text:
\section{Introduction}

Colourings of simple $3$--dimensional hyperbolic polytopes with elements of $\mathbb{Z}^3_2$ were first used by Vesnin \cite{Ves87} in order to produce closed hyperbolic $3$--manifolds from the so--called L\"obell polyhedra.

Later on, Davis and Januszkiewicz \cite{DJ91} used a similar idea in order to produce complex $n$--manifolds with torus actions. The fixed point set of the conjugation involution of any such manifold produces a real $n$--manifold endowed with $\mathbb{Z}_2$--action \cite[Corollary 1.9]{DJ91}. The latter gives rise to a $\mathbb{Z}^n_2$--colouring that corresponds to a manifold known as a small cover. The technique of colourings of right--angled polyhedra was then generalised in the works \cite{KMT, KS?}, and the recent work of Choi and Park \cite{CP2} provides an efficient method to compute cohomology rings of manifolds obtained via colourings. Right--angled polyhedra attracted a lot of interest per se and as constituent pieces of hypebolic manifolds, cf. \cite{Atkinson, Dufour, Kolpakov, KM, PV}.

Colourings of polytopes provide an accessible way to build hyperbolic manifolds with prescribed topological characteristics. Cf. the recent surveys \cite{Martelli, Vesnin} for more information about the recent results in this area.

One of the classes of manifolds with relatively simple topological structure are homology spheres. We are mostly interested in \textit{rational homology spheres} (termed $QHS$ for short) and, moreover, in those that are hyperbolic manifolds (which we call hyperbolic $QHS$).

Having a hyperbolic structure, however, implies that their fundamental groups are highly non--trivial, and this leaves only a narrow escape for hyperbolic $QHS$ to exist. For example, there are no hyperbolic QHS in dimension $2$. The first hyperbolic $QHS$ in dimension $3$ was constructed by Seifert and Weber \cite{SW}. A $QHS$ produced by $\mathbb{Z}^3_2$--colouring of the right--angled hyperbolic dodecahedron can be found in the work of Garrison and Scott \cite{GS}. There is still no known example of a hyperbolic $QHS$ in dimensions $\geq 4$. Moreover, it is known that even such a large class as arithmetic hyperbolic manifolds cannot produce a QHS of even dimension $n > 4$ \cite{emery-qhs}.

Recently, Reid \cite{Reid-lecture} posed the question on whether there exists an arithmetic hyperbolic $QHS$ in dimension $n\geq 3$ that bounds geometrically. We can answer it in the affirmative for $3$--dimensional QHS.

\begin{thm}\label{theorem:qhs-bounds}
There is an arithmetic hyperbolic rational homology $3$--sphere that bounds geometrically.
\end{thm}

It appears that we cannot use colourings
to produce hyperbolic rational homology spheres in higher dimensions. Indeed, compact right--angled polytopes exist in $\mathbb{H}^n$ only for $n \leq 4$ \cite{PV}. The only compact $4$--dimensional right--angled polytopes known so far appear to be the $120$--cell and the associated ``garlands'' produced by ``gluing'' several copies of the $120$--cell along isometric facets. However,
none of such polytopes can produce a manifold with Euler characteristic $2$ via colouring due to the fact that the orbifold Euler characteristic of the right-angled $120$-cell is $\frac{17}{2}$, and that the orbifold Euler characteristic is multiplicative under covers.

We might be able, nonetheless, to use colourings of right-angled $n$-cubes to produce Euclidean rational homology spheres, which exist only in odd dimension. In dimension $3$, there is one colouring up to equivalence that produces the Hantzsche--Wendt manifold \cite[p.~8]{FKS}. In higher dimensions, Proposition \ref{prop:Euclidean QHS} gives a combinatiorial condition to determine whether a colouring of an $n$-cube is a rational homology sphere. In even dimension, rational homology spheres have Euler characteristic $2$ and cannot be Euclidean, since the latter implies Euler characteristic $0$ via the Gauss--Bonnet formula.

As for spherical rational homology spheres, the canonical colouring of the right-angled $n$-simplex that associates the $i$-th standard basis vector to its $i$-th facet, $1 \leq i \leq n+1$, produces the $n$-sphere in any dimension $n\geq 1$.

\subsection*{Outline of the paper}

In Section~\ref{sec:preliminaries} we provide all the necessary definition and basic facts about hyperbolic manifolds obtained via colourings of right--angled polyhedra, including results about their cohomology and coloured isometries. In Section~\ref{sec:extensions} we introduce the concept of colouring extensions and prove some general results related to it. In Section~\ref{sec:3-qhs} we provide an easy algorithmic criterion for a coloured compact right--angled hyperbolic $3$--polytope to produce a QHS. In Section~\ref{sec:fpf-isometries} we show how to promote geodesical embeddings to geometrical boundaries, and prove Theorem~\ref{theorem:qhs-bounds}.

\section{Preliminaries}\label{sec:preliminaries}

A finite-volume polytope $\mathcal{P} \subset \mathbb{X}^n$ (for $\mathbb{X}^n = \mathbb{S}^n, \mathbb{E}^n, \mathbb{H}^n$ being spherical, Euclidean and hyperbolic $n$-dimensional space, respectively, cf. \cite[Chapters 1--3]{Ratcliffe}) is called {\itshape right-angled} if any two codimension $1$ faces (or facets, for short) are either intersecting at a right angle or disjoint. It is known that compact hyperbolic right-angled polytopes cannot exist if $n > 4$ \cite{PV}. The only compact right-angled spherical and Euclidean polytopes are the $n$-simplex and the $n$-parallelotope, respectively. A sufficient condition for an abstract $3$-polytope to be realizable as right-angled hyperbolic one is given in \cite[Theorem 2.4]{Vesnin}. There is no such classification for right-angled $n$-polytopes with $n\geq 4$.

\subsection{Colourings of right-angled polytopes}
One of the important properties of hyperbolic right-angled polytopes is that their so-called colourings provide a rich class of hyperbolic manifolds. By inspecting the combinatorics of a colouring, one may obtain important topological and geometric information about the associated manifold.

\begin{defn}
Let $\mathcal{S}$ be an $n$-dimensional simplex with the set of vertices $\mathcal{V}=\{v_1,\dots,v_{n+1}\}$ and $W$ an $\mathbb{Z}_2$-vector space. A map $\lambda: \mathcal{V} \rightarrow W$ is called {\itshape a colouring} of $\mathcal{S}$. Such a colouring $\lambda$ of $\mathcal{S}$ is {\itshape proper} if the vectors $\lambda(v_i), \ i=1,\dots, n+1$ are linearly independent.
\end{defn}

\begin{defn}
Let $K$ be a simplicial complex with the set of vertices $\mathcal{V}$. Then {\itshape a colouring} of $K$ is a map $\lambda: \mathcal{V} \rightarrow W$. A colouring $\lambda$ of $K$ is {\itshape proper} if $\lambda$ is proper on each simplex of $K$.
\end{defn}

Notice that if $\mathcal{P} \subset \mathbb{X}^n$ is a compact right-angled polytope then $\mathcal{P}$ is necessarily simple and the boundary complex $K_\mathcal{P}$ of its dual $\mathcal{P}^*$ is a simplicial complex. Below we shall provide a more general definition that works also for the case of non-compact polytopes of finite volume.

\begin{defn}
Let $\mathcal{P} \subset \mathbb{X}^n$ be a polytope with the set of facets $\mathcal{F}$ and $K_\mathcal{P}$ be the maximal simplicial subcomplex of the boundary of $\mathcal{P}^*$. A \textit{colouring} of $\mathcal{P}$ is a map $\lambda: \mathcal{F} \rightarrow W$, where $W$ an $\mathbb{Z}_2$-vector space. This map naturally defines a colouring of $K_\mathcal{P}$. Then $\lambda$ is called \textit{proper} if the induced colouring on $K_\mathcal{P}$ is proper.
\end{defn}

If the polytope $\mathcal{P}$ or the vector space $W$ are clear from the context, then we will omit them and simply refer to $\lambda$ as a colouring. The \textit{rank} of $\lambda$ is the $\mathbb{Z}_2$-dimension of $\mathrm{im}\, \lambda$. We will always assume that colourings are surjective, in the sense that the image of the map $\lambda$ is a generating set of vectors for $W$.

A colouring of a right-angled $n$-polytope $\mathcal{P}$ naturally defines a homomorphism, which we still denote by $\lambda$ without much ambiguity, from the associated right-angled Coxeter group~$\Gamma(\mathcal{P})$, that is generated by reflections in all the facets of $\mathcal{P}$, into $W$ with its natural group structure. Being a Coxeter polytope, $\mathcal{P}$ has a natural orbifold structure as the quotient $\mathbb{X}^n /_{\Gamma(\mathcal{P)}}$.

\begin{prop}[\cite{DJ91}, Proposition 1.7]\label{DJ}
If the colouring $\lambda$ is proper, then $\ker \lambda < \Gamma(\mathcal{P})$ is torsion-free, and $\mathcal{M}_\lambda = \mathbb{X}^n /_{\ker \lambda}$ is a manifold without boundary. Moreover, if $\mathcal{P}$ is compact, $\mathcal{M}_\lambda$ is closed.
\end{prop}

If the dimension of the vector space $W$ is minimal, i.e. equal to the maximum number of vertices in the simplices of $\mathcal{P}^*$, $\mathcal{M}_\lambda$ is called \textit{a small cover} of $\mathcal{P}$. This is equivalent to $\text{rank} \, \lambda = n$.

\begin{rem}\label{rem:manifold cover tesselation}
If $\lambda:\Gamma \to \mathbb{Z}_2 ^m$ is surjective, $M_\lambda$ is homeomorphic to the topological manifold $(\mathcal{P} \times \mathbb{Z}_2 ^m)/_{\sim}$, where
\begin{equation}\label{colouring 2}
    (p,g) \sim (q,h) \Leftrightarrow \left\{
        \begin{array}{ll}
            p=q \text{ and } g=h & \text{if } p\in \text{int}(\mathcal{P}) \\
           p=q \text{ and } g - h \in W_f & \text{if } p \in \partial \mathcal{P},
        \end{array}
    \right.
\end{equation}
with $f= F_{i_1} \cap \ldots \cap F_{i_l}$ being the unique face that contains $p$ as its interior point and $W_f = \lambda(\mathrm{Stab}_\Gamma(f))$ is the subspace of $W = \mathbb{Z}_2 ^k$ generated by $\lambda(F_{i_1})$, \ldots, $\lambda(F_{i_l})$.

In other words, this means that $(\mathcal{P} \times \mathbb{Z}_2 ^k)/_{\sim}$ can be obtained from $\mathcal{P} \times \mathbb{Z}_2 ^k$ by identifying distinct copies $F\times \{g\}$ and $F\times \{h\}$ through the reflection in $F \in \mathcal{F}$ (which acts on the orbifold $\mathcal{P}$ as the identity) whenever $g-h =\lambda(F)$. Then it is clear that $\mathcal{M}_\lambda$ can be tessellated by $2^k$ copies of $\mathcal{P}$.
\end{rem}

\begin{defn}
Let $\mathrm{Sym}(\mathcal{P})$ be the group of symmetries of a polytope $\mathcal{P}\subset \mathbb{X}^n$, which acts on the set of facets $\mathcal{F}$ by permutations. Two $W$-colourings $\lambda,\mu:\mathcal{F}\to W$ of $\mathcal{P}$ are called \textit{equivalent in the sense of Davis and Januszkiewicz} or, simply, $DJ$-\textit{equivalent}, if there exists a combinatorial symmetry $s \in \mathrm{Sym}(\mathcal{P})$ and an invertible linear transformation $m \in \mathrm{GL}(W)$ such that $\lambda = m \circ \mu \circ s$.
\end{defn}

It is easy to see that $DJ$-equivalent proper colourings of a polytope $\mathcal{P} \subset \mathbb{X}^n$ define isometric manifolds. The converse is also known to be true for orientable manifold covers of the $3$-cube \cite[Proposition 3.2]{FKS} and orientable small covers of compact, hyperbolic $3$-polytopes \cite[Theorem 3.13]{Vesnin}. Therefore, unless explicitly said, we shall always consider colourings up to equivalence.

\begin{defn}
We say that a $\mathbb{Z}_2^k$-colouring $\lambda$ is \textit{orientable} if the orbifold $M_\lambda$ is orientable. Here, $\lambda$ is not necessarily proper.
\end{defn}

Equivalence gives us the following criterion for orientability.

\begin{prop}[\cite{KMT}, Lemma 2.4]\label{orientability}
The orbifold $M_\lambda$ is orientable if and only if $\lambda$ is equivalent to a colouring that assigns to each facet a colour in $W \cong \mathbb{Z}^k_2$ with an odd number of entries $1$.
\end{prop}

\subsection{Computing the homology of colourings.} Given a right-angled polytope $\mathcal{P} \subset \mathbb{X}^n$ with a $\mathbb{Z}^k_2$-colouring $\lambda$, let us enumerate the facets $\mathcal{F}$ of $\mathcal{P}$ in some order. Then we can assume that $\mathcal{F} = \{ 1, 2, \ldots, m \}$. Let $\Lambda$ be \textit{the defining matrix} of $\lambda$ that consists of the column vectors $\lambda(1), \ldots, \lambda(m)$ exactly in this order. Hence $\Lambda$ is a matrix with $k$ rows and $m$ columns. More precisely, $\Lambda$ represents the abelianization of $\lambda$, i.e. the former is a map such that $\Lambda \circ \mathrm{ab} = \lambda$, where $\mathrm{ab}:\Gamma \to \mathbb{Z}_2 ^m$ is the abelianization map that takes $r_i$, the reflection of the facet $i$, to $e_i$.

Let $\mathrm{Row}(\Lambda)$ denote the row space of $\Lambda$, while for a vector $\omega \in \mathrm{Row}(\Lambda)$ let $K_\omega$ be the simplicial subcomplex of the complex $K=K_\mathcal{P}$ spanned by the vertices $i$, also labelled by the elements of $\{1, 2, \ldots, m\}$, such that the $i$-th entry of $\omega$ equals $1$.

Then the rational cohomology of $\mathcal{M}_{\lambda}$ can be computed via the following formula, c.f. \cite[Theorem 1.1]{CP2}.

\begin{equation}\label{eq:cohomology}
H^p(\mathcal{M}_{\lambda},\mathbb{Q})\cong \underset{\omega \in \mathrm{Row}(\Lambda)}{\bigoplus}\widetilde{H}^{p-1}(K_{\omega},\mathbb{Q}).
\end{equation}

Moreover, the cup product structure is given by the maps \cite[Main Theorem]{CP2}:

\begin{equation}\label{eq:cup products}
\widetilde{H}^{p-1}(K_{\omega_1},\mathbb{Q}) \otimes \widetilde{H}^{q-1}(K_{\omega_2},\mathbb{Q}) \mapsto \widetilde{H}^{p+q-1}(K_{\omega_1 + \omega_2},\mathbb{Q}).
\end{equation}

One practical application of Equation \ref{eq:cohomology} is the computation of Betti numbers of colourings of Euclidean $n$-cubes, which turns out to be very simple.

\begin{cor}[\cite{Ferrari}, Proposition 5.1.11]\label{cor:Ferrari}
Let $\mathcal{C}$ be an $n$-cube with opposite facets in pairs labelled with the numbers $\{2i-1,2i\}$, for each $i \in [n]$, and $\lambda$ be any colouring of $\mathcal{C}$. Let $T_j\subset \mathbb{Z}_2^{2n}$, $0\le j \le n$, be the sets such that
\begin{align*}
    T_1 =&\{e_1+e_2, \ldots, e_{2i-1}+e_{2i}, \ldots, e_{2n-1}+e_{2n}\} \\
    T_j =&\big\{x_1+\ldots+x_j \,\big|\, \{x_1, \ldots, x_j\} \subset T_1\big\}.
\end{align*}
For any $j \in \{1, \ldots, n\}$, we have the following:
$$\beta_j ^\mathbb{Q} (\mathcal{M}_\lambda)=\big|\mathrm{Row} (\Lambda) \cap T_j\big|. $$
\end{cor}

We conclude this section by proving the following useful proposition.

\begin{cor}\label{prop:orientability_criterion}
Let $\mathcal{P} \subset \mathbb{X}^n$ be a right-angled polytope with a proper colouring $\lambda$. Then the manifold $\mathcal{M}_{\lambda}$ is orientable if and only if the vector $\varepsilon=(1,\dots,1)$ belongs to $\mathrm{Row}(\Lambda)$.
\end{cor}

\begin{proof}
By Proposition \ref{orientability}, if $\lambda$ is orientable then the sum of all lines of $\Lambda$ equals exactly the vector $\varepsilon$.

Conversely, if $\varepsilon \in \mathrm{Row}(\Lambda)$, then $K_{\varepsilon}=K\sim \mathbb{S}^{n-1}$ and $\widetilde{H}^{n-1}(K_{\varepsilon},\mathbb{Q})\cong \mathbb{Q}$ then we immediately have $H^n(\mathcal{M}_{\lambda},\mathbb{Q})\cong \mathbb{Q}$ by Equation \ref{eq:cohomology}. Since $\mathcal{M}_\lambda$ is a manifold without boundary, then $\mathcal{M}_\lambda$ is orientable.
\end{proof}

\section{Colouring Extensions}\label{sec:extensions}

\begin{defn}
Let $\lambda:\mathcal{F}\to \mathbb{Z}_2 ^k$ be any colouring. A colouring $\mu:\mathcal{F}\to \mathbb{Z}_2 ^{k+1}$ is called \textit{an extension of} $\lambda$ if there is a linear projection $p:\mathbb{Z}_2 ^{k+1}\to \mathbb{Z}_2 ^k$
such that $\lambda=p\circ\mu$.
\end{defn}

\begin{prop}\label{prop:double-cover colouring}
Let $\lambda:\mathcal{F}\to \mathbb{Z}_2 ^k$ be any colouring and $\mu:\mathcal{F}\to \mathbb{Z}_2 ^{k+1}$ its extension. Then $\mathcal{M}_\mu$ double-covers $\mathcal{M}_\lambda$. Moreover, if $\lambda$ is proper, so is $\mu$.
\end{prop}

\begin{proof}
Let $\Gamma=\Gamma(\mathcal{P})$ be the reflection group associated with $\mathcal{P}$. Let $\lambda:\Gamma \to \mathbb{Z}_2^k$ and $\mu:\Gamma \to \mathbb{Z}_2^{k+1}$ be the homomorphisms induced by $\lambda$ and $\mu$, respectively. By definition, we have that $\lambda = p \circ \mu$, and it follows that $\mathrm{ker} \, \lambda=\mathrm{ker} \, (p \circ \mu)=\mu^{-1}(\mathrm{ker}\, p)$. Moreover, $\mathrm{Im}\,p\cong \mathbb{Z}_2 ^k$ and $|\mathrm{ker} \, p|=[\mathbb{Z}_2 ^{k+1}:\mathrm{Im}\,p]=2$. Thus $\mathrm{ker} \, p=\{0,v_0\}$ for some $v_0\in \mathbb{Z}_2^{k+1}$, $v_0 \neq 0$.

Since $\mu$ is surjective, there exists $u_0\in \mu^{-1}(v_0)\neq \emptyset$. Since $\mu$ is a homomorphism, $\mu^{-1}(v_0)=u_0+ \mathrm{ker}\, \mu $. Then $\mathrm{ker} \, \lambda = \mathrm{ker} \, \mu \sqcup (g_0+\mathrm{ker}\,\mu)$, and thus $\mathrm{ker}\,\mu \triangleleft_{2} \mathrm{ker}\, \lambda$. Hence $\mathcal{M}_\mu$ is a double cover of $\mathcal{M}_\lambda$.

Finally, assume that $\{\lambda(F_1), \ldots, \lambda(F_s)\} \subset \mathbb{Z}_2 ^k$ is a set of linearly independent colours. By using the fact that $\lambda = p \circ \mu$, we easily obtain that  $\mu(F_1), \ldots, \mu(F_s)$ are linearly independent. Hence, if $\lambda$ is proper then $\mu$ is proper too.
\end{proof}

One direct application of Equation \eqref{eq:cohomology} to extensions of colourings is the following.

\begin{prop}\label{prop:double-cover properties}
Let $\lambda:\Gamma \to \mathbb{Z}_2 ^k$ be a colouring and $\mu$ its extension. Let also $\Lambda$ and $\mathrm{M}$ be their respective defining matrices. Then, up to equivalence, $\mathrm{M}$ is the matrix obtained from $\Lambda$ by adding an extra row vector $v\in \mathbb{Z}_2 ^m =\mathrm{ab}(\Gamma)$, such that $v\notin \mathrm{Row}(\Lambda)$. Moreover, if $\lambda$ is orientable, so is $\mu$. Finally, for all $p\ge 0$,
\begin{equation*}
    H^p(\mathcal{M}_\mu,\mathbb{Q})=H^p(\mathcal{M}_\lambda,\mathbb{Q})\oplus \underset{\omega \in \mathrm{Row}(\Lambda)}{\bigoplus}\widetilde{H}^{p-1}(K_{\omega+v},\mathbb{Q}).
\end{equation*}
\end{prop}

\begin{proof}
Up to equivalence, the projection $p:\mathbb{Z}_2 ^{k+1} \to \mathbb{Z}_2 ^k$ is just the canonical projection onto the first $k$ coordinates, given that, otherwise, we can just pre- and post-compose it with a suitable maps in $GL_{k+1}(\mathbb{Z}_2)$ and $GL_k(\mathbb{Z}_2)$, respectively. Then, since $p\circ \mathrm{M} = \Lambda$, it is clear that $\mathrm{M}$ is the matrix $\Lambda$ with another row $v\in\mathbb{Z}_2^m$ added. Moreover, $\mu$ is surjective if and only if $\mathrm{M}$ is surjective, and the latter holds if and only if $v\notin \mathrm{Row}(\Lambda)$. The colouring extensions can be seen in red in the diagram below:

\vspace{0.25in}

\[
\begin{tikzcd}
\Gamma \arrow[overlay, r, red, "\mu"] \arrow[overlay, d, "ab"] \arrow[overlay, dr, out=90, in=0, looseness=2.5, "\lambda"]
& \mathbb{Z}_2 ^{k+1} \arrow[overlay, d, "p"] \\
\mathbb{Z}_2 ^m \arrow[overlay, r, "\Lambda"] \arrow[overlay, ur, red, crossing over, "M"]
& \mathbb{Z}_2 ^k
\end{tikzcd}
\]

Clearly, $\mathrm{Row}(\mathrm{M})=\mathrm{Row}(\Lambda)\sqcup\big(v+\mathrm{Row}(\Lambda)\big)$. If $\lambda$ is orientable, by Corollary \ref{prop:orientability_criterion}, $\epsilon \in \mathrm{Row}(\Lambda) \subset \mathrm{Row}(\mathrm{M})$, that is, that $\mu$ is orientable. We conclude by applying Equation \eqref{eq:cohomology}.
\end{proof}

In the case of non-orientable colourings, we can define a specific type of extension.

\begin{defn}
Let $\lambda:\mathcal{F} \to \mathbb{Z}_2 ^k$ be a colouring. The \textit{orientable extension} $\delta:\mathcal{F}\to\mathbb{Z}_2^{k+1}$ of $\lambda$ is given by $$\delta(F)=\lambda(F)+\Big(1+\sum_{i=1}^k \lambda(F)_i\Big)e_{k+1}.$$
\end{defn}

\begin{prop}\label{prop:orientable double covers}
Let $\lambda:\mathcal{F} \to \mathbb{Z}_2 ^k$ be a non-orientable colouring and $\delta$ its orientable extension. Then $\mathcal{M}_\delta$ is the orientable double cover of $\mathcal{M}_\lambda$.
\end{prop}

\begin{proof}
Up to equivalence, any basis of colours $\{\lambda(F_1),...,\lambda(F_k)\}$ in $\mathbb{Z}_2 ^k$ can be chosen to be the canonical vectors, and we have that $\delta(F_i)=\lambda(F_i)=e_i$. Then it is enough to take any colour $\lambda(F_0)$ with an even number of entries $1$, which exists since $\lambda$ is non-orientable, and we have that $\delta(F_0)_{k+1} = 1$. Thus $\{\delta(F_0),...,\delta(F_k)\}$ is a basis and $\delta$ is surjective.

Now, let $p:\mathbb{Z}_2 ^{k+1}\to \mathbb{Z}_2 ^k$ be the canonical projection onto the first $k$ coordinates: we have that $\lambda=p\circ \delta$. Then Proposition \ref{prop:double-cover colouring} implies that $\mathcal{M}_\delta$ is a double cover of $\mathcal{M}_\lambda$. Moreover, $\mathcal{M}_\delta$ is orientable by Proposition \ref{orientability}.
\end{proof}

Conversely, there is a criterion to tell whether a given colouring $\mu$ is an extension of some other colouring $\lambda$.

\begin{prop}\label{prop:stabilizer condition}
Let $\mu:\Gamma(\mathcal{P})\to W$ be a colouring, and let $W_p = \mu\big(\mathrm{Stab}_\Gamma(p)\big)$ for any vertex $p$ of $P$. Then $\mu$ is an extension of some proper colouring if and only if $\bigcup_{p} W_p \subsetneq W$.
\end{prop}

\begin{proof}
Assume that there is a projection $p:W\cong\mathbb{Z} _2^k\to\mathbb{Z}_2 ^{k-1}$ such that $p\circ \mu$ is a proper colouring. Then, for any codimension $s$ face $f=F_1\cap...\cap F_s$ of $\mathcal{P}$ we have $(p\circ\mu)(F_1)+...+(p\circ\mu)(F_s)\neq 0$. This means that $\mu(F_1)+...+\mu(F_s)\notin \mathrm{ker}\, p$. As in the proof of Proposition~\ref{prop:double-cover colouring}, we have that $\mathrm{ker}\, p=\{0,v_0\}$ for some $v_0\in W$ and, in particular, $\mu(F_1)+...+\mu(F_s)\neq v_0$ for any face $f=F_1\cap...\cap F_s$. It follows that $v_0\notin W_f$ for any such face $f$ and, in particular, for any vertex $q\in \mathcal{P}$.

Conversely, assume there is a vector $v_0\in W\setminus \bigcup_{q} W_q$. Then $\mu(F_1)+ \ldots +\mu(F_s) \neq v_0$ for any codimension $s$ face $f = F_1\cap \ldots \cap F_s$ of $\mathcal{P}$. Let $W\cong \mathbb{Z}_2 ^k$ and $p:\mathbb{Z}_2 ^k \to \mathbb{Z}_2 ^{k-1}$ be the
projection along $v_0$. Let us then set $\lambda = p\circ \mu$. This is a proper colouring since $\mu(F_1)+ \ldots +\mu(F_s)\neq v_0$ implies that  $\lambda(F_1)+ \ldots +\lambda(F_s)\neq p(v_0) = 0$ for all faces $f = F_1\cap \ldots \cap F_s$. By definition, $\mu$ is an extension of $\lambda$.
\end{proof}

\begin{example}[The Hantzsche--Wendt colouring]
Let $\lambda$ be the colouring of the $3$-cube defined in \cite[p.~8]{FKS} such that $\mathcal{M}_\lambda$ is the Hantzsche--Wendt manifold \cite{HW}. In particular, $\mathrm{rank}\,\lambda = 4$. However, we have that $\bigcup_{p} W_q = W$, and it follows from Proposition \ref{prop:stabilizer condition} that $\lambda$ is not an extension of any colouring.
\end{example}

\section{Rational Homology 3-Spheres}\label{sec:3-qhs}

A manifold $M$ is called a \textit{homology $n$-sphere},or $HS^n$, if $H_i(M, \mathbb{Z}) = H_i(\mathbb{S}^n, \mathbb{Z})$, for all $i = 1, \ldots, n$. Similarly, $M$ is called a \textit{rational homology $n$-sphere}, or $QHS^n$, if $H_i(M, \mathbb{Q}) = H_i(\mathbb{S}^n, \mathbb{Q})$, for all $i = 1, \ldots, n$. Clearly, any $HS$-- or $QHS$--manifold is orientable. Additionally, we say a $CW$-complex is a \textit{(rational) homology point}, or $(Q)HP$, if all its reduced $\mathbb{Z}$-- ($\mathbb{Q}$--) homology groups are trivial.

By applying Equation \ref{eq:cohomology}, we have the following.

\begin{lemma}\label{lemma:subcomplexes are HP}
An orientable $\mathcal{M}_{\lambda}$ is a $QHS^n$ if and only if for all $\omega \in \mathrm{Row}(\Lambda) \setminus \{0, \varepsilon\}$, $K_\omega$ is an $QHP$.
\end{lemma}

\begin{proof}
The only non-trivial cohomology groups of $\mathcal{M}_{\lambda}$ are $H_n(\mathcal{M}_{\lambda},\mathbb{Q})\cong H^0(\mathcal{M}_{\lambda},\mathbb{Q})\cong \widetilde{H}^{-1}(K_0,\mathbb{Q})\cong \mathbb{Q}$ and $H_0(\mathcal{M}_{\lambda},\mathbb{Q})\cong H^n(\mathcal{M}_{\lambda},\mathbb{Q})\cong \widetilde{H}^{n-1}(K_\varepsilon,\mathbb{Q})\cong \mathbb{Q}$. Therefore, every other simplicial subcomplex $K_\omega$ must have trivial reduced homology groups.
\end{proof}

In the case of colourings of $n$-cubes, by applying Corollary \ref{cor:Ferrari}, we have the following.

\begin{prop}\label{prop:Euclidean QHS}
Let $\mathcal{C}$ be an $n$-cube with its sides labelled as in Corollary \ref{cor:Ferrari}, and $T_i$ be its corresponding $T$-sets. Let $\mathcal{T}=\bigcup_{i<n} T_i$. Then we have that $\mathcal{M}_\lambda$ is a $QHS$ if and only if $\mathrm{Row}\Lambda \cap \mathcal{T}=\emptyset$.
\end{prop}

By applying Equation \ref{eq:cup products}, we get a useful consequence.

\begin{lemma}\label{lemma:HP condition}
Let $\mathcal{M}_{\lambda}$ be an orientable colouring and $\omega \in \mathrm{Row}(\Lambda)\setminus\{0,\epsilon\}$. Then $K_\omega$ is an $QHP$ if and only if $K_{\epsilon-\omega}$ is an $QHP$.
\end{lemma}

\begin{proof}
Assume that $K_\omega$ is not an $QHP$. Then $\tilde{H}^*(K_\omega,\mathbb{Q})$ has non-trivial $0$-- or $1$--cohomology. First, let $0\neq \alpha \in \widetilde{H}^0(K_{\omega},\mathbb{Q})$. By Equation \eqref{eq:cohomology}, $\alpha \in H^1(\mathcal{M}_{\lambda},\mathbb{Q})$. By \cite[Corollary 3.39]{Hatcher}, there exists $\beta \in H^2(\mathcal{M}_{\lambda},\mathbb{Q})$ such that $\alpha\smile \beta$ is the generator of $H^3(\mathcal{M}_{\lambda},\mathbb{Q})$. Then, by Equation \eqref{eq:cohomology}, $\alpha \smile \beta$ is the generator of $\widetilde{H}^2(K_\epsilon, \mathbb{Q})$, since $K_\epsilon$ is homotopically $\mathbb{S}^2$. Finally, by Equations \eqref{eq:cohomology} and \eqref{eq:cup products}, we obtain that $0\neq \beta \in \widetilde{H}^1(K_{\epsilon-\omega},\mathbb{Q})$, since otherwise the product $\alpha \smile \beta$ would not belong to $\widetilde{H}^2(K_\epsilon, \mathbb{Q})$. The case of $\widetilde{H}^1(K_{\omega},\mathbb{Q})\neq 0$ is completely analogous.
\end{proof}

Thus, we can improve Lemma \ref{lemma:subcomplexes are HP} algorithmically by checking only the connectivity of some graphs.

\begin{cor}\label{cor:algorithm}
An orientable $\mathcal{M}_{\lambda}$ is a $QHS^n$ if and only if for all $\omega \in \mathrm{Row}(\Lambda) \setminus \{0, \varepsilon\}$ the $1$-skeleton of $K_\omega$ is connected.
\end{cor}

\begin{proof}
If one proper subcomplex $K_\omega$ has a non-trivial cycle then, by Lemma \ref{lemma:HP condition}, the complementary complex $K_{\varepsilon-\omega}$ will be disconnected. It suffices therefore to check if all proper, non-empty subcomplexes $K_\omega$ are connected. Clearly the connectivity of $K_\omega$ depends only on the connectivity of its $1$-skeleton.
\end{proof}

In the case of double covers, the transfer homomorphisms \cite[Section 3.G]{Hatcher} can be used in order to obtain the following statement.

\begin{lemma}\label{lemma:QHS double-covers}
Let $Y$ be a closed manifold that is a double cover of another manifold $X$. If $Y$ is a $QHS$, then $X$ is either a $QHS$ or homologically trivial.
\end{lemma}

\begin{proof}
Let $\varphi$ be the involution acting on $Y$ such that $X\cong \faktor{Y}{G}$, with $G=\langle \varphi \rangle\cong \mathbb{Z}_2$. By \cite[Section 3.G]{Hatcher}, we have that $H^*(X,R)\cong H^*(Y,R)^G$ for any ring $R\ni |G|^{-1}$, where $H^*(Y,R)^G$ is the subalgebra of the algebra $H^*(Y,R)$ fixed by the induced action of $G$.

Then, we take $R=\mathbb{Q}\ni \frac{1}{2}$. If $Y$ is a $QHS$, we have that all its rational cohomology classes are trivial, except for $H^0(Y,\mathbb{Q})\cong H^n(Y,\mathbb{Q})\cong \mathbb{Q}$, where $n$ is the dimension of $Y$. Since $H^*(X,\mathbb{Q})$ is isomorphic to a
subalgebra of $H^*(Y,\mathbb{Q})$, the non-trivial cohomology classes of the former are at most those of the latter. Moreover, $H^0(X,\mathbb{Q})\cong\mathbb{Q}$, since $X$ is connected. If $X$ is orientable then $H^n(X,\mathbb{Q})\cong\mathbb{Q}$, and it follows that $X$ is a $QHS$. If $X$ is non-orientable then $H^n(X,\mathbb{Q})=0$, and it follows that $X$ is homologically trivial.
\end{proof}

\begin{rem}
The action of $G$ on the algebra can be seen directly by the action of $\varphi_*$ on the homology classes. Since $\varphi$ takes the connected $Y$ to its only connected component, $\varphi_*$ fixes its $0$-homology class. The action of $\varphi_*$ on the fundamental class $[Y]$, instead, is multiplication either by $+1$ or by $-1$, depending on whether $\varphi$ preserves or changes the orientation. Given that $\varphi^* (\alpha)=\alpha\circ\varphi_*$ for any cohomology element $\alpha$, we conclude that the action of $\varphi^*$ on the ring of cohomology is $\varphi^*(1+[Y]^*)=1\pm [Y]^*$, where the sign depends on whether $\varphi$ preserves orientation. If $\varphi$ is orientation-preserving then $X$ is orientable and, indeed, the whole ring is fixed under the action of $G$.
\end{rem}

Thus we can use the following algorithm in order to determine whether an extension of a colouring is a $QHS$.

\begin{lemma}\label{lemma:QHS extension algorithm}
Let $\lambda$ be a proper colouring such that $\mathcal{M}_\lambda$ is a $QHS^3$. Let $\mu$ be any extension of $\lambda$, obtained by adding a row vector $v$ to $\Lambda$. Then $\mathcal{M}_\mu$ is a $QHS^3$ if and only if for every pair $\{\omega,\epsilon-\omega\} \subset \mathrm{Row}(\Lambda)$, we have that $K_{\omega+v}$ is connected and has only trivial homology $1$--cycles.
\end{lemma}

\begin{proof}
By Proposition \ref{prop:double-cover properties}, we have that $\mathcal{M}_\mu$ is a $QHS$ if and only if $K_{\omega+v}$ is homologically trivial for every $\omega \in \mathrm{Row}(\Lambda)$. By Lemma \ref{lemma:HP condition}, $K_{\omega+v}$ is homologically trivial if and only if $K_{\epsilon-(\omega+v)}$ is so. Since $\epsilon-(\omega+v)=(\epsilon-\omega)+v$ and, by Proposition~\ref{prop:orientability_criterion}, $\epsilon \in \mathrm{Row}(\Lambda)$, we have that also $\epsilon-\omega \in \mathrm{Row}(\Lambda)$. Therefore, it is enough to check whether $K_{\omega+v}$ is homologically trivial for each pair $\{\omega,\epsilon-\omega\} \subset \mathrm{Row}(\Lambda)$. Since $K$ is homeomorphic to $\mathbb{S}^2$ and $K_{\omega + v}$ is a proper subcomplex of $K$, then  $K_{\omega + v}$ is homologically trivial if and only if it is connected and has only trivial homology $1$--cycles.
\end{proof}

\section{Geodesic Embeddings and Geometric Boundaries}\label{sec:fpf-isometries}

First, we describe a way of promoting geodesic embeddings to geometric boundaries.

\begin{lemma}\label{lemma-embed-bound}
Let $M$ be an orientable hyperbolic $n$-manifold that has a fixed point free involution $\varphi \in \mathrm{Isom}(M)$. If $M$ embeds geodesically then it also bounds geometrically.
\end{lemma}

\begin{proof}
Let $M$ embed into an orientable manifold $N'$ as a totally geodesic submanifold of codimension $1$. Let us consider $N$ obtained from $N'$ by cutting it along $M$ and taking a connected component. Then either $\partial N = M$ and we are done, or $\partial N = M \sqcup M$, and we can quotient out one copy of $M$ in $\partial N$ by self-identifying it via $\varphi$. Given that $\varphi$ is a fixed point free involution, the resulting metric space $N_\varphi$ will be a hyperbolic manifold with a single boundary component isometric to $M$. Moreover, $N_\varphi$ is orientable or not depending on whether $\varphi$ is orientation-reversing or not.
\end{proof}

\begin{prop}\label{prop:dodecahedron colourings that bound}
Let $\lambda:\Gamma(\mathcal{D})\to W$ be a proper colouring of the right-angled dodecahedron. If $\bigcup_q W_q \subsetneq W$, then $M_\lambda$ bounds geometrically. Equivalently, any extension of a proper colouring of $\mathcal{D}$ bounds geometrically.
\end{prop}

\begin{proof}
By \cite[Theorem 2]{Martelli 2}, $\mathcal{M}_\lambda$ embeds (c.f. also \cite{KRS}). If $\bigcup_q W_q \subsetneq W$ then, by Proposition \ref{prop:stabilizer condition}, $\lambda$ is an extension of some colouring $\mu$ and, by Proposition~\ref{prop:double-cover colouring}, we have that $\mathcal{M}_\lambda$ double-covers $\mathcal{M}_\mu$. Therefore, there exists a fixed point free involution $\varphi \in \mathrm{Isom}(\mathcal{M}_\lambda)$ such that  $\faktor{\mathcal{M}_\lambda}{\langle \varphi \rangle}\cong \mathcal{M}_\mu$. Then  $\mathcal{M}_\lambda$ bounds geometrically by Lemma \ref{lemma-embed-bound}.
\end{proof}

\begin{thm}\label{thm:arithmetic-QHS-that-bounds}
There is an arithmetic hyperbolic $QHS^3$ that bounds geometrically.
\end{thm}

\begin{proof}
Take the only orientable small cover $\lambda$ of $\mathcal{D}$ given in \cite[p. 6]{GS}. Thus
\begin{equation*}
\Lambda=\begin{pmatrix}
1 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 1 & 1 & 0 & 0 \\
0 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 1 \\
0 & 0 & 1 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 0 \\
\end{pmatrix},
\end{equation*}
where the labeling of the faces of $\mathcal{D}$ is given in Figure \ref{im:dodecahedron}. By Equation \eqref{eq:cohomology}, $\mathcal{M}_\lambda$ is a $QHS$. If we find an extension $\mu$ of $\lambda$ such that $\mathcal{M}_\mu$ is a $QHS$, then we are done by Proposition \ref{prop:dodecahedron colourings that bound}.

\begin{figure}[h]
    \centering
    \includegraphics[scale=0.42]{dodecahedron_extension.pdf}
    \caption{The dodecahedron used in the proof of Theorem~\ref{thm:arithmetic-QHS-that-bounds} with its face labelling. The red, green, blue and yellow subcomplexes are $K_{13}$, $K_{14}$, $K_{34}$ and $K_v$, respectively.}
    \label{im:dodecahedron}
\end{figure}

By Lemma \ref{lemma:QHS extension algorithm}, it is enough to find a row vector $v\in \mathbb{Z}_2 ^{12}$ such that the complexes $K_{\omega + v}$ are connected and without non-trivial cycles for $\omega \in \{0,(1,0,0)^T \Lambda,(1,0,1)^T \Lambda,(0,0,1)^T \Lambda\}$.

Recall that $\mathrm{Row}(\Lambda)=\{x^T \Lambda\mid x \in \mathbb{Z}_2 ^3\}$ and $\epsilon=(1,1,1)^T\Lambda$. Let $\omega= x^T \Lambda$. Then for a face $F^*$ of $\mathcal{D}$ we have that $F^* \in K_{\omega}$ if and only if $x \cdot \lambda(F) = 1$. Hence the complexes $K_{ij}=K_{(e_i+e_j)^T\Lambda}$ for $\{i,j\}\in\{1,2,3\}$ are precisely the subcomplexes of $K$ with vertices coloured by $e_i$ and $e_j$, while the subcomplexes $K_{i4}=K_{(e_i)^T\Lambda}$ are the subcomplexes coloured by $e_i$ and $e_1+e_2+e_3$.

Due to the constraint that $K_v$ be homologically trivial, the choice of vertices $(F_i)^*$ in $K$ such that $\mu(F_i)_4 = 1$ (or, equivalently, the choice of $v_i \neq 0$) should define a homologically trivial subcomplex. By choosing $K_v$ as the simplex $\{3,7,9\}$ around which the three complexes $K_{13}$, $K_{14}$, $K_{13}$ are ``wrapped'', we have precisely that all four subcomplexes $K_{v+\omega}$ are homologically trivial as shown in Figure~\ref{im:dodecahedron}.

Explicitly, the colouring $\mu$ with defining matrix
\begin{equation*}
\mathrm{M} = \begin{pmatrix}
1 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 1 & 1 & 0 & 0 \\
0 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 0 & 1 \\
0 & 0 & 1 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 0 \\
0 & 0 & 1 & 0 & 0 & 0 & 1 & 0 & 1 & 0 & 0 & 0 \\
\end{pmatrix}
\end{equation*}
is an extension of $\Lambda$ by Proposition \ref{prop:double-cover properties}, and $\mathcal{M}_\mu$ is a $QHS$ by Equation \eqref{eq:cohomology}.
Hence, by Proposition \ref{prop:dodecahedron colourings that bound}, $\mathcal{M}_\mu$ bounds geometrically. Finally, since $\mathcal{D}$ is arithmetic \cite[Lemma 3.8]{Vesnin}, it follows that $\mathcal{M}_\mu$ is also arithmetic.
\end{proof}

\begin{rem}
A computer search among all possible extensions of $\Lambda$ returned that there are, up to $DJ$--equivalence, $7$ extensions which are $QHS^3$. All of them have trivial coloured symmetry group \cite[Section 2.3]{KS?}. However, the number of equivalence classes up to isometry might be smaller, given that the exact equivalence between isometry classes and colouring classes of compact hyperbolic $3$-polytopes holds only for small covers \cite[Theorem 3.13]{Vesnin}.
\end{rem}

\vspace{-0.1in}

redpajama_set_name: RedPajamaArXiv


下載類別: 下載名稱: 適用環境: 版本名稱: 檔案大小 : 驅動程式 : MX860 series MP Driver Ver. Android is a mobile operating system developed by is based on a modified version of the Linux kernel Wear OS for wrist watches, other open source software, is designed primarily for touchscreen mobile devices such as smartphones , Google has further developed Android TV for televisions, addition, Android Auto for cars each with a specialized user interface.
Canon mx328 scanner driver for windows 7. Look up Canon canonical in Wiktionary, canon the free dictionary. 02( MX868) Windows 7/ Vista/ XP/ : version : 1.
Canon PIXMA MX328 driver Downloads for Microsoft Windows XP Vista 7 8 8. 1 10 32- bit and 64- bit, Macintosh and Linux Operating Systems.
Canon PIXMA E300 Setup Wireless, Manual Instructions and Scanner Driver Download For Windows, Linux Mac, The PIXMA E300 Series is an affordable and compact Wi- Fi Printer for easy wireless document printing and unlimited 4x6 photo printing directly from popular smart devices and cloud services. Make copies of your documents anywhere using the Capture and Copy Smartphone.
Canon PIXMA TS3122 Driver Download – PIXMA TS3122 Wi- fi All- in- One Inkjet Colour printer rising coming from Analects are examining out assist you to take care of your residence' s sizeable printing specifications. That also involves an all- in- one structure that supplies examine and replicating other than publishing, featuring you alongside with a single cell respond to.


Puri Green Resources (PGR), established in 2007, Indonesia, now operates all around Indonesia and South East Asia with workshop office in Yogyakarta.
PT. PURI GREEN RESOURCES, based in Indonesia, is a group of professional, highly specialized engineers and earth scientists, who use the most advanced technologies to provide unique technical studies and professional consultancy in the area of Mining & Mineral, Oil Palm Plantation, Green Energy, Surveying and Mapping, with an objective "to lead the field in technological development and quality".


Interesting ikea floor lamps for reading light ideas, contour 1 light arc floor lamp nova metropolitandecor, arc floor lamp ikea dutchgloworg. Retro modern arc floor lamp home lighting design ideas. Floor lamp with shelves houses flooring picture ideas.
Furniture Decorassistant To The Rescue!


text:
Barry Fudge: British Endurance Overview Part 2
Dr Barry Fudge completed his undergraduate degree and his PhD in Physiology from the University of Glasgow, UK. His PhD focused on the environmental factors leading to the success of elite east African runners. During that time he worked with a number of runners in Kenya and Ethiopia, some of whom are World record holders and/or World and Olympic medalists. Following that Barry was a Senior Physiologist at the English Institute of Sport for 5 years providing physiological support to British Athletics. Most notably he was an integral part of double Olympic, World and European champion Mo Farah's support team.
Other Parts in This Series:
Barry Fudge: British Endurance Overview (Part 1)
2017 Indoor International Opportunities - Endurance
Endurance Jobs - deadline Monday 9th Jan
Last Min Endurance Workshop: Sunday 11th September
Spencer Duval and Richard Nerurkar Masterclass

redpajama_set_name: RedPajamaCommonCrawl


text:
For Patients and Family
Join Our Fight
Types of Peripheral Neuropathies
WinSanTor Peripheral Neuropathy Blog
Stories of Neuropathy
Peripheral Neuropathy and Our Drug
Peripheral Neuropathy Drug Pipeline
For Investors & Media
Shareholders Services
Peripheral Neuropathy News & Events
Shareholders Services (Elementor)
Home » Shareholders Services (Elementor)
WinSanTor Inc. is a private, clinical-stage biotechnology company focused on the discovery and development of treatments for peripheral neuropathies, including diabetic peripheral neuropathy, chemo and HIV-induced peripheral neuropathy, and others. WinSanTor is currently studying its lead drug, WST-057, in a Phase 2 clinical trial in Canada for the treatment of human patients with diabetic peripheral neuropathy. Our research has been supported by leading stakeholders in the field, including the Juvenile Diabetes Research Foundation, National Institute of Diabetes and Digestive and Kidney Diseases (at the National Institutes of Health) and the Canadian Institutes of Health Research. We are headquartered in San Diego, California.
Where is WinSanTor's corporate headquarters?
WinSanTor is headquartered at 7220 Trade St., Ste. 370, San Diego, CA 92121
How can I purchase/sale WinSanTor common stock?
Since we are a private company, the only way to purchase stock is to be an accredited investor and to make the investment directly from the company. If you are an accredited investor and are interested, please contact our investors department by contacting (858) 208-0546 or info@winsantor.com.
For more information to see if you are an accredited investor please check: https://www.investor.gov/additional-resources/news-alerts/alerts-bulletins/updated-investor-bulletin-accredited-investors
Who is WinSanTor's legal counsel?
Wilson Sonsini is our legal counsel.
Where can I get the latest corporate news releases?
An archive of WinSanTor's press releases can be viewed at: News & Events
Who do I contact if I have additional questions?
You can submit queries to WinSanTor's investors department by contacting (858) 208-0546 or info@winsantor.com
Investment Portal
E-shares, once purchased, are listed and managed by the company and the investor through Capshare. Use the link below to log in or sign up. If you have any questions, feel free to use the chat icon located on the bottom, right-hand corner of the screen.
ACCESS INVESTMENT PORTAL
Facebook-f Twitter Linkedin Instagram Pinterest Youtube Tiktok
info@winsantor.com
media@winsantor.com
Our Solution to Peripheral Neuropathy
What Are Peripheral Nerves?
Exercising With Peripheral Neuropathy
Foot Care for Diabetic Peripheral Neuropathy
What Is Complex Regional Pain Syndrome (CRPS)?
Copyright WinSanTor, Inc. All Rights Reserved © 2018-2023


Chronic Fatigue Syndrome (CFS) is a condition many people struggle to come to terms with. Since there are no specific diagnostic tests, it remains a largely intangible and misunderstood illness. Many sufferers find it hard to explain their condition to family and friends. Responses 'it's just in your head' are common and make things even harder for CFS patients whose tiredness and mental and physical pain is a real experience. Many doctors are not aware of D-Ribose which is a natural body energizer that can be used to jump start and sustain energy production in CFS & Fibromyalgia.
In this article I am going to present you the exciting findings related to D-Ribose and how it can be used to treat CFS & Fibromyalgia. This article is based on the research work of Dr. Jacob Teitelbaum.
Dr. Jacob Teitelbaum is a clinical expert on chronic fatigue and fibromyalgia (a disorder characterized by widespread musculoskeletal pain accompanied by fatigue, sleep, memory and mood issues). He has dedicated over 30 years of his professional life to studying these conditions. Dr. Teitelbaum believes he now has some scientifically backed answers that can help explain and treat CFS.
As I mentioned earlier, there are no tests for CFS. The diagnosis is usually made after eliminating all other possible causes for fatigue (which is also one of the 13 signs of a thyroid disorder).
Problems sleeping; waking up after a night's sleep and feeling exhausted and unable to get up.
Brain fog and inability to think clearly, concentrate and memorize things.
Headaches, joint and muscle pain, sore throat, tender glands in your armpits and neck.
Symptoms can flare up after a physical or mental activity.
Depression is also a common occurrence, and can be brought on by the unexplained symptoms, fatigue and social rejection. Feeling depressed makes the symptoms even worse, closing the vicious cycle and isolating the person further.
Many doctors and GPs have little knowledge of CFS and might not be up to date with current research efforts. The symptoms are often treated in an isolated way, while the core of the problem remains unaddressed.
In his book, From Fatigue to Fantastic, Jack Teitelbaum looks into some of the eluding questions of CFS. Here is a short summary of his findings.
Most likely, the problem lies in insufficient energy production.
Imagine an athlete who had an intense couple of days of very strenuous training. Before his body is ready for extreme physical activity again, he will need to rest a bit.
In CFS, this much needed recuperation doesn't happen. Cells and tissues perpetually don't get enough energy, so they can't function properly. It is a bit like trying to run a marathon day after day. The body can't do it; it has exhausted its energy reserves and no new fuel is coming in.
Mitochondrial dysfunction lowers the levels of brain neurotransmitters (dopamine, acetylcholine, serotonin), which makes thinking processes harder and causes the dreaded brain fog.
Low energy production and lactic acid accumulation make recovery after exercise harder and result in muscle fatigue.
Mitochondrial dysfunction also influences digestion, immune system function and heart function.
These are just a few examples that show mitochondrial dysfunction might be at the root of it all and needs to be tackled if you want to recover.
How can we improve mitochondrial function and boost energy production?
There are natural treatments that can improve the function of our cellular energy furnaces. D-ribose seems to be the key in energy production and is receiving more and more scientific attention.
D-ribose is a five carbon sugar, naturally found in our bodies. It is unlike any other sugar and works like kindling for our precious internal furnaces. It is the key building block of ATP (adenosine triphosphate), which is the main energy molecule in the body. You need ribose to make ATP and keep the fire going.
In normal circumstances, healthy heart and muscles can make enough ribose to meet their needs. But sometimes tissues can get over-exhausted and the vital production starts legging behind. This can result in persistent pain, fatigue and stiffness that just don't want to go away.
Dr. Jacob Teitelbaum started using this knowledge to help his CFS and fibromyalgia patients. He also performed scientific studies to link ribose, fatigue and energy production.
Dr. Teitelbaum developed a treatment protocol that proved to be efficient. His patients take 5 grams (5000 milligrams) of D-ribose, 3 times a day, for 3 weeks. After that, the dose can be reduced to twice a day. He recommends using the Corvalen form of ribose as it is the least expensive and of highest quality. It's also conveniently packaged with a 5 gm dosing scoop in it.
Ribose is now available over the counter and many health shops stock it.
A study done by Dr. Jacob Teitelbaum and his team included 41 patients with a diagnosis of CFS or fibromyalgia. The patients were given a 280 g container of D-ribose. Each patient was instructed to take one scoop (5 g) of D-ribose 3 times per day mixed with food, water or another beverage until the container was empty.
The patients were assessed pre and post ribose administration. 66% of patients experienced significant improvement while on D-ribose. There was a 45% improvement in energy levels, and 30% improvement in general health and well being. Dr. Teitelbaum points out that usually an improvement of 10% for a single nutrient is seen as excellent, so D-ribose's potential might be truly remarkable.
Other studies that looked into the use of D-ribose were performed, both on animals and humans, and came to a similar conclusion. An exciting case study was published in the journal Pharmacotherapy in 2004 and described a case of a veterinary surgeon who was able to fully recover from fibromyalgia when taking ribose.
These new findings bring some practical solutions for CFS patients and might help them understand their illness better, as well as restore their lives.


text:
Q: Applications of the first isomorphism theorem I would like to know if possible  how to use the first isomorphism theorem to solve the following problems:
(1) Consider the general linear group $GL(n,R)$. Show that the set of all $n\times n$ matrices with determinant $1$ is a normal subgroup of $GL(n,R)$
(2) Show that the groups $(Z⁄nZ,+nZ)$ and $(Z_n,+n)$ are isomorphic.
I know the first isomorphism theorem states that: Let $φ\colon G\to G'$ be a group homomorphism and denote $\ker(φ)$ by $H$. Then $H$ is a normal subgroup of $G$ and the map $f\colon G⁄H\to φ[G]$ given by $f(gH)= φ(g)$ is an isomorphism.

A: Hint:
The  determinant map $\;\det: GL(n,\Bbb R)\to\Bbb R^*\;$ is a group homomorphism ...
Your second question is incomprehensible to me.

A: If for the second one, you mean $(\mathbb Z/n\mathbb Z, +_{n\mathbb Z})$, then consider it as: $$\{0+n\mathbb Z,1+n\mathbb Z,\cdots,(n-1)+n\mathbb Z\}$$ and work with this map: $$\phi: \mathbb Z/n\mathbb Z\to\mathbb Z_n,~~(m+n\mathbb Z)=m,~~~~0\leq m<n$$ Show it is an group isomorphism.

redpajama_set_name: RedPajamaStackExchange


text:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 2025 2026 2027 2028
UG.-1.065, Seminar mit Beamer
02.236 Praktikum
UG.-1.067, Konferenzrunde
UG.-1. 066_single desk (internet)
IMIB Räume - UG.-1.065, Seminar mit Beamer
06 Jul | 07 Jul | 08 Jul | 09 Jul | 10 Jul | 11 Jul | [ 12 Jul ] | 13 Jul | 14 Jul | 15 Jul | 16 Jul | 17 Jul | 18 Jul | 19 Jul


AirPlay has become a popular function of Apple devices, which can help users a lot in transferring files. However, not every one is clear of its features and how does AirPlay work. This guidance will introduce its basic information and its working process in detail. Read on and you will fall in love with this function.
Evernote is one software service based on cloud, which is designed to create, manage and store diverse of media files. It can store all your stuff in the cloud via your own individual account of evernote, such as text files, pictures, videos and etc.
This app is centered on the creating of notebooks and notes, but users can also upload files directly from your devices as well. When you upload a file in Evernote, it will sync up the new file across your entire account. Thus, you can access the file from a different machine. This feature is quite convenient for users to manage files.
Evernote has both the free version and the paid versions. The free version of it allows users to upload 60 MB of new notes a month with limited features. If you pay $69.99 one year for the account, you are allowed to upload 10 GB of new notes every month. As for the $120 per year account, users are able to upload 20 GB of new notes and can enjoy the shared 2 GB notes space.
OneNote is also one note-taking app with great features, which enables users to realize the free-form information gathering and multi-user collaboration. Users are able to enter typed or handwritten notes, audios, file attachments and other kinds of notes. This software can assist users to make your notes more tidy and centralized. You can search your notes in this program and you can also access your notebooks via OneDrive as well. This software is developed by Microsoft, which is accessible as one part of Microsoft Office and Windows 10.
Is OneNote free? Here I would like to tell you that it is free to download and use, and there is no restrictions or crippled features on it. If you really do not want to pay for the note-taking app, OneNote will be your best choice.
The comparison of Evernote Vs OneNote is a hot topic in the note-taking app market. Here I would like to list some aspects to show you the feature difference between them.
Evernote Vs OneNote comparison is very clear by viewing the chart shown above. As you can see, the two apps can support the same platforms and there are some big differences in other aspects.
After you know the answers to the questions of "What is Evernote" and "What is OneNote" and check out the comparison of Evernote Vs OneNote, you can continue to see how to convert Evernote to OneNote if you are fans of both note-taking applications. As for how to import Evernote to OneNote, the detailed step listed below will show you clearly.
1. Download and install the desktop version of Evernote on computer and log into your account.
2. On Evernote, choose one file from the section of "Notebooks" and then click on "File> Export Notes" to hit. Browse your computer to find a location to save the exported notes. In the end, tap on "Save" button to download the notes in the format of ENEX.
3. Go to Microsoft official website to download OneNote Importer and install it on computer with the on-screen instructions.
4. Open OneNote Importer and then click on "Get Started" button. Hit "Choose File" button to choose Evernote files that you have exported in the second step on computer.
5. After that, you need to sign in with the Microsoft account and then click on "Import" button to initiated the importing process.
6. Wait until the import procedure comes to an end. The time depends on how many notes you are importing.
The process to import Evernote to OneNote is not so hard for you to realize and you can refer to the steps shown above to have a try to test whether this method can work well.
iPhone notes are important for many users to arrange work and life. Sometimes, people may also want to check them on Mac more clearly. In the aim of reaching this target, you can resort to Leawo iTransfer for Mac. This tool has many good functions for you to manage files on iOS devices. It can also deal with the transfer issues among iTunes, iDevices and computers with some clicks. As for how to make this aim come true, you can continue to read the following steps for reference.
Insert iPhone into Mac and then run iTransfer for Mac. Your information on iPhone will show in the main interface automatically.
Hit "iPhone icon > LIBRARY > Notes" and you could view all your notes on Mac, then choose the notes you desire to export to your Mac in the right part of the tool.
Check the notes you want to move and then hit "Export" button. In the pop-up panel, you need to choose an output directory to save iPhone notes on Mac computer. Hit "Transfer Now" and then the process to export iPhone notes to Mac folder will begin. Wait for a few seconds and your iPhone notes will be available on Mac.
This process to view iPhone notes on Mac is recommendable for its convenience and high efficiency. You'd better now download and install iTransfer for Mac on computer to use this solution to realize your goal of exporting notes from iPhone to Mac.


text:
Friday Night Swing
Soulful Samba Tuesdays
Sunday Morning Prayers for World Peace
Jenner Coastal Kayak Tour
Hidden Wineries Van Tour
Carneros Wine Country Sip 'n' Cycle Bike Tour
Uptown Oakland Food and Drinks Tour
Local Food Adventures
Mission 18th Street Food Tour
Beyond Napa Valley Wine Tour
All-Star Craft Beer Crawl
Sunset Sail with Beer and Wine
Stand-up Comedy Show
Solo Stand-Up Sundays
Russian River Kayak Tour
Pencil, Charcoal, and Conte Drawing (2Hr)
Thai Cooking
Shooting & Sword Fighting
Shaolin Kung Fu (Sunday)
All Things To Do In San Francisco Explore Cultural & Sightseeing Wine Country
Schedule Description Cancellation Policy
outdoorssightseeingwatersportriver
Kayak the Russian River, cutting through California's Wine Country
Search for elusive and rare wildlife with your knowledgeable guide
Enjoy a riverside picnic lunch to fuel your sense of adventure
Indulge your adventurous side with an unforgettable experience on the waters
# Spots
Sat, Jan 18 10:00am 4.5 hours 0 $169.00
Sun, Jan 19 10:00am 4.5 hours 0 $169.00
Mon, Jan 20 10:00am 4.5 hours 10+ $169.00
Tue, Jan 21 10:00am 4.5 hours 10+ $169.00
Wed, Jan 22 10:00am 4.5 hours 10+ $169.00
Thu, Jan 23 10:00am 4.5 hours 10+ $169.00
Fri, Jan 24 10:00am 4.5 hours 10+ $169.00
Sat, Jan 25 10:00am 4.5 hours 10+ $169.00
Sun, Jan 26 10:00am 4.5 hours 10+ $169.00
Sat, Feb 1 10:00am 4.5 hours 10+ $169.00
Sun, Feb 2 10:00am 4.5 hours 10+ $169.00
Mon, Feb 3 10:00am 4.5 hours 10+ $169.00
Tue, Feb 4 10:00am 4.5 hours 10+ $169.00
Wed, Feb 5 10:00am 4.5 hours 10+ $169.00
Thu, Feb 6 10:00am 4.5 hours 10+ $169.00
Fri, Feb 7 10:00am 4.5 hours 10+ $169.00
Mon, Feb 10 10:00am 4.5 hours 10+ $169.00
Tue, Feb 11 10:00am 4.5 hours 10+ $169.00
Wed, Feb 12 10:00am 4.5 hours 10+ $169.00
Thu, Feb 13 10:00am 4.5 hours 10+ $169.00
Fri, Feb 14 10:00am 4.5 hours 10+ $169.00
Sat, Feb 15 10:00am 4.5 hours 10+ $169.00
Sun, Feb 16 10:00am 4.5 hours 10+ $169.00
Sun, Mar 1 10:00am 4.5 hours 10+ $169.00
Mon, Mar 2 10:00am 4.5 hours 10+ $169.00
Tue, Mar 3 10:00am 4.5 hours 10+ $169.00
Wed, Mar 4 10:00am 4.5 hours 10+ $169.00
Thu, Mar 5 10:00am 4.5 hours 10+ $169.00
Fri, Mar 6 10:00am 4.5 hours 10+ $169.00
Sat, Mar 7 10:00am 4.5 hours 10+ $169.00
Tue, Mar 10 10:00am 4.5 hours 10+ $169.00
Wed, Mar 11 10:00am 4.5 hours 10+ $169.00
Thu, Mar 12 10:00am 4.5 hours 10+ $169.00
Fri, Mar 13 10:00am 4.5 hours 10+ $169.00
Sat, Mar 14 10:00am 4.5 hours 10+ $169.00
Sun, Mar 15 10:00am 4.5 hours 10+ $169.00
Mon, Mar 16 10:00am 4.5 hours 10+ $169.00
Wed, Apr 1 10:00am 4.5 hours 10+ $169.00
Thu, Apr 2 10:00am 4.5 hours 10+ $169.00
Fri, Apr 3 10:00am 4.5 hours 10+ $169.00
Sat, Apr 4 10:00am 4.5 hours 10+ $169.00
More Times
10:00am 10:00am 10:00am 10:00am 10:00am 10:00am 10:00am 10:00am 10:00am 10:00am 10:00am 10:00am 10:00am 10:00am 10:00am 10:00am 10:00am 10:00am 10:00am 10:00am 10:00am 10:00am 10:00am 10:00am 10:00am 10:00am 10:00am 10:00am 10:00am 10:00am 10:00am 10:00am 10:00am 10:00am 10:00am 10:00am 10:00am 10:00am 10:00am 10:00am 10:00am 10:00am 10:00am 10:00am 10:00am 10:00am 10:00am 10:00am 10:00am 10:00am 10:00am 10:00am 10:00am 10:00am 10:00am 10:00am 10:00am 10:00am 10:00am 10:00am 10:00am 10:00am 10:00am 10:00am 10:00am 10:00am 10:00am 10:00am 10:00am 10:00am 10:00am 10:00am 10:00am 10:00am 10:00am 10:00am 10:00am 10:00am Last activity timeSat, Apr 4 at 10:00 am See more time slots
Mon, Jan 20 10:00 amTue, Jan 21 10:00 amWed, Jan 22 10:00 amThu, Jan 23 10:00 amFri, Jan 24 10:00 amSat, Jan 25 10:00 amSun, Jan 26 10:00 amMon, Jan 27 10:00 amTue, Jan 28 10:00 amWed, Jan 29 10:00 amThu, Jan 30 10:00 amFri, Jan 31 10:00 amSat, Feb 1 10:00 amSun, Feb 2 10:00 amMon, Feb 3 10:00 amTue, Feb 4 10:00 amWed, Feb 5 10:00 amThu, Feb 6 10:00 amFri, Feb 7 10:00 amSat, Feb 8 10:00 amSun, Feb 9 10:00 amMon, Feb 10 10:00 amTue, Feb 11 10:00 amWed, Feb 12 10:00 amThu, Feb 13 10:00 amFri, Feb 14 10:00 amSat, Feb 15 10:00 amSun, Feb 16 10:00 amMon, Feb 17 10:00 amTue, Feb 18 10:00 amWed, Feb 19 10:00 amThu, Feb 20 10:00 amFri, Feb 21 10:00 amSat, Feb 22 10:00 amSun, Feb 23 10:00 amMon, Feb 24 10:00 amTue, Feb 25 10:00 amWed, Feb 26 10:00 amThu, Feb 27 10:00 amFri, Feb 28 10:00 amSat, Feb 29 10:00 amSun, Mar 1 10:00 amMon, Mar 2 10:00 amTue, Mar 3 10:00 amWed, Mar 4 10:00 amThu, Mar 5 10:00 amFri, Mar 6 10:00 amSat, Mar 7 10:00 amSun, Mar 8 10:00 amMon, Mar 9 10:00 amTue, Mar 10 10:00 amWed, Mar 11 10:00 amThu, Mar 12 10:00 amFri, Mar 13 10:00 amSat, Mar 14 10:00 amSun, Mar 15 10:00 amMon, Mar 16 10:00 amTue, Mar 17 10:00 amWed, Mar 18 10:00 amThu, Mar 19 10:00 amFri, Mar 20 10:00 amSat, Mar 21 10:00 amSun, Mar 22 10:00 amMon, Mar 23 10:00 amTue, Mar 24 10:00 amWed, Mar 25 10:00 amThu, Mar 26 10:00 amFri, Mar 27 10:00 amSat, Mar 28 10:00 amSun, Mar 29 10:00 amMon, Mar 30 10:00 amTue, Mar 31 10:00 amWed, Apr 1 10:00 amThu, Apr 2 10:00 amFri, Apr 3 10:00 amSat, Apr 4 10:00 am
Last activity timeSat, Apr 4 at 10:00 am See more time slots
Select a time slot first! (212) 858 9559
Check out cute critters and build your biceps at the same time with this outdoor adventure tour!
During a guided half-day experience, you'll kayak Wine Country's scenic Russian River in search of some of the area's more sought-after wildlife. Along the way, you'll enjoy a setting of rolling hills and pastures along either bank, and your guide will point out some of the more interesting flora.
You'll also make a stop at Goat Rock Beach, where you'll enjoy a gourmet lunch that'll make you rethink PB&J picnics. A typical menu might include pesto pasta salad, fresh baked bread, exotic cheese, dessert, and more.
But enough about food. Osprey nests, elusive snow egrets, blue heron, and harbor seals await your discovery, as you paddle to the best spots, including the mouth of the Russian River.
Did that just seal the deal?
Note: Price includes $1 ticketing fee. Includes kayak and life jacket rentals, water, Wine Country gourmet lunch, and professional guides. Guide gratuity not included. Single kayaks available upon request, otherwise kayaks are tandem. Exact meeting location given upon confirmation of booking.
There is a minimum of 2 people to book. Price listed is per person.
Price $169.00 per guest
Duration / Session 4.5 hours
# Sessions 1
Cancellation notice must be provided at least 72 hours in advance in order to receive a full refund minus a $25 per person processing fee.
# Sessions 1 session
Select a time slot to book
Remove from Bucket List
Saved 143 times
Book as a Private Event
Invite Your Friends. Get $10
Why book on Vimbly?
Lowest Price Guarantee We promise the best price - and never charge a mark-up fee.
Safe and Secure Your information is secured by 128-bit encryption.
Satisfaction Guarantee If you attend and have a bad experience, we will refund you. See Vimbly Handshake
10400 CA-1, Jenner CA 95450
Verified Vimbly Provider
Carneros Wine Country Sip 'n' Cycle Bike TourGetaway Adventures
Wine Country Sip 'n' Cycle Bike Tour: CalistogaGetaway Adventures
Napa Valley Hiking TourGetaway Adventures
Hidden Wineries Van TourGetaway Adventures
Napa Valley Pedal 'N PaddleGetaway Adventures
Healdsburg Sip 'N CycleGetaway Adventures
Schedule for Start Date:


Become a Splendid Proposition – in Business and Life!
much more you have to offer at 100%?
Profitable? How Would You Improve your Social Capital?
inspiring others and to maximize ones true value.
Denmark (in Danish), Amsterdam/ Berlin, Singapore and Dubai in English.


The NZXT Phantom 410 Black CA-PH410-B1 has a Clearance for top 240mm dual radiator for water cooling solutions.
The Phantom 410 features screw-less HDD trays, and innovative right mounted HDD rails, a solution for easy hard drive replacement and installation.
headers that directly connect to the motherboard.
The Phantom 410 comes with three pre-installed fans (2x 120mm and 1x 140mm) with support for up to eight total fans and a 240mm dual radiator at the top of the case.
A newly designed 120mm/140mm pivoting internal fan slot allows you to increase cooling on your GPU. A single channel 30W fan controller allows you to easily adjust your airflow.


Sinds i today was looking for mine unreal and ut dvd's and cd's, i did a discovery on a unreal 1 version on a cd.
When i did patch the game when i did install the game i discovered that the unreal verion was version 200.
Mine question is that with what patch i must patch this older unreal version?
I did patch the game with the 78 mb big unreal i, then the error what i did get that i must first patch this unreal version with a older one.
wich version is that and wich unreal version do i have?
Maby its a rare version what i have.
edit problem is solved i did have the Original 200 version unreal 1.
Now what i did was the folowing i did must patch with 224 nand after that the 227i.
I think that everything is ok now so i can play unreal now.
There have been some rare versions of Unreal, so I wonder what you have in practice. Are there any differences in maps like vortex2? What is the filesize/date of that for example.
I mean the patch will work on it most likely just the maps won't get patched and german players already had conflicts wit their gore reduced version etc if they wanted to play online. Hence why some servers skipped Vortex2. But there was also that version of Vortex2 that the votlan map must have been based on which was a slight prerelease version or something.
Leo(T.C.K.) wrote: There have been some rare versions of Unreal, so I wonder what you have in practice. Are there any differences in maps like vortex2? What is the filesize/date of that for example.
There is indeed a vortex 2 map on this version of unreal. its dated 15-05-1998.
The Original unreal who is on the install disk is version 200.
The disk on the front cover is titled '' trio infernale'' containing resident evil ,carmagaddon and unreal 1.
All on sepreated disk so its not a dvd version but 3 seperated cd rom disks into 1 bundle.
uploaded the map for you leo tck.
Look @ the end of the page.Unpack with winrar.
Its a german verion of 3 games into 1 dubble cd case.
Its a early verion of unreal i think?
I didn't know this existed here.
Well that's actually just the standard Unreal map, there are no differences it seems.
It's not even the "censored" version of Vortex2.
What I'm looking for is something slightly before version 200 like the stuff votlan was based on as it still had the mover doors between the bridge and the final area. And unlike ONP or whatever it wasn't just redone, the texturing is same as in the beta version.
Leo(T.C.K.) wrote: Well that's actually just the standard Unreal map, there are no differences it seems.
Sadly it is not what you are looking for but i will take a look at mine unreal and ut collection this night.And will take a peek wich one is more early.
Maby just maby the one you are looking for still excist in mine collection.Stay tuned i will post here what i have.
I still know you are looking for the unreal history of epic games.
rtexturing is same as beta version so its not textured just like zorra's version i think.Walls are almost all grey and white with bubbles on it.
edit 2 i did take alook at other unreal games and i only have ut 2003,ut2004,unreal 1 wich came with the covers earlyer posted.
Unreal anthogie box set ofcourse ut 99 goty edition and unreal tournament 3.
No specials wich i did look for as an early unreal 1.
sadly no other version of unreal 1 i have so mine seeking this evening is over.
sadly i canot help you leo.
And yes i,m scarbelly.nl aka unriel.nl and lactantius.nl in the past.
I just learned alot and cut with the crap.
edited because before papercofee warned me for double post.
rjmno1 wrote: edited because before papercofee warned me for double post.
Oh, so you're that guy that once thought Unreal by Ubisoft on Amiga/DOS was Unreal alpha.
You thought everything was alpha/beta, I bet even the Future Crew stuff because it was called Unreal. Worse yet, please don't start looking for Unreal everywhere, there is also something called that way I accidentaly stumbled upon and it was nasty and had nothing to do with games. Don't look at it no matter what you do please. It comes with a text file saying warning though and you better read that first before trying to look at anything in the directory trust me.
I have learned leo, and i am very calm right now and you guys where right.I did not read it how it suposed to be.
And you guys where right about everything.Papercoffee and this crew of this forum learned me alot also about some rules who are dedicated to this forum and all other forums also.
Those rules are also for the beyound unreal forums wich i did,nt reply to.No i do and i,m more a complete person right now.
And i,m did learned reading becouse of you and delacroix also.
Just say hello to the guys if you wanna do that for me on the beyound unreal forums.
You guys make me things made bether dont forget that.
That was a special patch i think.
I dont look for unreal anymore ,you where seeking the history of unreal, and you guys did a great job collecting them and uploading then to other servers.And hopely stay there forever.
i just made to much mistakes on the beyound unreal forums i,m just saying sorry about that all.And i hope that you guys just can forget me because of mine bad english and mistakes i made.
I hope that those guys just can forgive me for ever.
I can now edit merge combine urls and uploading files, wich i canot back in those days.
I have LEARNED from you guys and dont forget that.
I was wrong back in those days on the beyound unreal forums.
I was mine mistake not yours.
I,m sorry about mine bad english.
Well, your english seems the same to me as it did many years ago, but I can guess what you mean most of the time.
Btw, forget and forgive are not always used in the same context. Forget you only use when you want people to forget yu ever existed or smething like that, lol..
Sometimes my spelling gets bad too but usually when my energy is low, etc.
Leo(T.C.K.) wrote: Well, your english seems the same to me as it did many years ago, but I can guess what you mean most of the time.


text:
CommBank resurrects CISO role
By Allie Coyne on Jan 15, 2015 1:52PM
Ben Heyes
[Updated] Cyber security chief gains new title.
The Commonwealth Bank has resurrected a dormant chief information security officer role, expanding the remit of former cyber security chief Ben Heyes.
The CISO role at CommBank has been vacant since 2011 following the departure of Graham Thomson, who spent three years in the position.
Heyes last month started work as the bank's new chief information security and trust officer after more than three years as its general manager of cyber security, privacy and operational risk, in which he led CommBank's digital protection group.
He retains his former responsibilities in the new CISO role, and remains within the bank's enterprise services group, but now has expanded scope over CBA's privacy function. His specific remit will be nutted out over the coming weeks.
Heyes is a vocal lobbyist for improved information security practices, which has helped increase awareness amongst the Commonwealth Bank's board and key stakeholders.
His team has prepared playbooks for stakeholders across the business as a result of a growing "thirst" for infosec knowledge, and Heyes recently attributed CommBank's approach to infosec as feeding into the "trust relationship we have with our customers".
Heyes also played a part in the Government's decision to announce an impending update to the nation's six-year old cyber security strategy, after lobbying for the ageing policy to be improved in order to better align with the current threat landscape.
"The longer term projection view for the cyber environment is negative - the threats are increasing, the capability of the people posing those threats is increasing and evolving, and at the same time there's been lots of media reporting about surveillance programs, and they have an adverse impact on online trust," Heyes told iTnews at the time of the announcement.
"Those factors threaten to undermine the development of the digital economy."
Clarification: This article initially stated the CISO role was newly created, based on provided information. CommBank has clarified that the role previously existed but has been vacant for several years.
bankingit ben heyes cisco commbank commonwealth bank infosec privacy security
By Allie Coyne
Cisco wants privacy to be a fundamental human right
Amex spotlights bank hypocrisy in screen scraping liability row
WA's P&N Bank hit by data breach


It's a message about giving and receiving. LOVE expands the more it is given, because LOVE, by its nature, can only beget more LOVE. It is a simple, yet powerful phrase that serves as a reminder of what we all have in common - a desire to be LOVED and to receive LOVE. And we all have the capacity to give LOVE because it resides within each of us and it is infinite.
Sign up with your email address to receive LOVE notes!
Use Code 15OFF to receive your discount at checkout.


text:
Was ist die ComFor?
Schüwer-Preis
Ankündigungen & Berichte
Messen & Festivals
Publikationsmonitor
Laufende Calls for Papers
Bibliothekenrundschau
Monitor 39: Neue Publikationen 2017
Veröffentlicht am 12.02.2018, 00:01
Im Monitor werden in unregelmäßigen Abständen aktuelle Publikationen aus den letzten 6 Monaten vorgestellt, die für die Comicforschung relevant sein könnten. Die kurzen Ankündigungstexte dazu stammen von den jeweiligen Verlagsseiten. Haben Sie Anregungen oder Hinweise auf Neuerscheinungen, die übersehen worden sind und hier erwähnt werden sollten? Das Team freut sich über eine Mail an redaktion@comicgesellschaft.de. -> Zu früheren Monitoren.
BDQ:
Essays and Interviews on Quebec Comics
Andy Brown (Hrsg.)
Conundrum Press
The comics community in Quebec has long been heralded as unique, blending the clear line aesthetic of Europe with the underground influences of North America. Think Tintin meets R. Crumb. Of course, most of the work is in the French language. And while artists such as Michel Rabagliati, Guy Delisle, and Julie Doucet are now internationally recognized, much of it is still unknown outside the province. Conundrum Press started its BDANG imprint in 2004 to rectify this situation by translating and publishing work from Quebec comic artists. BDANG stands for Bande Dessinée en ANGlais, or French comics in English. This volume is a companion to the imprint, collecting interviews and essays on Quebec comics, to give context to the history and breadth of the work. Read about the early strips in Montreal newspapers at the turn of the century, Albert Chartier, cartoonist of rural Quebec, the zany antics of Red Ketchup, the underground minicomics boom of the 1990s, the anglophones who found themselves a part of the mix, and the hallucinogenic punk prophet Valium.
The Marvel Studios Phenomenon:
Inside a Transmedia Universe
Martin Flanagan, Andrew Livingstone und Mike McKenny
~£ 17,39
Marvel Studios has provided some of the biggest worldwide cinematic hits of the last eight years, from Iron Man (2008) to the record-breaking The Avengers (2012), and beyond. Having announced plans to extend its production of connected texts in cinema, network and online television until at least 2028, the new aesthetic patterns brought about by Marvel's 'shared' media universe demand analysis and understanding. The Marvel Studios Phenomenon evaluates the studio's identity, as well as its status within the structures of parent Disney. In a new set of readings of key texts such as Captain America: The Winter Soldier, Guardians of the Galaxy and Agents of S.H.I.E.L.D., the thematics of superhero fiction and the role of fandom are considered. The authors identify milestones from Marvel's complex and controversial business history, allowing us to appraise its industrial status: from a comic publisher keen to exploit its intellectual property, to an independent producer, to successful subsidiary of a vast entertainment empire.
Animal Comics:
Multispecies Storyworlds in Graphic Narratives
David Herman (Hrsg.)
ISBN 978-1-3500-1531-9 (Hardcover)
Animal characters abound in graphic narratives ranging from Krazy Kat and Maus to WE3 and Terra Formars. Exploring these and other multispecies storyworlds presented in words and images, Animal Comics draws together work in comics studies, narrative theory, and cross-disciplinary research on animal environments and human-animal relationships to shed new light on comics and graphic novels in which animal agents play a significant role. At the same time, the volume's international team of contributors show how the distinctive structures and affordances of graphic narratives foreground key questions about trans-species entanglements in a more-than-human world. The writers/artists covered in the book include: Nick Abadzis, Adolpho Avril, Jeffrey Brown, Sue Coe, Matt Dembicki, Olivier Deprez, J. J. Grandville, George Herriman, Adam Hines, William Hogarth, Grant Morrison, Osamu Tezuka, Frank Quitely, Yu Sasuga, Charles M. Schultz, Art Spiegelman, Fiona Staples, Ken'ichi Tachibana, Brian K. Vaughan, and others.
Superheroes and Critical Animal Studies:
The Heroic Beasts of Total Liberation
J. L. Schatz und Sean Parson (Hrsg.)
Superheroes and Critical Animal Studies explores and puts into dialogue two growing field of studies, comic studies and critical animal studies. The book's aim is to create a form of praxis that people can use to actualize many of the values superheroes strive to protect. To this end, contributor chapters are divided into sections on the foundation of superhero representation and how to teach it, criticisms of particular superheroes and how they fall short of truly protecting the planet, and interpretations of specific characters that can be read to produce a positive orientation to the nonhuman world and craft strategies to promote liberation in the real world. Altogether, the book produces a form of scholarship on the media that is both intersectional in scope and tailored to have an impact on the reader beyond theorizing superheroes for theorization's sake.
Alan Moore, Out from the Underground:
Cartooning, Performance, and Dissent
Maggie Gray
This book explores Alan Moore's career as a cartoonist, as shaped by his transdisciplinary practice as a poet, illustrator, musician and playwright as well as his involvement in the Northampton Arts Lab and the hippie counterculture in which it took place. It traces Moore's trajectory out from the underground comix scene of the 1970s and into a commercial music press rocked by the arrival of punk. In doing so it uncovers how performance has shaped Moore's approach to comics and their political potential. Drawing on the work of Bertolt Brecht, who similarly fused political dissent with experimental popular art, this book considers what looking strangely at Alan Moore as cartoonist tells us about comics, their visual and material form, and the performance and politics of their reading and making.
Comics and Authorship:
Special Issue of Authorship 6(2)
Maaheen Ahmed (Hrsg.)
Open Access Zugriff
If media authorship can be understood "as a site of cultural tension" (Johnson and Gray 2013, 10), then a deeper understanding of comics authorship will also provide clues regarding the sustaining—and constraining— of creative practices in other media ecologies and intermedial interactions (such as, for instance, adaptations). For comics, this implies combining insights from comics scholars, practitioners as well as agents involved in the publication and dissemination of comics. This issue, building on the findings of extant scholarship on authorship in comics and other media, hopes to provide incentive for further adventures into the (almost) unknown of comics authorship.
Mitgliederprofile


The wonderful tea, the first grown and blended in Britain exclusively.
Straight from the Cornish countryside – Tregothnan Tea is the first tea grown and produced on British soil. It's not available anywhere else in the USA currently, so we're importing it over.
Our English Breakfast loose tea is now available in our brand new loose leaf tea caddies with luxe, British styling.
Our English Breakfast loose tea is a bold, malty and rich blend made with the widest variety of leaves ever grown in England, then blended with the finest Assam. This blend incorporates some of the 38 different varieties of Camellia sinensis that were gifted to Tregothnan from growers across the world at the end of the last millennia. When tea growers from Vietnam, India, Malaysia and China heard about our British quest to be the first growers of tea in the UK, bushes were sent in celebration of this momentus and pioneering undertaking and planted in the experimental section of Tregothnan's tea gardens.
Each box contains 14 individually sealed English Breakfast loose tea pouches for ultra freshness, meaning your last serving of tea will be as fresh as your first! We have measured the perfect quantity of loose leaf English Breakfast Tea and sealed in the 'bush to cup' freshness into airtight foil pouches. Easy to brew, just open the pouch and pour the contents into your tea infuser.
AVAILABLE IN THE USA ONLY!


By Mason Johnson on October 22, 2013.
Dr. T.H.M. Gellar-Goad is a postdoctoral fellow in the Classical Languages department at Wake Forest University. He currently teaches Greek and Roman COmedy and the Latin Prose Composition courses. His innovative teaching style, such as teaching his prose composition course in the model of a role playing game, creates a strong engagement in his students. His unique approach inspires students who have different ways of learning. He encourages creativity and that creativity gives students different ways to approach learning.


text:
Marketing authorisation holder lacks standing to challenge off-label prescription for unlicensed products
Healthcare & Life Sciences Sweden
The Swedish system for medicinal products – including its reimbursement system – is generally product based. Prescriptions as such are product based (ie, by brand name or generic product name) and the indication for which the product is intended cannot be filled in anywhere by the prescriber. Off-label prescriptions are therefore not generally possible in the 'official' prescription system.
However, when it comes to accessing unlicensed medicinal products, the system for licences on a named-patient basis works differently: the prescriber must add a rationale or motivation for the licence and provide supporting documentation. This rationale or motivation will normally include the indication. Prescription for the off-label use (of an unlicensed product) is possible under normal off-label prescription requirements in Sweden (ie, it should be based on science and proven experience). The Medical Products Agency (MPA) then assesses the treatment need of the individual patient and whether it can be fulfilled by a medicinal product approved in Sweden.
In a number of cases, the holder of a marketing authorisation has been found not to have standing before the courts in matters relating to licences on a named-patient basis. This is especially unsatisfactory for orphan drugs, as this article explains.
The medicinal products in question contain the active substance Idebenone, which is off-patent and has been allegedly used for a long time against various indications, such as certain mitochondrial diseases. The original product has been deregistered in Sweden, but remains available in other countries (eg, Italy).
In 2007 a company was granted orphan drug designation for a product containing Idebenone for treating Leber's hereditary optic neuropathy (the Idebenone orphan drug). A marketing authorisation for the product was granted to the company in 2015.
In the beginning of 2018, a prescriber together with a pharmacy (in accordance with regulations) filed a prescription of the unlicensed original product on a named-patient basis. The application was granted by the MPA. The decision was challenged by the marketing authorisation holder of the Idebenone orphan drug, which was the only approved product containing the substance on the Swedish market.
The administrative court found that the marketing authorisation holder lacked standing before the court, referring to its previous case law. The marketing authorisation holder appealed this decision to the administrative court of appeal.
In its appeal, the marketing authorisation holder argued that the named-patient licence for the original product had been incorrectly granted and that the general rule was that a licence on a named-patient basis could be granted only if the need for a medicinal product could not be fulfilled by a product approved in Sweden.
The marketing authorisation holder referred to Swedish case law on:
the granted standing of a marketing authorisation holder of an originator product to appeal the granted marketing authorisation of a generic of that product; and
the granted standing of the marketing authorisation holder of an originator product to appeal a decision in relation to its product being parallel distributed or imported.
The marketing authorisation holder further stated that:
the products were in direct competition with each other, which they should not be since only the Idebenone orphan drug had a valid marketing authorisation in Sweden; and
it would be financially and legally affected by the granted licence.
It was claimed that in all matters concerning a named-patient licence for Idebenone, the MPA should initially investigate whether the approved Idebenone orphan drug was suited for the treatment that the application concerned and explicitly state why the Idebenone orphan drug could not be used instead of the original product.
The MPA stated that the case law referred to by the marketing authorisation holder concerned a specifically regulated situation and could not be used as grounds for other situations.
The administrative court of appeal denied the appeal. According to the court, the circumstances in the case differed from the case law referred to by the marketing authorisation holder. Although the essential aim for all production, distribution and use of medicinal products in the European Union (ie, to safeguard public health) was still valid, the primary aim for a licence on a named-patient basis was to safeguard the treatment need of a specific patient and offer that specific patient good quality healthcare.
The court further reasoned that, when assessing an application for a licence on a named-patient basis, the MPA cannot assess whether a medicinal product fulfils the requirements to be approved as a fundamental element. Thus, the situation in the referenced case law was not relevant and there were no safeguarding reasons to grant the marketing authorisation holder standing before the court.
The court found no reason to question that the marketing authorisation holder's financial position would have be affected should the Idebenone orphan drug have been prescribed to the patient instead of a named-patient basis licence having been granted. However, the court held that this factor was due only to the companies being competitors and their respective interest in sales, finding no support in regulation or case law that such interest should be considered in a licence decision by the MPA or that this issue in itself could form the basis for standing before the court.
In conclusion, the court found that the marketing authorisation holder neither represented an interest protected by the legal system that should be considered within due process nor could be considered to have a legal interest worthy of consideration to have the legality of the decision questioned. Therefore, the administrative court had been correct in denying the marketing authorisation holder standing before the court.
In the case in question it would appear that the approved 'on-label' indication is quite rare, while there has been a wide off-label prescription for many indications which appear to be more prevalent. The treatment cost when using the Idebenone orphan drug is naturally high given the marketing authorisation procedure for that product, higher in fact than using the original product. Off-label prescription of the Idebenone orphan drug in the 'official' prescription system would therefore be quite costly.
The MPA guidelines for licences on a named-patient basis explicitly state that financial reasons cannot justify a licence on a named-patient basis (eg, the licensed product is cheaper than the approved alternative or the patient gets a product which is reimbursed when the approved alternative is not).
However, given the differences between the abovementioned systems, any off-label prescription for a licence on a named-patient basis will not breach regulations – while a product may contain the same active substance, it remains possible that no medicinal product for that indication approved in Sweden can fulfil the need of an individual patient.
For a marketing authorisation holder to which the MPA has not prescribed a licensed product based on the indication of its approved product, transparency is available by a freedom of information request of the rationale or motivation for the licence (any patient information will be redacted).
Nevertheless, it is questionable why cases where the holder of an orphan drug with a small patient population in Sweden should not get standing before a court to get a judgment on the substantive issues of a named-patient basis licence, as generally not many granted licences would be required to fulfil a large part of or even the full treatment need for Sweden. Consider, for example, a case where it is questioned whether the prescription for a named-patient licence is off or on label of an approved product.
For further information on this topic please contact Jonas Löfgren at Westerberg & Partners Advokatbyrå Ab by telephone (+46 8 5784 03 00) or email (jonas.lofgren@westerberg.com). The Westerberg & Partners Advokatbyrå Ab website can be accessed at www.westerberg.com.
Jonas Löfgren
Heavily discounted starter pack considered unethical grant to healthcare
Cannabis causes confusion in Sweden
Trilogue negotiations: originator company compensation for parallel imported products
Judgment on public procurement puts parallel importers at a disadvantage
Pharmaceutical companies request Patent and Registration Office to reassess decisions


text:
package raw

// HTML is the raw constructor for a safehtml.HTML.
var HTML interface{}

// Script is the raw constructor for a safehtml.Script.
var Script interface{}

// Style is the raw constructor for a safehtml.Style.
var Style interface{}

// StyleSheet is the raw constructor for a safehtml.StyleSheet.
var StyleSheet interface{}

// URL is the raw constructor for a safehtml.URL.
var URL interface{}

// TrustedResourceURL is the raw constructor for a safehtml.TrustedResourceURL.
var TrustedResourceURL interface{}

// Identifier is the raw constructor for a safehtml.Identifier.
var Identifier interface{}

redpajama_set_name: RedPajamaGithub


text:
Fashion Safety
Indian fashion industry needs to embrace the highest safety standards, says Dusanj-Lenz
Dusanj-Lenz is an advocate for gender equality, sustainability and champions the need for a fair and transparent fashion industry.
The Indian fashion industry needs to embrace the highest safety standards, says Suki Dusanj-Lenz, country co-ordinator for Fashion Revolution India. For this, India must first stop using chemicals that are banned in the rest of the world, she said, talking about a global movement that desires greater transparency, sustainability and ethics in the fashion industry. The movement followed the death of 1,138 workers in Dhaka while making garments in the Rana Plaza factory, which collapsed after a structural failure in the building on April 24,2013.
The workers were making garments for the international market. "The sad thing is the staff was complaining about the building but nobody listened," she said. Dusanj-Lenz is an advocate for gender equality, sustainability and champions the need for a fair and transparent fashion industry. "Carry Somers and Orsola De Castro came together and founded the Fashion Revolution, which has spread to 100 countries. We are working towards a safer, fairer, cleaner fashion industry", she says. Dusanj-Lenz is also Executive Director at the Swiss-Indian Chamber of Commerce and Executive Director at MARD, a people powered initiative campaigning against discrimination. The aim of Fashion Revolution was to unite the fashion industry and ignite a revolution to radically change the way clothes were sourced, produced and purchased so that what the world wears was made in a safe, clean and fair way. "We want to empower every spectrum of the supply chain to transform the industry into a more sustainable one." Would she like to share about the sustainability issues of the Indian fashion industry? "There are layers of complexities in the fashion industry but one thing for sure is that India must look to international standards for the safety of the staff "There are chemicals that are banned in other parts of the world, yet India still uses them. "Are our lives any less those of another country? In Kanpur the leather making industry is astonishingly hazardous to the staff. Have you watched that movie 'Erin Brokovich'? Remember that chemical that was banned in the US that is the subject of that movie. Well, the Indian industry still uses it and our staff is exposed to the dangers of such chemicals," she added.
"Let's not have the people that make our garments or shoes pay the price for our fashion," she added. Talking about sustainable fashion in India, Dusanj-Lenz said: "On the upside India also has some incredibly sustainable brands and a massive recyclability culture which we must celebrate and encourage. Sustainable Fashion Day at the LFW brought many of them together." She said around 80 per cent of the garment makers in India were women. "It's important that we hear their voice and work to campaign for them and not against them. Fashion Revolution wants to educate the consumer about the damage throw away fashion has on our environment. "We want to inform people about the dark side of polyester and viscose both in landfill and the chemical process... There is always a price to pay for cheap fashion. Someone somewhere is paying for it," she added.
LFW
Swiss-Indian Chamber of Commerce
Dusanj-Lenz
cosmetics safety
cosmetics chemicals
Central Government, Agence Francaise De Development and DPIIT Launched Swachhata Start-Up Challenge
Pimpri-Chinchwad Municipal Corporation Tops City E-Governance Index 2022
Ola Electric
Ola Electric Announces Futurefoundry
Lahori, The Desi Drink Brand Titillating Your Taste Buds
If You Are An Indian Farmer These Loans Can Help You Grow
Is India's Small Business Ready For Private Equity, Venture Capital?


text:
Q: LNK4098: defaultlib "mfc42d.lib" conflicts in Release build After several hours of stretching my hairs, I can't figure this out. In Debug version, it is working fine. But in release mode, I am getting this warnings and eventually an runtime error. As far as I know, these libraries are debug versions. Why is my release build looking for these libraries and how can I stop it? FYI, I looked at settings and project files to find a clue in vain.
 LINK : warning LNK4098: defaultlib "mfc42d.lib" conflicts with use of other libs; use /NODEFAULTLIB:library
 LINK : warning LNK4098: defaultlib "mfcs42d.lib" conflicts with use of other libs; use /NODEFAULTLIB:library
 LINK : warning LNK4098: defaultlib "msvcrtd.lib" conflicts with use of other libs; use /NODEFAULTLIB:library

A: Impossible to tell without more information why your project is including these. My guess is that you are linking with a debug configuration of some other library, which is pulling in those dependencies.  If you increase the verbosity of the linker settings then it may show you which files are including them.
The fix though is given in the error message. Add /nodefaultlib:mfc42d.lib/nodefaultlib:mfcs42d.lib  /nodefaultlib:msvcrtd.lib to the linker arguments.


text:
Underground Extension To Streatham
Home > Blog > Underground Extension To Streatham
Back in the late 1980s, plans were seriously looked at which could have seen a new Northern Line spur constructed between Kennington, and either Streatham, or along the proposed Bakerloo Line extension, towards Peckham.
Obviously, it never took place, but the plans for Crossrail 2 had indirectly resurrected the proposals, although this time as a possible extension of the Victoria Line instead.
The 1988 "strategic review" noted that the ground conditions in much of South London are poor for tunnelling, composing mainly of sand and gravel. In many areas, the new tunnels would pass below the water table, requiring compressed air, or a slurry shield for the tunnel boring machine to function.
Another report into the Bakerloo Line extension showed that for the possible extension down to Streatham, it would be water logged soil only as far as Brixton, after which the conditions for tunneling improved markedly.
Regardless of where the line would go, there was the question of turning around trains fast enough to meet a 30 trains-per-hour requirement, and there could either have been a loop, as at Kennington and Heathrow, or the construction of three platforms instead of the usual two.
If the loop were to have been adopted, a spur would have allowed for faulty trains to be stored off the line, and a novel idea of including a maintenance pit in the siding itself could have assisted with faster repairs.
The Streatham route follows the A23, running deep to pass beneath sewers and the Victoria Line at Brixton. There are four new stations on this line, at Brixton – interchange with Victoria. Line, Brixton Hill, Streatham Hill – interchange with BR services to West Croydon, and Streatham – interchange with BR services to Sutton. There is a terminating loop at Streatham. After Brixton, there is a sustained 1 in 50 gradient to Brixton Hill, but as the gradient of the street above is similar, the line remains at about 30 metres below ground level. It should be noted that there are gradients of similar slope and length on the Hampstead Line, so this one will not be a limiting factor on the line, even though it is more severe than is normally recommended. Beyond Brixton Hill, the line can be built on the hump station profile. Most of the alignment can be kept under streets, without introducing sharp curves, except between Streatham Hill and Streatham, near stations and around the terminal loop where it passes under houses.
None of the stations were described in any detail, although it was presumed that apart from the physical need to get down to the tunnels, most of the station building would reuse the existing British Rail station facilities.
The exception would have been either of the proposed Camberwell Green or Brixton Hill stations. Camberwell Green being a sub-surface station, tied in with a series of proposed subways under the local road junction.
The whole project, would have come to £264 million for the link to Streatham. Those costs excluded the need for additional trains, and a presumption that soil conditions didn't prove to be worse than expected.
While the link to Streatham is dead as far as the Northern Line is concerned, a report into Crossrail 2 noted that CR2 could relieve congestion on the Victoria Line to the level needed to support that line being extended down to Streatham. The line already extends past Brixton a decent enough distance in anticipation of a future extension.
And finally, following the recent consultation on the Bakerloo Line Extension, TfL is currently reviewing the case for the proposed extensions, including different route options and possible station locations across south London.
Source: www.ianvisits.co.uk