text:
\section{Introduction}

In 1997, in the early days of the field now called ``analysis on metric spaces'', Heinonen and Semmes \cite{HS} posed a list of ``Thirty-three yes or no questions about mappings, measures, and metrics,'' which have gone on to be quite influential. A number of these questions have been solved since the publication of this list, but many remain open.

In this paper, we resolve, in the negative, Question 8 from that list:

\begin{question}[\cite{HS}, Question 8]\label{q:HS}
\textit{If an Ahlfors regular metric space admits a regular map into some Euclidean space, then does it admit a bi-Lipschitz map into another, possibly different, Euclidean space?}
\end{question}

Precise definitions for the relevant terms in the question will be given in Section \ref{sec:notation} below. For now, a bi-Lipschitz map is simply an embedding that preserves distances up to a constant factor, and a regular map is a map that ``folds'' a metric space in a certain quantitative, $N$-to-$1$ manner. Thus, informally, Question \ref{q:HS} asks: if a metric space can be quantitatively \textit{folded} to fit into some Euclidean space, can it be quantitatively \textit{embedded} into some Euclidean space?

We give an explicit example showing that the answer to Question \ref{q:HS} (Question 8 of \cite{HS}) is ``no''. In fact, our example is a space that has already appeared in the literature as an interesting example in a different context. This is the ``slit carpet'' studied by Merenkov in \cite{Me}, which we denote $\ensuremath{\mathbb{M}}$. We postpone a formal definition of $\ensuremath{\mathbb{M}}$ to later in the paper, but the idea is the following. Start with the unit square $Q_0 = [0,1]^2$ in the plane. Cut a vertical ``slit'' in the square along the segment $\{\frac{1}{2}\} \times [\frac{1}{4},\frac{3}{4}]$. Now subdivide $Q_0$ into its four natural dyadic subsquares, and similarly remove a vertical slit of of half the side length from the center of each sub-square. Repeating this process in all dyadic squares of all scales in $Q_0$ leaves us with a remaining set $A\subseteq Q_0$, the complement of the countably many slits, which we equip with the \textit{shortest path metric}. The completion of $A$ in this metric is the slit carpet $\ensuremath{\mathbb{M}}$. See Figure \ref{fig:slitcarpet} below. (We give a slightly more careful definition of $\ensuremath{\mathbb{M}}$ as a certain limit below.) The name ``slit carpet'' comes from the fact that $\ensuremath{\mathbb{M}}$ is homeomorphic to the classical planar Sierpi\'nski carpet \cite[Lemma 2.1]{Me}. For an example of how $\ensuremath{\mathbb{M}}$ serves as a counterexample, see \cite{MW}, where the authors show that there is no quasisymmetric embedding $f: \ensuremath{\mathbb{M}} \to \ensuremath{\mathbb{R}}^2$.

\begin{figure}
	\centering
		\includegraphics[scale=0.2]{slit4.png}
		\caption{An approximation to the slit carpet $\ensuremath{\mathbb{M}}$}
	\label{fig:slitcarpet}
\end{figure}

Merenkov defined and studied $\ensuremath{\mathbb{M}}$ in the context of quasisymmetric mappings, showing that the double of $\ensuremath{\mathbb{M}}$ along its boundary gives the first known example of a space which is ``quasisymmetrically co-Hopfian'' for metric rather than topological reasons. In the course of defining $\ensuremath{\mathbb{M}}$, Merenkov observed that $\ensuremath{\mathbb{M}}$ is Ahlfors regular and that the natural map $\pi\colon \ensuremath{\mathbb{M}} \rightarrow Q_0 \subseteq \ensuremath{\mathbb{R}}^2$ given by ``collapsing the slits'' (which we define precisely in Section \ref{sec:notation}) is a regular mapping in the above sense, so $\ensuremath{\mathbb{M}}$ admits a regular mapping into some Euclidean space.

However, we prove the following:

\begin{theorem}\label{main-theorem}
There is no bi-Lipschitz map $f\colon \mathbb{M} \to B$, for any uniformly convex Banach space $B$.
\end{theorem}
In particular, $\ensuremath{\mathbb{M}}$ admits no bi-Lipschitz embedding into any $\ensuremath{\mathbb{R}}^n$, answering Question \ref{q:HS}, but also no such embedding into any $L^p$ space for $p\in (1,\infty)$.

The proof of Theorem \ref{main-theorem} is based on a technique appearing in seminal work of Burago-Kleiner \cite{BK}. This scheme begins by identifying a certain extremal pair of points, where the Lipschitz constant of the supposed embedding is nearly achieved. In the vicinity of such an extremal pair, with the aid of approximation, the mapping $f$ has to behave roughly linearly in this direction. Finally, this near-linearity is used to contradict some setting-dependent non-linear or non-Euclidean behavior. In our case, the non-Euclidean behavior arises from the presence of the slits at all locations and scales, which leads to a contradiction to the supposed bi-Lipschitz behavior of the map.

Interestingly, the idea of looking for maximal or almost-maximal directional expansion for Lipschitz functions appears in other contexts as well, namely questions of finding points of differentiability in small sets. See \cite{Fitzpatrick, Preiss}.

We conclude the introduction with two remarks concerning Question \ref{q:HS} and an open question.

\begin{remark}
A 2005 paper by Movahedi-Lankarani and Wells \cite[VII (p. 262)]{MLW} mentions that Tomi Laakso informed those authors that he had an example showing that the answer to Question \ref{q:HS} is ``no'', and in fact has the same property we prove for $\ensuremath{\mathbb{M}}$ in Theorem \ref{main-theorem}. So far as we know, Laakso's example has never appeared in print, and we do not know if his example or his proof is the same as ours, though our proof certainly owes some ideas to \cite{Laakso}.
\end{remark}

\begin{remark}
One way of seeing the difficulty in Question \ref{q:HS} is to observe that a now-standard technique of proving non-embedding theorems for metric spaces, Cheeger's differentiation theory, cannot possibly provide a ``no'' answer to the question. Cheeger's theory \cite{Ch} endows certain metric spaces, the so-called PI spaces, with a type of ``measurable differentiable structure''. Using this theory, Cheeger showed that PI spaces whose blowups, in the pointed Gromov-Hausdorff sense, are not bi-Lipschitz homeomorphic to Euclidean spaces cannot admit bi-Lipschitz embeddings into any $\ensuremath{\mathbb{R}}^n$, work which was later generalized by other authors \cite{CK, CK_Banach, CKS, GCD}. This provides a unified approach to many non-embedding theorems, including that of the Heisenberg group \cite{CK_Banach} and Laakso spaces \cite{CK_PI}

On the other hand, it also follows from Cheeger's theory that an Ahlfors regular PI space whose blowups are not bi-Lipschitz homeomorphic to Euclidean spaces cannot even admit a regular map into any Euclidean space. (This follows from the above remarks, the measure-preservation property of regular mappings, and \cite[Theorem 1.5]{GCDKin}.) So Cheeger's differentiation theory is not directly useful for answering Question \ref{q:HS}.
\end{remark}

Of course, a number of interesting Banach spaces do not fit into the uniformly convex framework. For embedding questions, the most interesting of these are probably $\ell^1$ and $L^1$.

\begin{question}\label{q:l1}
Does $\ensuremath{\mathbb{M}}$ admit a bi-Lipschitz embedding into $\ell^1$? Into $L^1?$
\end{question}
One way of approaching the question of an $L^1$ embedding is to see if $\ensuremath{\mathbb{M}}$ has ``Lipschitz dimension 1'' in the sense of \cite{CK}, which by Theorem 1.7 of that paper would force it to be bi-Lipschitz embeddable in $L^1$. Note that by \cite[Lemma 8.9]{GCDLip}, $\ensuremath{\mathbb{M}}$ has Lipschitz dimension $\leq 2$. However, we do not discuss Lipschitz dimension or Question \ref{q:l1} further in this paper.

\subsection*{Acknowledgments}
G.~ C.~ David was partially supported by the National Science Foundation under Grant No. DMS-1758709. S.~ Eriksson-Bique was partially supported by the National Science Foundation under Grant No. DMS-1704215.

\section{Notation and constructions}\label{sec:notation}

\subsection{Metric spaces and Banach spaces}
Our notation is fairly standard. If $X$ is a metric space, we denote its metric by $d$ unless otherwise specified. The diameter of a metric space is
$$\ensuremath{\ \mathrm{Diam\ }}(X) = \sup\{d(x,y):x,y\in X\}.$$
Open and closed balls in $X$ are denoted $B(x,r)$ and $\overline{B}(x,r)$, respectively.

If $X$ is a metric space and $d>0$, the $d$-dimensional Hausdorff measure on $X$ is defined by
$$ \mathcal{H}^d(E) = \lim_{\delta\rightarrow 0} \inf \sum_{B\in\mathcal{B}} (\ensuremath{\ \mathrm{Diam\ }}(B))^d,$$
where the infimum is over all covers $\mathcal{B}$ of $E$ by sets of diameter at most $\delta$. (See, e.g., \cite[Section 8.3]{He}.) Various other standardizations of Hausdorff measure exist that differ from this one by multiplicative constants.

The Hausdorff dimension of a space $X$ is $\inf\{ d: \mathcal{H}^d(X)=0\}$. A stronger, scale-invariant version of having Hausdorff dimension $d$ is the notion of \textit{Ahlfors $d$-regularity}, used in Question \ref{q:HS}. A metric space $X$ is Ahlfors $d$-regular if there are constants $C>c>0$ such that
$$ cr^d \leq \mathcal{H}^d(\overline{B}(x,r)) \leq C r^d \text{ for all } r\leq \ensuremath{\ \mathrm{Diam\ }}(X).$$

For Theorem \ref{main-theorem}, we also need to introduce the Banach space property of \textit{uniform convexity}. Recall that a Banach space $B$ is uniformly convex, if for every $\epsilon>0$, there exists a $\delta>0$ such that for any $x,y\in B$ with $\|x\|=\|y\| = 1$ and $\|x-y\| \geq \epsilon$, we have $$\left\|\frac{x+y}{2}\right\| \leq 1 - \delta.$$

\subsection{Lipschitz, bi-Lipschitz, and regular mappings}

Three basic classes of mappings are used in the rest of the paper. A mapping $f\colon X \rightarrow Y$ between metric spaces is called \textit{Lipschitz} if there is a constant $L>0$ such that
$$ d(f(x),f(y)) \leq L d(x,y) \text{ for all } x,y\in X.$$
It is called \textit{bi-Lipschitz} if there are constants $b, L>0$ such that
$$bd(x,y) \leq d(f(x),f(y) \leq Ld(x,y)$$
for all $x,y \in X$. The smallest $L$ and largest $b$ satisfying this are called the Lipschitz and lower-Lipschitz constants for $f$. The pair $(b,L)$ will be referred to as the bi-Lipschitz constants of $f$.

Lastly, a Lipschitz map $g\colon X \rightarrow Y$ is called \textit{regular} if there is a constant $C>0$ such that, for every ball $B\subseteq Y$ of radius $r$, the pre-image $g^{-1}(B)$ can be covered by at most $C$ balls of radius $Cr$.

In particular, regular mappings are always at most $C$-to-$1$, but the definition implies more than this. Regular mappings were introduced by David and Semmes \cite[Definition 12.1]{DS} as a kind of intermediate notion between Lipschitz and bi-Lipschitz mappings. One nice way in which regular mappings generalize bi-Lipschitz mappings is that they preserve the $d$-dimensional measure of all subsets, up to constant factors \cite[Lemma 12.3]{DS}.

\subsection{Construction of the slit carpet}
We now follow \cite[Section 2]{Me} to give a more careful definition of the slit carpet than that in the introduction. Though we use our own notation, the reader may wish to look at \cite{Me} for more details. Generalizations of this construction have also recently been studied by Hakobyan \cite{Hak}.

Let $Q_0=[0,1]^2$ be the unit cube in $\ensuremath{\mathbb{R}}^2$. Let $\mathcal{D}_n$ be the collection of dyadic sub-cubes of $Q_0$ at level $n$, that is cubes
$$D_{l,k} = [l2^{-n},(l+1)2^{-n}] \times [k2^{-n}, (k+1)2^{-n}]$$
for $l,k \in \ensuremath{\mathbb{N}} \cap [0,2^n-1].$  The collection of all such dyadic cubes is denoted $\mathcal{D}$.

For each $D_{l,k}^n \in \mathcal{D}_n$, consider the points
$$b_{l,k}^n = ((2l+1)2^{-n-1},(4k+1)2^{-n-2}) \text{ and } t_{l,k}^n=((2l+1)2^{-n-1},(4k+3)2^{-n-2}).$$

These define a vertical segment
$$s_{l,k}^n = [b_{l,k}^n,t_{l,k}^n] \subseteq Q_0,$$
which we call a \textit{slit} of level $n$. Note that $\ensuremath{\ \mathrm{Diam\ }}(s_{l,k}^n) = 2^{-n-1}$. We call the set
$$s_{l,k}^n \setminus \{b_{l,k}^n, t_{l,k}^n\}$$
the \textit{interior} of the slit $s_{l,k}^n$.

Define now $M_0 = Q_0 = [0,1]^2$, and, iteratively, $M_{k+1}=M_k \setminus \bigcup_{a,b} s_{a,b}^{k}$. (See Figure \ref{fig:carpets}.) Then define $\mathbb{M}_k$ as the completion of $M_k$ with respect to the shortest path metric $d_k$ on $M_k$. (We will continue to call this new complete metric on $\ensuremath{\mathbb{M}}_k$ by $d_k$.) This amounts to ``cutting along'' each slit of level $k$ or lower. Note that the $d_k$-diameter of each $\ensuremath{\mathbb{M}}_k$ is bounded by $3$.

\begin{figure}
\centering
\begin{subfigure}{0.3\textwidth}
  \centering
  \includegraphics[width=\linewidth]{slit1}
  \caption{$M_1$}
  \label{fig:carpet1}
\end{subfigure}
\begin{subfigure}{0.3\textwidth}
  \centering
  \includegraphics[width=\linewidth]{slit2}
  \caption{$M_2$}
  \label{fig:carpet2}
\end{subfigure}
\begin{subfigure}{0.3\textwidth}
  \centering
  \includegraphics[width=\linewidth]{slit3}
  \caption{$M_3$}
  \label{fig:carpet3}
\end{subfigure}
\caption{The first three $M_i$.}
\label{fig:carpets}
\end{figure}

As observed by Merenkov, for each $k\leq j$, there is a natural $1$-Lipschitz mapping $\pi_{j,k}\colon \ensuremath{\mathbb{M}}_j \rightarrow \ensuremath{\mathbb{M}}_k$ obtained by identifying opposing points on slits of levels greater than $j$ corresponding to the same point in $\ensuremath{\mathbb{M}}_k$. These maps compose in the natural way. We can then define the Merenkov slit carpet $\ensuremath{\mathbb{M}}$ as the inverse limit of the system
$$ \ensuremath{\mathbb{M}}_0 \xleftarrow{\pi_{1,0}} \ensuremath{\mathbb{M}}_1 \xleftarrow{\pi_{2,1}} \ensuremath{\mathbb{M}}_2 \xleftarrow{\pi_{3,2}} \dots,  $$
equipped with the metric
$$ d(x,y) = \lim_{k\rightarrow \infty} d_k(x_k, y_k)$$
for $x=(x_k)$ and $y=(y_k)$ such that $\pi_{k}(x_k)=x_{k-1}$, and similarly for $y_k$. Note that this is the limit of a bounded, increasing sequence.

Alternatively, one could also define $\ensuremath{\mathbb{M}}$ as the Gromov-Hausdorff limit of the $(\ensuremath{\mathbb{M}}_k,d_k)$, or directly by removing all the slits from $[0,1]$ and taking a metric completion with respect to the path metric.

For each $k$, there is a natural $1$-Lipschitz projection $\pi_k \colon \ensuremath{\mathbb{M}} \rightarrow \ensuremath{\mathbb{M}}_k$, given by $\pi_k((x_i))=x_k$. We let $\pi=\pi_0\colon \ensuremath{\mathbb{M}} \rightarrow \ensuremath{\mathbb{M}}_0 \cong Q_0.$ Merenkov proves the following about $\pi$:
\begin{lemma}[\cite{Me}, Lemma 2.3]
The map $\pi\colon \ensuremath{\mathbb{M}} \rightarrow \ensuremath{\mathbb{M}}_0\cong Q_0$ is regular.
\end{lemma}

Merenkov uses this lemma and other properties of $\pi$ to show that $\ensuremath{\mathbb{M}}$ is Ahlfors $2$-regular. (See \cite[p. 370]{Me}.)

We take the opportunity to introduce some further notation describing $\ensuremath{\mathbb{M}}$ that we will use below.

Each slit $s_{l,k}^n \subseteq Q_0$ has a pre-image in $\ensuremath{\mathbb{M}}$ under $\pi$ that is a topological circle. Set $m_{l,k}^n$ to be the midpoint of $s_{l,k}^n$ in $Q_0$, and let $m_{l,k}^{n,+}$ and $m_{l,k}^{n,-}$in $\ensuremath{\mathbb{M}}$ denote the two pre-images of $m_{l,k}^n$ under $\pi$. (There is one on each ``side''.) On the other hand, the top and bottom $t_{l,k}^n$ and $b_{l,k}^n$ have single pre-images under $\pi$. We denote those pre-images by $\tilde{t}_{l,k}^n$ and $\tilde{b}_{l,k}^n$, respectively.

Let
$$\mathcal{V}_n\mathrel{\mathop:}= \{(x,y) \in (Q_0)^2 : x=(l2^{-n},k2^{-n}), y = (l2^{-n},(k+1)2^{-n})\}$$
be the collection of all pairs of points defining vertical sides of the dyadic squares at level $n$, and $\mathcal{V} = \bigcup_{n\geq 0} \mathcal{V}$ the collection of all of these pairs at all scales. We say that a element of $\mathcal{V}$ is at level $n$ if $(x,y) \in \mathcal{V}_n$.

We use $\mathcal{V}$ to define a set of ``vertically adjacent'' pairs of points in the carpet $\ensuremath{\mathbb{M}}$. Let
$$ \mathcal{W}_n = \{ (v,w)\in\ensuremath{\mathbb{M}}^2 : (\pi(v),\pi(w))\in \mathcal{V} \text{ and } d(v,w) = |\pi(v)-\pi(w)| \}$$
and
$$\mathcal{W}=\cup_{n\geq 0} \mathcal{W}_n.$$
The point of the condition $d(v,w) = |\pi(v)-\pi(w)|$ in the definition of $\mathcal{W}$ is that, if $\pi(v)$ and $\pi(w)$ lie on a common slit in $Q_0$, then $v$ and $w$ must lie on the same ``side'' of that slit in $\ensuremath{\mathbb{M}}$. Note that, for instance, all of the following pairs are in $\mathcal{W}$:
$$ (\tilde{b}_{l,k}^n, m_{l,k}^{n,\pm}), (m_{l,k}^{n,\pm}, \tilde{t}_{l,k}^n).$$

\section{Proof of Theorem \ref{main-theorem}}

We begin with a few preliminary lemmas, and then give the proof of Theorem \ref{main-theorem}.

First, we observe that line segments in $Q_0$ between ``vertical pairs'' of points $(v,w)\in\mathcal{W}$ can be approximated by discrete paths which have a significant fraction of their length lying along slits.

\begin{lemma} \label{lem:approx} Let $(v,w)\in\mathcal{W}$. Then, for every $m > n$, there is a discrete path $(q_0, q_1, \dots, q_N)$ in $\ensuremath{\mathbb{M}}$ and a subset $G \subseteq \{0, \dots, N-1\}$ such that
\begin{enumerate}
\item\label{eq:approx1} $q_0=v$, $q_N=w$,
\item\label{eq:approx1.5} $d(q_1,q_0)=d(q_N,q_{N-1})\leq 2^{-m-1}$,
\item\label{eq:approx2} $$\sum_{i=0}^{N-1} d(q_i,q_{i+1}) = 2^{-n} + 2^{-m},$$
\item\label{eq:approx3} $$\sum_{i \in G} d(q_i,q_{i+1}) = 2^{-n-1},$$
\item\label{eq:approx4} if $i \in G$, then $[\pi(q_i),\pi(q_{i+1})] = s_{a,b}^m$ for some $a,b$, and
\item\label{eq:approx5} if $i\notin G \cup \{0,N-1\}$, then $(q_i,q_{i+1})\in\mathcal{W}$.
\end{enumerate}
\end{lemma}

\begin{proof}
Let $x=\pi(v)$ and $y=\pi(w)$, so that $(x,y)\in\mathcal{V}_n$.

There are $k,l$ so that $x=(l2^{-n},k2^{-n}), y = (l2^{-n},(k+1)2^{-n}$.  Let $m>n$  be arbitrary. We will first define a discrete path $(p_0, \dots, p_N)$ from $x$ to $y$ in $Q_0$.

We will take this path to be the original segment $[x,y]$ shifted by $2^{-m-1}$ to the either the left or right, and then discretized appropriately. We will now describe this discretization in detail.

The points $x$ and $y$ are dyadic of level $2^{-n}$. Therefore, no slit of level $\geq n$ intersects the horizontal lines through $x$ or $y$. Moreover, the assumption that $(v,w)\in \mathcal{W}$ implies that if, $v$ and $w$ lie on a common slit, then they lie on the same ``side'' of that slit.

Set $x^{\pm} = x\pm(2^{-m-1},0)$ and $y^{\pm}=y\pm(2^{-m-1},0)$. Let $v^{\pm}$ and $w^{\pm}$ be pre-images under $\pi$ of $x^{\pm}$ and $y^{\pm}$. (These pre-images are uniquely determined: since $m>n$, $x^{\pm}$ and $y^{\pm}$ cannot lie in the interior of a slit.) Then at least one pair of distances
\begin{equation}\label{eq:plus}
 d(v^+, v) \text{ and } d(w^+,w)
\end{equation}
or
\begin{equation}\label{eq:minus}
 d(v^-,v) \text{ and } d(w^-,w)
\end{equation}
are both equal to $2^{-m-1}$. Without loss of generality, we assume the former. (Note that if $l=0$, we take the first option, while if $l=2^n$ we take the second option.)

The line segment in $Q_0$ from $x^+$ to $y^+$, is half-covered by slits $s_{a,b}^m$. Let $N = 3\cdot 2^{m-n}+2$, and first define $p_0=x,p_N = y, p_{N-1} = y^+=(l2^{-n} + 2^{-m-1},(k+1)2^{-n})$. For the remaining $p_i$ ($i\in \{1, \dots, N-2\}$), we first represent $i=3s + j$, for $j=1,2,3$ and $s =0, \dots 2^{m-n}-1$. We then set

$$p_i = \left\{ \begin{array}{l r}
(l2^{-n} + 2^{-m-1}, k2^{-n} + s2^{-m}) & i = 3s+1, s =0, \dots 2^{m-n}-1 \\
 (l2^{-n} + 2^{-m-1}, k2^{-n} + s2^{-m}+2^{-m-2}) & i = 3s+2, s =0, \dots 2^{m-n}-1 \\
  (l2^{-n} + 2^{-m-1}, k2^{-n} + s2^{-m}+3\cdot 2^{-m-2}) & i = 3s+3, s =0, \dots 2^{m-n}-1 \\
\end{array} \right.$$

See Figure \ref{fig:approxpic}.

In other words, $(p_i)$ form a discrete path that starts at $x$, takes a step of size $2^{-m-1}$ to the right, proceeds up vertically with certain jumps until reaching the height of $y$, and then takes a step of size $2^{-m-1}$ to the left to reach $y$.

Observe that, for each $i\in \{1,\dots, N-1\}$, the point $p_i$ does not lie in the interior of any slit, and so has a unique pre-image $q_i\in \ensuremath{\mathbb{M}}$ under $\pi$. Moreover, we have
\begin{equation}\label{eq:qp}
d(q_i, q_{i+1}) = |p_i - p_{i+1}| \text{ for each } i\in\{0,\dots,N-1\} .
\end{equation}
Indeed, if $i\in\{1,\dots, N-2\}$ the step from $p_i$ to $p_{i+1}$ is in the vertical direction, in which case $d_k(p_i,p_{i+1})$ is the length of the segment $[p_i,p_{i+1}]$ for each $i$ and $k$. If we are in the horizontal step in which $i=0$ or $i=N-1$, equation \eqref{eq:qp} holds because of our understanding that both distances in \eqref{eq:plus} are $\leq 2^{-m-1}$.

With this definition of $(q_i)$ and \eqref{eq:qp}, \eqref{eq:approx1} and \eqref{eq:approx1.5} are immediate. Item \eqref{eq:approx2} is also simple:
$$\sum_{i=0}^{N-1} d(q_i,q_{i+1}) = \sum_{i=0}^{N-1} |p_i-p_{i+1}| = 2^{-n} + 2^{-m},$$
since the $(p_i)$ form of a discrete vertical geodesic path of length $2^{-n}$, plus two horizontal steps of size $2^{-m-1}$.

We now set
$$G = \{3s + 2 \ | \ s =0, \dots 2^{m-n}-1\}.$$
By the definition of $p_i$, it is easy to see that if $i\in G$, then $p_i=\pi(q_i)$ and $p_{i+1}=\pi(q_{i+1})$ are the bottom and top, respectively, of a slit $s^m_{a,b}$ in a cube of side length $2^{-m}$. This verifies \eqref{eq:approx4}.

Item \eqref{eq:approx5} is also simple by inspection: If $i\notin G\cup\{0,N-1\}$, then the formulae above for $p_i=\pi_i(q_i)$ and $p_{i+1}=\pi_i(q_{i+1})$ indicate that they are adjacent vertical corners of a dyadic square of side length $2^{-m-2}$, hence $(\pi(q_i),\pi(q_{i+1}))\in \mathcal{V}$. Moreover, as observed above, $d(q_i, q_{i+1})=|p_i-p_{i+1}|=|\pi(q_i)-\pi(q_{i+1})|$, which shows that $(q_i, q_{i+1})\in\mathcal{W}$.

Lastly, for item \eqref{eq:approx3}, we observe that
$$ \sum_{i \in G} |p_i-p_{i+1}|$$
is simply the total length of the slits in the vertical segment from $x+(2^{-m-1},0)$ to $y+(2^{-m-1},0)$, which is half the total length of that segment, and hence equal to $2^{-n-1}$. Item \eqref{eq:approx3} follows from this and \eqref{eq:qp}.

\begin{figure}
	\centering
		\includegraphics[scale=0.3]{approxpic.png}
		\caption{The points $p_i$}
	\label{fig:approxpic}
\end{figure}
\end{proof}

The next lemma concerns uniformly convex Banach spaces. In a uniformly convex Banach space, metric midpoints are unique. The uniform convexity property can be used to quantify this statement, as follows.

\begin{lemma} \label{lem:unifconvex} Suppose $x,y \in B$ are points, and $m\in B$ is an additional point. Then for every $\epsilon>0$, there exists an $\eta>0$ so that either

\begin{enumerate}
\item $$\max\{ \|x-m\|,\|y-m\|\} \geq \frac{1+\eta}{2}\|x-y\|$$ or
\item $$\left\|m-\frac{y+x}{2}\right\|  \leq \epsilon \|x-y\|.$$
\end{enumerate}
\end{lemma}

\begin{proof}
By translation and scaling, we can take $x=0$ and $\|y\|=1$. Apply the uniform convexity condition to $\epsilon$ to obtain a $\delta>0$. Let $\eta=\frac{1}{2}\min\{\epsilon,\delta\}.$ Suppose that the first property fails with this choice of $\eta$. Then by the triangle inequality we get

$$\frac{1-\eta}{2}\leq \|m\| \leq \frac{1+\eta}{2}$$
and
$$\frac{1-\eta}{2} \leq \|y-m\| \leq  \frac{1+\eta}{2}.$$
Define $\xi^1 = \frac{m}{\|m\|}$, and $\xi^2 = \frac{y-m}{\|y-m\|}$.  Note that
$$ \|\xi^1 - 2m\| \leq \eta \text{ and } \|\xi^2 - 2(y-m)\| \leq \eta.$$
Therefore,
$$\left\|\frac{\xi^2 + \xi^1}{2}\right\| \geq 1-\eta > 1-\delta.$$
Consequently, from the uniform convexity, $\|\xi^1-\xi^2\| \leq \epsilon$, and so $\|2m-2(y-m)\| \leq 2\eta + \epsilon$. In that case,
$$\|m-(y/2)\| = \frac{1}{4} \|2m-2(y-m)\|\leq \frac{\eta}{2}+\frac{\epsilon}{4} \leq \epsilon,$$
which gives the second possibility, as desired.
\end{proof}

On the other hand, the slit carpet $\ensuremath{\mathbb{M}}$ does not have unique midpoints, as the slits can be traversed on both ``sides''. The following lemma is immediate from the definition of $\ensuremath{\mathbb{M}}$.

\begin{lemma} \label{lem:midpoint} Suppose $s=s^{n}_{l,k} = [b_{l,k}^n,t_{l,k}^n]$ is any slit in $Q_0$. Recall the four associated points in $\ensuremath{\mathbb{M}}$ on $\pi^{-1}(s)$, which we called $\tilde{t}_{l,k}^n$, $\tilde{b}_{l,k}^n$, $m_{l,k}^{\pm,n}$.

Then
$$d(\tilde{t}^n_{l,k},\tilde{b}^{n}_{l,k}) = 2^{-n-1}$$
$$d(m^{n,\pm}_{l,k},\tilde{t}^n_{l,k}) = d(m^{n,\pm}_{l,k},\tilde{b}^n_{l,k}) = 2^{-n-2} = d(\tilde{t}^n_{l,k},\tilde{b}^{n}_{l,k})/2$$ and

$$d(m^{n,+}_{l,k}, m^{n,-}_{l,k}) \geq 2^{-n-1} = d(\tilde{t}^n_{l,k},\tilde{b}^{n}_{l,k}).$$
\end{lemma}

We are now ready to prove Theorem \ref{main-theorem}, that $\ensuremath{\mathbb{M}}$ admits no bi-Lipschitz embedding into any uniformly convex Banach space $B$. As noted above, the argument is heavily inspired by the framework of Burago and Kleiner \cite{BK} and also an argument of Laakso \cite{Laakso}.

\begin{proof}[Proof of Theorem \ref{main-theorem}]
Suppose that $B$ is a uniformly convex Banach space, and $f\colon \ensuremath{\mathbb{M}} \to B$ is a bi-Lipschitz mapping. Let $(b,L)$ be the bi-Lipschitz constants of $f$.

Recall the definitions of $\mathcal{W}$ and $\mathcal{W}_n$ from Section \ref{sec:notation} above.

 We define the maximal vertical distortion of $f$ by

 $$L_v = \sup_{(x,y) \in \mathcal{W}} \frac{|f(x)-f(y)|}{d(x,y)}.$$

Note that $L_v$ is bounded above by the Lipschitz constant $L$ of $f$, and below by the lower-Lipschitz constant $b>0$ of $f$. We proceed to derive a contradiction.

Fix $\epsilon = \frac{b}{4L}$ and apply Lemma \ref{lem:unifconvex} to obtain a corresponding $\eta>0$. Next, choose $\eta'>0$ so that $\frac{L_v}{L_v-\eta'} < 1+\eta$.

 Choose a pair $(x,y) \in \mathcal{W}_n$ so that
\begin{equation}\label{eq:nearmax}
L_v-\frac{\eta'}{4} \leq \frac{|f(x)-f(y)|}{d(x,y)}.
\end{equation}

 In particular, $|f(x)-f(y)| \geq 2^{-n}L_v + \eta' 2^{-n-2}$.

Then, choose $m>n$ large enough so that
\begin{equation}\label{eq:mbound}
(2L+L_v)2^{-m} < \eta'2^{-n-2}.
\end{equation}

Using Lemma \ref{lem:approx} (with $v=x$ and $w=y$), we can find a discrete path $q_0, \dots, q_N$ from $x$ to $y$ in $\ensuremath{\mathbb{M}}$ with the properties in the statement.

By Lemma \ref{lem:approx} \eqref{eq:approx5}, for $i \not\in G\cup\{0,N-1\}$, we have $(q_i, q_{i+1})\in\mathcal{W}$, and so
$$|f(q_{i+1})-f(q_i)| \leq L_v d(q_{i+1},q_i).$$

We now argue that there exists an $i \in G$ so that
\begin{equation}\label{eq:goodpt}
|f(q_{i+1})-f(q_{i})| \geq (L_v-\eta') d(q_{i+1},q_i).
\end{equation}
Suppose that this was not the case. In that case, using properties \eqref{eq:approx1.5}, \eqref{eq:approx2}, \eqref{eq:approx3}, and \eqref{eq:approx5} from Lemma \ref{lem:approx}, we have
\begin{align*}
|f(x)-f(y)| &\leq |f(q_1) - f(q_0) | + \sum_{i=1}^{N-2} |f(q_{i+1})-f(q_{i})| + |f(q_N) - f(q_{N-1})|\\
&\leq L2^{1-m} + \sum_{i \in G} |f(q_{i+1})-f(q_{i})| + \sum_{i \not\in G \cup \{0,N-1\}} |f(q_{i+1})-f(q_{i})| \\
&\leq L2^{1-m} + (L_v-\eta') \sum_{i \in G} d(q_{i+1},q_i) + L_v\sum_{i \not\in G}  d(q_{i+1},q_i)  \\
&= L2^{1-m} + L_v\sum_{i=0}^{N-1} d(q_{i+1},q_i) -\eta'\sum_{i \in G}  d(q_{i+1},q_i)  \\
&\leq L2^{1-m} +  L_v (2^{-n} + 2^{-m}) - \eta' 2^{n-1}\\
&= 2^{-n}\left(L_v - \frac{\eta'}{2}\right) + 2^{-m}(2L+L_v)\\
&< \left(L_v - \frac{\eta'}{4}\right)d(x,y),
\end{align*}
where in the last line we used \eqref{eq:mbound}. However, this contradicts \eqref{eq:nearmax}. Therefore, \eqref{eq:goodpt} holds for some $i\in G$.

We thus have an $i \in G$ so that $|f(q_{i+1})-f(q_{i})| \geq (L_v-\eta') d(q_{i+1},q_i)$. By Lemma \ref{lem:approx} \eqref{eq:approx4}, this coincides with a slit $s^{m}_{k,l}$, with $q_{i+1}=\tilde{t}^{m}_{k,l}$ and $q_i = \tilde{b}^{m}_{k,l}$. Now, consider the two pre-images $m^{m,\pm}_{k,l}$ under $\pi$ of the mid-point of this slit, as defined near the end of Section \ref{sec:notation}.

Set $M^{\pm} = f(m^{m,\pm}_{k,l})$, $X=f(q_i)$, and $Y=f(q_{i+1})$ in $B$. Since the pairs $(m^{m,\pm}_{k,l}, q_{i+1})$ and $(q_i, m^{m,\pm}_{k,l})$ are in $\mathcal{W}$, we have the following bounds:

\begin{align*}
\|M^{\pm} - X\| &\leq L_v d(m^{m,\pm}_{k,l}, q_i)  \\
&= L_v d(q_{i+1},q_i)/2 \\
&\leq \frac{L_v}{2(L_v -\eta')}\|Y-X\|\\
&< \frac{1+\eta}{2}\|Y-X\|.
\end{align*}

Similarly, we can conclude that
$$\|M^{\pm}-Y\| < \frac{1+\eta}{2}\|Y-X\|.$$

Consequently, from Lemma \ref{lem:unifconvex} we have that
$$ \left\|M^{\pm}- \frac{X+Y}{2}\right\| \leq \epsilon \|Y-X\|$$
and hence that
$$ \|M^{+}-M^{-}\| \leq 2\epsilon\|Y-X\| \leq 2\epsilon L d(q_{i+1},q_i) = \frac{b}{2}d(q_{i+1},q_i),$$
using our choice of $\epsilon = b/4L$.

On the other hand, since $f$ is bi-Lipschitz with lower Lipschitz constant $b$, we also have by Lemma \ref{lem:midpoint} that
$$ \|M^{+}-M^{-}\| \geq b d(m^{m,+}_{k,l}, m^{m,-}_{k,l}) \geq bd(q_{i+1},q_i)>0.$$

This is a contradiction.
\end{proof}

redpajama_set_name: RedPajamaArXiv


text:
Q: Three.js / jquery: controls and animation inside a div I've put the renderer domElement inside a div called plot_area:
var container;
var camera, controls, scene, renderer;
var numPoints, scale = 3;
init();
animate();

function init() {
    numPoints = document.getElementById('inputNumPoints').value;
    container = document.getElementById('plot_area');

    renderer = initRenderer(container);
    camera = initCamera();
    scene = initScene();
    controls = initControls(camera, container, render);

    drawAxes(scale, 0x444444, scene);
}

function animate() {
    requestAnimationFrame(animate);
    controls.update();
}

function render() {
    renderer.render(scene, camera);
}

Here are the initializers (mostly standard Three.js):
function initRenderer(container) {
    var renderer;
    if (Detector.webgl)
        renderer = new THREE.WebGLRenderer({ antialias: true });
    else if (Detector.canvas)
        renderer = new THREE.CanvasRenderer();
    else
        Detector.addGetCanvasMessage();

    renderer.setSize(800, 800);
    container.appendChild(renderer.domElement);

    return renderer;
};

function initCamera() {
    var camera = new THREE.PerspectiveCamera(45, 1, 1, 500);
    camera.position.set(0, -10, 0);
    camera.lookAt(new THREE.Vector3(0, 0, 0));

    return camera;
};

function initScene() {
    return new THREE.Scene();
};

function initControls(camera, container, renderFunc) {
    var controls = new THREE.OrbitControls(camera, container);
    controls.addEventListener('change', renderFunc);

    return controls;
};

And attached the controls to the very same div. Now when trying to rotate or pan (zooming is fine, though), div appears completely blank. Once I use the whole document as the scope for controls, everything works just fine.
I suspected there might (but shouldn't) have been a global/local name conflict, but the problem wasn't solved by renaming all the init* function parameters. Another guess was that some kind of copy constructor is called at return, so that the objects returned from init* are not really related to anything. (Yes, I'm no expert on js). Maybe, some trouble with request animation frame not working when out of focus?
Some examples: document-scoped controls, div-scoped controls.
Any suggestions as to what I'm doing wrong?

redpajama_set_name: RedPajamaStackExchange


To teach and engage at-risk youth (especially children in shelters and in the foster care system) into the field of science.
To inspire the next generation of scientists, mathematicians, and engineers.
Studying our route for our cross-country science tour. So excited! I can't wait to visit all of the children's shelters and foster organizations!! I'm planning to visit 14. I can't wait!!
My name is Angelica Krubeck and I am 12 years old. I love science. It's one of my favorite things to do. When I was 8, one of my friends opened up to me. She shared how she grew up in a shelter and how hard every day was. After that conversation, I decided I wanted to help kids like her in some way. Science I love and kids I love, so put them together and it just makes sense. I knew that some kids out there don't get the chance to be creative with science, like how I do. I strongly believe that no kid should be without the education and enjoyment of science! Not only does it help them get away from their worries for a little while, but it also provides education to them. I hope to inspire kids to do great things, to succeed in science, and to develop a love for science despite the challenges they are facing in their life.


text:
9 Things You Probably Didn't Know About Bipolar Disorder
by Caitlin Flynn
Caitlin Flynn
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It's a common misconception that bipolar disorder is synonymous with "mood swings." The mental illness, which, according to the National Institute of Mental Health, affects approximately 4.4 percent of American adults at some point during their lives, is often misunderstood by the public. It also frequently goes undiagnosed or misdiagnosed, meaning that many patients wait years before they're treated with the right medications and therapeutic techniques.
Related story Quick Tips For Actually Beating Holiday Stress
Like most mental illnesses, there's no shortage of myths and misconceptions about bipolar disorder. But there are also many lesser-known facts about bipolar that can help us better understand the illness. We asked mental health experts to weigh in on important things to know about bipolar disorder, ranging from symptoms to treatment. Here's what they told us.
Children can develop bipolar disorder
"Bipolar disorder is usually diagnosed in teens or early adulthood, but many of those people report experiencing symptoms during childhood," Dr. Sal Raichbach a psychologist and licensed clinical social worker at Ambrosia Treatment Center, tells SheKnows. The illness is more difficult to diagnose in children because its symptoms are similar to common childhood mental health issues like anxiety disorder and ADHD.
People don't cycle between depression & mania quickly
Contrary to common belief, Raichbach says that individuals with bipolar disorder aren't extremely happy one minute and completely depressed the next. "In reality, the cycles of bipolar disorder usually happen over the course of months or years rather than minutes," he explains.
Bipolar disorder can be genetic
Individuals who have a first-degree relative with bipolar disorder are more likely to develop the illness themselves. "If a parent has bipolar disorder, for example, his or her children have about a 10 percent chance of developing bipolar disorder," Dr. Bryan Bruno, medical director at Mid City TMS, tells SheKnows.
It's often misdiagnosed
"Misdiagnosis is common in people who have bipolar disorder," Bruno says. As an example, he notes that when patients are in stages of mania, they can be misdiagnosed with ADHD because of symptoms like racing thoughts, restlessness and being easily distracted.
The symptoms can worsen during pregnancy
Bruno tells SheKnows that many women's symptoms worsen when they're pregnant. "Approximately 45 percent of women with bipolar disorder have a relapse of either a depressive or manic episode during pregnancy," he says.
The hallmark of bipolar is mania
Although people often associate mood swings and irritability with bipolar disorder, Dr. Leesha M. Ellis-Cox, a psychiatrist, tells SheKnows that these symptoms are more commonly seen in a different mental illness: major depressive disorder. "The hallmark of bipolar disorder is mania," she explains. "A manic episode is required to make a diagnosis of bipolar disorder."
Ellis-Cox says symptoms of mania include extremely high energy, inflated self-esteem (grandiosity), racing thoughts, decreased need for sleep, risky behaviors such as spending sprees and promiscuity, talking faster than normal (pressured speech) and an increase in goal-directed activities.
It's dangerous to treat bipolar with only antidepressants
Ellis-Cox explains that treating bipolar disorder with only antidepressants can trigger a manic episode. A mood stabilizer is "the mainstay of pharmacologic treatment used for bipolar disorder" and all other medications are supplemental.
Bipolar disorder is frequently misdiagnosed as depression
"Research demonstrates that there is an average of eight years before an individual with bipolar disorder receives an accurate diagnosis," Ellis-Cox says. It's common for bipolar patients to initially be diagnosed with major depressive disorder. They're put on antidepressants, which can make symptoms worse.
There are support groups for those with bipolar disorder
If you or a loved one has bipolar disorder, it's important to remember that you're not alone. "One of the best ways to find relief from any mental health issue is to get help and support from those around you who have been there," Raichbach says. Groups like Depression and Bipolar Support Alliance and Emotions Anonymous offer a community that can provide support and encouragement.
A version of this story was published June 2018.
Before you go, check out our favorite and most affordable mental health apps:
More Stories from Health & Wellness
When (& How) You Should Talk to Your Kids About Masturbation
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by Nicole Lapin
CDC Says 'Highly Transmissible' Coronavirus Strain Will Be Dominant In the U.S. By March
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How to Unapologetically Love Your Body During Diet Season
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Watching Bridgerton With Your Teens? A Drive-By Sex Ed Guide To Make It Less Cringe

redpajama_set_name: RedPajamaCommonCrawl


Sometimes we use the word "just" when describing who we are and what we do. This podcast shares why our accomplishments, no matter big or small, should ever be described as "just" anything. Everything we do is far bigger than just.


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text:
Reprezentacja Antyli Holenderskich w piłce siatkowej kobiet to narodowa reprezentacja tego kraju, reprezentująca go na arenie międzynarodowej.

Osiągnięcia

Mistrzostwa Ameryki Północnej
  3. miejsce - 1971

Igrzyska Ameryki Środkowej i Karaibów
  3. miejsce - 1959

Udział i miejsca w imprezach

Mistrzostwa Ameryki Północnej

Igrzyska Ameryki Środkowej i Karaibów

Piłka siatkowa na Antylach Holenderskich
Antyle Holenderskie
Reprezentacje narodowe Antyli Holenderskich

redpajama_set_name: RedPajamaWikipedia


UbiCast will be at Learntec, in Karlsruhe (Germany) between the 24th and 26th of January 2017. Every year, over 7,250 HR decision-makers and IT managers from all over the world come to the trade fair and convention in Karlsruhe, where they can find out about the possibilities of digital learning from over 240 exhibitors.
Where? Karlsruhe Trade Fair Centre.
We will wait for you at booth G43, Hall 1!


text:
GOP convention protest rules are too tight
Published Mar. 29, 2012
The rules Tampa has proposed for regulating protests at this summer's Republican National Convention in many ways expand the public's ability to exercise the right of free speech. Groups of every size would find it easier and cheaper to legally demonstrate on public property. And the city would underscore its duty to ensure that all voices are heard, regardless of the message. But while these proposed changes generally bring the city's outdated restrictions on public gatherings into the modern era, they over-reach in the name of security.
To its credit, the city has worked in good faith with civil rights leaders and downtown-area residents and businesses to balance the unprecedented demands for convention security with the public's right to assemble and speak. And by putting a proposal on the table months before the convention's scheduled start Aug. 27, officials have provided enough time to embrace what makes sense and discard what does not. Tampa's City Council should address several troubling concerns when it takes its first look at the proposed ordinance on Thursday.
The so-called "Clean Zone" where restrictions on speech and movement would take effect is too large. It extends up to 2 miles in some directions from the convention site at the Tampa Bay Times Forum, reaching deep into the northern neighborhoods of Tampa Heights and Ybor City and across the Hillsborough River into West Tampa. It is farfetched to imagine these areas will see much impact from the convention. The city should narrow the Clean Zone footprint to make better use of its limited security and other resources and to minimize the hassle on area residents and businesses.
The one-hour time limit for any public gathering is too restrictive and nearly impossible to fairly enforce. It invites the move-along mentality that protesters and police have used in other cities as a pretext to spark a confrontation. The city can better accomplish the goal of giving competing groups equal time by better managing park space over the four-day event. The city also would outlaw too much in too many parts of town. Carrying slingshots or blasting caps into the crowd is one thing. But the list of items prohibited in the all-encompassing Clean Zone is broad enough to include breathing masks that many use to control a respiratory illness. And the measure would outlaw citywide such innocuous things as squirt guns and hair spray.
City officials say the intent is to keep these devices from harming people or property. That's fine, but the ordinance is written too broadly, and it leaves too much discretion to the police, many of whom will be extra-duty officers drawn from jurisdictions outside Tampa.
The measure creates more opportunities to be seen and heard, and it cuts some of the existing red tape. But it crosses the line in places by seeking to pre-empt almost any conceivable act that could spark a disturbance. The council should work with Mayor Bob Buckhorn's administration on a revised approach that better balances rights with security.
Up next:If law goes, opponents responsible for fixing health care


text:
It's not too late to prune your roses, but it might be too early
Marisa Thompson
Southwest Yard and Garden
Question: Is it too late to prune my roses?
Pat J., Artesia
Answer: No, it's not too late. There's more harm in pruning roses too early than too late. That's because pruning stimulates a flush of new growth, which is wonderful — as long as you're past the risk of more hard freezes in your area. That new green growth is especially prone to frost damage, and damaged branches would then need to be pruned back again. The optimal window for most rose pruning is two to four weeks before your expected last frost. Even when pruned at this time, an abnormal late freeze can do considerable damage to your rose plants, but it is much less likely.
According to https://www.plantmaps.com/, the average last frost in Las Cruces is early April, in Artesia and Roswell it's mid-April, Los Lunas and Albuquerque early May, and Taos early June. Many successful gardeners do holiday pruning, meaning in Las Cruces they might prune their roses around Valentine's Day, St. Patrick's Day in Albuquerque, and Tax Day in Taos.
I see two drawbacks to waiting until your area's expected last frost date to prune your roses:
You'll likely have to prune off some new growth, which will include some new buds. You'll still get flowers, but it'll take more time for new buds and flowers to develop.
You might wait so long that new flowers are already opening, and then you put off pruning until next year, like I do.
Many roses are impressively drought- and heat-tolerant. There are also flowering shrubs in the Rosaceae family that are native to New Mexico and are great options for low-water landscaping. Native or not, now is a great time to add a mulch (like woodchips, leaf litter, pine needles, etc.) under your bushes and around trees, and as a moisture-holding layer on the tops of your veggie beds.
I subscribe to a new newsletter from Divine Earth, a commercial pruning and landscape company in Albuquerque (https://divineearthnm.com/), and I was delighted to get their quick and clever tips on rose pruning:
ditch the fabric and rock
add some compost and mulch
prune most roses back hard.
I love that three out of their four "rose pruning tips" are about growing roses more sustainably. Any time is a great time to remove artificial weed barriers in ornamental landscapes. The trouble with them is that they're either too flimsy to keep weeds from popping through, or they do a great job keeping weeds under control, but at the expense of keeping water and air from moving down into the soil. That means the soil and ornamental plant roots in those areas are sure to suffer. And, after time, soil that blows in on top of that barrier can harbor weed seeds that grow just fine on top of the fabric or plastic. Landscape designers and installers across the region are officially giving up on weed barriers in urban landscapes.
It's also always a great time to pull back landscape rock from around the base of roses and other ornamental plants and replace it with a nice, thick top layer of woody, fibrous mulch. If you compost your kitchen and garden scraps, you can sprinkle a layer of that on top with your mulch. Check out NMSU Extension Guides H-110, "Backyard Composting" and H-164, "Vermicomposting," for helpful info for beginner composters.
Water your established roses to a depth of 18 to 24 inches about once every two to four weeks in spring, depending on your soil type and environmental conditions like wind and temperature. When temperatures get higher, it's recommended that we water our roses and other shrubs every one to three weeks from May through October. For newly planted roses, water will be needed more frequently and always to the same depth.
Special pruning note for climbing roses: wait until after bloom to prune. That's because climbing roses bloom on one- and two-year-old wood, so if you prune before bloom you'll be cutting away the current season's flowers. Other roses bloom on new branches that develop in spring.
Roses can be pruned back harder than most people think, so don't be shy. If you're worried, try your own mini trial at home by pruning some branches lightly, pruning some branches back severely, and leaving some alone. Take photos before pruning, after pruning, and throughout the season and share them with me on social media: @NMDesertBlooms. NMSU Extension Guide H-165, "Growing Roses," has lots more information about rose types and their care.
The Albuquerque Rose Society offers free pruning demos each year, and several are still coming up this season: March 14, 15, 21, and 22 from 10 a.m. to 3 p.m. (http://www.albuquerquerose.com/). I'll attend one of these sessions and post video to the blog version of this column next week (https://nmsudesertblooms.blogspot.com/).
For more gardening information, including decades of archived Southwest Yard & Garden columns, visit the NMSU Extension Horticulture page (http://desertblooms.nmsu.edu/), follow us on social media (@NMDesertBlooms), or contact your County Extension office (https://aces.nmsu.edu/county).
Marisa Thompson, PhD, is the Extension Horticulture Specialist for New Mexico State University and is based at the Agricultural Science Center at Los Lunas.
More Southwest Yard and Garden:
Best plant books for New Mexico gardeners and enthusiasts
When to prune trees in New Mexico
Inspiration from the Extension Master Gardener program


During the academic year 1940-1941, several giants of analytic philosophy congregated at Harvard, holding regular private meetings, with Carnap, Tarski, and Quine. Carnap, Tarski, and Quine at Harvard allows the reader to act as a fly on the wall for their conversations. Carnap took detailed notes during his year at Harvard. This book includes both a German transcription of these shorthand notes and an English translation in the appendix section. Carnap's notes cover a wide range of topics, but surprisingly, the most prominent question is: If the number of physical items in the universe is finite, what form should scientific discourse take? This question is closely connected to an abiding philosophical problem: What is the relationship between the logico-mathematical realm and the material realm? Carnap, Tarski, and Quine's attempts to answer this question involve issues central to philosophy today.This book focuses on three such issues: nominalism, the unity of science, and analyticity. In short, the book reconstructs the lines of argument represented in these Harvard discussions, discusses their historical significance (especially Quine's break from Carnap), and relates them when possible to contemporary treatments of these issues.
Carnap's Surprising Views on the Axiom of Infinity.Gregory Lavers - 2016 - Metascience 25 (1):37-41.
Can First-Order Logical Truth Be Defined in Purely Extensional Terms?Gary Ebbs - 2014 - British Journal for the History of Philosophy 22 (2):343-367.
Carnap and the Invariance of Logical Truth.Steve Awodey - 2017 - Synthese 194 (1):67-78.
Le rejet de la distinction de l'analytique et du synthétique par Alfred Tarski.Roger Schmit - 2008 - Archives de Philosophie 4 (4):609-629.
The Place of Quine in Analytic Philosophy.Scott Soames - forthcoming - In Gilbert Harman & Ernest Lepore (eds.), A Companion to W. V. O. Quine.
Putting the Bite Back Into 'Two Dogmas'.Paul Gregory - 2003 - Principia 7 (1-2):115-129.
Carnap and Quine on Empiricism.Robert Almeder - 1997 - History of Philosophy Quarterly 14 (3):349 - 364.


text:
Home / Books / 8 Young Adult eBooks Under $7.99
8 Young Adult eBooks Under $7.99
Posted by: Lisa Parkin March 12, 2012	1 Comment
Below are some awesome young adult ebooks coming at ya! Please note that many of these deals are temporary and may not stay around forever…or even more than a few days or weeks!
Being frugal has it's rewards, my friends. 🙂
The Frugal Fantasy Reader is a Read.Breathe.Relax. original feature that lists the latest fantasy and young adult Kindle book deals. Who says you can't read good books on a budget?
Young Adult eBooks
1. Airel (The Airel Saga, Book 1) by Aaron Patterson & Chris White
Price: $2.99; Free to borrow for Amazon Prime members
Description: "Airel is a story about an angel who falls so deeply in love with a woman that he chooses to fall from heaven to be with her. She gives birth to a daughter in Arabia, 1250BC. The girl is pursued ferociously, relentlessly by an enemy in the deepest darkness. In present day Boise, Idaho is just a girl: Airel. She's just your average high school student…who turns out to be anything but average. It's because of who she is, because of her ancestry, because of her lineage. Past and present crash in on each other in the final pages as what has been twisted comes dangerously unraveled."
2. Allegiance (Harlequin Teen) by Kayla Cluver
Description: "He couldn't help his past any more than he could help the way those intense, deep blue eyes pierced me and held me captive.
An eighteen-year-old queen in love with the enemy as their countries pass the point of no return…
Bound to a man she cannot love, Queen Alera of Hytanica must forget Narian, the young man who holds her heart. For Narian is destined to conquer Hytanica at the behest of his master, the powerful magic-user known as the Overlord. Alera doesn't truly believe Narian will fight against Hytanica—until Cokyrian troops attack with Narian commanding the charge.
Faced with the greatest betrayal a heart can know, Alera must set aside personal feelings and lead her kingdom through its darkest time. And when all hope, will and courage seem lost, she must find strength and remember that even the blackest night must have a dawn…."
3. Miss Peregrine's Home for Peculiar Children by Ransom Riggs
Description: "A mysterious island.
An abandoned orphanage.
A strange collection of very curious photographs.
It all waits to be discovered in Miss Peregrine's Home for Peculiar Children, an unforgettable novel that mixes fiction and photography in a thrilling reading experience. As our story opens, a horrific family tragedy sets sixteen-year-old Jacob journeying to a remote island off the coast of Wales, where he discovers the crumbling ruins of Miss Peregrine's Home for Peculiar Children. As Jacob explores its abandoned bedrooms and hallways, it becomes clear that the children were more than just peculiar. They may have been dangerous. They may have been quarantined on a deserted island for good reason. And somehow—impossible though it seems—they may still be alive.
A spine-tingling fantasy illustrated with haunting vintage photography, Miss Peregrine's Home for Peculiar Children will delight adults, teens, and anyone who relishes an adventure in the shadows."
4. Inside: Inside OutOutside In by Maria V. Snyder – This means BOTH Books
Description: "The world of Inside is simple. Do your job, stay out of the way and don't dream of anything better. Because as every Scrub knows, there are no other options.
Until Trella—the Queen of the Pipes, as some call her—gets involved with a revolution that will rock her world….
Trella was just doing a favor for a friend—her only friend. Hiding an injured man from the Pop Cops seemed easy enough—though dangerous. But then she discovered that the myths of Outside might be real….
Being Inside's hero only left Trella with more work. Ducking those responsibilities, she continued to explore her stark world—and found something she never expected. Strangers. From Outside…
5. Born at Midnight (Shadow Falls) by C.C. Hunter
Description: "One night Kylie Galen finds herself at the wrong party, with the wrong people, and it changes her life forever. Her mother ships her off to Shadow Falls—a camp for troubled teens, and within hours of arriving, it becomes painfully clear that her fellow campers aren't just "troubled." Here at Shadow Falls, vampires, werewolves, shapshifters, witches and fairies train side by side—learning to harness their powers, control their magic and live in the normal world.
Kylie's never felt normal, but surely she doesn't belong here with a bunch of paranormal freaks either. Or does she? They insist Kylie is one of them, and that she was brought here for a reason. As if life wasn't complicated enough, enter Derek and Lucas. Derek's a half-fae who's determined to be her boyfriend, and Lucas is a smokin' hot werewolf with whom Kylie shares a secret past. Both Derek and Lucas couldn't be more different, but they both have a powerful hold on her heart.
Even though Kylie feels deeply uncertain about everything, one thing is becoming painfully clear—Shadow Falls is exactly where she belongs…"
6. The Scorpio Races by Maggie Stiefvater
Description: "It happens at the start of every November: the Scorpio Races. Riders attempt to keep hold of their water horses long enough to make it to the finish line. Some riders live. Others die.
At age nineteen, Sean Kendrick is the returning champion. He is a young man of few words, and if he has any fears, he keeps them buried deep, where no one else can see them.
Puck Connolly is different. She never meant to ride in the Scorpio Races. But fate hasn't given her much of a chance. So she enters the competition — the first girl ever to do so. She is in no way prepared for what is going to happen."
7. Graceling by Kristin Cashore
Description: "Katsa has been able to kill a man with her bare hands since she was eight—she's a Graceling, one of the rare people in her land born with an extreme skill. As niece of the king, she should be able to live a life of privilege, but Graced as she is with killing, she is forced to work as the king's thug. When she first meets Prince Po, Graced with combat skills, Katsa has no hint of how her life is about to change. She never expects to become Po's friend. She never expects to learn a new truth about her own Grace—or about a terrible secret that lies hidden far away . . . a secret that could destroy all seven kingdoms with words alone. With elegant, evocative prose and a cast of unforgettable characters, debut author Kristin Cashore creates a mesmerizing world, a death-defying adventure, and a heart-racing romance that will consume you, hold you captive, and leave you wanting more."
8.The Emerald Talisman (Talisman Series, Book 1) by Brenda Pandos
Description: "You can run from your destiny, but you can't hide.
To be normal, sixteen-year-old Julia Parker would shed her empathic gift in a second. Life has been difficult since her mother's mysterious disappearance ten years earlier – an event she witnessed, but can't remember. Julia's situation becomes more complicated after a near death experience from a blood thirsty stalker. As high school students go missing it is clear there is a connection to her own experience–past and present. Someone has to stop the madness and a chance encounter with a creepy psychic foretells that only Julia is the key to stopping the madness, but it may require the life of the one she loves. "
I hope you love these awesome young adult ebooks! If you have any suggestions, I'd love to hear your recommendations in the comments!
Kindle deals The Frugal Fantasy Reader young adult ebooks	2012-03-12
+Lisa Parkin
Tagged with: Kindle deals The Frugal Fantasy Reader young adult ebooks
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About Lisa Parkin
I'm a hardcore lover of young adult fiction and have been reviewing books since 2011. Other interests include Downton Abbey, heat lightning storms, Harry Potter land and (begrudingly) one orange tabby.
April 2016 Young Adult Book Deals
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Bookishlilly
Inside Out was great and I hate that I still have not gotten around to reading Outside In. I also loved Born at Midnight!
Truly Bookish
New HuffPost Article: Top 10 Young Adult Books of 2013
Top Ten Books on My Spring and Summer 2013 TBR List
Know Your (Hunger Games) Meme


text:
Last Updated: Friday, 10 June, 2005, 14:35 GMT 15:35 UK
Attenborough given Order of Merit
The Order of Merit is restricted to only 24 British members
TV naturalist Sir David Attenborough has been invested with one of Britain's most coveted honours - the Order of Merit - at Buckingham Palace.
Sir David said he thought he had been chosen because he had reached "so many people through television".
Former Commons Speaker Baroness Betty Boothroyd also received the order.
This special award from the Queen is for people who have shown exceptional merit in learning, the arts, science, literature or the public services.
'Greatly honoured'
It is restricted to 24 British members and entitles those who have been awarded it to use the letters OM after their names.
The broadcasting career of Sir David, 78, has spanned more than 50 years, with acclaimed series including The Living Planet, The Trials of Life and The Life of Mammals.
The 13-part series Life on Earth, written and presented by Sir David in 1978, was alone watched by an estimated 500 million people worldwide.
In 1965 he was appointed controller of BBC2 and was responsible for the introduction of colour television into Britain. From 1969 to 1973 he was the BBC's director of programmes.
Writers' prize
Speaking after receiving the award during a private audience with the Queen, Sir David said: "How could anyone believe they actually deserved something like this?"
Lady Boothroyd, who was the first woman Speaker of the Commons, said earlier that she was "greatly honoured" at the award.
"I would like to think [the honour] is in recognition of my services to Parliament over many years and, of course, my Speakership of the House of Commons."
Andrea Levy, author of the novel Small Island, was presented with the 2005 Commonwealth Writers' Prize.
Queen's honour for Attenborough
28 Apr 05 | UK
Guide to the Honours
12 Jun 04 | UK
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How Could The Chattanooga Jihadi Been Stopped?
Posted by Bill O'Neill | Jul 19, 2015 | Uncategorized | 0 |
The FBI knew he was in Jordan for seven months in 2014.
That alone should have put him on the Terrorist Watch List. That alone should have caused the FBI, ICE and the CIA to have alerted the Hixon Tenn. Chief of Police to get a warrant to keep tabs on him. Plus, he was in the Middle East several other times.
Lets see. Muslim. Has a beard. Been in a Middle Eastern Country at some time during the last three years. Bought several guns. Went target shooting. American citizen. So far no red flags. Hated America. Hated Americans. Was he a Jihadi? Of course.
America doesn't have to incarcerate all Muslims like it did after Pearl Harbor to the Japanese to protect American's from Muslim Jihadi's. American citizens have the right to be protected from government. That includes Muslims. The Constitution makes it necessary for the government to get a warrant to search a suspected drug dealers car even if they aren't a citizen.
But the Constitution is not a suicide pact. No warrant is needed to investigate someone. The Federal Government is intercepting telephone calls and has the power to access just about any aspect of anyone's life which they have been doing for years as we know because of whistle-blowers like Edward Snowden. That seems like a massive violation of the powers of government but the time to argue that has passed. It's a fact. Governments cannot be trusted which is why the Iranian Nuclear Treaty isn't worth much as a way to protect Americans. Even worse, it's an agreement between seven different governments including Iran.
The Chattanooga Jihadi wasn't invisible. He could have been stopped or at least slowed sown if he thought he was under investigation by the local police. He should have been on the terrorist Watch List. Maybe he was but maybe the FBI was just too busy on July 17th, 2015. That's another reason the FBI, ICE and the CIA should have notified the local police or sheriff that there was a young man in Hixon with a beard who is on the Watch List. None of that happened. Perhaps the President didn't want to alarm Americans that there are Jihadis among us so he winked about protecting people from Jihadis. Just don't believe there was nothing that could have been done. Five U.S. Marines and a U.S. Sailor are dad because something that should have been done wasn't done.
PreviousIs The Confederate Flag Property? If So It's Protected By The Constitution. Can The Government Take Your Confederate Flag? Of course. The government has the power to take just about whatever it wants BUT it must pay for it.
NextAfter Chattanooga Why Aren't American Mosques Teaching Against Jihad?
Trump Trumps Liberalism. . . . The Diminution Of American Liberal Ideology. . . . Thoughts On Hatred White People
Libya is America's Friend
Dangerous Terrorist Inside the Gates
British And American Governments Kept 2,000 NAZI Missile Strikes Secret For 60 Years ………….. So Don't Trust The CDC To Tell The Truth About Ebola In America Either
— Exposing Hidden Government Practices since 1994
Jalen Hurts Lacks Intellectual Speed…. He Fails To Act Fast So He Has To Scramble To Compensate But He's Good Enough
People Are Not Poor Because Other's Are Rich… People Are Poor Because …..


Home › Forums › Announcements › Toy Soldier Standard Issue Field Kits in store NOW!
Toy Soldier Standard Issue Field Kits in store NOW!
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The Toy Soldier Standard Issue Field Kits have arrived at TSU-HQ!
These will replace the Toy Soldier Pack.
What does the Standard Issue Field Kit consist of?
Easy. 2 Shoulder patches, 1 Logo Patch, 1 Wristband, 1 Pin, and a 2oz tin to keep them all in, all for just $25!
If you've already got all the patches you could possibly need, you can get the tin by itself for $6.
And while we've still got enough, we'll chuck in some propaganda stickers/business cards to help get you started brainwashing the masses!
And yeah, I know the pictures are rather shoddy, but there'll be better images up tomorrow for the entire store.


(Bloomberg) -- Lyft Inc.'s IPO filing omits details necessary for investors and analysts to create a financial model of the company, according to an analyst who specializes in tech listings.
Nine days away from its Nasdaq debut, Lyft's executives are in Boston on Wednesday as part of a nationwide pitch to potential investors for its initial public offering. The share sale could raise up to $2.4 billion at a valuation north of $20 billion for the second-largest ride-hailing company. But buyers will need to fill in some blanks for themselves, said Rett Wallace, CEO of Triton Research Inc.
"It's never good when companies decide to not be straightforward about the math of their business, and these guys told us almost nothing you need to build a model," he said in a phone interview.
Citing Netflix Inc. and Spotify Technology SA as examples of more transparent firms, Wallace said Lyft "had an opportunity to be forthcoming" in its metrics, such as separating the acquisition costs of drivers versus passengers, disclosing churn rates or breaking out scooters and bikes.
One reason Triton is bearish about Lyft's missing metrics is the management compensation structure, which is based on two triggers -- a sale or IPO.
Triton, whose research focuses on upcoming technology IPOs, scores Lyft below its average for other listings in the sector. Initial public offerings since January 2018 with similar Triton scores underperformed through March 1, according to the firm's data.
Not everyone is viewing the company so cautiously. Within a day of starting investor meetings, Lyft already had enough commitments to sell all 31 million shares it's offering in the IPO. But it remains to be seen what price the investors are willing to pay.
D.A. Davidson gave Lyft its first buy rating this morning, citing impressive market share gains within the U.S. as demand for ride-sharing continues to grow. Analyst Tom White awarded a $75 price target, 15 percent above the midpoint of Lyft's $62 to $68 IPO price range. IPOs typically price at a 10 percent to 15 percent discount to the company's valuation.
A spokesperson for Lyft declined to comment.


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Making Monster Girls 6
For Science!
By: Eric Vall
Narrated by: Alex Perone, Marissa Parness
Series: Making Monster Girls, Book 6
Categories: Science Fiction & Fantasy, Fantasy
Narrated by: Alex Perone,Marissa Parness
Making Monster Girls 5: For Science!
The duchess has believed my con, and now she is almost mine. As soon as I make her my monster-girl, my coup of this city will begin. Then I will make every aristocrat my monster-girl and rule this place.
Duel your enemy and kill him. Take his assets, including his wives, as your own. Grow your estate and become the most powerful warrior mage this world has ever seen.
Princess Master 2
A few weeks ago, I was just a plumber. Now, I'm the husband of two insanely gorgeous, magical princesses, and I'm apparently also the hero of legend. So, even though evil minions and bastards keep trying to kill me, I can't complain too much, especially since I'm supposed to marry more princesses, bind them to me in a kinky ritual, and become their master...starting with a shy but sexy as hell mermaid.
Dragon Emperor 13: From Human to Dragon to God
Evan's royal campaign to win over the people of Rahma has taken him to the northern peninsula. And straight to the gates of the underwater city of Pullis. The Green Glass Sect is up to no good under the sea, and it's up to Evan and his party to save the merfolk from traitors and the ever-corrupting presence of miasma.
under the sea!
Soul Gem Collector 4
By: Logan Jacobs
I'm playing a dangerous game working for a crime syndicate while trying to overthrow them from within. And when the crime syndicate is working with our country's mortal enemies to destroy our kingdom, and will do anything to keep that information private, I have tread very carefully. But thanks to my talented and beautiful girlfriends, and my ability to capture souls in gems to cast magical spells, nothing is going to stop me.
gem collecter is my new favorite series
By STEVEN B COTRONE on 12-07-20
Remnant: Book 3
Remnant, Book 3
By: Randi Darren
Narrated by: Andrea Parsneau
Steve doesn't care who he was. He knows more than enough to realize it doesn't matter at all. Now living in what had once been the Creeplands and maintaining a thriving farm there, they are under constant siege from the Creep itself. It's still better than life in Lamals. And that's just how it is. After taking over the Citadel, removing Lynn from her place of power, stopping the Creep's advance, and starting to take over part of the Creeplands, he was certainly making a difference for himself, humans, and men everywhere.
more pieces to the puzzle
Dinosaur World 3
Portals continue to open faster and faster, spewing more and more aggressive dinosaurs across the world, and the situation has gone from bad to worse. Cities are out of supplies, small towns are being wiped out by the vicious reptiles, and it's taking everything they have for the military to maintain any semblance of order.Amid all the carnage and chaos, Jason, Becka, and Hae-won must journey north to rescue Becka's mother. Navigating safely through bloodthirsty dinosaurs and the worst humanity has to offer will be no easy task.
they finally left the starting zone
Dragon Conjurer
I was just your average college anthropology student. I went to class, worked my minimum-wage job, and studied for exams. Until I discovered that monsters are real and that I can summon the most powerful of them all: dragons. Now, I'm a Dragon Conjurer working for a secret agency/academy that protects the world from monsters behind the scenes, and two of the most beautiful girls I've ever met are in my squad and super into me. And it seems that they don't mind sharing. Life is about to become awesome.
Is Eric even trying anymore?
By kevin on 12-29-20
Dragons of Asgard
Narrated by: Christopher Boucher, Jessica Threet
My name is Volrath, and I am an Aesir of Asgard. I have no family name to speak of, but then I discovered I could tame, train, and breed the great dragons that are feared throughout Asgard. Now that I have this incredible power, it is my mission to scour the nine realms in search of more dragons to add to my menagerie. I am joined by a beautiful Light Elf and a powerful half-Valkyrie sorceress, and these women want to bind themselves to me and bear my children.
Mildly annoying if you know norse mythology
Monster Girl Islands 6
Narrated by: Daniel Wisniewski, Marissa Parness
Ben is really coming into his title of Draco Rex. Not only has he discovered a new species of dragon, but now Jemma has bonded to the baby fire-breather named Tirian. And there are more dragons out there just waiting to be found.
Great book
I am so close to triumph I can taste it, and everything is within my grasp. A bevy of scientifically engineered monster girls. The destruction of the Matriarchy. Wealth and power beyond reckoning. I just need to make The Duchess mine. For science.
the story gets better and better
By leonardo bastos on 08-23-20
Built to Serve
A Catgirl Harem Adventure (Build-a-Catgirl, Book 3)
By: Simon Archer
Narrated by: Melissa Moran
Ever since he bought his first catgirl in a pawnshop, Clark's life has gone all sorts of sideways...but in a good way. And, if his catgirls had their way, he'd be on top of the world. There's just one problem. Omnicorp has one last-ditch effort to try to take back not just his catgirls, but all the catgirls. And as a lover of catgirls, Clark can't let that happen.
Dragon Emperor 12
From Human to Dragon to God
Evan and his party continue on to the peninsula of Rahma, but an ultimatum from the king hangs over Evan's head. If he can't get the Lord of Atheson to swear fealty to the crown, then he has been tasked with breaking the peninsula off the continent and letting it sink to the bottom of the ocean.
needs more content less sex longer books
By Dragon on 11-01-20
T.A.P.: Origins
T.A.P., Book 1
By: Cebelius -
Narrated by: Daniel Wisniewski, Rebecca Woods
Can't win for losin'...As any gambler will tell you, luck runs hot and cold. For my many sins I've been forced to scrape a life out of poker games and side-jobs on the fringes of civil society. I thought I hit it big when I raked 50-grand off the table at a roadhouse in Texas. It is amazing what a win can cost you. Now, on the run from a drug cartel headed by an unstoppable juggernaut, pursued by a shape-shifting killer, and framed for attempted murder, I have to protect a girl with a bounty on her head.
Excellent from start to finish!
By Mr. Lee on 12-24-20
I was already a target, but now that I've created a harem of fiercely loyal and beautiful monster girls, the matriarchy won't rest until I'm destroyed. But I and the wonderful monster girls won't go down without a fight, and we will topple their disgusting system.
By James Jadoobirsingh on 05-29-20
Herald of Shalia 2
By: Tamryn Tamer
Narrated by: Amber Lee Connors, Kieran Flitton
Sebastian Frost was a man with an interesting reputation. He'd killed 12 giants, eight heroes, a duke, and even a prince. But nobody ever talked about any of that. All they talked about was the deviant, disgusting, detestable Herald of Shalia that shamelessly laid with elves. That was because in the strange world based on game mechanics Frost found himself in, laying with elves was somehow treated like laying with animals. Naturally, they weren't calling him Herald Frost the giant killer....
Love this series
By Winston Smith on 12-15-20
Incubus: Publisher's Pack
Incubus, Books 1-2
By: Brandon Varnell
Narrated by: Gabriel Michael, Rebecca Woods
Contains books one and two of Incubus, an urban harem fantasy series.
Forge of the Gods 3
Forge of the Gods, Book 3
Narrated by: Ron McKenzie-Lefurgey
Cameron's third year as the only male demigod of his generation starts with everything going right, only to be touched by tragedy. His mentor is dead, and everyone thinks she took her own life...but Cameron knows better. And he won't stop until he clears Sarah's name and, heck, maybe do a bit more than that. When you're a Greek demigod, you can do more about death than whine about it. You can go right down into the underworld and take the matter right to Hades.
Everything is unfolding exactly as I have planned it: I have created an entire legion of monster girls, conquered our duchy, and freed the enslaved men.
Now all that remains is to defeat the queen, create more monster girls, and liberate the entire realm.
It won't be easy, though, since the queen has sent her most powerful generals and armies to garrison the towns on our route to the royal capital, and we'll have to fight our way through the opposition.
But why kill the generals and their armies when I could capture and turn them into monster girls that love me, too?
©2020 Eric Vall (P)2020 Eric Vall
Metal Mage 15
What listeners say about Making Monster Girls 6
excellent acting
my favorite so far. kind of curious where book 5 is though. love this series.
Where is volume 5
This is getting ridiculous 1st that other book about the Capturing of princesses to save the world It went from 1 to 3 with no real rhyme or reason. A Whole pieces of the story alludes me now then it's very irritating. I want to know what happened in volume 5 so I can get a better grasp on what happened on volume 6 so for the love of God Someone fix this mess and put the books out in order.
I like it the story continues in a interesting direction, the Narrators did a great job narrating has usual. audible goofed where is book 5?
Troy Stevens
The last few books have been a disappointment.
I was really hopeful that we would have less Male Ego Stroking as the series progress like with Metal Mage, but it has just gotten worse. If all the women Charles transforms only love him where does that leave all the other males? When he used the blood of another male for the process and failed I thought he might think to blend it with his own for a different outcome. How is he to satisfy his "thousands of women"? Are the rest of the men just expected to become eunuchs? Is Charles getting dumber as he gains more power? He does sound like he is getting crazier. Seriously, goes right up to confront the Big Bad Woman in the final battle instead of using the power of invisibility of one Ashy-Blonde Catgirl and just subduing her? Totally could have come up with a better way to bring the battle about without being stupid. I really hate it when authors turn their smart MCs into complete morons. I expect some level of disbelief to be expected, but seriously, there is a limit. Please also discontinue the use of the phases "Buckets of cum" & "Gallon of semen". We all know that even an individual that has not had release in a long time is not going to produce that much and each time I hear the phrases it makes my ears bleed. The overall story is not so bad, but the teenage adolescent descriptions are grating.
this story is one of the best in the series and looking forward to the rest of the books
Shouou
Disappointed for a reason Spoiler
So I enjoyed most of the series so far. But Rayburns blood only works? Disappointed.
The Battles have begun
Its really starting to getting heated up. Looking forward to the next book. Keep up the great work
Bizzget
awesome simply awesome
love the script, the author and the voice actors........ NAIL it. the flow the chemistry. it's like old time radio i would enjoy with my great grandmother. please keep up the great work. can't get enough!
Great narration by both of them but i have to say that the voices of all of the girls are just amazing and can't wait to hear them again


In this episode I explain the correlation with the Law of attraction and letting go, I give practical advice on developing will power and explain my views on Aliens, Ets, and spirituality. We go deeeep. If you want to ask a question feel free to follow me on instagram below and I will update you for the next one.


text:
New laws aim for Medicaid reform
LITTLE ROCK � At the same time that the state Department of Human Services is preparing for a massive expansion of health care coverage under the federal Affordable Care Act, the agency is also gearing up to implement new state laws intended to overhaul the existing Medicaid program.
Legislators �pushed the envelope for Medicaid reform this session,� said Sen. David Sanders, R-Little Rock.
Most notable among the reform measures is Act 1499, sponsored by Sanders, which calls for the creation of the office of Medicaid Inspector General within the governor�s office.
The Medicaid inspector general�s office will investigate suspected fraud and abuse in the state Medicaid program, in conjunction with the attorney general�s Medicaid Fraud Control Unit, federal officials, state prosecutors and local, state and federal law enforcement agencies. The office also will seek to recover tax dollars lost to waste, fraud and abuse.
The inspector general will be appointed by the governor and will act independently of DHS, reporting directly to the state�s chief executive. The annual salary for the position for the next fiscal year cannot exceed $150,000.
The inspector�s general�s staff will include a chief counsel, whose starting pay cannot exceed $120,000. The rest of the staff will consist of 33 current DHS employees who will be shifted to the inspector general�s office from DHS� Program Integrity Unit.
�Then we have to look at where the IG will be housed, whether it�s in our building or another building,� said DHS spokeswoman Amy Webb. �The administrative stuff related to the IG will be funded through DHS, simply because it�s much easier to fund those things through our already-set-up procedures and budget rather than start up a whole new state agency.�
McDaniel and DHS officials support the change.
�Medicaid fraud enforcement has been one of my priorities since taking office,� McDaniel said Tuesday in an email to the Arkansas News Bureau. �To be sure, we need all the help we can get in that regard. We look forward to working with the new inspector general in finding ways to complement each other�s roles and missions.�
Webb said, �A program the size of Medicaid, we think it would benefit from a high-profile, administrative-level look. Our folks work very hard in the area of waste, fraud, abuse, misuse, that sort of thing, but we think this office will strengthen that effort.�
Sanders said DHS� Program Integrity Unit �is buried within the Medicaid bureaucracy. What this does, it sets it out. It is independent � and there is a high level of reporting to the legislative branch.�
Webb said the savings generated by the office should eclipse the cost of creating two new positions with six-figure salaries.
�The Medicaid program is a $5 billion program, and even if they just found 1 percent additional in fraud, that would definitely pay for itself,� she said.
The law also creates a new criminal offense, health care fraud, which can range from a Class A misdemeanor to a Class A felony, depending on the amount of Medicaid money that a person obtains through fraudulent means.
Other new Medicaid reform laws include:
� Act 1265 by Sen. Jonathan Dismang, R-Beebe, which requires DHS to track the reported incomes of people applying for Medicaid and determine whether they match the federal government�s records of their incomes.
� Act 1336 by Rep. Josh Miller, R-Heber Springs, which requires in-home caregivers who are paid through Medicaid to undergo drug tests and criminal background checks. A caregiver who tests positive for illegal drugs or has been convicted of a felony or �a crime involving moral turpitude or dishonesty� will be ineligible to receive further Medicaid money.
� Act 1436 by Sanders, which requires DHS once a year to a submit a list of all Medicaid providers in the state to the state Department of Finance and Administration. DF&A will then determine if any of the providers have not paid their state income taxes, and if so those providers will lose their contracts with DHS unless they can show good cause for non-payment.
� Act 1352 by Rep. Bruce Westerman, R-Hot Springs, which allows �ambulatory surgery centers� to perform procedures that can be done on an outpatient basis and to be reimbursed through Medicaid at a rate equal to 80 percent of the Medicare reimbursement rate for such procedures.
The reforms passed in the same legislative session in which lawmakers approved the so-called �private option� for extending health care coverage by using federal Medicaid dollars to subsidize private insurance for the state�s working poor.
Meanwhile, the phased-in implementation of Gov. Mike Beebe�s Payment Improvement Initiative is continuing. The initiative calls for health care providers in certain areas of care to be paid for bundled episodes of care instead of being paid for every service provided.
Also, DHS officials recently announced that the agency will contract with consultant Tom Emerick to conduct a review of the state Medicaid program, with an eye toward increasing collaboration between the public and private sectors.
Emerick is a former vice president of global benefit design for Walmart Stores who is credited with reducing the company�s health care costs.
�Think of it as a three-legged stool,� said Sanders, who supported the private option and pushed for the contract with Emerick. �You�ve got one leg, the reform; second leg, the private option; third leg is the long-term structural health care reform that we�re talking about � taking reforms that are happening in private markets right now and then taking those and implementing them at the state level. That�s never been done before.�


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I. Neuron Structure & Function
1. The Neuron
2. Ion Movement
3. Membrane Potential
4. The Membrane at Rest
5. Postsynaptic Potentials
6. Action Potentials
7. Voltage Clamp
II. Neuronal Communication
8. Synapse Structure
9. Neurotransmitter Synthesis and Storage
10. Neurotransmitter Release
11. Neurotransmitter Action: Ionotropic Receptors
12. Neurotransmitter Action: G-Protein-Coupled Receptors
13. Neurotransmitter Clearance
14. Drug and Toxin Effects
15. Epigenetics
III. Nervous System Organization
16. Anatomical Terminology
17. External Brain Anatomy
IV. Sensory Systems
18. General Principles of Sensory Systems
19. Vision: The Retina
20. Vision: Central Processing
21. Somatosensory Systems
22. Touch: The Skin
23. Touch: Central Processing
24. Taste
V. Motor System
25. Spinal Control of Movement
26. Planning of Movement
27. Basal Ganglia
28. Execution of Movement
VI. Behavior
29. Neural Control of Stress
30. HPA Axis
31. HPG Axis
32. Sexual Differentiation
33. Masculinizing Effects of Estrogen
34. Motivation and Reward
35. Social Bonding
36. Studying Fear
37. Post-Traumatic Stress Disorder
Additional Review Answers
Images of Animations
Foundations of Neuroscience
26 Planning of Movement
Video Version
There are a number of steps that must take place for voluntary movement to occur. Assessment of the surrounding environment and the body's location in space, followed by determining what action is appropriate, and then initiating that action. We will first focus on the cortical regions involved in planning of voluntary movement.
After work, you sit down on the couch to watch one episode of your favorite show. As the end credits appear, you realize it is now time to head to your study space and start working on class. To do this, you need to leave the couch, grab your computer from the table, get your coffee from the kitchen and head to a different room. All of these voluntary movements take a great deal of processing by the brain. You must assess your surrounding environment and your body's location in it, determine which actions need to be completed, and then actually initiate those actions. In this chapter we will focus on how the planning of voluntary movement occurs.
Cortical Anatomy
Much of the cortex is actually involved in the planning of voluntary movement. Sensory information, particularly the dorsal stream of the visual and somatosensory pathways, are processed in the posterior parietal lobe where Visual, tactile, and proprioceptive information are integrated.
Figure 26.1. Information from multiple sensory systems are processed in the posterior parietal lobe. Projections are sent from the primary somatosensory and primary visual cortices. 'Posterior Parietal by Casey Henley is licensed under a Creative Commons Attribution Non-Commercial Share-Alike (CC BY-NC-SA) 4.0 International License.
Connections from the posterior parietal lobe are then sent to both the premotor regions and the prefrontal cortex. The prefrontal cortex, which is located in the front of the brain in the frontal lobe, plays an important role in higher level cognitive functions like planning, critical thinking, and understanding the consequences of our behaviors. The premotor area lies just anterior to the primary motor cortex. This region helps plan and organize movement and makes decisions about which actions should be used for a situation.
Figure 26.2. Sensory information from the posterior parietal is processed in the prefrontal cortex and premotor area, both located in the frontal cortex. These areas then send information to the primary motor cortex located in the precentral gyrus. 'Motor Regions' by Casey Henley is licensed under a Creative Commons Attribution Non-Commercial Share-Alike (CC BY-NC-SA) 4.0 International License.
View the primary motor cortex using the BrainFacts.org 3D Brain
View the premotor cortex using the BrainFacts.org 3D Brain
View the prefrontal cortex using the BrainFacts.org 3D Brain
Role of Premotor Area
The premotor regions do send some axons directly to lower motor neurons in the spinal cord using the same pathways as the motor cortex (see Execution of Movement chapter). However, the premotor cortex also plays an important role in the planning of movement. Two experimental designs have demonstrated this role. Monkeys were trained on a panel that had one set of lights in a row on top and one set of buttons that could also light up in a row on the bottom. The monkeys would watch for a top row light to turn on. This would indicate that within a few seconds, the button directly below would light up. When the button turned on, the monkeys were supposed to push the button.
Therefore, there were two light triggers in the experiment. The first required no motor movement from the monkey but did give the monkey information about where a motor movement would be needed in the near future. The second required the monkey to move to push the button. When brain activity was measured during this study, neurons in the premotor cortex became active when the first light trigger turned on, well before any movement actually took place (Weinrich and Wise, 1928).
Figure 26.3. (A) Monkeys were trained to use a light panel. When lit, a light located in the top row informed the monkey that the button directly below would light up soon. Shortly after one of the top row lights turned on, the button directly below it would turn on, and the monkey would need to push that button for a reward. (B) When no lights are lit, premotor neurons fire at a baseline rate, and the monkey does not move. Neurons located in the premotor cortex increase action potential firing rate when the top row light turns on, even though the monkey makes no movement. The firing stops shortly after the monkey moves to push the bottom button after it turns on. (Based on Weinrich and Wise, 1928) 'Light Panel Experiment' by Casey Henley is licensed under a Creative Commons Attribution Non-Commercial Share-Alike (CC BY-NC-SA) 4.0 International License.
In another experiment, people were trained to move their fingers in a specific pattern. Cerebral blood flow was then measured when they repeated the finger pattern and when they only imagined repeating the finger pattern. When the movement was only imagined and not actually executed, the premotor regions along with parts of the prefrontal cortex were activated (Roland, et al, 1980).
Figure 26.4. People were trained to move their fingers in a pattern. When the pattern was repeated, brain activity was seen in the primary motor cortex, along with the premotor area and prefrontal cortex. When the pattern was only imagined, and no finger movement took place, brain activity was seen in the premotor area and prefrontal cortex. (Based on Roland, et al, 1980) 'Finger Movement Experiment' by Casey Henley is licensed under a Creative Commons Attribution Non-Commercial Share-Alike (CC BY-NC-SA) 4.0 International License.
These studies show that the premotor cortex is active prior to the execution of movement, indicating that it plays an important role in the planning of movement. The posterior parietal, prefrontal, and premotor regions, though, also communicate with a subcortical region called the basal ganglia to fully construct the movement plan. The basal ganglia are covered in the next chapter.
Sensory information is processed in the posterior parietal before being sent to motor regions of the brain
The prefrontal cortex and premotor cortex are critical for creating a movement plan
Test Yourself!
Video Version of Lesson
Roland PE, Larsen B, Lassen NA, Skinhøj E. Supplementary motor area and other cortical areas in organization of voluntary movements in man. J Neurophysiol. 1980 Jan;43(1):118-36. doi: 10.1152/jn.1980.43.1.118. PMID: 7351547.
Weinrich M, Wise SP. The premotor cortex of the monkey. J Neurosci. 1982 Sep;2(9):1329-45. doi: 10.1523/JNEUROSCI.02-09-01329.1982. PMID: 7119878; PMCID: PMC6564318.
Previous: Spinal Control of Movement
Next: Basal Ganglia
Foundations of Neuroscience by Casey Henley is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.