text:
\section{Introduction}
\pagenumbering{arabic}

Given a closed manifold $M^{n}$ endowed with a Riemannian metric
$g_{0}$, the Ricci flow determines a one parameter family of
metrics $g(t)$ via the geometric evolution equation
\begin{align}\label{Ricci equation}
\frac{\partial g}{\partial t}=-2Ric(g)
\end{align}
with initial condition \begin{displaymath} g(0)=g_{0}. \end{displaymath} Short time
existence and uniqueness for solution to the Ricci flow was first
shown in Hamilton's seminal paper \cite{Ha1}, using the Nash-Moser
theorem, and shortly after by DeTurck in \cite{De} who
substantially simplified the proof. Strictly related to the Ricci
flow is the evolution equation
\begin{align}\label{Ricci norm}
\frac{\partial g}{\partial t}=\frac{2}{n}rg-2Ric(g)
\end{align}
where $r=\frac{\int_{M}Rd\mu}{\int_{M}d\mu}$, which is called
normalized Ricci flow since has the remarkable property to
preserve the volume of the initial Riemannian manifold. As shown
in \cite{Ha1}, the evolution equations \ref{Ricci equation} and
\ref{Ricci norm} differ only by a change of scale in space and a
change of parametrization in time. Since its introduction, the
Ricci flow has been a very effective tool for studying the
topology of manifolds. In the most of first applications
\cite{Ha1}, \cite{Ha2}, \cite{Ha3}, \cite{Hu}, the normalized flow
is shown to converge to a canonical metric, e.g. in \cite{Ha1}
Hamilton proves that the normalized flow on any closed
$3$-manifold of positive Ricci curvature exists for all time and
converges to a positive constant sectional curvature metric. In
this sense, the Ricci flow may be regarded as a natural homotopy
between a given metric of positive Ricci curvature and a canonical
metric of constant sectional curvature in the same volume class.
Analogously, whenever the Ricci flow converges, it can be
considered as a natural homotopy between the initial metric and
the limit metric that is necessarily Einstein \begin{displaymath}
Ric(g_{\infty})=\frac{1}{n}\frac{\int_{M}R_{\infty}d\mu_{\infty}}{\int_{M}d\mu_{\infty}}g_{\infty}.
\end{displaymath} It is then natural to use the Ricci flow to study
properties of geometrical meaningful objects, such as the
eigenvalues of the Laplacian. In this paper we study, under a
technical assumption, the behavior of the spectrum of the
Laplacian when we deform a given initial metric by the
Ricci flow.\\
Throughout the paper, let $M^{n}$ be a closed manifold of
dimension $n$, and $C^{\infty}(S^{+}_{2}TM)$ the space of smooth
Riemannian metrics on $M^{n}$. For $g\in C^{\infty}(S^{+}_{2}TM)$,
let $\Delta_{g}=Tr_{g}\nabla^{2}$ be the Laplacian operator on
$C^{\infty}(M)$ and \begin{displaymath}
Spec(g)=\left\{0=\lambda_{0}(g)<\lambda_{1}(g)\leq\lambda_{2}(g)\leq...\leq\lambda_{k}(g)\leq...\right\}
\end{displaymath}
the spectrum of $\Delta_{g}$.\\
Given $g_{0}\in C^{\infty}(S^{+}_{2}TM)$, let $g(t)$ be the smooth
$1$-parameter family of metrics who solves the Ricci flow with
initial metric $g_{0}$. We can then regard each eigenvalue
$\lambda(g(t))$ as a function of one real parameter, and try to
study its evolution at least locally in time. This problem is
clearly related to the general problem concerning the behavior of
the spectrum under a suitable deformation $g(t)$ of $g_{0}$ in
$C^{\infty}(S^{+}_{2}TM)$. In this direction a classical result is
the following
\begin{theorem}
For $g\in C^{\infty}(S^{+}_{2}TM)$ and $h\in C^{\infty}(S_{2}TM)$,
let $g(t)=g+th$, $\left|t\right|<\epsilon$ for sufficiently small
$\epsilon>0$. Let $\lambda$ be an eigenvalue of $\Delta_{g}$ with
multiplicity $l$. Then there exist $f_{i}(t)\in C^{\infty}(M)$,
i=1,...,l, such that
\begin{enumerate}
\item $\lambda_{i}(t)$ and $f_{i}(t)$ depend real analytically on t,
$\left|t\right|<\epsilon$, for each $i=1,...,l$,
\item $\Delta_{g(t)}f_{i}(t)+\lambda_{i}(t)f_{i}(t)=0$, for each
$i=1,...,l$ and $t$,
\item $\lambda_{i}(0)=\lambda$, $i=1,...,l$, and
\item $\left\{f_{i}(t)\right\}^{l}_{i=1}$ is orthonormal with respect
to $\left\langle, \right\rangle_{g(t)}$ for each t.
\end{enumerate}
\end{theorem}
The above theorem is due to Berger \cite{Berg1}, and it is one of
the first attempt in studying the behavior of the spectrum under a
perturbation of the metric. On the other hand Bando and Urakawa
have extended the above theorem to a family of metrics which
depends real analytically on time, see \cite{Ura1}. Unfortunately,
the theorems of Berger and Bando-Urakawa does not apply directly
to a smooth $1$-parameter family of metrics generated by solving
an IVP of the Ricci flow type. Since the Ricci flow equation is a
parabolic equation for the metric see \cite{Ha1}, its solutions
are expected to not depend real analytically on the time variable.
More precisely, the Ricci flow equation implies that the scalar
curvature function of the evolving metric satisfies an heat-type
scalar equation. Hence if the solution flow were analytic in time,
we could analytically continue backwards in time, which implies
that the associated scalar curvature
equation admits solution for negative time.\\
In what follows we then assume that, under a Ricci flow
deformation $g(t)$ of a given initial metric, a result of the
Berger-Bando-Urakawa type holds, that is we assume the existence
and $C^{1}$-differentibility
of the elements $\lambda_{i}(t)$ and $f_{i}(t)$.\\
We remark that the problem of the spectrum variation under a
deformation of the metric given by a parabolic equation seems not
to be presented explicitely before. However in the celebrated
paper \cite{Perelman}, a similar geometric problem is cosidered
from a different point of view. In this paper Perelman introduces
a riemannian functional whose gradient flow is the Ricci flow
modulo diffeomorphisms. It turns out that this functional is the
lowest eigenvalue $\lambda_{1}$ of the operator $-4\Delta+R$,
therefore proving that the quantity $\lambda_{1}(g(t))$ is
nondecreasing along the flow. For the details and applications of
this important observation we refer to the original paper.

\section{Variation Formulas}
Let $(M^{n},g(t))$ be a solution of the Ricci flow on the maximal
time interval $[0,T)$ and consider the associated Rayleigh-Ritz
quotient \begin{displaymath} \lambda(t)=\frac{\int_{M}{\left|\nabla
f_{t}\right|}^{2}d\mu_{t}}{\int_{M}f^{2}_{t}d\mu_{t}}, \end{displaymath}
which defines the evolution of an eigenvalue of the Laplacian
under the flow. We can then consider the change rate of any
eigenvalue taking the time derivative of the Rayleigh-Ritz
quotient which defines it. For simplicity we consider normalized
eigenfunctions i.e. \begin{equation}\label{marchia}
\int_{M}f_{t}d\mu=0,\\
\int_{M}f^{2}_{t}d\mu=1, \end{equation} then
\begin{align} \notag
\frac{d\lambda}{dt}=&\int_{M}\frac{d}{dt}{\left|\nabla
f\right|}^{2}d\mu+\int_{M}{\left|\nabla
f\right|}^{2}\frac{d}{dt}d\mu \\ \notag
=&\int_{M}\frac{d}{dt}(g^{ij})\nabla_{i}f\nabla_{j}fd\mu+2\int_{M}\left\langle
\nabla f^{'},\nabla f\right\rangle d\mu-\int_{M}R{\left|\nabla
f\right|}^{2}d\mu \\ \notag
=&2\int_{M}g^{ik}g^{jl}R_{kl}\nabla_{i}f\nabla_{j}fd\mu+2\int_{M}\left\langle
\nabla f^{'},\nabla f\right\rangle d\mu-\int_{M}R{\left|\nabla
f\right|}^{2}d\mu \\ \notag =&2\int_{M}Ric(\nabla f,\nabla
f)d\mu+2\int_{M}\left\langle \nabla f^{'},\nabla f\right\rangle
d\mu-\int_{M}R{\left|\nabla f\right|}^{2}d\mu,
\end{align}
for the time derivative of the volume element see \cite{Ha1}. Now,
using \ref{marchia} we get the following two integrability
conditions
\begin{align}
&\int_{M}f^{'}d\mu=\int_{M}fRd\mu \label{integrability1}\\
&\int_{M}f^{'}fd\mu=\frac{1}{2}\int_{M}f^{2}Rd\mu\label{integrability2}.
\end{align}
Finally, by \ref{integrability2} we have
\begin{align} \notag
2\int_{M}\left\langle \nabla f^{'},\nabla f\right\rangle
d\mu=&-2\int_{M}f^{'}\Delta f d\mu \\ \notag =&2\lambda
\int_{M}f^{'}f d\mu=\lambda \int_{M}f^{2}R d\mu. \\ \notag
\end{align}
We have thus proved the following proposition
\begin{proposition}\label{evolution1}
Let $(M^{n},g(t))$ be a solution of the unnormalized Ricci on the
smooth manifold $(M^{n},g_{0})$. If $\lambda(t)$ denotes the
evolution of an eigenvalue under the Ricci flow, then \begin{displaymath}
\frac{d\lambda}{dt}=\lambda \int_{M}f^{2}R
d\mu-\int_{M}R{\left|\nabla f\right|}^{2}d\mu+2\int_{M}Ric(\nabla
f,\nabla f)d\mu. \end{displaymath} where $f$ is the associated normalized
evolving eigenfunction.
\end{proposition}
As shown below, an analogous equation holds for the normalized
Ricci flow
\begin{proposition}\label{evolution2}
Let $(M^{n},g(t))$ be a solution of the normalized Ricci on the
smooth manifold $(M^{n},g_{0})$. If $\lambda(t)$ denotes the
evolution of an eigenvalue under the normalized Ricci flow, then
\begin{displaymath} \frac{d\lambda}{dt}=-\frac{2}{n}r\lambda+\lambda
\int_{M}f^{2}R d\mu-\int_{M}R{\left|\nabla
f\right|}^{2}d\mu+2\int_{M}Ric(\nabla f,\nabla f)d\mu. \end{displaymath}
where $f$ is the associated normalized evolving eigenfunction.\\
\end{proposition}
\begin{proof}
In the normalized case, the integrability conditions read as
follows
\begin{align} \label{bella1}
&\int_{M}f^{'}d\mu=\int_{M}fRd\mu, \\ \label{bella2}
&2\int_{M}ff^{'}d\mu=\int_{M}f^{2}Rd\mu-r,
\end{align}
since \begin{displaymath}
\frac{d}{dt}d\mu=\frac{1}{2}Tr_{g}(\frac{2}{n}rg-2Ric)d\mu=(r-R)d\mu.
\end{displaymath} We can then write
\begin{align}\notag
\frac{d\lambda}{dt}=&\int_{M}\frac{d}{dt}{\left|\nabla
f\right|}^{2}d\mu+\int_{M}{\left|\nabla
f\right|}^{2}\frac{d}{dt}d\mu \\ \notag
=&\int_{M}\frac{d}{dt}(g^{ij})\nabla_{i}f\nabla_{j}fd\mu+2\int_{M}\left\langle
\nabla f^{'},\nabla f\right\rangle d\mu\\ \notag
&+\int_{M}(r-R){\left|\nabla f\right|}^{2}d\mu \\ \notag
=&-\int_{M}g^{ik}g^{jl}(\frac{2r}{n}g_{kl}-2R_{kl})\nabla_{i}f\nabla_{j}fd\mu+2\int_{M}\left\langle
\nabla f^{'},\nabla f\right\rangle d\mu\\ \notag
&+\int_{M}(r-R){\left|\nabla f\right|}^{2}d\mu \\ \notag
=&2\int_{M}Ric(\nabla f,\nabla
f)d\mu-\frac{2r}{n}\int_{M}\left|\nabla
f\right|^{2}d\mu+2\lambda\int_{M}ff^{'}d\mu\\ \notag
&+\int_{M}(r-R){\left|\nabla f\right|}^{2}d\mu \\ \notag
=&2\int_{M}Ric(\nabla f,\nabla
f)d\mu-\frac{2r}{n}\lambda+\lambda\left(\int_{M}f^{2}Rd\mu-r\right)+r\lambda\\
\notag &-\int_{M}R\left|\nabla f\right|^{2}d\mu \\ \notag
=&-\frac{2}{n}r\lambda+\lambda \int_{M}f^{2}R
d\mu-\int_{M}R{\left|\nabla f\right|}^{2}d\mu +2\int_{M}Ric(\nabla
f,\nabla f)d\mu.
\end{align}
\end{proof}

It is now interesting to write down proposition \ref{evolution1}
and proposition \ref{evolution2} in some remarkable particular
case.
\begin{corollary}\label{surface}
Let $(M^{2},g(t))$ be a solution of the unnormalized Ricci flow on
a closed surface, then \begin{displaymath}
\frac{d\lambda}{dt}=\lambda\int_{M}f^{2}Rd\mu. \end{displaymath}
\end{corollary}
\begin{proof}
In dimension $n=2$ we have \begin{displaymath} Ric=\frac{1}{2}Rg, \end{displaymath} then
\begin{align}\notag
\frac{d\lambda}{dt}&=\lambda \int_{M}f^{2}R
d\mu-\int_{M}R{\left|\nabla f\right|}^{2}d\mu+2\int_{M}Ric(\nabla
f,\nabla f)d\mu\\ \notag
&=\lambda\int_{M}f^{2}Rd\mu-\int_{M}R{\left|\nabla
f\right|}^{2}d\mu+\int_{M}R{\left|\nabla f\right|}^{2}d\mu \\
\notag &=\lambda\int_{M}f^{2}Rd\mu.
\end{align}
\end{proof}
\begin{corollary}\label{variation1}
Let $(M^{2},g(t))$ be a solution of the normalized Ricci flow on a
closed surface with normalized initial metric, then
\begin{align}\notag
\frac{d\lambda}{dt}&=\lambda\int_{M}f^{2}Rd\mu-r\lambda=\lambda\int_{M}R(f^{2}-1)d\mu
\\ \notag
\end{align}
\end{corollary}
\begin{proof}
Obvious.
\end{proof}
\begin{remark}
Because of the Gauss-Bonnet theorem the above variation formula
can be written as \begin{displaymath}
\frac{d\lambda}{dt}=\lambda\int_{M}f^{2}Rd\mu-\lambda4\pi\chi(M),
\end{displaymath} where $\chi(M)$ is the Euler characteristic of the surface.
\end{remark}

Let us now consider the behavior of the spectrum when we evolve an
initial metric that is homogeneous. As shown in \cite{Ha1}, the
Ricci flow preserves the isometries of the initial Riemannian
manifold. We conclude that the evolving metric remains homogeneous
during the flow. This important observation implies the following
\begin{corollary}\label{homogeneous1}
Let $(M^{n},g(t))$ be a solution of the unnormalized Ricci on the
smooth homogeneous manifold $(M^{n},g_{0})$. If $\lambda(t)$
denotes the evolution of an eigenvalue under the Ricci flow, then
\begin{displaymath} \frac{d\lambda}{dt}=2\int_{M}Ric(\nabla f,\nabla f)d\mu.
\end{displaymath}
\end{corollary}
\begin{proof}
Since the evolving metric remains homogeneous, the thesis follows
from proposition \ref{evolution1} and the fact that an homogeneous
manifold has constant scalar curvature.
\end{proof}
\begin{corollary}
Let $(M^{n},g(t))$ be a solution of the normalized Ricci on the
smooth homogeneous manifold $(M^{n},g_{0})$. If $\lambda(t)$
denotes the evolution of an eigenvalue under the Ricci flow, then
\begin{displaymath}
\frac{d\lambda}{dt}=-\frac{2}{n}R\lambda+2\int_{M}Ric(\nabla
f,\nabla f)d\mu. \end{displaymath}
\end{corollary}
\begin{proof}
In the homogeneous case the average scalar curvature can be
written as \begin{displaymath}
r=\frac{\int_{M}R d\mu}{\int_{M}d\mu}=R.\\
\end{displaymath}
\end{proof}

\section{Applications}
In this section we show how the variational formulas can be
effectively applied to derive some interesting properties of the
evolving spectrum. First we concentrate on $3$-manifolds, next we
discuss the Riemannian
surface and in particular the $2$-sphere.\\
Let $(M^{3},g_{0})$ be a closed three manifold with positive Ricci
curvature. It is well known that the Ricci flow on such manifold
exists on a limited maximal time interval $[0,T)$, see \cite{Ha1};
we shall then show that the eigenvalues of the Laplacian diverges
as $t\rightarrow T$. The result is independent of the technical
assumption explained in the
introduction.\\
\begin{proposition}
Let $(M^{3},g(t))$ be a solution of the Ricci flow on a closed
$3$-manifold whose Ricci curvature is positive initially, then
\begin{displaymath} lim_{t\rightarrow T}\lambda(t)=\infty. \end{displaymath}
\end{proposition}
\begin{proof}
On a closed manifold $M^{n}$, for any smooth functions $f$ holds
the celebrated Reilly formula \begin{displaymath} \int_{M}\left|\nabla\nabla
f\right|^{2}d\mu+\int_{M}Ric(\nabla f,\nabla
f)d\mu=\int_{M}(\Delta f)^{2}d\mu. \end{displaymath} Since \begin{displaymath}
\left|\nabla\nabla f\right|^{2}\geq\frac{1}{n}(\Delta f)^{2},
\end{displaymath} we have the inequality \begin{equation} \label{basta}
\frac{n-1}{n}\int_{M}(\Delta f)^{2}d\mu\geq\int_{M}Ric(\nabla
f,\nabla f)d\mu. \end{equation} For any solution of the Ricci flow on a
closed three manifold with positive Ricci curvature there exists
$\epsilon>0$ such that the condition \begin{displaymath} Ric\geq\epsilon Rg
\end{displaymath} is preserved along the flow, see \cite{Ha1}. Therefore
\begin{displaymath} \frac{2}{3}\lambda^{2}(t)\geq\int_{M}Ric(\nabla f,\nabla
f)d\mu\geq\epsilon\int_{M}R\left|\nabla
f\right|^{2}d\mu\geq\epsilon R_{min}(t)\lambda(t), \end{displaymath} and then
\begin{displaymath} \lambda(t)\geq\frac{3}{2}\epsilon R_{min}(t). \end{displaymath} The
thesis follows since \begin{displaymath} lim_{t\rightarrow T}R_{min}(t)=\infty,
\end{displaymath} see again \cite{Ha1}.
\end{proof}

\begin{proposition}
Let $(M^{3},g(t))$ be a solution to the Ricci flow on a closed
manifold whose Ricci curvature is positive initially. Then there
exists $\overline{t}\in [0,T)$ depending on $g_{0}$ such that for
each $t\in[\overline{t},T)$ the eigenvalues of the Laplacian are
increasing.
\end{proposition}
\begin{proof}
Let $0<\epsilon\leq\frac{1}{3}$ be a constant such that \begin{displaymath}
Ric\geq\epsilon Rg \end{displaymath} is preserved under the flow. By
proposition \ref{evolution1} we can then write
\begin{align}\notag
\frac{d\lambda}{dt}&\geq\lambda \int_{M}f^{2}R
d\mu-\int_{M}R{\left|\nabla
f\right|}^{2}d\mu+2\epsilon\int_{M}R\left|\nabla f\right|^{2}d\mu
\\ \notag
&\geq\lambda\left\{R_{min}(t)+(2\epsilon-1)R_{max}(t)\right\}.
\end{align}
As proved in \cite{Ha1}, for each $\eta>0$, we can find
$T_{\eta}\in[0,T)$ such that for $t\in [T_{\eta},T)$ \begin{displaymath} R\geq
(1-\eta)R_{max} \end{displaymath} hence the proposition follows easily.
\end{proof}

\begin{proposition}
Let $(M^{3},g(t))$ be a solution of the Ricci flow on a closed
homogeneous $3$-manifold whose Ricci curvature is nonnegative
initially, then the eigenvalues of the Laplacian are increasing.
\end{proposition}
\begin{proof}
Since in dimension three the nonnegativity of the Ricci tensor is
preserved under the Ricci flow, the thesis follows easily from
corollary \ref{homogeneous1}.
\end{proof}
\begin{proposition}
Let $(M^{n},g(t))$ be a solution of the Ricci flow on a closed
homogeneous $n$-manifold whose curvature operator is nonnegative
initially, then the eigenvalues of the Laplacian are increasing.
\end{proposition}
\begin{proof}
As shown in \cite{Ha2}, in any dimension the nonnegativity of the
curvature operator is preserved along the Ricci flow. Since the
nonnegativity of the curvature operator implies the nonnegativity
of the Ricci tensor the thesis follows from corollary
\ref{homogeneous1}.
\end{proof}

\begin{proposition}
Let $(M^{n},g(t))$ be a solution of the Ricci flow on a closed
homogeneous manifold, then \begin{displaymath}
\frac{d\lambda}{dt}\leq2\frac{(n-1)}{n}\lambda^{2}. \end{displaymath}
\end{proposition}
\begin{proof}
By \ref{basta} \begin{displaymath} \int_{M}Ric(\nabla f,\nabla
f)d\mu\leq\frac{n-1}{n}\int_{M}(\Delta f)^{2}, \end{displaymath} we have thus
\begin{align}\notag
\frac{d\lambda}{dt}&=2\int_{M}Ric(\nabla f,\nabla
f)d\mu\leq2\frac{(n-1)}{n}\int_{M}(\Delta f)^{2} \\ \notag
&=2\frac{(n-1)}{n}\lambda^{2}.
\end{align}
\end{proof}

We conclude studying the spectrum of Riemannian surface evolving
under the flow. Our result is the following
\begin{proposition}\label{monotone}
Let $(M^{2},g_{0})$ be a closed surface with nonnegative scalar
curvature, then the eigenvalues of the Laplacian are increasing
under the Ricci flow.
\end{proposition}
\begin{proof}
Under the unnormalized Ricci flow on a surface, we have \begin{displaymath}
\frac{\partial}{\partial t}R=\Delta R+R^{2}, \end{displaymath} see
\cite{Chow1}. By the scalar maximum principle, the nonnegativity
of the scalar curvature is preserved along the flow. We conclude
using corollary \ref{surface}.
\end{proof}
Let us now consider the normalized flow on a surface and the
associated variation of the eigenvalues of the Laplacian. Let
$(\mathbb S^{2},g)$ be a closed Riemannian manifold diffeomorphic to
the two dimensional sphere. In \cite{Chow2}, Chow proved that the
normalized Ricci flow on $(\mathbb S^{2},g)$ exists for all time and
converges to a smooth metric $g_{S}$ of constant curvature, that
is the standard metric. On the other hand, a classical result of
Hersch \cite{Hersch} states that $g_{S}$ maximizes $\lambda_{1}$
among all the Riemannian metrics of the same volume. In
particular, if $g_{S}$ is the standard metric on $\mathbb S^{2}$
normalized to volume one, we have \begin{displaymath} \lambda_{1}(g_{S})=8\pi,
\end{displaymath} see \cite{Gal}. We then conjecture that the smallest
positive eigenvalue of the Laplacian $\lambda_{1}(t)$ is
monotonically increasing along the Ricci flow $g(t)$ on
$\mathbb S^{2}$.
\begin{conjecture}
Let $(\mathbb S^{2},g_{0})$ be a topological sphere endowed with a
smooth metric normalized to volume one and let $g(t)$ be the
unique solution of the normalized Ricci flow
\begin{align}\notag
&\frac{\partial g}{\partial t}=(r-R)g \\ \notag &g(0)=g_{0}.
\end{align}
Then $\lambda_{1}(g(t))$ is increasing for all $t\in [0,\infty)$
and converges to $\lambda_{1}(g_{S})=8\pi$.
\end{conjecture}
 Actually the convergence of $\lambda_{1}(g(t))$ to
$\lambda_{1}(g_{S})=8\pi$ as $t\rightarrow\infty$ follows easily
from the fact that $g(t)\rightarrow g_{S}$ in the
$C^{\infty}$-topology, see \cite{Chow2}. In fact, it is simple to
prove that the spectrum of the Laplacian depends continuously on
the metric even with respect to the $C^{0}$-topology, see
again \cite{Gal}.\\
 Unfortunately, there are some difficulties in proving the above
conjecture. It is in fact well known that the standard metric on
$\mathbb S^{2}$ does not maximize $\lambda_{2}$, see \cite{Nad}. Hence
it is not possible to prove in general that the variation formula
of corollary \ref{variation1} is positive on $\mathbb S^{2}$. This
suggests that the "shape" of the evolving first eigenfunction of
the Laplacian plays a fundamental role in proving such kind of
conjecture.

\section{examples}
In this section we determine the behavior of the evolving spectrum
on self-similar solutions to the Ricci flow, which are called
\emph{Ricci soliton}. Let $(M^{n},g(t))$ be a solution to the
Ricci flow with initial condition $g(0)=g_{0}$. The solution
$g(t)$ is called Ricci soliton if there exist a smooth function
$\sigma(t)$ and a $1$-parameter family of diffeomorphisms
$\left\{\psi_{t}\right\}$ of $M^{n}$ such that
\begin{align}\label{ricci soliton}
g(t)=\sigma(t)\psi^{*}_{t}(g_{0})
\end{align}
with $\sigma(0)=1$ and $\psi_{0}=id_{M^{n}}$. Now, taking the time
derivative in \ref{ricci soliton} and evaluating the result for
$t=0$, we get that the metric $g_{0}$ satisfies the identity
\begin{align}\label{lie soliton}
-2Ric(g_{0})=2\epsilon g_{0}+L_{X}g_{0},
\end{align}
where $\epsilon=\frac{\sigma^{'}(0)}{2}$ and $X$ is the vector
field on $M^{n}$ generated by $\left\{\psi_{t}\right\}$ for $t=0$.
Conversely, given a metric $g_{0}$ which satisfies \ref{lie
soliton} there exist $\sigma(t)$ and $\left\{\psi_{t}\right\}$
such that $g(t)=\sigma(t)\psi^{*}_{t}(g_{0})$ is a solution to the
Ricci flow with initial condition $g(0)=g_{0}$. In particular we
can choose $\sigma(t)=1+2\epsilon t$ and $\left\{\psi_{t}\right\}$
as the $1$-parameter family of diffeomorphisms generated by the
vector fields \begin{displaymath} Y_{t}=\frac{1}{\sigma(t)}X, \end{displaymath} see
\cite{Chow1}. In summary, each self-similar solution to the Ricci
flow can be written in the canonical form \begin{displaymath} g(t)=(1+2\epsilon
t)\psi^{*}_{t}(g_{0}). \end{displaymath} We then say that the soliton is
expanding, shrinking, or steady, if
$\epsilon>0$, $\epsilon<0$, or $\epsilon=0$ respectively.\\
Now, let $(M,g)$ and $(N,h)$ be two closed Riemannian manifolds
and \begin{displaymath} \varphi:(M,g)\longrightarrow(N,h) \end{displaymath} an isometry,
we then have the following remarkable identity
\begin{align}\notag
\Delta_{g}\circ\varphi^{*}=\varphi^{*}\circ\Delta_{h}
\end{align}
see \cite{Gal}. Given a diffeomorphism $\psi:M^{n}\longrightarrow
M^{n}$ we have that \begin{displaymath} \psi:(M^{n},\psi^{*}g)\longrightarrow
(M^{n},g) \end{displaymath} is an isometry, we conclude that
$(M^{n},\psi^{*}g)$ and $(M^{n},g)$ have the same spectrum \begin{displaymath}
Spec(g)=Spec(\psi^{*}g) \end{displaymath} with eigenfunctions
$\left\{f_{k}\right\}$ and $\left\{\psi^{*}f_{k}\right\}$
respectively. We have thus that if $g(t)$ is a Ricci soliton on
$(M^{n},g_{0})$ then
\begin{align}\label{spec soliton}
Spec(g(t))=\frac{1}{\sigma(t)}Spec(g_{0}),
\end{align}
that is $Spec(g(t))$ is "proportional" to the initial spectrum
$Spec(g_{0})$ and shrinks, is stationary, or expands depending on
wheter $\epsilon$ is positive, zero, or negative. By \ref{spec
soliton}, we can also compute explicitely the change rate of each
eigenvalue of the Laplacian on a soliton \begin{displaymath}
\frac{d\lambda}{dt}=-\frac{\sigma^{'}(t)}{\sigma(t)^{2}}=-\frac{2\epsilon}{(1+2\epsilon
t)^{2}}. \end{displaymath} It could be now interesting to combine the above
formula with proposition \ref{evolution1} and try to study some
geometrical aspect of the soliton. This will be studied elsewhere.
\section{Remark}
The variation formula of proposition \ref{evolution1} also appears
in an equivalent form in \cite{Qian}, see section 7 theorem 7.3,
where it is derived as a consequence of a general formula for the
variation of the $L^{2}$-norm of a time dependent function on a
manifold evolving under the Ricci flow.

\section{Acknowledgements}
The author would like to thank Professor Claudio Procesi for
suggesting the study of the Ricci flow and Professor Stefano
Marchiafava for many valuable advices and suggestions. In
particular, Professor Stefano Marchiafava first pointed out to the
author the problem of the spectrum variation under a Ricci
deformation of the metric.

redpajama_set_name: RedPajamaArXiv


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The start of the Ballenger Creek Linear Trail on Kingsbrook Drive is shown. The top new trail priority for the county's Bicycle and Pedestrian Advisory Committee will be the Frederick and Pennsylvania Railroad Trail.
Staff photo by Bill Green
County plans multiple trail options
A trail connecting northern Frederick with Walkersville and Woodsboro will be Frederick County's next trail project, followed by trails that will ultimately connect the C&O Canal towpath with the center of the county, and the town of Thurmont to the Catoctin Furnace area in Cunningham Falls State Park.
For years, the county has focused on finishing the Ballenger Creek Trail, which cuts through the neighborhood south of Frederick from near Ballenger Creek Elementary School to New Design Road.
But with that project nearing completion, the county will look to three other trails, although the three have varying timetables for completion.
The county's first priority as determined by the Bicycle and Pedestrian Advisory Committee will be the Frederick and Pennsylvania Railroad Trail, which would stretch from the end of a trail in the city of Frederick along East Street to north of Monocacy Boulevard, then head out to Walkersville before ending in Woodsboro.
The 10-mile stretch would follow the Pennsylvania Railroad tracks out to Woodsboro. It would be built on an old rail bed until it reaches Md. 26, at which point it would run along the existing tracks to Woodsboro.
The county is in the process of seeking money from the Maryland Department of Transportation to fund the design and construction of the trail, said Ron Burns, transportation engineering manager for the county's Division of Planning and Permitting.
On Wednesday, the county received an $80,000 grant from the Transportation Planning Board of the Metropolitan Washington Council of Governments, for the first phase of its second trail priority, a path that will ultimately stretch 8 miles from the C&O Canal towpath along New Design Road to English Muffin Way outside of Frederick.
The trail will be built in three phases, Burns said: from English Muffin Way south to Mountville Road; from Mountville to south of Adamstown, and from south of Adamstown to the canal towpath.
"The real need is south of English Muffin [Way] right now, Burns said.
The grant will fund 30 percent of the planning and design for the first phase.
By connecting to the towpath, the trail will ultimately connect to the Great American Rail Trail, a cross-country network of paths stretching across 12 states from Washington, D.C., to the state of Washington.
The project "checks off a lot of boxes" in what the county should look for in projects, said Shayne Boucher, a member of the county's Bicycle and Pedestrian Committee.
The committee was formed last year to help implement the county's Bikeways & Trails Plan, passed by the County Council to help promote biking and walking in the county.
The third trail is the H&F Trolley Trail, stretching from Thurmont to Catoctin Furnace.
That project is the third priority because of issues with some property owners in getting access to the trail, Burns said.
Thurmont Mayor John Kinnaird also serves on the Bicycle and Pedestrian Advisory Committee, and said the key factor in the committee's decision was which projects offered a chance to get done more quickly and could tie in to existing segments.
While the Thurmont trail is important to the town, Kinnaird said he was happy with the committee's choices.
"They didn't take the one that I wanted, but I like what they did," he said.
The trail to Walkersville will offer an incentive to tie into the city of Frederick's trail, while the canal towpath is well used, and the new trail will help get people between the towpath and Frederick, Kinnaird said.
As for when work will start on the various projects, Burns said much of that will depend on when funding from various sources becomes available.
"We're just going to take it year by year," he said.
Transportation Safety Board
Ron Burns
John Kinnaird
BMedic May 20, 2019 8:44am
Yet the existing trail in the western parts of town remain unmaintained.
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ddegrangejr May 20, 2019 6:40am
I sure wish the city would use the old tracks that run along East Street and through the old Coca Cola plant to make some sort of path leading up to the Wegman's.It would be nice to have a different grocery store to bike to and would also give the kids at TJ Middle another place to walk other than the middle of the street to get home.
EABiker May 20, 2019 7:31am
Good luck crossing Rt 26 at rush hour!
William Smith May 20, 2019 7:12pm
Nobody seemed to care for my idea of a "Bike-a-pult". Enter your weight. It measures the wind speed and direction. Drop in a quarter and press the launch button. And, as long as you didn't lie about your weight, you'll reach the other side, intact. More or less.
FrederickTrails May 20, 2019 12:28pm
@ddegrangejr - that's the project described in priority #1
ddegrangejr May 21, 2019 12:52am
[thumbup] Didn't have my glasses on, or read it right or my brain may have just been not working all together.
Hello, Frederick: 52 Fun Things
18. Celebrate freedom with fireworks and music
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Keep the conversation about local news & events going by joining us on Facebook, Twitter and Instagram. Recent updates from The News-Post and also from News-Post staff members are compiled below.
Our local business directory includes detailed information for featured businesses as well as customer reviews and direct links to related events.
The Centers for Advanced Orthopaedics MMI Division
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405 N Burhans Blvd, Hagerstown, MD 21740
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The Sennheiser HD 650 over-ear headphones are known for some of the richest sounds from a pair of open back headphones. But at $370 on Amazon, they still come at a high price. Luckily, Sennheiser paired up with Massdrop, a discounted shopping site, to create an upgraded version of the 650s at a much better price.
Right now you can get the Massdrop X Sennheiser HD 6XX for just $199.99 on Massdrop. These bad boys have the same great sound as the 650s, but they're fitted with a detachable 6-foot cable instead of a 10-foot one, so you no longer need to worry about getting tangled in a long cable while you rock out.
It should be noted that because of the open back design, it won't prevent sound from being heard by those nearby. So you might not want to use them on a train ride or in an open-plan office—unless you want everyone around you to hate you. That being said, they still make for a great at-home headphone especially at this amazing price. The headphones are still in production, so while you won't get them right away, you're guaranteed to get them hot off the assembly line.


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CLUTCH'S FIRST EVER IN STORE ACOUSTIC PERFORMANCE, GREAT WHITE GUITARIST TALKS ABOUT LEAD SINGER SITUATION, plus two live videos. CHARLIE BENANTE TALKS ABOUT NEW ANTHRAX ALBUM "WORSHIP MUSIC."
Maryland rockers CLUTCH took part in their first-ever acoustic in-store performance on Saturday, May 28 at Earshot Music & Movies in Greenville, South Carolina. The band's set consisted primarily of selections from its "Basket Of Eggs" project from the "Blast Tyrant" deluxe reissue.
The charitable food pantry "Loaves And Fishes" was also on site that afternoon collecting canned food and non-perishables for the region's recent weather-related victims. Earshot and Weathermaker Music set up a large "food basket" inside the retailer and those who donated a canned or non-perishable food item received a free CLUTCH tour poster and were first in line to have it autographed by the band after their acoustic performance.
Fan-filmed video footage of the performance can be viewed below.
The "Blast Tyrant" deluxe reissue sold 2,500 copies in the United States in its first week of release, landing at position No. 26 on Top Hard Music Albums chart, more than seven years after the original version debuted at No. 15. The double-disc package, which features the "Basket of Eggs" bonus CD, triumphed in the Northeast, where it broke into the Top 10 at the mammoth Newbury Comics chain, and was the No. 1-selling double disc.
CLUTCH kicked off a nine-date headlining tour on May 20 in Reading, Pennsylvania. The trek features MAYLENE & THE SONS OF DISASTER as main support. CLUTCH is keeping the average ticket price for these shows to a fan-friendly $17.50. CLUTCH has also confirmed a headlining run for this July, with CORROSION OF CONFORMITY serving as direct support. The tour will kick off with two special shows (July 20-21) in the New York area.
RockMusicStar.com recently conducted an interview with GREAT WHITE guitarist Mark Kendall. A couple of excerpts from the chat follow below.
RockMusicStar.com: I'm sure one of the first questions you get asked in interviews these days, is the one I'm about to ask. For all of the GREAT WHITE fans out there following along, can you please clarify what is going on with the lead-singer situation?
Mark: What's happened is Jack (Russell) has had a ton of health issues that have literally made it impossible for him to perform. He was doing it (performing) with (the aid of) stools and we were getting ridiculed. People were saying, "Why are you taking that man out there (on stage) in that condition?" He's getting a lot better, he just had another surgery, so hopefully he pulls it out. In the meantime, we've been using a guy called, Terry Ilous, who used to be from XYZ. He's just filling in until Jack gets well, and the shows are going great. He does a real good job, so that's going great.
RockMusicStar.com: That's good to hear. While some people may be aware that Jack is not out on the road with you guys right now, many people want to know whether or not he will be back with the band at some point.
Mark: He wants to. In fact, he's working out with a trainer and wants to come back. His voice is fine, but he just has to get himself a little more mobile before we take him out. We don't want to do like, wheelchairs in the airport, if you know what I mean.
RockMusicStar.com: I understand. I know that no matter how old you guys get, playing rock and roll, you still want to bring a certain level of entertainment with your live shows.
Mark: Absolutely. We still want to have energy on stage. I don't think he wants to go out, and have to sit down when we play. It's just not good for our style of music.
RockMusicStar.com: Before Terry, you had Jani Lane (formerly of WARRANT) filling in for Jack. What happened with that?
Mark: You're correct. He did a great, great job, it's just – he's got his own solo career and stuff. He did it as a favor for awhile, and then he became unavailable. He did a really good job. I was actually surprised.
RockMusicStar.com: Now that you've been playing with a couple different singers since Jack has been unable to perform, have you adjusted the set list at all, to accommodate their range, or vocal personality?
Mark: Terry seems to have all of his range still, while Jack has a few notes missing from the past. So he (Jack) doesn't like to do certain songs, to where we've been able to kind of pull them out with Terry, because he can hit every note. Jack has always been kind of a perfectionist, and always tries to sing the songs pretty close to the record. He doesn't want to go out, and do like a Freddie Mercury, and singing the songs an octave lower. He hates the idea of using a (pre-recorded background) tape, so there's certain songs that he didn't like to do, that we brought back to the set. So we can play more of the hits, and every song we've done videos for in the past — the MTV songs and stuff. It's just a handful of songs. Just a few that we haven't played in awhile.
Read the entire interview from RockMusicStar.com.
ANTHRAX drummer Charlie Benante spoke to Revolver magazine about the status of the recording sessions for the band's long-awaited new
studio album, "Worship Music", tentatively due in September via Megaforce Records in the U.S. and Nuclear Blast Records in Europe.
"Worship Music", which was originally supposed to be released in 2009 and be the band's first CD with singer Dan Nelson, will mark the first new ANTHRAX recording to feature vocalist Joey Belladonna in 20 years.
"Some of the songs we tweaked, some of the songs we did more than tweak," said drummer Charlie Benante. "Some we started from scratch, and some were written just for this album."
"With Joey singing them, they sound like classic ANTHRAX. The hair on my arms stood up when he started singing them. It was ANTHRAX once
Guitarist Scott Ian agreed. "The songs like sound like metal. They sound like ANTHRAX circa 1987 through a 2011 filter."
"I think this record is more of a celebration for us," Benante added. "We haven't had a new record since 2003. The ups and downs in between really reflect the mood of this record. There is a lot of aggression, emotion and power. I feel like this is once again back to our New York style and attitude."
Songtitles set to appear on "Worship Music" include "Fight 'Em 'Til You Can't", "I'm Alive", "Crawl", "The Giant", "Earth On Hell" and "Down Goes The Sun".
During a chat with RockMusicStar.com, ANTHRAX singer Joey Belladonna was asked if working on the band's new songs was a challenge
because of the fact that most of the material was written for previous vocalist, Dan Nelson. "I kind of hate that someone was already singing this stuff and now I have to kind of dance around it and do it all over," he said. "They [the rest of ANTHRAX] have in their mind already how they want it to sound, so it's kind of hard to shake it away. They are not going to say to me, 'Go on and do something totally different and we will just dig it.' [Laughs] It's hard, but I'm not worried about it."
acoustic performance, Anthrax, Charlie Benante, CLUTCH, CLUTCH TOUR, GREAT WHITE, Jack Russell, Mark Kendall., NEW ALBUM, New Anthrax album, Worship Music
SEE SHATNER GET GOLDEN GODS AWARD AND DUFF MCKAGAN'S "LOADED" PERFORM PRIEST'S "ELECTRIC EYE," WITH STEVE JONES AND COREY TAYLOR HERE! ACE FREHLEY TO PLAY ERIE COUNTY FAIR IN AUGUST.


Find out more about acupuncture mats vs. acupuncture. Our very own Natalie Willits was interviewed for this article on the difference between acupuncture mats and acupuncture! Here's a link to the article.
We had so much fun on our photoshoot! Here are some of the "backstage" photos!
Seattle Met Top Doc 2018!
Matt Ferguson and Stephanie Gianarelli win Seattle Met's Top Doc in the East Asian Medicine category for the second year! Congratulations!
Clinic Director, Stephanie Gianarelli on Q13!
Congratulations to Stephanie Gianarelli and Matt Ferguson for being recognized by their peers in the medical community as a Seattle Top Doc for East Asian Medicine!


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Living the beach
Silicon Beach ... family-style
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Abbot Kinney Pioneers Modern Day Venice
Silicon Beach's Venice area is an eclectic beach community that traces its roots to land developer Abbot Kinney. An educated and well-traveled man who spoke six languages, Kinney was determined to bring culture to his new home with his Venice-of-America project intended to share the social and cultural heritage of Venice, Italy. Intended to be built on marshy swampland, Kinney's project became known as "Kinney's Folly."
Kinney, however, had the last laugh. His project opened July 4, 1905 with a crowd of 40,000 and hotels, an arcade, the Pleasure Pier, a yacht club and surf bath house, country club, tennis and croquet facilities, an aquarium, chariot track, miniature railroad, boat house, and seven canal waterways complete with gondolas imported from Italy navigated by singing Italian gondoliers.
Despite his best efforts to interest people in culture, Kinney found what they really wanted were the gondola, camel and railroad rides. Despite his best efforts to incorporate a cultural exhibition, Venice ended up with a carnival atmosphere that has persisted to modern day.
Along with his love of culture, Kinney was also a avid exercise buff, and sports in Venice were also encouraged. Aquatic contests were a natural for the area. The largest skating arena in Southern California opened in Vence in 1906. Beauty pageants followed in 1912, reaching a peak in the 1930's and '40's with Miss California contests held at the Pier Auditorium.
Kinney died in 1920 and controlling interest in the Abbot Kinney Company was passed to his son Thornton. Shortly after Abbot Kinney's death, a fire completely destroyed the Pier, a serious blow to the profitability of Venice. Thornton Kinney rebuilt and reopened to great fanfare in July 1921.
Venice has always been a hotbed of political strife with the competing interests of the amusement supporters versus the clergy and residential population. In 1923, Santa Monica sought to annex Venice, but was defeated by the voters who, instead, threw in with the City of Los Angeles. Some have called this choice the most unfortunate event in Venice history.
By the late 1920's, the automobile was becoming more popular and Venice businessmen found the canals impeding commercial progress. Sadly, the picturesque waterways were filled in in 1929. Today's Windward Circle was once a swimming lagoon and the centerpoint for the canal grid. The current Main Street was Coral Canal, Cabrillo Avenue was Cabrillo Canal, Grand Boulevard was Grand Canal, Market Street was Aldabaran Canal, San Juan Avenue was Venus Canal and Windward Avenue was Lion Canal.
The canals that still exist today (Carroll, Howland, Linnie, Sherman, Eastern and Grand) were part of the Short Line Canals. Although not filled like the primary canals, expense prevented utility and safety improvements to the lots abutting these canals and they sold poorly. Rent was cheap and hippy and other counterculture enthusiasts were drawn to the area in the 1960's.
The 70's brought social services agencies to Venice to combat the social problems wrought by the 60's. Both the St. Joseph Center and Venice Family Clinic started. SPARC was created in 1976 to develop art to change the community, and has become the largest repository of information about murals and other public art in Venice.
The 90's brought rehabilitation and redevelopment to much of Venice. Real estate prices boomed. West Washington Boulevard was renamed Abbot Kinney Boulevard. The "boulevard" has gone from bohemian to casual cosmopolitan to ultra trendy. Artists and entertainment industry stars co-exist. More recently, digital tech entrepreneurs have joined the mix and "Silicon Beach" was born.
Everywhere you look, you can see indications of Abbot Kinney's influence and Venice persists today as a funky, eclectic, casual, liberal and hip place to live. For more photos of modern day Abbot Kinney Blvd. and the Venice vibe, head over to my Instagram Account.
Venice Schools
Median Price For Single Family Homes In Venice:
424.272.13391611 Electric Avenue,Venice,CA 90291


On Thursday Oct. 12 Southside residents of Atlanta and Housing Justice League members and supporters delivered a new report to City Hall showing gentrification and displacement from BeltLine development in Atlanta's historically Black Southside. The report by the Atlanta advocacy group Housing Justice League and Research|Action Cooperative, shows Southside residents are already being displaced by the Atlanta BeltLine greenway development even in neighborhoods that it has not yet touched. The Atlanta BeltLine, which will ultimately be a 22-mile loop of green parks, trails, and streetcars circling inside city neighborhoods along discontinued rail beds, is a force for gentrification and displacement of long-time, low-income residents, many of them Black.
Proceeding the actual delivery of the report to City Council and the Mayor, participants of the research project gathered with their supporters, City candidates and elected officials, the press, and others on the steps in front of City Hall to hear from Southside Residents. All of the speakers emphasized the importance of community involvement and accountability in city planning in order to meet the critical needs of long-time residents and avoid the historical and continuing patterns of racism, displacement, and disinvestment.
Atlanta failed to enact protections against displacement that have been effective in other parts of the country. It still has time to do so as the BeltLine turns its development eye to more of the historically Black Southside.
Housing Justice League is itself helping to model what this kind of planning could look like for the city at large. The community-directed research report is part of Housing Justice League's broader BeltLine For All campaign, seeking to create spaces that center resident voices and promote community engagement in the development process. The Monday following the press release (Oct. 16), Housing Justice League will officially launch the broader campaign with a community-centered event where people will be able to learn more about the research, connect, and sign up to volunteer and lift up their perspectives through the campaign.
To learn more about the policy BeltLine for All will push for to turn around the unjust development practices displacing residents read the full report!


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KHORIKOS is one of New York City's most distinguished vocal ensembles. We present unique programming that puts invigorating interpretations of early vocal music in conversation with works by today's most dynamic composers. We seek to weave together musical languages and themes that span centuries, and to deliver an unprecedented level of artistry and expressive focus.
KHORIKOS offers a fresh take on an age-old art form.
ALEC GALAMBOS
CARAH NASEEM
JESSE PECKHAM
FOUNDING DIRECTOR
"...shot full with emotion and brave stabs of color."
Kile Smith, Grammy-Nominated Composer
"I got goosebumps, and I don't think I was the only one. It was very magical, powerful."
Gisele Regatao, TheGreeneSpace WNYC/WQXR/NationalPublicRadio
"It's an absolutely beautiful, angelic sound"
Monica Ellis - Bassoonist, The Imani Winds
"Other-worldy, spiritual. Very beautiful and very delicate"
Panelist @TheGreeneSpace WNYC/WQXR/NationalPublicRadio
"beautifully rendered"
"...truly a cut above in a performance that was stunning from start to finish."
Jeffrey Williams for New York Concert Review
"What ecstatic excellence poured out of this small group, which stood in a humble semicircle of two rows, in front of the risers. They sang selections from six centuries of a cappella music, in six different languages, with such purity and passion. I can't recall the last time I attended a vocal event this good—and I've been swimming in a spring season full of choral concerts, all of which have had their "moments.""
Frank Daykin, for New York Concert Review
Since its inception in 2005, KHORIKOS has quickly gained a reputation for excellent programming and stunning performances, and is now regularly invited to perform world premieres and at prestigious venues in NYC and worldwide. In 2008, the ensemble toured the Czech Republic as a part of the Svatováclavský hudební festival, and on September 23rd, 2009, KHORIKOS performed the NYC premiere of Eric Whitacre's Nox Aurumque. In the Spring of 2010, KHORIKOS released its first professionally-produced CD: a live concert recording called "Modern Masters," which was nominated for Best Classical A Cappella Album for the 2011 CASA Music Awards. During the Summer of 2011, KHORIKOS performed at the Kennedy Center, Avery Fisher Hall and the Wang Theater in Boston as a part of the "Songs of Life Festival" and the World Premiere of A Melancholy Beauty. Collaborators included The National Philharmonic, The Boston Modern Orchestra Project, The Indianapolis Children Choir and the Philip Kutev National Folklore Ensemble, Bulgaria. On April 22nd, 2012 KHORIKOS appeared on a joint program at Avery Fisher Hall in "Over the Stone" with Bryn Terfel, and on April 23rd and 25th, 2012, KHORIKOS performed the acclaimed Yunus Emre oratorio by Ahmed Adnan Saygun under the direction of Turkish conductor Rengim Gökmen with the TURKSOY Symphony Orchestra, at Avery Fisher Hall and the Music Center at Strathmore. In the summer of 2012, KHORIKOS was selected to compete in WQXR/WNYC the Jerome L. Greene Space's "Battle of the Boroughs," and was voted to represent the Borough of Manhattan in competition against rock, funk and indie bands. In the Fall of 2012, KHORIKOS premiered Cantos de Vida Nueva by Chilean composer Javier Farias at the Instituto Cervantes and performed with Mason Jar Music at the Rockwood Music Hall. The remainder of the 2012-2013 season included a world premiere of Robert Carl's The Geography of Loss at Merkin Concert Hall, and the world premiere of Jan Jirasek's King Lavra at the Czech Center Bohemian National Hall and at Roulette.
Since 2016, KHORIKOS has been led by Principal Conductor Alec Galambos. Mr. Galambos took the charge of KHORIKOS's artistic endeavors by jumping in midway through the 2015-2016 season, rapidly developing a vision for a new recurring concert series. "SAROS Cycles" epitomizes the core mission of KHORIKOS by revealing expressive connections between music new and old. In March 2016, "SAROS Cycles: Life, Death, Love" continued in KHORIKOS' tradition of showcasing conducting talent from within the ensemble, as part of Mr. Galambos's effort to develop musical leadership among singer-members and a shared accountability to artistic quality. Building on the momentum of this first concert, Mr. Galambos made his conducting debut at Lincoln Center's Alice Tully Hall in a guest appearance in "Living Colors: The Music of Ivo Antognini" on March 22, 2016. The SAROS Cycles series continues to showcase diverse and unique programming, blend musical traditions from across centuries, languages, and themes, and highlight KHORIKOS's signature artistic rigor and commitment to emotional and engaging performances.
KHORIKOS kicked off the 2016-2017 season with a collaboration with Chicago's Marion Consort, a small vocal ensemble specializing in Early music, in a series of performances titled "Antiphony," highlighting the call-and-response dynamic featured in double-choir music and in artistic collaborations more generally. This collaboration entailed three performances featuring both ensembles: one in New York on September 17, 2016; one in Chicago on October 15, 2016; and one in Milwaukee on October 16, 2016. Next, KHORIKOS engaged Piffaro, the Renaissance Band, for a performance of Philadelphia-based composer Kile Smith's Vespers at The Church of St. Luke in the Fields in New York City on November 19, 2016. KHORIKOS has had a collaborative relationship with Smith since performing his Where Flames a Word in 2014 and Chambered Nautilus in 2015, which was a winner of the 2015 ORTUS International New Music Competition.
KHORIKOS reiterated the "SAROS Cycles" series with "Lamentations and Light" on March 25th, 2017, at The Shrine Church of St. Anthony of Padua in New York City. This performance featured works from Tallis to Tavener, including the stunning and rarely performed Bendita Sabedoria by Heitor Villa-Lobos. Rounding out the 2016-2017 season, KHORIKOS traveled to Boston to participate in the Boston Early Music Festival's fringe concert series. In a performance entitled "Musica Reservata: 500 Years of Chamber Singing" at The First Lutheran Church of Boston on June 17, 2017, KHORIKOS showcased a variety of dramatic settings of the Lamentations of Jeremiah. KHORIKOS performed the same program the next day at St. Paul's Church in Wallingford, Connecticut—a community church for several of KHORIKOS's singers—and featured a guest performance by New Haven's Saecula Singers, under the direction of Tom Brand.
KHORIKOS began the 2017-2018 season by affirming its commitment to cultivating new music with the third ORTUS International New Music Competition. Inaugurated in 2014 by Founding Director Jesse Peckham, the ORTUS International New Music Competition solicits music for a cappella choir from composers all over the world, aiming to revive works that may have already enjoyed a premiere but are still new to audiences. For the project's third iteration, KHORIKOS presented works by ten living composers, culminating in an unforgettable performance on September 23, 2017. On December 9th and 10th, KHORIKOS performed "Caritas," featuring repertoire from the ensemble's 2015 album of the same name, including such holiday classics as Coventry Carol and In the Bleak Midwinter alongside unique contributions to a new wintry canon in Graham Lack's Four Lullabies and arrangements of German folk songs by Vytautas Miškinis.
The 2017-2018 season featured "SAROS Cycles: A Journey of Days in One Night," highlighting Joby Talbot's León and two brand-new scores: Mr. Galambos's arrangement of composer Sarah Kirkland Snider's The Song for a cappella choir, and a fresh transcription of Vultum tuum deprecabuntur, a rare motet cycle from Franco-Flemish Renaissance giant Josquin des Prez. Defined by themes of desperation and hope, the set also included music by Francis Poulenc, Guillaume de Machaut, and Bohuslav Martinů, among others. Summer 2018 saw KHORIKOS's debut at National Sawdust, performing world premieres from Daniel Zlatkin and Gala Flagello to critical acclaim. Following a successful crowdfunding campaign, the group collaborated with Grammy-nominated and Emmy-winning engineer Dan Dzula to record "Joy and Grief and Rest," KHORIKOS's first album since 2015, as well as Josquin's "Vultum tuum deprecabuntur."
The 2018-2019 season saw KHORIKOS embarking on its first ever micro-commissioning project, enlisting four of the group's seasoned composer-collaborators and virtuoso violinist Leonard Fu for "Four Winds: New Music and Silence," a reflection on spoken and unspoken communication. The commissioning and workshopping process culminated in world premieres from Graham Lack, Kala Pierson, Evelin Seppar, and Kile Smith. During that cycle, KHORIKOS debuted Vespers 360, a pioneering 360-degree video project featuring ambisonic spatial audio produced by Dan Dzula, in which listeners on Facebook, Youtube, or in a VR headset can immerse themselves in the center of a blended choral sound, as KHORIKOS sings the expansive 16-voice movement of Kile Smith's groundbreaking Vespers. In spring 2019, "SAROS Cycles: Our Nature" highlighted the complicated role of natural imagery in music by juxtaposing Osvaldo Golijov's double-choir Coral del Arrecife with works by Josquin, Alonso Lobo, Maurice Bourbon, James MacMillan, transcriptions of Ravel, and the world premiere of KHORIKOS singer-member Benjamin Martinson's Gerard Manley Hopkins Looks at the Sky.
Opening the 2019-2020 season, KHORIKOS released three albums of recorded music, celebrating the past five years of the group's repertoire: "Joy and Grief and Rest," Josquin's "Vultum tuum deprecabuntur," and a digital collection of bonus material from KHORIKOS's live discography entitled "Joy and Grief and Rest and Home." From the latter collection, the group's recording of Thomas Tallis's "Sancte Deus" was featured by Spotify's editorial staff in their Classical New Releases playlist, reaching hundreds of thousands of listeners. KHORIKOS celebrated the release with a live performance of Joy and Grief and Rest at the Dimenna Center for Classical Music in New York City.
In summer 2019, KHORIKOS toured to Serbia and Montenegro with the generous support of the U.S. Embassy in Belgrade. They performed in the 54th Days of Mokranjac Festival, and won the competition portion with an adventurous repertoire of new music and a fresh interpretation of the works of the beloved Serbian national composer Stevan Mokranjac. They performed in art spaces, galleries, and churches across the country, and in the 5th International Choir Festival in beautiful Herceg Novi, Montenegro, enjoying acclaim in national TV and print media.
During the same season, KHORIKOS was featured on BBC Radio by host Dean Craven, in an airing of the ensemble's 2017 performance of composer Katie Bamford's Ecstacy. KHORIKOS received generous support from the Aaron Copland Fund for Music and the Lower Manhattan Cultural Council.
In the remaining 2019-2020 season, KHORIKOS continued to explore the timeless tradition of contrapuntal writing with the world premiere of Andrew Smith's O Antiphons, performed at venues across Manhattan.
Amidst the ongoing COVID-19 pandemic, we've had to pause the remainder of our concert season. We eagerly await safer conditions for singing together and performing live. In the meantime, we've released Tavener 360, our second foray into spatial audio, and an effort to bring the immersive experience of live performance to audiences at home.
We're looking forward to a brighter public health outlook in 2021, so that we can resume preparing to present our 4th ORTUS International New Music Competition, introducing New York City to another group of inspiring choral composers from around the world.
© 2019 by KHORIKOS


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Drug Information Websites
Click on the "Web Sites" tab for links to drug information web sites.
Provides information from FDA-approved package inserts and new information from the FDA.
Drug identification tool. Pill identifier with search by pill color and shape. Information about U.S. prescription and OTC drugs including consumer's ratings and comments. Advertising enables the web site to remain free of charge, but the Drug monographs are the site are from Micromedex, Facts & Comparisons, and the FDA.
You must first register individually, but there is no charge for using this web site. Search by drug name or condition. Drug monographs include prices, brands, and photographs of pills, and the information from the manufacturers' package inserts (the information that is in the PDR).
Orange Book
FDA website that provides ratings of bioequivalence. Search by active ingredient, proprietary names, patent, applicant holder, or application number. Includes a current listing of approved generic products.
The National Library of Medicine in partnership with the Food and Drug Administration is beta testing Pillbox, a reference system for tablet and capsule medications. The site currently contains 5,693 records - 779 of which have images.
The system combines high-resolution images of tablets and capsules with FDA-approved appearance information (imprint, shape, color, etc.) to enable users to visually search for and identify an unknown solid dosage pharmaceutical.
RX List
Top 200 list of drugs based on number of prescriptions dispensed. Searches include drug brand, nonproprietary name, imprint, NDC code. Drug monographs contain indications, pharmacological action, side effects, and more). Summaries of package inserts are included.
<< Previous: Statistics


Your Body (きみのからだ, Kimi no Karada?) is the 8th chapter of Karneval by Touya Mikanagi.
The doctor informs Hirato that Nai is not a human, but an animal: a Niji, something which Hirato and Gareki finds humorous. As Gareki and the doctor go to check up on Nai, Gareki becomes flustered due to his reflection on the way he treated an "animal". Meanwhile, Hirato and Yogi discuss taking Nai to the Research Tower to be professionally examined. Back in the examination room, Gareki and Nai reconcile, with Nai informing Gareki that Karoku told him to cut him off, something which amuses Gareki. Later, as the new day begins, Hirato prepares to travel to the Research Tower.
Characters in bold denote the character's proper appearance.


text:
Early impact of Covid-19 on private sector employees finance homeownership in Kingdom of Saudi Arabia
Raed Khamis Alharbi (College of Administration and Financial Science, Taif University, Taif, Saudi Arabia)
International Journal of Housing Markets and Analysis
Article publication date: 22 September 2021
For almost two years, the economic shocks and financial uncertainty created by the Covid-19 pandemic have affected all sectors. The private sector employees may be the worst hit. This is because of the lockdown across many countries, including the Kingdom of Saudi Arabia (KSA), leading to income irregularities. Studies exploring private-sector employees concerning housing finance for the houses purchased and how the lockdown has affected their sources of income for repayment plans are scarce. Therefore, this study aims to investigate the possible early negative impacts of Covid-19 on private sector employees' housing finance homeownership in KSA.
A phenomenology type of qualitative research was used. Data were sourced from three cities (Riyadh, Al-Qassim and Medina) and three mortgage banks across KSA. Virtual interviews via Zoom and WhatsApp video calls were conducted with engaged participants (bankers, government agencies and private sector employees). Thematic analysis was adopted, and the analysed data was presented in themes.
Findings show that the partial and full lockdown resulted in income irregularities in many private businesses. Also, findings identified downsizing, leading to large-scale unemployment, half-monthly income for employees, loss of profit, human resources wastage, etc. Findings reveal that because of the economic shock, many homeowners have not been able to meet up with their monthly mortgage repayment obligation. Also, the absence of financial support in form of socioeconomic needs has not helped the matter.
The paper is limited to the early negative impacts of Covid-19 on private sector employees' housing finance homeownership in KSA and data collected via Zoom and WhatsApp video calls across the three main cities. The recommendations that will emerge from this study may be adopted by other Gulf and Islamic countries with similar homeownership repayment challenges.
This study would stir key stakeholders, especially the policymakers and mortgage institutions to consider future policy principles that focus on who is at the highest risk for housing-related hardships because of the Covid-19 or future pandemic. The outcome can be used to develop an equitable housing policy framework to foster long-term economic mobility and be validated in the future by scholars.
Similar research in this area is limited, which makes this study one of the pioneering attempts to investigate the early negative impacts of Covid-19 on private sector employees' housing finance homeownership in KSA. The paper sheds light on the emerged early negative impacts and proffer feasible possible solutions to promote homeownership amongst Saudi citizens.
Thanks to the participants for providing knowledgeable contributions to enhance the findings of this paper. Also, the author appreciates the comments, suggestions, and recommendations provided by the anonymous reviewers, which collectively helped hone and strengthen the quality of this manuscript during the blind peer-review process. Special thanks to Dr Andrew Ebekozien, a Senior Research Associate with the University of Johannesburg, South Africa, for proofreading this manuscript.
Alharbi, R.K. (2023), "Early impact of Covid-19 on private sector employees finance homeownership in Kingdom of Saudi Arabia", International Journal of Housing Markets and Analysis, Vol. 16 No. 1, pp. 5-21. https://doi.org/10.1108/IJHMA-08-2021-0093


Welcome to Mentor for Bank Exams. Read Current Affairs GK Questions Answers 3 April 2018 on this post from below. We have updated the top current affairs of the Day and we hope these question answers will improve your GK and Current Affairs sections.
1. Defence Minister is in Russia to attend the 7th Moscow Conference on International Security. Name the Defence minister of India.
Explanation: Defence Minister Nirmala Sitharaman is in Russia to attend the 7th Moscow Conference on International Security. This is her first visit to Russia in her capacity as the Defence Minister.
2. Name the International Airport has been adjudged the cleanest airport in the country.
Explanation: Mangalore International Airport has been adjudged the cleanest airport in the country. In the survey conducted across 53 airports in the country by Airports Authority of India (AAI), New Delhi, Mangaluru airport was adjudged the cleanest.
3. Which country topped in Global start-up ecosystem index 2017?
Explanation: India ranked 37th in the global start-up ecosystem in 2017, according to a report released by global startup ecosystem map Startupblink. The list was topped by the United States followed by the United Kingdom.
4. Which country has become the partner country for the International Frankfurt Trade Fair, Ambiente 2019 to be held in February 2019?
Explanation: India will be the partner country for International Frankfurt Trade Fair, Ambiente 2019 to be held during February 8-12, 2019 in Germany. India will take over the partner country globe from the Netherlands.
5. 'Rupashree' a new scheme to provide marriage assistance to girls coming from economically weaker families is intorduced by which Indian state?
Explanation: The state government of West Bengal introduced a new scheme called 'Rupashree' in order to provide marriage assistance to girls coming from economically weaker families with a budgetary allocation of Rs 1500 crore.
6. Who has been appointed as the new president of NASSCOM?
Explanation: Debjani Ghosh will take over as president of the IT industry association. She succeeds R Chandrashekhar, who is leaving office upon the completion of his term.
7. Name the the newest payments banks to start its operations as a payments bank with effect from April 3, 2018.
Explanation: Jio Payments Bank Limited has commenced operations as a payments bank with effect from April 3, 2018. Reliance Industries Ltd was one of the 11 applicants which were issued in-principle approval for setting up a payments bank in August 2015.
8. Utkal Diwas is the foundation day of which Indian state?
Explanation: On April 1, 1936, Odisha was formed and since then the day is celebrated to mark the contributions and sacrifices made by people of the state in the formation days. The day is also called as "Utkal Divas".
9. The 5th Indo-Kyrgyzstan joint training exercise KHANJAR V was held in which state?
Explanation: The 5th Indo-Kyrgyzstan joint training exercise 'Khanjar V' culminated with a 'Joint Tactical Validation Exercise' in Mizoram. The exercise which started on March 16, included understanding tactics of platoon level, developing interoperability.
10. SoftBank has signed a _____ million dollar deal with China's energy conglomerate Golden Concord (GCL) to produce and sell solar equipment in India.
Explanation: SoftBank has signed a $930-million deal with China's energy conglomerate Golden Concord (GCL) to produce and sell solar equipment in India. GCL will invest for a 40% stake in the joint venture, with SoftBank taking the rest.
11. World Autism Awareness Day Celebrated on 2nd April every year. What is the theme for the year 2018?
Explanation: World Autism Awareness Day is an internationally recognised day on 2 April every year, encouraging Member States of the United Nations to take measures to raise awareness about people with autism throughout the world. Theme of 2018 – Empowering Women and Girls with Autism.
12. Who has won the Men's Single trophy of Miami Open 2018?
Explanation: American John Isner won his first ever Masters 1,000 title with a 6-7 (4-7) 6-4 6-4 victory over German Alexander Zverev in the Miami Open final.
13. Name the Indian bank that has been dismissed by the Reserve Bank of India to import raw gold and silver for FY19?
Explanation: The Reserve Bank of India (RBI) has dropped Axis Bank, which has been one of the largest importers of bullion, from the list of lenders allowed to ship in gold and silver for the current fiscal year. Two other small banks Karur Vyasa and South Indian Bank, were also dropped from the RBI list.
14. Carlos Alvarado named as the President of which country?
Explanation: Carlos Alvarado, the candidate for Costa Rica's center-left ruling party, was elected as the next president of Costa Rica.
15. Which city has been ranked the top city in the short-term Momentum Ranking of JLL's annual 'Global City Momentum Index' 2018?
Explanation: Hyderabad has been ranked the top city in the short-term Momentum Ranking of JLL's annual 'Global City Momentum Index'. The report identifies urban economies and real estate markets which are currently undergoing the most rapid growth. The report ranked Bengaluru, Pune, Kolkata and Delhi in top 10 cities.
16. In the recently released Bloomberg Billionaires Top 100 Index, name the billionaire who was declared as the richest in Asia with a net worth of $47.2 billion.
Explanation: In the recently released Bloomberg Billionaires Top 100 Index, from Asia, Alibaba co-founder Jack Ma (ranked 13th) is the richest with a net worth of $47.2 billion and is followed by Tencent co-founder and CEO Pony Ma (17) with a $41.1 billion net worth.


text:
Conferences | Training Courses | Market Reports | Managed Events | Past Conferences | Update Me
Conferences \ Organ-on-a-Chip World Congress 2019 \ Agenda \ Danilo Tagle
Danilo Tagle's Biography
Co-Located Conferences
Danilo Tagle, Associate Director For Special Initiatives, Office of the Director, National Center for Advancing Translational Sciences at the NIH (NCATS)
Dan Tagle is associate director for special initiatives at NCATS. He also recently served as acting deputy director of NCATS and has served as acting director of the NCATS Office of Grants Management and Scientific Review and as executive secretary to the NCATS Advisory Council and Cures Acceleration Network Review Board. Prior to joining NCATS, Tagle was a program director for neurogenetics at the National Institute of Neurological Disorders and Stroke (NINDS), where he was involved in developing programs concerning genomics-based approaches for basic and translational research in inherited brain disorders.
Prior to joining NINDS in 2001, Tagle was an investigator and section head of molecular neurogenetics at the National Human Genome Research Institute and has been involved in the highly collaborative effort toward the positional cloning of genes for Huntington's disease, ataxia-telangiectasia and Niemann-Pick disease type C. He has served on numerous committees and advisory boards, including the editorial boards of the journals Gene and the International Journal of Biotechnology.
Tagle obtained his Ph.D. in molecular biology and genetics from Wayne State University School of Medicine in 1990. He was an NIH National Research Service Award postdoctoral fellow in human genetics in the laboratory of Francis S. Collins, M.D., Ph.D., at the University of Michigan. Tagle has authored more than 150 scientific publications and has garnered numerous awards and patents.
The NIH Microphysiological Systems Program: In Vitro Tools for Drug Development and Precision Medicine
Tuesday, 15 October 2019 at 14:00
Add to Calendar ▼2019-10-15 14:00:002019-10-15 15:00:00Europe/LondonThe NIH Microphysiological Systems Program: In Vitro Tools for Drug Development and Precision MedicineOrgan-on-a-Chip World Congress 2019 in Coronado Island, CaliforniaCoronado Island, CaliforniaSELECTBIOenquiries@selectbiosciences.com
Approximately 30% of drugs have failed in human clinical trials due to adverse reactions despite promising pre-clinical studies, and another 60% fail due to lack of efficacy. One of the major causes in the high attrition rate is the poor predictive value of current preclinical models used in drug development despite promising pre-clinical studies in 2-D cell culture and animal models. The NIH Microphysiological Systems (Tissue Chips) program led by NCATS is developing alternative approaches and tools for more reliable readouts of toxicity and efficacy during drug development. Tissue chips are bioengineered microphysiological systems utilizing human primary or stem cells seeded on biomaterials manufactured with chip technology and microfluidics that mimic tissue cytoarchitecture and functional units of human organs. These platforms can be a useful tool for predictive toxicology and efficacy assessments of candidate therapeutics. Effective partnerships with stakeholders, such as regulatory agencies, pharmaceutical companies, patient groups, and other government agencies is key to widespread adoption of this emerging technology. Tissue chips can also contribute to studies in precision medicine, environment exposures, reproduction and development, infectious diseases, microbiome and countermeasures agents.
Add to Calendar ▼2019-10-14 00:00:002019-10-15 00:00:00Europe/LondonOrgan-on-a-Chip World Congress 2019Organ-on-a-Chip World Congress 2019 in Coronado Island, CaliforniaCoronado Island, CaliforniaSELECTBIOenquiries@selectbiosciences.com
Related Conferences
Point-of-Care Diagnostics, Global Health & Biosensors 2019
Location: Coronado Island, California
Lab-on-a-Chip & Microfluidics World Congress 2019
3D-Culture & Organoids 2019
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Q: Write data chunks to S3 file through stream instead of creating temporary file Node.js I am trying to write chunks of CSV formatted data to a file in Amazon S3 instead of writing to a temporary file through the WriteStream then creating a ReadStream on that file and sending it to S3. My program pulls rows of data from a database, processed it then formats each row in a CSV like so using S3's upload() api
let recordsCSVFormatted;
let offset = 0;
const batchSize = 500;
const writer = fs.createWriteStream('./someFile.csv')

do {
  recordsCSVFormatted = await getRecords(limit, offset); // gets records from DB, formats it in CSV string
  writer.write(recordsCSVFormatted);
  offset += batchSize;
} while (typeof recordsCSVFormatted === 'undefined' || (recordsCSVFormatted && recordsCSVFormatted.length))

const reader = fs.createReadStream('./someFile.csv');

// just assume here that Key and Bucket are provided in upload, they are in actual code
await new AWS.S3({...s3Opts}).upload({Body: reader}).promise() // pass the readable in here for AWS

How can I skip the step of creating a temporary file and then passing the file to AWS as a stream? I want to be able to stream the chunks of CSV information directly.

A: Solved this by implementing the Readable class and implementing a custom read() function for S3 upload to consume

redpajama_set_name: RedPajamaStackExchange


MVD Express: What Makes us Different?
How we set ourselves a part from the crowd!
You guessed right: there's something different about us at MVD Express.
No, it's not our hair…but thanks for noticing! It's also not our super attractive smiles that you see when you walk in.
You already know what it is: We're different because of the superior service that we provide!
We know you're busy. You've got a million and one things to do every day—the last thing you want to do is hang out with us all day. We're different because (although we love you), we aren't selfish. We'll share you with the rest of the world after giving you fast, friendly service that will get you in, done and on your merry way ASAP.
We know you wouldn't have it any other way!
From small to huge ultra-complicated MVD issues, we've got your back! Come in to any one of our convenient locations around New Mexico for superior service for all your MVD needs.
Yeah, we know we're different…but we know you love it!


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Q: Using BIOS interrupts in x86 I am trying to implement string operations on QEmu in real-mode. Here is the read and print function that I made:
int readString(char* line)
{
 int i = 0;
 char in = 0x0;
 while (in != 0xd)
   {
    in = interrupt(0x16, 0x0, 0x0, 0x0, 0x0);
    *(line + i) = in;
    interrupt(0x10,0xe*0x100+in,0x0,0x0,0x0);
    i++;
   }
 *(line + i) = 0x0;
 return i;
}

int printString(char* string)
{
 int i = 0;
 while (*(string + i) != '\0')
   {
    char al = *(string + i);
    char ah = 0xe;
    int ax = ah * 256 + al;
    interrupt(0x10,ax,0,0,0);
    i++;
   }
 return i;
}

These functions are called in the following main program:
void main()
{
 char* line;
 printString("Reading from input:\n\r");
 readString(line);
 printString("Line read is:\n\r");
 printString(line);
}

The readString function takes the input from the keyboard, prints it to the screen (on QEmu) as we type the input string and stores the result in the argument passed (which is pointer to char).
But the cursor doesn't seem to move after the readString function. And the call to printString function afterwards (in the main function) causes the string to be overwritten. For example, if I write "Hello ", then I expect output to be:
Reading from input:
Hello Line read is:
Hello _

Here "_" is the cursor.
But instead the actual output coming is:
Reading from input:
Line read is:
Hello

The cursor is under the "H" of the Hello above (in actual output) and the initial "Hello" in the second line of the expected output is overwritten. Why is the cursor not moving as I print the string?

A: When the user presses enter, you will get the CR character (code 13, \r). However the bios output function interprets this as strictly a carriage return, that is it moves the cursor back to the start of the line. You need to add the LF (code 10, \n) yourself. For example:
int readString(char* line)
{
 int i = 0;
 char in = 0x0;
 while (in != 0xd)
   {
    in = interrupt(0x16, 0x0, 0x0, 0x0, 0x0);
    *(line + i) = in;
    interrupt(0x10,0xe*0x100+in,0x0,0x0,0x0);
    /* add LF to CR */
    if (in == 13) interrupt(0x10,0xe*0x100+10,0x0,0x0,0x0);
    i++;
   }
 *(line + i) = 0x0;
 return i;
}

int printString(char* string)
{
 int i = 0;
 while (*(string + i) != '\0')
   {
    char al = *(string + i);
    char ah = 0xe;
    int ax = ah * 256 + al;
    interrupt(0x10,ax,0,0,0);
    /* add LF to CR */
    if (al == 13) interrupt(0x10,0xe*0x100+10,0x0,0x0,0x0);
    i++;
   }
 return i;
}


The thermal comfort of an occupant can affect his or her wellbeing in a number of ways and I will go through some of them here; however first I will describe thermal comfort and how to quantify it.
The thermal comfort of a person is described as "that condition of mind that expresses satisfaction with the thermal environment and is assessed by subjective evaluation". The thermal comfort of an individual is personal and varies greatly from person to person. The subjective evaluation usually suggests a survey is needed to get the personal input from each of the occupants of a building. The large range of conditions and number of people required to give proper averages make this impractical in the majority of cases and cannot be done pre-occupation. A different approach consists of measuring environmental conditions and then calculating the thermal comfort indices, which relate to the measured values and calculated indices as if a range of people were surveyed.
The standards BS EN ISO 7730 and ASHRAE 55 give methods for taking the environmental measurements and subsequent calculations to give quantified numbers to compare thermal comfort between buildings and different conditions within the same building. The measured values required by the standard are air speed, turbulence intensity (using the standard deviation of air speed), air temperature, black globe temperature/operative temperature and relative humidity.
The thermal comfort calculations provide values for the Draught risk, Predicted Mean Vote (PMV) and the Predicted Percentage Dissatisfied (PPD). The Draught risk is an indication of the percentage of people that would perceive a draught given the measured conditions and uses the air temperature, air speed and turbulence intensity. The PMV is a prediction of the average vote of a large group of people occupying the space as if a survey was conducted on a scale of -3 to +3; where "-3" indicates feeling cold, "+3" indicates feeling hot and "0" is comfortable. The PPD is an estimate of the percentage of people who would find the space uncomfortable, based on the PMV results.
The calculations of PMV and PPD take into consideration the insulation provided by clothing (CLO) and the activity of the people working/living in the space (MET). The CLO is a measure of the average clothing insulation and the MET is a measure of the heat output from an average person doing a stated task in the space. The standards give methods to calculate the CLO and MET for a space, however, the actual individual values can change drastically depending the occupiers of the space, e.g. an office space versus a supermarket or factory floor where the activity level is significantly different, therefore the specific CLO and MET must be chosen carefully to give true indicative values of PMV and PPD.
One thing to note is that the PPD has a calculated minimum of 5 per cent as for the same CLO and MET there will always be some people who will feel either hot or cold however this is normally compensated by changing an individual's CLO, i.e. if a person is in an office and wearing a jacket, and the dress code allows, they will remove it when feeling hot, etc.
The effect on wellbeing of the thermal comfort is becoming a focus of study and coming to the attention of building owners and occupiers. The reason for the focus is that detrimental thermal comfort can have a large effect on the morale and in some cases even the mental and physical health of the occupants of any building. Any problems with morale or health can affect the productivity of the occupants. A measurement of the thermal comfort, either pre-occupation by heat-load testing or of the occupied building, can indicate any problems or show that the building conforms with the expected comfort levels required, e.g. the BS EN ISO 7730 standard has classifications of the space depending on the PMV, PPD and other factors.
The distraction caused by adverse thermal comfort can be significant and lead to occupants feeling the space is uncomfortable even if/when the conditions in the space have improved, e.g. either through changes to the ventilation system, or by moving an individual to a more suitable thermal environment. If a space is felt to be too hot or too cold for too long and no actions are taken, the perception of the occupants of their thermal comfort can become biased. Perceived long term thermal discomfort can be hard to dispel and productivity can be negatively affected.
The effect of thermal comfort on wellbeing of people can be significant and if ignored, it may affect the morale, health and productivity of people in the space. Thought should be made to the thermal comfort of the occupants of a space prior to and during occupancy to minimise any adverse effects on wellbeing.


Location of Tinley Park in Cook County, Illinois.
With the railroad came industry and commerce. 1905 saw the Diamond Spiral Washing Machine Company found its first factory in Tinley Park. Local businessmen established an electric utility in 1909. A bottling facility for soda was operated in Tinley Park until the 1950s. Inventor John Rauhoff developed and manufactured a waterproofing additive for cement called Ironite, later used in the construction of Hoover Dam. In the latter part of the 20th century, Tinley Park was, and remains to be, an area of rapid suburban expansion to the west and south of the original site, with over 11,000 housing units constructed between 1970 and 1994.
The Hollywood Casino Amphitheatre (formerly named "The World Music Theater", "Tweeter Center Chicago", and until 2015, "First Midwest Bank Amphitheatre"), an outdoor venue which seats 28,000, is located in Tinley Park.
Tinley Park is located at 41°34′26″N 87°48′14″W / 41.57389°N 87.80389°W / 41.57389; -87.80389 (41.573800, −87.803891).
According to the 2010 census, Tinley Park has a total area of 16.039 square miles (41.54 km2), of which 16.02 square miles (41.49 km2) (or 99.88%) is land and 0.019 square miles (0.05 km2) (or 0.12%) is water. The village lies on the Tinley Moraine and/or the Valparaiso Moraine.
In the village, the population was spread out with 26.6% under the age of 18, 8.1% from 18 to 24, 31.0% from 25 to 44, 23.5% from 45 to 64, and 10.7% who were 65 years of age or older. The median age was 36 years. For every 100 females, there were 93.8 males. For every 100 females age 18 and over, there were 90.5 males.
The median income for a household in the village was $61,648, and the median income for a family was $71,858 (these figures had risen to $70,480 and $84,072 respectively as of a 2017 estimate). Males had a median income of $50,595 versus $34,401 for females. The per capita income for the village was $25,207. About 1.1% of families and 2.5% of the population were below the poverty line, including 2.5% of those under age 18 and 3.6% of those age 65 or over.
Tinley Park is divided between two congressional districts. Most of the village, including all the area in Bremen Township and Rich Township, as well as the area in Will County, is in Illinois's 1st congressional district; the area in Orland Township south of 167th Street, as well as most of the area southwest of 163rd Street and Ozark Avenue, is in the 3rd district.
Tinley Park includes four public elementary school districts - Kirby School District 140, Community Consolidated School District 146, Summit Hill Elementary School District 161, and Elementary School District 159.
The town also includes three parochial Pre-K through 8 elementary schools: St. George, which is Catholic; Trinity Lutheran, affiliated with the LCMS; and Southwest Chicago Christian School of Tinley Park.
Victor J. Andrew High School (Consolidated High School District 230) and Tinley Park High School (Bremen Community High School District 228) are both secondary schools located in Tinley Park. A small portion of Tinley Park students go to Lincoln-Way East High School.
Most residents of Tinley Park are located within the residency boundaries for Moraine Valley Community College; the rest reside in the community college district for South Suburban College. A very small portion of Tinley Park goes to Joliet Junior College.
^ "Tinley Park, IL - Official Website - Mayor". Tinleypark.org. Retrieved 22 August 2017.
^ a b "Population and Housing Unit Estimates". United States Census Bureau. Retrieved June 9, 2017.
^ a b "Profile of General Population and Housing Characteristics: 2010 Demographic Profile Data (DP-1): Tinley Park village, Illinois". United States Census Bureau. Retrieved March 20, 2013.
^ "America's Best Place to Raise Your Kids". BusinessWeek. November 17, 2009. Retrieved 2009-11-18.
^ "Tinley Park Among Safest US Cities: Report". Patch.com. 4 August 2017. Retrieved 22 August 2017.
^ Bureau, U.S. Census. "American FactFinder - Results". Factfinder.census.gov. Retrieved 22 August 2017.
^ "Tinley Park music theater gets new name, again". Chicago Tribune. Retrieved January 25, 2015.
^ "First Midwest Bank Amphitheatre". In Concert With You. First Midwest Bank. Retrieved May 17, 2013.
^ Profile of Selected Social Characteristics, Tinley Park, Illinois. U.S. Census Bureau. Accessed 2007-07-11.
^ Bureau, U.S. Census. "American FactFinder - Community Facts". factfinder.census.gov. Retrieved 22 August 2017.
^ "Summit Hill School District 161 - Frankfort, Illinois". www.summithill.org.
^ "About Our District Archived 2017-01-09 at Archive.today." Elementary School District 159. Retrieved on January 9, 2017.
^ "Tinley Park Campus". Swchristian.org. Retrieved 17 May 2016.


Lady Beatrix Westport was once destined to be the most successful debutant the ton has ever seen. Now, it is all she can do to recover from the brutal coaching accident which killed her entire family. Now, she has only one purpose. Continue her family line and secure her father's earldom. When she meets Captain Duke, who awakens her heart and desires, she knows he's the best choice for husband. But will her dedication to her duty destroy her only chance at love?
Captain Adam Duke loves adventure and justice. After spending his entire life working to free slaves, he comes to London to open offices. When he meets the wounded Lady Beatrix, he immediately feels a deep connection to her and longs to free her from her pain. But he refuses to be just the stud she longs for. Can he convince her to choose a life of love and adventure or will her broken past drive them apart?
My Wild Duke by Eva Devon is a welcome addition to her Duke's Club series, bringing together a woman who wants to forget the world with a man who finds her unforgettable.
From the moment Captain Adam Duke spied Lady Beatrix Westport, he's instantly captivated by her. It was not just her beauty and resolute dignity he that drew him, but rather the aura of innate sadness that surrounded her. Adam understands pain and grief, and he correctly casts Beatrix as a lost soul. He wants to meet her, to befriend her and show her that one can move past loss.
Adam reminds Beatrix of the girl she was before tragedy struck – when her days were filled with laughter and she embraced life to the fullest. Viewing Adam's confident nature and wild appearance (he is American after all *gasp*), Beatrix vows he is a man she has no interest in meeting as he reminds her of the freedom and joy she has lost.
Eva Devon creates a lovely story of the healing power of love and learning to find your true self in one another. Adam and Beatrix are beautiful together. All the love and kindness (and yes, passion) Adam showers on Beatrix help bring her out of the darkness. Adam is a multi-faceted character with a fascinating backstory and strong sense of justice. I would have liked to see him in action as a sea captain, perhaps with Beatrix along on one of his "raids." That's really my only complaint with My Wild Duke – I wish there was more of it!


A diesel fired, electric hot water blaster for automotive, construction and industrial applications. Hot water pressure washers are great for removing grease and oil in commercial kitchens, garage floors, machinery and other applications. Also known as Pressure Cleaner and Gerni.


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Q: Cloning and editing a site on wordpress I just cloned an existing site on cpanel. It is a real estate website. I want to edit some text in the cloned site. How do I do this. Any help please. I'm on the cpanel but I have no idea where to go.

A: Have you thought about using a plugin to achieve your goal?  You could easily use a tool such as:
  https://wordpress.org/plugins/all-in-one-wp-migration/
  or
  https://wordpress.org/plugins/wp-clone-by-wp-academy/
And deploy them on a different server or WP Installation.  WP-Clone in particular makes this process fairly simple and straight forward.  Not sure if I read your question right, but it seems to me that you want a simple, quick method of achieving this goal rather than manually exporting a database and/or Wordpress install.  Hope that helps.  Cheers.