text:
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        Attributes = @()
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}

function Assert-MofSchemaScriptParameters() {
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        [Parameter(Mandatory=$True)]
        [string]$mofFileName
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    $hasErrors = $false
    $mofSchemas = Get-MofSchemaObject -fileName $mofFileName
    $mofData = $mofSchemas | Where-Object { $_.ClassName -eq (Get-Item $mofFileName).Name.Replace(".schema.mof", "") }
    $psFile = $mofFileName.Replace(".schema.mof", ".psm1")

    $tokens = $null
    $errors = $null
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    $functions | ForEach-Object {
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                $parameterAttribute = $paramToCheck.Attributes | Where-Object -FilterScript { $_.TypeName.ToString() -eq "parameter" } -ErrorAction SilentlyContinue

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                if ($null -ne $mofParameter.ValueMap) {
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                        $mofParameter.ValueMap | ForEach-Object {
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                        $psValidateSetParams | ForEach-Object {
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                                Write-Warning "File $psFile has parameter $($mofParameter.Name) that contains '$_' in the $($function.Name) function which is not in the valuemap in the schema"
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                if ($null -eq $mofParameter.EmbeddedInstance) {
                    if ($null -eq ($paramToCheck.Attributes | Where-Object -FilterScript { $_.TypeName.ToString() -match $mofParameter.DataType })) {
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                        Write-Warning "File $psFile has parameter $($mofParameter.Name) in function $($function.Name) that does not match the data type of the schema"
                    }

                    if ($mofParameter.IsArray -eq $true) {
                        if ($null -eq ($paramToCheck.Attributes | Where-Object -FilterScript { $_.TypeName.ToString() -match $mofParameter.DataType -and $_.TypeName.IsArray -eq $true })) {
                            $hasErrors = $true
                            Write-Warning "File $psFile has parameter $($mofParameter.Name) in function $($function.Name) that is marked as an array in the schema but is not an array in the PowerShell module"
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                    }
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                        "MSFT_Credential" {
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                                Write-Warning "File $psFile has parameter $($mofParameter.Name) in function $($function.Name) that does not match the data type of the schema"
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    return (!$hasErrors)
}

Export-ModuleMember *


Eastern Partners, LLC ("Eastern") is a Dallas-based real estate firm with projects in Texas, Colorado, Georgia, California, & South Carolina.
A 4000 square foot luxury residence offering ski in / ski out convenience w/ all of the modern luxuries, finishes, views & conveniences.
Arcady is a 9200 square foot remodel of a 1928 Georgian-Style home in the prestigious Highland Park neighborhood in Dallas. The entire home was extensively remodeled and expanded to meet today's wants and needs while preserving the architectural integrity of the original home.


In the future to be part of a larger warband.
a future warrior to climb the ladder?
and is running the battlefield.
In the background two models in progress on the painting table.
the other is a mercenary.
Last edited by Pascal Tognon on December 6th, 2012, 2:23 pm, edited 2 times in total.
It depends on how often the particular Necron phased out.
The more he did, the less of the Necrontir remains in him.
and the third an Inquisitorial henchman.
Last edited by Pascal Tognon on December 6th, 2012, 2:23 pm, edited 1 time in total.
but repainted by a tinkerer who could use them for his own needs.
Replaced the AI and they obey him now.
I really don't like the figure.
or better said, a few company-names before Urban Mammoth.
He will be known as "Colour Blind Willy Lobster".
still have got to base and varnish him.
It is a Van Saar Juve.
And the second figure a Teacher in Psychic matters, formerly tasked to train David Eluvar.
He joins the Knight Commander in his quest.
The figure is a 40K Figure, maybe even a Rogue Trader-era figure, and is BADLY sculpted/cast.
Varnishing and basing still to be done.
to be part of a new Inquisitorial warband.
A Jokaero Weaponsmith, named Thierry d' Ook.
I quite curious about the squat, what model are you using?
A Mantic Figure, Warpath series.
The model is from Urban Mammoth.
And the good Inquisitor is finished!
a Gaus weapon and chain sword?
And the next figure is finished.
'Fat' Mack Mc Duff, a mercenary, formerly of the Cadian Guard.
The figure started life as a GW Chaos Cultist.
I really like the format of those cards! How did you do it? Is there a tutorial anywhere? Nice work!
it is done in Adobe Photoshop.
with the colours somewhat muted and the surface detail enhanced.
The rest are colour swathes and filters.
Easy, but difficult to do without Photoshop.
the mercenary with the chainsword and laspistol.
Next up: the Gue'vesa, but those are in a different topic.


text:
\section{Introduction}
It is a common topology homework exercise to prove that any embedding of an orientable $n$-manifold $M$, such as the $n$-sphere $\mathbb{S}^{n}$, into $\mathbb{R}^{n+1}$ is separating\footnote{That is, the complement of the image of the embedding has at least two components.}. However, we have never seen this homework problem posed with ``embedding" replaced by ``immersion". At first glance it only seems to  complicate the problem for no good reason. But the truth is subtle, with topological and PL immersions behaving differently from their smooth cousins. Topological and PL immersions do come up in ``nature" so one cannot avoid them, and when one does not avoid them one discovers some interesting topology. This paper is about immersions of spheres but we will open with a geometry tale.

\subsection*{A geometry tale}
One place to look for an immersion of an $n$-sphere is at the \emph{cut locus}\footnote{The \emph{cut locus} of $p$ is the set of \emph{cut points} of $p$ along all the geodesics starting from $p$. A \emph{cut point} of $p$ along a geodesic ray $\gamma_v$ with initial velocity $v$ is the point $\gamma_v (t_0)$, where $t_0$ is the first time after which $\gamma_v([0,t])$ stops being the minimizing geodesic from $p$ to $\gamma_v (t)$.} of a point $p$ in some closed, Riemannian manifolds $M^{n}$. Not any Riemannian manifold, but those that have small diameter and small upper bound on the sectional curvatures. In such circumstances, the cut locus of $p$ is the image of an (topological) immersion of a $(n-1)$-sphere whose complement is connected. We give an short explanation of this in the next paragraph.

Recall that if the sectional curvature of $M$ is bounded from above by some number $\kappa >0$, then by comparing to the round sphere of radius $(1/\sqrt{\kappa})$ one deduces that the exponential map $\exp_p$ at $p\in M$ is a local diffeomorphism on the ball of radius $(\pi/\sqrt{\kappa})$. Suppose (for simplicity) that $M$ has both the curvature and diameter $\leq 1$.
Then for each unit tangent vector $v \in T_p(M)$, if one follows the unit-speed geodesic ray $\gamma_v$ starting at $p$ in the direction of $v$, one reaches at some time $t=t_v \leq 1$ a \emph{cut point} $f(v) =\gamma (t_v)$ along $\gamma$. Letting $v$ vary over the unit sphere in $T_p(M)$ and taking into account $t_v$, one obtains a  \emph{star-shaped}\footnote{``Star-shaped" means a sphere about the origin of $\mathbb{R}^{n}$ which in polar coordinates has the form $\{(\Omega, \rho(\Omega) )\}$ for some continuous function $\rho\colon \{\text{angles}\} \rightarrow\mathbb{R}^+$. Such embedded spheres have bicollared neighborhoods and thus are topologically flat.} \emph{locally flat} embedding $\mathbb{S}^{n-1}$ into $T_pM$, namely the set $ C: = \{t_v v\; |\; v \in T_p^1(M)\}$, which bounds a topologically flat ball $B$ on which the map $\exp_p$ is injective. Since $\exp_p$ is a local diffeomorphism on a ball of radius $\pi$, when restricted to $C =\partial B = \mathbb{S}^{n-1}$ it gives a topologically flat immersion
\[f\colon \mathbb{S}^{n-1} \rightarrow M\]
whose image is exactly the cut locus of $p$, the complement of which is $\exp_p(\text{int}(B))$, which is diffeomorphic to an open ball and thus is connected.

This was how Buser and Gromoll (\cite{BuserGromoll}) showed that $\mathbb{S}^2$ does not admit a metric with small curvature\footnote{By ``small curvature" we mean that the sectional curvatures have a small upper bound. The lower bound of the sectional curvature can be very negative. } and small diameter. If $\mathbb{S}^2$ admits such a metric, then one could use this metric to obtain an non-separating immersion of $\mathbb{S}^1$ into $\mathbb{S}^2$, which, as a consequence of the Jordan Curve Theorem, is impossible.

In the same paper, Buser and Gromoll explained how Gromov constructed metrics on $\mathbb{S}^3$ with upper bounds on the  curvature $\kappa$ and diameters approaching zero. Closed manifolds that admit such metrics are called \emph{almost negatively curved}. It is interesting that $\mathbb{S}^3$ is almost negatively curved, but for our purpose this implies there is a non-separating immersion of $\mathbb{S}^2$ into $\mathbb{S}^3$, in fact one with contractible image. Thus the modification of the homework problem above has a surprising answer (in topological and PL categories): It would be a ``trick question". So we ask,

\begin{question}
Are there PL immersions of $\mathbb{S}^{n-1}$ into $\mathbb{R}^{n}$ , for each $n\geq 3$, that have contractible image and in particular are non-separating? If so, how can we obtain them?
\end{question}

The metrics on $\mathbb{S}^3$ described in \cite{BuserGromoll} are obtained by modifying the round metric by installing a number of ``short-cuts" that make the diameter small without changing the topology or increasing the curvature. These ``short-cuts" are not at all like the worm holes of a science-fiction, which are easy plot device installed at the expense of changing the topology. They are much more delicate in that they preserve the topology of the manifold. The resulting metrics are stranger than fiction and there is little hope in extracting an explicit immersion of $\mathbb{S}^2$ from them. However, back in the 1950's, such immersions of $\mathbb{S}^2$ had already been discovered, apparently by R. H. Bing.

\subsection*{The house that Bing built}
Topologists are often introduced to the idea of a \emph{contractible}, but not \emph{collapsible}, complex through the example of ``the house with two rooms", also called ``the house that Bing built", which is the 2-complex $X\subset \mathbb{R}^3$ as drawn in Figure 1.

\begin{figure}[h!]
\label{2d-bing}
\centering
\includegraphics[scale=0.43]{Figure1.png}
\caption{The house with two rooms.}
\end{figure}

This 2-complex $X$ has a regular neighborhood $\mathcal{N}(X)$ that is P.L. homeomorphic to $\mathbb{D}^3$ and possesses a mapping cylinder structure $\mathcal{N}(X) \cong \partial\mathcal{N}(X) \times [0,1] / n \times 1 \equiv n' \times 1$ iff $f(n) = f(n')$, where the map $f\colon\partial \mathcal{N}(X) \rightarrow X$ is required to be a PL immersion (of $\mathbb{S}^2$). In particular, pushing along the mapping cylinder lines yields a strong deformation retraction $r_t: \mathcal{N}(X) \rightarrow X$, $t \in [0,1]$, with $r_1$ the retraction. To see the non-separating immersion $f\colon \mathbb{S}^2\rightarrow \mathbb{R}^3$, imagine shrink-wrapping Figure 1 with a very flexible spherical membrane that will enter the long tubes and then stretch to fill the chambers to which the tubes lead.

In higher dimension we call an $(n-1)$-complex $Y^{n-1} \subset \mathrm{int}(\mathbb{D}^n)$ a \emph{Bing house} if its PL regular neighborhood $\mathcal{N}(Y^{n-1})$ is a PL $n$-ball. This implies the existence of a collapse $\mathbb{D}^n \searrow Y^{n-1}$ and, of course, a strong deformation retract $r_t \colon \mathcal{N}(Y) \rightarrow Y$. As a consequence, $\mathcal{N}(Y^{n-1})$ possesses a mapping cylinder structure induced by some PL immersion $f\colon \partial\mathcal{N}(Y^{n-1}) \rightarrow Y^{n-1}$. Clearly, a $(n-1)$-dimensional Bing house gives a non-separating immersion $\mathbb{S}^{n-1} =  \partial\mathcal{N}(Y^{n-1})\rightarrow\mathbb{R}^n$.

\subsection*{Difficulties in higher dimensions}
When the dimension $n$ is greater than 3, there are several ways to attempt to generalize the Bing house, but usually we found ourselves leaving the world of PL immersions and instead building more singular maps. The main difficulty of the naive approach, which will become apparent Section \ref{sec: inductive argument}, revolves around a 2-disk of singular image points (i.e. points over which the map does not have full rank); a problem already present in dimension $n=4$. The map obtained from the naive approach might look, at places, like the projection $\mathbb{D}^2\times I \rightarrow \mathbb{D}^2$, which are problematic because it is unclear how to perturb away these singularities.

Another attempt would be to look for these immersions in places in ``nature" where they might show up. So let us return to the geometry tale but this time we will look in higher dimensions.
It turns out that the $4$-sphere is also almost negatively curved (\cite{GGNP}). But again, seeing the 3-dimensional Bing house inside seems hopelessly difficult.

The goal of this paper is to give explicit constructions of higher dimensional Bing houses and PL immersions with contractible images of $(n-1)$-spheres for all $n\geq 3$ .
\begin{theorem}\label{main theorem}
For every $n \geq 3$, there is a Bing house $Y^{n-1} \subset \mathbb{D}^n$.
\end{theorem}

\begin{remark}
Note that the theorem fails for $n = 2$, but again holds for $n=1$.
\end{remark}

\subsection*{A cautionary example}
The suspension $\Sigma$ of the Bing house does not give an immersion of $\mathbb{S}^3$ since the retraction map has singularities (points not covered by an immersion) corresponding to the two cone points of $\Sigma$.
\newline

This paper is organized as follows. In Section \ref{sec: 3d Bing house} we give an explicit construction of a 3-dimensional Bing house. In section \ref{sec: inductive argument} we will describe two distinct routes to higher dimensional generalizations. One is to simply adapt the 3-dimensional construction to higher dimensions. The second is an inductive construction which yields a $Y^{n+2}$ from a $Y^n$. Given $X := Y^2$ and $Y^3$ as starting points, all dimensions $n \geq 2$ are thus accounted for.

\begin{acknowledgement}
The second author is thankful to be at the Max Planck Institut f\" ur Mathematik in Bonn. She is grateful for its hospitality and financial support.
\end{acknowledgement}

\section{A $3$-dimensional Bing house}\label{sec: 3d Bing house}
In this section, we give an explicit construction of a 3-dimensional Bing house $Y^3$. Let us reserve $X$ for the classic 2-dimensional Bing house drawn in Figure 1. The deformation retraction of $\mathbb{D}^3$ to $X$ may be visualized as: ``insert two balloons through the tubes and inflate."
\newpage

Inverting about a point on the ``middle floor" the Bing house may alternatively be rendered in $\mathbb{S}^3$ as:
\begin{figure}[h!]
\label{2d-bing-inverted}
\centering
\includegraphics[scale=0.46]{Figure2.png}
\caption{}
\end{figure}

Our job now is to make precise a certain $3$-dimensional generalization of Figure \ref{2d-bing-inverted} which we sketch schematically in Figure 3.

\begin{figure}[h!]
\label{schematic}
\centering
\includegraphics[scale=0.55]{Figure3.png}
\caption{}
\end{figure}

Here in text is a brief description of the $3$-dimensional ``pieces" of $Y^3$. The drawing in Figure 3 is in $\mathbb{S}^3 \times [-2, 2]$. Locate a genus 2 Heegaard surface $\Sigma$ in $\mathbb{S}^3 \times 0$.
\newpage

\noindent
The first three pieces of $Y^3$ are:
\begin{itemize}
\item[(1 $\&$ 2)] the \emph{interior} handle bodies to $\Sigma \times \{\pm 1\} \subset \mathbb{S}^3 \times \{\pm 1\}$ each with a (different) standard basis circle neighborhood deleted,
\item[(3)] and the exterior handle body to $\Sigma \times \{0\} \subset \mathbb{S}^3 \times \{0\}$ with two trivial (and unlinked) circle neighborhoods deleted.
\item[(4 $\&$5)] The next two pieces are drawn as tubes (and we call them \emph{tubes}) but they are actually tubes cross circle $((\mathbb{D}^2 \times \partial \mathbb{D}^2) \times \mathbb{S}^1)_{\text{up}/\text{down}}$, where the extra circle factor parametrizes, longitudinally, the total of 4 deleted circles within the first three pieces.
\item[($6_{-}$ $\&$ $6_+$)] Next, add the vertical wall $\Sigma \times [-1, 1]$, which is actually two pieces $6_{-} = \Sigma\times[-1,0]$ and $6_{+} = \Sigma\times[0,1]$.
\item[(7 $\&$ 8)] Finally, the two pieces rendered as vertical disks are actually $\mathbb{D}^2 \times \mathbb{S}^1$'s with the extra circle again corresponding to the longitudinal parametrization of the 4 deleted circles.
\newline
\end{itemize}

So in total we have $3 + 2 + 2 + 2 = 9$ pieces, which we have labeled 1, 2, 3, 4, 5, $6_{-}$, $6_+$, 7 and 8. Each of these pieces, in its interior, will be covered $2\rightarrow 1$ by the map $r_1\colon \mathbb{S}^3 \rightarrow Y^3$. That is, implicitly we will be patterning $\mathbb{S}^3$ into 18 puzzle pieces which glue up (immersively) to form $Y^3$.
For reference, here are the pieces:

\begin{figure}[h!]
\label{}
\centering
\includegraphics[scale=0.51]{Figure4.png}
\caption{}
\end{figure}

\bigskip

Next, let us make it completely explicit where pieces 4, 5 and 7, 8 are located in $\mathbb{S}^3 \times [-2,2]$. By symmetry we only need to discuss pieces 4 and 7 (tube and $(\text{disk} \times \mathbb{S}^1)$), as pieces 5 and 8 are mirror images of these. Call $\tilde{S}^3$ the PL embedded copy of $\mathbb{S}^3$ consisting of
\[((\text{inside } \Sigma) \times 1)\; \cup \;(\Sigma \times [0,1])\; \cup\; ((\text{outside } \Sigma) \times 0).\]
In $\tilde{S}^3$ we may draw the boundary $\partial(\text{tube}_4)$ of $\text{tube}_4$:

\begin{figure}[h!]
\label{}
\centering
\includegraphics[scale=0.44]{Figure5.png}
\caption{}
\end{figure}

\[\;\]
\begin{figure}[h!]
\label{tube-2}
\centering
\includegraphics[scale=0.5]{Figure6.png}
\caption{The horizontal shades of the ``hoop" in Figure 6 are the $D^2$-factors in piece $7 \cong \mathbb{D}^2\times\mathbb{S}^1$.}
\end{figure}

\newpage

\begin{remark}
A quick check verifies that $Y^3$ is simply connected and has vanishing integral homology and hence is contractible.
\end{remark}

Our next step is to build a (generically) $2 \rightarrow 1$ immersion of some closed 3-manifold $M$ onto $Y^3$. We will construct the source 3-manifold $M$ piece by piece and at the end verify it is indeed a 3-sphere. It is not much extra work simultaneously describe the regular neighborhood $\mathcal{N}$ of $Y^3 \subset \mathbb{S}^3 \times [-2,2]$. What we will be verifying is that $\mathcal{N} \overset{\text{PL}}{\cong} \mathbb{D}^4$ and $\partial \mathcal{N} \overset{\text{PL}}{\cong} \mathbb{S}^3$, and that for a natural mapping cylinder structure $f\colon \partial \mathcal{N} \rightarrow Y^3$ on $\mathcal{N}$, $f$ is a PL immersion.
\newpage

\subsection*{Assembling the pieces into a 3-sphere}

Kirby calculus notation for $1 \cup 2 \cup 6$ is:
\begin{figure}[h!]
\label{}
\centering
\includegraphics[scale=0.37]{Figure7.png}
\caption{}
\end{figure}

\bigskip

Now let us understand $4 \cup 3 \cup 6_- \cup 2 \cup 5 \cup 8_2$ (and its symmetric partner $5 \cup 3 \cup 6_+ \cup 1 \cup 4 \cup 7_2$). The subscripts mean use two copies of 8 and 7. Notice with this convention that every piece is now used twice corresponding to the (generic) $2 \rightarrow 1$ nature of $r_1$.

Start with $4 \cup 3 \cup 6_- \cup 2$. The $\text{tube}_4$ merely adds a collar, and $3 \cup 6_- \cup 2$ is simply a genus 2 Heegaard decomposition of a $3$-sphere $\mathbb{S}^3$ with the neighborhood of two trivial circles deleted from the exterior handlebody. At the level of Kirby diagrams we have:

\begin{figure}[h!]
\label{}
\centering
\includegraphics[scale=0.51]{Figure8.png}
\caption{}
\end{figure}

\bigskip

The $\text{tube}_5$ effects the attachment of a trivial ``round 1-handle" to $\mathbb{S}^3$ (a round 1-handle in this dimension is $(\mathbb{D}^1 \times \mathbb{D}^2, \partial \mathbb{D}^1 \times \mathbb{D}^2) \times \mathbb{S}^1$) and the two copies of 8 effects a round 2-handle attachment ($(\mathbb{D}^2 \times \mathbb{D}^1, \partial \mathbb{D}^2 \times \mathbb{D}^1) \times \mathbb{S}^1$). Looking back at Figure 6, observe that the regions labeled 5 and 8 constitute a (Morse canceling pair)$\times \mathbb{S}^1$. That is a circle's worth of canceling critical points of index 1 and 2 (detail in Figures 8 and 9 below). Now adding 5 yields:
\begin{figure}[h!]
\label{}
\centering
\includegraphics[scale=0.4]{Figure9.png}
\caption{}
\end{figure}

\begin{figure}[h!]
\label{}
\centering
\includegraphics[scale=0.37]{Figure10.png}
\caption{}
\end{figure}

\newpage

The upshot is that both $4 \cup 3 \cup 6_- \cup 2 \cup 5 \cup 8_2$ and its symmetric partner $5 \cup 3 \cup 6_+ \cup 1 \cup 4 \cup 7_2$ are 3-spheres minus the neighborhood of an unknotted simple closed curve (i.e. solid tori). Furthermore, the meridians of these two solid tori glue to the $x$ and $y$ longitudes of $1 \cup 2 \cup 6$, surgering the $3$-manifold represented by the central rectangle in Figure 4,
\[ \partial ((\text{genus 2 handlebody})\times I)\cong (\mathbb{S}^1 \times \mathbb{S}^2) \# (\mathbb{S}^1 \times \mathbb{S}^2)\]
to $\mathbb{S}^3$. This completes the proof that the 18 pieces in fact glue up to $\mathbb{S}^3$.

\subsection*{PL regular neighborhood of $Y^3$} We may now proceed to draw 4-dimensional Kirby diagrams for the PL regular neighborhood of the image $Y^3$.

\[\mathcal{N}(1 \cup 2 \cup 6) = (\mathbb{S}^2 \times \mathbb{D}^2) \natural (\mathbb{S}^1 \times \mathbb{D}^3) \natural (\mathbb{S}^1 \times \mathbb{D}^3),\] or in Kirby calculus:
\begin{figure}[h!]
\label{}
\centering
\includegraphics[scale=0.27]{Figure11.png}
\caption{}
\end{figure}
\newpage

We now proceed to add the remaining thickened pieces and draw the corresponding Kirby diagrams---omitting the 3-handles.

Due to a theorem of Trace \cite{Trace} based on work of Laudenbach and Poenaru \cite{LP} (see remark 4.4.1 of \cite{Gompf} for an exposition) it is not necessary to record the 3-handle attaching 2-spheres of a 4-dimensional handlebody with connected boundary in order to define the diffeomorphism type of the 4-manifold. Thus tracking only 1 and 2-handles, we get Figure 12.

\begin{figure}[h!]
\label{}
\centering
\includegraphics[scale=1.01]{Figure12.png}
\caption{}
\end{figure}

This completes the construction of a 3-dimensional Bing house $Y^3 \subset \mathbb{D}^4$.

The conclusion that the natural PL mapping cylinder structure on $\mathcal{N}(Y^3)$ defines a PL-immersion from $\mathbb{S}^3 = \partial \mathcal{N}(Y^3) \rightarrow Y^3$ follows from inspection. There are three local (PL) models for a point $y \in Y^3$. It can be
\begin{itemize}
\item[(1)] in the interior of a sheet,
\item[(2)] at a $(\text{triple point } Y) \times \mathbb{R}^2$, or
\item[(3)] (the cone on the 1-skeleton of tetrahedron)$\times \mathbb{R}$.
\end{itemize}
Unlike at the cone points of the suspension of the Bing house, for each of these models a neighborhood of $y$ is covered by a finite number of $\mathbb{R}^{n-1}$-sheets (sheets of the immersion of $\mathbb{S}^{n-1}$).
The approach via mapping cylinder lines to any such $y$ from any complementary region is locally (PL) one-to-one in a neighborhood of $y$. That is, $Y^3$ is covered by PL immersed $\mathbb{R}^3$-charts. This completes the proof of Theorem \ref{main theorem} for $n=3$ and $4$.

\section{To higher dimensions}\label{sec: inductive argument}

Now we come to a fork in the road, and we will take both paths. One is by relabeling the pieces in Figure 3. The other one is an inductive construction.

\subsection{Relabeling Figure 3}
To produce Bing houses $Y^{n-1}$ in $\mathbb{D}^n$ for $n \geq 5$, we can explain a straightforward relabeling of Figure 3 appropriate for the higher dimension. This is Figure 13.
\begin{figure}[h!]
\label{}
\centering
\includegraphics[scale=0.5]{Figure13.png}
\caption{}
\end{figure}
The proof is parallel to what we did for $n=4$ (and will not be repeated) up to the Kirby calculus discussion summarized by Figure 12. Doing the handlebody theory carefully in higher dimension would require establishing the notations for a generalized Kirby calculus and drawing \emph{all} handles since we no longer have the convenience of Trace's Theorem. Fortunately all this is unnecessary, since the PL Poincare conjecture can be used to conclude that for $n \geq 5$, $\mathcal{N}(Y^{n-1}) \overset{\text{PL}}{\cong} \mathbb{D}^n$. This is because the lower dimensional argument extends far enough to imply $Y^{n-1} \cong \{\ast\}$, and $\partial \mathcal{N}(Y^{n-1}) \overset{\text{PL}}{\cong} \mathbb{S}^{n-1}$. So in pursuing this first fork we are content to leave the reader with Figure 13.

\subsection{An inductive construction}
The second branch of our road to high dimensions is to give an inductive procedure for producing a Bing house $Y^{n+2}$ given a Bing house $Y^n$ as starting point. Because the induction ``skips over" a dimension we need both the classical $X = Y^2$ and the just constructed $Y^3$ as starting points. We explain the induction in some detail.

Let us define a \emph{rank-2 Bing hut} as something a bit weaker than a Bing house. It will be PL complex $Z^{n-1} \subset \mathbb{D}^n$ with a PL regular neighborhood, $\mathcal{N}(Z)$, PL homeomorphic to a PL $n$-ball $\mathbb{D}^n$. It is convenient to let $Z^{n-1} \cap \partial \mathbb{D}^n = \mathbb{S}^{n-2}$, the equator between hemispheres $N$ and $S$ of $\partial \mathbb{D}^n = \mathbb{S}^{n-1}$. Furthermore, $\mathcal{N}(Z)$ must possess a mapping cylinder structure induced by a map $g: \partial \mathcal{N}(Z) \cong \mathbb{S}^{n-1} \rightarrow Z$ which is required to be a PL immersion on the interior $\dot{A}$ of a compact co-dimension zero PL submanifold $A$ of $\partial \mathcal{N}(Z)$. The closure $\overline{\partial \mathcal{N} \setminus A}$ is further required to consist of finitely many PL copies of $\mathbb{D}^2 \times \mathbb{S}^{n-3}$, and $g$ restricted to each copy, is the projection (modulo the selection of suitable PL coordinates in domain and range) $D^2 \times \mathbb{S}^{n-3} \xrightarrow{\pi_1} D^2$, $D^2 \subset Z$ (see Figure 14). In other words $\mathcal{N}(Z)$ contains distinguished 2-handles and on these the mapping cylinder structure is the rank 2 projection.

\begin{figure}[h!]
\label{local-model}
\centering
\includegraphics[scale=0.42]{Figure14.png}
\caption{Local model for $g$ near 2-handles $(\mathbb{D}^2\times \mathbb{D}^{n-2}, \partial \mathbb{D}^2\times \mathbb{D}^{n-2})$.}
\end{figure}

The (second) proof of Theorem \ref{main theorem} will be complete by combining  Lemmas \ref{rank-2-bh} and \ref{making-bh} below.

\begin{lemma}\label{rank-2-bh}
For all $n \geq 3$ there is a rank-2 Bing hut $Z^{n-1} \subset \mathbb{D}^n$.
\end{lemma}

\begin{lemma}\label{making-bh}
If $Y^{n-3} \subset \mathbb{D}^{n-2}$ is a $(n-3)$-dimensional Bing house and $Z^{n-1} \subset \mathbb{D}^n$ an $(n-1)$-dimensional rank-2 Bing hut, then replacing the distinguished disks $D^2_s \subset Z^n$ with copies of  $\mathbb{D}^2 \times Y^{n-3}$, we obtain an $(n-1)$-dimensional Bing house $Y^{n-1} = (Z^{n-1} \setminus D_s^2) \cup (D_s^2 \times Y^{n-3})$. One level of pairs $(\mathcal{N}(Y^{n-1}), Y^{n-1}) = (\mathcal{N}(Z^{n-1}) \setminus \text{2-handles}, (Z^{n-1} \setminus D_s^2) \cup D_s^2 \times Y^{n-3})$.

The subscript ``$s$" labels the 2-handles over which the original projection is rank-two, in our case there are precisely two such 2-handles so $s\in \{1,2\}$.
\end{lemma}

\begin{proof}[Proof sketch of Lemma \ref{rank-2-bh}]
	$Z^{n-1}$ is built in a few steps in Figure 15.

\begin{figure}[h!]
\label{building-bh}
\centering
\includegraphics[scale=0.75]{Figure15.png}
\caption{}
\end{figure}

One may now check that Figure 15(d), in fact, is a rank-2 Bing hut. To aid in this checking, note two maps: the fold map $f_1: \mathbb{S}^{n-1} \rightarrow \mathbb{D}^{n-1}$ takes the hemispheres $N, S \subset \mathbb{S}^{n-1}$ each 1-1 onto $\mathbb{D}^{n-1}$, and the natural degree one map $f_2: \mathbb{S}^{n-1} \rightarrow (\mathbb{S}^{n-2} \times \mathbb{S}^1) \cup D^2$ where $D^2$ attaches to $\ast \times \mathbb{S}^1$ degree one.

The north polar region $N$ of $\mathbb{S}^{n-1} = \partial B^n$ maps to the ``inside" of $Z^{n-1}$ essentially by $f_1\vert_N \#_{\text{tube}} f_2$. The map to the ``outside" of $Z^{n+1}$ is built by rounding $f_1\vert_S$ along the ``ruff" $S^{n-2} \times S^1$. However, the hemisphere $S$ will not retract to the outside of $Z^{n-1}$ until the element of fundamental group generated by the tube is canceled by the disk labeled $D'^{2}$. The 2-handle of $\mathcal{N}(Z^{n-1})$ with $D'^{2}$ as core surgers the outer boundary from $(\mathbb{S}^1 \times \mathbb{S}^{n-1} \setminus \mathbb{D}^{n-1})$ to $(\mathbb{S}^{n-1} \setminus \mathbb{D}^{n-1}) \cong \mathbb{D}^{n-1}$.

	Using PL coordinates to construct the two distinguished $n$-dim 2-handles in $(\mathcal{N}(Z^{n-1}), Z^{n-1})$ we see that the map giving mapping cylinder coordinates to $(\mathcal{N}(Z^{n-1}),Z^{n-1})$ has the form shown in Figure 14. In particular, restricted to the ``belt region" of the 2-handle, $\mathbb{D}^2 \times \mathbb{S}^{n-3}$, $g\colon \mathbb{S}^{n-1}\rightarrow Z$ assumes the form of first coordinate projection, ``bent" toward the attaching region as shown in Figure 16 (with $\mathbb{D}^2$ dimensionally reduced to $\mathbb{D}^1$).
\begin{figure}[h!]
\label{lemma-figure}
\centering
\includegraphics[scale=0.35]{Figure16.png}
\caption{Arrows represent the rank-2 map $g$.}
\end{figure}
The shaded boundary collar of the belt parametrizes (under $g$) the attaching region of the distinguished 2-handle.

This completes our sketch of Lemma 1.
\end{proof}

\begin{proof}[Proof sketch of Lemma \ref{making-bh}]
We use the letter $Y$ now also a glyph for the Bing house $Y^{n-1}$. We may now insert into the mapping cylinder structure shown in Figure 16 a copy of the $(n-2)$-dimensional mapping cylinder structure on $(\mathcal{N}(Y^{n-1}), Y^{n-1})$. This is done fiber-wise over each preimage of $p \in D^2$ under the ``bent" $g$ illustrated in Figure 16. The result is:

\begin{figure}[h!]
\label{lemma-2-figure}
\centering
\includegraphics[scale=0.4]{Figure17.png}
\caption{}
\end{figure}

This substitution restores the immersive property and the rank-2 hut becomes a house. In this argument it is not necessary to quote the high dimensional PL Poincare conjecture since we have constructed the collapse of $\mathbb{D}^n$ to $Y^{n-1}$ explicitly.
\end{proof}

\section{Appendix}

\begin{theoremA}
A $C^1$-immersion $f \colon \mathbb{S}^2 \looparrowright \mathbb{D}^3$ cannot parametrize a Bing house $Y$.
\end{theoremA}

\begin{proof}
The map $f$ determines the following equivalence relation $T$ on $\mathbb{S}^2$, which we call \emph{tangent-equivalent}. Two points $a, b \in \mathbb{S}^2$ are \emph{tangent-equivalent} if and only if they have identical $1$-jets under $f$. That is, $f(a) = f(b)$ and $df\mid_a = df\mid_b$. Clearly, this is an equivalence relation.

Let $X =\mathbb{S}^2/T$ be the quotient space. Let $Y$ denote the image of $f$. Since we have no genericity assumptions on $f$, both $X$ and $Y$ may be rather ``wild" topological spaces. To see this, note that for any closed set $C$ we may find a smooth function vanishing to first order precisely on $C$.  An intermediate example between ``wild" and ``reasonable" is the union of the $xy$-plane and the surface obtained by revolving the graph of $z = x^4(\sin(1/x) -1)$ around the $z$-axis. Locally two sheets of $Y$ could meet tangentially at the closed subset consisting of concentric circles of radii $1/k$ for $k\in \mathbb{Z}^+$ and the center of these circles. When $f$ is ``reasonable", one should think of $X$ as a finite $2$-complex.

However, despite how ``wild" $X$ is, there is always  an obvious notion of a tangent space at every point $x\in X$, even when $x$ is not a manifold-point. Thus, there is an obvious notion of a \emph{$C^1$ (or smooth) immersion} $X\looparrowright \mathbb{R}^3$.

It is also clear that $f$ factors as a composition $f = h\circ g $ of $C^1$ immersions:
$$ \mathbb{S}^2  \stackrel{g}\looparrowright X \stackrel{h}\looparrowright Y.$$

One can think of the space $X$  as a ``wild branched surface"\footnote {It is what is called a \emph{non-singular branched $n$-manifold} in \cite{Williams}.}.

The equivalence relation $T$ induces a function $m\colon\mathbb{S}^2\rightarrow \mathbb{Z}^+$ from the $2$-sphere to the natural numbers which counts the cardinality of the equivalence class to which each point belongs ($m$ stands for \emph{multiplicity}). The condition that $f$ is $C^1$ has several immediate implications.
\begin{itemize}
\item[1.] An easy compactness argument shows that the range of $f$ is in fact finite.
\item[2.] $m$ is upper semi-continuous\footnote{That is, $m^{-1}((-\infty, a))$ is open in $\mathbb{S}^2$.}. This means that multiplicity can jump down but not up.
\newline
\end{itemize}

If  $f$ is reasonable enough so that $X$ is a finite 2-complex, then we can see clearly by sheet counting that the multiplicities $m$ obey the additivity rule\footnote{In other words, the multiplicity function behaves locally as an invariant transverse measure taking values in $2\mathbb{Z}^+$.} at switches familiar from traintracks in one lower dimension.
Let $d$ be the largest common divisor of $m (\mathbb{S}^2)$. Then the function $(m/d)$ takes integer values, locally obeys additivity and assumes an \emph{odd} value on at least some sheet of $X$ (and therefore some sheet of $Y$).

The advantage of having an immersion of a branched manifold (that is also a finite complex) is that one can, thinking of it as a homology cycle, divide the multiplicities of the sheets by a common divisor and still get a mod-$2$ homology cycle. This is a difference between smooth immersions and PL immersions (e.g. the classical Bing house is the image of a from $\mathbb{S}^2$ that is generically 2-to-1, but when the sheets of the classical Bing house are labeled without multiplicity, each by 1, they do not constitute a cycle with $\mathbb{Z}_2$, or any other, coefficient system).

In the case when $X$ is a finite 2-complex, with the weighting $(m/d)$, $X$ and its immersed image $Y$ may be interpreted as a homology cycle with $\mathbb{Z}_2$ coefficients.
Note that we cannot replace ``$\mathbb{Z}_2$ coefficients" by ``$\mathbb{Z}$ coefficients" since following long loops in $X$ (or $Y$) can reverse a local sheet orientation. In fact, the example of Boy's surface warns us not to expect global additivity with $\mathbb{Z}$ coefficients.

However, $\mathbb{Z}_2$ coefficients are perfectly adequate (in the classical case) to complete the proof for the case when $X$ is a finite 2-complex. Consider a short arc $\alpha$ transverse to a sheet of $Y$ at a point where $h \colon X \looparrowright Y$ is locally $1-1$. Such points are open dense in $Y$ by the $C^1$-condition. Now use the property of any spine of $\mathbb{D}^3$ that its complement has the homotopy type of $\mathbb{S}^2$ (and in particular is connected) to connect the ends of $\alpha$ up by an arc $\beta$ in $\mathbb{D}^3\setminus Y$ to form a simple closed curve $\gamma = \alpha \cup \beta$ meeting the $\mathbb{Z}_2$-cycle $Y$ in a single point. This is a homological contradiction.
\newline

Therefore, all we need do now is to regularize our hypothetical $C^1$-Bing house from a possibly ``wild" Bing house to a finite simplicial $2$-complex whose homological properties are easier to study. If this paper were being written in the 1950's, it is possible that the authors and auditors alike would know enough about the many variants of (co)homology theories available for the study wild spaces to finish the proof by merely identifying the appropriate replacement for $\mathbb{Z}_2$ singular (or simplicial) homology used for the classical case above. Lacking such scholarship we instead use a simple geometric trick to regularize Y without disturbing its dual loop $\gamma$. More precisely, what is left to prove is the following lemma.

\begin{lemmaB}[Sheet compression]\label{sheet flattening}
 Any $C^1$-immersion $f \colon \mathbb{S}^2 \looparrowright \mathbb{D}^3$ parametrizing a Bing spine is regularly homotopic to a parametrization $f'\colon \mathbb{S}^2 \looparrowright \mathbb{D}^3$ of another Bing spine $Y$ which is an immersion of a $C^1$ branched 2-manifold $X$ that is also a finite 2-complex.
\end{lemmaB}

\begin{proof}
The idea is first to strictly increase the equivalence relation $T$ to $T'$ by building regular homotopy $f_t$ from $f$ to $f'$ so as to ensure that all the nonempty pre-images $m_{f'}^{-1}(n)$, for $n\in 2\mathbb{Z}^+$, are codimension zero PL submanifolds of $\mathbb{S}^2$. After a routine perturbation to make the branching loci (the boundaries of these codimension zero PL submanifolds) of $f'$ mutually transverse, $X$ will be a classical branched surface and $Y$ will be its $C^1$-immersed image.

By upper-semi-continuity, the set $D_{2n} \subset \mathbb{S}^2$ of highest multiplicity $2n$ (the maximum of $m$) is closed. We now press together the sheets of $f$ near $D_{2n}$ to enlarge $D_{2n}$ to $D'_{2n}$, a codimension zero PL submanifold. Now, $D'_{2n}$ can be constructed in an arbitrarily small $\varepsilon$-neighborhood $N_\varepsilon(D_{2n})$, for some $\varepsilon >0$, i.e. $D'_{2n}\subset N_\varepsilon(D_{2n})$. By picking $\varepsilon$ sufficiently small we can avoid \emph{coincidental} upward jumps in $m$ that would occur if the expanded multiplicity-$2n$ sheets happened to become tangent to other independent sheets. Avoiding this is possible because in a T4-space disjoint closed set can be engulfed in disjoint open sets.

One may proceed inductively downward, next enlarging $D_{2n-2}$ to a  codimension zero PL submanifold $D'_{2n-2}$, using a relative version of the previous argument which leaves $D'_{2n}$ unchanged. This inductive step and the final perturbation mentioned above complete the proof of Lemma B.
\end{proof}

By choosing the short arc $\alpha$ in the interior of its ($\text{odd}\times d$)-weight sheet, all the choices of $\varepsilon'$s in the proof of Lemma B can be made small enough that the successive deformation never touch a small neighborhood of the closed loop $\gamma$. Now we see that $\gamma$ is also geometrically dual to the (singular) $\mathbb{Z}_2$-cycle carried by $Y'$, which is homologically impossible. We have completed the proof of Theorem A.
\end{proof}

A careful reading of this proof reveals that it uses no low dimensional features. Branched 2-manifolds are merely branched $n$-manifolds when $n=2$ (see \cite{Williams} for an exposition of branched $n$-manifolds). Neither does the proof use the fact that $f$ is a map from $\mathbb{S}^2$ but not any other surface.
The argument readily generalizes to show:

\begin{theoremA'}
For any $n\geq 2$, there is never a $C^1$-immersion $M^{n-1} \looparrowright \mathbb{D}^n$ from a closed manifold $M^{n-1}$ parametrizing a Bing house $Y$ in $\mathbb{D}^n$.
\end{theoremA'}

\begin{remark}
The above argument also shows that any smooth (or $C^1$) immersion from a closed manifold $M^n\rightarrow \mathbb{R}^{n+1}$ must have disconnected complement. So the homework problem mentioned at the beginning of the paper is correct if the embedding is replaced by an immersion as long as it is smooth (or $C^1$). The readers who has read up to this point could safely assign it to their students as a homework problem, even with the hypothesis on orientability of $M$ dropped.
\end{remark}

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After formative years spent in Dublin, HOLDEN were spotted by now sadly defunct French label Lithium and they released their first album, L'Arrière-Monde, in 1998. The group, formed by Armelle Pioline and Mocke, then recorded Pedrolira, Chevrotine and Fantômatisme, three albums which are essential for any fan of enlightened French pop. Each of the records received critical acclaim and the band attracted a growing audience.
Stylish and inventive, HOLDEN's music fits somewhere between straight pop tunes and experimental pop, all assisted by an inspired guitar, evocative lyrics and the most alluring French voice.
They have been produced by Uwe Schmidt (ATOM™, SENOR COCONUT) since Pedrolira, and in early summer 2011, they released L'Essentiel, a double album which traces their career from the beginning in Ireland. With Catchers due to play 7ème Ciel in August 2011, we were delighted to welcome another band whose name was inspired by the JD Salinger novel The Catcher in the Rye.


(ORANGE, TX) – Join us at Shangri La Botanical Gardens and Nature Center the evening ofAugust 18th, starting at 6 p.m. for a back-to-school kickoff celebration free of charge, presented by International Paper. Bring the entire family for an evening stroll through the gardens, family-friendly games and activities focusing on sustainability, and an outdoor full-length animated feature film. A school supply donation drive will be held to benefit area school children in need. Set up a lawn chair or blanket, have some popcorn, and enjoy a movie with the entire family!
For more information, visit shangrilagardens.org. Garden Rules Apply.
Shangri La Gardens and Nature Center encompasses 250+ acres in the heart of Orange, Texas, along the swamps and wetlands associated with Adams Bayou. Shangri La integrates its botanical gardens and nature center together to create a unique understanding of the natural world in Southeast Texas. Imagine a place where you can stroll along garden paths surrounded by a profusion of flowers, watch birds for hours from the comfort of a Heronry Blind or just spend time relaxing with friends and family. Or, you can explore your wild side and take a naturalist-led excursion along Adams Bayou to discover the wonders of nature, encounter wildlife in their natural habitats, and gain new insights into the importance of preserving the environment. No matter what motivates you to come outdoors, explore Shangri La-it's a year- round delight for the senses.


National Institute for Research in Reproductive Health [NIRRH] is a premier research institute of the Indian Council of Medical Research (ICMR) and is situated in central Mumbai. The institute was established in the year 1970 with the purpose of addressing the various issues of reproductive health in accordance with the national needs and priorities. The Institute is affiliated to the University of Mumbai which awards degrees to the M.Sc. and Ph.D students in the areas of Biotechnology, Life Sciences, Biochemistry and Applied Biology. The Institute is one of the few centres in India, which can boast of a team of basic, clinical and operational research scientists and state-of-art laboratories equipped with modern facilities to carry out research on various components of reproductive health. Research programmes have also been initiated in new emerging areas such as stem cell biology, toxicology and trans-genesis. The Institute is a WHO Collaborating Centre for Research and Training in Reproductive Health. Collaborations are undertaken with national and international organizations in a global effort to promote research and dissemination of information on reproductive health matters.
Why to JoinNational Institute for Research in Reproductive Health [NIRRH]?


text:
Puthunagaram is een census town in het district Palakkad van de Indiase staat Kerala.

Demografie
Volgens de Indiase volkstelling van 2001 wonen er 16367 mensen in Puthunagaram, waarvan 50% mannelijk en 50% vrouwelijk is. De plaats heeft een alfabetiseringsgraad van 73%.

Plaats in Palakkad

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text:
Teslas death ray tv show episode list
Teslas death ray tv show episode list. Tesla's Death Ray: A Murder Declassified (TV Series 2017 2019-03-26
Tuesday, March 26, 2019 5:43:40 PM Bennett
Watch Tesla's Death Ray: A Murder Declassified online at sampfordpeverell.com
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Cookies Websites use cookies that have been placed on this site by its operator: EpisoDate. History's most brilliant mind was also its most dangerous. The radio, cell phone, and alternating current electricity have all revolutionized the way humans live and they all have one very important person in common: Nikola Tesla. While he was making millions, he also made enemies. Recently declassified documents may help solve the mystery. You can withdraw your consent at any time. The show is currently in its 1st season.
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Guildball / Season Three
Guild Ball: Season Three Rule Changes
by Alex Vian · Published November 29, 2016 · Updated November 29, 2016
Guild Ball Season Three is here, with new nerfs, new rules, new guild plots, but not yet any new models. Over the next few days, Midwest Wargaming will cover the changes in their entirety – and when new models come, you better believe they'll be covered.
First up, of course, are the new rules.
The 'biggest' change is the change which was made to mascots. Mascots now may (all) return to the game after being taken out, and are now worth only 1 VP each time they are taken out. Steamforged did a three part write up on their thinking in this arena, so clearly this is a big change to what Mascots bring to the table.
The biggest development to arise out of this change, however, are changes to things like Beloved Creature and other 'upon removal' effects and revive effects for the various mascots. Be sure to check out Dirge, Princess, and Salt before you play with them in Season Three!
The most significant new rule is, of course, part of the initiative phase, and a minor rule change with a monumental effect on the game. After rolling for initiative, and after resetting momentum to 0, the team which does not have initiative gains 1 Momentum! In Season 3 of Guild Ball, you either start your turns (after the first, as we'll cover later) with initiative or with precious momentum to use to defend yourself against a charge, score a quick goal, or open up with a teamwork play.
This little change will completely change every single game of Guild Ball. Most importantly, a player may now actually choose to go last in a round, in order to automatically gain an all-important momentum point.
It's important to note, however, that the kicking team at the start of the game does NOT gain this Momentum point – there is no 'Initiative phase' during the first turn of the game:
ICY SPONGE
There has been a more subtle change to the Icy Sponge rule, in that not only do mascots have a 'recovery level' on their health bar, but the vast majority of models have only one recovery level, rather than two. Players will get back in the game more quickly, and only rarely will Season Three see players wait an extra turn before returning their player to the game, as there will be no benefit. As an example, let's look at the Brewers' Tapper:
In Season Two, Tapper has two recovery levels, allowing him to come back in at either 6 wounds immediately on the next turn, or 12 wounds if he waits one turn before.
In Season Three, Tapper's wound bar looks just a bit different, because he comes back at 9 wounds, with no option to wait an extra round:
Completely gone is the option to heal up a bit more after waiting for another round for one of your folks to heal – probably because nobody took this option, with its corresponding loss of both an activation and generated influence.
The book's section on the Maintenance Phase is also reworded to reflect this change.
KICK-OFFS
While the wording for the Kick-offs section has changed by adding one clause, the actual way kick offs work has not changed. The Kick-off is now a pass, albeit one that cannot target a friendly model.
GOAL KICKS
The wording, but not the function, has also been changed for Goal Kicks. The goal kick is drawn back towards the goal until it can rest on the ground if it lands on top of an obstacle after scattering.
TAP IN
Related to Goal Kicks, but definitely deserving of its own section is the change to Tap-In. Tap-In is no longer a plot card but is now a core rule. Basically, if you are within [4″] of the enemy goal-post the model making the shot gets a [-1] TN check. Now you actually have a reason to get closer to the goal than to constantly stay at maximum kick distance.
CARD LAYOUT
The last changes aren't particularly significant. Cards have a new layout in the Character Play and Model Type Sections. Both are on display on the new Veteran Siren card:
Rather than writing out 'This character play may be used once per turn' over and over on every single one of the majority of the character plays in the game, Steamforged now represents this trait of a character play in a column marked 'OPT.' A check mark in this column indicates the character play may only be used once per turn.
Meanwhile, on the back of the card, you can see another change which is foreshadowed by the front of Vet Siren's card:
A model's 'Position on the Team,' Veteran, Mascot, or Captain, is now a separate row on the bottom of the 'Model Type' section, in addition to the model's gender, race, nationality, and position on the field. The team position 'Veteran' is not specifically mentioned in the Season 3 Rulebook, but it's more clear now that both (Veteran) Siren and Siren have the same name and cannot both be used in the same team at the same time.
Sike! The Interception Rules are the same, meaning that the target of a failed pass can somehow still intercept a pass intended for that model. This is apparently a personal pet peeve of mine and not a problem to anybody else, but it's incredibly stupid, and still a rule in Season Three. Is it so much to ask for just one thing to make sense? You can't intercept a pass intended for yourself!
Stay tuned over the next week as Midwest Wargaming breaks down the new Season Three Guild Plots and the changes to each Guild's roster, including the gutting of Gutter and radical changes to Avarisse & Greede,
UNION PLAYERS
A change up that is in the Organized Play rules, which will be applicable in tournament play and the like: Players that did not choose the Union as their Guild may only select a single eligible Union model for their roster. This is really going to shake up the rosters that you see across the table.
Tags: SirenTapperVet Siren
Alex Vian
A reformed Warhammer Fantasy player based in the Twin Cities, Alex plays Malifaux, Guild Ball, X-Wing, and Armada. He also is the host of the Malifaux Tactics podcast here at Midwest Wargaming: Lecture Notes from the Breach
Butchers Season 3 - Midwest Wargaming
[…] fellow MWWG contributor, TheGreatSerpent, explained in his latest article, Mascots changed quite a bit. In fact, the changes to Mascots in the core rules is arguably more […]
Morticians Season 3 - Midwest Wargaming
[…] changed a lot, and you can find those changes in one of our previous articles about Season 3 Guild Ball changes. In addition to all that though, Dark Doubts changed too. Before, it inflicted a [-4] MP penalty […]
Next story Butchers Season 3
Previous story Situations where Exemplar Errants are better than Idrian Skirmishers


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Malý Čepčín – wieś i gmina (obec) w powiecie Turčianske Teplice, kraju żylińskim, w północno-centralnej Słowacji. Znajduje się w Kotlinie Turczańskiej nad rzeką Teplica. Wieś lokowana w roku 1254.

Przypisy

Miejscowości w powiecie Turčianske Teplice


This track will get em movin and a shakin!
It's a Motown Christmas! You could almost get away with listening to this track year round since it's merely a simple love song at its core.
Everyone already knows this song but it's an absolute classic. I feel like this song is used a lot in Hugh Grant movies?
Hot Tracks Whenever I Damn Well Feel Like It!
Every once and while there is a song that has a sound so timeless that it sounds like nothing that has come before, or will happen after. That being said, I'm hearing the Ting Ting's meet The Kills.
This song is just good ol' fun!
Been listening to a lot their album Mademoiselle lately. This song reminds me so much of Spun by The Brian Jonestown Massacre. Lovin' that tambourine; these guys have such a wicked sound.
I KNOW WHAT DAY IT IS!
Here are three songs from all-time greats, although they may never again attain their previous lofty heights. But who knows? Stranger things have happened. At the very least, all three songs have been in heavy rotation for me lately.
You might be familiar with Noel Gallagher as the featured vocalist on the Chemical Brothers track "Let Forever Be" (the accompanying music video is not my all-time fave, but it's easily in the Top 5 discussion). These days he's doing his own thing, fronting his own band. (Fun fact: Noel previously fronted another with his brother Liam. they were called Oasis. They did ok for themselves.) I've thought that the post-90s output of The Brothers Gallagher has been good-not-great, but the latest offering from Noel Gallagher's High Flying Birds is pretty high flying. Eminently listenable, and quite possibly loveable. I'm getting there.
Beige has to be the least exciting colour in the history of colour. Even something neutral like grey has variations like cool and warm grey, and it's quite versatile really. Calling a song Being Beige is the kind of move that might make people wonder why they'd want to click on a song about being the most boring, bland colour/person/feeling in the world.
Here's the first song from the brand-new Pumpkins album Monuments to an Elegy. It's produced by Howard Willing, aka The Bear, who previously produced a heck of a lot of artists, including later work by the Pumpkins, and (for you, Derek), Trouble in Shangri-La, by Stevie Nicks. It sounds anything but boring.
Remember the first time you heard The Strokes and they sounded low-fi and gritty? The sound that characterized Is This It? would define The Strokes, although they dropped it a couple of albums into their career. Well, if that was gritty, then it was polishing-grade sandpaper compared to the coarser sounds from Julian Casablancas + The Voidz. But this is also the first time since those early Strokes-days that Casablancas is feeling artistically fulfilled. So here's this garage/metal/pop mashup.
Just look at this video! It's by Michel Gondry in his earlier days, and it's a trip and a half. God, I love it. The song is fantastic, too.


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PowerPoint PowerPoint could be the demonstration program. PowerPoint is also flexible, and may generate a slip show using among many procedures. PowerPoint is just a graphics-based program that lets you produce energetic presentations. Microsoft Powerpoint the various tools you should produce good pictures, including banners. Microsoft PowerPoint doesn't offer an option expense for the glides, but there are some creative solutions to apply anything in the same direction. Microsoft PowerPoint is a software plan that offers you the option to produce your own personal format or even select from the numerous theme patterns which can be presented in the PowerPoint collection. Microsoft Powerpoint is certainly one of typically the most popular demonstration programs accessible today. Right-click on the slip that's currently shown in a demonstration if you wish to demonstrate an invisible slide. You will discover the initial slip that contains the concept of the song. Start a picture that you intend to seem on the slide. Go through the fall that you want to modify. Choose the PowerPoint go that you need to edit. If you are performing a demonstration for a customer, for instance, you are able to pick to create the client's logo. Once you open a display that has macros, an orange bar seems at the the top of screen. Trusting the themes to gather work, if they're presentations for work or individual sites, implies that you do not obtain the features of understanding the interior functioning of the application you are using. Go to the positioning where you will need to help keep the demonstration and offer a demonstration name. Once you make a new speech, you have the option of selecting one of many available themes or planning your own. Efficient presentations let presenters to explain their points clearly and concisely. PowerPoint presentations are becoming an essential part of corporate conferences.


Expect a response within 1 - 3 months after close of submissions. If you have not heard from us after 3 months please inquire.
- Please submit 1 to 5 poems, 1 craft essay, or 1 book review, using the forms below.
- Previously published is also fine, as long as it was in print, not online, and as long as you as the author retain all copyright. Because we strive to be the first online publisher of your poem, if it has appeared anywhere that is publicly accessible on the web (including on your blog) then it is considered previously published. Please feel free to contact us and we will provide clarification on a case by case basis.


SigScale is an open source company focused on cloud native signalling solutions for communications service providers' virtualized core networks. Based in Colombo, the company is not just a trailblazer in Sri Lanka but for the global IT industry, carrying out pioneering work in the field of public, wireless internet service provision. With the launch of SigScale's new online charging system (OCS), at the WISP America conference in Tennessee, Encyte was selected to revamp their existing website.
One of the biggest challenges that this site posed was the relative complexity of SigScale's highly technical business. Encyte worked closely together with the SigScale management team, to garner a comprehensive understanding of their products and services, as well as carrying out research into competitor products and the current market environment. Once our team managed to do this, we worked on making the content more accessible to a wider spectrum of website visitors whilst also remaining relevant to the key demographics that the company was targeting. The other major challenge posed by the project was the tight deadline, the website was to be delivered in. Working on a highly expedited schedule, we managed to successfully deliver prior to the commencement of the crucial conference. Encyte was able to boost Sigscale's web presence and effectively communicate their new product's features and benefits.


flag. Catch this in prereq check to give users to proper error message.
from CAKE qdisc on MIPS allowing us to bump CAKE to latest version.
containing header will be adjusted to the right value.
the netlink attribute-based statistics in CAKE.
drivers holding the fragments have wrapped around.
source feeds to be available during build.
(seems to share this behavior with other tplinks based on mt7628).
Enables support for Dynack feature.
by allowing more time for an ACK to arrive back before issueing a retransmission.
- If the distance becomes greater, retries start to occur and comms can get lost.
This feature is currently only supported in ath9k.
it is also disabled by default.
Disabling it can be done by providing a valid fixed value.
In my usecase, we have mesh wifi device installed on ships/platforms.
Currently, the coverage class is set at 12000m fixed.
compared to the fixed setting of 12000m being used.
communication was lost as the ACK's never arrived within the max allowed timeframe.
cfg80211_get_station (or actually the underlying implementations).
switch to non-optimal neighbors for certain destinations.
Bump iproute2/tc support of cake.
"LZMA ERROR 1 - must RESET board to recover"
Booting the same kernel via TFTP works for some reason.
Move to i2c pins pinmux node to the pinctrl node.
partitions are detected from inside the "firmware" partition.
[ 1.111324] 0x000001480000-0x000001880000 : "kernel"
[ 1.121005] 0x000001880000-0x000007900000 : "ubi"
[ 1.283912] 0x000007900000-0x000008000000 : "reserve"
[ 1.296407] 0x000001480000-0x000007900000 : "firmware"
[ 1.468043] no rootfs found after FIT image in "firmware"
[ 2.426931] 0x000001480000-0x000001880000 : "kernel"
[ 2.440420] 0x000001880000-0x000007900000 : "ubi"
ubiattach: error!: bad MTD device number: "6 mtd10"
needed for sysupgrade anymore. Remove it to fix things.
Only tested for the R7800 but all of them should behave equal.
that is located after the firmware partition.
by 68 MB from 32 MB to 100 MB.
increasing the package installation possibilities greatly.
The "bootargs_root=" that was appended to it should not be there.
mimicking what is also done by uboot upstream.
to other devices as well.
or if the user deletes the uboot configuration when upgrading uboot.
uboot configuration stored in flash would not have noticed this issue.
to 30 instead of 31.
Patch has also been submitted upstream.
clock detects as 40MHz while it is actually 25MHz.
This is due to messed up bootstrap resistor configuration on the PCB.
Provided GPL code just forces 25MHz reference clock.
to boot at 1040MHz while the stock is 650MHz.
So this PR depends on PR #672 to remove 40MHz reference clock.
Thanks to Sven Eckelmann <sven@narfation.org> for properly patching that.
Add support for detecting TP-Link Pharos v2 boards.
They use different format in product-info partition than v1 boards.
It backports remaining brcmfmac changes from 4.17.
It backports brcmfmac commits from kernel 4.17.
> * rework bus layer attach code.
> * remove duplicate variable declaration.
9 months agoRevert "LEDE v18.06.0-rc1: adjust config defaults"
9 months agoRevert "LEDE v18.06.0-rc1: revert to branch defaults"


Kouassi Kla is Managing Director of Corlay Togo, ranking third marketer of the Republic of Togo.
He holds a Master of Business Administration (MBA) in Finance in 1983 from the University of Baltimore, Maryland, USA.
Kla's Professional career started in December 1983 in the Finance Department of Phillips Petroleum Company, an American upstream company based in Côte d'Ivoire prior to joining Texaco Côte d'Ivoire in 1990 in the downstream.
With 32 years of experience in the petroleum industry with high profile multinational companies in upstream and downstream, Kla held increasing responsibilities as Deputy General Manager of Texaco Côte d'Ivoire, Managing Director of Texaco Togo and Texaco Benin, Managing Director of Texaco Cameroun.
We are redefining standards in meeting the fuel needs of our customers in West Africa.
We currently offer cylinders under four (4) packagings: 3 kg; 6 kg; 12.5 kg and 25 kg.
The following are best practices for handling our cylinders at home, while transporting and while refilling.
We have numerous re-sellers and distributors nationwide. Click on our map to find a location nearest to you.
Corlay Togo is committed to selecting the best possible lubricant dealer, with the focus on the determining factors of Business Risk, Organizational Risk and Reputation Risk, consistent with the long-term best interests of the Company as it shall determine in its sole discretion.
Fuel quality: frequent trainings and daily basis controls are conducted by our team to check out for potential contamination, water presence, leakage.
Lubricants and LPG quality: all these appealing products are certified and delivered in eco-friendly sealed packages very respectful of the environment.
Safety and security: Dealing properly in risky situations is one of the core training provided regularly to our team. A dedicated team with expertise in safety are mandated to ensure and guarantee security to our customer through our installation and equipment.
Our convenience stores are shelved in order to provide a wide and extensive range of useful products. Some of them are even open 24 hours to provide more convenience to our customers.


Skymark, a leading independent manufacturer of flexible film packaging solutions, has won a double gold award for its holographic print at the prestigious European Flexographic Industry Association (EFIA) annual print awards.
The manufacturer, which has sites in Scunthorpe and Ilkeston, was recognised in the technical innovation and in the creative use of flexographic categories for it's 'in register' holographic bubble, rainbow and sparkle effects.
The judging panel, made up of industry representatives from a cross section of printers, suppliers, brand owners and retailers, praised Skymark for its far-reaching innovation in flexible packaging, something not seen for some time. The high quality and creative effect from Skymark can enhance existing designs and add value to any product.
Many companies, who have previously offered the holographic effect process, are based in Eastern Europe and the Far East. Skymark is currently the only UK based printer able to create this solution – an in register, patterned holographic effect for flexible packaging.
The EFIA Annual Print Awards recognise excellence in flexographic printing across a number of skills and techniques. The gala dinner was held at the Vox Conference Centre at Resorts World in Birmingham on March 16, 2017.


We have reiterated the sobriquet of 'Spice Land' for India Our business footprint and loyal customers across the world are our testimonials for consistently delivering the finest grade of spices in multifarious forms year after year.
With the philosophy of 'reaching our customers heart through their taste buds', we at Cilantro Spices have been successful in taking the Indian spices and taste to millions of homes across the globe. We take pride in the fact that Ramdev has established India's heritage across the world through Indian food, the Indian way.
We continually strive and never reduce the quality of a product to make it cheaper. We do everything we can to make our products better: taste better, smell better, last longer and remain fresh as possible.
Black pepper is the fruit of the black pepper plant from the Piperaceae family .
Popularly known as "elaichi" in hindi, "aelakka" in malayalam .
Coriander seed is the fruiting body of the coriander plant, which is a popular .
Cumin, scientifically known as Cuminum cyminum, belongs to the family Apiaceae.
Fennel seeds are highly aromatic and flavorsome dried seeds of fennel plant.
Cilantro Spices are the legend supplier in Basic Spices, Whole and Powder Spices, Blended Spices, Instant Mixes, Indian Groceries, Pickles, Chutneys, Papad, Khakhra, Frozen Vegetables (IQF) & many other food categories and ranks amongst a few brands that have a nationwide presence in the organized sector in India.Indian spices are loved by people from all over the world. Spices are the real reason behind exotic flavour's in Indian food. Indian cooks use a variety of spices for seasoning traditional Indian recipes. The popularity of Indian recipes has increased worldwide demand for Indian spices.


text:
Home » News » Housing Allowance for DKI DPRD Members Increases to IDR 70 Million per Month
Jakarta, CNN Indonesia —
Chairman of the DKI Jakarta DPRD Prasetio Edi Marsudi ensure that housing allowances for council members increase by IDR 10 million this year.
It is known, in the Decree of the Ministry of Home Affairs (Kemendagri) regarding the Evaluation of the 2022 DKI Jakarta Regional Budget Draft and the DKI Jakarta Governor's Draft Regulation on the 2021 APBD Elaboration, the Ministry of Home Affairs highlighted the allocation of the DKI DPRD's salary and allowance expenditure budget of Rp. 177.37 billion.
That number increased by Rp. 26.42 billion compared to last year, which was Rp. 150.94 billion. One of the contributors to the increase was the council's housing allowance spending.
"[Tunjangan perumahan] increase by Rp. 10 million if I'm not mistaken," said Prasetio after the Budget Board meeting discussed the results of the Ministry of Home Affairs' evaluation of the 2020 DKI Jakarta Regional Budget Raperda, Thursday (13/1).
Pras said that his party and the DKI Provincial Government had finished holding a meeting to discuss the results of the Ministry of Home Affairs' evaluation.
"Completed, the evaluation is complete and the remaining money is put into BTT (Unexpected Costs)," he said.
Previously, the Chairman of Commission A of the DKI Jakarta DPRD, Mujiyono, said that the housing allowance for this year's council is budgeted to increase by Rp. 10 million per person per month.
He explained, previously the council received a housing allowance of Rp. 60 million. With this addition, each member of the council will receive a housing allowance of around Rp. 70 million per month.
"According to the appraisal, there has been an increase in housing allowances, which have not increased for more than 4 years, approximately Rp. 10 million before tax deduction," said Mujiyono, as quoted by Antara. detik.com.
(yoa/arh)
Categories News Tags dprd dki jakarta, HOUSING ALLOWANCE
Marine biologist very excited after seeing very rare rainbow-colored octopus


* Set checked state of a compound button.
From project cw-omnibus, under directory /Location/Periodic/src/com/commonsware/android/perloc/.
From project iosched_3, under directory /libprojects/abs/src/com/actionbarsherlock/internal/view/menu/.
From project android_packages_apps_CMSettings, under directory /src/com/cyanogenmod/settings/switches/.
From project AnySoftKeyboard, under directory /src/com/anysoftkeyboard/ui/tutorials/.
* Utility routine to setup a checkobox based on a preference.
From project callmeter, under directory /src/de/ub0r/android/callmeter/widget/.
From project creamed_glacier_app_settings, under directory /src/com/android/settings/accounts/.
From project cw-android, under directory /Basic/CheckBox/src/com/commonsware/android/checkbox/.
From project droid-comic-viewer, under directory /src/net/robotmedia/acv/ui/settings/.
From project forMegaADK, under directory /MegaAdkLed/src/com/tomovwgti/megaadk/.
From project Funf-Ohmage, under directory /src/edu/mit/media/funf/funfohmage/.
From project gddsched2, under directory /trunk/android/src/com/google/android/apps/iosched2/ui/.
From project GSM-Signal-Tracking-, under directory /gpstracker/src/nl/sogeti/android/gpstracker/viewer/.
From project ignition, under directory /ignition-support/ignition-support-samples/src/com/github/ignition/samples/support/.
From project iosched, under directory /android/src/com/google/android/apps/iosched/ui/.
From project iosched2011, under directory /android/src/com/google/android/apps/iosched/ui/.
From project iosched_2, under directory /android/src/com/google/android/apps/iosched/ui/.
From project k-9, under directory /src/com/fsck/k9/fragment/.
From project ListViewTipsAndTricks, under directory /src/com/cyrilmottier/android/listviewtipsandtricks/.
From project mobilis, under directory /MXA/src/de/tudresden/inf/rn/mobilis/mxa/activities/.
From project nantes-mobi-parkings, under directory /android/src/main/java/fr/ippon/android/opendata/android/.
From project NineOldAndroids, under directory /sample/src/com/jakewharton/nineoldandroids/sample/droidflakes/.
From project ohmagePhone, under directory /src/org/ohmage/triggers/types/location/.
From project Ohmage_Phone, under directory /src/org/ohmage/storagemonitor/.
From project OpenBike, under directory /src/fr/openbike/android/ui/widget/.
* @param balloonBottomOffset - The bottom padding (in pixels) to be applied when rendering this view.
From project opensudoku, under directory /OpenSudoku/src/cz/romario/opensudoku/gui/inputmethod/.
From project opensudoku-blackberry, under directory /opensudoku/src/net/bmagro/blackberry/opensudoku/gui/inputmethod/.
From project PinDroid, under directory /src/com/pindroid/fragment/.
From project platform_packages_apps_settings, under directory /src/com/android/settings/.
From project rbb, under directory /src/com/btmura/android/reddit/app/.
From project RebeLauncher, under directory /src/com/dirtypepper/rebelauncher/catalogue/.


text:
Kapaa High School Foundation est. 1995
Donate Now+
Foundation Officers
Home Uncategorized 2014 Foundation Student Grants Awarded
2014 Foundation Student Grants Awarded	Posted June 6, 2014	by cesaki
From left to right: Shania Weiss, Kelsie Lima, Cassidy Yatsko, Kekai Gonslaves, and Foundation Scholarship Committee Chair Michelle Domingcil
The Kapaa High School Foundation awarded grants of $1000 each to four Seniors who demonstrated extraordinary commitment to community service while pursuing their academic goals.
Shania Weiss plans to attend the University of Hawaii this fall with plans to major in Nursing. Being from a family of seven children, she understood from an early age that she would have to be responsible for providing for her own college education. Besides being a caregiver to her younger siblings, she worked 30 hours a week during high school to cover her school and personal expenses. She also participated in Swimming and Cross Country and was captain of her Team Surfing Club. In spite of her hectic schedule, she graduated as a valedictorian of her class with a 4.2 gpa.
Shania is described as a mature, independent, and bright young lady. In the Interact Club she held a leadership role as one of the Committee chairs, planning and supporting social and community service events throughout the year. According to Interact Club advisor Joan Kealalio, "her passion for helping other people is in her soul."
Kelsie Lima will be heading to UC Davies in the fall to major in Veterinary Science. Her passion for animals led to to spend many hours as a volunteer at the Kauai Humane Society as a veterinary assistant.
Kelsie is also active in her church as a key alter server and helps to train new alter servers. Her pastor Father William Shannon describes her as being polite, friendly and highly energetic.
Kelsie' was born in China and orphaned at an early age. In her words, "my world was bleak until these wonderful people came and adopted me. Because of my parents, I received a proper education, knowledge, and experience I have been able to travel and learn about different parts of the world. I developed a sense of being loved and I have been able to develop dreams." She now dreams of returning the aloha that was shown to her to the people of Hawaii.
Cassidy Yatsko will be attending Boise State University in the Fall to pursue a a degree in Psychology. Her goal is to be a school counselor.
Cassidy grew up in a family that believed in compassion and community service. Growing up, she spent a lot of time at her Dad's workplace, Friendship House, a rehabilitation program for people with mental illness. She became inspired by by how the members responded to the treatment they received, getting jobs, going back to school and finding housing. Her spirit of volunteerism led her to become a Youth Group leader for All Saints Church for seven years, participating in projects that took her to Los Angeles to help the homeless, and helped to run an afternoon program in gang ridden housing projects in East LA. As President of the Kapaa High Interact Club and a member of the National Honor society, she helped plan, organize and worked on numerous service projects throughout the years. At the All Saints Church she was known as being "literally filled with joy in being able to serve others."
Although she participated in countless hours of community service, Cassidy showed her ability to manage here time well. She graduated as one of the valedictorians of the Class of 2014.
Kekai Gonsalves will be attending Brigham Young University in Provo, Utah with plans to major in English. Besides focusing on her academic goals(she was a valedictorian of the Class of 2014,) Kekai held three passions; athletics, church, and community service.
A gifted athlete, Kekai excelled in soccer, basketball, and track.During her Junior year she was named captain and league all star for soccer and basketball. On the track team she was chosen as MVP. However, during most of her senior year she was sidelined with a knee injury. In spite of her physical and emotional pain, she demonstrated good sportsmanship and a good heart by attending all of the games to cheer her teammates on.
At the Church of Latter Day Saints, Kekai served as President of the Mia Maid Class, Laurel Class and Secretary of the LDS Seminary Class. These classes are structured to teach young women about the Scriptures, how to make good choices, and live virtuous lives. They do service projects and give support to new members that seek guidance. For her Laurel Class project, Kekai organized an event to recognize and honor the kupunas at their church. Trinette Kaui, her youth advisor, relates that Kekai was always a positive person that everyone loves to be around.
During her senior year, Kekai was elected Class President, one of the most demanding postions in student government. She was also National Honor Society President and a member of the Interact Club. Being committed to these three leadership and service organizations required her to be somewhere involved in a meeting or project almost every day. She also excelled academically, graduating as one of the valedictorians of her class.
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Next month, Walmart employees in the US will receive pay increases.
in USA News, World News
Walmart announced that it will be increasing the starting wages for its U.S. workers next month, with wages ranging from $14 to $19 per hour.
The company's President and CEO, John Furner, informed employees of this change in a memo on Tuesday, stating that the pay raises will be reflected in their March 2 paychecks and will be a combination of targeted and regular annual pay increases.
The pay increases will affect workers at 3,000 stores, raising the average pay to $17.50 per hour from $17. Currently, starting wages at Walmart vary between $12 and $18 per hour depending on the location. Due to the ongoing labor shortage, competition for low-wage retail workers remains fierce, and as a result, Walmart and its competitors have raised wages and added benefits in recent years to retain workers, including coverage for in vitro fertilization, fertility testing, and financial assistance for surrogacy and adoption.
With this latest pay raise, Walmart, the largest retailer and biggest private employer in the country, is now closer to its competitors, such as Target and Amazon, who have raised their minimum wage to $15 per hour.
Walmart is raising its base pay from $12 to $14 an hour. The company says the raises are expected to bring its average hourly wage up to "more than" $17.50 an hour. https://t.co/4Iva237Yig
— CNN (@CNN) January 24, 2023
Amid an ongoing custody dispute with Jason Sudeikis, Olivia Wilde is returning to filmmaking.
Three individuals have died and a suspect has been found dead in a shooting incident that occurred in Yakima, Washington. The police are investigating the case.


The atoms of a chemical element can exist in different types. These are called isotopes. They have the same number of protons (and electrons), but different numbers of neutrons. Different isotopes of the same element have different masses. Mass is the word for how much substance (or matter) something has. Things with different masses have different weights. Because different isotopes have different numbers of neutrons, they do not all weigh the same or have the same mass.
Different isotopes of the same element have the same atomic number. They have the same number of protons. The atomic number is decided by the number of protons. Isotopes have different mass numbers, though, because they have different numbers of neutrons.
The word isotope, meaning at the same place, comes from the fact that isotopes are at the same place on the periodic table.
In a neutral atom, the number of electrons equals the number of protons. Isotopes of the same element also have the same number of electrons and the electronic structure. Because how an atom acts is decided by its electronic structure, isotopes are almost the same chemically, but different physically to their original atoms.
Heavier isotopes react chemically slower than lighter isotopes of the same element. This "mass effect" is larger for protium (1H) and deuterium (2H), because deuterium has twice the mass of protium. For heavier elements, the relative atomic weight ratio between isotopes is much less, and the mass effect is usually small.
Atomic nuclei are protons and neutrons held together by the nuclear force.
Because protons are positively charged, they repel each other. Neutrons, which are neutral, stabilize the nucleus. Because they are in the nucleus, the protons are pushed slightly apart. This reduces the electrostatic repulsion between the protons. They still exert the attractive nuclear force on each other and on protons. One or more neutrons are necessary for two or more protons to bind into a nucleus. As the number of protons increases, so does the number of neutrons needed to have a stable nucleus.
In nature some elements only have a single isotope. For example, fluorine 19F is the only stable isotope, of several, of fluorine. Other elements have many isotopes. For example, xenon has 9 isotopes. Of the 81 elements with a stable isotope, the largest number of stable isotopes for any element is ten (for the element tin).
Some isotopes are radioactive. These are called radioactive isotopes. Others are not radioactive. These are called stable isotopes.
Hydrogen has three common isotopes. The most common isotope of hydrogen is called protium (1H). A hydrogen atom with an extra neutron (atomic mass of 2) is called deuterium(2H). Hydrogen with one proton and two neutrons (atomic mass of 3) is called tritium(3H). Protium and deuterium are stable isotopes, while tritium is a radioactive isotope.
The heaviest elements in the periodic table are all radioactive. All of the isotopes of radon, thorium, and uranium are radioactive, since they are very heavy. This is because the nuclear forces inside the nucleus of the atom have a tough time holding together all the particles with so many protons and neutrons inside.
This page was last changed on 3 March 2019, at 17:25.


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SB19 Makes History By Hitting No. 1 Spot On Billboard's "Hot Trending Songs" Chart
SB19 is taking their "I'm fire" lyrics from their hit song "Bazinga" seriously as the group has just hit the No. 1 spot on Billboard's "Hot Trending Songs" chart. Mega-group BTS had the top spot for weeks since the new chart was introduced, and SB19 is the first act to take over the highly-coveted ranking with their latest release, "Bazinga." Previously ranked at No. 8, "Bazinga" skyrocketed to the top spot, surprising many for taking over a position BTS has had their lock on. SB19 has had a steady incline in the music world, garnering fans from all over the globe with their talent and transparency, and is also known as the act that is spearheading the breaking of boundaries and highlighting P-Pop and OPM on a global level. Just this year, the group was nominated for a Billboard Music Award and was up against heavy-hitters such as BTS, BLACKPINK, SEVENTEEN, and Ariana Grande, making their nomination historic! The group's fanbase, A'TIN, is a force to be reckoned with and their love and support for SB19 seems to be the driving force for the group to continue creating music, expanding their reach and releasing content consistently. It was just announced today that the group will be hitting theaters with their third anniversary concert, "Our Zone," set to play in certain cinemas. Check out the announcement below and continue to stream and listen to "Bazinga" now available on all music platforms! Congratulations, SB19!
I'M FIRE I LINGERRRR YEAH 🔥
Wow! Thank you A'TIN for bringing us to the Top Spot on the @billboard #HotTrendingSongs !
💿 Stream Bazinga here: https://t.co/xJetLm9yJL #SB19 #SB19BillboardHTSTop1#Bazinga_SB19 Dominates BBHTS pic.twitter.com/93BocAXh2Q
— SB19 Official 🇵🇭 (@SB19Official) December 7, 2021
Arambulo Live December 7, 2021 Bazinga, BTS, SB19
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