text:
\section{Piecewise affine functions}

We start with a brief overview of affine and piecewise affine
functions; we refer the reader to \cite{Ovchinnikov:02,Aliprantis:06a}
and \cite[Chapter 7]{Aliprantis:07} for details.

Fix $m\in\mathbb N$. By an \term{affine} function we mean a function
$f\colon\mathbb R^m\to\mathbb R$ of form $f(x)=\langle v, x\rangle+b$ for some
$v\in\mathbb R^m$ and $b\in\mathbb R$. Its kernel $\{f=0\}$ is an
\term{affine hyperplane} in $\mathbb R^m$.
It is easy to see
that any two affine functions which agree on a non-empty open set are
equal. We write $\mathcal A$ for the vector space of all affine
functions on $\mathbb R^m$. Clearly, $\mathcal A$ is a subspace of
$C(\mathbb R^m)$, the space of all real-valued continuous functions on
$\mathbb R^m$.

Let $\Omega$ be a convex closed subset of $\mathbb R^m$ with non-empty
interior. Following \cite{Aliprantis:07}, we call such a set a
\term{solid domain}. A continuous function
$f\colon\Omega\to\mathbb R$ is called \term{piecewise affine} if
it agrees with finitely many affine functions. That is, there exist
$f_1\dots,f_n\in\mathcal A$ such that for every $x\in\Omega$
there exists $i\le n$ with $f(x)=f_i(x)$. Equivalently (see
Definition~7.10 and Theorem~7.13 in~\cite{Aliprantis:07}), a function
$f\colon\Omega\to\mathbb R$ is piecewise affine iff there exist
distinct affine functions $f_1,\dots,f_n$ and subsets $S_1,\dots,S_n$
of $\Omega$ such that
\begin{enumerate}
  \item on $S_i$, $f$ agrees with $f_i$;
  \item\label{pa-perfect} $S_i=\overline{\Int S_i}\ne\varnothing$ for every $i$;
  \item $\Int S_i\cap\Int S_j=\varnothing$ whenever $i\ne j$;
  \item $\bigcup_{i=1}^nS_i=\Omega$.
\end{enumerate}
In particular, it follows from~\eqref{pa-perfect} that the set
$\{f=f_i\}$ has non-empty interior for every $i=1,\dots,n$. The sets
$\{f_i\}_{i=1}^n$, $\{S_i\}_{i=1}^n$, and
$\bigl\{(S_i,f_i)\bigr\}_{i=1}^n$ are called the \term{components},
\term{regions}, and \term{characteristic pairs} of $f$,
respectively. The characteristic pairs of $f$ are unique up to
re-ordering. We write $\mathcal{PA}(\Omega)$ for the space of all
piecewise affine functions on $\Omega$. We put
$\mathcal{PA}=\mathcal{PA}(\mathbb R^m)$.

Suppose $f\in\mathcal PA(\Omega)$ with characteristic pairs
$\bigl\{(S_i,f_i)\bigr\}_{i=1}^n$. For each pair $(i,j)$ with $1\le
i,j\le n$ and $i\ne j$, the set
\begin{math}
  \bigl\{x\in\mathbb R^m\mid f_i(x)=f_j(x)\bigr\},
\end{math}
or $\{f_i=f_j\}$ is a hyperplane in $\mathbb R^m$. Let $C$ be the
union of all such hyperplanes. Then $C$ is a closed set with empty
interior. It is easy to see that the set $(\Int\Omega)\setminus C$ is
open, dense in $\Omega$, and naturally
partitioned into a finite number of convex open subsets. We call these
subsets the \term{cells} of $f$.

Let $K$ be a cell of $f$. Since $K$ is disjoint from $C$, no two
components agree at any point of $K$. It follows that there exists a
component $f_i$ such that $f$ agrees with $f_i$ on $K$, so that
$K\subseteq S_i$. It also follows that for every $j\ne i$ we either
have $f_j(x)<f(x)$ for all $x\in K$ or $f_j(x)>f(x)$ for all $x\in K$.

\begin{example}
  Let $m=1$ and $f(t)=\min\bigl\{\abs{t},1\bigr\}$. Then $f$ is
  piecewise affine on $\mathbb R$, with components $f_1(t)=t$,
  $f_2(t)=-t$, and $f_3(t)=1$, and with regions $S_1=[0,1]$,
  $S_2=[-1,1]$, and $S_3=(-\infty,-1]\cup[1,+\infty)$. Note that $S_3$
  is not connected. The cells of $f$ are $K_1=(-\infty,-1)$,
  $K_2=(-1,0)$, $K_3=(0,1)$, and $K_4=(1,+\infty)$.
\end{example}

Recall that under pointwise order, the space $C(\Omega)$ is a vector
lattice. It is easy to see that $\mathcal{PA}(\Omega)$ is a (vector)
sublattice of $C(\Omega)$.

Let $A$ be a subset of a vector lattice $V$. Recall that
  \index{$A^\vee$}\index{$A^\wedge$}
  \begin{eqnarray*}
    A^\vee&=&\bigl\{x_1\vee\dots\vee x_n\mid
      n\in\mathbb N,\ x_1,\dots,x_n\in A\bigr\}
    \quad\mbox{and}\\
    A^\wedge&=&\bigl\{x_1\wedge\dots\wedge x_n\mid
      n\in\mathbb N,\ x_1,\dots,x_n\in A\bigr\}.
  \end{eqnarray*}
If $A$ is a linear subspace of $V$ then
$A^{\vee\wedge}=A^{\wedge\vee}$ and this set is exactly the sublattice
generated by $A$ in $V$; see, e.g., \cite[Lemma~1.21]{Aliprantis:07}.

Since $\mathcal A\subseteq\mathcal{PA}$ and $\mathcal{PA}$ is a
sublattice of $C(\mathbb R^m)$, it follows that
$\mathcal A^{\wedge\vee}\subseteq\mathcal{PA}$. In fact,
\cite[Theorem~7.23]{Aliprantis:07} asserts that
$\mathcal{PA}=\mathcal A^{\wedge\vee}$, hence $\mathcal{PA}$ is
exactly the sublattice of $C(\mathbb R^m)$ generated by $\mathcal
A$. Moreover, if $\Omega$ is a solid domain in $\mathbb R^m$ and
$f\in\mathcal{PA}(\Omega)$ with component set $F=\{f_i\}_{i=1}^n$ then
$f\in F^{\wedge\vee}$ or, more precisely, $f$ agrees with the
restriction to $\Omega$ of a function in $F^{\wedge\vee}$. Since every
function in $F^{\wedge\vee}$ is defined on all of $\mathbb R^m$, it
follows that every function in $\mathcal{PA}(\Omega)$ extends to a
function in $\mathcal{PA}$.

We write $B_\infty^m$ for the closed unit ball of
$\ell_\infty^m$:
\begin{displaymath}
  B_\infty^m=\bigl\{x\in\mathbb R^m\mid\max\limits_{1\le i\le
    m}\abs{x_i}\le 1\bigr\}.
\end{displaymath}
For $n\in\mathbb N$, we write $\Omega_n$ for the ball of radius $n$
centred at zero in $\ell_\infty^m$; i.e., $\Omega_n=nB_\infty^m$.

\section{Locally piecewise affine functions}

A function $f\colon\mathbb R^m\to\mathbb R$ is said to be
\term{locally piecewise affine} if its restriction to any bounded
solid domain $\Omega$ is in $\mathcal{PA}(\Omega)$. The following
lemma is straightforward.

\begin{lemma}\label{on-balls}
  Let $f\colon\mathbb R^m\to\mathbb R$. Then $f$ is locally piecewise
  affine iff the restriction of $f$ to $\Omega_n$ is in
  $\mathcal{PA}(\Omega_n)$ for every $n\in\mathbb N$.
\end{lemma}

We write $\mathcal{LPA}$ for the collection of all locally piecewise
affine functions on $\mathbb R^m$. Clearly, $\mathcal{LPA}$ is a
sublattice of $C(\mathbb R^m)$ and
$\mathcal A\subsetneq\mathcal{PA}\subsetneq\mathcal{LPA}$.

\bigskip

Let $F\subset C(\mathbb{R}^m)$. We say that $F$ is \term{locally
  finite} if for every compact set $C$ all but finitely many functions
in $F$ vanish on $C$. That is, the set
\begin{math}
  \bigl\{f\in F\mid\exists x\in C\ f(x)\ne 0\bigr\}
\end{math}
is finite. Just as in Lemma~\ref{on-balls}, it is easy to see that $F$
is locally finite iff for every $n$ all but finitely many functions in
$F$ vanish on $\Omega_n$. Clearly, any subset of a locally finite
set of functions is again locally finite. Additionally, if
$F\subset C(\mathbb{R}^m)$ is a locally finite set of functions, then
$F^\vee$, $F^\wedge$ and consequently $F^{\vee\wedge}$ are all locally
finite. If $F$ is a sequence, then $F$ is termed a \term{locally finite
sequence of functions}.

It is a standard fact that $C(\mathbb R^m)$ is not order complete. Yet
we have the following.

\begin{lemma}\label{sup-lf}
  Every locally finite subset of $\mathcal{PA}$ has a supremum and an
  infimum in $C(\mathbb R^m)$, which belong to $\mathcal{LPA}$ and
  agree with the pointwise maximum and minimum, respectively.
\end{lemma}

\begin{proof}
  Let $F\subseteq\mathcal{PA}$ be a locally finite set. For every
  point $x\in\mathbb R^m$, all but finitely many members of $F$ vanish
  at $x$. Hence, $h(x)=\max\bigl\{f(x)\mid f\in F\bigr\}$ is
  defined. Similarly, on every open ball $B$ in $\mathbb R^m$, $h$ is
  the pointwise maximum of a finite subcollection of $F$, so that $h$ is
  continuous on $B$; it follows that $h\in C(\mathbb R^m)$. It follows
  from the definition that $h=\sup F$ in $C(\mathbb R^m)$. It also
  follows that on every ball, $h$ agrees with a finite subset of $F$,
  hence $h$ is locally piecewise affine.  The proof for the infimum
  is similar.
\end{proof}

We write $\one$ for the constant one function on $\mathbb R^m$.

\begin{lemma}\label{affine-Uryson}
  For every $\varepsilon>0$ there exists
  $f\in\mathcal{PA}$ such that $0\le f\le\one$, $f$
  equals $1$ on $B_\infty^m$, and vanishes outside of
  $(1+\varepsilon)B_\infty^m$.
\end{lemma}

\begin{proof}
  Put $g(x)=\norm{x}_{\infty}=\max_{i\le m}\abs{x_i}$ for
  $x\in\mathbb R^m$. Put $h\colon\mathbb R_+\to\mathbb R_+$ so that
  $h$ is continuous, equals $1$ on $[0,1]$, vanishes on
  $[1+\varepsilon,+\infty)$ and is affine on $[1,1+\varepsilon]$. Let
  $f=h\circ g$. Being the composition of two piecewise affine
  functions, $f$ is itself piecewise affine. It is easy to verify that
  $f$ satisfies the rest of the requirements.
\end{proof}

\begin{theorem}\label{lf-sup}
  For every $0\le f\in\mathcal{LPA}$ there exists a locally finite
  sequence $(f_i)$ in $\mathcal{PA}_+$ such that
  $f=\sup f_i$.
\end{theorem}

\begin{proof}
  Let $(c_n)$ be an enumeration of all integer points in $\mathbb
  R^m$. Consider the ``boxes'' $K_n=c_n+B_\infty^m$ and $\widetilde
  K_n=c_n+2B_\infty^m$.

  Fix $n$. Since $f$ is continuous, it is bounded on $K_n$. Let $M>0$
  be such that $f(x)<M$ for all $x\in K_n$. As in
  Lemma~\ref{affine-Uryson}, we can find a piecewise affine function
  $g_n$ such that $0\le g_n\le M\one$, $g_n$ equals $M$ on $K_n$, and $g_n$
  vanishes outside $\widetilde K_n$. Put $f_n=f\wedge g_n$. We
  will show that the sequence $(f_n)$ satisfies all the requirements.

  By construction, $0\le f_n\le f$, $f_n$ agrees with $f$ on $K_n$ and
  vanishes outside $\widetilde K_n$.  Observe that $f_n$ is piecewise
  affine because on $\widetilde K_n$ it agrees with $f\wedge g_n$, which
  is piecewise affine on $\widetilde K_n$ and $f_n$ vanishes outside
  of $\widetilde K_n$. The sequence $(f_n)$ is locally finite because
  for every $n$ the only members of the sequence that do not vanish on
  $K_n$ are $f_n$ itself and the members corresponding to the
  (finitely many) boxes that meet $\widetilde K_n$. Finally,
  $f=\sup f_n$ because $0\le f_n\le f$ and $f_n$ agrees with $f$ on
  $K_n$ for every $n$.
\end{proof}

\section{Characteristic pairs of locally piecewise functions}

Recall that every piecewise affine function is determined by its components
and regions. The following theorem provides a similar characterization
for locally piecewise affine functions.

\begin{theorem}
  A function $f\colon\mathbb R^m\to\mathbb R$ is locally piecewise
  affine iff there exist a sequence of distinct affine functions
  $(f_i)$ and a sequence $(S_i)$ of subsets of $\mathbb R^m$ such that
 \begin{enumerate}
  \item\label{lpa-agree} on $S_i$, $f$ agrees with $f_i$;
  \item\label{lpa-perfect} $S_i=\overline{\Int S_i}\ne\varnothing$ for every $i$;
  \item\label{lpa-disjoint} $\Int S_i\cap\Int S_j=\varnothing$ whenever $i\ne j$;
  \item\label{lpa-union} $\bigcup_{i=1}^\infty S_i=\mathbb R^m$;
  \item\label{lpa-finite} every bounded set meets only finitely many $S_i$'s.
 \end{enumerate}
\end{theorem}

\begin{proof}
  Suppose that $f$ satisfies the five conditions; show that it is
  locally piecewise affine. First, observe that $f$ is
  continuous. Indeed, suppose that $x_n\to x$ in $\mathbb R^m$ but
  $f(x_n)\not\to f(x)$. Passing to a subsequence, we can find an
  $\varepsilon>0$ such that $\bigabs{f(x_n)-f(x)}>\varepsilon$ and
  $x_n\in B(x,1)$ for every $n$. By~\eqref{lpa-finite}, the ball
  $B(x,1)$ meets only finitely many $S_i$'s. Hence, passing to a
  further subsequence, we may assume that the sequence $(x_n)$ is
  contained in $S_i$ for some $i$. Since $S_i$ is closed, we have
  $x\in S_i$. It follows that $f(x_n)=f_i(x_n)\to f_i(x)=f(x)$; a
  contradiction. Thus, $f$ is continuous. By~\eqref{lpa-finite} again,
  every bounded solid domain $\Omega$ is contained in the union of finitely
  many $S_i$'s; it follows that the restriction of $f$ to $\Omega$ is
  in $\mathcal{PA}(\Omega)$, so that $f$ is locally piecewise
  affine.

  Suppose now that $f$ is locally piecewise affine. Fix
  $n\in\mathbb N$. The restriction of $f$ to $\Omega_n$ is in
  $\mathcal{PA}(\Omega_n)$; consider the affine components of this
  restriction. By collecting the affine functions associated with
  $\Omega_n$ for all $n\in\mathbb N$, we produce a sequence $(f_i)$
  in $\mathcal A$ such that for every $n$ there exists $k_n$ such that
  $f$ agrees with $f_1,\dots,f_{k_n}$ on $\Omega_n$. By dropping
  repeated terms, we may assume without loss of generality that all
  the members in this sequence are distinct.

  For every $i$, put $U_i=\Int\{f=f_i\}$ and
  $S_i=\overline{U_i}$. Since $f_i$ is a component of the
  restriction of $f$ to $\Omega_n$ for some $n$, it follows that
  $U_i\ne\varnothing$. It is easy to see that \eqref{lpa-agree}
  and~\eqref{lpa-perfect} are satisfied. To show~\eqref{lpa-disjoint},
  suppose that $\Int S_i$ meets $\Int S_j$ for some $i$ and $j$. This
  follows that $f_i$ and $f_j$ agree on an open set, hence $f_i=f_j$
  and, therefore, $i=j$.

  Fix $x\in\mathbb R^m$ and take $n\in\mathbb N$ such that
  $x\in\Int(\Omega_n)$. Let $K_1,\dots,K_l$ be the cells
  generated in $\Omega_n$ by $f_1,\dots,f_{k_n}$. Since
  $\bigcup_{j=1}^lK_p$ is dense in $\Omega_n$, we have
  $x\in\overline{K_p}$ for some $p\le l$. Note that $K_p$ is open and
  $f$ agrees with some $f_i$ on $K_p$. It follows that
  $K_p\subseteq U_i$ and, therefore, $x\in S_i$. This
  yields~\eqref{lpa-union}.

  Finally, we will show that $\Int(\Omega_n)$ only meets
  $S_1,\dots,S_{k_n}$; this will immediately yield~\eqref{lpa-finite}.
  Suppose that $\Int(\Omega_n)$ meets $S_i$ for some
  $i\in\mathbb N$. It follows that $\Int(\Omega_n)$ meets
  $U_i$. This implies that $U_i$ meets $K_r$ for some $r\le l$. Note
  that $f$ agrees with $f_j$ on $K_r$ for some $j\le k_n$. It follows
  that $f_j$ and $f_i$ agree on the non-empty open set $K_r\cap U_i$,
  hence $j=i$ and, therefore, $i\le k_n$.
\end{proof}

As before, the sets $\{f_i\}_{i=1}^\infty$, $\{S_i\}_{i=1}^\infty$, and
$\bigl\{(S_i,f_i)\bigr\}$ are called the \term{components},
\term{regions}, and \term{characteristic pairs} of $f$,
respectively.

\section{$\mathcal{LPA}$ is uniformly dense in $C(\mathbb R^m)$}

It is of interest whether every continuous function on $\mathbb R^m$
can be approximated in some sense by piecewise affine functions. We
will consider two kinds of denseness here: uniform denseness and order
denseness. We start with uniform denseness. It is easy to see that
$\mathcal{PA}$ is not uniformly dense in $C(\mathbb R^m)$ even for
$m=1$.

\begin{theorem}
  $\mathcal{LPA}$ is uniformly dense in $C(\mathbb R^m)$. That is, for
  every $f\in C(\mathbb R^m)$ and every $\varepsilon>0$ there exists
  $h\in\mathcal{LPA}$ such that $\abs{f-h}\le\varepsilon\one$.
\end{theorem}

\begin{proof}
  The proof is analogous to that of Theorem~\ref{lf-sup}. Let
  $f\in C(\mathbb R^m)$ and $\varepsilon>0$.

  First, we consider the case when $f\ge 0$.  Let $(c_n)$ be an
  enumeration of all integer points in $\mathbb R^m$. Consider the
  ``boxes'' $K_n=c_n+B_\infty^m$ and $\widetilde K_n=c_n+2B_\infty^m$.

  Fix $n$. Observe that $\mathcal{PA}(\widetilde K_n)$ is a sublattice of
  $C(\widetilde K_n)$. It clearly contains constant functions. It is
  easy to see that it separates points. Indeed, let
  $x,y\in\widetilde K_n$ with $x\ne y$. Then $x_j\ne y_j$ for some
  $j\le m$. That is, $e_j^*(x)\ne e_j^*(y)$,
  where $e_j^*$ is the $j$-th coordinate functional. Clearly, $e_j^*$ is an
  affine function. Since $\widetilde K_n$ is compact, it now follows
  from the lattice version of Stone-Weierstrass Theorem that
  $\mathcal{PA}(\widetilde K_n)$ is uniformly dense in
  $C(\widetilde K_n)$, see, e.g., Theorem~11.3 on page~88
  of~\cite{Aliprantis:98}. It follows that there is
  $h_n\in\mathcal{PA}(\widetilde K_n)$ such that
  $\bigabs{h_n(x)-f(x)}<\varepsilon$ for all $x\in\widetilde
  K_n$. Extend $h_n$ to a piecewise affine function $\tilde h_n$
  in $\mathcal{PA}$.

  Since $h_n$ is continuous on $\widetilde K_n$, it is bounded on
  $\widetilde K_n$. Let $M_n>0$ be such that $h_n(x)<M_n$ for all
  $x\in\widetilde K_n$. As in Lemma~\ref{affine-Uryson}, we can find
  $g_n\in\mathcal{PA}$ such that $0\le g_n\le M_n\one$, $g_n$ equals
  $M_n$ on $K_n$, and $g_n$ vanishes outside $\widetilde K_n$.

  Consider the sequence of functions
  $\bigl(\tilde h_n\wedge g_n\bigr)$. Since $g_n$ vanishes outside of
  $\widetilde K_n$, all but finitely many terms of this sequence
  vanish on $K_n$; it follows that the sequence
  $\bigl(\tilde h_n\wedge g_n\bigr)$ is locally finite. Let
  $h=\sup_n\tilde h_n\wedge g_n$; by Lemma~\ref{sup-lf} this supremum
  exists, agrees with the pointwise maximum, and belongs to $\mathcal{LPA}$.

  For every $n$ and every $x\in K_n$, we have
  \begin{displaymath}
    h(x)\ge(\tilde h_n\wedge g_n)(x)=h_n(x)\wedge M_n=h_n(x)\ge f(x)-\varepsilon.
  \end{displaymath}
  It follows that $h\ge f-\varepsilon\one$, so that $h-f\ge
  -\varepsilon\one$.

  On the other hand, for every $n$ and every $x\in\widetilde K_n$ we
  have
  \begin{displaymath}
     (\tilde h_n\wedge g_n)(x)\le h_n(x)\le f(x)+\varepsilon.
  \end{displaymath}
  Since $\tilde h_n\wedge g_n\le g_n$, it vanishes outside of
  $\widetilde K_n$. It follows that
  $\tilde h_n\wedge g_n\le f+\varepsilon\one$. Taking sup over $n$ we
  get $h\le f+\varepsilon\one$, so that
  $h-f\le\varepsilon\one$. Therefore, $\abs{h-f}\le\varepsilon\one$.

  Suppose now that $f$ is an arbitrary function in $C(\mathbb
  R^m)$. Then $f=f^+-f^-$, with $0\le f^+,f^-\in C(\mathbb R^m)$. By
  the first part of the proof, we find $h_1$ and $h_2$ in
  $\mathcal{LPA}$ such that
  $\abs{f^+-h_1}\le\frac{\varepsilon}{2}\one$ and
  $\abs{f^--h_2}\le\frac{\varepsilon}{2}\one$. Put $h=h_1-h_2$, then
  \begin{displaymath}
    \abs{f-h}\le\abs{f^+-h_1}+\abs{f^--h_2}\le\varepsilon\one.
  \end{displaymath}
\end{proof}

\section{$\mathcal{PA}$ is $\sigma$-order dense in $C(\mathbb R^m)$}

Recall that a sublattice $F$ of an Archimedean vector lattice $E$ is
said to be \term{order dense} if for every $0<x\in E$ there exists
$y\in F$ with $0<y\le x$. Equivalently, for every $0<x\in E$ we have
$x=\sup A$ where $A=\{y\in F\mid 0\le y\le x\}$; see, e.g.,
\cite[Theorem~1.34]{Aliprantis:06}. Note that the set $A$ may be
viewed as an increasing net. Therefore, $F$ is order dense in $E$ iff
every element of $E_+$ is the supremum of an increasing net in $F_+$.

Let $f\in C(\mathbb R^m)$. Suppose that $f>0$; that is, $f(x)\ge 0$
for every $x\in\mathbb R^m$ and $f(c)>0$ for some $c\in\mathbb R^m$.
It follows easily from Lemma~\ref{affine-Uryson} that there exists a
locally piecewise function $h$ such that $0<h\le f$. This means that
$\mathcal{PA}$ is an order dense sublattice in $C(\mathbb R^m)$.  It
follows that if $0\le f\in C(\mathbb R^m)$ then $f$ is the supremum of
an increasing net $(f_\alpha)$ in $\mathcal{PA}$, that is,
$f_\alpha\uparrow f$. This leads to two natural questions.

\begin{question}\label{q:seq}
  Can we replace a net with a sequence?
\end{question}

\begin{question}\label{q:non-pos}
  How do we deal with non-positive functions?
\end{question}

The answer to the first question is related to the countable sup
property. Recall that a vector lattice $E$ has the \term{countable sup
  property} if every increasing net $(x_\alpha)$ in $E$ with
$x=\sup x_\alpha$ has an increasing subsequence with the same
supremum. Thus, to answer the first question, it suffices to prove
that $C(\mathbb R^m)$ has the countable sup property.

Recall that for a sequence $(x_\alpha)$ in a vector lattice $E$, the
notation $x_\alpha\uparrow$ means $(x_\alpha)$ is increasing;
$x_\alpha\uparrow\le x$ means $x_\alpha\uparrow$ and $x_\alpha\le x$
for every $\alpha$, and $x_\alpha\uparrow x$ means $x_\alpha\uparrow$
and $x=\sup_\alpha x_\alpha$. Note that $f_\alpha\uparrow f$ in
$C(\Omega)$ does not imply pointwise convergence. For
$f,g\in C(\mathbb R^m)$, the notation $f<g$ means $f\le g$ and
$f\ne g$. For $f\in C(\mathbb R^m)$ and a solid domain $\Omega$ in
$\mathbb R^m$, we write $f_{|\Omega}$ for the restriction of $f$ to
$\Omega$; we view it as an element of $C(\Omega)$.

\begin{lemma}\label{restr}
  Let $(f_\alpha)$ be a net in $C(\mathbb R^m)$ and
  $f\in C(\mathbb R^m)$.  Then $f_\alpha\uparrow f$ in
  $C(\mathbb R^m)$ iff ${f_\alpha}_{|\Omega_n}\uparrow f_{|\Omega_n}$
  in $C(\Omega_n)$ for every $n$.
\end{lemma}

\begin{proof}
  Suppose that $f_\alpha\uparrow f$ in $C(\mathbb R^m)$. Fix $n$.  It
  is clear that $({f_\alpha}_{|\Omega_n})$ is an increasing net in
  $C(\Omega_n)$ and $f_{|\Omega_n}$ is an upper bound of this
  net. Suppose it is not the least upper bound. Then there exists
  $g\in C(\Omega_n)$ such that ${f_\alpha}_{|\Omega_n}\le g$ for every
  $\alpha$ but $g(t_0)<f(t_0)$ for some $t_0\in\Omega_n$. Since
  $\Omega_n$ is a solid domain, we may assume that
  $t_0\in\Int\Omega_n$. It follows easily that there exists a
  neighborhood $V$ of $t_0$ and $\varepsilon>0$ such that
  $V\subseteq\Int\Omega_n$ and $g(t)<f(t)-\varepsilon$ for all
  $t\in V$. Find $0<h\in C(\mathbb R^m)$ such that $h(t_0)>0$,
  $h(t)<\varepsilon$ for all $t\in V$, and $h$ vanishes outside
  $V$. Then $f-h<f$, yet $f_\alpha\le f-h$ for every $\alpha$; this
  contradicts $f=\sup f_\alpha$.

  Conversely, suppose that ${f_\alpha}_{|\Omega_n}\uparrow f_{|\Omega_n}$
  in $C(\Omega_n)$ for every $n$. First, we claim that
  $f_\alpha\uparrow\le f$ in $C(\mathbb R^m)$. Indeed, fix any
  $t_0\in\mathbb R^m$. Find $n$ so that $t_0\in\Omega_n$. It follows
  from ${f_\alpha}_{|\Omega_n}\uparrow f_{|\Omega_n}$ that
  $f_\alpha(t_0)\uparrow\le f(t_0)$. In particular, $f$ is an upper
  bound of $(f_\alpha)$ in $C(\mathbb R^m)$.

  On the other hand, suppose that $g$ is an upper bound of
  $(f_\alpha)$ in $C(\mathbb R^m)$. Fix any n.  Then
  $g_{|\Omega_n}\ge{f_\alpha}_{|\Omega_n}\uparrow f_{|\Omega_n}$ yields
  $g_{|\Omega_n}\ge f_{|\Omega_n}$. This is true for all $n$;
  therefore, $g\ge f$. It follows that $f=\sup_\alpha f_\alpha$.
\end{proof}

\begin{theorem}
  $C(\mathbb R^m)$ has the countable sup property.
\end{theorem}

\begin{proof}
  Let $(f_\alpha)_{\alpha\in\Lambda}$ be a net in $C(\mathbb R^m)$
  indexed by some directed set $\Lambda$ such that
  $f_\alpha\uparrow f$ for some $f\in C(\mathbb R^m)$.  Fix
  $n\in\mathbb N$. By Lemma~\ref{restr}, we have
  ${f_\alpha}_{|\Omega_n}\uparrow f_{|\Omega_n}$ in $C(\Omega_n)$.
  Recall that every vector lattice which admits a strictly positive
  functional has the countable sup property; see, e.g.,
  \cite[Theorem~2.6]{Aliprantis:03}. Since the Riemann integral is a
  strictly positive functional on $\Omega_n$, it follows that
  $C(\Omega_n)$ has the countable sup property. Therefore, the net
  $({f_\alpha}_{|\Omega_n})$ has a subsequence whose supremum in
  $C(\Omega_n)$ is $f_{|\Omega_n}$.

  We will now inductively construct a double sequence $(\alpha_{n,k})$ in
  $\Lambda$ indexed by pairs $(n,k)\in\mathbb N^2$ satisfying the
  following two conditions
  \begin{enumerate}
  \item $(\alpha_{n,k})$ is increasing: if $n_1\le n_2$ and $k_1\le
    k_2$ then $\alpha_{n_1,k_1}\le\alpha_{n_2,k_2}$;
  \item for every $n$ we have ${f_{\alpha_{n,k}}}_{|\Omega_n}\uparrow
    f_{|\Omega_n}$ as $k\to\infty$.
  \end{enumerate}
  For $n=1$, let $(\alpha_{1,k})_{k=1}^\infty$ be an increasing
  sequence in $\Lambda$ such that ${f_{\alpha_{1,k}}}_{|\Omega_1}\uparrow
    f_{|\Omega_1}$ as $k\to\infty$; it exists by the preceding
    paragraph.

  Suppose that we have constructed $\alpha_{i,k}$ for all
  $i=1,\dots,n-1$ and all $k$. We will now construct $\alpha_{n,k}$
  for all $k$. Find an increasing sequence
  $(\beta_k)$ in $\Lambda$ such that
  ${f_{\beta_k}}_{|\Omega_n}\uparrow f_{|\Omega_n}$ in
  $C(\Omega_n)$ as $k\to\infty$. Now choose $\alpha_{n,1}$ to be any index greater
  than $\beta_1$ and $\alpha_{n-1,1}$. Choose $\alpha_{n,2}$ to be any index greater
  than $\beta_2$, $\alpha_{n-1,2}$, and $\alpha_{n,1}$. Proceed
  inductively: once we have defined
  $\alpha_{n,1},\dots,\alpha_{n,k-1}$, choose $\alpha_{n,k}$ to be any
  index greater than $\beta_k$, $\alpha_{n-1,k}$, and
  $\alpha_{n,k-1}$. This yields
  \begin{displaymath}
    f_{|\Omega_n}\ge {f_{\alpha_{n,k}}}_{|\Omega_n}\ge {f_{\beta_k}}_{|\Omega_n}\uparrow f_{|\Omega_n},
  \end{displaymath}
  so that ${f_{\alpha_{n,k}}}_{|\Omega_n}\uparrow f_{|\Omega_n}$ in $C(\Omega_n)$ as
  $k\to\infty$.  Also, it is easy to see that $(\alpha_{n,k})$ is
  increasing.

  Consider $(\alpha_{k,k})_{k=1}^\infty$. This is clearly an
  increasing sequence in $\Lambda$. If $n\le k$ then
  $\alpha_{n,k}\le\alpha_{k,k}$, so that
  $f_{\alpha_{n,k}}\le f_{\alpha_{k,k}}\le f$. This yields
  ${f_{\alpha_{k,k}}}_{|\Omega_n}\uparrow f_{|\Omega_n}$ in
  $C(\Omega_n)$ as $k\to\infty$. It now follows from Lemma~\ref{restr}
  that $f_{\alpha_{k,k}}\uparrow f$ in $C(\mathbb R^m)$.
\end{proof}

\begin{corollary}\label{odense-pos}
  For every $0\le f\in C(\mathbb R^m)$ there exists a sequence $(h_n)$
  of positive piecewise affine functions such that $h_n\uparrow f$ in
  $C(\mathbb R^m)$.
\end{corollary}

Thus, Question~\ref{q:seq} has the affirmative answer. We now pass to
Question~\ref{q:non-pos}. We answer it through order convergence. In
literature, there are two slightly different definitions of an order
convergent net in a vector lattice, which are, generally, not
equivalent. We refer the reader to
\cite{Anderson:67,Abramovich:02,Abramovich:05}. In our case, it will
be irrelevant which of the two definitions is used for the following
two reasons: first, both definitions yield the properties that we will
be using and, second, by~\cite{Anderson:67}, the two definitions agree
in vector lattices which have the countable sup property; hence, they
agree in $C(\mathbb R^m)$.

\begin{proposition}
  Every function in $C(\mathbb R^m)$ is the order limit of an order
  convergent sequence of piecewise affine functions.
\end{proposition}

\begin{proof}
  Let $f\in C(\mathbb R^m)$. Decompose it as $f=f^+-f^-$. By
  Corollary~\ref{odense-pos}, there exist positive sequences $(g_n)$
  and $(h_h)$ in $\mathcal{PA}$ such that $g_n\uparrow f^+$ and
  $h_n\uparrow f^-$ in $C(\mathbb R^m)$. It follows that the sequence
  $(g_n-h_n)$ converges in order to $f$ in $C(\mathbb R^m)$.
\end{proof}

\bigskip
\textbf{Acknowledgement.} We would like to thank Foivos Xanthos for
valuable discussions.

redpajama_set_name: RedPajamaArXiv


text:
/*
 * To change this license header, choose License Headers in Project Properties.
 * To change this template file, choose Tools | Templates
 * and open the template in the editor.
 */
package Gui2D.SpriteController.SingleSprite.SingleSpriteGrouping.misc;

import Gui2D.SpriteController.SingleSprite.SingleSpriteGrouping.Abstract_sprite;

/**
 *
 * @author jonas
 */
public class Lamppost extends Abstract_sprite {

    /**
     * Sets the Candle sprite
     */
    @Override
    public void setSprite() {
        super.getSprite().setSpritePosX(155);
        super.getSprite().setSpritePosY(709);
        super.getSprite().setSprite_width(20);
        super.getSprite().setSprite_height(111);
        super.getSprite().setWidth(20);
        super.getSprite().setHeight(111);
    }
}

redpajama_set_name: RedPajamaGithub


text:
Community// December 21, 2018
T-Mobile CEO John Legere Is on a Crusade to Cure Cancer
Like millions of people, John Legere has seen loved ones bravely battle cancer, which is why he's on a $2 million mission to eradicate this disease. Will you join him?
T-Mobile Stories
Outspoken, philanthropic T-Mobile CEO John Legere is hell-bent on finding a cure for cancer, a disease that affects so many of us and our loved ones across the country and around the world, including his own family and friends.
Which is why, this holiday season, he's teaming up with the Dana-Farber Cancer Institute in the #MatchtoConquerCancer campaign, where he'll personally match donations, dollar for dollar, up to $1 million, through December 31, 2018. That would add up to a total of $2 million in funds that he knows first-hand, through his own work with Dana-Farber, will have an enormous, life-saving impact for so many.
Dana-Farber oncologist Dr. Barrett Rollins talks to John Legere about the importance of the genetic research he and his team are conducting in the fight to cure cancer.
"I wanted to do something big to generate awareness and support for their treatment and research," says Legere, "because it is life-saving work that can impact millions of people."
Dana-Farber's breakthroughs on Profile—a tumor genome mapping project—are helping doctors treat their patients in a more precise way and helping scientists better understand why cancers behave the way they do. Profile provides the genetic signature of each person's disease, which allows doctors to deliver drugs designed to target the specific mutations causing cancer to grow. The result is more effective treatment with fewer side effects.
Legere strongly believes that a lack of resources should never stand in the way of cancer research, which is why he's so committed to doing something about it. Will you join him?
To donate, go to: dana-farber.org/johnlegere
#Philanthropy,
breakthrough,
giving,
giving back,
// March 9, 2019
The Future of Healthcare: "We can gain insight into DNA at the single-cell level to help cure disease" with Charlie Silver CEO of Mission Bio
by Christina D. Warner, MBA
Community// September 19, 2019
Social Impact Heroes: "Why Catherine Ivy and the Ivy Foundation have contributed over $91 million to accelerate drug and treatment discovery for brain cancer"
by Yitzi Weiner
Women Of The C-Suite: "Be so focused on your goal that you are unafraid to do what it takes to achieve it" with Becky Chapman Weaver of the St. Baldrick's Foundation
by Chaya Weiner

redpajama_set_name: RedPajamaCommonCrawl


This timely drama about factory closures in the Rust Belt features a strong cast of veteran actors, including Peter Gerety, Billy Brown and Talia Shire.
The plight of people living in the Rust Belt — many of whom helped to determine the results of the 2016 election — is at the center of Robert Jury's affecting drama Working Man, which received its world premiere at the Santa Barbara Film Festival. Although the film is probably a tad too leisurely to find a major distributor, it deserves attention for the fine performances at the center of this well drawn canvas.
Veteran actor Peter Gerety (who has numerous credits in theater, film, and television) plays Allery Parkes, a factory worker who learns in the opening scene that the plant where he has worked for decades is closing. Besides the loss of income, Allery is confounded by the loss of his comfortable routines; he has no idea how to spend his days if he is not working. So he decides that the only solution is to pack his lunch and return to the shuttered plant and go through the motions of working. At first his wife (Talia Shire), his neighbors and co-workers are bemused and bewildered by his somnambulistic adherence to his workaday patterns. Then they become more concerned, and eventually several of them decide to join him at the desolate factory, dreaming that they might be able to persuade the owners to re-open the business.
Allery finds a strong ally in an African-American neighbor, Walter (played by Billy Brown, known for his role in the hit TV series How to Get Away with Murder), a newer member of the community who becomes an even stronger advocate for action against the factory's owners. Walter's volatility adds a jolt of electricity to the film, which moves along too sluggishly in the first half. Gradually we learn that Walter is a more complex character than the other townspeople realize, and the drama intensifies.
Shire as Allery's wife Iola also seems an overly passive character in the movie's first half, but as family secrets are revealed, Iola becomes less of the meek housewife that she appeared to be and turns into a more assertive character. Shire, known for her roles in the Godfather and Rocky films, has been less visible in recent years, but she has a great speech in the second half of Working Man that reminds us of what we've been missing.
All of the cast members — including J. Salome Martinez, Kirsten Fitzgerald, and Bobby Richardson — add verisimilitude. Some of these actors were found in the Chicago area, where the film was shot. One of these local actors, Patrese McClain as Walter's ex-wife, has a cameo late in the film that adds special punch to the film.
The sense of place is well captured by cinematographer Piero Basso and production designer Sarah Sharp. Morgan Halsey's editing in the first half falters, but it gains urgency in the more compelling second half of the picture. (At 108 minutes, the film seems overlong and might benefit from 10 or 15 minutes of trimming.) Despite its flaws, fine acting by both veterans and newcomers, along with an extremely timely subject, give the film a pungent flavor.


text:
Discografia

Album studio
 2007 - The Submarine
 2009 - Go Forth, Find Mammoth
 2013 - Even The Stars Are A Mess

Singoli
 More Than Life
 Poison In Our Pocket
 Head, First, Down
 I Remember
 Killer
 Bright White Lights
 A Shot To The Star

Collegamenti esterni
  Whitley su artistwiki.com
  Pagina ufficiale su MySpace

redpajama_set_name: RedPajamaWikipedia


Keep your LEE Pro1000 or 3 hole turret toolheads organized and tidy. Storage rack also has a slot to store your shellplate (Pro1000). Available in natural tumbled aluminum or black powdercoat finish. Keep you valuable bench space clear and mount the rack out of the way on the wall or inside a cabinet.


Coffs Day Hospital had its official opening on the 6th of November. Many local referers, doctors, and business owners attended the ceremony which was headed by local MP: Andrew Fraser.
Guests were invited for drinks and canapes, as well as a tour of the brand new facilities and state-of-the-art equipment.
News outlets also attended the event, and our own Director of Nursing, Beverley Sainty-Jones, was interviewed about the hospital and its facilities. Follow the link below to view the video.
The opening marks the first day in what Coffs Day Hospital hopes will be a long and rewarding journey in providing high quality healthcare to the Coffs Harbour community.
Coffs Day Hospital is located at 69 Albany Street, Coffs Harbour. Coffs Day Hospital is part of the Presmed group of day hospitals.


text:
Relationships, Unlearning, and New Narratives: Reflections from the Soros Justice Fellows Conference
Photo above: Yanitza Cubillette, Hearing Youth Voices (far left) and Lucas Codognolla, CT Students for a Dream (far right)
In August, three young adult leaders from Connecticut were selected by Open Society Foundation's Youth Exchange to travel to Phoenix, Arizona to join leading organizers, advocates, scholars and journalists from across the country at OSF's annual Soros Justice Fellows conference. What are they bringing back to Connecticut as a result? Read on to learn more about personal discoveries sparked by their experience as well as their reflections on what's needed to RUN (Relationships, Unlearning, and New Narratives) more powerful and inclusive social justice campaigns in our state.
Relationships. The Youth Exchange brought together 15 young leaders between the ages of 18-25 from around the country. Nominated by current and former Soros Fellows, these young leaders are playing critical leadership roles at important movement organizations, including the BYP100 the People's Institute for Survival and Beyond, and more. One of the most valuable takeaways from the conference, Lucas explains, was the relationships forged with other Youth Exchange fellows: "the youth that were there built a really strong bond." Weeks later, Lucas explains, "we are still talking over Facebook and connecting with each other. It was a really good group, working on different issues and struggles but open to learning about each others' work and trying to find synergy in each others' work."
"I felt like I could talk to anyone in that room and have a conversation and connection with someone about our work, regardless of our age differences, and the relationships with the other youth Exchange members are especially strong," explains Yanitza. "It definitely beyond, 'oh, you're a cool person, let's be friends.' We continue to talk with each other and support each other around work and projects that are going on in each of our organizations, and also other areas of interest. For example, as a result of conversations that we had at the conference, another Youth Exchange fellow and I are both working on compiling black and brown-owned businesses in our local communities."
Photo: Farron Harvey, Youth Council for Justice (top row middle)
Farron, who was engaged in social justice education programs as a teen and spent two years abroad in the Peace Corp prior to becoming a youth organizer at the Youth Council for Justice, says she came back from the conference thinking more deeply about how to cultivate relationships of support and solidarity among groups who are similarly impacted by issues but too often do not work alongside one another. "As I kept reflecting on what I learned during the conference the recurring theme for me was – okay, so how do communities, such as Blacks and immigrants, who are both suffering from privatized prisons and mass incarceration come together in solidarity? How can we support each other and use our networks to make effective change?"
Unlearning. On the second day of the conference, Lucas attended a tour and site visit to Florence and Eloy, towns described as modern day "penal colonies" with more than a dozen immigrant detention centers between them. "On the morning of the tour I was low key freaking out, but it felt like an important tour to go on." Though Lucas and fellow leaders and members of C4D share the experience of being undocumented, Lucas shared the tours of the detention centers pushed him to "see conditions and relate to the stories on another level. When I came back to CT, I called some of our leaders who have been detained to reflect on our experiences, and they really appreciated me reaching out." Going to the conference, Lucas explains, "made me really think about how to start building connections with other organizations in Connecticut and also across other movements working to reform the criminal justice system and dismantle the prison industrial complex because we are all being affected by these systems. For us, it's going to take some time to learn together and also do some unlearning together. In our campaign sometimes we fall into the trap of the 'good' vs. 'bad' immigrant narrative. We are good students, overachievers, deserve right to go to college. Folks that don't fit into that narrative sometimes get thrown under the bus, and our team is becoming more aware of that."
Immigration and Customs Enforcement (ICE) detention center in Eloy, AZ
New Narratives. For Yanitza, one of the most challenging and powerful aspects of the conference was a day-long training on public narrative: "It really intense to walk into a new space, with all these new faces and be expected to share very real vulnerable parts of ourselves in a very short period of time. When you are sharing some of these things, it's stuff that hurts, it's reliving a wound. People talked about their struggle being trans; I talked about my father being deported." At the same time, Yanitza explains, "the workshop was eye opening. As an organizer, I know the importance of stories. As an individual and as an organization we are good at recognizing that stories are powerful, but we don't always connect to a sense of purpose of how we are using those stories. If we are more strategic about how we tell the stories, it will move more people. I'm actually using the framework and questions in an exercise we're doing today with our youth leaders. What is the story of me, of us, of now?"
The reflections that Youth Exchange members brought back – awareness of the intersection of the immigration and justice systems, the need to develop cross-cutting analysis and new narratives, and the importance of forging deep relationships in solidarity across issue areas – are particularly timely. Just weeks after the Youth Exchange members returned from Arizona, the Department of Justice announced it would end the federal use of private prisons; the decree, however, does not apply to the hundreds of privately run immigrant detention centers around the country. While Connecticut is not home to private prisons or immigrant detention centers, residents of our state have been incarcerated at private prisons and detention facilities out of state. As Yanitza noted, "as triggering as the [conference] was I very much appreciated being in a space that was so focused on immigration and justice reform. The interconnection between those systems are really important and isn't highlighted enough … it made that urge and desire to want to work together even more. CT is small enough – we are too small, too close to each other not work together."


text:
Embodiment of Pure Love
This incident took place at Simandhar City. Once, a brahmachari bhai (celibate brother) experienced a severe toothache. He had to undergo a root canal treatment. While doing the treatment, a tiny fragment of tooth lodged in the gums and couldn't be removed. The doctors tried to dig it out. In spite of getting a local anesthesia, his whole body shook at the slightest touch of the vein. The pain was unbearable.
As he hadn't returned until late, Niruma phoned him. Until that time, in spite of all the pain, he had remained quiet and tried to apply Gnan (tried to keep separation from the body as per Dada's five principles). But, as soon as Niruma phoned and he heard her voice, he broke down. All his efforts of maintaining separation from the pain stopped and he started sobbing uncontrollably. Handing over the phone to the doctor he said, "I won't be able to talk to Niruma."
On enquiring further, the doctors explained everything to Niruma. Niruma asked, "Shall I come?". The bhai refused and said, "If this is what happened to me on just hearing her voice, then what will be my condition if she comes here"?
So Niruma said to the doctors, "Don't worry. Continue with your work. I'll do vidhi (silent auspicious blessings performed by the Gnani for the salvation of the disciple)." At last the fragment was dislodged at 1.00 a.m. in the morning.
He now desperately felt the need to just rush to Niruma and put his head on her lap and cry his heart out. Only then, will all the pain cease. He went straight to Niruma. She was sitting on her bed. He put his head in her lap and cried constantly for 10-15 minutes. All the pain withheld for hours came out at once, he cried a lot. Niruma kept patting him. When he lifted his head, Niruma's clothes were covered in blood.
"Niruma, blood!" he said feeling ashamed. "It doesn't matter. Does it still hurt?" Niruma asked.
It was 2.00 a.m. in the morning. Niruma immediately asked Deepakbhai, "Make a call to America. It'll be morning there. Talk to our doctor mahatma and take down the name of the painkiller from him. They do painless surgeries, so they have this knowledge."
Niruma got his bed shifted to her room and said, "You sleep here tonight. You are not going anywhere." Thereafter Niruma stroked his head gently, while Deepakbhai massaged his feet. He fell asleep instantly. When he got up in the morning he saw that Niruma and Deepakbhai were still sitting there, in the same position. Niruma was stroking his forehead and Deepakbhai, his feet. He was amazed they had not slept at all!
For the following five days, Niruma herself prepared khichdi (boiled mix of rice and lentils), added ghee and made it into liquid form with a hand mixer and then fed him. In this way for five days, three times a day he had to eat the same type of food. By doing this, he healed gradually and Niruma took care of him until he fully recovered.
Afterall Our Gnani…an embodiment of pure love…


text:
Q: Turning Sencha Touch-based app into a true native iPhone app? As I understand, Sencha Touch is just a javascript library that lets you create websites that respond to multitouch and other features you find in native iPhone apps. So... Your end result is accessed on Safari on the iPhone, and not as a native iPhone app. Is there a way to convert this to a native app?

A: In principle yes. You could write some kind of a wrapper application. This application would have an 'UIWebView' as the main view which is then used to browse the web. This would allow you to keep your HTML5-based app and wrap it in a native objective-c app.
If you want to write a "real" native app your would have to switch languages from HTML5, CSS and JS to Objective-C, which is really different.

A: Yes, you can convert a Sencha Touch app to native. You have to use PhoneGap, or Nimblekit to do so. You can also write your own native wrappers - it's not very hard on iPhone, but more of a challenge on Android. We don't have a tutorial on this yet, but the phonegap guys have done this with at least one sencha app that they built. [I work for sencha]
Update: Here is a crazily detailed tutorial on using PhoneGap with Sencha

A: So here is a question for the Sencha guys here, is there other documentation for Sencha Touch available beyond the API reference and sample apps on your site?
We are currently trying to switch a prototype application from JQTouch to Sencha, but are finding it challenging to get going with Sencha Touch; while there is a lot of documentation it doesn't seem to be the right documentation.
A really simple solution would be to make the API reference online allow comments so as we and others figure out how to use Sencha touch we could provide comments (look at php.net's manual to see how this worked for them.)

A: While I don't know exactly how Sencha works, if you just want to be able to take advantage of the multitouch features of the iDevices in a native application, this is very well documented in Apple's portal, including sample code; and even third party resources which you can find by using google.
In iOS 3.2 and higher, Apple has made handling touch events easier with introducing gesture recognizers, and they're simply wonderful to use.
Have a look over these resources, http://developer.apple.com/iphone will get you started. There are links to videos, text resources, and sample code as I mention that will give you a solid foundation to do what you need to.

A: Why would you want to convert? If you are writing successful apps with Sencha then stay with it. There are advantages to web based apps.

*

*You can build them in a more accessible toolkit html/css/javascript.

*You can deploy them more easily and quickly by setting them up on a web server.

*You can update them on the fly etc.

If you produce a "native" app then you need to register with and pay for the Apple dev programme and the process for submitting an app is quite laborious and of course it might get rejected.
Apple themselves use the web based applications route, look up AdLib and PastryKit here on Stackoverflow. THese two libraries are Apples version of Sencha.
There are of course advantages to writing native apps. They have a very rich development set of tools and (in my opinion) will always function better then most web based apps and there is the marketing machine of the app store you can plug into.
But you can successfully go either way.

redpajama_set_name: RedPajamaStackExchange


Subdivision means to divide land or buildings into separate parts each with a separate computer register (certificate of title). Subdivision also means to adjust the boundaries of any title, or even to amalgamate two titles into one larger title.
If you want to subdivide your land, you'll always need a resource consent. It's a very technical type of consent, so this section gives you information about how subdivision consents work, and some things you might need to consider.
When do I need a subdivision resource consent?
You need a subdivision consent from the Council for any subdivision that you want to do, including boundary adjustments.
Like any resource consent, subdivision consents are processed and assessed under the Resource Management Act 1991.
The Tasman Resource Management Plan contains the rules covering things such as size, shape, frontage and access of lots.
The Long Term Council Community Plan (LTCCP) covers things such as requirements for development contributions.
The Council's Engineering Standards & Policies 2013 covers the installation of new works and services.
For subdivision close to the coast, the New Zealand Coastal Policy Statement is also relevant.
The National Environmental Standard on contaminated soil and human health addresses how we manage and / or reduce the the risk to humans from historically contaminated land.
How long will it take, and can I do it myself?
You may find the subdivision of land is often a time consuming process as it involves a number of steps. The very simplest of subdivisions can take three to four months to complete. More complicated or larger ones will take a lot longer. Despite some statutory time periods, the time it take us to complete a subdivision generally relies entirely on you as the applicant.
While you may be able to do some of the subdivision processes yourself, there are some tasks that you will need to involve professionals - such as land surveyors, engineers and lawyers.
If you are thinking about subdividing your land, please make sure you discuss your plans with one of our subdivision planners before you prepare your application. To arrange this, please call the Customer Services team on 03 543 8400 [or use the electronic form to make online request].
When we grant you a subdivision consent, the Council may require that certain conditions are included on the new title of the property. These capture the agreement between the Council and the land owner when the landowner will have an ongoing obligation.
obligations to meet landscaping or engineering requirements.
As an agreement between the Council and the land owner, if the land owner doesn't meet their side of the agreement, then we do take steps to enforce the obligation or restriction in the consent notice.
As the land owner, you can ask us to consider changing or cancelling any consent notice at any time after the deposit of the survey plan. We have to take into account the original reason for the consent notice when we assess your application.
The process to change or cancel a consent notice is a type of resource consent application.
What sort of issues do I need to consider during subdivision?
We require detailed assessments of these natural hazards as part of the subdivision application to determine the level of risk to any new building site, road or infrastructure.
The risks from natural hazards are required to be mitigated to an acceptable level or consent may be declined.
The planning maps of the TRMP identify some (but not all) of these hazard areas.
If the land being subdivided was used for activities such as a historic orchard, timber treatment, fuel storage, a rubbish dump or contains an old sheep dip the soil may be contaminated in some places. As part of processing a subdivision consent we may required an assessment of any contamination.
If contmaination is found, remediation of the contamination to acceptable levels is a necessary part of the subdivision process.
The Council holds information on the HAIL Register about many of these potentially contaminated sites, and we will provide it on request. You get this information when by applying for a Land Information Memorandum (LIM).
You must assess the stormwater discharge, diversion or drainage into water from any new roads, accesses or rights of way created as part of a subdivision. Your assessment must also take into account the stormwater from any future dwellings built on the new lots created.
Any stormwater generated by a subdivision must be discharged to a stormwater system that has enough capacity or else you may have to provide onsite detention.
A specific stormwater discharge consent will be required if the stormwater discharge, diversion or drainage into water cannot meet the permitted activity criteria of rule 36.4.2.1 of the TRMP then you must also apply for a specific discharge consent.
If your subdivision is within established townships a wastewater connection may available if the Council network has capacity. The majority of rural areas will need you to provide onsite wastewater treatment for your subdivision.
the volume of the discharge.
While you will find a number of proprietary systems available, you may find other more passive (low energy) forms of onsite treatment are appropriate for your site. A wastewater consultant or engineer can help.
You will need a specific wastewater discharge permit for new discharges in the Wastewater Management Area (Coastal Tasman Area). There are other areas in Tasman which also have more stringent wastewater rules, called 'special domestic wastewater disposal areas'.
You must provide a reliable and potable water supply for new residential dwellings. This water supply may include water stored from roofs.
For subdivisions within the business and industrial zones a water connection is usually required by the conditions of any approved consent.
The majority of the rural water supply systems are fully allocated.
Unformed road reserve, roads within a proposed subdivision and rights-of-way are required to be formed in accordance with the requirements of Section 18.8, Rule 16.2.2.1 and Figure 16.2A of the TRMP. The detailed construction standards are contained in the Council's Engineering Standards & Policies 2013.
A right-of-way is a particular type of easement, which allows the owners of one property - the 'dominant' party - to have vehicle and/or pedestrian access over a portion of another property - the 'servient' party.
by application to the Council under Section 348 of the Local Government Act.
Generally any change requires the agreement of both the dominant and servient parties. The Council permission may also be required if the right-of-way was a condition of a subdivision consent.
The Tasman Resource Management Plan has minimum formation standards for rights-of-way which we can require as a condition of any consent to create a right-of-way. Please refer to the Engineering Standards for construction details for right-of-ways.
If your subdivision has land adjacent to the coast or riverbank, then the Council will consider if an esplanade reserve or esplanade strip is needed for future public access or the protection of conservation values.


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Ti Kaye Resort – St. Lucia
For seeing the best that the Galapagos Islands have to offer underwater, going the live-aboard dive yacht is the way to do it with the M/V Galapagos Sky certainly one to do it with.
I'm not usually a fan of using words such as "ultimate," "amazing" or "best ever" in a review. But, there are certain destinations and experiences that deserve superlatives. This is certainly the case for my most recent liveaboard trip aboard the Galapagos Sky.
Big animal encounters like this whale shark is what diving in the Galapagos Islands are all about.
Straddling the Equator, 590 miles west of South America's Pacific Coast, the Galapagos Islands showcase a biosphere that once inspired Darwin's theory of evolution. On islands and surrounding rock formations, marine iguanas, giant land tortoises and tropical sea birds capture the imagination. And the diversity isn't confined to the land. Inside the 140,000 square kilometer marine reserve that surrounds these islands, species such as sea lions and penguins, normally indigenous to cooler regions, live side-by-side with a host of sharks, reef fish and sea turtles commonly found in more tropical climates.
Green Turtle getting shadowed by a leatherbass.
The prolific range of marine life found in these waters results from the convergence of five major oceanic currents that converge on the lonely cluster of islands on the equator.
When the south Equatorial Current arrives from the west, it is joined by the colder, plankton rich Humboldt Current. This cool, nutrient laden water is further enriched by deep upwellings generated by the Cromwell or Equatorial Undercurrent, which brings up even cooler nutrient-laden water. When the three currents mingle and rise to sunlit depths generate, it creates ideal conditions for massive plankton blooms, which are essential for sea birds and larger forms of marine life.
The variety of cetaceans in the Galapagos is impressive, and includes bottlenose dolphins to pilot whales, false killer whales, orcas and sperm whales. At times, these waters are even visited by the ocean's largest creature, the blue whale. During my most recent trip, we were fortunate to see one of these majestic leviathans pass in front of our bow while on the way to Fernandina Island.
Galapagos Sky liveaboard dive yacht.
The M/V Galapagos Sky is a purpose-built liveaboard launched in the year 2000 by Santiago Dunn, and operated under the name of Sky Dancer as part of the Peter Hughes fleet.
Before it was known as the Galapagos Sky, the vessel went by the name Sky Dancer back back 2001.
My first introduction to this boat was in 2001, when I spent a memorable week enjoying a winning combination of good food, good service and exceptional diving. Today, the parent operation is known as Ecoventura, and the Sky is considered one of the premier luxury liveaboard dive yachts in the Galapagos.
My most recent visit to the Sky was late 2016. And now, I'll use one of my infrequent superlatives to say that I was "ecstatic" to be back aboard. There was an immediate sense of familiarity, as the boat is obviously maintained to a high standard, and offered the same comforts and amenities I remembered.
Galapagos Sky Master Cabin with king bed. Photo courtesy of DivEncounters
Guest accommodations aboard this 100-foot yacht include eight private en-suite cabins, hosting a maximum of 16 passengers. Cabins are split four-and-four, with four Master Staterooms on the upper Dolphin deck, and four Deluxe Staterooms located just below on the Iguana deck, which also holds the main saloon. The Masters command a slight premium, as they have slightly more interior space, offer the option of a king-sized bed or two twins, and have large picture windows. All staterooms provide individual climate control, and include a private head and shower, where guests will bind a mirrored cabinet and wardrobe, bathrobes, hairdryer, and marine-safe biodegradable toiletries.
Deluxe Cabins are trimmed in rich woodwork, and offer twin beds and a private en suite bathroom. Photo courtesy of DivEncounters
The interior décor of the Sky has a very yacht-like feel, with polished hardwood floors and furnishings. The booth seating of the dining is reminiscent of an upscale restaurant, and each table enjoys ocean views through large picture windows. The saloon area includes a large wrap-around settee that invites mixing and mingling. All furnishings have undoubtedly been replaced more than once since my first visit, because everything from the upholstery to the trim work looked brand new. Even the salon's bar seemed to have benefited from some upgrades.
The Sky's eight-member crew follows the Peter Hughes tradition of passenger-pampering, from nightly turn down service in your cabin, to morning coffee delivery, and attentive meal service that creates a refined yet not overly pretentious ambiance. The menu varies between international fare and local recipes, and all beverages including wine and beer are gratis with dinner during the voyage.
Galapagos Sky dive deck.
Of course, the real meat and potatoes of any liveaboard dive yacht is the dive deck. The Sky's large, semi-enclosed aft dive deck is well designed to accommodate 16 guests, plus two guides with plenty of room to suit-up at the same time without bumping into one another. There is individual gear storage beneath each diver's station on the bench seats, and heated fresh water showers for rinsing after the dive. The deck also includes a large two-tiered camera table and a separate charging station with 110 and 220-volt power. The camera rinse tank can hold about three full size DSLR systems at a time, so when there are a lot of serious photographers aboard, the usual post-dive protocol is to dunk once and move the camera to the table. In addition to offering cameras and Scubapro brand dive equipment for rent, the Sky provides complimentary 32 percent nitrox for qualified divers. In my opinion, if you are not already nitrox certified, get it before you go!
Map showing a typical one-week itinerary normally taken by the M/V Galapagos Sky.
The Galapagos is a dream destination for many, but probably not the best place for new divers who have yet to master buoyancy control or their overall comfort level in the water. Currents are nearly present on all dives, sometimes mild but other times quite strong. And don't pack a tropical-weight wetsuit, because although these islands straddle the equator, the water can be surprisingly chilly, with temperatures sometimes getting as low as 50 to 58 degrees Fahrenheit.
All dives from the Galapagos Sky are conducted as drifts staged from a pair of 22-foot inflatable launches.
Because conditions at most sites are not conducive to diving from an anchored or moored boat, the Galapagos Sky conducts all dives from 22-foot, outboard powered inflatables. After a through and usually entertaining pre-dive briefing on the aft deck, the crew loads all gear into the launches for a short run—usually five to ten minutes—to the starting point of the dive. Each launch carries up to eight divers, plus a divemaster/guide. As a matter of protocol, all dive guides working in the waters of the Galapagos are trained Park Naturalists in addition to being certified dive instructors or divemasters.
Silky sharks are not usually considered a coastal species, but they can be found along the shores of a number of the islands of the Galapagos, as well as right next to the Galapagos Sky itself.
The Sky's 8 day / 7 night cruise itinerary covers 5 1/2 days of diving. From the mainland airport in Guayaquil, Ecuador, guests typically catch a flight that arrives on the island of San Cristobal around noon on Sunday. After paying a $100 park fee (cash only), they are then transported to the boat for introductions and other formalities such as required safety briefings and a vessel orientation. That afternoon, there is time for a check out dive at a nearby site, which gives everyone a chance to get accustomed to the boat's diving practices in a non-challenging environment.
From San Cristobal, our trip began with an overnight move to Santa Cruz Island to dive at Punta Carrion and around the northeast tip of Isla Pinzón. These sites are a great introduction to Galapagos diving. Most profiles run from 40 to 90 feet over volcanic rock and sand bottom, and the marine life in this area is extremely varied. On any given dive you can expect white-tipped reef sharks, marbled stingrays, green turtles, Galapagos fur seal and sea lions, eagle rays, cownose rays and mobula rays swimming in formation. My favorite smaller find is the region's indigenous red-lipped batfish, which has lips so red it would make Revlon cosmetics jealous.
Red-lipped batfish (Ogcocephalus darwini) is one of the more interesting small finds that await in the waters of the Galapagos.
Following our third dive, the Sky set sail for the Wolf-Darwin volcanic ridge, which lies some 100 miles to the northwest. The voyage takes 16 to 18 hours over predominately open sea, where wave heights frequently running three to six feet. The small, uninhabited islands of Wolf and Darwin are the eroded crests of extinct volcanoes that rise from depths of more than 3.000 feet to become towering rocky precipices some 500 to 800 feet high. The most famous site in this area is the Arch at Darwin Island.
Schooling scalloped hammerhead sharks (Sphyma lewini) still remain the big ticket draw for both Darwin and Wolf Island.
The waters surrounding the Arch are a dynamic zone, where currents and surge converge around the submerged promontory of Darwin Island. In the course of a single dive, you may find schooling hammerhead sharks, large numbers Galapagos and silky sharks, eagle rays, thick schools of skipjack and yellowfin tuna, plus even a pod or two of bottlenose dolphins.
During the months from July through November is the best time of year for encunters with some of the largest (40 to 45 feet) whale sharks anywhere.
In the months from June to September, this is the place to be for encounters with truly large whale sharks, which may reach lengths of 45 feet. Another diver favorite are the massive schools of bigeye jacks that form giant swirling funnel-shape formations known as Jack-nados. Other times, the jacks may appear like a massive blue steel wall, large enough to conceal a 40-foot whale shark. It can be quite a surprise when a shark breaks through the curtain.
The Galapagos Islands are one of the few dive destinations where there is a good chance of seeing open-water species like this large yellowfin tuna making a pass at a school of creole fish.
While waters of the islands to the south are generally cool, Darwin and Wolf are more affected by the warmer waters of the Panama Current and the North Equatorial Countercurrent. The convergence of the two brings water temperatures that can rise as past the 80-degree mark during the months from December through March. One of the more obvious indicators of this warmer water is the higher number of hard corals present. But even the rocks that are not covered with coral are seldom barren, and are often covered with layers of barnacles sharp enough to do a nasty job on a prized wetsuit or ungloved hand. During the months of June through October, water temperatures fall into the cool range of 20.5 to 24 C (69 to 75 degrees). But these are also the best months for encounters with Darwin and Wolf's big-ticket encounters, from packs of Galapagos, Silky and schooling hammerheads to whale sharks.
Marine iguanas are air-breathing reptiles, but they can hold their breath for up to half an hour, and dive to depths of 100 feet to graze on algae.
After spending a full three days around Wolf and Darwin islands, the Sky works its way south, venturing to the northwestern corner of Fernandina Island to visit Cabo Douglas for a marine iguana dive. For underwater viewing of marine iguanas as well as Galapagos Penguins, flightless cormorants, more green sea turtles, sea lions and horn sharks, Cabo Douglas is a must do. But be warned, the water here can get pretty chilly. Our coldest dive of the trip was at Punta Vincente Roca, off the western side of Isabela Island, where water temps plunged to about 16 C (low 60 degrees). Our goal at the site was mola mola (ocean sun fish). The site's steep wall is reputed to be a favorite place to see these bizarre creatures. We didn't run into one, but the dive was not a loss as we had a great fly by from a large school of golden cownose rays.
Large school of yellowtail grunts.
On the way back to port, we hit Cousins Rocks near Bartolome. This site is a large volcanic pinnacle awash in marine life, including large schools of barracuda, eagle rays, sea lions and sea turtles. Also interesting was a unique variety of black coral growing on its the more vertical profiles. If you allow time to search the corals, there are opportunities for finding longnose hawkfish, frogfish and seahorses among the branches.
Touring the Islands of Evolution
The volcanic slopes of Bartolome Island make for dramatic landscape photos.
In addition to serving as dive platforms, the Sky's launches are used to cruise the shorelines and rock outcroppings, which are home to penguins, flightless cormorants, marine iguanas, sea lions, blue footed and Nazca Booby birds, magnificent frigates and Noddy Terns. There are also a limited number of opportunities for land excursions. The Galapagos Park Authority sets the rules for land tours conducted by liveaboard dive boats, which are usually confined to Bartolome Island. This tour lacks the wildlife you would expect to see in the Galapagos, however, the climb to the top of the island's volcanic shoreline and hillside offers a breathtaking view with its own brand of raw beauty.
A shore excursion to the Highlands of Santa Cruz to see the island's indigenous species of Galapagos Tortoises in their natural environment is often arranged for guests on the Galapagos Sky.
During the Sky's return back towards port on Saturday, an additional land tour is generally offered for a visit to see the Santa Cruz's indigenous species of Galapagos Tortoises in their natural environment. Once back in San Cristobal, a final morning land excursion is provided which includes a visit to the Interpretation Center where for a presentation of some of the more interesting natural and human history of the Galapagos. Afterwards, take a walk through town before going back to the airport for late-morning departure.
Diving Season in the Galapagos
There is no such thing as an "off season" when diving in the Galapagos, though there are some seasonal differences both in water conditions and the abundance of certain species. January through May brings warmer and often clearer waters, along with a greater number of manta rays. June is peak season for schools of scalloped hammerheads, and the cooler water from July through November attract more whale sharks.
The article was originally written for the blog page on Caradonna Dive Adventures website.
Ocean Arts, Inc. provides the content creation services for Caradonna Dive Adventures Travel website and blogsite, as well as an active part in their social media campaigns in facebook.
Diving the Galapagos Islandseagle raysFeatured PostsGalapagos IslandsGalapagos SkyGalapagos tortoisegreen sea turtleshammerhead sharksLive aboard dive yachtMarine iguanasOgcocephalus darwiniRed-lipped batfishschooling hammerheadsScuba Divingsilky sharkswhale sharks


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Secret disservice
Robert Kaiser
ONE OF THE MOST IMPORTANT DECISIONS the bishops at the Second Vatican Council (1962-65) made was their refusal to go along with the secrecy that Vatican officials tried to impose upon them. The Vatican bureaucrats of the Roman Curia had long been used to the notion that they knew what was best for the pope's "subjects." The subjects needed only to pray, pay, and obey.
Instead, the bishops took their cues from Blessed Pope John XXIII, who believed that power is not to dominate but to serve. If they were going to serve the people, they concluded, they would have to make the people privy to what they were doing at this council, which wrote a charter that would give the church back to the people. Journalist John Cogley probably summed up the council best with one of his "Poems on Postcards" in America magazine:
Who Is the Church?
And so the giants of the council— Cardinals Leo Josef Suenens, Julius Döpfner, Josef Frings, Bernard Alfrink, Franz König, Augustin Bea, and the Melkite Patriarch Maximos IV— started leaking their speeches to the press. Breaking the rule of secrecy at that time seemed like a deliberate affront to members of the Roman Curia. But it wasn't only the rule-breaking that bothered the Vatican bureaucrats. The leakers were also giving us an inside look at a process that helped demythologize the church, and diminish curial power as a result.
For more than a month the bishops were locked in argument over whether to have the Mass in Latin or in the vernacular— the everyday languages of the people. As we overheard the pros and the cons, we realized that the church of God was pretty darned human. The church's pyramidal structure— God telling the pope, the pope telling the bishops, the bishops telling the priests, the priests telling the nuns, and the nuns telling us— just collapsed.
During the council's four sessions, many of the church's unnecessary rules also went kerplop. We stopped thinking, for example, that the church could send us to hell for eating a hamburger on a Friday. Instead, we began to focus on who we are and what we are here to do: trying to establish Christ's reign of justice and peace, here and now, on Earth, and, this way, obtain salvation. The Mass was no longer a thing in itself. The Liturgy of the Word and the Liturgy of the Eucharist compelled us to go out and change the world.
All that should have helped create a new kind of people's church, but a funny thing happened on the way to the 21st century. Members of the Roman Curia took the power back and bound it up with the glue of secrecy.
Over the past 22 years, we have seen 21 synods— meetings of bishops from various parts of the world— in Rome. In continuation of Vatican II, they were supposed to bring about a measure of democracy, but the synods were declared secret on the grounds that bishops who came to Rome were "accountable to no one but the Holy Father, and the Holy Father accountable to no one but Jesus. The Coca-Cola Corporation doesn't invite the press into its board meetings."
The quote comes from Belgian Cardinal Jan Schotte, who is in charge of the synod process. It was his answer to my asking him at a news conference to provide members of the Vatican press corps with a live TV feed of the synod's deliberations last October.
He seemed momentarily stunned when I suggested that the church shouldn't take its cue from Coca-Cola but from the gospel. If the Holy Father wants to be accountable to Jesus, I said, he should remember that in Matthew 25 Jesus identified himself with the poor and those who didn't have enough to eat. If the synod's deliberations were for the people, then the people needed to know about them. If they didn't know, then they were poor and deserved to be fed.
Schotte didn't know how to answer that. Later, after the news conference, he asked me if I had anything to do with a one-page story in Newsweek about the consistory of cardinals last May. He wondered how Newsweek could give such a detailed report on an event that was closed to the press. I said I was amazed myself, because the pope's own press chief, Joaquin Navarro-Valls, had tried so hard to cover it up. But Navarro-Valls' move was trumped by a few Vatican reporters who succeeded in finding cardinals— like Roger Mahony of Los Angeles, Theodore McCarrick of Washington, and Godfried Daneels of Brussels— who were happy to give us copies of their talks.
Only a week before, I had written an open letter to Navarro-Valls, complaining that his press briefings were thin and sometimes even misleading and asking him what he was trying to hide. I pointed out that the Holy Father had called the cardinals to Rome "to present their ideas for a new evangelization," which means finding new ways to bring people the Good News.
"If this news is so good," I wrote, "why conduct your discussions about it in secret? Or is the church preparing to launch a new kind of stealth gospel?" I suggested that Navarro-Valls was captive to those curial officials who feel they needn't tell anyone anything except what they choose to parcel out. "Are we talking about a power problem here?" I asked. Navarro-Valls didn't respond.
Now, all unwitting, Schotte was answering my question about power. He told me that American presidents have to be accountable to the people, because "in the United States, the people are sovereign. In the church, the pope is sovereign. We cannot do anything to destroy his soverneignty."
Now it was my turn to be speechless. As someone who became fully formed in the faith at Vatican II, I could not believe a high Vatican official was still speaking of the pope as an absolute ruler, much less say he is accountable only to Jesus.
Other than Schotte, I cannot find many in the Vatican who hold that view, in theory at least. Cardinal Joseph Ratzinger, the chief defender of the faith, is fond of using the concept of communio to describe the family of the church, which he says is supposed to model the perfect communication that goes on between the three divine persons of the Trinity itself. No secrecy there. Archbishop John Foley, who heads the Pontifical Council for Social Communications, has written beautifully about the church's need to follow the communications model of Jesus, who insists on "candor and truthfulness in others, while condemning hypocrisy . . . and any kind of communication that was perverse." Foley quotes Pope John Paul II: "We want to make the church into a house of glass." That doesn't sound like secrecy either. In theory.
In practice, however, the official church, in Rome at least, falls far short of Ratzinger's communio. Ratzinger himself stays aloof from press inquiries, Navarro-Valls has issued an order that no one inside the Vatican is to speak to the press without his prior approval, and, while the pope seems to like the house-of-glass metaphor, Schotte is still going around and pulling down all the shades.
Sometimes the official church seems to do its darnedest to cover up for priests in trouble. Last summer, my colleague Rory Carroll, a correspondent in Rome for The Guardian in England, took a trip to Signa, a village outside Florence, to hear an African priest, Father Athanase Seromba, explain to parishioners why the United Nations Tribunal for Rwanda sought his extradition on charges of genocide.
Seromba, 38, is alleged to have participated in the 1994 extermination of 800,000 minority Tutsis by the ruling Hutu tribe. Survivors claim the priest, a Hutu, herded up to 2,500 Tutsi parishioners into his church at Nyange before ordering two bulldozers to crush them in one of the genocide's most notorious bloodbaths.
Carroll didn't find Seromba in Signa. Neither did U.N. officials who had come looking for him. The Italian government refused to hand him over. A church spokesman, Riccardo Bigi, said the hierarchy had provided a hiding place in Tuscany to help Seromba escape media attention. "We know where he is but would rather not say where. He will spend a few days in peace to avoid curious journalists. I don't know when he will return."
Sadly, as numerous recent revelations of scandals in the United States as well as other countries have made clear, the official church has also frequently covered up for priests accused of sexual abuse.
The crux of the problem is that the official church simply isn't accountable— and won't be until a pope will take the practical steps to make it accountable. One good way to start: Renounce this sovereignty dodge. Another way: End the culture of secrecy.
Robert Kaiser is a contributing editor of Newsweek in Rome and the dean of the Vatican press corps. He recently published his memoir, Clerical Error: A True Story (Continuum).


These thoughts ran in Cathy's mind as her eyes took the passing clouds through the small window of the aircraft. Cathy, short for Catherine, was a young college going girl from Lisbon, Portugal. She was a beautiful girl, of creamy complexion, slim and of medium height. But where here face emitted exquisite and delicate features, her eyes kind of betrayed the pain and the fear that lurked in her mind.
She turned to look at her companion, Sanjose, her fellow classmate and her boyfriend. Sanjose was of the same age as Cathy. Tall, dark and with sharp features, he was the cynosure of girls' attention. But to him, Cathy was everything. Little did he realize that 3 weeks ago when Cathy had first popped the question to him to accompany her and the students of her University on their annual college trip to Goa in India instead of some traditional place in Europe, his nonchalant yes answer would be so readily accepted by her.
Cathy had always wanted to visit Goa but had dared not venture alone. Her parents wouldn't have allowed it. It was only at Sanjose's behest, her parents had agreed to let her go to visit her ancestral place. And in no time, their classmates too had readily agreed to make this trip. For the students, this was a novel idea to visit the land that their forefathers had ruled over centuries ago. The land they had learnt about in high school.
Goa, one of the smallest states of India, is located on the western coast of the country facing the vast Arabian sea. Till 1961, Goa had been a Portuguese colony since 1510 when Afonso de Albuquerque captured the island state and brought it under the Portuguese rule. Soon the land of Goa turned into a great trade center under the Portuguese.
In the years to come, various Viceroys ruled Goa and the locals managed to live without much of negative repercussions though there were some strict regimes to follow which the locals bravely followed. But at times, the Portuguese did witness some revolts from certain sections of the locals who demanded freedom. However, their actions were quickly and harshly curtailed by the Portuguese authority.
But in 1925, with the rise of power of a dictator in Portuguese, lots of new and strict laws and bans came into force. The locals soon started demanding collectively for a free Goa but their actions and pleas went unheard until 1961 when the Indian Army liberalized it and brought it under its fold after years of peaceful negotiations with the Portuguese authorities had failed. Thus ended the Portuguese rule in Goa.
Cathy's thoughts were broken as the captain's voice boomed from the speakers, announcing that the aircraft will be landing in about 30 minutes on the Indian soil at the Dabolim Airport. She kind of felt elated but at the same time she felt some apprehension.
She peered outside to look at the vast Arabian Sea spread out below. It looked so majestic in the shimmering sunlight. In the distance, she could see the land as it loomed nearer and nearer as the aircraft made a slow descent. Her breathing became heavy. She was nearing her goal.
The aircraft made a smooth landing at the Dabolim airport and slowly taxied itself to a stop in front of one of the terminals. The group of 20 students all bumbling with excitement, picked up their handbags and rushed excitedly to the exit ahead of the other passengers.
Cathy remained seated, eyes closed trying to savor the uncanny feeling that she felt. She then took a deep breath to ease her heavy heartbeats. Letting out a huge sigh, she opened her eyes and slowly pulled herself up from her seat. She pulled open the overhead cabinet and dragged her handbag out and with baited steps, walked to the exit.
She slowly peered outside and watched the airport with anticipation. This was the modern world. This wasn't what she had expected but then this was the airport in the heart of the city. And her destiny lay on the outskirts of the city where there was hardly much of human dwellings. Once again, taking a deep breath, she started down the staircase and then took that final step to touch the ground. Finally, she was standing on the land of her ancestors.
She stood still, closed her eyes for a brief second and then bent down. As her fingers touched the ground, she opened her eyes and brought her hand to her lips to kiss it. This was it… her motherland. Her dreams were unraveling. And then she heard the soft laughter that's been ringing in her ears since she was a baby. She closed her eyes again for a second and the laughter slowly diminished. She was getting closer to understanding the mysterious laughter… the mysterious words that has been haunting her since she was a baby.


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Home Efficiency Startup Consulting
Four Proven Ways to Reduce the Carbon Footprint of the Food You Serve Five Best Budget Green Startup Business Opportunities to Start Right Now
With Election 2010 Behind Us, Where Do Progressives Turn?
By Scott Cooney On March 2, 2012 · Leave a Comment · In Policies of Sustainability
With oil money behind much of the Tea Party's success, GreenBusinessOwner.com argues that the only way to move society forward is to break our addiction to oil. The beauty is that politics are largely irrelevant, and we don't have to wait for election night 2012 to participate once again.
Election 2010 is over, and the Tea Party-backed GOP picked up a handful of seats in the U.S. Senate in addition to retaking the U.S. House of Representatives. It's a frustrating setback for progressives after feeling like the country had finally grasped the ineffectiveness of the GOP's borrow-and-spend philosophies, no-bid contracts with Halliburton, and "Can't do" attitude on energy efficiency, independence from foreign oil, and renewables. Here, I argue that turning our collective energy to the green economy may be our most powerful way of fighting back against corruption, deception, and deliberate manipulation from some well-heeled funders of the Tea Party madness.
Much like the overwhelming turnout that propelled the Democratic party to a sweeping victory in 2008, the 2010 tide that swept the GOP to a majority in the House of Representatives and several Senate seat victories (though not a majority) was fueled by anger. In 2008, it was anger over the loose regulatory environment that led to the collapse of the financial industry. In 2010, it was anger over….President Obama?
Many on the left didn't grasp the power behind the Tea Party and its anger until it was too late. But where did the hatred and animosity actually come from?
Was it health care reform? The fact that we can never again be denied coverage due to a pre-existing condition? Or that we can't simply be dropped after years of faithfully paying our premiums once we get sick? Death panels, where Tea Partiers really believed the official party line that Grandma would be murdered by President Obama?
Was it deficits? Well, sure, deficits aren't good, but they're also nothing new. Ronald Reagan started the deficit fiesta in the 1980's by cutting taxes and increasing military spending. His rival in the GOP primary in 1980, George H.W. Bush, called it voodoo economics, but Reagan was able to convince Americans they could have their cake and eat it, too. After all, it's popular to cut taxes. It's also popular to increase government spending. Unfortunately, as we've found since the 1980's, any politician that tries to point out the obvious reality check here becomes wildly unpopular very quickly.
The real answer of where the anger came from is oil. And not from the Gulf spill, either.
You may never have heard of Koch Industries. Mostly an oil refining business, it's the second largest privately held company in the U.S. In addition to oil, KI has brands including Brawny paper towels, Dixie cups, Georgia-Pacific lumber, and Stainmaster carpet (make a mental note of these, and promise me you'll never buy them again). The two brothers who own Koch Industries are ranked among the wealthiest Americans, and of course, Obama
's suspension of the Bush tax cuts for the wealthiest Americans probably didn't make them happy.
The Koch brothers have poured money into politics. It is widely believed that these two brothers were the primary funders behind the Tea Party and its angry mobs. The Koch brothers and two Texas oil companies were also behind the failed attempt to bring down California's landmark clean energy and green jobs law (AB 32), by funding a dirty campaign (Proposition 23, California, 2010) that would have crippled the clean tech sector had it passed. Fortunately, California voters saw through the deception and Proposition 23 did not pass.
So let's get back to the question at hand: where do we stand now? In 2008, a tremendous hope criss-crossed the nation that President Obama and a progressive congress would be able to create a clean energy campaign with legs. The possibility that Obama and a Democratic Senate can get any clean air, green jobs, or clean energy legislation past a Republican dominated House of Representatives is doubtful.
While what happens on the political stage in Washington is obviously a piece of the picture, it's only that: a piece. The bottom line is that the green economy is coming, and perhaps the most effective way we can move the country (and the world) toward a clean, healthy future is to vote with our dollars.
WE MUST BREAK OUR ADDICTION TO OIL.
Consider the facts:
For the past few years, reversing a century-long trend, the number of small, family owned farms in the U.S. actually increased
Organic food sales continue to grow, despite a slumping economy (up 6% last year)
Clean tech became the number 1 patent classification last year, surpassing IT and biotech
The number of farmer's markets in the United States continues its exponential growth: from 1,755 in 1994 to 5,274 in 2009
California recently approved 4,143 new megawatts of solar thermal development
You can lease a brand new, all electric Nissan Leaf for $200 per month
The cost of wind energy continues to come down all the time, and coal, natural gas, and oil will only get more expensive
Last year, green building was the only building sector that showed any signs of life. With energy efficiency a key priority of most companies (and thanks to Executive Orders by President Obama, also the Federal Government), expect LEED buildings to become the industry standard within a fairly short time horizon
Big companies are pouring money into sustainability. GE's ecomagination challenge and Philips Livable Cities Award highlight the new economy approach to creating a sustainable world and making money at the same time.
I could go on, but suffice it to say, none of these things will stop just because Republicans now have control of one half of the Legislative branch of the U.S. government.
My conclusion, my hope, and my ask of you is that you take some time to evaluate your purchases. Plastic comes from oil. Gasoline comes from oil. Can you cut your consumption of both? If you can, you take money away from Koch Industries. It's really that simple.
The green economy is coming, and there is nothing any well-heeled anti-government political backers can do about it.
Tagged with: Election 2010 • Koch Industries • Oil money • Tea Party
Scott Cooney
Scott Cooney (twitter: scottcooney) is an adjunct professor of Sustainability in the MBA program at the University of Hawai'i, green business startup coach, author of Build a Green Small Business: Profitable Ways to Become an Ecopreneur (McGraw-Hill), and developer of the sustainability board game GBO Hawai'i. Scott has started, grown and sold two mission-driven businesses, failed miserably at a third, and is currently in his fourth. Scott's current company has three divisions: a sustainability blog network that includes the world's biggest clean energy website and reached over 5 million readers in December 2013 alone; Pono Home, a turnkey and franchiseable green home consulting service that won entrance into the clean tech incubator known as Energy Excelerator; and Cost of Solar, a solar lead generation service to connect interested homeowners and solar contractors. In his spare time, Scott surfs, plays ultimate frisbee and enjoys a good, long bike ride. Find Scott on Google Plus
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Stem Cells are cells capable of self renewal and repair of degenerative or damaged areas of inflammation in our bodies like joints, discs, and tendons though there are multiple other uses being investigated today.
There are two types of Stem Cell therapy we offer. Adult Stem Cell therapy and Human Amniotic Membrane Umbilical Therapy. During your consultation we will go over each and select the safest and most effective one for you.
Adult Stem Cell therapy is typically the harvesting of your own stem cells derived from your bone marrow, adipose, or fat. Research suggest that these stem cells have a high success rate at rejuvenating damaged tissue and joints allowing our bodies to repair itself naturally.
Amniotic Membrane therapy (Amniox) is a different approach with the same end goal in mind. Amniotic membrane is harvested from approved donors at birth from the umbilical cord and placenta. It is prepared and cryopreserved under strict FDA guidelines. Once administered in the area it is able to pull your body's own Stem cells into the area to start the rejuvenation and regeneration process. Due to its ability to modulate inflammation there is a lower risk associated with rejection. By reducing inflammation and rejection risks you stand to reap the rewards of your Stem cell program safer and sooner.
Stem Cells follow a signaling process from our bodies. Once they are injected into a bone, hip, or cartilage they will begin to develop in that area. Cells delivered into a joint or disc will develop into cartilage where as cells delivered into a bone will develop into bone cells. After all our bodies desperately want to self-heal. This is the ultimate natural healing process to date.
Stem cells are naturally occurring in our body from the time we are born until the time we die.
LifeXMD is compromised of a group of highly efficient and experienced Physicians and medical professionals who are passionate about helping and healing our clients through alternative and preventative medicine. For many years we have pride ourselves in being leaders in the preventative and alternative medicine field. After all you cant put a price on quality of life.
Are there cancer risks associated with either Amniotic or Adult Stem Cell therapy?
Absolutely not! There is no evidence to support any claims of cancer issues.
At this time insurance does not cover either of these regenerative therapies. However, we do find our pricing to be very competitive and affordable in many cases. The best part is there is very little if any down time or missed work from a treatment.
The cost varies based on many things. What type of therapy best suited for you? What level of treatment you need? The amount of sites in need of treatment? You can call us at 248-953-9529 to setup a complimentary consultation with one of our Personal Care Coordinators who will discuss if you are a potential candidate.