The county attorney is the chief prosecutor for the district, representing the government in criminal cases. The attorney investigates crimes, decides whether or not to bring charges against suspects, negotiates plea bargains, and tries cases before juries or judges. The attorney may also serve as legal counsel for the government.


This term, we will be learning about healthy eating and the importance of having a balanced diet. We will study the different food groups and begin to identify their different roles in our bodies.
For your homework, we would like you to record any food or drink that you consume on Saturday, Sunday, Monday and Tuesday. Please record this using the template we have provided. This information will be used in our second Science lesson so please make sure your handwriting is clear.


We left Alcudia, Majorca on 19th July and headed over to Mahon in Menorca. The first few hours we had to motor as there was very little wind but by midday the wind was about 10 knots or so and now a south easterly gave us enough wind to be able to switch off the engine and sail. After 10 and a half hours we dropped the anchor in the small and only anchorage in Mahon.
All great, out the way in the very shallow water, which we can do as we only need 1.1metres to float. The wind had got up and was blowing about 25 knots but that is not normally a problem. All OK until 3.30am and then an alarm rings out. S**t it's the anchor alarm, we must be dragging. Oh boy, yes we were. We hit the boat behind with our bowsprit and managed to pull his anchor out and so he was now dragging too and then there were three of us all together. Ian sprung into action and managed to get us out the way quickly and so we dropped the anchor again. We waited to see if all was ok but after 15 minutes we were dragging again. Up the anchor comes and then dropped it again, it still would not set, this is a Rocna anchor (we only bought it in Gibraltar in October) that everyone raves about. We have another anchor, an aluminium Spade, which we have for occasions when you want an anchor to hold you in one direction so it's dropped off the back of the boat. So out this came but we dropped it over the bow as this was going to be our primary anchor for the night. The Spade set with no problem whatsoever. All this in the pitch black. Ian and I took a turn to sit on anchor watch we weren't taking any chances.
Before the excitement of the night before we had already decided to go into one of the marinas in Mahon for the following night as we wanted to do a final stock up, fill up with water and fuel before our trip across to Sardinia. We'd been told it was not so easy to get provisions and water plus the diesel was a lot more expensive at €1.75 a litre. The marina was a few pontoons with one electric supply and one water supply on each of the pontoons so it was a bit of a fight to get use of them, all this for the princely sum of €83! We met up with our Mahe Mates, Karen and Ronnie on CopyCat who we'd last seen 9 months before in Faro, Portugal. It was great to see them after all this time. It was also reassuring being moored up after the antics of the previous night.
We'd had rain which had lots of red sand in it so the boat was looking the dirtiest it had for a long time. Before we left the marina we gave the boat a clean and she was looking lovely again. We left shortly after to go back to the anchorage. A couple of hours later the clouds started building and yes you've guessed it rained and not just a little it was torrential and whilst raining the sun had the cheek to show its face, like it was smirking at us. Thankfully no red sand, so at least she stayed clean and we did get a rainbow.
The guy, Ingmar, whose boat we had hit, was still there so we invited him and his partner, Elvyra over for a drink. Ingmar had been very understanding about our dragging and he had managed to polish the mark out of his boat and there was no other damage. We discovered they will also be in Licata for the winter so we will see them again.
The time had come to say Adios to Espana and head off to Sardinia. We'd seen a lot of different parts of Spain and it's a fabulous country, we will look back fondly at our time there.
"one of the best sails in years".
Sunset on trip from Mahon to Alghero 23.7.18.
Sun setting behind the clouds 23.7.18.
We continued to sail through the night. Eventually by 5.30am we had to switch on the engine as the wind had died so much. We'd been under sail for 22 hours. We finally arrived in Alghero at 8am on Tuesday 24th July after 26 hours, so a pretty speedy crossing and we only burnt 8 litres of diesel. We averaged 7.5 knots and covered 190 miles. We dropped the anchor outside the harbour wall and hopped into bed to catch up on some sleep.
BTW I FORGOT TO MENTION ….. in my last blog the mini tsunami. This occurred during our time in Alcudia. We did notice the strong winds, so much so that we didn't leave the boat that day, in particular because we had had problems setting our anchor. Anyhow we didn't actually notice it, the only thing that was odd was that the boat at one stage didn't swing into the wind, which is the norm. It transpired that some of the restaurants on the beach front were flooded and there was a boat in the harbour that we saw on YouTube looked like it was on an ice rink as it skidded sideways on the water, but a bit of a non event for us, thankfully.
This entry was posted in 2018 - Spain on August 12, 2018 by cuffy40.


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text:
\section{Introduction}
 The Jones-Wenzl idempotent, discovered by V. F. R. Jones in \cite{Jon1},  is an idempotent element in the Temperley-Lieb algebra. Originally, it was described as a certain symmetrizer using the Artin braid group and the projection to the Temperley-Lieb algebra.  In the late 1980's, H. Wenzl in \cite{Wen} discovered a recursive formula to the Jones-Wenzl idempotent. This formula is now widely used as the definition, see \cite{Lic}.

The Jones-Wenzl idempotent has played a significant role in defining quanum invariants of knots and $3$-manifolds. For example, W. B. R. Lickorish's Kauffman bracket skein theoretic approach to the Witten-Reshetikhin-Turaev $3$-manifold invariants in \cite{Lic1} uses a linear combination of the trace (closure) of the idempotent elements along a framed knot or link. Similarly, the colored Jones polynomial quantum knot invariant is defined by taking the trace of the $n^{th}$ Jones-Wenzl idempotent along a $0$-framed knot in $S^3$, see \cite{Le, PBIMW}. These idempotent elements are also used to decorate the edges of a tetrahedra to obtain the quantum $6j$-symbols that are used in the definition of the Turaev-Viro quantum $3$-manifold invariants, see \cite{TV}.

The Jones-Wenzl idempotent has been a vital tool for simplifying computations and proving theorems in knot theory. An example of this is seen in X. Cai's proof of a closed formula for the Gram determinant of type $A$ in \cite{Cai} and a closed formula for its generalization in \cite{BIMP}. In fact, this paper was conceived by needing properties of the Jones-Wenzl idempotents when it is closed in the twisted $I$-bundle of the M\"obius band in hopes to take a similar approach to \cite{Cai} and \cite{BIMP} to prove a closed formula for the Gram determinant of type $Mb$.

In Section \ref{IntroJW} we introduce the original definition of Jones-Wenzl idempotents and also the RKBSM of the twisted $I$-bundle of the M\"obius band, then in Section \ref{MBcrossingless} we give an illustration of the two different models of the M\"obius band as well as the antipodal properties of the crosscap. In Section \ref{JWMB} we prove many corollaries to the trace of Jones-Wenzl idempotents intersecting or surrounding the crosscap, then we end with a formula for when $n-1$ curves from $f_n$ are closed around the crosscap and the last arc is closed through the crosscap.
\subsection{Acknowledgements}

This work was supported by the Australian Research Council grant DP210103136.

	\section{Introduction to Jones-Wenzl idempotents}\label{IntroJW}

The first formal definition of the Temperley-Lieb algebra, denoted by $\mathit{TL}_n$, was given by R. J. Baxter in \cite{Bax2} while describing the work of physicists  N. Temperley and E. Lieb in \cite{TL}.  Jones independently introduced $TL_n$ in \cite{Jon1} while working on von Neumann algebras.

\begin{definition} \label{TEMPERLEY:tln}
Let $R$ be a commutative ring with unity and $d \in R$. Let $n \in \mathbb{N}$ be fixed, then the $n^{th}$ \textbf{Temperley-Lieb algebra}, $\mathit{TL}_n$, is defined to be the unital associative algebra over R with generators $ e_1, \dots , e_{n-1}$, identity element $1_n$,
and relations
\begin{enumerate}
    \item $e_i e_{j} e_i = e_i \text{ for } |i-j|=1$,
    \item $e_i e_j = e_j e_i \text{ for } |i-j|>1$,
    \item $e_i^2 = d e_i$.
\end{enumerate}
\end{definition}

 L. H.  Kauffman in \cite{Kau2}, motivated by utilizing the Kauffman bracket, considered the Temperley-Lieb algebra over $R=\mathbb{Z}[A^{\pm1}]$, where $A$ is an indeterminate and $d = -A^2 -A^{-2}$. He then constructed a graphical interpretation using tangles.

We will consider an \textbf{$n$-tangle} to be a rectangular shaped disk with $n$ marked boundary points on the left (input points) and $n$ marked boundary points on the right (output points). Kauffman's graphical interpretation of the Temperley-Lieb algebra is obtained from the basis of crossingless tangles where the identity element corresponds to an $n$-tangle with $n$ parallel arcs in which each $i^{\mathit{th}}$ input point is connected to the $i^{\mathit{th}}$ output point, and each $e_i$ corresponds to an $n$-tangle
that has one input and one output cap on the $i^{\mathit{th}}$ and $i+1^{\mathit{th}}$ position as illustrated in Figure \ref{TEMPERLEY:graphical}. For simplicity we will label an arc by $n$ to denote $n$ parallel arcs as shown in Figure \ref{TEMPERLEY:fig1}.

\begin{figure}[ht]
\centering
\begin{subfigure}{.49\textwidth}
\centering
$\vcenter{\hbox{
\begin{overpic}[scale = .5]{tnid}
\put(53, 48){$n$}
\end{overpic} }} $
\caption{Identity element.} \label{TEMPERLEY:fig1}
\end{subfigure}
\begin{subfigure}{.49\textwidth}
\centering
$\vcenter{\hbox{
\begin{overpic}[scale = .5]{tnei}
\put(33, 20.5){$n-i-1$}
\put(45, 76){$i-1$}
\end{overpic} }} $
\caption{$e_i$.} \label{TEMPERLEY:fig2}
\end{subfigure}
\caption{The graphical interpretation of $\mathit{TL}_n$.}\label{TEMPERLEY:graphical}
\end{figure}

\begin{definition}
The \textbf{$n$-tangle algebra} is an $R$-module with basis elements consisting of $n$-tangles where multiplication of two $n$-tangles is defined by identifying the right side of the first $n$-tangle to the left side of the second $n$-tangle while respecting the boundary points and by letting any resulting trivial curve be denoted by $d$, see Figure \ref{JONESWENZL:mutip} for an illustrative example. Kauffman's diagrammatic interpretation of the Temperley-Lieb algebra, also known as the \textbf{diagrammatic algebra}, is a subalgebra of the $n$-tangle algebra. It is generated by tangles with no crossings where homotopically trivial curves are denoted by $d \in R$.
\end{definition}

\begin{figure}[ht]
$$e_3 e_3 =\vcenter{\hbox{\begin{overpic}[scale=.5]{tne3e3.pdf}
\end{overpic}}} = d \vcenter{\hbox{\begin{overpic}[scale=.5]{tne3.pdf}
\end{overpic}}}= d e_3.$$
\caption{An illustration of  multiplication.}\label{JONESWENZL:mutip}
\end{figure}

\begin{theorem}\cite{Kau2}
The diagrammatic algebra is isomorphic to $TL_n$ and can be thought of as a diagrammatic interpretation of it.
\end{theorem}

We will give Jones' constructive definition of the Jones-Wenzl idempotent by using the relative Kauffman bracket skein module (RKBSM) and the Artin braid group before introducing Wenzl's recursive formula. In doing so, we will first introduce the RKBSM and emphasize that the RKBSM of the twisted $I$-bundle of the M\"obius band and the RKBSM of $\textit{Ann} \times I$ are different modules even though the two manifolds are homeomorphic. This will give us motivation to study the Jones-Wenzl idempotent in the twisted $I$-bundle of the M\"obius band. Furthermore, the corollaries and proposition  in the last section will show that there are distinct differences when simple closed curves intersect the crosscap.

\begin{definition}
Let $M$ be an oriented $3$-manifold and  $\{x_i\}_{i=1}^{2n}$ be the set of $2n$ framed points on $\partial M$. Let $I=[-1, 1]$, and let $\mathcal{L}^{\mathit{fr}}(2n)$ be the set of all relative framed links (which consists of all framed links in $M$ and all framed arcs, $I \times I$, where $ I \times \partial I$ is connected to framed points on the boundary of $M$) up to ambient isotopy while keeping the boundary fixed in such a way that $L \cap \partial M = \{x_i\}_1^{2n}$. Let $R$ be a commutative ring with unity,  $A \in R$ be invertible, and let $S_{2,\infty}^{\mathit{sub}}(2n)$ be the submodule of $R\mathcal{L}^{\mathit{fr}}(2n)$ that is generated by the Kauffman bracket skein relations:

\begin{itemize}
    \item [(i)]$L_+ - AL_0 - A^{-1}L_{\infty}$, and
    \item [(ii)] $L \sqcup \pmb{\bigcirc}  + (A^2 + A^{-2})L$,
\end{itemize}
where \pmb{$\bigcirc$} denotes the framed unknot and the {\it skein triple} $(L_+$, $L_0$, $L_{\infty})$ denotes three framed links in $M$ that are identical except in a small $3$-ball in $M$ where the difference is shown in Figure \ref{KBSM:skeintriple}.

Then, the \textbf{relative Kauffman bracket skein module} (RKBSM) of $M$ is the quotient: $$\mathcal{S}_{2,\infty}(M, \{x_i\}_1^{2n}; R, A) = R\mathcal{L}^{\mathit{fr}}(2n) / S_{2,\infty}^{\mathit{sub}}(2n).$$
\end{definition}

\begin{figure}[ht]
\centering
\begin{subfigure}{.25\textwidth}
\centering
$\vcenter{\hbox{\includegraphics[scale = .35]{cross.pdf}}} $
\caption{$L_+$.} \label{KBSM:Lplus}
\end{subfigure}
\centering
\begin{subfigure}{.25\textwidth}
\centering
$\vcenter{\hbox{\includegraphics[scale = .35]{crossA.pdf}}} $
\caption{$L_0$.} \label{KBSM:Lzero}
\end{subfigure}
\centering
\begin{subfigure}{.25\textwidth}
\centering
$\vcenter{\hbox{\includegraphics[scale = .35]{crossB.pdf}}} $
\caption{$L_{\infty}$.} \label{KBSM:Linfinity}
\end{subfigure}
\caption{The skein triple.} \label{KBSM:skeintriple}
\end{figure}

\begin{theorem}\label{rkbsmsib}\cite{Prz}
Let $F$ be a surface with $\partial F \neq \varnothing$. If $F$ is orientable then let $M = F \times \ I$ , otherwise let $M = F \hat{\times} I$. Let all $\{x_i\}_1^{2n}$  be marked points that lie on $\partial F \times \{0\}$. Then $\mathcal S_{2, \infty}(M, \{x_i\}_1^{2n}; R, A)$ is a free $R$-module whose basis is composed of relative links in $F$ without trivial components. When $n=0$, the empty link is also a generator.
\end{theorem}

J. H. Przytycki's corollary to Theorem \ref{rkbsmsib} explicitly details the differences between the RKBSM of $\mathit{Ann} \times I$ and the RKBSM of $Mb \hat{\times} I$ even though both manifolds are homeomorphic to the solid torus.

\begin{corollary}\label{rkbsmcor}\cite{Prz}

\begin{enumerate}
    \item $\mathcal{S}_{2,\infty}(\mathit{Ann} \times I, \{x_i\}_1^{2n}; R, A)$ where $\{x_i\}_1^{2n}$ are located in the outer boundary component of the annulus is a free $R[x]$-module with $D_n = \binom{2n}{n}$ basis elements, where $x$ denotes the homotopically nontrivial curve in the annulus and $d=-A^2-A^{-2}$ denotes the homotopically trivial curve in the annulus. The basis is the set of all crossingless connections in the annulus with no trivial components or boundary parallel curves.  \\

    \item $\mathcal{S}_{2,\infty}(Mb \hat\times I, \{x_i\}_1^{2n}; R, A)$ is a free $R$-module. The standard basis contains an infinite number of elements of the form $bz^i$, $bxz^i$ for $i \geq 0$, where $x$ denotes the simple closed curve that intersects the M\"obius band once, $z$ denotes the boundary parallel curve of the M\"obius band, and $b$ is an element in the set of crossingless connections in the M\"obius band with no trivial components or boundary parallel curves for which the arcs do not intersect the crosscap. The rest of the elements in the standard basis are from a finite number of crossingless connections consisting of a collection of $n-k$ arcs for $0 \leq k <n$ that non-trivially intersects the crosscap. Among the finite collection there are $\binom{2n}{k}$ crossingless connections that intersect the crosscap $n-k$ times.
\end{enumerate}

\end{corollary}

\begin{definition}The \textbf{Artin braid group} is defined by the following group presentation:
$$ B_n = < \sigma_1, \dots, \sigma_{n-1} ; \sigma_i \sigma_j = \sigma_j \sigma_i \text{ for } |i-j| >1,
\sigma_{i\pm1} \sigma_i \sigma_{i\pm1} = \sigma_i \sigma_{i \pm 1} \sigma_i>. $$
\end{definition}

The Artin braid group can be interpreted using $n$-tangles where elements of $B_n$ are positive braids. More precisely, an element in $B_n$ can be represented as an $n$-tangle with positive crossings such that the boundary of each arc is attached to one input and one output point and when read from left to right each generator $\sigma_i$ corresponds to the positive crossing of the $i^{\mathit{th}}$ and $i+1^{\mathit{th}}$ arcs. That is, the $i^{\mathit{th}}$ generator element $\sigma_i$ is a positive transposition of the $i^{\mathit{th}}$ and $i+1^{\mathit{th}}$ arcs.  \\

Furthermore, there exists an epimorphism $p: B_n \to S_n$ from the Artin braid group to the permutation group that uniquely interprets a braid word. Let $p$ be defined by sending generators of $B_n$, $\sigma_i$, to the transpositions in $S_n$; $s_i = (i, i+1)$ for $1 \leq i \leq n-1$. For a permutation $\pi \in S_n$, let $b_{\pi}$ denote the unique minimal positive braid word such that $p(b_{\pi}) = \pi$.

\begin{definition}\label{JONESWENZL:Asymmetrizer}
Let $\mathbb{Z}[A^{\pm1}]$ denote the ring of Laurent polynomials in the variable $A$ and $\mathbb{Q}(A)$ denote the field of rational functions in the variable $A$; whose elements are functions of the form $P/Q$ where $P, Q \in \mathbb{Z}[A^{\pm1}]$.
We define an \textbf{unnormalized $A$-symmetrizer}, $F_n \in \mathbb{Z}[A^{\pm1}]B_n$,  by the following
$$F_n = \sum_{ \pi \in S_n} (A^3)^{| \pi |} b_{\pi}, $$
and the normalized symmetrizer, also known as the \textbf{$A$-symmetrizer} and denoted by $f_n \in \mathbb{Q}(A)B_n$, by the formula
$$f_n = \frac{1}{[n]_{A^4}!} F_n, $$

where $|\pi|$ denotes the minimal length of the permutation $\pi$ written as elementary transposition generators,  $[n]_{A^4} = 1 + A^4 + A^8 + \cdots + A^{4(n-1)} = \frac{A^{4n}-1}{A^4-1}$ and
$[n]_{A^4} ! = \prod\limits_{i=1}^{n} [i]_{A^4}$. \\
$F_n$ evaluated in $\mathcal{S}_{2,\infty}(D^2 \times I, \{x_i\}_1^{2n}; R, A) $ is an element in the Temperley-Lieb algebra and the normalization is chosen so that $f_n$ is an idempotent element in $\mathit{TL}_n$. The most recognized name for this $A$-symmetrizer is the \textbf{Jones-Wenzl idempotent}. We will denote this element as a square with $n$ strands entering and $n$ strands exiting, as shown in Figure \ref{JONESWENZL:jwfig} and $f_n$ will denote the Jones-Wenzl idempotent.
\end{definition}

\begin{figure}[ht]
$$\vcenter{\hbox{\begin{overpic}[scale=.35]{JW1.pdf}
\put(13, 35){$n$}
\end{overpic}}}$$
\caption{The Jones-Wenzl idempotent.}\label{JONESWENZL:jwfig}
\end{figure}

Wenzl's recursive formula uses the Chebyshev polynomial of the second kind.

\begin{definition}
The $n^{th}$ \textbf{Chebyshev polynomial of the first kind} is defined recursively by the initial conditions $T_0 (d)= 2, \  T_1(d) = d$ and Equation \ref{Chebyshevfirst kindEq}.
\begin{equation} \label{Chebyshevfirst kindEq}
T_n(d) = d T_{n-1}(d) - T_{n-2}(d).
\end{equation}

The $n^{th}$ \textbf{Chebyshev polynomial of the second kind} is defined recursively by the initial conditions $S_0 (d)= 1, \  S_1(d) = d$ and the same recursive relation as the first kind, $S_n(d) = d S_{n-1}(d) - S_{n-2}(d)$.
\end{definition}

When we substitute $d = -A^{2}-A^{-2}$, the Chebyshev polynomial of the first kind has the following closed formula
$$T_{n}(d) = (-1)^n(A^{2n}+A^{-2n}),$$
and the Chebyshev polynomial of the second kind has the following closed formula,denoted by $\Delta_n$,
$$\Delta_n=(-1)^n\frac{A^{2n+2}-A^{-2n-2}}{A^2-A^{-2}}=(-1)^nA^{-2n}[n+1]_{A^4}. $$

\begin{theorem}\cite{Wen} \label{JONESWENZL:wenzltheorem}
	A recursion formula for the $n^{\mathit{th}}$ Jones-Wenzl idempotent, $f_{n}$, is described in Equation \ref{JONESWENZL:wenzlrecursion}:
\begin{equation} \label{JONESWENZL:wenzlrecursion}
f_n  =
\vcenter{\hbox{\begin{overpic}[scale=.48]{JW5.pdf}
\put(9, 44){\fontsize{7}{7}$n-1$}
\end{overpic}}}
 - \frac{\Delta_{n-2}}{\Delta_{n-1}}
\vcenter{\hbox{\begin{overpic}[scale=.48]{JW6.pdf}
\put(4, 42){\fontsize{6}{6}$n-1$}
\put(91, 42){\fontsize{6}{6}$n-1$}
\put(48, 35){\fontsize{6}{6}$n-2$}
\end{overpic}}}.
\end{equation}

\end{theorem}

The following lemma can be obtained from Wenzl's recursive formula as discussed in \cite{Lic} or from the constructive definition of the Jones-Wenzl idempotent as detailed in \cite{PBIMW}.
\begin{lemma} \label{JONESWENZL:thmfnbasis}\cite{Lic}
\begin{enumerate}
\item[(a)] $(f_n-1)$ is an element of the algebra generated by $\{ e_i\}_{i=1}^{n-1}.$
\item[(b)] $e_i f_n = f_n e_i = 0$ for $1 \leq i \leq n-1$.
\item[(c)] $f_n f_n = f_n$.
\end{enumerate}
\end{lemma}

A direct application of the next corollary will be given in Section \ref{JWMB}.

 \begin{corollary}\label{JONESWENZL:corollarytrace}\cite{Lic} Let $\mathit{tr}_1(f_n)$ be obtained from $f_n$ by closing the top string in $f_n$ (see Figure \ref{JONESWENZL:trace}). Then  $$\mathit{tr}_1(f_n)=\frac{\Delta_{n}}{\Delta_{n-1}}f_{n-1}.$$
\end{corollary}

\begin{figure}[ht]
\centering
$\vcenter{\hbox{\begin{overpic}[scale=.4]{fn_1.pdf}
\put(5, 34){\fontsize{9}{9}$n-1$}
\end{overpic}}} = \frac{\Delta_n}{\Delta_{n-1}}
\vcenter{\hbox{\begin{overpic}[scale=.4]{JW1.pdf}
\put(8, 39.5){\fontsize{9}{9}$n-1$}
\end{overpic}}}$
\caption{Illustration of $\mathit{tr}_1 (f_n)$.}
\label{JONESWENZL:trace}
\end{figure}

When defining the colored Jones polynomial, many authors tend to use the term ``decorating a knot by the Chebyshev polynomial" when describing taking the trace of $f_n$ along a framed knot. This is because the trace of $f_n$ along the standard annulus $S^1 \times I$ where $S^1$ is the trivial knot is equal to the Chebyshev polynomial of the second kind as stated in the next corollary.

\begin{corollary}\label{Cor:chebyshev}\cite{Lic} Let $S_{n}(z)$ denote the $n^{th}$ Chebyshev polynomial of the second kind and $z$ denote the homotopically non-trivial curve in the annulus. Then
$$\mathit{tr}_{Ann}(f_n) = S_{n}(z). $$
\end{corollary}

\begin{lemma} \label{JONESWENZL:lemmacircle} \cite{Lic}
$$ \vcenter{\hbox{
\begin{overpic}[scale = .35]{WRTcfn4.pdf}
\put(67, 35){ $b$}
\put(52, 43){ $a$}
\end{overpic} }} = \varsigma \vcenter{\hbox{
\begin{overpic}[scale = .35]{WRTcfn1.pdf}
\put(50, 35){ $b$}
\end{overpic} }},$$
where $\varsigma = \frac{(-1)^a\left( A^{2(b+1)(a+1)} - A^{-2(b+1)(a+1) }\right)}{A^{2(b+1)} - A^{-2(b+1)}}$.
\end{lemma}

The following result is a well known corollary to Lemma \ref{JONESWENZL:lemmacircle}, we will see similar corollaries in Section \ref{JWMB} for elements in the twisted $I$-bundle of the M\"obius band.
\begin{corollary}\cite{Lic}
\begin{equation}
\vcenter{\hbox{
\begin{overpic}[scale=.3]{Hopffn1.pdf}
\put(-5,0){\fontsize{9}{9}$m$}
\put(45,0){\fontsize{9}{9}$k$}
\end{overpic}}} = (-A^{2(k+1)}-A^{-2(k+1)})^m \Delta_k = ((-1)^{k}T_{k+1})^m \Delta_k,
\end{equation}
where $d = -A^2-A^{-2}$ and $T_{n}(d) = (-1)^n(A^{2n}+A^{-2n})$ is the $n^{th}$ Chebyshev polynomial of the first kind.
\end{corollary}

\section{Crossingless connection in the M\"obius band}\label{MBcrossingless}

Throughout this paper we will use the crosscap model of the M\"obius band where the boundary will be given in a rectangular form when marked points are included,  as shown in Figure \ref{Mobiusmodelscc2}, otherwise it will be displayed as a smooth circle as shown in Figure \ref{Mobiusmodel2}. The three homotopically distinct arcs fixed on the boundary of the M\"obius band are given in Figure \ref{Mobiusmodelscc}.  In order to relate the arcs from the first and second model, a convention was chosen on the two distinct arcs fixed on the boundary that do not intersect the crosscap.

\begin{figure}[ht]
\centering
\begin{subfigure}{.45\textwidth}
\centering
$\vcenter{\hbox{\begin{overpic}[scale=.8]{mobius5.pdf}
\end{overpic}}}$
\caption{Formed from $[0,1] \times [0,1]$ by identifying $\{0\} \times [0,1]$ with $\{1\} \times [0,1]$ as shown by the arrows.}
\label{mobiusmodelscc1}
\end{subfigure} \quad
\begin{subfigure}{.45\textwidth}
\centering
$\vcenter{\hbox{\begin{overpic}[scale=.8]{mobius4.pdf}
\end{overpic}}}$
\caption{Consists of a crosscap and highlights the boundary of the M\"obius band.}
\label{Mobiusmodelscc2}
\end{subfigure}
\caption{Two models of the M\"obius band with 3 homotopically distinct arcs fixed on the boundary.}
\label{Mobiusmodelscc}
\end{figure}

\begin{figure}[ht]
\centering
\begin{subfigure}{.45\textwidth}
\centering
$\vcenter{\hbox{\begin{overpic}[scale=.8]{mobius6.pdf}
\put(16, 55){\fontsize{9}{9}$d$}
\put(60, 77){\fontsize{9}{9}$z$}
\put(55, 30){\fontsize{9}{9}$x$}
\end{overpic}}}$
\caption{First model.}
\label{mobiusmodel1}
\end{subfigure} \quad
\begin{subfigure}{.45\textwidth}
\centering
$\vcenter{\hbox{\begin{overpic}[scale=.8]{mobius7.pdf}
\put(58, 32){\fontsize{9}{9}$d$}
\put(22, 60){\fontsize{9}{9}$z$}
\put(43, 57){\fontsize{9}{9}$x$}
\end{overpic}}}$
\caption{Second model.}
\label{Mobiusmodel2}
\end{subfigure}
\caption{Two models of the M\"obius band with 3 homotopically distinct simple closed curves in M\"obius band denoted by $d, x,$ and $z$, respectively.}
\label{Mobiusmodel}
\end{figure}

Figure \ref{Mobiusmodel} pictorially describes the three homotopically distinct simple closed curves in the M\"obius band. If a simple closed curve intersects the crosscap more than once then the number of intersection points can be reduced by two at a time. The following example will illustrate the process of removing two intersection points from the crosscap. Similar moves can be applied to arcs attached to the boundary that intersect the crosscap more than once.

\begin{example}
We will illustrate,  in the first model then the second model,  the removal of two intersection points of the crosscap from a simple closed curve. In the two examples, the curve will be multicolored in order to show which portion of the curve passes through the crosscap.

 Suppose we have a simple closed curve that is homotopically trivial and intersects the crosscap twice then, as shown in Equation \ref{FirstModel2ptsd}, we may use a sequence of isotopy moves to remove the two intersection points.

\begin{equation}\label{FirstModel2ptsd}
\vcenter{\hbox{\begin{overpic}[scale=.4]{mobius9.pdf}
\end{overpic}}} \sim \vcenter{\hbox{\begin{overpic}[scale=.4]{mobius15.pdf}
\end{overpic}}}  \sim  \vcenter{\hbox{\begin{overpic}[scale=.4]{mobius10.pdf} \end{overpic}}}.
\end{equation}

In Equation \ref{SecModel2ptsd}, we will illustrate the removal of the same intersection points presented in the second model.

\begin{equation}\label{SecModel2ptsd}
\vcenter{\hbox{\begin{overpic}[scale=.5]{mobius12.pdf}
\end{overpic}}} \sim \vcenter{\hbox{\begin{overpic}[scale=.5]{mobius13.pdf}
\end{overpic}}}  .
\end{equation}

Now, suppose we have a homotopically non-trivial curve that intersects the crosscap twice, for example the curve illustrated in Equation \ref{FirstModel2ptsz}. Then, we may remove the two intersection points by using one isotopy move as given below.
\begin{equation}\label{FirstModel2ptsz}
\vcenter{\hbox{\begin{overpic}[scale=.4]{mobius8.pdf}
\end{overpic}}} \sim \vcenter{\hbox{\begin{overpic}[scale=.4]{mobius11.pdf}
\end{overpic}}}.
\end{equation}

Equation \ref{SecModel2ptsz} gives an illustration of this move in the second model.

\begin{equation}\label{SecModel2ptsz}
\vcenter{\hbox{\begin{overpic}[scale=.5]{mobius16.pdf}
\end{overpic}}} \sim
\vcenter{\hbox{\begin{overpic}[scale=.5]{mobius14.pdf}
\end{overpic}}}.
\end{equation}

\end{example}

	\section{Jones-Wenzl idempotents in the M\"obius band}\label{JWMB}
In this section we will introduce various properties associated to the Jones-Wenzl idempotents in the twisted $I$-bundle of the M\"obius band.

\begin{figure}[ht]
\centering
$\vcenter{\hbox{\begin{overpic}[scale=.4]{Mbfn2.pdf}
\put(10, 39){\fontsize{9}{9}$n$}
\end{overpic}}}$
\caption{Illustration of the unique element in $Mb_n$ with $n$ arcs intersecting the crosscap, denoted by $1_{Mb_n}$.}
\label{Mobius:mn}
\end{figure}

\begin{lemma}\label{Lemma:eipull} Let $(Mb_n)_k$ denote the set of elements of $Mb_n$ that intersect the crosscap $k$ times, and let $1_{Mb_n}$ denote the unique element in $Mb_n$ that intersect the crosscap $n$ times, then
$$1_{Mb_n} e_i = e_{n-i} 1_{Mb_n} \in (Mb_n)_{n-2}.$$
\end{lemma}

\begin{proof}
This is a direct result from the antipodal property of the crosscap that is explained in Section \ref{MBcrossingless} and illustrated in Equations \ref{lemma:mbei} and \ref{lemma:e1mb}.

\begin{equation}\label{lemma:mbei}
1_{Mb_n} e_i = \vcenter{\hbox{\begin{overpic}[scale=.35]{Mbfn6.pdf}
\put(4, 54){\fontsize{8}{8}$n-i-1$}
\put(62, 54){\fontsize{8}{8}$i-1$}
\put(46, 5){\fontsize{8}{8}$n-i-1$}
\put(4, 5){\fontsize{8}{8}$i-1$}
\end{overpic}}} = \vcenter{\hbox{\begin{overpic}[scale=.35]{Mbfn7.pdf}
\put(4, 54){\fontsize{8}{8}$n-i-1$}
\put(62, 54){\fontsize{8}{8}$i-1$}
\put(46, 5){\fontsize{8}{8}$n-i-1$}
\put(4, 5){\fontsize{8}{8}$i-1$}
\end{overpic}}} \in  (Mb_n)_{n-2}.
\end{equation}
\begin{equation}\label{lemma:e1mb}
e_{n-i} 1_{Mb_n}  = \vcenter{\hbox{\begin{overpic}[scale=.35]{Mbfn8.pdf}
\put(4, 54){\fontsize{8}{8}$n-i-1$}
\put(62, 54){\fontsize{8}{8}$i-1$}
\put(46, 5){\fontsize{8}{8}$n-i-1$}
\put(4, 5){\fontsize{8}{8}$i-1$}
\end{overpic}}} = \vcenter{\hbox{\begin{overpic}[scale=.35]{Mbfn7.pdf}
\put(4, 54){\fontsize{8}{8}$n-i-1$}
\put(62, 54){\fontsize{8}{8}$i-1$}
\put(46, 5){\fontsize{8}{8}$n-i-1$}
\put(4, 5){\fontsize{8}{8}$i-1$}
\end{overpic}}} \in  (Mb_n)_{n-2}.
\end{equation}
\end{proof}

\begin{corollary}\label{JONESWENZL:antipodal} Sliding $f_n$ through the crosscap is achieved by the following equations.
\begin{eqnarray}
\vcenter{\hbox{
\begin{overpic}[scale = .35]{JonesWMob11.pdf}
\put(4, 49){\fontsize{8}{8}$n$}
\put(74, 21){\fontsize{8}{8}$n$}
\end{overpic} }}  &=&
 \vcenter{\hbox{
\begin{overpic}[scale = .35]{JonesWMob12.pdf}
\put(4, 49){\fontsize{8}{8}$n$}
\put(74, 21){\fontsize{8}{8}$n$}
\end{overpic} }} \label{mob:fnslide1}\\
&=& \vcenter{\hbox{
\begin{overpic}[scale = .35]{JonesWMob13.pdf}
\put(4, 49){\fontsize{8}{8}$n$}
\put(74, 21){\fontsize{8}{8}$n$}
\end{overpic} }}. \label{mob:fnslide2}
\end{eqnarray}
\end{corollary}

\begin{proof}
By Lemma \ref{JONESWENZL:thmfnbasis}(a) and Lemma \ref{Lemma:eipull}, all of the $e_i$'s coming from the left $f_n$ from left hand side of Equation \ref{mob:fnslide1} can be pulled through the crosscap. Furthermore, for each $e_i$ this action results in a turn back on the second $f_n$. Therefore, we obtain our desired result after applying Lemma \ref{JONESWENZL:thmfnbasis}(b). Equation \ref{mob:fnslide2} is obtained similarly.
\end{proof}

We will now present the three direct corollaries to Lemma \ref{JONESWENZL:lemmacircle} that are obtained from closing $f_b$ through the crosscap.
\begin{corollary}
$$\vcenter{\hbox{
\begin{overpic}[scale = .3]{HopfdecMB1.pdf}
\put(45, 57){\fontsize{8}{8}$n$}
\end{overpic} }} = \frac{x}{\Delta_1}(-1)^{n}T_{n+1}(d) \Delta_n ,$$
where $T_{k}(d) = (-1)^k(A^{2k}+A^{-2k})$ is the $k^{th}$ Chebyshev polynomial of the first kind.
\end{corollary}
\begin{proof}
Let $a=n$ and $b=1$ in Lemma \ref{JONESWENZL:lemmacircle}. Then by closing $f_b$ through the crosscap we have
$$ \vcenter{\hbox{
\begin{overpic}[scale = .3]{HopfdecMB1.pdf}
\put(35, 50){\fontsize{6}{6}$n$}
\end{overpic} }} = \frac{(-1)^n (A^{4(n+1)}-A^{-4(n+1)})}{A^4-A^{-4}}\vcenter{\hbox{
\begin{overpic}[scale = .3]{HopfMb2.pdf}
\end{overpic} }}.$$
After simplification we have our desired result, where $x$ denotes the simple closed curve that intersects the crosscap once.
\end{proof}

\begin{corollary}
$$\vcenter{\hbox{
\begin{overpic}[scale = .3]{HopfdecMB2.pdf}
\put(45, 57){\fontsize{8}{8}$n$}
\put(17, 40){\fontsize{8}{8}$m$}
\end{overpic} }} = \frac{(-1)^n(A^{2(n+1)(m+1)}-A^{-2(n+1)(m+1)})}{A^{2(n+1)}-A^{-2(n+1)}}\vcenter{\hbox{
\begin{overpic}[scale = .3]{HopfMb9.pdf}
\put(17, 40){\fontsize{8}{8}$m$}
\end{overpic} }}.$$
\end{corollary}

\begin{proof}
This is obtained from directly applying Lemma \ref{JONESWENZL:lemmacircle} where $a=n$, $b=m$, and $f_b$ is closed through the crosscap.
\end{proof}
\begin{corollary}
$$\vcenter{\hbox{
\begin{overpic}[scale = .3]{HopfdecMB3.pdf}
\put(45, 57){\fontsize{8}{8}$m$}
\put(17, 40){\fontsize{8}{8}$n$}
\end{overpic} }} = ((-1)^{n}T_{n+1}(d))^m \vcenter{\hbox{
\begin{overpic}[scale = .3]{HopfMb9.pdf}
\put(17, 40){\fontsize{8}{8}$n$}
\end{overpic} }}.$$
\end{corollary}

\begin{proof}
We may remove one of the $m$ meridional curves by applying Lemma \ref{JONESWENZL:lemmacircle} where $a=1$ and $b=n$ and closing $f_b$ through the crosscap. After simplification we have
$$ \vcenter{\hbox{
\begin{overpic}[scale = .3]{HopfdecMB3.pdf}
\put(45, 57){\fontsize{8}{8}$m$}
\put(17, 40){\fontsize{8}{8}$n$}
\end{overpic} }}  =  ((-1)^{n}T_{n+1}(d)) \vcenter{\hbox{
\begin{overpic}[scale = .3]{HopfdecMB3.pdf}
\put(34, 57){\fontsize{8}{8}$m-1$}
\put(17, 40){\fontsize{8}{8}$n$}
\end{overpic} }} .$$
We obtain our desired result after repeating this argument $m-1$ more times.
\end{proof}

The following corollary is obtained from Corollary \ref{Cor:chebyshev} by gluing a crosscap to the inner boundary of the annulus.
\begin{corollary}\label{coro:TraceMBAnn} Let $z$ denote the homotopically non-trivial curve in the M\"obius band that does not intersect the crosscap, then
$$\vcenter{\hbox{
\begin{overpic}[scale = .3]{HopfMb23.pdf}
\put(29, 13){\fontsize{8}{8}$n$}
\end{overpic} }}   = S_n(z). $$
\end{corollary}

\begin{corollary}
\begin{eqnarray*}
\vcenter{\hbox{
\begin{overpic}[scale = .45]{HopfMb1.pdf}
\put(43, 78){$m$}
\put(60, 50){$n$}
\end{overpic} }} &=& \frac{\Delta_{m+n}}{\Delta_{n}}\vcenter{\hbox{
\begin{overpic}[scale = .45]{HopfMb14.pdf}
\put(59, 67){$n$}
\end{overpic} }}.
\end{eqnarray*}
\end{corollary}

\begin{proof}
Apply Corollary \ref{JONESWENZL:corollarytrace}  $m$ times when closing $n$ strands from $f_{n+m}$ through the crosscap then closing the rest away from the crosscap.
\end{proof}

Let $\mathit{tr}_{Mb_1}(f_n)$ be obtained from closing one arc from $f_n$ through the crosscap and closing the rest of the arcs in such a way that it surrounds the crosscap, as shown in Figure \ref{Mobius:trace}. Then
Lemma \ref{JONESWENZL:corollarytrace} can no longer be directly applied. Instead we start with applying Wenzl's recursion formula, Theorem \ref{JONESWENZL:wenzlrecursion}, to obtain a recursive formula for $\mathit{tr}_{\mathit{Mb}_1}(f_n)$.

\begin{figure}[ht]
\centering
$\vcenter{\hbox{\begin{overpic}[scale=.4]{HopfMb3.pdf}
\put(35, 10){\fontsize{6}{6}$n-1$}
\end{overpic}}}$
\caption{Illustration of $\mathit{tr}_{Mb_1}(f_n)$.}
\label{Mobius:trace}
\end{figure}

\begin{lemma}\label{lemma:Mb1}
$$ \mathit{tr}_{\mathit{Mb}_1}(f_n) = xS_{n-1}(z) - \frac{\Delta_{n-2}}{\Delta_{n-1}} \mathit{tr}_{\mathit{Mb}_1}(f_{n-1}).$$
\end{lemma}
\begin{proof}
By applying Wenzl's formula to the $x$-curve we have the following recursive formula.
\begin{eqnarray*}
\vcenter{\hbox{
\begin{overpic}[scale = .4]{HopfMb3.pdf}
\put(35, 10){\fontsize{6}{6}$n-1$}
\end{overpic} }} &=& \vcenter{\hbox{
\begin{overpic}[scale = .4]{HopfMb4.pdf}
\put(35, 8){\fontsize{6}{6}$n-1$}
\end{overpic} }} -\frac{\Delta_{n-2}}{\Delta_{n-1}} \vcenter{\hbox{
\begin{overpic}[scale = .4]{HopfMb5.pdf}
\put(35, 8){\fontsize{6}{6}$n-1$}
\end{overpic} }}.
\end{eqnarray*}
By Corollary \ref{coro:TraceMBAnn} and Lemma \ref{JONESWENZL:thmfnbasis}(c),

\begin{eqnarray*}
\vcenter{\hbox{
\begin{overpic}[scale = .4]{HopfMb3.pdf}
\put(35, 10){\fontsize{6}{6}$n-1$}
\end{overpic} }} &=& x S_{n-1}(z) -\frac{\Delta_{n-2}}{\Delta_{n-1}} \vcenter{\hbox{
\begin{overpic}[angle=180, scale = .4]{HopfMb3.pdf}
\put(33, 73){\fontsize{6}{6}$n-2$}
\end{overpic} }}.
\end{eqnarray*}
\end{proof}

\begin{proposition}
$$\mathit{tr}_{Mb_1}(f_n) = \frac{x}{\Delta_{n-1}}\sum_{k=0}^{n-1} (-1)^{n-1+k} S_{k}(z)\Delta_{k}. $$
\end{proposition}

\begin{proof}
The base case is trivial,
$$\mathit{tr}_{Mb_1}(f_1) = \vcenter{\hbox{
\begin{overpic}[scale = .3]{HopfMb2.pdf}
\end{overpic} }}=x .$$

Suppose $\mathit{tr}_{Mb_1}(f_{n-1}) = \frac{x}{\Delta_{n-2}}\sum_{k=0}^{n-2} (-1)^{n-2+k} S_{k}(z)\Delta_{k}.$ Then by Lemma \ref{lemma:Mb1},
\begin{eqnarray*}
  \mathit{tr}_{\mathit{Mb}_1}(f_n) &=& xS_{n-1}(z) - \frac{\Delta_{n-2}}{\Delta_{n-1}} \mathit{tr}_{\mathit{Mb}_1}(f_{n-1}) \\
&=&  xS_{n-1}(z) - \frac{x}{\Delta_{n-1}} \sum_{k=0}^{n-2} (-1)^{n-2+k} S_{k}(z)\Delta_{k} \\
&=& \frac{x}{\Delta_{n-1}}  S_{n-1}(z) \Delta_{n-1} + \frac{x}{\Delta_{n-1}} \sum_{k=0}^{n-2} (-1)^{n-1+k} S_{k}(z)\Delta_{k}.
\end{eqnarray*}
\end{proof}

redpajama_set_name: RedPajamaArXiv


The Tri-Cities are located in the most arid part of Washington State. In fact, the annual rainfall of 6-8 inches is drier than most parts of Arizona. Because of the combination of climate, soil conditions, and human interaction with the land, dust is often an inevitable result.
Ecology's Webpage on Outdoor Dust is here. This page includes information on health effects, monitoring and what you can do to protect yourself in the event of dust events.
Windblown dust is common where soil has been disturbed. Weather conditions, the natural environment, and human activities can cause windblown, construction, or fugitive dust which contributes to air pollution. High winds can raise large amounts of dust from areas of dry, loose, or disturbed soil.
There is dust moving off my property, what should I do about it?
The WAC governing fugitive dust is here, paragraphs 3 and 9a.
Sources of fugitive dust are required under this regulation to control the movement of dust off their property. The BCAA Urban Fugitive Dust Policy (FDP) is an available resource for providing owners and operators information of methods for controlling fugitive dust. These methods are called "reasonable precautions." It is in the best interest of the owners and operators to control the fugitive dust on their property by being familiar with the FDP and with the applicable State and local regulations. If there are no precautions taken and dust impacts others, the BCAA can take enforcement actions with penalties up to $10,000 per day.
For those that are being impacted by dust from sources, complaints can be made to the BCAA office. The information needed is the complainant's name, daytime phone number, the name of the site, owner, or contractor, and any other descriptive information about the situation. This will later help the BCAA to identify and contact the source owner or operator.
If the BCAA has not received any complaints about the source in the past, the Inspector will issue a warning letter outlining the regulations to the owner or operator of the source. If previous complaints have been received the Inspector may issue a Notice of Correction (NOC) or a Notice of Violation (NOV). The NOC outlines a specific list of requirements that the source must take to avoid a penalty. The NOV is essentially a ticket for violating the fugitive dust regulation.
I am being impacted by dust and it is causing property damage or creating a health problem. What can I do about it?
In order do begin the enforcement process, it is very important that the BCAA receives a complaint for the person being impacted. This complaint will help the BCAA to identify and contact the source owner or operator. Upon receiving your complaint, one of the BCAA Inspectors will contact the owner or operator of the source of dust. In many cases, contact by the BCAA will encourage the source owner or operator to control the dust. Once the source owner or operator has been informed on the regulations and has chosen not to follow them, the BCAA can increase enforcement efforts. If previous complaints have been received the BCAA may issue a Notice of Correction (NOC) or a Notice of Violation (NOV). The NOC outlines a specific list of requirements that the source must take to avoid a penalty. The NOV is essentially a ticket for violating the fugitive dust regulation. Penalties of up to $10,000 per day can also be assessed.


text:
22 May 1859, Edinburgh M.D., Kt, KStJ, D.L., LL.D., Sportsman, Writer, Poet, Politician, Justicer, Spiritualist Crowborough, 7 July 1930
A Life in Movies
Prof. Challenger
Brigadier Gerard
Sir Nigel
Captain Sharkey
All fictions
> Search Fictions
Essays, Articles
Prefaces
His Handwriting
Pastiches
and receive a nice ACD lapel pin.
John de Lancie
From The Arthur Conan Doyle Encyclopedia
John de Lancie as the narrator in the play The Lost World (1998)
John de Lancie as Lord John Roxton in the play The Lost World (1998)
John de Lancie (born 20 march 1948) is an American actor best known for his role as "Q" in the Star Trek saga from 1987 to 2001.
In 1998, Leonard Nimoy and John de Lancie adapted The Lost World on stage, in which all the characters were played by Star Trek actors. He introduced the play and played Lord John Roxton.
TV/Theatre
1998 : The Lost World (as Narrator / Lord John Roxton)
Conan Doyle on screen
Conan Doyle on stage
Retrieved from "https://www.arthur-conan-doyle.com/index.php?title=John_de_Lancie&oldid=39341"
About The Arthur Conan Doyle Encyclopedia
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redpajama_set_name: RedPajamaCommonCrawl


text:
Mom Charged with Murder for Allegedly Going Outside for Cigarette and 'Me Time' With Kids in Tub squib
Murder charges were filed late last week in Tennessee against a 32-year-old mother-of-two who was already facing aggravated child abuse, neglect and endangerment charges stemming from the death of her 11-month-old son.
Online court records accessed by PEOPLE state Lindsee Leonardo of Knoxville was charged Friday with first-degree murder for her role in the death of her infant son, Aiden Leonardo.
Aiden died after being left in the bathtub after his mom allegedly stepped away to have a cigarette and listen to music on her phone, say authorities.
On Jan. 8 at about 8 p.m., Leonardo called 911 after she found Aiden floating face-up in her home's bathtub.
She allegedly told investigators she had left the 11-month-old and her 23-month-old child in the bathtub alone in 4 to 6 inches of water while she stepped outside "to smoke a cigarette and have some 'me time.'"
RELATED: Tenn. Baby Dies After Mom Allegedly Goes Outside for Cigarette and 'Me Time,' Leaving Kids in Tub
She also allegedly listened to two songs on her phone before returning to the bathroom and finding Aiden unresponsive.
Leonardo allegedly told police the older child turned on the water, which filled the entire tub.
Aiden regained a heartbeat as medics worked on him in the ambulance to the hospital.
Want to keep up with the latest crime coverage? Sign up for PEOPLE's free True Crime newsletter for breaking crime news, ongoing trial coverage and details of intriguing unsolved cases.
The child died the next night at a nearby hospital.
Leonardo is being held on $350,000 bond. She's yet to enter pleas to the charges against her.
It was unclear Thursday who her lawyer is.
Continue reading on PEOPLE...


In this paper we introduce the notion of weakly prime left ideals in near-subtraction semigroups. Equivalent conditions for a left ideal to be weakly prime are obtained. We have also shown that if (M, L) is a weak $m^*$-system and if P is a left ideal which is maximal with respect to containing L and not meeting M, then P is weakly prime.


Rhesus macaques are exceptionally adapted to coexisting with human and thrive near human settlement in both urban and agricultural areas. There are numerous populations of non-human primates (Macaca mulatta) living in and around the Raj-Gardh fort Dumraon, Buxar but none have been documented. A survey of Raj-Gardh Garrison monkey M. mulatta was carried out and studied its ecology and behavior during January 2013 to December 2014 in Dumraon. Macaque position in the group was observed based on the rank and "central male subgroup" together with two or three oldest males that was observed most dominant. Troop also co-dominant, along with females, their infants and juveniles. The home ranges of this species M. mulatta were observed between .01 to 2.5 km2 in day. Feeding activity was found mostly during morning & evening time and resting between 10 AM to 3 PM when temperature was high. M. mulatta is sexually dimorphic with males and females both have represented separate hierarchies. The rhesus groups were characterized by female philopartry with residue natal group but male dispersal. Mating observed mostly in the month of November to January and infants handled by close female relatives and protected by adult males. In the first few days the infant was carried ventrally by the mother. Loss of natural habitat and increased conflict between human and non-human primates were found to be the major threat for the Raj-Gardh Macaques of the region.


text:
Q: Leaflet.contextmenu callbacks I'm struggling with a problem in the Leaflet.contextmenu library.
I got a number of different maps, saved in a global Array. Then I'm using the contextmenu options to have a contextmenu in my maps. When I want to define my callback functions, I can't access my arrMap[id], because the function doesn't know the id I'm using.
My question here is: How can I give an object (the id, for example) into a callback function of the Leaflet.contextmenu library?
function x(){
    arrMap[id] = new L.map('map'+id,{
        contextmenu: true,
        contextmenuWidth: 140,
        contextmenuItems: [{
            text: 'Messung an dieser Position einfügen',
            callback: newMeasurement
        }, {
            text: 'zeige Koordinaten',
            callback: showCoordinates
        }, {
            text: 'Karte hier zentrieren',
            callback: centerMap
        }]
    });
}

function newMeasurement(e){
//do something with e AND ID
}

I thought about something like:
//function x(){...
callback: newMeasurement(e,id)
//...}

function newMeasurement(e,id){
  console.log(id);
}

...but that's not working :(
Thanks everybody for the help!

A: You need to create a closure over the value you want.
First, read the «How do JS closures work?» question.
Then, read the MDN reference for closures. And then, this question about how to create different Leaflet event handlers passing a different value to each handler function

Read those first. Try to understand the concept. I mean it. If you blindly copy-paste code, then the gods of stackoverflow will kill a kitten.

Now, you want to have an event handler function, which will receive just one parameter, like
function newMeasurement(ev){
    // do something with 'ev' AND 'id'
}

That function needs to receive one parameter, and needs to have an id variable somewhere. OK then, let's create a function that returns a function:
function getMeasurementHandler(id) {
    return function(ev) {
        doSomething(ev, id);
    }
}

That way, if you run e.g.:
var handlerForId1234 = getMeasurementHandler(1234);

That is more-or-less equivalent to
var handlerForId1234 = function(ev) { doSomething(ev, 1234); }

Let's put it all together:
for (var id=0; id<4; id++) {
    arrMap[id] = new L.map('map'+id, {
        contextmenuItems: [{
            text: 'Somethingsomething',
            callback: getEventHandlerForId(id)
        }]
    });
}

getCallbackFuncForId(id) {
    return function(ev) {
        console.log('Event ', ev, ' in ID ', id);
    }
}

redpajama_set_name: RedPajamaStackExchange


text:
Pascal Conq, né à Saint-Brieuc en 1962, est un architecte naval français. Associé à Jean-Marie Finot, il a conçu certains des  IMOCA, monocoques de course au large, parmi les plus performants des trente dernières années.

Biographie
Pascal Conq découvre la voile en baie de Morlaix avec son père, directeur des services techniques de la station biologique de Roscoff. Il devient moniteur de voile et, passionné par l'ingénierie navale, commence des études d'architecture en 1979. En 1982, il met au point un système de quille pendulaire sur un Micro.

En 1985, il remporte le Tour de France à la voile à bord du Côte d'Armor de son cousin Yannick Dupetit. La même année, il obtient son diplôme d'architecte et s'associe avec Jean-Marie Finot, déjà créateur de l'Écume de mer et du First Class 8. Le cabinet se tourne alors vers la course au large, tout en poursuivant ses travaux pour les voiliers de croisières. Ils conçoivent ainsi une quinzaine de prototypes Mini 6.50 à partir de 1987. Leurs Minis, larges, légers et rapides aux allures portantes, contribuent au développement des voiliers open. En 1990, ils créent le Figaro Bénéteau pour la Solitaire du Figaro.

Jean-Marie Finot et Pascal Conq se distinguent particulièrement par leurs constantes innovations dans la conception des monocoques de 60 pieds open. Leurs réalisations dominent largement les années 1990 et le début des années 2000 avec quatre victoires dans le Vendée Globe (1993 avec Alain Gautier sur Bagages Supérior, 1997 avec Christophe Auguin sur Geodis, 2001 avec Michel Desjoyeaux sur PRB et 2005 avec Vincent Riou sur le même PRB) et trois dans le BOC Challenge (1991 avec Christophe Auguin avec Groupe Sceta, 1995 avec Christophe Auguin sur Sceta-Calberson et 1999 avec Giovanni Soldini sur Fila).

Dans les années 2000, Pascal Conq contribue à la création de la Class40 et le Groupe Finot conçoit le Pogo 40.

Liste des 60 pieds conçus
 1989 : Générali-Concorde pour Alain Gautier
 1990 : Groupe Sceta pour Christophe Auguin
 1992 : Bagages Supérior pour Alain Gautier
 1994 : Sceta-Calberson (futur Geodis) pour Christophe Auguin
 1995 : Groupe LG 2 pour Gerry Roufs
 1996 :
 Aquitaine Innovations pour Yves Parlier
 PRB pour Isabelle Autissier
 1997 : Fila pour Giovanni Soldini
 1998 :
 Gartmore pour Josh Hall
 Team Group 4 pour Mike Golding
 Sodebo pour Raphaël Dinelli
 Somewhere pour Marc Thiercelin
 UBP pour Dominique Wavre
 1999 : PRB pour Michel Desjoyeaux
 2007 :
 Générali pour Yann Eliès
 Hugo Boss pour Alex Thomson
 Brit Air pour Armel Le Cléac'h
 2008 : DCNS 1000 pour Marc Thiercelin

Article connexe
 First 300 spirit, 30 pieds conçu en collaboration avec Jean-Marie Finot

Notes et références

Liens externes

Ingénieur et architecte naval
Naissance en janvier 1962
Naissance à Saint-Brieuc
Naissance dans les Côtes-du-Nord

redpajama_set_name: RedPajamaWikipedia


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Daimler Industry News
Daimler to end New York Stock Exchange listing due to low volume
May 14, 2010 Omar Rana
Daimler AG CEO Dieter Zetsche
Daimler AG, the world's second largest producer of luxury vehicles (BMW is No. 1), said today it will end its stock listing in New York due to low trading volumes.
"Daimler continues to place great importance on having an international shareholder base," Chief Financial Officer Bodo Uebber said in the statement. "The trading center for our shares, however, clearly is Frankfurt — and that is also the case for our international investors."
In a letter to the New York Stock Exchange today, Daimler said it will delist the stock and the 8.5 percent notes due Jan. 18, 2031 issued by Daimler Finance North America LLC. Daimler, whose primary listing is in Frankfurt, stated that U.S. trading accounted for less than 5 percent of total volume in the past year.
– By: Stephen Calogera
Source: Automotive News (Subscription Required)
Carbon Fiber Car Rear View Side Mirror Rain Board Eyebrow Guard Sun Visor 2Pcs
← Nissan opens LEAF reservations to general public, 9,500 reservations taken so far
U.S. Mahindra pickups delayed yet again to Dec. 2010 →


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Home / Stock Picks / Stocks to Sell / 7 Bank Stocks to Leave in the Vault
7 Bank Stocks to Leave in the Vault
Bank stocks have had a good run, but that may not be the case moving forward
By Louis Navellier, Editor, Growth Investor May 31, 2019, 1:49 pm EDT May 31, 2019
Source: Shutterstock
After the Trump tax cut in 2017, it was easy to see that big corporations were the big winners. They could extend their massive stock buyback programs into 2018 and keep earnings growing until the economy got back up to speed. But it also helped the banks, especially regional bank stocks.
They were able to increase their lending and much of the red tape that was put on bigger national banks was reduced for the regionals, like lowering reserve requirements to induce lending.
Also, an improving economy, steady interest rates and low inflation all contributed to their ability to lend with better margins. But the culmination of Q4 with the December selloff, gave some pause to the industry.
However, given the economic picture in the U.S., regional banks looked like their run would continue, regardless of trade wars and external factors.
Things are changing. Some financial stocks still have what it takes, but others are getting increasingly unstable, and they're overbought at this point. The seven bank stocks to leave in the vault are at the tip of a growing iceberg.
My Portfolio Grader has rated all of these stocks with ratings at D or below.
Barclays (BCS)
Barclays PLC ADR (NYSE:BCS) is a U.K.-based bank that has been operating in and beyond the British Empire since 1896. But as the empire shrank, so did BCS influence.
Today it remains a respected global banking institution, but it has had its troubles in recent decades. One of its biggest problems now is Brexit. With no idea how Brexit will (or won't) be delivered, the City — the financial center of London — is losing businesses.
The British economy is on hold and investors are looking for more clarity in their banking partners and their investment money.
That explains why BCS is flat year-to-date and off 30% in the past 12 months. Things aren't getting any better at this point. Best to watch this one from afar, even with its 4.4% dividend.
Umpqua (UMPQ)
Umpqua Holdings Corp (NASDAQ:UMPQ) is a mid-cap regional bank that is headquartered in Portland, Oregon.
With roots going back to the timber industry in the 1950s, UMPQ has grown with Oregon, especially Portland. But like the timber industry in the Pacific Northwest, times are a little tougher for this regional bank these days.
It has locations across Oregon, Washington, Idaho and California. And it has an array of customers, from individuals to large corporations. But the investment side of the business is slowing since investors aren't investing like they were in 2018. Treasuries yields are dropping. And housing starts are slowing. None of which are good for a banks' asset portfolio.
UMPQ stock is up a mere 1.5% YTD and off 32% in the past year. Its 5.2% looks generous, but isn't worth the risk at this point.
UBS Group (UBS)
UBS Group AG (NYSE:UBS) has been around in one form or another for more than 155 years and remains the largest bank in Switzerland. In the good ol' days, it had quite a brisk international business since the Swiss had such rigorous privacy laws.
And even now, half the billionaires in the world still have accounts with the bank.
But the privacy laws have changed significantly and the financial crisis in 2008 laid UBS low. When it re-emerged, it had transitioned into more of an investment bank that also specialized in wealth management.
It remains a significant financial institution, but this isn't a good time for the bank since it is still sorting out its issues from a decade ago and is trying to navigate the challenges of its global business. This isn't the time to bank on UBS stock.
While it delivers a generous 6% dividend, the stock is off 26% for the year and 7% year to date.
State Street (STT)
State Street Corp (NYSE:STT) is a holding company that operates State Street Bank. But its chief income generator is an investment services and wealth management company.
The problem is, while the markets have been chugging along up now, the amount of investment in the markets is down overall. That means after the big December selloff and subsequent rally, some of the sidelined cash didn't make it back in the markets.
That's pretty evident in STT's late April Q1 earnings release. Its fee income was off considerably. Fee income is the money the company makes off account-related fees. And the stock has been punished for it.
STT stock is off 43% in the past year and 11% YTD. In the past 3 months, it's off 23%, which shows the effect of that dour earnings report. Its 3.4% dividend isn't even that tempting.
PacWest Bancorp (PACW)
PacWest Bancorp (NASDAQ:PACW) is headquartered in Beverly Hills, California. That may give you an idea of the customers that they are looking to attract.
And PACW isn't a bank for individuals, rather a bank that focuses on services for mid-sized companies. You can imagine that its reach up and down California means it has a good book of business in tech, aerospace, shipping and agriculture.
But the thing is, the tech sector is getting hit because of the trade war with China, as are the aerospace and ag sectors. It announced Q1 earnings in mid-April and they weren't encouraging. It beat earnings expectations by a penny but came in below expectations on revenue, which was off 3% for the same quarter last year.
PACW stock has been trending down for the past year, off 31% in that time. And while it's up 9% YTD, that's because of the January rally; since then, its general trend has been downward.
Its 6.6% dividend may look tempting, but it comes at the price of performance.
KeyCorp (KEY)
KeyCorp (NYSE:KEY) may have started in Albany, New York over 190 years ago, but now it has operations across the Northeast, Midwest and West. It operates in 15 states and has over 1,100 branches.
But KEY did not have a strong Q1 and its quarter-to-quarter numbers were also down significantly. The biggest red flag to all this is the fact that conditions should be ideal for a regional bank that spans a number of different regions.
However, the Midwest manufacturing and agriculture sectors aren't strong and tech is challenged. And that showed in Q1 numbers — earnings missed, revenue missed, net interest income was down as was noninterest income. Also down were net interest margin and return on average assets, while book value rose.
Even its 4.2% dividend isn't worth the trouble at this point.
BankUnited (BKU)
BankUnited Inc (NYSE:BKU) was the 2009 reincarnation of a failed bank under the same name. It was capitalized by private equity firms like Blackstone Group (NYSE:BX), Carlyle Group (NASDAQ:CG) as well as Secretary of Commerce Wilber Ross.
It operates in South Florida as well as the New York, New Jersey and Connecticut areas. While it has retail and commercial operations, it focuses on the commercial side.
The trouble with the bank now is, the economy is slowing and with U.S. Treasury yields dropping, it is going to have a challenging year providing growth. A bank's Treasury portfolio is a large part of its revenue since it has to have a good chunk of ready reserves to cover its loans. Lower rates mean lower margins on its loan book.
BKU stock is off 23% in the past year, yet YTD it's up 9%. But don't think that means there's bullish sentiment. The stock rallied in January and has slid off those highs. Its paltry 2.6% dividend isn't a game changer.
Louis Navellier is a renowned growth investor. He is the editor of four investing newsletters: Growth Investor, Breakthrough Stocks, Accelerated Profits and Platinum Growth. His most popular service, Growth Investor, has a track record of beating the market 3:1 over the last 14 years. He uses a combination of quantitative and fundamental analysis to identify market-beating stocks. Mr. Navellier has made his proven formula accessible to investors via his free, online stock rating tool, PortfolioGrader.com. Louis Navellier may hold some of the aforementioned securities in one or more of his newsletters.
Article printed from InvestorPlace Media, https://investorplace.com/2019/05/7-bank-stocks-to-leave-in-the-vault/.
©2019 InvestorPlace Media, LLC
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This paper accurately calculates the interrelated behavior of pressure, temperature, and liquid dropout for multicomponent two-phase flow. The computational method developed has been used in field-scale applications where pressure and temperature profiles were calculated for a gas-gathering system in which liquid dropout was occurring.
Engineering analysis of two-phase fluid flow in pipes has focused primarily on the problem of predicting pressure drop. Phase-behavior aspects of the problem traditionally have been simplified to obtain manageable calculation methods. During the last 10 to 15 years, it has be come possible to treat two-phase pipeline problems with empirical numerical techniques that yield reasonably accurate pressure drops. When used with high-speed computers, it seems reasonable to expect that these methods might profit from a more rigorous treatment of the hydrocarbon phase-behavior aspects of the problem.
Nearly all two-phase pipeline simulation currently is performed using "black-oil" simulators. A black-oil model's validity rests on the assumption that the hydrocarbon mixture is composed of only two components (denoted oil and gas), each with fixed composition. The gas is said to be dissolved in the oil, with the amount of dissolved gas decreasing with decreasing pressure. The oil component in the pipeline generally is defined as stock-tank oil. A black-oil model usually treats PVT properties (solution gas, densities, and viscosities) as properties (solution gas, densities, and viscosities) as single-value functions of pressure. More sophisticated models include the temperature effect on fluid properties as well. A linear temperature profile sometimes is considered, but laboratory data are seldom available to calibrate the thermal effects.
The multicomponent or compositional approach is designed for gas condensate and volatile oil systems that are not handled easily using the black-oil method. These fluids are represented as N-component hydrocarbon mixtures, where N might equal 9 with components methane, ethane, propane, i-C4, n-C4, i-C5, n-C5, C6, and C7 +. A single equation of state then is used to determine physical properties.
The term "compositional" is borrowed from reservoir engineering and implies that the overall or in-situ fluid composition varies point-by-point with distance. In other words, the mole fraction of each component is a function of pressure, temperature, and slip between the phases, which in turn vary with distance. The compositional problem then is distinguished from a multicomponent-type problem then is distinguished from a multicomponent-type problem that assumes uniform composition with distance. problem that assumes uniform composition with distance. When a multicomponent gas-liquid mixture flows through a pipe, the composition, pressure, temperature, and liquid holdup distributions are related. The purpose of this study is to calculate each distribution accurately, while properly accounting for the steady-state interaction between them. The proposed model computes changing compositions of liquid and gaseous phases in the pipeline in accordance with the resulting pressure and temperature profiles. These profiles are calculated using the principles of heat balance, momentum balance, and principles of heat balance, momentum balance, and phase equilibrium. phase equilibrium. Phase Behavior of Hydrocarbon Fluids Phase Behavior of Hydrocarbon Fluids Hydrocarbon fluids usually are classified as to the phase behavior exhibited by the mixture.


Since the early stages of her career, Ogasawara has been giving concerts with her excellent ensembles within Germany as well as on the international stage. She is an all around well versed and harmonious partner.
Also a word of admiration to the amazing pianist Oagasawara: she successfully managed a difficult balance between leading, accompanying and integrating in the general sound; an apparent paradox of submissive dominance.
Tomoko Ogasawaras'piano playing shows a precious instinct for tone, a high technical skill, a musical profundity, an absolute depandability, and a great sensitivity for synergy and interaction.
We would especially like to mention the exceptional pianist Tomoko Ogasawara, through her effortless performance of Mozart, her lithe and virtuosic ability were revealed. The Japonese pianist studied in Germany, which one can continually see. Despite the germanic rigidity, she kept her playing fresh and through that allowed the poetry and whimsy of the work to reveal itself.


It has been a _very_ long time since I last updated and I apologise profusely to the 3 people who read my blog. Thanks, by the way, for hanging on through my silence.
Quite honestly, the REASON I take so long to post is because so much happens between posts that I don't know where to START! So, I wait and write a few things down and think, Oh, yes, I need to tell them about that!
Before long there are 20 things on my list of things I want to tell you about and I do not know where to start. Do I go with a timeline? Do I go with the biggest/most important news first? Do I tell you the little things and ease you into the big things?
I am going to attempt to give you an update that includes all the things I can remember I wanted to tell you. They will most likely not be in order, but as they come to me.
Let's start with what happened while my husband was in Oregon, fighting the terrible wildfires. I sorted the yard out: pulled the weeds, raked up the rocks and glass and bottle tops and junk that the previous tenant left behind. (He liked to throw beer bottles around, for fun) I planted grass and nurtured it and watered it and talked to it and did my best to keep the weeds at bay while it grew.
I had grass! It was beautiful and soft and green and I was super proud. Then the crazy wind storms came, and the monsoon rains (yes, monsoon rains in the desert) and the weeds and I fought a battle royale on a daily basis. We spent a lot of time inside.
After that, it got hot. Stupidly hot. I'm from Africa, we know hot… but this heat here in the New Mexico desert is diabolical. It was also humid for a few months, and the mosquitoes reigned supreme, despite my best efforts. I was COVERED in bites every single day even after dousing myself in mosquito repellent from the moment I woke. I'm allergic to mosquito bites so I now have many more nasty scars to add to my collection.
I did, however, get a SUPER tan! I also lost a lot of weight and not just because I shaved my 30-inch hair off – down to the scalp – but also because I was outside every day working in the yard and sweating profusely. I used the dog clippers on my head – it was that hot and I was that desperate.
Speaking of the dogs – I discovered a few new places to walk and we attempted to get into a routine of walking early in the mornings at least every second day. One place we found was NMSU, the agricultural section – lots of farms, cows, sheep and goats. The dogs love it. It's also very shady and there are NO THORNS!
The other place was the Mesilla Valley Bosque State Park. It's wild and strange but beautiful, nonetheless. We only walked the one path we found – about a 25 to 30-minute walk and just under a mile – as the other path was always under water after all the rain. We recently started walking the other path and it's FAR longer (nearly 2 miles) and takes us almost an hour to walk. The dogs LOVE it too! We met our first rattlesnake last year and we politely and respectfully turned around and went back the way we came after I realised it wasn't moving from its spot in the middle of the path. Just to be safe, we got the dogs vaccinated against rattlesnake venom. We also clipped the dogs earlier in the year before husband left for Oregon, just as it started getting hot. They all got puppy cuts – well, the girls did. Odin we just brushed well and I clipped down a little bit.
I applied all over town at every conceivable place I could think of. I got rejected for either NOT being a student or being overqualified until I tweaked my resume a bit and excluded all my I.T. work. I then worked, briefly, for a budget hotel chain. The pay was crap, the work was EXHAUSTING and seemingly pointless (to me) as you just repeated the same thing every day, but it was a job and I stuck with it as long as I could. I continued my search though, while I worked there. I got a job, eventually, at a father-and-son-owned health food store as a cashier. Through them, and the experience I gained with them, I also got a call back from Walmart and I began working there as well. I enjoyed the work at the small store, even if it was a bit boring sometimes – it was a nice quiet pace and I learned a great deal. Walmart was crazy – busy, loud, frenetic, but excellent money. Mind-numbing and exhausting at the same time.
I worked at both for a few months and then, on a whim – I really wanted to be back home with my dogs and my husband as I was working late night shifts and long hours and I missed them – I applied to a few positions back in the Medical Transcription field. I got two or three responses and wrote their entrance tests and aced all three (according to the recruiters who responded with a firm offer) but the first one offered freelance inconsistent work (I've been there, done that, and I didn't want to be left in that predicament again) even if it was well-paid. The second, and the one I actually responded to with a view to beginning a career with them, offered shift work (afternoons/evenings) but also had many convoluted and specific tech requirements. On paper, my computer and I were a perfectly reasonable match, but the three weeks it took to try and get it working was ridiculous and I had to tell them thanks, but no thanks. I spent those weeks at home, unable to work, as they needed me "available" during office hours in case the tech people wanted to ask me to do something to tweak a setting, etc. I responded to the other offer I got from the third company and that's who I am working for now! I went through their intense and rigorous training program and did well, and now I am waiting on the next step – being assigned my own doctor! While I wait, I am doing more training and BEING PAID FOR IT. It's intense and detailed work and while I do enjoy the meticulous attention to detail needed, and the chance to work in the medical field again (I've always loved it!) it is mentally exhausting sometimes. Also, I'm a perfectionist, so I beat myself up over the slightest error even when my trainer tells me I'm doing great work. But I'm getting there and enjoying it, and just counting the days until payday.
My husband has finally transferred from Oregon to here, so we are now truly "settled" in one place for a while. Now, we just need to get all our "stuff" down here – from Oregon storage and also my stuff from back home that I've been trying to get here since I left in 2011!
Azzie had a strange issue a few months ago where she seemed to lose peripheral vision in her left eye and was bumping into things, standing on things, and falling off the pavement on the left (that's the side she walks on) and leaning against walls. We had her checked out by two vets, and also took her to an eye specialist in El Paso, but they could find nothing physically wrong… they all suggested an MRI and other imaging, but told us that it would _start_ at around $5000. We were given a few other options, non surgical and not as expensive, but we were told they were just "shots in the dark" as none of the vets had any clue what was causing it and it was all pointing to a neurological issue. We were pretty stressed about it, and worried about our sweet girl, who was miserable, restless, and not her happy self at all. I spoke to my mum and she reminded me about our dogs back home who had had "mini strokes" at various points in their lives and that Azzie's symptoms sounded very much like those. So, we told the vet we were going to give her time to recover on her own and see how it went. We gave it two weeks to see if there was ANY improvement. Thankfully, there was. I took them for a walk about 5 days after our visit to the specialist, and Azzie was much more responsive and not leaning on the lead like before. She also didn't fall off the pavement nearly as much if I checked her, gently, with the lead as she started bumbling off to the left. Fast forward to today, and she's almost 100% better. She is listening, paying attention when I speak to her (before she was totally ignoring me and would just lean as far over to the left as she could before my arm gave out – she's a VERY strong dog) and hasn't fallen off the pavement or walked into anything for a while now. Unfortunately, this means she is most likely prone to these strokes – mini or otherwise, they are still worrying – and we'll have to keep a careful eye on her. I lost my Mishka to a final, massive stroke, but she was 17 years old when it happened. Azzie is only turning 7 next month. Speaking of birthdays! Gina turned 10 years old at the end of February! That's a MASSIVE feat for our Bernese! We are so happy! And she's doing well, with minimal joint issues. I started her on the Vet's Best Aches and Pains and it (After a few days of an upset stomach, of course – she's always been very sensitive to new stuff) really helped a great deal, especially in the mornings when she would normally be very stiff and creaking. Odin's nominated birthday followed a day or so later, and he is probably 6 or 7 years old. I'm thinking 7, as he has quite a bit of grey around the muzzle now, compared to when I look back at the photos of him when he arrived in Germany, frail and timid.
Our neighbour, Hank, has a visitor for the summer, and she is lovely. A wild biker woman but kind and friendly, and she's an animal lover, so she's okay in our books. She has a gorgeous little terrier mix called Buddy, and he and Odin are quickly becoming friends. Gina, being Gina, is her usual silly, grumbly self, and Azzie is Azzie – confused and wanting to be friends one moment, and then ignoring him the next.
Husband and I have been working very hard on our yard and garden as well. Everything is neat and tidy and we've planted an olive tree – named Olly, of course – and we've made space for two fruit trees. We're thinking a peach and a cherry tree. We've also potted some BEAUTIFUL flowering plants – a Carolina Jessamine (lovely yellow trumpet flowers), a Pink Jasmine (tiny white and pink flowers), and the Japanese Honeysuckle is starting to come back beautifully after the winter. We also planted flowers in big pots and seeded our herb garden with Thyme, Rosemary, Lavender, Sage, Sweet Basil, Echinacea, Arugula, Chives, and lots of Mint. We have a lovely English Rosemary plant which we transplanted from pot to garden and we also potted some shallots and garlic, just to see what happened. We're so excited! We also put grass seed down all over the yard, including re-seeding the empty patches in the already existing grass (which is coming in nicely now) and then a layer of manure on top of it all. Things are looking green out there and we're hoping the grass finally takes in all the places where it wasn't before as well. There's nothing quite like working with your hands in the earth, with living, growing things and watching the butterflies, bees, birds, and bugs come buzzing back into view. We're trying to keep the birds well fed so that they don't eat all the grass seeds before they can germinate!
I'm sure there's more to add, but that's all I can think of right now.
Hope you enjoyed the update and thanks for reading!


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Glitter & Toast
MEDIA RELEASE: Star Wars: The Force Awakens releasing in IMAX® 3D
For fans like me it seriously does NOT get more exciting than this …
Ster-Kinekor: Great Moments at their Greatest
Dated: 11 December 2015
(Star Wars: The Force Awakens releasing in IMAX® 3D)
WATCH STAR WARS: THE FORCE AWAKENS IN STER-KINEKOR'S IMAX® CINEMAS FOR AN INTER-GALACTIC EXPERIENCE OF EPIC PROPORTIONS
"The force is calling to you, just let it in…"
The wait is nearly over… with just a few days to go until the South African release of the highly anticipated Star Wars: The Force Awakens in IMAX® 3D on 16 December 2015.
The film releases at Ster-Kinekor cinemas countrywide – including its IMAX and Cine Prestige theatres – two days before its US release. This seventh installment in the Star WarsTM Saga promises to be an adventure of epic proportions as audiences travel back to a galaxy far, far away!
As Star WarsTM fever grips South Africa, Ster-Kinekor has announced that advance bookings to watch the film in its IMAX® 3D theatres have reached record levels. To date, more than 34 500 tickets have already been purchased to watch Star Wars: The Force Awakens at Ster-Kinekor cinemas across South Africa.
Of these pre-sales, more than half the tickets – 18 300 (as at 09 December) – are bookings to watch the film in IMAX® 3D, which offers the most immersive cinematic experience in which to watch this latest film in the Star WarsTM Saga. Come 16 December, Ster-Kinekor estimates that pre-ticket sales across all its cinema offerings – IMAX® 3D, Cine Prestige 3D and in 2D and 3D at all other Ster-Kinekor cinemas – could reach record-breaking levels.
This figure also represents the most advance bookings of any IMAX title for Ster-Kinekor, which is quite an achievement, considering that this number of tickets is spread across only six screens: the IMAX theatres at Gateway in Durban, The Grove in Pretoria, CapeGate in Cape Town, Baywest Mall in Port Elizabeth, Cradlestone Mall in Krugersdorp, and the new IMAX Theatre at Eastgate in Johannesburg.
Star WarsTM fans of all ages who have followed the saga will now be able to return to that galaxy far, far away, meet new heroes and villains, and welcome back some old friends in Star Wars: The Force Awakens. Set 30 years after Star Wars: Return of the Jedi, cinema-goers will be able to delve into the events that transpired after the Rebel Alliance triumphed over the evil Galactic Empire over the forest moon of Endor.
The IMAX® 3D release of Star Wars: The Force Awakens has been digitally re-mastered into the image and sound quality of an IMAX Experience® with proprietary IMAX DMR® (Digital Re-mastering) technology. The crystal-clear images coupled with IMAX's customised theatre geometry and powerful digital audio, create a unique environment that will make audiences feel as if they are in the movie, and part of the Star WarsTM action. For an experience of universe-sized proportions, witness this adventure unfold in 3D at a Ster-Kinekor IMAX cinema near you.
Lucasfilm and visionary director J.J. Abrams join forces to take you back again to a galaxy far, far away as Star WarsTM returns to the big screen with Star Wars: The Force Awakens.
The film stars Harrison Ford, Mark Hamill, Carrie Fisher, Adam Driver, Daisy Ridley, John Boyega, Oscar Isaac, Lupita Nyong'o, Andy Serkis, Domhnall Gleeson, Anthony Daniels, Peter Mayhew and Max Von Sydow. Kathleen Kennedy, J.J. Abrams and Bryan Burk are producing with Tommy Harper and Jason McGatlin serving as executive producers. The screenplay is written by Lawrence Kasdan & J.J. Abrams and Michael Arndt. Star Wars: The Force Awakens releases in South African theatres on 16 December 2015.
View STAR WARS: THE FORCE AWAKENS trailer here: http://www.sterkinekor.com/#/trailer/7758/IMAX%203D%20-%20Star%20Wars:%20The%20Force%20Awakens%20/
For more information on Star Wars: The Force Awakens in Ster-Kinekor and IMAX® 3D cinemas, download the Ster-Kinekor App on your smart phone for updates and to book tickets from your mobile. To find out what other exciting promotions Ster-Kinekor has on offer, visit www.sterkinekor.com or sterkinekor.mobi. Follow @sterkinekor on Twitter or Ster-Kinekor Theatres on Facebook. For queries, call Ticketline on 0861 MOVIES (668 437) or book at the box office.
Published by Janice
Social media marketer, blogger, avid reader, proof-reader and reviewer. Drinks tea. Very OCD. Chocaholic. Tendency to think I'm losing my mind - but that's normal ... right??	View all posts by Janice
HOLIDAYING AT HOME – BEING A TOURIST IN JOZI (PART 1)
FILM REVIEW – Star Wars: The Force Awakens
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You are here: Home / Alternatives / Alternatives for Specific Infections
Alternatives for Specific Infections
Related VCC Links
A Historical Overview of Polio Treatments from The Rodale Encyclopedia of Common Diseases (3/1/2011)
Magnesium As First Line Therapy in the Management of Tetanus (2/10/2011)
Chickenpox (1/25/2009)
What If My Child Gets the Measles? (11/14/2008)
Fever as a Treatment for Influenza (9/29/2008)
Sodium Ascorbate Treatment of Whooping Cough by Suzanne Humphries, MD
Ascorbic Acid (Vitamin C) Treatment of Whooping Cough – Canadian Medical Association Journal Aug. 1937
Homeopathic Family Medicine: Chickenpox by Will Taylor, MD
Efficacy of Lemon-Juice in Diphtheria – April 1866 American Journal of the Medical Sciences
Breastfeeding Protects from Haemophilus Influenzae (a list of medical article references)
Vitamin D & Prevention of Flu and Respiratory Illness (also discusses the use of Vitamin D)
Vitamin D for influenza – Canadian Family Physician
Lessons from a Century After the Flu Epidemic of 1918: How Conventional Medicine Killed Millions and How Homeopathic Medicines Saved Millions By Dana Ullman, MPH, CCH
Homeopathic Remedies for the Flu – An Overview
What if my child gets measles? (article from VRANewsletter; winter & spring, 1996)
Doctors once successfully treated measles By Dr. W. Gifford-Jones
Vitamin A Protocol for Measles, Dr. Jaquelyn McCandless MD
Tetanus Toxoid Vaccination (emphasizes risks and includes contraindications and alternate methods of prevention)
Magnesium as Tetanus Therapy
Iodine: Its Use in the Treatment and Prevention of Poliomyelitis and Allied Diseases By J.F. Edward, MD The Manitoba Medical Review. Reprint 76, 1954 (pdf)
See our Alternatives Section for more information.
Alternatives and Antidotes to Infectious Diseases


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Quarterback and Wife Raise $150,000 for the Andy & Jordan Dalton Foundation
(Ft. Worth, TX)— Former TCU quarterback and Cincinnati Bengal Andy Dalton, along with his wife Jordan, hosted Fiesta & Goal on Monday night at Joe T. Garcia's. The event was created to raise funds for the Andy & Jordan Dalton Foundation.
Guests mingled with the Daltons while enjoying cocktails and a buffet of Joe T. Garcia's famous fajitas as the community rallied behind the Daltons, showing their support through sponsorships, live and silent auctions and general donations.
Through the efforts of Monday's event, Fiesta & Goal raised nearly $150,000 for the Andy & Jordan Dalton Foundation and will help support programming in the Fort Worth area.
The first of these programs, Andy & Jordan's Hub, was recently revealed in the Infusion Center of Cook Children's Medical Center. The Hub is a locker filled with iPads, notebook computers, DVD players, gaming systems and other items intended to help patients and their families pass time during treatment or recovery.
The foundation's next step is to establish the Pass It On Fund in Fort Worth, a grant program that provides medical equipment to families with severely/chronically ill children or special-needs children who are financially in need.


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Cindy Crawford and Her Family Step Out in Style to Support Son Presley
Celebrity Families
Cindy Crawford and Family at Daily Front Row Awards 2017
April 4, 2017 by Monica Sisavat
Cindy Crawford attended the star-studded Daily Front Row Awards in LA on Sunday with husband Rande Gerber and their kids, 15-year-old daughter Kaia and 17-year-old son Presley. The brood was on hand to support Presley, who was the recipient of this year's emerging model award. "My whole family's so supportive of me. It's just so comforting to have them here," Presley told ET. "It's making everything a lot easier." Modeling certainly runs in Cindy's family, and Presley shared some advice he once got from his mom at the event. "Best piece of advice is, 'If you don't want to do something, don't do it,'" and "When it comes to walking, don't fall." The up-and-coming model also revealed that his love for the profession came about two years ago during a photo shoot with Kaia, adding, "I had so much fun. I kinda realized, 'Oh, maybe I can work with this.'"
A Closer Look at the Fabulous Life of Cindy Crawford's Family
The Crawford family has a lot to celebrate lately; in addition to Presley's honor, Kaia recently landed her first beauty campaign with Marc Jacobs. The campaign also features fellow models Sofia Mechetner and Dilia Martins, both of whom Kaia told Teen Vogue were very natural and fun to work with.
Cindy CrawfordKaia GerberPresley GerberCelebrity FamiliesCelebrity BabiesRande GerberRed Carpet
Full House? Kate Middleton Says Prince William Doesn't Want Any More Kids
Chris Martin Tried to Visit 15-Year-Old Apple at Her First Job, and It, Uh, Did Not Go Well
by Karenna Meredith 6 hours ago
Sia Just Announced That She Adopted a Son, and We Are So Excited For Her
Amy Schumer's Delirious Post-Egg-Retrieval Videos Show That Sometimes You Just Need to Laugh
The Jonas Brothers Re-Created an Iconic Keeping Up With the Kardashians Fight on TikTok


Pull up a chair on the verandah and drink in the glorious view... You'll be entranced by the peaceful panorama of folding green velvet hills, manicured horse paddocks, lily-strewn dams and a creek where platypus play. Set in a prime location just minutes from the townships of Cooran, Pomona and Cooroy, this 18 acre property offers absolute privacy, stunning views and a recently renovated, high set Queensland-style home with three bedrooms, two bathrooms and a wonderfully spacious, chic interior freshly painted in shades of linseed grey and white. High ceilings, polished floors and big picture windows give this timber home a generous, open feel that's connected to the beautiful landscape via sliding glass doors and wide, wraparound verandahs on all four sides.
The open plan living room with its combustion stove flows seamlessly to the dining area and sleek, newly updated kitchen complete the framed picturesque mountain views just outside. A large utility room off the kitchen provides overflow pantry space and storage as well as laundry and linen press while the hallway contains more storage cupboards and a clever 'nook' for office work or study.
There are three large, attractive bedrooms, with mirrored robes, fans and views of the established gardens. The master bedroom opens to the verandah and features reverse cycle air conditioning and a refreshed ensuite with shower and new vanity. The main bathroom has a bath, shower, vanity and separate WC. Need more room? The house is highest and there is ample room to build in under the house to suit your needs.
This sophisticated home is ideal for a family of horse lovers or hobby farm. The grounds feature six fully fenced paddocks (all with access to water), two portable 4 x 4 stables, a stable with crush, room beneath the house for a tack room or workshop, a two bay shed, side annex with power and plumbing and, above all, permanent water from the creek and a five-metre deep, spring-fed dam.
If you are looking for peace, privacy and a place to enjoy your animals and the benefits of country life within minutes of town or easy commuting distance to the Sunshine Coast or Gympie, this could be it. Properties like this don't last long so arrange an inspection today!


Our new little addition is so loved!
Babylist allows you to shop from a wide variety of shops like Amazon, Target, BuyBuyBaby, and many other boutiques/stores.
Thank you for the prayers and love as we await our 5th family member. We are so grateful to have friends and family who are just as excited as us to welcome this sweet little baby into the world.


Here is my technical model of the Tabernacle, which follows the "letter of the Law", so to speak, found in the book of Exodus. It serves as the basis for my three "Messianic Images", which are admittedly more artisticly driven then they are technical. For instance, my first image (which depicts the rib cage of Christ) doesn't show the boards on the South, as they would obstruct the view of the interior that I wanted to show. This technical layout is meant to "bridge the gaps" between symbolic art, Biblical scholarship, and sound reason.
Since Moses never told us the depth of the boards, the length of the tenons, or the exact positioning of the corner boards and pillars, EVERY model (out of the many you can find online) has to make assumptions here. Mine is no different. To be honest, it is impossible for anyone to know exactly how the Tabernacle was laid out, without an amazing archeological find. In other words, one of the boards would have to be found and measured to "prove" one's theoretical layout. That being said, I think that a very strong case can be made for the above layout using deductive reasoning and mathematics, as you will see below.
As I've protrayed in my "Messianic Images", it's my belief that the boards were mini representations of Noah's Ark (which was 300x50x30 cubits). Since Scripture doesn't specifiy the length of the two tenons under each board or the board's depth, I used the mathematical relationship between the two related dimensions that we know for certain--the width of both the Ark and the boards. Since Noah's Ark was 50 cubits wide, and the boards were 1.5 cubits wide, we can easily determine the mathematical scale between the two objects, which is 1 to 33.333 (infinitely repeating 3's). This ratio can now be applied to the two unknown dimensions, making the visible board length (the upper portion not covered by the silver bases) 9 cubits and the board depth 0.9 cubits (0.5 for the board and 0.2 on either side for the gold rings).
It should be noted here, for those thinking my measurements are wildly inventive, that several Jewish Rabbis and authorities agree that the boards were essentially 1 cubit thick. A quick internet search on your part will validate my claim. Click here, for instance, to read a Tabernacle description given at Jewish Encyclopedia.com. In like manner, the reputable New Advent Catholic Encyclopedia also supports the 1-cubit board thickness and says of the silver bases that they were "about 1 cubit high". Click here to read their Tabernacle description.
Watch this updated video (uploaded on 4/3/2015) for a full description of the Tabernacle's layout, featuring a model I built.
Why have I gone through all this trouble?
As you can see, I have spent countless hours on this project. Scripture study. Online research. Mathematical puzzling. Computer illustrations..... It's been alot of work. You might find yourself wondering, "What's the point? Why go through all this trouble? Why spend all this time on a mere theory?"
1) I love to contemplate the Scriptures. God's inaudible voice is indescribably beautiful to me. This project has captivated my mind with wonderful themes, especially the wounds of our Lord, bringing me much joy in the process. I wish the whole world could know this joy!
2) The human heart loves a good mystery. We love to puzzle. People spend millions of dollars every year, trying to find things that will get our minds churning. I sometimes think that this is why God seems to hide His face from us. It's not so much that He is displeased with us; He just knows that it's in our best interest to learn how to seek Him. He knows that the human mind delights in "being blown away" by things mysterious and unattainably deep. Let me tell you, there is no mystery deeper than God. His voice is as the sound of many waters. What a joy it is to dive down to explore the depths of that Endless Ocean!
3) I didn't want to release these "Messianic Images" without having done my homework first. Saint Paul instructed Timothy, "Do your best to show yourself to God as one approved, a workman who has no need to be ashamed, rightly handling the word of truth." I may be a Catholic layperson now, but I did attend Seminary as a Protestant preparing for ministry. Theology has to be taken very seriously, and I never want to present "half-baked" ideas to the public. I believe that I am "doing my best", as Saint Paul exhorts, but whether I am "approved by God" is yet to be seen. The Lord knows how sincerely I desire to be faithful and completely orthodox, and I trust that He will refine me and my works however He sees fit and in His time. In all things, I want everything I say and do to be in keeping with the teachings of Christ as expressed through His one, holy, Catholic, and Apostolic Church. All of the priests I have consulted so far have told me that, while being admittedly theoretical in nature (lacking certain archealogical "proofs"), the images express ideas that are entirely consistent with Catholic doctrine. May God keep me there, and may He have mercy on me should I err unintentionally.
Jesus, I trust in Your mercy.
4) Perhaps most importantly, this has been a labor of love. I believe that these images have the potential of shedding some light into dark places. Skeptics may be encouraged to examine the claims of Christ a little more seriously, while lukewarm souls may be encouraged to contemplate the wounds of Christ more deeply, causing them to glow with a burning love for the Savior. Let every heart adore Him!
For the sake of this potential good, I don't want my work to be dismissed lightly, which means that I need to present the strongest logic I can conceive of, with the help of the Lord. This is my aim. I have done my best.
Now it's up to you to decide whether you agree with me or not. I could say that it doesn't matter to me whether or not you agree, because I'm not really interested in winning an argument so that I can puff out my chest and say "I win!" On the other hand, I do care; for I'm convinced that there are beautiful truths to contemplate here that will stir your heart with love for God and His dear Son. That's something I care deeply about, and if one more soul burns a little brighter as a result of my work, all the hours I've poured into this project will have been well spent.
"The Missing Rib of the Tabernacle"
"The Western Wall of the Tabernacle"
"The Eastern Gates of the Temple"
Feel free to e-mail me with any comments, or visit my main site here.