text:
Q: FreeMarker convert string with commas to number I need to convert a locale specific string value having either commas or dot in between to indicate thousands separator, to a number in FreeMarker by removing the decimal places. For example: 13,456.79 to 13,456 OR 23.675,98 to 23.675
Using ?number throws exception saying this string can't be converted to a number. I see a similar question here:
Convert string with commas into integer in Freemarker but no solution exist. Is there a way to do so?

A: I would parse the variable as Integer before (in the Controller/Business layer) exposing it to the template (and react in case of problems with the format).
In my opinion templates should handle nothing more than the presentation of (valid) data.
Alternately...
You can try to transform the string...
<#function string_to_int s >
    <#local a = s?replace(",", "") >
    <#return a?keep_before_last(".") />
</#function>

${string_to_int("13,456.79")}

will output

13456

A: Given the limitations like locale specific numbers where decimal and thousands separator characters can either be a dot or a comma, and since I only needed to display the value and not do any numeric calculations based on the number value, I resolved this by simply ignoring the last 3 characters of the string using substring. This will remove the decimal separator and 2 decimal places (assumption being that there are always 2 decimal places).

redpajama_set_name: RedPajamaStackExchange


text:
Federal Court of Appeals Dismisses State Law Negligence Claim Against Prison Doctor Without Prejudice
November 27, 2018 | by John C. Manoog III
When someone acts carelessly and causes harm to another, a negligence claim may lie under Massachusetts law. In some situations, the injured individual may have another claim as well. For example, the plaintiff in a recent case filed in federal court alleged that she had been the victim of negligence with regard to certain medical care (that she claimed she needed while a pre-trial detainee), while also asserting a civil rights claim under civil law. If you have questions of this nature, be sure to reach out to a Massachusetts personal injury attorney for answers.
The plaintiff in a recent federal case was a pre-trial detainee at a correctional institute. She filed suit against the defendants, a doctor and the healthcare group that employed him, seeking compensation for injuries she allegedly suffered due to the worsening of a medical condition that she had had for some time. According to the plaintiff, she had psoriasis and psoriatic arthritis and had been taking a certain medication prior to being lodged at the correctional institute (from which she was eventually released). She claimed that the defendants should have allowed her to continue taking that particular medication (rather than a combination of less expensive alternatives) and that their failure to do so amounted to a violation of her civil rights under federal law and also constituted negligence under Massachusetts state law.
The United States District Court for the District of Massachusetts granted summary judgment to the defendants on the plaintiff's federal claim, holding that a reasonable jury could not find that there was deliberate indifference to the plaintiff's serious medical needs by the defendants. The court also dismissed (without prejudice) the plaintiff's negligence claim after ruling that she did not have a viable claim under federal law. The plaintiff appealed.
The Court's Decision on Appeal
The United States Court of Appeals for the First Circuit affirmed. The plaintiff argued on appeal that the defendants knew enough about her medical history to "make it obvious" that the course of treatment prescribed for her (which included various, less expensive medications than the one that the plaintiff had been taking before becoming a pre-trial detainee) amounted to a refusal to provide essential care, thus triggering a claim for violation of her civil rights under the 8th Amendment and 42 U.S.C. § 1983. The appellate court disagreed, however, pointing out that the defendant doctor's only involvement was to review non-formulary medication requests. Because the plaintiff could not prove that the defendants acted with deliberate intent to harm her or with wanton disregard for her health, the court of appeals dismissed her federal claim.
The appellate court did not reach the issue of whether the plaintiff had stated a state law claim for negligence. However, because her negligence claim was dismissed without prejudice after the federal claim was denied, the plaintiff may be able to pursue her negligence claim in state court.
Speak to a Massachusetts Injury Lawyer
There are many ways in which one person or business's neglect can cause serious harm or even death to another. If you or a loved one has been hurt because another party breached a duty of care that was owed to you or loved one, you may have a claim for compensation. At the Law Offices of John C. Manoog, III, we handle many types of negligence and personal injury cases. To schedule a free consultation, call us at 888-262-6664, and we will be happy to set up an appointment in our Hyannis or Plymouth offices at your convenience. Nos falamos Portugues.
Plaintiff's Medical Malpractice Action Fails Due to Insufficient Proof, Says Massachusetts Appeals Court
Massachusetts Court Holds That Hospital Owed No Duty to Stabbing Victim After Mental Health Patient Was Released
Posted in: Medical Malpractice, Negligence and Personal Injury

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text:
\section{Conclusion and Completions}\label{S:ccl}
The DSC approach to computational fluid dynamics allows for
simulation of turbulent flow in a plain and natural way.
Cellular coarse-graining efficiently prevents turbulent pile up
and preserves the large eddies.

Since the energy cascade starts long before transition to turbulence
(actual\-ly it is effective over the entire energy spectrum~\cite{Po},
\cite[pp.~72~ff.]{BIL}\,), a well-timed coarsening routine should
escort every DSC fluid flow algo\-rithm.
Periodic coarse-graining significantly improves algorithm stability,
even in the laminar regime -~this without overly altering the flow dynamics,
if the coarsening period is chosen as outlined in section~\ref{S:sec2}.
Handy criteria for a good choice -~in relation to mesh refinement,
e.g.~- should be subject to further study.

Details of implementation and special applications are clearly
beyond the scope of the present study.
However, we leave off with some examples for the purpose of illustration.

The graphics displayed have been computed with author's test program
\textsc{DANSE}. The latter combines a TLM Maxwell field solver with a DSC
heat transfer and fluid flow algorithm written in the lines of this paper.

In particular, the computations for coaxial RF power transmission line RL100-230
(motivated by an ion cyclotron resonance heating experiment in plasma physics)
are in excellent keeping with reference computations (\textsc{Fluent})
and empirical data:
For a line with inner conductor made of copper and air dielectric at atmospheric
pressure the heating process has been simulated in horizontal position
from standby to steady state operation with 160 KW transmitted CW power
at 100 MHz frequency, with outer conductor cooled at 40 degrees Celsius
temperature. Simultaneously, a Maxwell field TLM algorithm run
in the same mesh provided the skin effect heat sources.
\input{edge.tex}
\input{karman.tex}
\input{RL100-230_flow.tex}
\input{RL100-230_temp.tex}
\input{RL100-230_Tprofile.tex}

\section{Introduction}\label{S:int}
Discrete schemes have to master the cursed situation that they
first create by breaking space into pieces.
Mesh cell systems, however fine, can never be perfect substitute
for continuous space. Already in linear algorithms they produce
artefacts, such as unphysical \emph{spurious solutions},
and more harmful things happen in the non-linear case.

In fluid dynamics, when the non-linear spectral transfer properties
of the Navier-Stokes equations
(the \emph{energy cascade}; cf. \textsc{Pope} \cite{Po})
come into play beyond the transition to turbulence,
eddies are locally excited, down to very short scale;
cf. \textsc{Kolmogorov} \cite{Ko}.
Eddies smaller than the cell size cannot be properly resolved by a mesh
of realistic coarseness and thus tend to induce local fluctuations that
artificially pile up. Large eddy simulation (LES) aims to discard
such divergences through regularizing the flow by means of a suitable
averaging filter, and to screen its essential \emph{large patterns}
in this way.

LES stands for the most promising line in modern turbulence modelling.
The name has been coined by \textsc{Deardorff} in 1970,
who first applied LES methods to turbulent channel flow \cite{De}.
Important elements had yet been kept ready, formerly.
Already \textsc{Reynolds} \cite{Re} used temporal flow averages
that as \emph{Reynolds averages}
play still a r\^ole in conventional turbulence models.
In 1922, \textsc{Richardson} \cite{Ri} proposed mesh cell averages
for smoothing down local fluctuations. Such so called \emph{box filters}
stand today for one line of LES. Spatial filters of varied type indeed
classify modern LES methods. Excellent insight into the state of the
art is gained from the recent book of \textsc{Berselli} et al. \cite{BIL},
which not only exposes the elaborate mathematical framework but also
addresses many items of conventional turbulence modelling
(the prominent $k\!-\epsilon$ model of
\textsc{Launder} and \textsc{Spalding} \cite{LS}, e.g.).

The present paper differs from most related work in the field in that
it sharply separates the natural and technical aspects
of turbulent instability and strictly focusses on the
latter within the \emph{computational context} in hand.
The natural part, viz. essentially (modulo discretization)
the Navier-Stokes equations for viscous incompressible flow,
are thereby taken as a \emph{physical given}.
This is in obvious contrast to widespread use:
In many conventional turbulence models, as in some lines of LES,
turbulent pile-up is controlled by modifying the underlying dynamic
equations or even the physical constants.
Such models use, for instance, Reynolds number dependent
global parameters -~usually an \emph{eddy viscosity}, e.g.~-
or time and space filtered Navier-Stokes equations or any
(e.g. stochastic) variant.
All this is allowed, of course, as long as it provides numerical
data in harmony with observation. Also, a profound change of the
inner dynamics can very efficiently delimit turbulence and thus
lead to a convergent scheme.
It is yet, obviously, tuning the underlying \emph{physical phenomenon}
rather than eliminating the technical cause of divergences
that are manifestly an \emph{artefact of discretization}\/.
(Turbulence is still enigmatic in many respects, but \emph{divergence}
is certainly not a feature of turbulent flow -~observed in the continuum
of nature, e.g.)

Therefore, the central point of attack in discarding turbulent pile-up
will be in this paper the weaknesses of discretization,
while the Navier-Stokes equations are directly discretized as taken
from physics -~which not only combats the desaster at the origin,
but also yields validated results.

\section{DSC schemes}\label{S:sec1}
A mesh cell system is not just poor surrogate continuous space,
but it always introduces its proper structure.
Cellular meshes, with that we are dealing here,
artificially impose local \emph{cell-boundary duality}
upon space~\cite{He1}
-~and it is this simple fact that dual scattering channel
(DSC) schemes match in a canonical fashion.

DSC schemes are finite volume methods of a very specific type.
In technical detail, they are extensively dealt with in~\cite{He1},
so it is sufficient here to recapitulate their essential features
in a crash course like manner.
The algorithm is characterized by a two-step cycle of iteration
which alter\-nately updates the computed fields within cells and on
their interfaces. If the updating instructions are explicit, then
a \emph{near-field interaction} principle gives rise to a scattering
process interpretation known as \emph{Johns' cycle}~\cite{He1}.
A pair of vectors that represent the same field within a cell and
on its surface essentially constitutes a \emph{scattering channel}.
Equivalently, scattering channels are sometimes defined as pairs of
distributions that 'measure' the field within a cell and on one of
its faces.
The well known primal DSC scheme is \textsc{Johns}' TLM algorithm,
wherein scattering channels are visualised as transmission
lines~\cite{JoB}.
In many applications, such as computational fluid dynamics, the
TLM picture of wave propagation fails, but one can still go back
to the far more general DSC setup.

Within any \emph{physical interpretation\,}, cf.~\cite{He1}\,,
each scattering channel represents a pair of scalar or vector valued
distributions
$z^p\,=\,(\,p\,,\,Z\,)\,$ and $z^n\,=\,(\,p\,\sptilde,\,Z\,)\,$
which evaluate a physical field $Z\/$ on the surface and in the interior,
respectively, of a mesh cell. A distribution
$\,p\,$ pertinent to a cell face is called a \emph{port}
and $\,p\,\sptilde\/$ its \emph{nodal image},
and the two are related by pull-back, viz.
\vspace{-8pt}
\begin{equation}\centering\label{1.1}
(\,p\,\sptilde,\,Z\,)\;
=\;(\,p\,\circ\,\sigma\,,\,Z\,)\;
=\;(\,p\,,\,Z\,\circ\,\sigma^{-1}\,)\;,
\end{equation}
for every $\,Z\,$ (\,of class $\,C^{\,\infty}\,$, e.g.\,)\;,
where $\,\sigma\,$ denotes the spatial translation
${\sigma:\mathbb{R}^3\,\to\,\mathbb{R}^3}$
that shifts the geometric \emph{node} (i.e. the cell centre) in the
(centre of) the respective face.

It follows that there exists a \emph{scattering channel representation\,}
of DSC states:
If $M$ denotes the mesh cell system, $\,{\partial\zeta}\,$
the boundary of cell $\,{\zeta\in M}\,$
($\,{\partial\zeta}\,$ is naturally identified with the set of ports
with nodal image in $\,\zeta\,$), and $L_{\,\zeta}^{\,p}$ the
span of the $z_{\,\zeta}^{\,p}\;$ (i.e. the linear \emph{range} space),
then each state in the mesh permits a unique representation in the space
\begin{equation}\centering\label{1.2}
P\;:\,=\;\prod\nolimits_{\,\zeta\in M}\;
\prod\nolimits_{\,p\in\partial\zeta}\;
L_{\,\zeta}^{\,p}\,\times\,L_{\,\zeta}^{p\sptilde}\;,
\end{equation}
with canonical projections
${\pi_{\,\zeta}^{\,p,\,n}\,:\,P\,\to\,P_{\,\zeta}^{\,p,\,n}}$
into the port and node components of cell $\zeta\;$.
Furthermore, there is a natural involutary isomorphism
${nb\,:\,P\,\to\,P\,}$,
\vspace{-8pt}
\begin{equation}\centerin
nb\,:\,(\,z^{\,p}\,,\,z^{\,p\sptilde}\,)\,\mapsto\,
(\,z^{\,p\sptilde},\,z^{\,p}\,)\;,
\end{equation}
called the \emph{node-boundary map}, which hence maps
${P^{\,p}}$ onto ${P^{\,n}}$ and vice versa.
(The cell index $\zeta$ is omitted here and in the following
without danger of confusion.)

It stands to reason that the nodal images of different ports
(e.g. on different faces of the same cell)
can represent the same physical field in a node
and may even coincide there as distributions -~just as two ports pertinent
to neighbouring cells obviously represent the same field on a common face,
if they \emph{connect} two channels on it.
In fact, the scattering channel representation of DSC states in \eqref{1.2}
is in general highly \emph{redundant}
-~which may be utilized for process parallelization~\cite{He1}.

Within the algorithm, the port and node components are updated at even
and odd integer multiples, respectively, of half a timestep ~${\tau}\,$
and are usually constantly continued as step functions over the
subsequent time intervals of length $\tau\,$.

Note that \emph{existence}, not necessarily explicit \emph{construction}
or \emph{application}, of a scattering channel representation
characterizes DSC schemes, and that less redundant representations
are actually used in many implementations.
In fact, the scattering channel representation is basically a
theoretical means for describing (and deriving) certain DSC properties
-~such as the following.

A fundamental principle -~closely related to the \textsc{Courant-Levi}
stability criterion~- is \emph{near-field interaction}.
It requires that every updated state of a node or face depends
only states (along with their history) in scattering channels
\emph{connected} to the respective node or face -~the latter
\emph{here} being for once identified with its adjacent face,
if such exists in any neighbouring cell.

As a consequence of near-field interaction, every DSC process allows
for an interpretation as a \emph{multiple scattering process} in the
following sense.

Let for any process $\,z\,=\,{\,(\,z^{\,p}\,,\,z^{\,n}\,)(\,t\,)\,}$
\emph{incident\/} and \emph{outgoing fields}
$\,{z_{\,in}^{\,p}}\,$ and $\,{z_{\,out}^{\,n}}\,$
be recursively defined as processes in
${\,P^{\,p}\,}$ and ${\,P^{\,n}\,}$, respectively, by setting
$\,{z_{\,in}^{\,p}\,(\,t\,)\,
:\,=\,z_{\,out}^{\,n}\,(\,t-\frac{\tau}{2}\,)\,
:\,=\,0\;}\,$,\;\;for $\,t\,<\, 0\,$, \newline
and for $\,0\,\leq\,t\,=\,m\tau\,$;\,$\,m\in\mathbb{N}\,$\::
\vspace{-8pt}
\begin{equation}\centering\label{1.4}
\begin{split}
\begin{aligned}
z_{\,in}^{\,p}\,(\,t\,)\;
&:\,=\; z^{\,p}\,(\,t\,)\,
-\,nb\circ z_{\,out}^{\,n}\,(\,t\,-\,\frac{\tau}{2}\,)\;,\\
z_{\,out}^{\,n}\,(\,t\,+\,\frac{\tau}{2}\,)\;
&:\,=\; z^{\,n}\,(\,t+\,\frac{\tau}{2}\,)\,-\,nb\circ z_{\,in}^{\,p}\,(\,t\,)\;.
\end{aligned}
\end{split}
\end{equation}
Then, at every instant holds \,$\,{z^{\,p}\,(\,t\,)}\,
=\,{nb\circ z_{\,out}^{\,n}\,(\,t\,-\,\frac{\tau}{2}\,)}\,
+\,{z_{\,in}^{\,p}\,(\,t\,)}\,$\,
and \\
$\,{z^{\,n}\,(\,t\,+\,\frac{\tau}{2}\,)}\,
=\,{nb\circ z_{\,in}^{\,p}\,(\,t\,)}\,
+\,{z_{\,out}^{\,n}\,(\,t\,+\,\frac{\tau}{2}\,)}\,$\,.
Also, near-field interaction implies that every state is only a function of
states incident (up to present time $\,t\,$) on scattering channels
connected to the respective node or face.
\newline
More precisely, by induction holds:
\begin{utheorem
There exists a pair of functions
$\,\mathcal{R}\,$ and $\,\mathcal{C}\,$,
defined on back in time running sequences of incident and outgoing
fields, respectively,
such that for every cell $\,{\zeta\in M}\,$
the process $\,z_{\,\zeta}^{\,n}\,=\,{\pi_{\,\zeta}^{\,n}\circ z}\,$
complies with
\vspace{-8pt}
\begin{equation}\centering\label{1.5}
z_{\,\zeta}^{\,n}\,(\,t\,+\,\frac{\tau}{2}\,)\;
=\;\mathcal{R}\,(\,(\,z_{\,in}^{\,p}\,(\,t\,-\,\mu\tau\,)\,)
_{\,p\in\partial\zeta\,;\;\mu\in\mathbb{N}}\,)\;
\vspace{-8pt}
\end{equation}
and the port process
$\,z_{\,\zeta}^{\,p}\,=\,\pi_{\,\zeta}^{\,p}\,\circ\,z\,$
satisfies
\vspace{-10pt}
\begin{equation}\centering\label{1.6}
\begin{aligned}
z_{\,\zeta}^{\,p}\,(\,t\,+\,\tau\,)\;
=\;\mathcal{C}\,(\,(\,z_{\,out}^{\,n}\,(\,t\,+\,\frac{\tau}{2}-
\mu\tau\,)\,)_{\,n\,\mid\,\partial\zeta\,;\;\mu\in\mathbb{N}}\,)\;.\\
\hfill\scriptsize{(\;\text{'$\;\mid\,$' short-hand for
'in any of the (\emph{\.1 or 2\,}) cells adjacent to'}\;\;)}
\end{aligned}
\end{equation}
\end{utheorem}
\begin{uremarks}
\vspace{-8pt}
\hspace{24pt}
\begin{itemize}
\item[(i)]
The statements immediately imply that
$\,z_{\zeta,\,out}^{\,n}\,$ and $\,z_{\zeta,\,in}^{\,p}\,$
are themselves functions of states incident
on connected scattering channels, since
\vspace{-8pt}
\end{itemize}
\begin{equation}\centering\nota
\begin{aligned}
\quad\; z_{\zeta,\,out}^{\,n}\,(\,t\,+\,\frac{\tau}{2}\,)\,
&=\,\mathcal{R}\,(\,(\,z_{\,in}^{\,p}\,(\,t\,-\mu\tau\,)\,)_{\,p\,\in\,
\partial\zeta\,;\;\mu\in\mathbb{N}}\,)\,
-\,nb\circ\,z_{\zeta,\,in}^{\,p}\,(\,t\,)\quad\text{and}\\
z_{\zeta,\,in}^{\,p}\,(\,t\,)\,
&=\;\mathcal{C}\,(\,(\,z_{\,out}^{\,n}\,(\,t\,-\,\frac{\tau}{2}-\mu\tau\,)\,
)_{\,n\,\mid\,p\,;\;\mu\in\mathbb{N}}\,)\;\;+\\[-3pt]
&\qquad\qquad\qquad\qquad\qquad\qquad
-\;nb\circ\,z_{\zeta,\,out}^{\,p\sptilde}\,(\,t\,-\,\frac{\tau}{2}\,)
\end{aligned}
\vspace{-4pt}
\end{equation}
\begin{itemize}
\item[(ii)]
$\,\mathcal{R}\,$ and $\,\mathcal{C}\,$ are called, respectively, the
\emph{reflection} and \emph{connection\/} maps of the DSC algorithm, and
a \emph{field excitation} may be implicit in $\,\mathcal{C}\,$, cf.~\cite{He1}.
\end{itemize}
\begin{itemize}
\item[(iii)]
Near field interaction implies computational stability, if the reflection
and connection maps are
\nolinebreak{$\,\alpha$-\emph{passive}}\,,
i.e. contractive in this sense~\cite{He2}.
\end{itemize}
\end{uremarks}

\section{Coarse-graining}\label{S:sec2}
Mesh cell systems import artificial defects into space
-~which yet sometimes carry their remedy in themselves, at least in part:
For instance, the cellular mesh, by separating the virtually unresolved
cell interior from the coarse-grained cell-boundary \emph{skeleton grid\/},
necessarily fixes -~and hence \emph{delimits\/}~-
the scale of local resolution.
A clever design always takes into account the coarsening effect of the
cellular mesh -~which, on the other hand, provides quasi free of charge
a basis for large eddy approximation in the DSC setup of computational
fluid dynamics.
In fact, already intuitively DSC schemes go along with kind of natural
large pattern approximation that -~in a sense now made precise~-
associates \emph{cell averages} to some nodal quantities.

The following definition is independent of any particular application
and therefore given without reference to fluid dynamics.

\begin{udefinition} (coarse-graining)
\newline
For any port
${\,p\in\partial\zeta\,}$ with nodal image $\,p\sptilde\,$
let ${\,B^{p}\,}$ denote the set
of all ports on $\,\partial\zeta\,$, the nodal images of which
coincide with $\,p\sptilde\,$ as distributions.
Also, let ${\,w_{\,r}\,\in\,[\,0\,,\,1\,]\,}$;
${\,r\in\,B^{p}\,}$, be a set of \emph{weights}
such that
${\,\sum\nolimits_{\,r\in B^{p}} w_r\,=\,1\,}$.

Then, every DSC field which in the scattering channel representation
on each component ${\,q\in\,B^{p}\,\subset\,\partial\zeta\,}$ equals
${\,(\,z^{\,q}\,,\;z^{\,q\sptilde})\,}$ with
\vspace{-4pt}
\begin{equation}\centering\label{2.1}
z^{\,q\sptilde}\quad=\quad\sum\nolimits _{\,r\in B^{p}}\,w_r\;z^{\,r}
\vspace{-4pt}
\end{equation}
is named an (\,\emph{in $\zeta\,$ and with weights $w_{\,r}\,$}\,)
\emph{coarse-grained field} (\,\emph{pertinent                 \linebreak
to $\,p\,$} -~or also \emph{to its nodal image $\,p\sptilde\,$\,}).
\end{udefinition}

The nodal state of every such field, coarse-grained in any cell, is hence
a convex superposition -~i.a. a \emph{weighted mean\,}~- of states
that represent the field on the cell surface.
Also, substituting a DSC field with any coarse-grained field
that (obviously) leaves the cell boundary states unchanged
is then called \emph{coarsening this field\;} (in any component).

Should such an innocent looking procedure \emph{untie the Gordian knot
of turbulence\/} ? Remember that our modest aim is repairing some defects
of discretization -~rather than resolving the fundamental questions of
turbulence in the way mathematical physics should do that.
What matters here is that in the DSC setup of CFD well-timed periodic
coarse-graining of the flow efficiently prevents turbulent pile-up,
all with retaining the large eddies.
Note that the coarsening period should be taken as small as necessary
to ensure stability and precision, but large enough against the time
step (by one order of magnitude at least -~as a rule of thumb):
Clearly, coarsening inevitably also interferes with the flow dynamics.
However -~since the \emph{skeleton field\/} on the cell boundaries
is left unchanged~- the perturbation is minimal, and in fact negligible,
for suitable periods.
Through removing only the turbulent fluctuations of very short range
(below a scale given by cell size) which tend to artificially pile-up,
coarsening regularises the flow to just such a mild degree that its essential
\emph{large} patterns are preserved.

\section{Viscous Boussinesq-incompressible flow}\label{S:sec3}
The port and node distributions of a DSC algorithm can be
\emph{finite integrals}
-~as is the case for the TLM method, where finite path integrals over
electric and magnetic fields are evaluated in a discrete approximation
to Maxwell's integral equations [He4-6].
In the case at hand, they are simply \linebreak \emph{Dirac measures} that
pointwise evaluate the fields within the cells and on their surfaces,
and composites of Dirac measures which approximate the gradients of these
fields; cf.~section~\eqref{S:sec4}.

In the \emph{Oberbeck-Boussinesq\/} approximation \cite{Obb,Bss}
all material fluid properties are assumed as constant
-~\emph{except fluid density which only in the gravitational term
varies linearly with temperature}.
The energy equation of a \emph{Boussinesq-incompressible\/} fluid
of velocity $\,\vec{u}\,$ with thermal diffusivity $\,\alpha\,$,
heat source(s) $\,q\,$,
and negligible viscous dissipation and heat capacity is then the
\emph{convection-diffusion} equation for the temperature $\,T\,$,
cf.~\cite{GDN},
\begin{equation}\centering\label{3.1}
\frac{\partial\,T}{\partial\,t}\,
+\,div\,(\,T\,\vec{u}\,)\;=\;\alpha\,\Delta\,T\;+\;q\;.
\end{equation}
The Navier-Stokes \emph{momentum equations\/} for (\,the k-th component of\,)
a Newtonian fluid of dynamic viscosity $\,\eta\,$,
under pressure $\,p\,$,
and in a gravitational field of acceleration $\vec{g}$
take the form [e.g. Ptk]
\begin{equation}\centering\label{3.2}
\frac{\partial}{\partial\,t}\,(\,\varrho\,\vec{u}_{\,k}\,)\;
+\,div\,(\,\varrho\,\vec{u}_{\,k}\,\vec{u}\,)\;
+\;grad\,p_{\,k}\,
=\;\eta\,\Delta\,\vec{u}_{\,k}\;
+\;\varrho\;\vec{g}_{\,k}\;r.
\end{equation}
With
$\,\varrho_{\,\infty}=const\,$ and
$\,\varrho\,(\,T\,)=\varrho_{\,\infty}\,\beta\,
(\,T\,(\,t\,,\vec{x}\,)\,-\,T_{\,\infty}\,)\;$, wherein
$\beta\,=\,\varrho^{-1}\,\partial\,\varrho\,/\,\partial\,T$,
this becomes in the OB-approximation
\begin{equation}\centering\label{3.3}
\frac{\partial\,\vec{u}_{\,k}}{\partial\,t}\,
+\,div\,(\,\vec{u}_{\,k}\,\vec{u}\,)\,
+\,\frac{grad\,p_{\,k}}{\varrho_{\infty}}\,
=\,\frac{\eta}{\varrho_{\infty}}\,\Delta\,\vec{u}_{\,k}\;
+\,\beta\,(\,T\,(\,t,\,\vec{x}\,)
- T_{\infty}\,)\,\vec{g}_{\,k}\,.
\end{equation}
Integrating these equations over cell $\zeta$ with boundary
${\partial\zeta\;}$
and applying Gauss' theorem to integrals over
$\,{\Delta}\,=\,{div\,grad\,}$ and
$\,div\,(\,f\,\vec{u}\,)\,$
yields with time increment $\tau\,$
the following updating instructions for nodal $T$ and $\vec{u}_{\,k}$\,,
these quantities and $q\,$ averaged over the cell volume
${V_{\zeta}}$
\vspace{-4pt}
\begin{equation}\centering\label{3.4}
\begin{aligned}
T\,(\,t+\frac{\tau}{2}\,)\,
&=\;T\;+\\
&+\;\frac{\tau}{V_{\zeta}}\,
\int\nolimits_{\partial\,\zeta}(\,\alpha\,grad\,T\,
-\;T\,\vec{u}\,)\,\cdot\,dS
\end{aligned}
\vspace{-10pt}
\end{equation}
and
\vspace{-10pt}
\begin{equation}\centering\label{3.5}
\begin{aligned}
\vec{u}_{\,k}\,(\,t+\frac{\tau}{2}\,)\,
&:\,=\;\vec{u}_{\,k}\,
+\;\tau\,(\,\beta\,(\,T\,-\,T_{\infty}\,)\,\vec{g}_{\,k}\,
-\,\frac{grad\,p_{\,k}}{\varrho_{\infty}}\,\,)\;+\\
&+\;\frac{\tau}{V_{\zeta}}\;
\int\nolimits_{\partial\,\zeta}\,(\,\frac{\eta}{\varrho_{\infty}}\
grad\,\vec{u}_{\,k}\,
-\,\vec{u}_{\,k}\,\vec{u}\,)\,\cdot\,dS\;.
\end{aligned}
\end{equation}
In equations \eqref{3.4} and \eqref{3.5} the former updates
(at time $t-\tau/2\/$) of the \emph{nodal} quantities enter the right-hand
sides in the \emph{first line}, and the last former updates (at time $t\/$)
of the \emph{cell face} quantities enter the \emph{second line}\/.

The nodal values of $\,T\,$ and $\,\vec{u}_{\,k}$ are updated
at the reflection step
-~after coarsening the velocity field, e.g. with weights
proportional to the pertinent cell face areas,
whenever the coarsening period is attained~-
while the port quantities that enter the surface integrals at the
right-hand sides are updated on the connection step of the iteration cycle.
The next section outlines how we can proceed with that
in a non-orthogonal hexahedral mesh.

\section{The non-orthogonal hexahedral cell}\label{S:sec4}
The physical interpretation of a DSC algorithm associates a
smoothly varying (\/e.g. in time and space $\,C^{\,\infty}$-\,)
scalar or vector field $\,Z\,$ to port and node states
$\,z^{\,p}\,$ and $\,z^{\,n}\,$ of a mesh cell system.

Let any hexahedral cell be given by its eight vertices.
Define then \emph{edge vectors} ${(_{\nu} e)_{\nu=0,...,11}}\/$,
\emph{node vectors\/} ${(_{\mu} b)_{\mu = 0,1,2}}$,
and \emph{face vectors\/} ${(_{\iota} f)_{\iota = 0,...,5}}$,\,
using the labelling scheme of figure~\ref{F:1}\,a
\vspace{-4pt}
\begin{equation}\label{4.1}\centering
\begin{split}
\begin{aligned}
_{\mu}b\;&:\,=\quad\frac{1}{4}
&& \!\!\sum\nolimits_{\nu = 0}^{3}\,_{_{(4\mu+\nu)}}e\,\,
&&\mu\,=\,0,1,2\\
\text{and}\quad
_{\iota}f\;&:\,=\;\,\frac{(-1)^{\,\iota}}{4}
&&\,(\,\,_{_{(8+2\iota)}}e\,
+_{_{(9+2(\iota+(-1)^{\iota}))}}e\,)
\,\,\land &&\\
& &&\;\;\land\,(\,_{_{(4+2\iota)}}e\,
+_{_{(5+2\iota)}}e\,)\,\,&&\iota\,=\,0,...,5\,,
\end{aligned}
\end{split}
\vspace{-3pt}
\end{equation}
with all indices understood cyclic modulo 12\, and $\,\land\,$
denoting the cross product in $\mathbb{R}^3$.
\vspace{-25pt}
\input{fig23.tex}
At every cell face ${\iota\in\{0,...,5\}}\/$ and for any
given $\tau\in\mathbb{R}_{+}\,$ the following time shifted finite
differences of $\,Z\,$ in directions ${ _{\mu} b }$ (\,$\mu = 0,1,2\,$)
form a vector valued function
\vspace{-4pt}
\begin{equation}\label{4.2}\centering
\begin{split}
_{\iota}\!{\nabla}^{B} Z_{\mu}\,(\,t\,)\;:\,=\;
\begin{cases}
\,2\,(-1)^{\iota}(\,Z^{n}\, _{\mid\,t-\tau/2}
-\,_{\iota}Z^{p}\,_{\mid\,t}\,)\quad
&\text{if $\mu\,=\,[\iota / 2]$}\\
\,(\,\,_{2\mu+1} Z^{p}\,-\,_{2\mu} Z^{p}\,\,)
\,_{\mid\,t -\tau\,}\quad
&\text{if $\mu\,\neq\,[\iota / 2]$}\,
\end{cases}
\end{split}
\vspace{-4pt}
\end{equation}
($\,[\,x\,]$ denotes the \emph{integer part} of $\,x\in\mathbb{R}\,$).
The time increments are chosen conform with the updating conventions
of DSC schemes (as will be seen in a moment) and are consistent.
In fact, in the first order of the time increment ${\,\tau\,}$
and of the linear cell extension,
the vector ${\,_{\iota}\!{\nabla}^{B} Z\,}$
in the centre point of face ${\,\iota\,}$ approximates
the scalar products of the node vectors with the gradient
${\,\nabla Z\,}$.
More precisely, let for a fixed centre point on face ${\,\iota\,}$
and $\,\epsilon \in \mathbb{R}_{+}\,$ the \emph{$\epsilon$-scaled cell}
have edge vectors
$\,_{\iota}e\sptilde\,:\,=\,\epsilon\,\,_{\iota}e\,$.
Let also $\,_{\iota}{\nabla}^{B\sptilde}Z_{\mu}\,$ denote
function \eqref{4.2} for the $\epsilon$-scaled cell (with node vectors
$\,_{\mu}b\sptilde\,=\,\epsilon\,_{\mu}b\;$).
Then at the fixed point holds
\vspace{-4pt}
\begin{equation}\label{4.3}\centering
\begin{split}
<\,_{\mu}b\,,\,\text{grad($Z$)}\,>\,\,\,
=\,\,_{\mu}b\cdot\nabla Z\,\,
=\,\,\lim_{\epsilon\to 0}\,\,\lim_{\tau \to 0} \, \,
\frac{1}{\epsilon}\,_{\iota}\!{\nabla}^{B^{\sptilde}}Z_{\mu} \, ,
\end{split}
\vspace{-4pt}
\end{equation}
as immediately follows from the required $C^1$-smoothness of the field $Z$.

To recover the gradient
${{\nabla}Z\,}$ from \eqref{4.2}
in the same order of approximation,
observe that for every orthonormal
basis $\,{(_{\nu}u)_{\nu=0,...,m-1}}\,$ of
$\mathbb{R}^{m}\,\text{or}\,\,\mathbb{C}^{m}\,$, and for
any basis $\,{(_{\mu}b)_{\mu = 0,...,m-1}}\,$ with coordinate
matrix ${\beta_{\nu}^{\mu}}\,=\,{<\,_{\nu}u\,,\, _{\mu}b\,>}$,
the scalar products of every vector $\,a\,$ with $\,{_{\mu} b}\,$ equal
\vspace{-4pt}
\begin{equation}\label{4.4}\centering
\underbrace{<\,_{\mu}b\,,\,a\,>}_{\qquad=\,:
\,\,{\alpha}_{\mu}^{B}}\,\,=\,\sum\nolimits_{\nu=0}^{m-1}\,
\underbrace{<\,_{\mu}b\,,\,_{\nu}u\,>}_{\,\,\,
({\bar{\beta}}_{\mu}^{\nu})\,=\,({\beta}_{\nu}^{\mu} )^{^{*}}}\,
\underbrace{<\,_{\nu}u\,,\,a\,>}_{\qquad=\,:\,\,{\alpha}_{\nu}}
\,\,=\,\bar{\beta}_{\mu}^{\nu}\,{\alpha}_{\nu}\;
\vspace{-4pt}
\end{equation}
(\,at the right-hand side, and henceforth, we observe
\textsc{Einstein}'s summation convention -~yet without summing
over indices that anywhere appear also as a left-hand subscript\,),
hence
\vspace{-6pt}
\begin{equation}\label{4.5}\centering
{\alpha}_{\nu}\,=\,
{\gamma}_{\nu}^{\mu}\alpha_{\mu}^{B}\,,
\qquad\text{with}\qquad({\gamma}_{\nu}^{\mu})
\,:\,=\,{({(\beta_{\nu}^{\mu})}^{*})}^{-1}\quad .
\vspace{-4pt}
\end{equation}
This applied to the node vector basis ${ _{\mu}b\,}$ and \eqref{4.3}
yields the approximate gradient of $\,Z\,$ at face $\iota$
\vspace{-6pt}
\begin{equation}\label{4.6}\centering
_{\iota}\!\nabla Z_{\nu}\quad
=\quad{\gamma}_{\nu}^{\mu}\,\,\,_{\iota}\!{\nabla}^{B}Z_{\mu}.
\vspace{-4pt}
\end{equation}
The scalar product of the gradient with face vector
${_{\iota}f^{\nu}}\,=\,{<\,_{\iota}f,\,_{\nu}u>}\,$,\\
$\,\nu\in\{0,1,2\}\,$ is thus
\vspace{-6pt}
\begin{equation}\label{4.7}\centering
_{\iota}S\;
=\;_{\iota}f\,\cdot\,_{\iota}\!\nabla Z\;
=\!\!\underbrace{_{\iota}f^{\nu}\;
{\gamma}_{\nu}^{\mu}}_{\qquad\;=\,:\,\,_{\iota} s^{\mu}}
\!\!_{\iota}\!{\nabla}^{B} Z_{\mu}\,\,
=\,\,_{\iota} s^{\mu}\,\,_{\iota}\!{\nabla}^{B} Z_{\mu}\;.
\vspace{-4pt}
\end{equation}
Continuity of the gradient at cell interfaces yields
linear updating equations for $Z^p$ on the two adjacent faces.
In fact, for any two neighbouring cells
$\zeta$, $\chi$ with common face, labelled $\iota$
in cell $\zeta$ and $\kappa$ in $\chi\,$, continuity requires
\vspace{-6pt}
\begin{equation}\label{4.8}\centering
_{\iota}^{^{\zeta}}\!S\quad=\quad-\,\,_{\kappa}^{^{\chi}}\!S\,.
\vspace{-4pt}
\end{equation}
Substituting \eqref{4.7} for
$\,_{\iota}^{^{\zeta}}\!S\,$ and $\,_{\kappa}^{^{\chi}}\!S\,$
and observing the time shifts in \eqref{4.2}
\linebreak
provides the updating relations for
$\,Z^{\,p}\,$ at the cell interfaces.
To make these explicit, we first introduce the quantities
$\,{_{\iota}z_{\mu}^{\,p,\,n}}\,$, ($\,\iota\,=\,0,...,5\,$;
$\mu\,=\,0,1,2\,$)
\vspace{-6pt}
\begin{equation}\label{4.10}\centering
\begin{split}
_{\iota}z_{\mu}^{n}\,(\,t\,)\quad :\,=\quad
\begin{cases}
\,\,2\,(-1)^{\iota}\,\,Z^{\,n}\,_{\mid\,t}\qquad
&\text{if $\mu\,=\,[\iota /2]$}\,\,\\
\,\,(\,_{2\mu +1} Z^{\,p}
-\,_{2\mu} Z^{\,p}\,)_{\mid\,t-\tau/2}\qquad
&\text{else}\,
\end{cases}\;,
\end{split}
\vspace{-4pt}
\end{equation}
which in virtue of \eqref{1.1} yields
$\;{_{\iota}z_{\mu}^{\,p}}\,=\,{(\,p\,,\,Z\,)}\,
=\,{(\,p\sptilde,\,Z\circ\,_{\iota}{\sigma}^{-1}\,)}\,
=\\=\,{_{\iota}z_{\mu}^{\,n}\,\mid{Z\,\circ\,_{\iota}{\sigma}^{-1}}}\,$,
where $\,_{\iota}{\sigma}\,:\,n\,\mapsto\,p\,$
denotes the nodal shift pertinent to face $\,\iota\,$.\;
In particular
\vspace{-4pt}
\begin{equation}\label{4.11}
_{\iota}z_{[\iota/2]}^{\,p}\,(\,t\,)\quad=\quad
\,\,2\,(-1)^{\iota}\,\,_{\iota}Z^{\,p}\,_{\mid\,t}\;,
\end{equation}
which together with \eqref{4.10} is consistent for
$\,\mu\,\neq\,[\iota/2]\,$ with
\vspace{-4pt}
\begin{equation}\label{4.12}
_{\iota}z_{\mu}^{\,n}\,(\,t+\tau/2\,)\quad
=\quad -\;\frac{1}{2}\,(\,_{\,2\mu+1}z_{\mu}^{\,p}\,
+\, _{\,2\mu}z_{\mu}^{\,p}\,)\,(\,t\,)\;.
\vspace{-4pt}
\end{equation}
From (\,\ref{4.2}, \ref{4.7}, \ref{4.10}, \ref{4.11}\,) follows that
\vspace{-4pt}
\begin{equation}\label{4.13}
\begin{split}
_{\iota}S\,_{\mid\,t+\tau}\quad
&=\quad\,_{\iota}s^{\mu}\,(\,_{\iota}z_{\mu}^{\,n}\,_{\mid\,t+\tau/2}\,
-\,2\,{(-1)}^{\iota} {\delta}_{\mu}^{[\iota/2]}\,\,
_{\iota}Z^{\,p}\,_{\mid\,t+\tau}\,) \\
&=\quad _{\iota}s^{\mu}\,(\,_{\iota}z_{\mu}^{n}\,_{\mid\,t+\tau/2} \,
-\,{\delta}_{\mu}^{[\iota/2]}\,\,
_{\iota}z_{\mu}^{\,p}\,_{\mid\,t+\tau}\,)
\; .
\end{split}
\vspace{-4pt}
\end{equation}
Continuity of $\,Z\;$, i.e.
$\,_{\iota}^{^{\zeta}}Z\,^{p}\,=\,_{\kappa}^{^{\chi}}Z\,^{p}\,$,\,
with (\ref{4.8}, \ref{4.10}) then implies
\vspace{-6pt}
\begin{equation}\label{4.14}
_{\iota}^{^{\zeta}}z\,_{[\iota/2]}^{p}\,(\,t+\tau\,)\,=\,
\,\frac{\,_{\iota}^{^{\zeta}}s\,^{\mu}\,\,
_{\iota}^{^{\zeta}}z\,_{\mu}^{n}\,(\,t+\tau/2\,)\,
+\,_{\kappa}^{^{\chi}}s\,^{\nu}\,\,\,
_{\kappa}^{^{\chi}}z\,_{\nu}^{n}\,(\,t+\tau/2\,)}
{_{\iota}^{^{\zeta}}s\,^{[\iota/2]}
+\,( -1 )^{\iota +\kappa}\;_{\kappa}^{^{\chi}}s\,^{[\kappa/2]}}\;.
\vspace{-4pt}
\end{equation}
For completeness we agree upon setting
$\,_{\iota}^{^{\zeta}}z\,_{\mu}^{p}\,(\,t+\tau\,)\,
:\,=\,_{\iota}^{^{\zeta}}z\,_{\mu}^{n}\,(\,t+\tau/2\,)\,$
for $\,\mu\,\neq\,[\iota/2]\,$
(although this contains a slight inconsistency
in that continuity might be infringed; this can easily be remedied
by taking the arithmetic mean of the two adjacent values).
 -~In fact, our agreement doesn't do harm, since any discontinuity
disappears with mesh refinement.

We dispose, hence, of a complete set of recurrence relations for
$\,{z^{\,p}}\,$ (\,given $\,{z^{\,n}}\,$ by the former reflection step)
which at the same time determine
the field components on face~$\iota$ and their gradients
\vspace{-6pt}
\begin{equation}\label{4.15}\centering
_{\iota}\!\nabla Z_{\nu}\quad
=\quad{\gamma}_{\nu}^{\mu}\; _{\iota}z_{\mu}^{\,p}.
\vspace{-4pt}
\end{equation}
Essentially this constitutes the connection step of the algorithm.
\newline
Nodal gradients are similarly (and even more simply) derived, using
\vspace{-6pt}
\begin{equation}\label{4.16}\centering\notag
{\nabla}^{B} Z_{\mu}^{\,n}\,(\,t\,+\frac{\tau}{2}\,)\;\;:\,
=\;\;(\,_{2\mu+1} Z^{\,p}\,-\,_{2\mu} Z^{\,p}\,)\,(\,t\,)\;;
\quad\mu\,=\,0,\,1,\,2\;
\vspace{-4pt}
\end{equation}
in the place of \eqref{4.2}, and then again \eqref{4.6}.
With the node and cell-boundary values and gradients of $\,T\,$ and
$\,\vec{u}\,$ the nodal updating relations for the latter are
immediately extracted from equations~(\,\ref{3.4}, \ref{3.5}\,)
in section~\ref{S:sec3}\,. For equation \eqref{3.4} this is
essentially (up to the convective term) carried out in
\cite{He1}, section~5, and the procedure remains straightforward
in the case at hand.
Note that a well-timed LES coarsening routine, cf. section~\ref{S:sec2},
should be periodically carried out before the nodal step of the iteration
cycle in order to obviate instablities called forth by the energy
cascade~\cite{Po}.

The updating relations thus obtained are explicit and consistent
with near-field interaction (\,only adjacent quantities enter\,).
So, they can optionally be transformed into scattering relations
for incident and reflected quantities \eqref{1.6} along the
guidelines of section~\ref{S:sec1} -~with established advantages
for stability estimates \cite{He2}.

\section{Pressure}\label{S:sec5}
Unlike compressible flow -~wherein a thermodynamic \emph{state equation}
relates pressure to density and temperature~-
Boussinesq-incompressible flow is conserved by pressure acting
like a potential against violations of the local flow balance.
Hence, the pressure is directly coupled to the flow divergence by
\emph{Poisson's equation}:
\vspace{-0.15cm}
\begin{equation}\centering\label{5.1
\Delta p\,=\,(\,\varrho_{\infty}/\tau\,)\,div\,\vec{u}\,.
\vspace{-0.10cm}
\end{equation}
The solution $p$ for fluid velocities updated in the connection step
provides a pressure gradient, which in the next reflection step
-~via equations (\ref{3.3},\ref{3.5})~- repairs sporadic violations
of the flow balance.
Systematic test computations have shown that additional
\emph{divergence clearing}, as proposed by the author in earlier
papers, e.g.~\cite{He3}, is not necessary (nor even profitable)
-~and may be rather on the debit of computational performance and stability.

In integral form, after using Gauss' Theorem, equation \eqref{5.1} becomes
\vspace{-0.15cm}
\begin{equation}\centering\label{5.2
\quad\tau\,
\int\nolimits_{\,\partial\zeta}\, grad\,p\,\cdot\,dF\quad
=\quad\varrho_{\infty}\,
\int\nolimits_{\,\partial\zeta}\,\vec{u}\,\cdot\,dF\;,
\vspace{-0.10cm}
\end{equation}
which can be solved by a Gauss-Seidel routine or by successive
overrelaxation, carried out after updating the face velocities
in the connection step.

In each iteration, firstly the discrete cell boundary integral
${\,I_{\partial\zeta}}\,: =\,{\int _{\partial\zeta}\vec{u}\cdot dF\,}$
is computed and explicitely -~by solving a linear equation in
$\,I_{\partial\zeta}\,$ and the cellular pressures~- the unique $\,p^{n}\,$
that exactly compensates $\,I_{\partial\zeta}\,$
so that \eqref{5.2} is satisfied in every cell. In a second run
over the mesh, continuity of the pressure gradient is re-established
at the cell interfaces by updating the face pressures along the
lines of the last section (viz. taking $\,Z\,$ as $\,p\,$ there).
The loop is reiterated until (usually after a few iterations) equations
\eqref{5.2} hold with sufficient precision.

redpajama_set_name: RedPajamaArXiv


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text:
Ugly Truths About Secession
Once upon a time, there was a really close baseball game. Extra innings. Tied for eternity. Then one team got a base hit, and it was just enough for them to score.
Some people on the losing team groaned, but they shook the hands of the winning team, and talked with each other about training harder for the next game. But one little boy could no contain his anger. He grabbed his glove and his bat, and charged off the field.
The little boy climbed a hill near the field. He stood at the top and yelled, "I don't want to play anymore. I'm taking my stuff, and I'm going home. I really mean it this time."
The rest of the players drifted away, heading to their respective homes and separate lives. The little boy remained on the hill, shouting.
"I mean it! I'm going home, and I'll never play with any of you ever, ever again!"
Oh, wait, that wasn't a baseball game. That was reaction to a presidential election.
I understand that half the country didn't get the president they voted for. But talking of secession, of leaving the United States, benefits no one.
There are two reasons an individual would petition for secession. One, they want to send Washington / the president a message. Two, they really want to secede.
To the first group of people: Stop it. You're making yourselves look ridiculous, and you're wasting energy. Do you really think the president cares if you voted for him or not, or how angry you still are today? He doesn't give a damn. You could get five million signatures for secession and he wouldn't care. If the president were the sort of person who listened to your concerns and cared about ending divisiveness, you wouldn't be protesting in the first place. So cut it out. You're not helping a cause. You're looking foolish, and wasting time and energy.
Also, if you're doing this just to make a point, it's an empty gesture. Don't pull this kind of crap unless you mean it. You're like the little boy after the baseball game, telling all the other kids you won't play with them again. When you do show up for the next game, the other kids will mock the hell out of you...and you'll deserve it.
To the people who genuinely want to secede from the United States: find your passport, pack a bag, and leave. That's the only way your plan is going to work.
The big court case on point is Texas v. White, 74 US 700 (1869). The legal issue in the case was whether or not Texas remained part of the US following the Civil War, since Texas seceded from the the US to join the Confederacy.
Here's the chunk of language from the case modern secessionists must confront:
When, therefore, Texas became one of the United States, she entered into an indissoluble relation. All the obligations of perpetual union, and all the guaranties of republican government in the Union, attached at once to the State. The act which consummated her admission into the Union was something more than a compact; it was the incorporation of a new member into the political body. And it was final. The union between Texas and the other States was as complete, as perpetual, and as indissoluble as the union between the original States. There was no place for reconsideration or revocation, except through revolution or through consent of the States.
(bolding and underlining done by this author, for emphasis)
So, if you want your state to secede, you've got a couple of options. One, revolution. You need a military for that, a military that can successfully take on the US Military. Not likely. Also, there's the whole thing of people dying at the hands of their fellow countrymen. We did it once; let's not have a repeat. If the ghosts of your Civil War era ancestors could weigh in on this issue, they'd bop you over the head, because they know what a bad idea this is.
Option number two for secession: consent of the States. This is the one that has people petitioning. Does this option have a real likelihood of success? No. For one thing, the other states aren't likely to agree to any state leaving. Second, you'd have to hold a state vote on secession. And I gotta tell you, even states that went red for the presidential election aren't likely to vote yes for secession. The issues are totally different. You're talking about yanking apart economies, infrastructure, military institutions, legal systems, etc. As a citizen of Texas, will I need a passport to go to Louisiana? What about the Social Security my mother accrued...if she lives in Texas, and Texas secedes, does she forfeit her Social Security? Bet she does. And if you put secession to a vote in Texas, people are going to talk about things like this. Odds are, they'd end up voting no.
Bottom line: petitioning for secession isn't the way to make a point, and seceding isn't practical
Do you really feel strongly about leaving the US? Do it. Vote with your feet. I suggest you research options in Central America. Several countries in that part of the world have established communities of expats from the USA. Some of them allow US citizens to own property, and welcome retirees. Skip Canada; it's almost impossible to get a job if you aren't Canadian. But countries where there are established US expat communities offer some opportunities for jobs: there's networking in the community, for one, and professionals like lawyers or doctors can make some money working for their fellow countrymen. Local companies will even hire US expats, if you have the right skill sets. If you get enough secessionists together, you could start a business in the other country. See? Something pracitcal to do with all your energy and passion.
But forget secession. That's sandlot talk.


text:
Grand Mufti Denies Presence of Temples
The Grand Mufti of Jerusalem denied the historical presence of Jewish temples atop a contested holy site that has been a flashpoint in the ongoing violence wracking the Jewish state.
Countering historical evidence and a publication released decades ago by a precursor to his office, the Grand Mufti of Jerusalem denied the historical presence of Jewish temples atop a contested holy site that has been a flashpoint in the ongoing violence wracking the Jewish state.
Speaking in Arabic to Israel's Channel 2, Sheikh Muhammad Ahmad Hussein said that the Temple Mount, known as Haram al-Sharif to Muslims, was a mosque "3,000 years ago and 30,000 years ago" and "since the creation of the world."
The grand mufti, who was appointed by Palestinian Authority President Mahmoud Abbas in 2006, said in the same interview, "This is the al-Aqsa mosque that Adam, peace be upon him, or during his time, the angels built."
During the interview, the Times of Israel reported, Hussein denied there had ever been a Jewish presence atop the Temple Mount, in clear contradiction of historical evidence,
including "A brief guide to Al-Haram Al-Sharif" published by the Supreme Moslem Council in 1924. The council was led by the then-grand mufti, Haj Amin al-Husseini.
The document, which has circulated widely online, acknowledges the sanctity and long history of the site.
"Its identity with the site of Solomon's Temple is beyond dispute," the document reads in part. "This, too, is the spot, according to the universal belief, on which 'David built there an altar unto the Lord, and offered burnt offerings and peace offerings.' "
There's a sentence associated with the holy site, said Dr. Robert Satloff, executive director of The Washington Institute for Near East Policy, that "the Temple Mount/Haram al-Sharif is the site of Solomon's temple and al-Aqsa is the site of Muhammad's ascension to heaven."
"One is a faith statement and the other is rooted in fact. Both are powerful and relevant, but it's a mistake to equate the two statements," said Satloff. "And that's regrettably what the mufti has done, and in so doing, he erases history, which is self-defeating, because the whole point of building the al-Aqsa mosque" was to enshrine the history of the space.
The al-Aqsa mosque was commissioned in the eighth century by Caliph Abd al-Malik ibn Marwan.
What Hussein said on Israeli television underscores "the fact that the current denial of the historical Jewish presence on the Temple Mount is a political statement of recent origin," said Satloff. "It's a political fact that reflects a political dispute and in that sense needs to be addressed in a political fashion."
Haj Amin al-Husseini was the grand mufti of Jerusalem in pre-state Israel when the pamphlet was published. He is the same Husseini whom Israeli Prime Minister Benjamin Netanyahu recently said inspired Adolf Hitler to exterminate the Jews. Netanyahu walked back his comments after harsh criticism from prominent historians and Holocaust memorial organizations, and German Chancellor Angela Merkel reiterated Germany's responsibility for the genocide of 6 million European Jews during World War II.
Still, Husseini, who died in exile in Beirut in 1974, was a fierce anti-Zionist and ally of Hitler. He met with the Nazi leader in November 1941, extracting support for the eradication of a Jewish presence in the Holy Land, although there is no evidence that he told Hitler to exterminate the Jews. Husseini focused his meeting on obtaining Nazi backing for "the independence and unity of Palestine, Syria and Iraq" under Arab rule.
The Temple Mount is frequently a flashpoint in Jerusalem. Non-Muslims may visit, but only Muslims may pray there. The site is overseen by the Jordanian Waqf, with security provided by Israeli forces. Palestinian authorities blamed unspecified Israeli moves to change the status quo for the flare-up of violence that has seen Palestinians resort to stabbing attacks against Israeli civilians. The Israeli government vehemently denies that any change had taken place atop the holy site.
Whether Jews should visit the site at all is contested. Israel's Ashkenazi Chief Rabbi David Lau and Sephardi Chief Rabbi Yitzhak Yosef issued a statement last week reiterating a previous decree barring Jews from visiting the Temple Mount, lest they accidentally stumble upon the site of the biblical "holy of holies," where only specific people may tread, and "infringe on the purity" of the sacred place. Others, like Rabbi Yehuda Glick, campaign for expanded Jewish access on the Temple Mount. Glick was shot in the chest four times last year by Mutaz Hijazi, who
allegedly said "I'm very sorry, but you're an enemy of al-Aqsa, I have to" before firing.
U.S. Secretary of State John Kerry traveled to Europe and then Jordan last week in an effort to resolve the ongoing violence.
Kerry, speaking alongside Jordanian Foreign Minister Nasser Judeh on Saturday, announced that Netanyahu and King Abdullah II had agreed to 24-hour video coverage of all sites on the Temple Mount. Kerry characterized the installation of cameras as a "game-changer" that could discourage "anybody from disturbing the sanctity" of the site.
Satloff believes that while the cameras may offer a technical solution, because they do not address the political nature of the issue, the cameras are "regrettably, unlikely to impact the situation."
Judeh underscored Jordan's interests in the contested holy site and called Jordan a "stakeholder" in any negotiated peace between Israel and the Palestinians.
"When it comes to the Palestinian-Israeli peace, all of the final status issues between the Palestinians and the Israelis touch the very heart of Jordan's national security and national
interests," as Jordan is home to millions of Palestinian refugees, said Judeh.
Israeli police intervened on Monday when technicians, at the behest of the Muslim Waqf in charge of the Temple Mount, began installing cameras. Israel maintains that the cameras will only be installed after Israeli and Jordanian technical teams finalize the arrangements.
In remarks to the press days before, Netanyahu said, "I think it's time for the international community to say clearly to President Abbas: Stop spreading lies about Israel, lies that Israel wants to change the status quo on the Temple Mount, lies that Israel wants to tear down the al-Aqsa Mosque and lies that Israel is executing Palestinians. All that is false."
Contact: mapter@jewishexponent.com
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» McCormick Black Pepper — An Important Source of Antioxidants?
McCormick Black Pepper — An Important Source of Antioxidants?
NOTE: The next new Mouse Print* story will be published on Monday, January 6, 2014 (our trusty mouse needs time off to hunt for his annual supply of dairy-free cheese substitute since unfortunately he is lactose intolerant).
One commercial proclaims, using words to the effect that "sprinkling black pepper on scambled eggs is an important source of antioxidants".
Wow, more antioxidants than a 1/2 cup serving of watermelon. Not so fast.
According to the FDA, watermelon is not one of those fruits particularly dense with vitamin C (a key antioxidant).
A serving size is defined as two cups, and contains 25% of the daily requirement of vitamin C. If you wanted to get the equivalent boost of vitamin C from black pepper, you would have to sprinkle about a full teaspoon of pepper on your eggs. Ha choooooo. The recommended 1/4 teaspoon that McCormick suggests that you sprinkle on eggs will only provide you with 6.25% of your daily requirement of vitamin C according to them. Hardly something to boast about as a boost of antioxidants. As noted in the comments (thanks, Leeann), there are other antioxidants in watermelon too, but they are in very small amounts.
NutritionData.com suggests that even a full teaspoon of black pepper is not particularly nutrient-rich (but not all nutrients are listed on nutrition facts labels).
The goal is to reach "people who maybe weren't superinvolved cooks … but were still interested in healthy eating," said Jill Pratt, VP-marketing for consumer products. The company looked at some common meals "and found a way to make them a little bit healthier by amping up the antioxidants in them," she said.
No matter how you spin it, black pepper is NOT an important source of antioxidants in your diet based on the amount of pepper you might actually use to spice up an individual serving.
Perhaps McCormick should just stick to advertising how much flavor their seasonings add to food. Advertising the extremely minor health benefits of spices is crossing a line.
And don't forget these spices are irradiated – effectively making them a dead food.
They never said 'Vitamin C" did they? There are many different antioxidants that are present in the peppercorn. Try an internet search, you'd be surprised what you can learn.
Edgar replies: Leeann, they make the claim about antioxidants comparing it to watermelon. The only antioxidant in watermelon is vitamin C. So yes, they are in this instance referring to vitamin c.
In reply to Edgar above: Watermelon does have other antioxidants, including lycopene. So your logic is flawed. The total amount of antioxidants in peppercorns is comparable to watermelon as stated by McCormick.
Edgar replies: I stand corrected, Leeann. Watermelon does contain lycopene (not listed on the nutrition facts label). According to the USDA, one and half cups of watermelon contains between 9-13 milligrams of lycopene. The McCormick ad uses a serving size comparison of one half cup of watermelon. So that portion would have only between 3 and 4 milligrams of lycopene. That minuscule amount barely nudges up the antioxidant content of 1/4 of a teaspoon of black pepper. The point is McCormick is giving consumers a false sense of the beneficial value and benefit of a few shakes of pepper, not that their equivalency claim was wrong.
>>Edgar replies: Leeann, they make the claim about antioxidants comparing it to watermelon. The only antioxidant in watermelon is vitamin C. So yes, they are in this instance referring to vitamin c.<< Actually, Vit. A is also an antioxidant. Edgar replies: Patrick, thanks for pointing that out. The problem remains, as the post states at the end, the normal portion of black pepper usage -- a couple of shakes (or even 1/4 teaspoon) -- is so small and insignificant, that even if it was the most powerful antioxidant on earth (it is in the top 50), this tiny amount is going to make little difference in your nutrition. Think of this analogy: a new suntan lotion claims to be the ultimate protection for sunburn because it contains the most protective ingredient ever invented. But, if you use only one drop on your knee, it will do little to protect you overall from sunburn.
I never thought about pepper as a source of much of anything besides flavor. Knowing that there is some actual good in it is worthwhile. However, I do think that their claim bloats the facts (about antioxidants) to make them appear more important than they are.
Isn't it possible that McCormick adds something to their formula that is not present in generic black pepper?


A-589 TCG Işın one of the salvage vessels of Turkish Navy has been very busy since 16th January 2012.
On 16th January one T-37 training plane from Turkish Air Force crashed off Foça, İzmir during a routine training flight. A-589 TCG Işın was of the ships that was dispatched to find the wreck of the planer and to recover the bodies of the pilots.
On 31th January a Cambodian flagged merchant ship M/V Vera sunk off the coast of Ereğli, Zonguldak after taking water during a powerful snow storm. TCG Işın is at the scene of the incident and is searching for the bodies of the missing 8 sailors.
TCG Işın started her life as ARS-25 USS Safeguard. She was laid down on 5 June 1943 by the Basalt Rock Company in Napa, California; launched on 20 November 1943; and commissioned on 30 September 1944 at the Southern Pacific Docks,Vallejo, California. In US Navy service she took part in 2. World War, Korean War and Vietnam War.
She was decommissioned from US Navy and struck from the Naval Vessel Register, 6 August 1987. She was transferred under the Security Assistance Program, to Turkey, 18 August 1987. Although the article in Wikipedia claims her fate is unkonwn, I can tell she is well and still working hard.
She can tow large ships and refloat stranded ships. with the equipment on board she can support assisted dives up to 190 feet.
She will be replaced as the new Moship and Ratships ordered by the Turkish Navy from Istanbul Shipyards will enter service in a couple of years.


Whoa! You could get whiplash watching the state budget negotiations.
The Appropriations Committee finally passed out a budget on a divided report, and the score was House Republicans against the world.
Democrats acquiesced to Republicans in agreeing to support a constitutional amendment that would require a two-thirds vote to raise any tax. That was a halfway measure toward the Republican hopes to abolish the income tax by constitutional amendment. But halfway is what it's about, right? Compromise.
No way, said the House Republicans. Without their votes, the budget could not survive a LePage veto. Like a mouse is snatched up by an owl, the budget was snatched up by legislative leadership. Having been worked largely behind closed doors by the Appropriations Committee, it came blinking into the sunshine just long enough to travel from that second floor committee room to the third floor when it again vanished behind the doors of the leaders.
Yes, the people who had just spent five months examining the budget line by line, listening to hundreds of hours of testimony from the Maine public (and Maine lobbyists), were left sitting on the outside.
They couldn't even press their noses to the glass, because there was no glass, just a door.
It is discouraging, to say the least, for an Appropriations Committee to put its heart and soul into the making of a budget only to have it taken away by leadership at the last minute.
And no offense, but leadership – and anyone else who has not served on the committee – may be on top of the policy issues, but they are not cognizant of the myriad details of a budget and how a nudge here makes a hole there.
At any rate, it mattered not, because when leadership tried to reach an agreement last week, the House Republicans shot that down, too. The new proposal restored cuts to the income tax and broadened the sales tax base, both of which were proposals the governor had in his original budget. The agreement to put the two-thirds vote on tax increases into the constitution vanished.
"No, no, a thousand times no," said the House Republicans. If there are any statesmen in this debacle, it is the two presiding officers, Senate President Mike Thibodeau and House Speaker Mark Eves. Time and again they have urged the troops back to the table. Both have been willing to make concessions in order to get the job done. Thibodeau has been particularly restrained in not throwing fuel on the fire. Predictably, he is taking a beating from the House R's and the governor as well. He should take it as a badge of honor.
The governor's contribution to a budget resolution? It was to dismiss the idea that a state shutdown would be all that dire. It's simple, said he. He would just extend the current budget a month at a time, by 1/12th of the current year's total.
Three problems with that logic, governor. First, Maine has no provision to "extend" a budget. Second, the state's bills are not evenly divided by month. Much more may come due in one month than in another. And third, it is exactly what Congress does with "continuing resolutions" that makes us think of them as irresponsible banana heads, not to put too fine a point on it.
In the meantime, the governor is living up to his promise to veto all bills sponsored by Democrats, an ill-considered action if ever there was one. Of the first 12 to fall victim to his threat, the legislature overrode his veto on 10 of them. And not just with the aid of a few Republicans, but with most of them.
Note to governor: You are losing the legislature. Never mind the Democrats, the Republicans are no longer willing to be the wind beneath your increasingly quirky wings. You have three years left in your second term. It will be a long, cold slog with no one but Ken Fredette at your side.
Other governor's initiatives are going down to defeat, too. His bill proposing that the Attorney General be appointed by the governor went down 115-32 in the House. Republican representatives present voted 33-32 against the bill. The governor's bill to allow the governor to appoint the state treasurer? Dead. The governor's bill proposing a constitutional amendment to eliminate the income tax? Dead.
The budget is not the only unfinished bill in the system. While legislative leadership announced Monday night that a deal had been reached, it is by no means a sure thing.
When you are reading this, the legislature should have adjourned. T'ain't likely.


This original, hand woven extreme yarn footstool will make a statement in any room, while its sqeezably soft top make it cozy and inviting.
The Demetrius has that ever so cool Scandi-Hygge vibe that everyone is talking about, and as an original design, it will be a talking point which ever room it resides. It would make a wonderful wedding gift, or new home gift. For those with smaller spaces, it is the perfect piece to compliment a room without overtaking it.
It is soft, comfortable and functional from living space, to nursery to bedroom.
There are several colour choices available and colours can be combined, to create your own statement piece. If there is a colour you would like, or a combination I haven't already considered, please message me and I will be happy to create your one off piece.
Each footstool is hand crafted, and covered in a neutral fabric that compliments each of the hand woven tops.
The footstool itself meets all fire regulations and the base is FSC certified.
The legs of The Demetrius are mid-century that have been painstakingly refubished, but still have a bit of that vintage charm.
The Demetrius is made from an extremely chunky cotton/poly blend, that makes you want to hug it. The top is easily removable, as it has a bit of an elastic band feel to it. These tops can be handwashed at 30 degrees, making it both stylish and functional in any household.


Oscar Ouma in action against Fiji. Kenya shocked Fiji thanks to a try from Amonde after the hooter.
This entry was posted in Kenya Rugby Articles, Kenya Rugby Sevens Pictures, Kenya Sports news and commentary and tagged kenya rugby photos, kenya rugby pictures, Kenya sevens. Bookmark the permalink.


Organise your vacation program in Greece with our specialists.
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text:
Die römisch-katholische Kapelle Ste-Véronique im  Weiler La Véronique, einem Ortsteil von Bannalec im Département Finistère in der Bretagne, ist seit 1914 als Monument historique klassifiziert.

Geschichte
Die der heiligen Veronika geweihte Kapelle ersetzt ein älteres Gotteshaus, das sich etwa 200 Meter südlich vom heutigen Standort befunden hat und vermutlich im Jahr 1597 im Zuge kriegerischer Auseinandersetzungen zerstört wurde. Die neue Kapelle wurde zwischen 1605 und 1610 im Auftrag des Barons de Kermeno in nachgotischen Formen auf dem Grundriss eines lateinischen Kreuzes errichtet. Die Sakristei wurde im Jahr 1662 hinzugefügt. Die Kapelle bewahrt drei ältere Glasfenster aus dem 16. Jahrhundert.

Das Bauwerk war im Jahr 2019 Drehort für die Folge Bretonische Geheimnisse der Kriminalfilmreihe Kommissar Dupin. Die Handlung des Romans und der Verfilmung spielt allerdings nicht in Bannalec im Finistère, sondern weiter östlich im Wald der Brocéliande bei Rennes.

Literatur
 Le Patrimoine des Communes du Finistère. Flohic Editions, Band 1, Paris 1998, ISBN 2-84234-039-6, S. 58–59.

Weblinks

Einzelnachweise

Kirchengebäude im Département Finistère
Kirchengebäude im Bistum Quimper
Veronikakirche
Gotische Kirche
Gotisches Bauwerk in der Bretagne
Erbaut im 17. Jahrhundert
Monument historique (Kapelle)
Monument historique seit 1914
Steveronique
Steveronique

redpajama_set_name: RedPajamaWikipedia


On Tuesday 30.10.2018 we organized the very first Helsinki Design Thinking Hackathon, gathering 120+ participants from various backgrounds to solve real life challenges of Artificial Intelligence and its relation to customer experience. The challenges were provided by our four partners Alko Oy, LähiTapiola, VR Group and Finnair.
It was fascinating to see how well all the participants were able to throw themselves into the game, although they were surrounded by people they didn't know from before. Everyone bravely trusted the process of design thinking although many times they felt they were running out of time or got stuck with the ideation.
"I particularly enjoyed candies, superb facilitator, great team member, challenging challenge!"
"It was organized well & it flowed well."
"I enjoyed the atmosphere and meeting with a diverse bunch of fascinating persons."
We would like to give thanks to all of you who were involved in the Hackathon, we can't wait for the next one to come! 🚀 In the meantime, you can check our Service Design, Digital Design and Development offering.
Ps. If you would like to arrange a Hackathon together with us or otherwise would like to hear how Nordic Morning could help your company's development using Design Thinking methods, reach out - we are happy to come and discuss things further!


An audacious attempt to find explorer Sir Ernest Shackleton's ship Endurance has been called off after the expedition team lost an undersea drone beneath Antarctic ice.
Endurance, which was lost in an ice floe off Antarctica more than 100 years ago, is one of the world's most famous undiscovered shipwrecks.
The Weddell Sea, where Endurance was lost, is one of the harshest environments on the planet and the expedition to find the wreck has generated worldwide interest.
AUV7 was operating beneath a vast ice floe when it was lost, according to the Weddell Sea Expedition, and was on the final leg of a mission that had lasted more than 30 hours. There is a possibility that the drone captured images of the Endurance on the seabed before contact was lost, researchers say. With the drone lost beneath the ice, however, we will never know whether it spotted the famous wreck or not.
"Everyone at Ocean Infinity is deeply disappointed that at the eleventh hour, we were not able to produce the images of what is without doubt the most challenging shipwreck in the world to locate," added Oliver Plunkett, CEO of undersea drone manufacturer Ocean Infinity, in the statement.
Endurance's Captain, Frank Worsley, carefully recorded the ship's final coordinates before she broke up and descended below the ice. The modern expedition used these coordinates to plan its search for the wreck.
Despite failing in its attempt to find Endurance, the project amassed a wealth of scientific information, according to said Prof. Julian Dowdeswell, the expedition's chief scientist and director of the Scott Polar Research Institute in Cambridge University. "Through the scientific data gathered during the Expedition, we have deepened our knowledge and understanding of Antarctic oceanography and ecosystems, and our observations on the glaciology and geology will play a critical role in our understanding of Antarctic ice shelves and sea ice and, importantly, the changes that are occurring here today," he said, in the statement.
Ocean Infinity's Plunkett noted that data collected by the Weddell Sea Expedition's drones will prove useful in understanding the polar impact of climate change.
Prior to starting its search for Endurance, the Weddell Sea Expedition completed scientific research at the Larsen C ice shelf that made headlines in 2017 when a huge iceberg dubbed A68 broke off the ice mass. The iceberg is the size of Delaware.


Sometimes I'm too tired to cook. But I do it anyway. On the rare occasion when I succumb to lethargy, I feel it's a defeat. Why should living alone entail a less full life? Why shouldn't I expect of myself a dinner at table? A life eating on the couch watching TV is a half-life and like all carbon-based things I feel my life seeping out of me when I do it. Reading and listening to music at the table is an ongoing commitment to making my single life as rich as I can. When I feel too tired to prepare a meal, I lower my expectations, but I don't abandon them. Half the effort an ordinary weekday meal requires comes in figuring out what I want to eat.
So, here is a simple idea. I am enjoying adding diced potatoes the dishes I have always thought would be weighed down by additional starch. A little potato adds umami, another dimension to a dish. This one is a no-brainer.
Dice half a chorizo link and four fingerling potatoes. Scrape the kernels off one ear of corn. Pour 2 teaspoons of olive oil or lard in a small skillet over a medium-low flame. Add a minced garlic clove or two and a minced shallot. Let them soften in the fat. Then add the chorizo. Spread the chorizo out so that the pieces are not crowded. Leave them be for two or three minutes. Stir and let them be for another couple of minutes. Add the potatoes, stir, and let them brown with the chorizo. Add the corn, mix it all together. Season with salt and pepper. Put in a bowl and have with a small salad.


Load your family into the 2016 GMC Yukon XL. Under the hood you'll find an 8 cylinder engine with more than 350 horsepower, and load leveling rear suspension maintains a comfortable ride. Four wheel drive allows you to go places you've only imagined. Top features include power windows, a built-in garage door transmitter, a blind spot monitoring system, power door mirrors and heated door mirrors, a power liftgate, an overhead console, a trailer hitch, and power seats. Features such as automatic climate control and leather upholstery prove that economical transportation does not need to be sparsely equipped. Power adjustable pedals allow the driver to optimize his or her driving position, enhancing visibility, comfort and safety. Rear passengers enjoy the seat heating functionality, keeping them warm during the winter months. Third row seats provide an even greater maximum passenger capacity. For drivers who enjoy the natural environment, a power moon roof allows an infusion of fresh air. State-of-the-art amenities such as steering-wheel memory and pedal memory yield a more personal driving experience. You and your passengers will enjoy the stereo system, which includes a CD player with MP3 capability, and 9 speakers, providing excellent sound throughout the cabin. Rear LCD monitors provide entertainment that your passengers will appreciate no matter how far the drive. Safety equipment has been integrated throughout, including: dual front impact airbags, front side impact airbags, traction control, brake assist, a panic alarm, onStar, and 4 wheel disc brakes with ABS. You'll never lose visibility with rain sensing wipers, which activate automatically when the drops start to fall. A Carfax history report indicates just one previous owner. You will have a pleasant shopping experience that is fun, informative, and never high pressured. Please don't hesitate to give us a call.


Meg Ryan is the latest movie actress to move into TV after signing up to star in and produce a comedy for NBC.
The 51-year-old actress will play a one-time hotshot editor-turned-soccer-mom who returns to the New York City publishing house where she once worked, only to find her former intern is now her boss.
Her character decides it is time to re-join the workforce after separating from her husband and tries to juggle all of the responsibilities in her life, including pleasing her neurotic employer, looking after her kids, going through a divorce, and keeping her meddlesome mother-in-law at bay.
The sitcom will be written by Emmy Award nominee Marc Lawrence.
The actress recently revealed she prefers to live outside of Hollywood for a quieter life with her boyfriend John Mellencamp and eight-year-old daughter Daisy.
Fellow big screen star Halle Berry recently confirmed a move into TV also. She has signed up for drama series 'Extant' for rival network, CBS.


This study has increased the viability of miniature ion thruster technology, advanced state-of-the-art discharge modeling, and revealed important aspects of discharge plasma processes. These extensions of existing ion thruster technology and understanding are necessary to fulfill the needs of future space missions. Experimental comparisons of the discharge performance of an array of miniature (3cm diameter) ion thruster discharge configurations were conducted and showed that a 3-ring configuration with length-to-diameter of 1.0 exhibited the best performance. A compact and lightweight version of this configuration, using small accelerator grid holes, exhibited discharge losses of 250-550eV/ion and propellant efficiency of as much as 87%. This performance represents a significant advancement in miniature (less than 5cm diameter) ion thruster technology and demonstrates that a miniature ion thruster of low magnet and thruster weight can yield desirable performance.
A multi-component hybrid 2-D computational Discharge Model was developed to help identify important ion thruster discharge processes and investigate miniaturization issues. Combining experimental and computational results reveals that magnetic field optimization for a miniature ion thruster is bracketed by considerations of primary electron utilization and discharge stability. Discharge Model analysis of the larger (30cm diameter) NSTAR thruster revealed that the peak observed in the NSTAR beam profile is due to double ions that are created by over-confinement of primary electrons on the thruster axis. Design sensitivity results show that, at the NSTAR thruster scale, efficient confinement of primary electrons is relatively easy to achieve; therefore, efforts to improve thruster performance should focus on effectively utilizing the primary electrons to minimize double ion production and maximize the number of single ions extracted to the beam.
The observations from this study have furthered the understanding of discharge processes and should improve future ion thruster design and modeling efforts. The Discharge Model advances state-of-the-art ion thruster modeling and provides a framework for a complete thruster model that can be used for long-life performance assessment and life validation.


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The Author: Gerhard Knothe, National Center for Agricultural Utilization Research, Agricultural Research Service, U.S. Department of Agriculture, Peoria, IL, USA.
Triacylglycerol esters are the most common esters in which fatty acids occur naturally. In nature, triacylglycerols rarely exist in the form of a glycerol triester of only one fatty acid, but rather they are mixed species, i.e. glycerol esterified with more than one fatty acid. Figures 1 to 3 depict 1H-NMR spectra of various glycerol esters of stearic acid.
Besides the tripling of the integration values of the protons in the fatty acid chain, the NMR spectrum of tristearin, the triacylglycerol ester of stearic acid, shows the peaks for the sn-2 proton at about 5.3 ppm (triplet of triplets) and two distinct absorptions (4.17 and 4.33 ppm; both are doublets of doublets) of the sn-1 and sn-3 protons (HA1 and HA2; see structure inscribed in part a of Fig. 1). These assignments have been described in the literature (Lie Ken Jie and Lam, 1995), where also the dependence of these signals on the fatty acid chain attached to the glycerol moiety is discussed. The sn-2 (HB) protons for the triacylglycerols of saturated fatty acids were reported at 5.241-5.283 ppm in CDCl3, with values around 5.27 ppm common for mid-to long-chain fatty acid moieties. The sn-1 and sn-3 protons were reported at 4.142 to 4.161 ppm and 4.298 to4.326 ppm. The chemical shift ranges were similar for triacylglycerols of ABA and AAB type with saturated fatty acid chains.
For triacylglycerols with acetylenic bonds with the structure illustrated (and with n = 0-10) the shifts were observed at 4.299 - 4.338 ppm (HA2), 4.123-4.302 (HA1; with the extreme value of 4.302 ppm for n = 0; n = 1 gave 4.231 ppm with increasing upfield shift with increasing n) and 5.260-5.331 ppm (HB; again the extreme of 5.331 ppm for n = 0; n = 1 gave 5.305 ppm). The situation was more complex for mixed triacylglycerols of AAB and ABA types with acetylenic fatty acids. For n ≥ 6, the positions of the fatty acid chains could not be unambiguously determined.
For triacylglycerols of type AAA with fatty acid chains containing Z (cis) double bonds (fatty acid as illustrated with n = 0-10), HA = 4.299 - 4.350 ppm (4.350 ppm for n = 0; n = 1 gave 4.315 ppm), HA' = 4.140 - 4.268 ppm (4.268 ppm for n = 0; n = 1 gave 4.180 ppm), HB = 5.266 - 5.358 ppm (5.358 ppm for n = 0; n = 1 gave 5.284 ppm). For triacylglycerols of type AAA with similar fatty acid chains but containing E (trans) double bonds, HA = 4.296 - 4.363 ppm (4.363 ppm for n = 0; n = 1 gave 4.301 ppm), HA' = 4.138 - 4.291 ppm (4.291 ppm for n = 0; n = 1 gave 4.165 ppm), HB = 5.263 - 5.384 ppm (5.384 ppm for n = 0; n = 1 gave 5.268 ppm).
Table 1. Chemical shift of protons in the fatty acid chains of AAA-type triacylglycerols (source: Lie Ken Jie and Lam, 1995).
R (in Glyc-O-CO-R)a
Chemical shifts
CH=CH
Saturated
—CH3 2.073 (α), 2.087 (β) - -
—CH2CH3 2.353, 2.356 1.138, 1.144 - -
—(CH2)2CH3 2.307, 2.312 1.651, 1.659 - -
—(CH2)3CH3 2.324, 2.331 1.632 - -
—(CH2)16CH3 2.307 1.609 - -
Acetylenic
—C≡C—(CH2)7CH3 - - 2.334 (H-4) -
—CH2—C≡C—(CH2)7CH3 3.269 - 2.181 (H-5) -
—(CH2)2—C≡C—(CH2)7CH3 2.499 (m) - 2.111 (H-6) -
—(CH2)3—C≡C—(CH2)7CH3 2.452 1.788 2.217 (4-H); 2.127 (7-H) -
—(CH2)4—C≡C—(CH2)7CH3 2.343 1.723 2.146 (5-H and 8-H) -
—(CH2)7—C≡C—(CH2)7CH3 2.310 1.616 2.129 (8-H and 11-H) -
Z-Ethylenic
—CH=CH—(CH2)7CH3 5.762, 5.770 6.264, 6.278 2.635 see H at C2 and C3
—CH2—CH=CH—(CH2)7CH3 3.101 see -CH=CH- 2.015 (5-H) 5.325
—(CH2)2—CH=CH—(CH2)7CH3 2.363 2.035 (6-H) 5.325; 5.403, 5.443
—(CH2)3—CH=CH—(CH2)7CH3 2.322 1.675 2.056 (4-H), 1.991 (7-H) 5.323; 5.391, 5.431
—(CH2)4—CH=CH—(CH2)7CH3 2.322 1.635 2.036 (5-H and 8 H) 5.369
—(CH2)7—CH=CH—(CH2)7CH3 2.309 1.610 1.999 (8-H and 11 H) 5.338
E-Ethylenic
—CH=CH—(CH2)7CH3 5.816, 5.829 6.986, 7.012 2.197 see 2-H and 3-H
—(CH2)2—CH=CH—(CH2)7CH3 2.358 2.308 1.951 (6-H) 5.420
—(CH2)3—CH=CH—(CH2)7CH3 2.308 1.675 1.980 (4-H and 7-H) 5.381
—(CH2)7—CH=CH—(CH2)7CH3 2.308 1.606 1.971 (8-H and 11-H) 5.379
aGlyc = glycerol moiety.
Figure 1a. 1H-NMR spectrum of tristearin.
Figure 1b. 1H-NMR spectrum of tristearin expanded in the region of 4-6 ppm.
In 1,3-distearin (Fig. 2), the signals of the sn-1 and sn-3 protons overlap (4.20 ppm integration value 4). The two remaining signals of integration value 1 are assigned to the protons at sn-2, namely 4.13 ppm, (overlapping the signals of the sn-1 and sn-3 protons, proton attached to the sn-2 carbon) and 2.48 ppm (doublet, OH proton at sn-2).
Figure 2. 1H-NMR spectrum of 1,3-distearin.
The 1H-spectrum of 1-monostearin (Fig. 3) is more complex. Each of the seven protons on the glycerol moiety gives a distinct signal. The two slightly overlapping downfield doublets of doublets at 4.18 and 4.25 ppm are again assigned to the carbon carrying the fatty acid chain (sn-1), similar to the assignments in di- and tristearin. The multiplet signals of the two protons directly attached to the sn-3 carbon are also split and observed at 3.64 and 3.73 ppm. The signal of the proton attached to the sn-2 carbon is observed at 3.97 ppm. The signals of the hydroxy protons overlap the triplet of the C2 protons in the fatty acid chain, giving this signal a theoretical integration value of 4. These assignments are verified by 2D heteronuclear correlation.
Figure 3. 1H-NMR spectrum of 1-monostearin.
Lie Ken Jie, M.S.F. and Lam, C.C. 1H-Nuclear magnetic resonance spectroscopic studies of saturated, acetylenic and ethylene triacylglycerols. Chem. Phys. Lipids, 77, 155-171 (1995).