Amilcare and his son Davide on board the 911 SC "Vezza" by Autorlando-Sport.
After the official debut of the team and the riders at the Monegasque event in 2018, this year the whole team was called to reconfirm the excellent work done, looking for a placement that went beyond the 31th class place and so it was because the classification speaks of a resounding 23rd class place on over 160 cars registered of which "only" 146 arrived at the finish line.
Compared to the previous year the preparation of the race was improved and the car was tested in an even more meticulous way to obtain a result that the riders hoped from the beginning and in which together with the team they never stopped believing. This year there were no further difficulties due to the heavy snowfall that affected the French area that forced the lowering of the average in some special and even the cancellation of 4 trials, the number of 4,5,6 and 9 between Sunday and Monday.
The 316 participants, the 2500km to do in 6 days, the impervious mountain passes, the snow, the ice, the opponents, and the strict time controls to be respected during the transfers did not frighten Davide and Amilcare who demonstrated during the various have now become in tune with the event by gathering extraordinary results in the special tests, classifying very often within the top50 reaching even 4i class in the special n°2.
The preparation and commitment pay and the cultured result can only be a confirmation of what teams and drivers can do when there is collaboration, understanding, determination and mutual respect. First of all thanks to Davide and Amilcare, Adriano and Ennio, who once again brought the team Autorlando-Sport to the top, been busy for years on the biggest European Motorsport stages, starting this 2019 which will be full of surprises another time in the best of ways.
AUTORLANDO SPORT ON MANY FRONTS AGAIN; AT 67° TRENTO BONDONE AND AT MONZA FOR THE CLASSIC ENDURANCE RACING.
EUROPEAN GT4 SERIES ON STAGE AT HUNGARORING WITH AUTORLANDO SPORT AND THE COUPLE GHEZZI GIOVANELLI.
6H RACE OF VALLELUNGA LAST SEASON ENDURANCE FOR AUTORLANDO SPORT PORSCHE GT3 R.


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Hechelbach ist ein geographischer Name:

Gewässer:
 Hechelbach (Steinaer Bach), linker Zufluss des Steinaer Bachs (zur Zschopau) bei Saalbach, Stadt Hartha, Landkreis Mittelsachsen, Sachsen
 Hechelbach (Wieseth), linker Zufluss der Wieseth bei Oberschönbronn, Markt Herrieden, Landkreis Ansbach, Bayern
 Hechelbach (Zenn), linker Zufluss der Zenn bei Unteraltenbern, Markt Obernzenn, Landkreis Neustadt an der Aisch-Bad Windsheim, Bayern

Orte:
 Hechelbach (Obernzenn), Dorf von Markt Obernzenn, Landkreis Neustadt an der Aisch-Bad Windsheim, Bayern

Siehe auch:
 Hechelgraben
 Hegelbach

redpajama_set_name: RedPajamaWikipedia


Sébastien holds a Ph.D. in environmental studies from Yale University, an M.Phil. in international relations from the University of Cambridge, an LL.M. in international law from the London School of Economics, and B.C.L. and LL.B. from McGill University. Sébastien recently served as the president of Génération d'idées, a think tank focused on the interests and participation of Quebeckers aged 20 to 35. Prior to his appointment at McGill University, he worked for the Centre for International Sustainable Development Law, the Canadian Centre for International Justice, Amnesty International Canada, and the United Nations International Criminal Tribunals for Rwanda and the former Yugoslavia.
Sébastien has received numerous awards and honours, including the Transnational Environmental Law Fifth Anniversary Issue Prize, the 2012 Public Scholar Award from the Yale Graduate School of Arts & Sciences, a Doctoral Scholarship from the Pierre Elliott Trudeau Foundation, a Doctoral Fellowship from the Social Sciences and Humanities and Research Council of Canada, and a Public Interest Law Articling Fellowship from the Law Foundation of Ontario. Sébastien currently serves as the Principal Investigator for a SSHRC Insight Development Grant on the role of human rights in transnational climate change law and advocacy.
Sustainable development, transnational law, public policy, environmental law and governance, climate change, human rights, disability, social innovation, and socio-legal research.
Sébastien Duyck, Sébastien Jodoin, Alyssa Johl, Eds. Routledge Handbook of Human Rights and Climate Governance (Routledge 2018).
Sébastien Jodoin, Forest Preservation in a Changing Climate: REDD+ and Indigenous and Community Rights in Indonesia and Tanzania (Cambridge, UK: Cambridge University Press, 2017) (open-access electronic version available here) (link to publisher's website).
Sébastien Jodoin & Sarah Mason-Case, "What Difference Does CBDR Make? A Socio-Legal Analysis of the Role of Differentiation in the Transnational Legal Process for REDD+" (2016) 5(2) Transnational Environmental Law 255-284 (link to article on journal's website).
"This book brings together leading scholars and practitioners to offer a timely and comprehensive analysis of the opportunities and challenges for integrating human rights in diverse areas and forms of global climate governance. The first half of the book explores how human rights principles and obligations can be used to reconceive climate governance and shape responses to particular aspects of climate change. The second half of the book identifies lessons in the integration of human rights in climate advocacy and governance and sets out future directions..."
"provides a comprehensive socio-legal examination of how global efforts to fight climate change by reducing carbon emissions in the forestry sector (known as REDD+) have affected the rights of indigenous peoples and local communities in developing countries. Grounded in extensive qualitative empirical research conducted globally, the book shows that the transnational legal process for REDD+ has created both challenges and unexpected opportunities for the recognition and protection of indigenous and community rights."


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#import "NSObject.h"

@class MKRisonParser;

@interface MKURLSerializer : NSObject
{
    MKRisonParser *_parser;
}

- (id)_modeKeyForString:(id)arg1;
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@end

redpajama_set_name: RedPajamaGithub


Tell your public step by step in this technical topic how to do it. All you need are some basic pointers to get you started. What importance do they carry? Begin with your argument number one. Each year would come and go, but I never -discovered the sport that sparked a real passion within my soul. There are websites in new categories including health, tech, freelance writing, blogging, pet, travel, business, finance, music etc.
One good way to alleviate anxiety is to prepare for the types of topics that are likely to come up. Jim, I think I am interested in anything unique that I can learn from, or things which provoke thought. The more the student invests his time and effort into this practice, the better results he will receive. This manual, however, can turn mandatory writing into an exciting venture! Sign out of your email account, Facebook, Twitter, Skype, and anything else that might make sounds or pop alerts up on your screen. For a while now, been thinking of going back to writing especially since I feel like just doing promotional work in my local area is not good enough. Islington has a lot of competition, 30 other courses within a 30 minute drive from Toronto and several located within 5-10 minutes.
The notion of ignoring distractions and focusing solely on the task ahead is constantly scrutinised by psychologists in order to determine the underlying factors resulting in poor performance Carroll, 2013 …. Using Copperfield, Great Expectations, and Dombey and Son, defend or refute this claim. We recommend fixing them a bit once your teacher returns the checked version to you. Feel free to post anything I really need an idea. In any case, try to compose an essay on your own without any help. One thing am sure though is that I will be using their services for a long time.
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I use Calibre for formatting for Kindle. To what extent does gender actually dictate thought process? Formatting is one of the steps on the way to your desired grade. What do other sports do I think I have been asked to write about golf as a hobby. Doing so, you automatically create a focus of your ideas and make it easier not to use unimportant information. You can find out more about contributing to iWorkwell. However, the golfer who accomplishes this has improved only one out of four areas needed in order to become a complete player.
But will these topics appeal to your readers? Aim to provide a skill that is of value to them, though be careful not to pick a topic that is either overly simple or complex. Thank you again and I look forward to reading more posts from you. Keep the good and hard-work up. Basically, these two types of writing are the same. Luckily, there is a simple way you discover good topics for a research paper: simply write from what you love! There are always people who will not understand right away, but are too shy to admit it. To discover the main point you want to make in your speech, determine what the specific purpose is of teaching your audience about this topic. Because high-circulation golf magazines only work with professional freelance writers, you need to have at least 5-7+ years of related experience before an editor will spare some free time to look over your query.
Every student should be forever grateful to essays as it makes a student competent to come up with greater and tougher write ups in future. Facebook 0 Twitter 0 Google+ 0 Viber WhatsApp Best 100 Persuasive Essay Topics essay writing is important college and university writing assignment. Whenever you need immediate help with your assignment, turn to the which can compose an argumentative essay on any topics in several hours. Some golfers, we are told, enjoy th Golf. Our List of Good Demonstration Topics Speech topics can be broad. The persuasive essay has a set of strict rules that must be followed in order to receive good grading from your course professor. Avoid straying from the topic so as not to lose your reader.


Offer a distinct decor style with this warm and scene-stealing decor pillow. This accent piece presents mixed floral patterns in shades of red, yellow, brown and white on a gray background.
Offer a distinct decor style with this warm and scene-stealing decor pillow. This accent piece presents mixed floral patterns in shades of red, yellow, brown and white on a gray background. Use this square pillow with other statement accessories and place it anywhere inside your home. This 18" pillow is constructed with 100% fine-quality cotton material.


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package matgm50.jrose.core.display;

public interface IDisplayHandler {

    void onScreenResize(int width, int height);

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New appointments at Drytac and Soyang
Industry News January 24, 2023
Drytac appoints Cathy Radoncic as Northeast US Territory Manager
Drytac, the leading international manufacturer of self-adhesive materials for the large-format print and signage markets, is delighted to announce the appointment of Cathy Radoncic as its new Northeast Territory Manager for the US, with immediate effect.
Cathy brings a wealth of knowledge and experience to the Drytac team, having worked in the print industry for more than 35 years across a range of management roles with both manufacturers and suppliers.
In this management role of Northeast Territory Manager, Cathy will be responsible for Drytac's operations in Maine, New Hampshire, Vermont, Massachusetts, New York, Rhode Island, Connecticut, Pennsylvania, New Jersey, Delaware, Maryland and Virginia.
Cathy will oversee both the building and ongoing support of the Drytac dealer network across the Northeast US region, working with customers and the wider Drytac team to further enhance the manufacturer's presence in the market.
"Adding Cathy to our US team is a real coup for us," says Hayden Kelley, CEO at Drytac. "She is hugely respected within the industry and will bring an incredible level of knowledge and experience to the company."
Cathy adds: "I'm delighted to be joining Drytac. I'm looking forward to working with our dealers and customers across the Northeast region and supporting them to identify the solutions that will help them to grow their businesses."
Soyang Europe welcomes Gareth Newman as Technical Applications Manager
Soyang Europe, the leading manufacturer and distributor of digitally printable wide- and superwide-format media and the supplier of leading-edge print production hardware solutions from many of the industry's best known printer brands, is delighted to announce the appointment of Gareth Newman as its new Technical Applications Manager, with immediate effect.
An experienced industry professional, Gareth has worked in the print industry for almost 10 years, serving in a host of production, support and management positions, and will bring a wealth of knowledge to the Soyang Europe/Josero team.
With his extensive applications knowledge, Gareth will be able to offer specialist advice, support and customer training on new software and hardware products. In this new role, Gareth will be responsible for delivering both in-house and on-site product demonstrations, as well as being the go-to person for technical queries.
Gareth will also be profiling machines to Soyang Europe materials and working with the sales and marketing team to help highlight the company's market leading offerings.
"We are delighted to welcome Gareth to our team," says Mark Mashiter, managing director at Soyang. "We are always on the lookout to add talented staff to our team; I look forward to working with him and seeing our customers benefit from his knowledge."
Gareth adds: "I am really pleased to be joining Soyang Europe at such an exciting time for the business."
Tags: banners, drytac, print, printing, soyang
Soyang Europe welcomes Tracy Dineen as Fujifilm Product Manager
Soyang Europe welcomes Tracy Dineen as Fujifilm Product Manager Soyang Europe, the leading manufacturer and distributor of digitally printable wide-format and superwide-format media and surface…
Industry News August 7, 2022
Soyang Europe acquires Josero in 'match made in heaven!'
Soyang Europe, a leading manufacturer and distributor of digitally printable wide-format and superwide-format media and surface coverings has announced its acquisition of Josero. By joining forces,…
Industry News May 31, 2022
Drytac's market leading products to feature at The Print Show 2022
Drytac, the leading international manufacturer of self-adhesive materials for the large-format print and signage markets, is delighted to announce its products will be showcased on…
Drytac promotes Amanda Lowe to Global Marketing Director
Drytac, the leading international manufacturer of self-adhesive materials for the large-format print and signage markets, is delighted to announce the promotion of Amanda Lowe (formerly Amanda…
Industry News October 2, 2022
Drytac's Shaun Holdom appointed to ISA-UK council
Drytac's Global Product Manager Shaun Holdom will bring his three decades' experience in the sign and graphics industry to the ISA-UK council. Drytac is delighted…
Industry News November 25, 2020
Hull based, Sovereign Signs wins tender to rebrand 17 of 450 stores for the retail giant Currys.
Hull-based signage manufacturer and installer Sovereign Signs supported leading electrical retailer Currys with a major rebrand by using materials from Soyang Europe to create a wide range…
Industry News January 9, 2022


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Home > FACW > FACSCH > FACSCH_BK_CONTRIBUTIONS > 264
Contributions to Books
'Global Civil Society': A Sceptical View
David Rieff
Download Full Text (463 KB)
American University, WCL Research Paper No. 2008-69Abstract:The editors of the leading yearbook of global civil society studies offered to the authors of this article an opportunity to present a skeptical account of global civil society as the opening chapter in the 2004/5 yearbook. The article examines the standard account of global civil society as the transnational equivalent, in a globalized world, of civil society in a domestic society, and further as, in Kofi Annan's oft-repeated view, international NGOs as the representatives of the peoples of the world to international organizations such as the UN. The article attacks this standard view, arguing that the analogy between transnational NGOs and civil society organizations in a domestic democratic society is fatally flawed. Civil society does not act as the representative of citizens to a domestic democratic state, because citizens also vote; their democratic claims are not intermediated exclusively or even primarily by civil society organizations, but directly at the ballot box. International organizations are undemocratic and will always be that way, and international NGOs, for their part, cannot "represent" the peoples of the world and cannot substitute for democracy. The article then asks why international NGOs and international organizations such as the UN have so aggressively adopted the ideologically-laden language of civil society. The authors argue that this ideologically elevated language of civil society offers legitimation to each party - undemocratic international organizations gain faux-democratic legitimacy from international NGOs claimed to represent the peoples of the world, while NGOs gain legitimacy, access, and status as the people's representatives in global governance. The system nonetheless remains undemocratic and, the article suggests, undermines commitment to actual democracy by substituting values of human rights for democracy. The authors conclude by calling on international NGOs to give up faux-claims of representativeness and a promised role in global governance in favor of a return to narrower missions, discrete tasks, and measurement of success based on competence and efficiency. The article is a sharp attack upon inflated claims for global civil society, international organizations, and global governance.
Global Civil Society, international organizations, international law, nongovernmental organizations, NGO, international nongovernmental organizations, civil society, United Nations, liberal internationalism, sovereignty, democracy, democratic deficit, globalization, legitimacy
Anderson, Kenneth and Rieff, David, "'Global Civil Society': A Sceptical View" (2005). Contributions to Books. 264.
https://digitalcommons.wcl.american.edu/facsch_bk_contributions/264


For a school with a difference, Alexander Agricultural College is based just outside of Sydney. Students can take part in full time courses Cert III, IV and Diploma Agriculture, Cert III in Horse Husbandry and traineeships in dairy and rural studies. SkillsOne chats to several of the teachers about what is taught in their Horse Husbandry course.
To show that there is more to riding horses than just westerns they are critical to the operation of a farm. Why does a stock horse need to be maintained?
At approximately 7.30am, the students and their teacher will be collecting the horses in the paddock, brushing them down and saddling them up to ride to the various paddocks in the property. CB Alexander Agriculture College, Tocal is just outside Maitland (a two hour drive from Sydney).
The College is run by the NSW Department of Primary Industries and has 105 full time students. The Tocal campus is 5,000 acre commercially run property. They offer full time courses Cert III, IV and Diploma Agriculture, Cert III in Horse Husbandry and traineeships in dairy and rural studies. They also offer short courses on the weekend in pastures, crops and horses and study by correspondence.
The Horse Husbandry Course is very popular (with a waiting list). This course teaches students about horse breaking and breeding. Lyn Walsh and Warwick Lawrence teach the course. Lyn Walsh started as a wool classer and came to the college to help with the sheep course. Eventually she moved across to the horses and has been doing the course since 1989.
The horse husbandry courses teaches the students how to ride properly on the horses which were broken in last year (feet in the right place, not too much reign etc). They also teach the horse to lie down (which helps if they are flighty) and stand on a 44 gallon drum. The students learn how to trim a horse's hoof and fix a loose shoe (but it's not a farrier course). They also assist with the sale of the stock horses.
The horses are quite "green" as they were only broken in last year. This means that they are more flighty and will react with the lightest touch. It is therefore important for the rider to be experienced. Once people finish the course, they may be employed as a stable hand or work with a trainer, on a stud farm at the polo, or other similar jobs.
Make a Guitar in 10 Weeks!


Japanese Marshmallow shop Yawahada selling cute cat and paw shaped marshmallows for your coffee and tea. The bottoms of these adorable marshmallow cats & paws are made heavy so they can float perfectly and peak out the top of your drink. They're available in sets for about 840 yen, or about ten bucks.
However, they've turned out to be so popular, these cute confectionery cats are back-ordered for at least a month. Currently on sale in Japan only, but they are working on shipping internationally soon.