text:
\section*{Introduction}
V.~Arnold observed a strange duality between the 14 exceptional unimodular singularities \cite{Ar}. One of the features of this duality is that dual singularities have Saito dual characteristic polynomials of the classical monodromy transformations \cite{S1, S2}.  For a fixed positive integer $d$ and for a rational function $\varphi(t)$ of the form $\prod\limits_{m|d}(1-t^m)^{s_m}$, the Saito dual
of $\varphi$ with respect to $d$ is
$$
\varphi^\ast(t) = \prod\limits_{m|d}(1-t^{d/m})^{-s_m}.
$$
(For quasihomogeneous singularities, in particular for the quasihomogeneous representatives of the 14 exceptional unimodular singularities, $d$ is the (quasi)de\-gree of the function.)

A system of weights $\underline{w}=(w_1, \ldots, w_n;d)$ for a quasihomogeneous  polynomial $f$  defines a natural grading on the ring ${\mathbb C}[x_1, \ldots, x_n]/(f)$ with the Poincar\'e series
$$
P_{\underline{w}}(t)=\frac{1-t^{d}}{\prod\limits_{j=1}^n (1-t^{w_j})}\,.
$$
Here, in general, we do dot assume that the system of weights is reduced, i.e., we permit the greatest common divisor of the weights $w_1, \ldots , w_n$ to be greater than 1.
The system of weights $\underline{w}$ defines a ${\mathbb C}^\ast$-action on ${\mathbb C}^n$:
$$
\lambda\ast(x_1, \ldots, x_n)=(\lambda^{w_1}x_1, \ldots, \lambda^{w_n}x_n).
$$
This action may have orbits of different types (i.e., with different isotropy subgroups) on the zero-level set $X_f$ of the polynomial $f$. The orbit invariants give rise to a rational function ${\rm Or}_{\underline{w}}(t)$: see, e.g., \cite{Trieste}.

Let $\widetilde{\zeta}_f(t)=\zeta_f(t)/(1-t)$ be the reduced zeta function of the classical monodromy transformation $h_f:V_f\to V_f$ of $f$ ($V_f$ is the Milnor fibre of $f$). For $n=3$ and for an isolated singularity $f$, the reduced zeta function $\widetilde{\zeta}_f(t)$ coincides with the characteristic polynomial of the monodromy transformation. In \cite{MRL} it was shown that, for the reduced system of weights $\underline{w}$ of $f$, one has
\begin{equation}\label{ourSaito}
P_{\underline{w}}(t){\rm Or}_{\underline{w}}(t)=\widetilde{\zeta}^\ast_f(t),
\end{equation}
where $\widetilde{\zeta}^\ast_f(t)$ is the Saito dual (with respect to the degree $d$) of the reduced zeta function $\widetilde{\zeta}_f(t)$.

Arnold's strange duality can be considered as a special case of mirror symmetry. In \cite{ET} it was shown that Arnold's strange duality can be generalized to a duality between so called invertible polynomials (see Section~\ref{Sect:Inv}). For an invertible polynomial $f$ the dual polynomial is the Berglund-H\"ubsch transpose $f^T$ of $f$ (Section~\ref{Sect:Inv}). The relation between the characteristic polynomials of the monodromy transformations of the dual exceptional unimodular singularities generalizes in the following way.

For a rational function $\varphi(t)$ of the form $\prod\limits_m(1-t^m)^{s_m}$, its $k$th ``power'' $\varphi^{(k)}(t)$ is defined by
$$
\varphi^{(k)}(t)=\prod_m(1-t^{\frac{m}{\gcd{(m,k)}}})^{\gcd{(m,k)}s_m}.
$$
If $\varphi(t)$ is the zeta function of a transformation $h:Z\to Z$, then $\varphi^{(k)}(t)$ is the zeta function of the $k$th power $h^k$ of the transformation $h$.

For a rational function $\varphi(t)=\prod\limits_m(1-t^m)^{s_m}$, its (formal) $k$th ``root'' (or ``root'' of degree $k$) is a rational function $\psi(t)=\varphi^{(1/k)}(t)$ of the same form such that $\psi^{(k)}(t)=\varphi(t)$. A $k$th ``root'' of a rational function does not always exist and, in general, is not well defined. Note that the function $\varphi(t)=\prod\limits_m(1-t^m)^{s_m}$ has a ``root'' of degree $k$ if and only if each factor $(1-t^m)^{s_m}$ has a ``root'' of this degree.

An invertible polynomial has a canonical system of weights which may be non-reduced (Section~\ref{Sect:Inv}).
In \cite{ET} it was shown that, if $n=3$ and $f$ is a non-degenerate invertible polynomial with the canonical system of weights being reduced, then
\begin{equation}\label{ET}
P_{\underline{w}}(t){\rm Or}_{\underline{w}}(t)=\widetilde{\zeta}^{(1/c^T)}_{f^T}(t),
\end{equation}
where $c^T$ is the greatest common divisor of the canonical weights of $f^T$.
Together with (\ref{ourSaito}) this implies that in this case
\begin{equation}\label{dual_reduced}
\widetilde{\zeta}^\ast_f(t)=\widetilde{\zeta}^{(1/c^T)}_{f^T}(t).
\end{equation}

We shall show that the equation (\ref{dual_reduced}) has a generalization of the form
\begin{equation}\label{duality}
\widetilde{\zeta}^{(1/c)\ast}_f(t)=\left(\widetilde{\zeta}^{(1/c^T)}_{f^T}(t)\right)^{(-1)^{n-1}}
\end{equation}
for a number of cases when the canonical systems of weights both of $f$ and $f^T$ may be non-reduced and also when $n$ is arbitrary. Moreover, we show that in these cases the ``roots'' of the zeta functions are zeta functions of roots of the monodromy transformations defined by a geometric construction.

\section{Invertible polynomials} \label{Sect:Inv}
A quasihomogeneous polynomial $f$ in $n$ variables is said to be invertible (see, e.g., \cite{Kr}) if it is of the form
\begin{equation}\label{inv}
f(x_1, \ldots, x_n)=\sum\limits_{i=1}^n a_i \prod\limits_{j=1}^n x_j^{E_{ij}}
\end{equation}
for some coefficients $a_i\in{\mathbb C}^\ast$ and for a matrix $E=(E_{ij})$ with positive integer entries and with $\det E\ne 0$.
For simplicity we assume that $a_i=1$ for $i=1, \ldots, n$. (This can be achieved by a rescaling of the variables $x_j$.)
An invertible quasihomogeneous polynomial $f$ is non-degenerate if it has (at most) an isolated critical point at the origin in ${\mathbb C}^n$.

According to \cite{KS}, an invertible polynomial $f$ is non degenerate if and only if it is a (Thom-Sebastiani) sum of invertible polynomials (in groups of different variables) of the following types:
\begin{enumerate}
\item[1)] $x_1^{p_1}x_2 + x_2^{p_2}x_3 + \ldots + x_{m-1}^{p_{m-1}}x_m + x_m^{p_m}$ (chain type; $m\ge 1$);
\item[2)] $x_1^{p_1}x_2 + x_2^{p_2}x_3 + \ldots + x_{m-1}^{p_{m-1}}x_m + x_m^{p_m}x_1$ (loop type; $m\ge 2$).
\end{enumerate}

\begin{sloppypar}

An invertible polynomial (\ref{inv}) has a canonical system of weights $\underline{w}=(w_1, \ldots, w_n;d)$, where $w_i$ is the determinant of the matrix $E$ with the $i$th column substituted by $(1, \ldots, 1)^T$ and $d=\det E$. One has $f(\lambda^{w_1}x_1, \ldots, \lambda^{w_n}x_n) = \lambda^d f(x_1, \ldots, x_n)$. The canonical system of weights may be non-reduced, i.e., one may have $c=\gcd(w_1, \ldots, w_n)\ne 1$.

\end{sloppypar}

\begin{example}
Let $f(x_1,x_2,x_3)=x_1^3x_2+x_2^4x_3+x_3^5$. One has $\underline{w}=(16,12,12;60)$, $c=4$.
\end{example}

The Berglund-H\"ubsch transpose $f^T$ of the invertible polynomial (\ref{inv}) is defined by
$$
f^T(x_1, \ldots, x_n)=\sum\limits_{i=1}^n a_i \prod\limits_{j=1}^n x_j^{E_{ji}}\,.
$$
If the invertible polynomial $f$ is non-degenerate, then $f^T$ is non-degenerate as well.

If the canonical system of weights of $f$ is reduced, the canonical system of weights of $f^T$ can be non-reduced. The canonical (quasi)degrees of $f$ and $f^T$ coincide.

\begin{example} Let $f(x_1,x_2,x_3)=x_1^5x_2+x_2^2+x_3^3$. Then $f^T(x_1,x_2,x_3)=x_1^5+x_1x_2^2+x_3^3$. One has $\underline{w}_f = (3,15,10;30)$, $c=1$, $\underline{w}_{f^T}=(6,12,10;30)$, $c^T=2$.
\end{example}

\section{Geometric roots of the monodromy}
Let $f$ be a  quasihomogeneous polynomial in $n$ variables with weights $w_1, \ldots, w_n$ and degree $d$. (We do not suppose, in general, the system of weights to be reduced.) The monodromy transformation $h_f$ of $f$ can be constructed in the following way. Let $\Gamma_t:{\mathbb C}^n\to{\mathbb C}^n$ be defined by $$
\Gamma_t(x_1, \ldots, x_n)=\left(\exp\left({2\pi i w_1t}/{d}\right)x_1, \ldots, \exp\left({2\pi i w_nt}/{d}\right)x_n \right).
$$
The map $\Gamma_t$ sends the Milnor fibre $V_1=f^{-1}(1)$ to the Milnor fibre $V_{\exp(2\pi it)}=f^{-1}(\exp(2\pi it))$. Then $h_f=\Gamma_1:V_1\to V_1$.

Suppose that there exists an action of the cyclic group ${\mathbb Z}_k$ on ${\mathbb C}^n$ such that the generator of ${\mathbb Z}_k$ acts by
$$
\Sigma(x_1, \ldots, x_n)=(\sigma^{m_1}x_1, \ldots, \sigma^{m_n}x_n),
$$
where $\sigma=\exp\left({2\pi i}/{k}\right)$, and
$$
f(\Sigma(x_1, \ldots, x_n))=\sigma f(x_1, \ldots, x_n).
$$
Let $\widehat{h}_f=\Sigma^{-1}\circ\Gamma_{1/k}$. The map $\widehat{h}_f$ sends the Milnor fibre $V_1$ to itself.
Since $\Gamma_t$ and $\Sigma$ commute, one has $\widehat{h}_f^k=\Sigma^{-k}\circ\Gamma_1=h_f$.
We shall call $\widehat{h}_f$ {\em a geometric  root} of degree $k$ of the monodromy transformation $h_f$.

One can see that the map $\widehat{h}_f$ is the monodromy transformation of the germ $f^k$ on the quotient ${\mathbb C}^n/{\mathbb Z}_k$.

For an invertible polynomial (\ref{inv}) the required action of the group ${\mathbb Z}_k$ exists if and only if the system of equations
\begin{equation}\label{modk}
E \left( \begin{array}{c} m_1 \\ \vdots \\ m_n \end{array} \right) \equiv \left( \begin{array}{c} 1 \\ \vdots \\ 1 \end{array} \right) \mbox{ mod } k
\end{equation}
has a solution (in ${\mathbb Z}_k^n$). If $k$ is prime this means that
$${\rm rk}\, E_k={\rm rk}\,\left( E_k \left| \begin{array}{c} 1 \\ \vdots \\ 1 \end{array} \right) \right. ,$$
where $E_k$ is the matrix obtained from $E$ by reduction modulo
$k$. If in addition ${\rm rk}\, E_k<n$, a solution of ($\ref{modk}$) is not unique.

\section{Duality of zeta functions}

\begin{theorem} \label{theo1}
Let $f$ be a non-degenerate invertible polynomial in $n$ variables of chain or loop type and let $c$ be the greatest common divisor of the canonical weights of $f$. Then there exist geometric roots of degree $c$ of the monodromy transformation $h_f$, all of them have the same (reduced) zeta function $\widetilde{\zeta}_f^{(1/c)}(t)$, and
\begin{equation}\label{eq_theo1}
\widetilde{\zeta}_{f^T}^{(1/c^T)}(t) =
\left(\widetilde{\zeta}_{f}^{(1/c)^\ast}(t)\right)^{(-1)^{n-1}}\, ,
\end{equation}
where $f^T$ is the Berglund-H\"ubsch transpose of $f$, $c^T$ is the greatest common divisor of the corresponding weights, and ${}^\ast$ means the Saito dual with respect to the common canonical degree $d=d^T$ of $f$ and $f^T$.
\end{theorem}

\begin{proof}
Let
$$
f(x_1, \ldots, x_n)=x_1^{p_1}x_2 + x_2^{p_2}x_3 + \ldots + x_{n-1}^{p_{n-1}}x_n + x_n^{p_n}
$$
be a polynomial of chain type. Let
$$
\langle q_1, \ldots, q_k\rangle := q_1\cdots q_k -  q_2\cdots q_k + \ldots + (-1)^{k-1}q_k+(-1)^k.
$$
The canonical weights of $f$ are:
$$\langle p_2, \ldots, p_n\rangle, p_1\langle p_3, \ldots, p_n\rangle , \dots, p_1\cdots p_{n-2}\langle p_n\rangle, p_1\cdots p_{n-1};
$$
the degree is equal to $p_1\cdots p_{n}$. The equation (\ref{modk}) on the exponents defining the required ${\mathbb Z}_c$-action has the following solutions (their number being equal to $c$):
$m_1=m$, $m_2=1-mp_1$,
$$m_j=(-1)^j\langle p_2, \ldots, p_{j-1}\rangle  + (-1)^{j-1}mp_1\cdots p_{j-1} \mbox{ for }j\ge 2,
$$
where $m$ is an arbitrary integer $\mod c$. The monodromy zeta function $\zeta_f(t)$ of $f$ can be computed, e.g., with the use of the Varchenko formula \cite{Var} and is equal to
$$
\zeta_f(t)=\prod_{j=1}^n \left(1-t^{p_j\cdots p_n/c_j}\right)^{(-1)^{n-j}c_j}\,,
$$
where $c_j=\gcd{(\langle p_{j+1} ,\ldots , p_n\rangle, p_j\langle p_{j+2} , \ldots ,p_n\rangle, \ldots, p_j\cdots p_{n-2}\langle p_n\rangle, p_j\cdots p_{n-1})}$. We shall prove that a ``root'' of degree $c$ of $\zeta_f(t)$ is equal to
\begin{equation}\label{root}
\prod_{j=1}^n \left(1-t^{p_j\cdots p_n}\right)^{(-1)^{n-j}}\,.
\end{equation}
It looks rather envolved to check the number theoretical conditions on the exponents $p_j$ and the greatest common divisors $c_j$ and $c$ which give this fact. Moreover the formal ``root'' of $\zeta_f(t)$ may not be unique. Instead of that we shall show that the zeta function of the corresponding geometric root $\widehat{h}_f = \Sigma^{-1} \circ \Gamma_{1/c}$ is equal to (\ref{root}). This follows from the fact that, on the coordinate torus $\{(x_1, \ldots , x_n) \, : \, x_i=0 \mbox{ for }i <  j, x_i \neq 0 \mbox{ for } i \geq j\}$ corresponding to the variables $x_j, \ldots , x_n$, the order of the map $\Sigma^{-1} \circ \Gamma_{{1}/{c}}$ is equal to $p_j \cdots p_n$ (at each point), $j=1, \ldots , n$.

One has
$$
\Sigma^{-1} \circ \Gamma_{{1}/{c}}(x_1, \ldots , x_n)= (\exp(2\pi i b_1)x_1, \ldots , \exp(2 \pi i b_n)x_n),
$$
where
$$b_j := \frac{(-1)^{j+1} \langle p_2, \ldots , p_n \rangle + (-1)^j mp_1 \cdots p_n}{c\,p_j \cdots p_n}, \quad j=1, \ldots , n.
$$
The numerator is obviously divisible by $c$ (because $w_1=\langle p_2, \ldots , p_n \rangle$ and $d=p_1 \cdots p_n$ are divisible by $c$). One has to show that the numerator divided by $c$ has no common factor with $p_j \cdots p_n$. One can see that a common factor of $p_s$ ($s=j, \ldots, n$) and the numerator is a common factor of $p_s$ and $\langle p_{s+1}, \ldots , p_n \rangle$. Therefore it is a common factor of all the weights $w_1, \ldots , w_n$ and thus divides $c$. Therefore, the numerator divided by $c$ has no common factor with $p_s$.

The polynomial $f^T$ is also given by the formula (\ref{root}) with $p_1, \ldots , p_n$ substituted by $p_n, \ldots , p_1$ respectively. One has
\begin{eqnarray*}
\widetilde{\zeta}_f^{(1/c)}(t) & = & (1-t)^{-1} \prod_{j=2}^n (1-t^{p_j \cdots p_n})^{(-1)^{n-j}} (1-t^d)^{(-1)^{n-1}}, \\
\widetilde{\zeta}_{f^T}^{(1/c^T)}(t) & = & (1-t)^{-1} \prod_{j=2}^n (1-t^{p_1 \cdots p_{j-1}})^{(-1)^j} (1-t^d)^{(-1)^{n-1}}
\end{eqnarray*}
and therefore
$$
\widetilde{\zeta}_f^{(1/c)\ast}(t) =  (1-t^d)  \prod_{j=2}^n (1-t^{p_1 \cdots p_{j-1}})^{(-1)^{n-j-1}}(1-t)^{(-1)^n} = \left( \widetilde{\zeta}_f^{(1/c^T)} (t) \right)^{(-1)^{n-1}}.
$$

Let
$$
f(x_1, \ldots, x_n)=x_1^{p_1}x_2 + x_2^{p_2}x_3 + \ldots + x_{m-1}^{p_{m-1}}x_m + x_m^{p_m}x_1$$
be a polynomial of loop type. The canonical weights of $f$ are
$$
\langle p_2, \ldots , p_n \rangle, \langle p_3, \ldots , p_n,p_1 \rangle, \ldots , \langle p_n, p_1, \ldots , p_{n-2} \rangle, \langle p_1, \ldots , p_{n-1} \rangle
$$
and the degree is equal to $d=p_1 \cdots p_n + (-1)^{n-1}$. The solutions of (\ref{modk}) are given by the same formulae as above.

At first glance this looks somewhat strange: the systems of equations are different. However, one should keep in mind that they are solved modulo different greatest common divisors of the weights. Moreover, for the same exponents $p_1, \ldots , p_n$, the greatest common divisors of the weights for the chain and for the loop types are relatively prime.

The zeta function is
$$
\zeta_f(t)= (1- t^{d/c})^{(-1)^{n-1}c}.
$$
It is obvious that a formal ''root'' of degree $c$ of $\zeta_f(t)$ is equal to $(1-t^d)^{(-1)^{n-1}}$. Let us show that the zeta function of the geometric root $\widehat{h}=\Sigma^{-1} \circ \Gamma_{1/c}$ of degree $c$ of the monodromy transformation of $f$ is also equal to $(1-t^d)$. For that one has to show that the order of the map $\widehat{h}$ on the (maximal) torus $\{ (x_1, \ldots , x_n) \, : \, x_i \neq 0, i=1, \ldots , n \}$
is equal to $d$ at each point. One has
$$
\Sigma^{-1}\circ\Gamma_{1/c}(x_1, \ldots, x_n)=(\exp{(2\pi i b_1)}x_1, \ldots, \exp{(2\pi i b_n)}x_n)\,,
$$
where $b_j=\frac{w_j-m_jd}{cd}$. The greatest common divisor of all $w_j-m_jd$ and $d$ is just $c$ and therefore all
ratios $\frac{w_j-m_jd}{c}$ ($j=1, \ldots, n$) together have no common factor with $d$. One has $\widetilde{\zeta}_{f}^{(1/c)}(t)=\widetilde{\zeta}_{f^T}^{(1/c^T)}(t)= (1-t^d)^{(-1)^{n-1}}/(1-t)$. This implies (\ref{eq_theo1}).
\end{proof}

\begin{example} Let $f(x_1,x_2,x_3)=x_1^3x_2+x_2^4x_3+x_3^5$, $f^T(x_1,x_2,x_3)=x_1^3+x_1x_2^4+x_2x_3^5$. One has $c=4$, $c^T=10$, $d=d^T=16$,
$$
\widetilde{\zeta}_f(t) = \frac{(1-t^5)(1-t^{60/4})^4}{(1-t^{20/4})^4(1-t)}, \quad
\widetilde{\zeta}_{f^T}(t) = \frac{(1-t^3)(1-t^{60/10})^{10}}{(1-t^{12/2})^2(1-t)}.
$$
The reduced zeta functions of the geometric roots of the monodromy transformations of $f$ and $f^T$ are
$$
\widetilde{\zeta}^{(1/4)}_f(t) = \frac{(1-t^5)(1-t^{60})}{(1-t^{20})(1-t)}, \quad
\widetilde{\zeta}^{(1/10)}_{f^T}(t) = \frac{(1-t^3)(1-t^{60})}{(1-t^{12})(1-t)}.
$$
They obviously are Saito dual. Note that a ''root'' of degree 4 of $\widetilde{\zeta}_f(t)$ is not well defined, e.g.
$$
\frac{1-t^{60}}{(1-t^5)^3(1-t)}
$$
is another ''root''.
\end{example}

Let $f(x_1, x_2, x_3)=x_1^{2}+ x_2^{2} + x_3^{p}$. In this case $f^T=f$ and $f$ has a singularity of type $A_{p-1}$ at the origin. The reduced monodromy zeta function of $f$ is equal to $(1-t^p)/(1-t)$ and coincides with the reduced monodromy zeta function of the polynomial $x^p$ in one variable.
It is Saito self dual with respect to the degree $p$ of the polynomial $x^p$, but not with respect to the canonical degree of $f$ equal to $4p$. There exist geometric roots of the corresponding degrees for the polynomial $x^p$, but not for $f$.

\begin{theorem}\label{theo2}
Let $f$ be a non-degenerate invertible polynomial in 3 variables such that both $f$ and $f^T$ have critical points at the origin and f is not of the form $x_1^{2}+ x_2^2 + x_3^{p}$ (up to permutation of the variables).
Then the following statements hold:
\begin{itemize}
\item[{\rm 1)}]  If both reduced monodromy zeta functions $\widetilde{\zeta}_f(t)$ and $\widetilde{\zeta}_{f^T}(t)$ have ``roots'' (of degrees $c$ and $c^T$ respectively), then they have ``roots'' $\widetilde{\zeta}_f^{(1/c)}(t)$ and $\widetilde{\zeta}_{f^T}^{(1/c^T)}(t)$ such that
\begin{equation}\label{eq_theo2}
\widetilde{\zeta}_{f^T}^{(1/c^T)}(t) =
\widetilde{\zeta}_{f}^{(1/c)*}(t)\,,
\end{equation}
where $*$ means Saito dual with respect to the common canonical degree $d=d^T$.
\item[{\rm 2)}]   In all these cases except $f(x_1,x_2,x_3)=x_1^{p_1}x_2+x_2^{p_2}x_1+x_3^{p_3}$ with $p_3=p_1p_2-1$ and $\gcd{(p_1-1, p_2-1)}=1$, the monodromy transformations of both $f$ and $f^T$ have geometric roots, all geometric roots of each of them have the same reduced monodromy zeta functions and these functions are Saito dual to each other (with respect to $d=d^T$).
\item[{\rm 3)}]   If $\widetilde{\zeta}_f(t)$ has a ``root'' of degree $c$, then either $\widetilde{\zeta}_{f^T}(t)$ also has a ``root'' of degree $c^T$, or $f(x_1, x_2, x_3)=x_1^{2}x_2+ x_2^p + x_3^{p}$ with $p$ odd (and then $\widetilde{\zeta}_{f^T}(t)$ has no ``root'' of degree $c^T$).
\end{itemize}
\end{theorem}

\begin{proof}
This is already proved for polynomials of chain and loop types (Theorem~\ref{theo1}). (In these cases geometric roots of the monodromy transformations always exist.) We have to prove this for the other types.

In what follows we consider all polynomials up to permutation of the variables. Let $s_m$ be the power of the binomial $(1-t^m)$ in the decomposition of $\widetilde{\zeta}_f(t)$:
$$
\widetilde{\zeta}_f(t)=\prod_{m\ge 1}(1-t^m)^{s_m}.
$$

\smallskip
a) Let
$f(x_1, x_2, x_3)=x_1^{p_1}+ x_2^{p_2} + x_3^{p_3}$
(Brieskorn-Pham type). One has $f^T=f$. We assume that $p_1\le p_2\le p_3$. Note that $p_1 \geq 2$. The canonical weight system of $f$ is
$(p_2p_3, p_1p_3, p_1p_2; p_1p_2p_3)$. The reduced monodromy zeta function of $f$ is
\begin{equation}\label{zeta_a}
\widetilde{\zeta}_f(t)=\frac{\prod\limits_{i}(1-t^{p_i})(1-t^{p_1p_2p_3/c})^c}{\prod\limits_{i<j}(1-t^{p_ip_j/c_{ij}})^{c_{ij}}(1-t)}\,,
\end{equation}
where $c_{ij}=\gcd{(p_i,p_j)}$.

If the exponents $p_1$, $p_2$, $p_3$, are pairwise coprime, i.e. $c=c_{ij} =1$, then the reduced zeta-function (\ref{zeta_a}) is Saito self-dual with respect to $d=p_1p_2p_3$. The monodromy transformation of $f$ has geometric roots if and only if the exponents $p_1$, $p_2$, $p_3$ are pairwise coprime.

If $p_1<p_2$, then $s_{p_1}=1$ and in order to have a ``root'' of $\widetilde{\zeta}_f(t)$ of degree $c$ one needs $\gcd{(p_1,c)}=1$. In this case $\gcd{(p_1, p_2p_3)}=c_{12}=c_{13}=1$, $c=c_{23}=\gcd{(p_2, p_3)}$. If in addition $p_2<p_3$, then $s_{p_2}=1$ and in order to have a ``root'' of $\widetilde{\zeta}_f(t)$ one needs $\gcd{(p_2,c)}=1$.
This implies that $c=1$.

If $p_1<p_2=p_3$ and $\gcd{(p_1,c)}=1$, then $c_{23}=c=p_2$ and $s_{p_2}=2-c$. If $c\ne 2$, then $\widetilde{\zeta}_f(t)$ has no ``root'' of degree $c=p_2$. If $c=2$, then $p_1=1$ and $f$ has no critical point at the origin.

If $p_1=p_2<p_3$, then $s_{p_1}=2-p_1$ and $p_1\vert c$. If $p_1\ne 2$, then $\widetilde{\zeta}_f(t)$ has no ``root'' of degree $c$. If $p_1=2$, then $f$ is of the form $x_1^2+x_2^2+x_3^p$ excluded from
consideration.

Finally if $p_1=p_2=p_3$, then $c=p_1^2$, $s_{p_1}=p_1^2-3p_1+3$, $c>s_{p_1}>0$, and $\widetilde{\zeta}_f(t)$ has no ``root'' of degree $c$.

\smallskip
b) Let
$f(x_1, x_2, x_3)=x_1^{p_1}x_2+ x_2^{p_2}x_1 + x_3^{p_3}$. One has $f^T=f$. The canonical weight system of $f$ is
$(p_3(p_2-1), p_3(p_1-1), p_1p_2-1; p_3(p_1p_2-1))$. The reduced monodromy zeta function of $f$ is
\begin{equation}\label{zeta_b}
\widetilde{\zeta}_f(t)=\frac{(1-t^{p_3})(1-t^{p_3(p_1p_2-1)/c})^c}{(1-t^{(p_1p_2-1)/c_{1}})^{c_{1}}(1-t)}\,,
\end{equation}
where $c_{1}=\gcd{(p_2-1,p_1-1)}$.

If $\gcd{(p_3,c)}=1$, then $c=\gcd{(p_2-1,p_1-1)}=c_1$ and geometric roots of the monodromy transformation of $f$ of degree $c$ exist. (They exist for $x_1^{p_1}x_2+ x_2^{p_2}x_1$ due to Theorem~\ref{theo1} because $c=c_1$, and for $x_3^{p_3}$ since $\gcd{(p_3,c)}=1$.) The geometric roots have one and the same reduced zeta function
$$
\widetilde{\zeta}^{(1/c)}_f(t)=\frac{(1-t^{p_3})(1-t^{p_3(p_1p_2-1)})}{(1-t^{p_1p_2-1})(1-t)}\,,
$$
which is Saito self dual with respect to $d=p_3(p_1p_2-1)$.

Suppose that $\gcd{(p_3,c)}\ne 1$. In this case geometric roots of the monodromy transformation of $f$ do not exist.

If $p_3 \neq (p_1p_2-1)/c_1$, then $s_{p_3} \equiv 1\mod c$ and $\widetilde{\zeta}_f(t)$ has no ``root'' of degree $c$.

If $p_3=(p_1p_2-1)/c_1$, then $p_3\vert c$ and $s_{p_3} \equiv 1-c_1\mod c$. If $c_1\ne 1$, then (since $p_3\vert c$) in order to have a ``root'' of degree $c$ of $(1-t^{p_3})^{s_{p_3}}$ it is necessary that $p_3\vert (c_1-1)$, however $p_3> p_1-1$ and $p_3> p_2-1$ and therefore $p_3>c_1$. Thus $\widetilde{\zeta}_f(t)$ has no ``root'' of degree $c$. If $c_1=1$ (i.e. $p_3=p_1p_2-1$) then
$$
\widetilde{\zeta}_f(t) = \frac{(1-t^{p_3})^{p_3}}{1-t} ,
$$
 a ``root'' of $\widetilde{\zeta}_f(t)$ of degree $c=p_3$ exists, moreover it is unique, namely equal to $\widetilde{\zeta}^{(1/c)}_f(t)=\frac{1-t^{d}}{1-t}$, and thus is Saito self dual.

\smallskip
c) Let
$f(x_1, x_2, x_3)=x_1^{p_1}x_2+ x_2^{p_2} + x_3^{p_3}$. The transpose $f^T$ is obtained from $f$ by interchanging the exponents $p_1$ and $p_2$. The canonical weight system of $f$ is
$(p_3(p_2-1), p_3p_1, p_1p_2; p_1p_2p_3)$. The reduced monodromy zeta function of $f$ is
\begin{equation}\label{zeta_c}
\widetilde{\zeta}_f(t)=\frac{(1-t^{p_2})(1-t^{p_3})(1-t^{p_1p_2p_3/c})^c}{(1-t^{p_1p_2/c_1})^{c_1}
(1-t^{p_2p_3/c_2})^{c_2}(1-t)}\,,
\end{equation}
where $c_{1}=\gcd{(p_2-1,p_1)}$, $c_2=\gcd{(p_2,p_3)}$.
Geometric roots of the monodromy transformation of $f$ exist if and only if $\gcd{(p_3,c)}= 1$. (In this case $c=c_1$, geometric roots for $x_1^{p_1}x_2+ x_2^{p_2}$ exist due to Theorem~\ref{theo1} because $c=c_1$, and for $x_3^{p_3}$ since $\gcd{(p_3,c)}=1$.) In this case $c_2=1$ and the reduced zeta function of any geometric root of the monodromy transformation of $f$ is equal to
$$
\widetilde{\zeta}^{(1/c)}_f(t)=\frac{(1-t^{p_2})(1-t^{p_3})(1-t^{p_1p_2p_3})}{(1-t^{p_1p_2})
(1-t^{p_2p_3})(1-t)}\,.
$$
In this case one also has $\gcd{(p_3,c^T)}= 1$ and
$$
\widetilde{\zeta}^{(1/c^T)}_f(t)=\frac{(1-t^{p_1})(1-t^{p_3})(1-t^{p_1p_2p_3})}{(1-t^{p_1p_2})
(1-t^{p_1p_3})(1-t)}=\widetilde{\zeta}^{(1/c)*}_f(t)\,.
$$

Suppose that $\gcd{(p_3,c)}\ne 1$. If $s_{p_3}=1$, then a ``root'' of degree $c$ of $\widetilde{\zeta}_f(t)$ does not exist. Otherwise $p_3$ has to coincide with $p_2$, or with $p_1p_2/c_1$, or with $p_2p_3/c_2$.
In all these cases $p_2\vert p_3$ (and therefore $p_3=p_2p_3/c_2$), and $p_2\vert c$.

If $p_2\ne p_3$, then $s_{p_2}$ is equal either to 1 (and therefore no ``root'' of $\widetilde{\zeta}_f(t)$ exists), or to $(1-c_1)$ (if $p_1p_2/c_1=p_2$). In the latter case, for the existence of a ``root'', it is necessary that $p_2\vert (c_1-1)$. However, $c_1<p_2$ and this can only happen if $c_1=1$. This implies that $p_1=1$. In this case $f^T$ has no critical point at the origin.

If $p_2=p_3$, then $c_2=p_2$, $p_2 | c$, and $s_{p_2} \mod c$ is equal either to $(2-p_2)$, or to $(2-c_1-p_2)$ (if $p_2=p_1p_2/c_1$, i.e. $p_1=c_1$). In the first case a ``root'' of $\widetilde{\zeta}_f(t)$ can only exist if $p_2=2$. Then $c_1=1$, $c=2$, $s_{2p_1}=-1$ and no ``root'' of $\widetilde{\zeta}_f(t)$ of degree 2 exists.
In the second case either $c_1=p_2-1=p_1$, $s_{p_2}=3$ and therefore a ``root'' exists if and only if $p_2=p_3=3$, $p_1=2$ (in this case the polynomial $f$ has a singularity of type $\widetilde{E}_6$), or $c_1\le (p_2-1)/2$, $-3p_2/2<s_{p_2}\le -p_2+1$ and a ``root'' of $\widetilde{\zeta}_f(t)$ can exist only if $s_{p_2}=-p_2$, i.e. $c_1=p_1=2$ and $p_2$ is odd.

If $p_1=2$ and $p_2=p_3=p$ is odd,
$$
\widetilde{\zeta}_f(t)=\frac{(1-t^{p})^p}{1-t}
$$
and a ``root'' of degree $c=2p$ exists.
In this case
$$
\widetilde{\zeta}_{f^T}(t)=\frac{(1-t^2)(1-t^p)(1-t^{2p})^{p-2}}{1-t}
$$
and a ``root'' of degree $c^T=p$ does not exist.
\end{proof}

\begin{remarks}
{\bf 1.} For the invertible polynomials in the last table of \cite{ET}, no roots of the monodromy zeta function exist.

\noindent {\bf 2.}
One can show that for a non-degenerate invertible polynomial in two variables a ``root'' of the monodromy zeta function exists if and only if a geometric root of the monodromy transformation exists. In this case, a geometric root of the monodromy transformation of $f^T$ also exists and
$$
\widetilde{\zeta}_{f^T}^{(1/c^T)}(t) =
\left(\widetilde{\zeta}_{f}^{(1/c)^\ast}(t)\right)^{-1}\, .
$$
\end{remarks}

redpajama_set_name: RedPajamaArXiv


text:
Q: Cannot implicitly convert type System.data.datatable to Microsoft.Office.Interop.Excel  public DataTable populateVendorGridView()
        {

            DataSet ds = new DataSet();
            ds = (DataSet)Session["VendorInvoiceid"];

            return ds.Tables[0]; //getting error here
        }

A: a DataTable type exists in both namespaces:
Microsoft.Office.Interop.Excel

and
System.Data

which are imported into your file.
You have to explicitly reference the correct namespace for the return type of populateVendorGridView:
public System.Data.DataTable populateVendorGridView()
{
    ...

redpajama_set_name: RedPajamaStackExchange


text:
Home Happenings 'I wish my people the best' — Saraki breaks silence on 'shocking' defeat
'I wish my people the best' — Saraki breaks silence on 'shocking' defeat
By my backyard story February 26, 2019 0
Senate President Bukola Saraki has reacted to his loss in Saturday's election, wishing the people of the state the best.
Ibrahim Oloriegbe, candidate of the All Progressives Congress (APC), had defeated Saraki who ran on the platform of the Peoples Democratic Party (PDP).
The APC also cleared seats in the house of reps and senate.
In a statement on Tuesday, Saraki said those who emerged winners of Saturday's polls in Kwara are not his enemies.
He said although the elections were generally peaceful, card readers were not used in over 70 percent of the polling units, leading to cases of over voting.
"Whatever the final outcome of the election, I wish the candidates that have emerged all the best in their attempts to serve our people,"Yusuph Olaniyonu, Saraki's media aide, quoted him as saying.
"It is my prayers that the good people of Kwara State will always have the best from any government both at state and federal levels.
"As a product of a family and a political structure that is, from its foundation, devoted to the service and development of our state and its people, it is my wish that our people will always have a good deal at all times.
"The new development will even provide the people the opportunity to compare and contrast. After all, the people who have emerged from last Saturday's election are not my enemies. They are fellow Kwarans."
The senate president said candidates of the Peoples Democratic Party (PDP) are the best for Kwara.
"Therefore, I enjoin our people to come out en mass on election day and vote for them. I am going to work with our party leaders to further sell the PDP candidates to the general public," he said.
"I thank all Nigerians for their goodwill and to enjoin all of us that as we patiently await the outcome of the presidential election, we pray for peace, unity and genuine development in our country.
"It is also our prayers that at all times, the wish of the people will always prevail in the choice of the leadership and the electorate will always enjoy the benefit of good governance."

redpajama_set_name: RedPajamaCommonCrawl


text:
S The Rake's Progress
BBC Radio 3, 2 October 1971 18.55
Opera in three acts and an epilogue by STRAVINSKY
Libretto by W. H. AUDEN and CHESTER KALLMAN
(gramophone records)
SADLER'S WELLS OPERA CHORUS COLIN TILNEY (harpsichord)
ROYAL PHILHARMONIC ORCHESTRA conducted by THE COMPOSER Act 1
Unknown: W. H. Auden
Unknown: Chester Kallman
BBC Radio 3 is a radio service which began broadcasting on 30 September 1967. It replaced Third Programme.
Feedback about S The Rake's Progress, BBC Radio 3, 18.55, 2 October 1971
Please leave this link here so we can find the programme you're referring to: http://genome.ch.bbc.co.uk/09fad05dd90b43c48ff90be0db333cd8


text:
COTTON, GILES
Save this entry to MyTSHA »
Paul M. Lucko, rev. by Anthony L. Carr
COTTON, GILES (ca. 1814–ca. 1883). Giles Cotton, former slave and member of the Texas legislature, was born around 1814 in South Carolina. He was most likely the slave of Ethan A. Stroud, a plantation owner who moved from Chambers County, Alabama, to Robertson County, Texas, in 1837. According to Cotton's 1869 voter's registration card, he arrived in the Robertson Colony in present-day Robertson County, Texas, near the area of Calvert in 1837. Apparently he was married by 1840 to a woman named Miley, and his oldest known son was born in Robertson County in 1840. After the death of Ethan Stroud, in 1847 Cotton was moved to Limestone County (near Mexia) and became the property of Ethan's son Logan A. Stroud. He became a favored slave of Stroud and worked as a teamster transporting goods from the port of Galveston to the Limestone area. After emancipation, in 1867, he moved back to the area of Calvert in Robertson County, where he worked as a farmer.
In late 1869 voters from Robertson, Leon, and Freestone counties elected Cotton, running as a Republican, to the House of the Twelfth Texas Legislature. He served from February 10, 1870, to January 14, 1873, and was on the Agriculture and Stock Raising Committee and Privileges and Elections Committee. He supported legislation that made Calvert the Robertson County seat. The United States census for 1870 reported that Cotton and his wife, Rachel, could neither read nor write and lived with their seven children. Robertson County marriage records show that a formal marriage between the couple occurred on September 5, 1870. The 1880 census listed Cotton as a farmer with his wife Rachel and five children in the household. Cotton apparently died near Hammond in Robertson County either in 1883 or 1884. Tax records as well as legislative records have often had Cotton's first name misspelled as Jiles or Silas.
J. Mason Brewer, Negro Legislators of Texas and Their Descendants (Dallas: Mathis, 1935; 2d ed., Austin: Jenkins, 1970). Walter F. Cotton, History of Negroes of Limestone County from 1860 to 1939 (Mexia, Texas: Chatman and Merriwether, 1939). Francis T. Ingmire, Robertson County, Texas Marriage Records, 1838–1875 (St. Louis: Frances T. Ingmire, 1980). Legislative Reference Library of Texas: Silas G. Cotton (http://www.lrl.state.tx.us/legeLeaders/members/memberDisplay.cfm?memberID=4421&searchparams=chamber=~city=~countyID=0~RcountyID=~district=~first=~gender=~last=cotton~leaderNote=~leg=~party=~roleDesc=~Committee=), accessed August 6, 2014. Doris Hollis Pemberton, Juneteenth at Comanche Crossing (Austin: Eakin Press, 1983). Merline Pitre, Through Many Dangers, Toils and Snares: The Black Leadership of Texas, 1868–1900 (Austin: Eakin, 1985).
See related articles by:
Twelfth Legislature (1870-1871)
Slaves, Free Blacks, and Freedmen
Antebellum Texas
Politics and Government (African-American)
Image Use Disclaimer
All copyrighted materials included within the Handbook of Texas Online are in accordance with Title 17 U.S.C. Section 107 related to Copyright and "Fair Use" for Non-Profit educational institutions, which permits the Texas State Historical Association (TSHA), to utilize copyrighted materials to further scholarship, education, and inform the public. The TSHA makes every effort to conform to the principles of fair use and to comply with copyright law.
For more information go to: http://www.law.cornell.edu/uscode/17/107.shtml
If you wish to use copyrighted material from this site for purposes of your own that go beyond fair use, you must obtain permission from the copyright owner.
The following, adapted from the Chicago Manual of Style, 15th edition, is the preferred citation for this article.
Handbook of Texas Online, Paul M. Lucko, rev. by Anthony L. Carr, "COTTON, GILES," accessed July 16, 2019, http://www.tshaonline.org/handbook/online/articles/fcodn.
Uploaded on June 12, 2010. Modified on August 7, 2014. Published by the Texas State Historical Association.


Pleasure P and Amara La Negra link up for "Bust A Whine" produced by the acclaimed beat maker, Don Corleone who's known for his hits with Rihanna.
The single is a part of Pleasure's compilation album, Sequence, that's slated to drop October 5th.
This isn't Pleasure's typical R&B ballad, as it captures club and Miami vibes.


text:
Located 105 miles upriver from the Gulf of Mexico,
New Orleans is the largest city in the US state of Louisiana.
Straddling the lower reaches of the Mississippi River,
this port city has long been
at the crossroads of exploration, trade and commerce.
New Orleans is a melting pot of cultures
that has happily simmered away since 1718.
So, what's in the pot?
Cultural influences from France, Africa, Brazil and the Deep South
mix with Catholicism, Voodoo, Cajun zydeco, and Dixieland jazz
to make New Orleans one of the most lively and popular destinations
in the USA.
"Let the Good Times Roll"; that's the motto New Orleans lives by.
And newcomers usually waste no time
in heading to where the good times roll the loudest, The French Quarter
the birthplace of Jazz!
Lined with bars, clubs and restaurants,
"The Quarter" is home to one of the most party-friendly streets in the world,
Bourbon Street.
But the French Quarter is more than just a good time.
It's also where you'll find many of the city's prime attractions.
Start your day in "The Big Easy" with a Cafe au Lait in Jackson Square.
Riding tall in the saddle is Andrew Jackson,
the General whose rag-tag army of locals humiliated the British
in the Battle of New Orleans.
Jackson Square is lined with many of the city's grand old buildings,
like St. Louis Cathedral.
On either side of the Cathedral are the Cabildo and the Presbytere,
just two of several historic French Quarter buildings
which make up the Louisiana State Museum.
Across the square is the 1850 House,
which recreates life in a row-house from the Antibellum era.
Just around the corner,
The Old U.S. Mint preserves the city's mercantile and musical treasures.
While it's tempting to spend your entire visit in the French Quarter-
and some folks never leave- New Orleans offers plenty of other flavors too.
Cross over Canal Street into the Warehouse district,
an area of renovated grain-stores and sugar presses,
now packed with galleries and chic boutiques.
A little further Uptown in Memorial Hall,
the faces and voices from the American Civil War
reach out across the cannon-smoke of time.
Just nearby, discover why the National World War Two Museum
has been hailed as the most important Second World War repository in America.
Climb aboard a St Charles Streetcar bound for the Garden District.
Here, amid the Victorian cottages and stately plantation homes,
you'll find Lafayette Cemetery.
Join a tour run by local volunteers or explore the crypts on your own.
But be warned;
the cemetery is regarded as one of the country's most haunted!
When it's time to rejoin the living,
follow your nose across the road to another New Orleans institution,
Commanders Palace Restaurant.
Ride the streetcar a few stops further west to Audubon Park.
The park is home to the charming Audubon Zoo
which features a quaint southern touch, an alligator-filled swamp.
The zoo is part of the Audubon Nature Institute
which includes the Insectarium and The Aquarium of the Americas.
While at the nearby New Orleans Museum of Art,
explore paintings, ceramics and sculptures
from across the ages and from around the world.
Visiting New Orleans outside the Carnival Season?
Just head across the river to the Mardi Gras Museum
which brings one of the worlds greatest festivals to life all year round.
New Orleans' distinctive and sometimes fiery cuisine
will ensure you never miss a beat.
Local specialties like gumbo, po' boys, and praline are available everywhere.
But it's the music here that truly feeds the soul.
So when the sun starts to set,
head for one of the many jazz or blues clubs on Frenchman Street,
before heading back to Bourbon Street
where the New Orleans good times roll on, and on, and on.
B2 US orleans quarter museum bourbon street jackson jazz
New Orleans Vacation Travel Guide | Expedia
Billy W. Chou posted on 2017/05/18


જૂન13 by મુર્તઝા પટેલ- નેટ પર વેપાર!
This entry was posted in અવનવું, ક્રિયેટિવિટી and tagged Breast Care, Cancer Awareness, Creativity Health, Gujarati, Health Awareness, India, Indian Woman, Innovation, Marketing.
← યોગી, ઉદ્યોગી અને ઉપયોગી !


I have sold a property at # 46 7488 SOUTHWYNDE AV in Burnaby.
Welcome home! Beautiful & quiet garden-lvl 2 bdrm + den T/H at popular Ledgestone in booming South Slope. Built by Georgie Award-winning Adera [one of BC's best builders], this unit offers a fantastic layout with 2 lrg patios situated atthe front & back of the unit. The living space is great for entertaining & offers a lrg kitchen that opens to the living/dining area & a cozy electric fireplace. The spare bdrm is perfect for guests or a growing family, & the den offers more than enough room for your home office. Nestled in a quiet community-oriented setting, steps from schools, shopping, transit & loads of exciting new development, this home offers great value in a terrific neighbourhood.


text:
Q: Having trouble with tcp mode on HAProxy running on OPNsense I'm trying to setup HAProxy to do simple tcp passthrough to different backends based on SNI. However, I have serious issues on my clients if I do so:

*

*Firefox: PR_END_OF_FILE_ERROR

*Brave/Chrome/Safari: ERR_CONNECTION_CLOSED (works after several reloads but the error shows again intermittently)

If I contact the backends directly, bypassing HAProxy, I have no such issues. So something in HAProxy is not configured right but I fail to see what it is.
Technical Details:

*

*HA-Proxy version 2.0.14

*Running on OPNsense 20.1.x, 20.7.x (FreeBSD 11.2, 12.1)

*In a virtual machine on ESXi 6.7U3

My config looks like this:
global
    # NOTE: Could be a security issue, but required for some feature.
    uid                         80
    gid                         80
    chroot                      /var/haproxy
    daemon
    stats                       socket /var/run/haproxy.socket group proxy mode 775 level admin
    nbproc                      1
    nbthread                    1
    tune.ssl.default-dh-param   1024
    spread-checks               0
    tune.chksize                16384
    tune.bufsize                16384
    tune.lua.maxmem             0
    log /var/run/log local0 info

defaults
    log     global
    option redispatch -1
    timeout client 30s
    timeout connect 30s
    timeout server 30s
    retries 3

# Frontend: https_passthrough (https tcp mode main ip)
frontend https_passthrough
    bind x.x.x.x:443 name x.x.x.x:443
    mode tcp
    # tuning options
    timeout client 30s

    # logging options
    # ACL: service_sni
    acl acl_5f34555b7fae76.76760871 req.ssl_sni -i service.example.com

    # ACTION: service_https_passthrough
    use_backend service_https_passthrough if acl_5f34555b7fae76.76760871
    # WARNING: pass through options below this line
    tcp-request inspect-delay 10s

# Backend: service_https_passthrough ()
backend service_https_passthrough
    # health checking is DISABLED
    mode tcp
    balance source
    # stickiness
    stick-table type ip size 50k expire 30m
    stick on src
    # tuning options
    timeout connect 30s
    timeout server 30s
    server service_https_passthrough 10.0.1.105:443

If the connection fails I find entries like
https_passthrough https_passthrough/<NOSRV> -1/-1/0 0 SC 1/1/0/0/0 0/0

in the logs. But as I said, the backend servers are up and running 24/7 and work fine all day from internal LAN (also routing/firewall/VLANs involved here) so I doubt it is a firewall issue.
Any help appreciated.

A: Looks like adding these two lines to the frontend config fixed the issue for me:
tcp-request inspect-delay 5s
tcp-request content accept if { req_ssl_hello_type 1 }

Derrived from a HAProxy blog post.


Michael continues to weaken and move away from us!
Hurricane Michael continues to weaken with max sustained winds now down to 90 mph near the center. Tropical storm force winds (39 mph+) will be possible mainly over our southeastern counties (Pike & Bullock). Michael will move rapidly northeastward this evening and our weather will quickly improve overnight and early Thursday morning. We're finally going to get a taste of Fall on Friday. High temperatures top out near 80 with sunshine and a nice northwest breeze. Saturday and Sunday look excellent with abundant sun and highs in the upper 70s to low 80s. The next chance for rain won't be from a tropical system, but we could see some showers early next week. Temperatures stay seasonable with highs in the 70s Monday through Wednesday.
Reports from an Air Force Reserve Hurricane Hunter aircraft indicate that maximum sustained winds have increased to near 140 mph (220 km/h) with higher gusts. Michael is an extremely dangerous category 4 hurricane on the Saffir-Simpson Hurricane Wind Scale. Some additional strengthening is possible before landfall. After landfall, Michael should weaken as it crosses the southeastern United States.
Hurricane-force winds extend outward up to 45 miles (75 km) from the center and tropical-storm-force winds extend outward up to 185 miles (295 km). NOAA buoy 42039 to the northeast of the center recently reported sustained winds of 54 mph (85 km/h) and a wind gust of 63 mph (101 km/h). The estimated minimum central pressure based on Hurricane Hunter aircraft data is 943 mb (27.85 inches).
A Hurricane Warning is in effect for Alabama/Florida border to Suwannee River Florida. A Tropical Storm Warning is in effect for Alabama/Florida border to the Mississippi/Alabama border and Suwanee River Florida to Chassahowitzka Florida.
WIND: Hurricane conditions are expected within the hurricane warning area along the U.S. Gulf Coast today, with tropical storm conditions expected to begin during the next few hours. Hurricane conditions will also spread well inland across portions of the Florida Panhandle, southeastern Alabama and southwestern Georgia. Tropical storm conditions are expected in the tropical storm warning area during the next several hours, and are possible within the tropical storm watch area by that time. Hurricane conditions are possible within the hurricane watch area today. Tropical storm conditions are expected to spread northward within the warning area along the southeast U.S. coast beginning tonight, and are possible in the watch area by late Thursday and Thursday night.
RAINFALL: Michael is expected to produce the following rainfall amounts through Friday…Florida Panhandle and Big Bend, southeast Alabama, and portions of southwest and central Georgia…4 to 8 inches, with isolated maximum amounts of 12 inches. This rainfall could lead to life-threatening flash floods. The remainder of Georgia, the Carolinas, and southern Virginia…3 to 6 inches, with isolated maximum amounts of 8 inches. This rainfall could lead to life-threatening flash floods.


Stewards Academy was thrilled to welcome back former Newfoundland trainee teacher Dr Robert Anstey for a flying visit last week. Dr Anstey has remained in close contact with his former History department colleague Deputy Headteacher Marie Erwood, since he completed his teacher training at Stewards in 1994.
He has since gone on to achieve great things in his career. He is now the Headteacher of Alexander Academy in Vancouver and has been honoured to receive the Canadian teacher of the year award, as well as becoming a published author. Dr Anstey was in England in order to pursue the International Baccalaureate Award for his school at Oxford University. He had a whirlwind two days at Stewards meeting former colleagues, going in to speak to classes and meeting individual pupils. The children found him to be warm, genuine in his passion for education and indebted to Stewards for giving him such invaluable training in his future career.


I found this recipe on Pinterest – I love Pinterest!!!
Mix almond meal, bi-carb, baking powder and spices into a bowl. Stir in eggs and honey, and mix until combined. Stir in pumpkin. Fold in pecans, chocolate chips and raisins/cranberries. Pour batter into a well-greased baking pan and sprinkle coconut flakes on top. Bake for 30-40 minutes at 180 degrees C.
Serve at room temp with lashings of fresh butter or cream cheese.


text:
LFTW Games Blog
Author: J Whorley
Where My Players At?
Post author By J Whorley
No Comments on Where My Players At?
If you wade through the sea of apps in either Apple's App Store or Google's Play Store you will find an abundance of games in all shapes and sizes. There may seem to be unlimited iterations of action games, trivia games, word search games, card games and so on. Unfortunately, what you won't find within that wealth of games is a multitude of high quality mobile games specifically targeting African Americans.
One can easily hypothesize a multitude of reasons for the small number of African American game apps. For example, it could be the dearth of African American app development companies, the relatively small number of African American developers or the high cost of app development. Why all those reasons may be true, the one reason that may supersede them all is the fact that African Americans are a minority.
African Americans make up just over 13%* of the U.S. population. Every businessperson knows there usually is significantly greater potential to make money with a product that appeals to 100% of the population as opposed to a product that appeals to just 13%. Sure there may be exceptions to this rule but it can be a significant gamble to find out.
13% of the U.S. population equates to about 43.8 million African American men, women and children. LFTW's fist app, Black Star Word Search, falls into the puzzle game category and puzzle games appeal predominately to female players. So, for the sake simplicity, one can immediately cut the potential pool of players in half from 43.8 million down to 21.9 million.
The pool shrinks again once age is accounted for. For example, Black Star Word Search isn't a children's game and nor do we expect a large cohort of players over the age of 75. A super conservative approach would be to assume the app will appeal primarily to women between the ages of 25 and 54. That age group is about 41% of the African American female population, which further reduces the potential pool of players down from 21.9 million to about 9 million.
Not all of the 9 million women in our pool will own a smart phone. According to the Pew Research Center approximately 78% of African Americans use smart phones. So now Black Star Word Search's potential audience has dropped from a pool of 9 million down to about 7 million.
Of those that use smart phones, only about 16% Apple's iPhone. So if you make an app just for the iPhone your potential pool of players shrinks to about 1.2 million.
Developer's Choice
Unfortunately, this math is most likely the driving factor as to why there is such a small number of quality African American game apps. Most game apps are free and rely on advertising to earn income. Each display ad equates to minute fractions of a penny, so apps require tens of thousands, or hundreds of thousands, of daily players just to cover development and maintenance costs, let alone profits. Whether the app development company is owned by African Americans or otherwise, investing tens (or hundreds) of thousands of dollars and months (or years) in development may not be a wise financial decision when your potential pool of players is so relatively small.
For example, not all 7 million women in the potential pool of players will play Black Star Word Search. Will it be 1% of the pool? Or perhaps ½% is more realistic? It could be that ½ of ½% would be the best case scenario. Either way you slice it the potential number players is most likely only going to be in the thousands – the single digit thousands at that. For most major app development companies that small volume of players is a rounding error, and creating an app specifically for such a small group is simply not worth the investment in time, effort and money.
*US Census Bureau
© 2021	LFTW Games Blog


text:
Atholl John Anderson  (born 1943) is a New Zealand archaeologist who has worked extensively in New Zealand and the Pacific. His work is notable for its syntheses of history, biology, ethnography and archaeological evidence. He made a major contribution to the evidence given by the iwi (tribe) Ngāi Tahu to the Waitangi Tribunal.

Early life
Anderson was born in 1943 in Taranaki and is descended from Ngāi Tahu on Rakiura (Stewart Island). He grew up in Dunedin and Nelson.

Education
Anderson conducted a survey of archaeological sites in Tasman Bay for his Masters degree in geography from the University of Canterbury which he received in 1966. This masters thesis title was Maori occupation sites in back beach deposits around Tasman Bay. He then completed a Diploma in Teaching and in 1968 became assistant principal of a school in Karamea on the West Coast of the South Island. In 1970 he began an MA in Anthropology at the University of Otago which he completed in 1973 with First Class Honours. His thesis was on the subsistence behaviour at Black Rocks peninsula in Palliser Bay, where he participated in a University of Otago archaeology research project from 1969 to 1972. He received a Commonwealth Scholarship which enabled him to go to Cambridge University where he undertook fieldwork in northern Sweden and completed his PhD thesis, Prehistoric Competition and Economic Change in Northern Sweden, in 1976.

Career
Anderson took up his first academic position in 1977 at the University of Auckland. The following year he was appointed as an assistant lecturer in the Anthropology Department at the University of Otago, progressing to a personal chair in the department. He left Otago in 1993 to take up the Establishment Chair of Prehistory at the Australian National University in Canberra, Australia.

On his return to Otago in 1978 Anderson commenced a major programme of fieldwork, the Southern Hunters Project, at 20 sites in the south of New Zealand. Important sites were excavated at Pūrākaunui, Lee Island in Lake Te Anau and the Shag River mouth. The focus of many of the excavations was on prehistoric economics, the use of the marine environment and moa hunting. As a result, Anderson examined the chronology of colonisation and re-dated moa hunting sites throughout New Zealand such as at Wairau Bar and Houhora.

After moving to Canberra in 1993 Anderson undertook fieldwork throughout the Pacific as part of two projects, the Indo-Pacific Colonisation Project and the Asian Fore-Arc Project. Themes of his work were the sequence of settlement of the islands of the Pacific, migration, dispersal and voyaging, and sustainability. His other interests in birds, fauna and extinction resulted in an extinct Fijian crocodile, Volia athollandersoni, being named after him.

Anderson followed up his earlier work in southern New Zealand with the Southern Margins Project which commenced in 1998. It showed that Polynesian voyaging into the sub-polar regions (Chatham Islands, Rakiura and Auckland Islands) occurred about 700 years ago.

While he is primarily an archaeologist Anderson has used archaeology, history and ethnography extensively in his work. In an interview about his 1998 book The Welcome of Strangers: an Ethnohistory of Southern Maori AD 1650–1850 he described it as a book that "draws together the disparate sources of information about later southern Māori in an attempt to describe, in some detail, the origins and migrations of the historical peoples, their social and economic organisation, their distribution in the landscape and their responses to the arrival of European culture." In 2015 he collaborated with historians Judith Binney and Aroha Harris to publish Tangata Whenua: a history which won an Ockham New Zealand Book Award in 2016. The authors used environmental science, geology, linguistics, archaeology and history to investigate the migration and settlement of New Zealand.

In addition to his academic work Anderson has served on the New Zealand Historic Places Trust (now Heritage New Zealand) and as an advisor to Te Runanga o Ngāi Tahu. He researched Ngāi Tahu's Treaty of Waitangi claim to the Waitangi Tribunal.

Anderson retired in 2008 to live in the Wairau Valley, Marlborough.

Awards and honours
 1991 Fellow of the Royal Society of New Zealand
1996 Fellow of the Australian Academy of the Humanities
2001 Federation Medal of Australia for services to archaeology
2002 Fellow of the Society of Antiquaries of London
2002 Doctorate of Science, University of Cambridge
2006 Companion of the New Zealand Order of Merit, for services to anthropology and archaeology, in the 2006 New Year Honours
2015 Humanities Aronui Medal, Royal Society of New Zealand
 2016 Prime Minister's Award for Literary Achievement
2019 Honorary Doctor of Laws, University of Otago

Selected publications

 Anderson, A., 1983. When all the moa ovens grew cold : nine centuries of changing fortune for the southern Māori. Dunedin [N.Z.]: Otago Heritage Books.
 Anderson, A., 1986. Te Puoho's last raid : the march from Golden Bay to Southland in 1836 and defeat at Tuturau. Dunedin [N.Z.]: Otago Heritage Books.
 Anderson, A., 1989. Prodigious birds : moas and moa-hunting in prehistoric New Zealand. Cambridge: Cambridge University Press. (Reprinted 2003)
 Anderson, A. 1998. The welcome of strangers : an ethnohistory of southern Maori A.D. 1650-1850. Dunedin, N.Z.: Otago University Press.
 Anderson Atholl, Judith Binney & Aroha Harris. 2015. Tangata whenua : a history. Wellington, New Zealand : Bridget Williams Books.

See also
 'Ata– an island at the southern end of the Tongan archipelago
 Moeraki
 Palmerston, New Zealand
 Polynesia

References

External links

 Archaeological reports by Atholl Anderson on Heritage New Zealand website

Living people
Historians of the Pacific
Historians of Polynesia
20th-century New Zealand historians
New Zealand archaeologists
Fellows of the Royal Society of New Zealand
Academic staff of the University of Otago
University of Otago alumni
University of Canterbury alumni
Alumni of the University of Cambridge
20th-century archaeologists
21st-century archaeologists
1943 births
People from Taranaki
Ngāi Tahu people
Companions of the New Zealand Order of Merit

redpajama_set_name: RedPajamaWikipedia


A study has found that people who regularly eat leafy greens rich in nitrates could have a significantly reduced risk of developing sight loss.
UV rays from the sun can lead to vision loss and cataracts if eyes are not adequately protected.
Here are 5 ways to protect your eyesight and to stop developing eye problems or eye conditions, including tips on how to prevent it by changing your lifestyle.
Find out the pros and cons of contact lenses including the different types of contact lenses and finding which works best for you and your daily routine.
Find out how you can protect your eyes from cataracts as well as knowing the causes, symptoms and treatment of cataracts.
Here are 6 points to consider if you think you have cataracts including the cataracts symptoms and eye conditions.
International awareness day is held to increase understanding of the sight problems faced by people with the rare eye condition, aniridia.
The Queen underwent cataract surgery recently, at age 92. A US study has found that this common surgical procedure could help women live longer.


text:
Q: Ant Design: Vertical submenu pop up grow from bottom to top Is it possible to display the popup of a vertical submenu "the other way around" ? I have one SubMenu item in a fixed Sidebar at the bottom of my page. It contains links for the users profile and the logout link. But since it is at the bottom of the page the submenu will open and part of it is outside the of the page.
Here is a screenshot of the current situation.

I searched for options the documentation but I couldn't find a suitable solution for the problem. So basically what I want to achieve is growing the popup from bottom to top and not top to bottom.
Here is the source for the Sidebar component. It is quite a early stage so there are still other improvements to the code to do.
import React from 'react';
import { connect } from 'react-redux';
import { Layout, Menu, Icon } from 'antd';

import { withRouter } from 'react-router-dom';

import styled from 'styled-components';

import { toggleSidebar } from '../../actions/ui';
import { logoutUser } from '../../actions/user';

const { Sider } = Layout;
const SubMenu = Menu.SubMenu;

const Logo = styled.div`
  height: 32px;
  background: rgba(255, 255, 255, 0.2);
  margin: 16px;
`;

const UserMenu = styled(SubMenu)`
  position: fixed;
  text-align: center;
  bottom: 0;
  cursor: pointer;
  height: 48px;
  line-height: 48px;
  color: #fff;
  background: #002140;
  z-index: 1;
  transition: all 0.2s;
`;

const mapStateToProps = state => ({
  ui: state.ui
});

const mapDispatchToProps = dispatch => {
  return {
    toggleSidebar: () => dispatch(toggleSidebar()),
    logoutUser: () => dispatch(logoutUser())
  };
};

class Sidebar extends React.Component {
  componentDidMount() {}

  render() {
    const { ui, logoutUser } = this.props;
    return (
      <Sider
        collapsed={ui.sidebarCollapsed}
        //onCollapse={toggleSidebar} // toggle is disabled
        style={{
          overflow: 'auto',
          height: '100vh',
          position: 'fixed',
          left: 0
        }}
      >
        <Logo />
        <Menu theme="dark" defaultSelectedKeys={['1']} mode="inline">
          <UserMenu
            key="sub1"
            placement="topLeft"
            title={

                <Icon type="user" />
                User

            }
          >
            <Menu.Item onClick={logoutUser} key="3">
              Logout
            </Menu.Item>
            <Menu.Item key="4">Profile</Menu.Item>
          </UserMenu>
        </Menu>
      </Sider>
    );
  }
}

export default withRouter(
  connect(
    mapStateToProps,
    mapDispatchToProps
  )(Sidebar)
);

Is there a way to achieve this ?

A: Yes it should be possible. <Menu>uses the rc-menu package, and supports all the properties from this package, even if they are not documented in the and.design doc page.
Menu position is guided by the builtinPlacements property, which in turn uses https://github.com/yiminghe/dom-align, which gives you lot of flexibility in how to position the elements.


Where possible, we know that many youth services are plugging the gaps but this isn't sustainable nor is the work recognised and funded.
Piecemeal adjustments will no longer do, and we need to see an overarching strategy for young people at risk in NSW.
That funding levels are appropriate to need, and funding is invested in early intervention and prevention, not just crisis.
That the NSW government report on progress made regarding previous inquiries.


text:
Hotel Management Institutes In Kolkata
Here is the list of Top 25 Indian Business Schools (or Management Colleges) of 2017. We update this list frequently, so you have the latest rankings!
The plight of the rural poor in eastern India, for example, may be explained by issues related to water management. Agriculture in the high rainfall and flood-prone eastern Gangetic plains area is lar.
The Materials Recovery Facility (MRF) Summit, hosted by the Institute of Scrap Recycling Industries. programs are an integral part of their future integrated solid waste management plan in North Am.
and Board of Governors of the Indian Institute of Management, Kolkata. Ram Nath Kovind represents the rural, agrarian, and economically and socially underprivileged sections of the society. Apart from.
Ashe High Country Vacations Sochi (Russian: Со́чи, IPA: ( listen)) is a city in Krasnodar Krai, Russia, located on the Black Sea coast near the border between Georgia/Abkhazia and Russia. The Greater Sochi area, which includes territories and localities subordinated to Sochi proper, has a total area of 3,526 square kilometers (1,361 sq mi) and sprawls for 145 kilometers (90 mi) along the shores of the Black Sea near. With the right planning, Caribbean vacations can be. Winter and summer are high season." Still, many of Roggmann's clients travel between November and April, when the weather is cooler in Virginia. From OregonLive of Dec.
Asutosh College, kolkata, Asutosh College is affiliated to 'The University of Calcutta, West Bengal'.
Two youths arrested for allegedly assaulting a 20-year-old Mass Communication student publicly by tearing off her clothes and threatening her with rape were today denied bail by a Delhi court. Metropo.
So it was yesterday, when the two stars shared the stage for hours, to protest against the Centre delaying the setting up of the Cauvery Management Board for release. match between Chennai Super Ki.
The sought after awards in the sector was organized on 13th August, 2017 (Sunday) at Taj Hotel in Bangalore. India Business Awards 2017, recognized achievers, innovators and leaders for demonstrating.
The city government can now collect payments for business licences, hotel taxes. is a senior associate in PwC's cities and urbanisation team. Sarah Colenbrander is a senior researcher with the Inte.
Due to the technological improvements and digital trends, the travel industry and online hotel booking sector has been experiencing a major transformation. Modernization and the advancement in the tra.
financial institutes, manufacturing, and media in India as well as across the US, Singapore and the Middle East. Funding: $1.2 Mn in 2 Rounds from Mumbai Angels, Indian Angel Network, Kishore Ganji, a.
Kolkata, Mumbai and Pune. The IBS Business School have till yet produced more than 43 thousand students who were employed in.
India's expansion of its colleges and universities with collaboration with US. For the rest of the finances I am depending on my parents and a loan," she said. While management education, engineeri.
Menstruation While Travelling With Guy Friends Post Graduation Vacation Ideas Travel Brands Canada Osprey: Best Luggage Brands for Durability "If you're planning to travel extensively, go on a round-the-world backpacking trip, or jetset full-time, this is the absolutely top luggage brand. As well as live coverage, Discovery is looking further down the track at golf programming that could extend to analysis, equi. In Asia Pacific the Company already has a strongly established structure which allows it to grow at a high pace through the addition of hotels under management agreements which bring in greater manage. The Travel Coproration. We are passionate about 'Making Travel Matter' and
Panel discussion was chaired by Mr. Hari Sukumar, Vice President, Operations, (Jaypee Palace Hotel & Convention Centre. local community empowerment and efficient resource management, amongst other.
In Telangana, the authorities were using pamphlets and local media to inform people to avoid going outdoors and to drink plenty of water, the state's disaster management chief BR. a top official at.
The FINANCIAL — NEW DELHI, INDIA (27 September 2018) — The Mayor of Kolkata Municipal Corporation launched a flood forecasting and early warning system (FFEWS) for Kolkata City to help city officials.
The city government can now collect payments for business licences, hotel taxes, ground rents. Sarah Colenbrander is a senior researcher with the International Institute for Environment and Develop.
Military Hawaii Vacations "Hawaii is paradise, so we just here to spend out vacation to enjoy the beach sunshine," said a. US officials met secretly with Venezuelan military officers who were plotting a coup against Venezue. Tickets for Richie's second "All the Hits" concert went on sale to Hawaii residents and military at 12:30 p.m. today at. $55.75 and top out at $495.75 for front-row meet-and-greet packages. GovArm provides leisure and vacation travel services for government and military personnel, including retirees. With services ranging from condominium rentals, cruises, car rentals, hotel reservations, and vacation packages, there is something for everyone. Least Expensive Mexican
Competitive Exams after 12th The topic covers about competitive exams options after completion of Class 12.
Kolkata, the remaining metropolitan. their online selling business or manage things on their own using their innovative inventory and order management software Disclaimer: This is a contributed pos.
Seminar: A seminar on the "Performance of Indian business giants" was held at the Justice K.S. Hegde Institute of Management at Nitte in Udupi district recently. Among the top 100 companies, 30 were s.
The court on September 4 rapped the police for its "lethargic attitude" in its probe into the death of Pushkar while hearing a plea by the hotel's management seeking. leader Shashi Tharoor's wife S.
"The RSC Cumbria Section, in collaboration with the Nuclear Institute (Cumbria Branch), would like to. He was a member of CoRWM (Committee on Radioactive Waste Management) from 2007 to 2016 and has.
Japan Vacation Spots
Csa Travels


text:
This privacy policy applies to any information that TinyVid collects or receives from you. By using TinyVid you agree to the terms of this privacy policy.
All content uploaded or converted via TinyVid remains the property of the original owner. By making any content available through this action, you represent and warrant that you own all rights necessary to properly do so. See the Copyright Policy for details. You grant TinyVid a non-exclusive, royalty free right, to use these videos for the purpose of video playback within the site and embedded players.
This site may use browser "cookies" to store session information. You can reject cookies by using browser settings but you may not be able to log in and convert or upload videos as a result.
Specifically, Google, as a third party vendor, uses cookies to serve ads on this website. Google's use of the DART cookie enables it to serve ads to you based on your visit to this website and other websites on the Internet. You may opt out of the use of the DART cookies by visiting the Google ad and content network privacy policy.
We may change our privacy policy from time to time. This page will be updated when we do so. If you have any questions about this privacy policy you can contact privacy@tinyvid.tv.


text:
Home / Historical Biographies / Thomas Erskine Carson
Thomas Erskine Carson
1845 18 Whig
1853 Speaker 11 Whig
Adams, Franklin
Thomas Carson was born in Mercersburg, Franklin County on August 6, 1791. The son of Irish immigrant David Carson and the former Jean Oliver, Thomas received only informal education but emerged proficient enough in English literature and grammar to receive a tuition appointment as community schoolteacher. While a schoolmaster, he married Agnes King of Mercersburg in 1815. To make ends meet, the young educator gave up teaching for the greater remuneration of the hat-making trade, opening a successful mercantile shop in Mercersburg.
Carson embarked on a public career as a magistrate, Franklin County auditor, and became the county's 1834 Whig choice for the Pennsylvania House of Representatives. He served in the House through 1843, representing Franklin and Adams counties.[i] He entered the state Senate in 1845, serving a three-year term, however met defeat for re-election at the hands of fellow Whig William R. Saddler. A devoted Whig, Thomas retooled his campaign, winning a second upper house election in 1851, advocating high tariff protectionism and the free public school system. During the last year of his second term (1853), the Senate elected Carson, Speaker.
Thomas represented the Whig caucus as chair of the 1851 Election Districts Committee and the 1852 Pensions and Gratuities Committee. He supported the popular election of judges, stricter regulation of the borough system, the repeal of the Walker Tariff, and federal reprisal against slave kidnappers.
The Honorable Thomas E. Carson retired from the upper house in 1854, replaced by Whig David Mellinger. He died in Mercersburg shortly thereafter, April 26, 1857.
"His sterling integrity and uniform fidelity to all official duties intrusted [sic] to him, stamp him as one of the few public men in our commonwealth, who are proof against all the seductive influences of public life – one whose large abilities and clear perceptions are overshadowed by his modest demeanor and freedom from the arts of the popular politician."
[i] History of Franklin County, Pennsylvania (Chicago: Warner, Beers & Co., 1887), 848.


Cutler has not thrown 20 touchdowns in a season since 2010! But this is the year that all changes. He racked up 19 TDs and averaged 259 yards in the 10 games he started and finished. He only gained over 300 yards or attempted 40 passes twice, but the less he drops back to pass, the more likely he is to start 16 games. Only in the final week of the season did he attempt less than 30 passes. With huge targets in Marshall, Jeffery and Martellus Bennett, the red zone is Cutler's friend. We ranked him 15th in our QB rankings.
Only Pierre Thomas and Danny Woodhead caught more passes out of the backfield in 2013. turning 3 of them into touchdowns gave him 12 on the year and only Jamaal Charles, Marshawn Lynch and Knowshon Moreno scored more. LeSean McCoy was the only back to rush for more yards. Do you see where I am going here?! You want Matt Forte! We ranked him 4th in our RB rankings.
A lock for 100 receptions, 100 yards and 10 touchdowns. We ranked him 6th in our WR rankings.
Jeffery had two, 200 yard receiving games last season, one with Cutler and one with McCown. No need to worry about the Cutler/Marshall relationship affected targets for Jeffery. In 7 starts, Cutler targeted Jeffery 8 or more times. He saw 89 targets from Cutler, catching 50 for 773 yards and 3 scores. We ranked him 8th in our WR rankings.
Bennett improved on a career year with the New York Giants, catching 65 passes for 759 yards (up from 55/626) and scored 5 touchdowns for a second season in a row. There is no reason he can't duplicate those numbers. That is of course if he stops wrestling his own teammates! He did catch 3 of his 5 TDs in the Bears first two games, and averaged under 4 receptions per game after September for 44.5 yards. He is a safe pick with little upside. We ranked him 12th in our TE rankings.


Our friends in the marketing world long ago came up with the notion of the Unique Selling Proposition (USP). Simply put, the USP is the impelling reason why a customer would choose one product over another. It is that "thing" that gives a company's product or service a distinct advantage over the competition. It may be price, quality, reputation, benefits, or some other reason which drives customers to a particular product or service.
Programs – Serve or meet a need in a way that other organizations don't. Offer a program or service that has the promise to make a meaningful difference in the lives of those you serve and is not currently being offered by other organizations. An example might be the higher education institution that utilizes every professor and professional staff member to serve as mentors to first-year students. Such a program would evidence uncommon concern for students during the all-important first year.
Volunteers – Involve people that other organizations wish they could. Who is involved in your organization? Who serves on your Boards and on Advisory Councils? There is the old saying, "You are known by the company you keep." If you want to strengthen your UGP, get more people of influence and affluence involved.
There are currently over 1.5 million registered 501 (c)3 organizations in the U.S. Competition for the charitable gift dollar is strong. Can your organization do more to be distinctive? Most can. And by establishing your UGP, you can help ensure that your distinctiveness turns into more donors and more charitable gift dollars.


text:
Ritesh Kotak
Ritesh has dedicated his working career to exploring how technology could be used to co-create trust between our communities and public institutions. He started an eight-year career within policing which involved two police agencies within Canada along with several international assignments. He led the creation of the Cyber-Crimes unit and the Research and Innovation portfolio focusing on digital transformation. Ritesh then transitioned to the Private sector where he worked with different Fortune 500 Tech companies on global projects related to Cyber Security, Investigations and Next-Generation IoT applications for Smart Cities projects.
In 2019, Ritesh decided to return to school to commence his Juris Doctor at the University of Ottawa. He felt that better understanding of the legal profession would allow him to work on projects that promoted access to justice by leveraging technology. While completing his JD, he interned at the Samuelson-Glushko Canadian Internet Policy and Public Interest Clinic.
In addition, while completing his law degree, he participated in two hackathons. The first was in the summer of 2020, where Ritesh and three colleagues entered an international tech law competition and developed an automated workflow to generate refund claims to airlines for COVID-related cancellations. This project placed second place in the world. The second hackathon was a Pan-Canada competition where he and two colleagues developed a free automated privacy breach reporting tool kit for small businesses. The toolkit placed first in the competition and they decided to pursue the project and launched jusTech to assist the small business community. The project has now received funding, featured in the media and is expanding to include additional features to further assist businesses.
Ritesh has worked and presenting around the world including the World Internet Conference in China, the training academy for the Jamaican Constabulary Force, the Major City Chiefs/FBI National Executive Institute Conference, NATO-sponsored Cybersecurity Conference in North Macedonia and several other events in the Middle East, North America and Europe. Ritesh has appeared as a witness in the House of Commons- Industry, Science, Technology Committee addressing competitiveness in Canada. He frequently provides interviews to mainstream media to highlight organizational achievements and provide analysis & insights into tech-related stories. Ritesh is a member of National E-Crimes Council and has been awarded the Alumni100 award from the University of Edinburgh Business School. Ritesh holds a BBA (University of Toronto), MBA (University of Edinburgh/ Exchange at Peking University) and an Executive Certificate for completing the Emerging Leaders Program from Harvard University's Kennedy School of Government.
There is no question that this was once again one of the most captivating conferences that I have attended—with not only one good idea—but many. It is wonderful how the panels all have different points of view that foster challenging perhaps our previous opinions or at the very least give us more information to have an informed opinion. Our team thought it was time well spent indeed!
McCurdy Financial
Amazing event as always!!!
Imprint Plus
A wonderful event. I met some incredible people and was very inspired. You have gathered such an amazing group of people.
Vicki SaundersFounderSheEO


text:
Home Armenia Putin, Pashinyan Discuss Regional Developments During Moscow Meeting
Putin, Pashinyan Discuss Regional Developments During Moscow Meeting
Iran Says Has Documents on Transfer of Terrorists to Azerbaijan
MOSCOW — Russian President Vladimir Putin and Armenian Prime Minister Nikol Pashinyan met in Moscow on Tuesday for talks that apparently focused on the Nagorno-Karabakh conflict.
An Armenian government statement said they discussed "ongoing developments" in and around the conflict zone, efforts to shore up stability in the region and the implementation of Russian-brokered agreements to establish transport links between Armenia and Azerbaijan. Russian-Armenian relations were also on the agenda, added the statement.
Neither the government nor the Kremlin announced any agreements reached by the two leaders.
"We will talk in a formal and informal setting — have lunch together, discuss current affairs, talk about prospects," Putin told Pashinyan in his opening remarks at what was their fourth meeting in less than a year. He said they will talk about a short-term and long-term "settlement in the region."
"Unfortunately, we still cannot speak of a full stabilization of the situation in our region," Pashinyan said for his part. He stressed that Russia continues to play the "key role" in international efforts to resolve the Karabakh conflict.
Russian Defense Minister Sergei Shoigu and his Armenian counterpart Arshak Karapetyan also met in Moscow on Monday.
The Armenian Defense Ministry said they discussed Russian-Armenian military ties, the situation on the Armenian-Azerbaijani border and "a number of issues relating to regional security." It did not elaborate.
The Russian Defense Ministry issued no statements on Shoigu's latest talks with Karapetyan.
Putin also said on Tuesday that he wants to "compare notes" with Pashinyan with regard to next month's summit of ex-Soviet states, including Armenia, Azerbaijan and Russia. The leaders of all three countries are expected to attend it.
Both Pashinyan and Azerbaijani President Ilham Aliyev expressed readiness earlier this month to meet with each other. Their most recent face-to-face meeting was hosted by Putin in Moscow in January.
Sossie says:
Did Pashinyan mention to Putin that Russia betrayed Armenia last year?
Did they discuss the fact that Russia is siding with Azerbaijan and Turkey over Russia's ally, Armenia?
Did Putin explain why he continues to humiliate Armenia?
Did Putin mention why he favors letting Turkey into the Caucasus and Caspian and encouraging pan-Turkism?
Foreign Missions Briefed On Karabakh Operation
YEREVAN (RFE/RL) — Armenia's First Deputy Defense Minister Davit Tonoyan met with…
Ruling Bloc Lawmakers: Most Armenians Do Not Want Regime Change or Pre-Term Elections
YEREVAN — Prime Minister Nikol Pashinyan and lawmakers representing his My Step…
Turkish Journalists to Honor Slain Armenian Colleagues on Genocide Day
By Sandy Smith Huliq.com Turkey's main association of journalists will add the…
Ken Khachigian to MC AMAA Centennial Banquet
By Joyce Abdulian LOS ANGELES — Ken Khachigian, distinguished Armenian-American political consultant,…


text:
Home History Management Administration Activities Golden Jubilee Retirees Faculty Alumni Gallery Contact Us Notice Board
GOLDEN JUBILEE Year: 1964 - 2014 :: For membership registration please visit www.cftrisalumni.org
Inauguration of Golden Jubilee functions was held on 1st November 2014, at 9.30 am in the school, Please click the link below for report and photo gallery.
GJ Organizing Commitee
Golden Jubilee Logo
Golden Jubilee Celebrations
C F T R I School is celebrating its Golden Jubilee.
The CFTRI School, which was started in a small room attached to the C F T R I residential quarters, is today one of the reputed schools in the city. Started in 1964, the school has walked through 50 successful years and is celebrating its Golden Jubilee from June 2014.
Founded in 1964, the school started in a small way with only nursery classes and I standard. Subsequently, classes uptp VI standard were started. By this time the school was shifted to the Assistant Director's quarter. In 1969, the school started functioning in the former palace stables, converted to Men's hostel. Since then, the school has been growing by leaps and bounds. To meet the demands of th egrowing number of students, more number of classes had to be started. By 1974, all the classes started functioning in the new building.
In 1970, CFTRI Education Society was formed. The management of the school which was hitherto in the hands of the founder member was taken over by the CFTRI Education Society. The constitutional frame work of CFTRI Educational Society was drawn up by an interested and involved group of Scientists like Dr. H.A.B. Parpia, Mr N.P. Dani, Mr K.M. Dastur and Mr m.M Krishnaiah, Dr K.R Bhattacharya, Mr Veeraraju and Mr Subramanyan. Also a friend and well wisher from the Department of education, Dr Ram Kulkarni contributed a lot to the thought process as well as help and facilities that could be taken from the Education Department. This interaction was initiated by Mrs Caroline Parpia, the founder of the school.
The growth of the school was rapid. There was steady increase in the enrolement of the students. The first batch of X standard students appeared for the SSLC examination in the year 1979. The school has now grown into a composite institute offering complete instructional facilities from nursery to X standards comprising about 1220 students. The school has unique distinction in securing 98 to 100 percent results in X standard public exams all these years.
CFTRI School is a school with a difference: It is set up with high ambitions and noble objectives. These were to provide education for intellectuality, morality and spirituality. The school aim to impart quality education based on science and technology and the values of our traditional Indian culture. The school follows the theme "Sarvashikshana Abhiyana" - 'Education for all' and the school logo reflects its theme "KNOWLEDGE IS POWER".
Now, it is time to celebrate, to introspect, to consolidate and to plan for its future. Hence in the year long Golden Jubilee celebrations of C F T R I School – a dream destination for students and staff , we intend to enthusiastically involve ourselves in achieving our aim.
The Golden Jubilee celebrations was formally launched on 1st November 2014 in connection with Kannada Rajyotsava marking the beginning of the celebration. As we celebrate we also hope to conceive and start new initiatives to take CFTRI School to its next highest level in the coming decades. All are invited to join in this effort.
An elaborate program of activities has been drawn for the year. There are several inter and intra school activities to make it memorable.
We request all our ex-students to join hands with us to take your alma-mater to reach its zenith. We also invite you to contribute to achieve its greatness. Let us contribute to the institution's glory by excelling in what we do ourselves, as alumni, students and staff.
Looking back over the years, one cannot help but admire the remarkable alround growth achieved by the school ever since its inception in 1964. The school owes to the parents of the students - past and present - as well as CSIR-CFTRI for its present infrastructural facilities. The dedicated band of pioneers who started the school during sixtees and selfless service of a host of office bearers of te CFTRI Education Society from seventees till now deserve our gratitude and thanks for bringing the school to its pre-eminent postion in the Mysore city.
Golden Jubilee is a great landmark in the history of an institution to look forward with courage and cofidence to scale new heights. The school has chalked out an abitious plan to expnad its infrastrucural facilitiesqualitatively and quantitatively by setting up Golden Jubilee Open Air Auditorium, Modern Science Lab, Modern Mid-day Meal Facility, Upgradation of Sports Ground, Language & E-Learning Lab, Robotic Lab & Video Conferencing Facility, Reconstruction of Nursery Block & Play Area, Green Campus Initiative, Bio-gas facility for Mid-day meal , Bio-composting and Vermi composting facility, Solar Lighting and Electricity Facility. Any contributions made will be greatly appreciated as it will go a long way in improving the infrastructure to provide facilities, attracting the best faculty who would enhance the talents of the students.


You don't have to consider yourself the most qualified baseball coach or even know a whole lot about baseball in general. What you do need is a big heart and lots of love, a passion for serving and an ability to give our players plenty of smiles and encouragement. We would love for you to be part of something truly special!
If you are interested in Coaching or being an Assistant Coach, please email grace@miracleleaguedfw.org for more information.


Member for Gippsland Darren Chester at Traralgon Railway Station recently. Mr Chester says the Federal Government is committed to funding regional passenger rail upgrades.
PEOPLE living in the Latrobe Valley can be assured the Nationals, as part of the Federal Coalition Government, are committed to funding better regional rail services in Gippsland.
All levels of government and the community agree on the need to upgrade the Gippsland Line; there is just a dispute on how we get there.
As your local MP, and Transport and Infrastructure Minister, I look forward to making announcements related to Gippsland transport infrastructure in the Federal Budget next week.
Although public transport is primarily the responsibility of the Victorian State Government, I believe it is right for the Federal Government to play a role in helping to make our region a more attractive place to live and invest, by boosting regional passenger rail.
The debate relating to the Gippsland Line over the past week has been confusing for many people locally, due to questions over how the upgrades would be paid for.
On Sunday, the Victorian Government announced a $1.4 billion state-wide package for regional rail, to be paid for entirely by the Federal Government, under the now closed Asset Recycling Initiative (ARI).
Premier Daniel Andrews did not commit a single cent of state funds, and the ARI is now closed.
However, this does not mean all hope is lost for Gippsland Line funding. First, we will need to see a plan and a business case, which is yet to be delivered to the Federal Government.
I am confident there will be other ways for the state and federal governments to work together to fund the upgrades – which I'm committed to doing.
But this means we will also need to see a contribution from the Victorian State Labor Government to regional rail, using its own money.
If State Labor can pay for the Melbourne Metro and Level Crossing Removals in the suburbs, it can also spend state money on regional rail for Gippsland. They have done it in the past, and they can do it in the future. That's the fair thing to do.
I understand many people don't care who pays for the rail upgrades; they just want to see the work done.
I have some sympathy for that point of view, but I have to get value for money for the taxpayer, and the Victorian Government can't expect a free ride.
I am confident we can reach an agreement in the weeks ahead.
Darren Chester is the Federal Member for Gippsland, and Minister for Infrastructure and Transport.


text:
87 bytes added, 17:29, 24 October 2017
→Balcony
# If the back door opens into a backyard that has a gate to a courtyard or street then the back door should have a mezuzah on the right side going into the house because the house is used more than the backyard.<ref>The Maharil (responsa 94) wrote that if the back door opens into a backyard that has a gate to a street then the direction of the mezuzah is determined by which way the door opens. Taz 289:3 quotes it. Chelkat Yakov YD 161 writes that even though the Maharil writes that when there are two doors to a backyard the mezuzah is determined by the way the door opens, the Levush holds that we would put up the mezuzah going into the house since it is used more than the backyard. Furthermore, the Bet Meir and Chavot Daat disagree with the Maharil altogether even when the backyard has no other exit. Therefore, the Chelkat Yakov concludes that since the house is used more than the courtyard that trumps the rule of the fact that the majority of the walking is from the house to the courtyard. [http://www.yutorah.org/sidebar/lecture.cfm/788640/rabbi-hershel-schachter/the-laws-of-mezuzah/ Rav Hershel Schachter in "The Laws of Mezuzah" (min 34-42)] agreed.</ref>
===Balcony===
# A balcony or deck that opens to a house and has no other entrance or exit is should have a mezuzah on the right going from the house to the same as a room with only one entrancebalcony.<ref>The Maharil quoted by the Taz 289:4 writes that if a house opens to enclosed courtyard and it doesn't have any other opening then certainly the doorway to the courtyard is considered an entrance to the courtyard since there's no other way in. However, the Bet Meir 289 argues with the Maharil and says that since the house is used more than the courtyard it is considered an entrance into the house. Chazon Ish YD 168:5 (cited by Yabia Omer) and Bnei Tziyon Binyan Tzion (cited by Chelkat Yakov) agree with the Bet Meir. Maharam Shik 287, Maharsham 1:71 and 3:154, and Chelkat Yakov YD 162 agree with the Maharil against the Bet Meir. The Daat Kedoshim agrees with the Bet Meir unless it is an area less than 4x4 amot which might not be obligated at all in which case he follows the Maharil. Rav Ovadia Yosef in Yabia Omer YD 4:23:6 cites the Masechet Mezuzah ch. 2 which amazingly has an explicit dispute between the Tana Kama and Rabbi Yosi about this exact case where a house opens to a courtyard that doesn't have another entrance. Rav Ovadia quotes dozens of sources whether we generally follow Rabbi Yosi over Tana Kama or not and additionally if it is possible to disregard this source since it is post-talmudic. In any event, he is convinced of the argument of the Bet Meir but still follows the opinion of the Maharil being that he was quoted by the Bet Yosef and is an earlier source.</ref>
===Straight or Diagonal===
Retrieved from "https://www.halachipedia.com/index.php?title=Special:MobileDiff/19760"


Nothing helps you feel more connected to the world around you than traveling. Seing the people and plaes that have sculpted what and who we are today is a life=changing experience that always leaves you feeling a part of something bigger than yourself.
Faith-based travel is the perfect way to build comunity by intimately exploring the roots and stories of your faith with fellow believers.


Each September the organization City of Asylum hosts an event on the North Side that combines poets (who are usually exiled from another country) and jazz music (which almost always involves alto saxophonist Oliver Lake). In previous years, the event has happened on Sampsonia Way, the street that looks like an alley where museum/installation space the Mattress Factory is located. The street was closed off and a stage was set up at one end. This blend of close residential buildings and businesses made for an interesting production a few years ago. On the balcony of one of the houses, a Chinese poet shouted his prose in his native tongue while locally-born actor David Conrad translated across the alley on another building. Lake performed that year with the World Saxophone Quartet.
This year, the event was moved to Allegheny Commons West Park, right next to the National Aviary, where a huge tent was set up, with a pretty clear view of the stage wherever you sat, with numerous video screens all around the space too.
Lake brought his big band this time, who released a really solid album called Wheels about a year ago. Among other people, the band includes Darius Jones, the wild and woolly alto player who has released a few albums on AUM Fidelity and recently did a second album with pianist Matthew Shipp. I just reviewed the latter release so I felt like I needed to check out the show to see him in particular and also because I haven't gone to these events in probably about five years.
Knowing that I might be complicating things, I took my seven-year old son with me. He's no stranger to live music. A few weeks ago, he accompanied me to JJ Wright's local performance. And he did see Anthony Braxton perform at the Aviary at the ripe old age of 10 months (sleeping through a lot of it). Plus he has been to a bunch of Pittsburgh Symphony concerts for kids, and has headphones to wear when things get too loud. But all of that doesn't necessarily mean that he'll sit through a whole concert.
This marked the 10th anniversary of City of Asylum, which was given much fanfare to start the show. Then Lake came out and recited his own piece called "You Look Marvelous" which was an homage to the late Amiri Baraka. He called the band onstage by holding a droning note that everyone echoed as they made a procession through the audience to the stage.
"Plan" opened the set, letting everyone know this wasn't your typical big band. The stop-start lines of the theme gave way to a solo by Lake that was marked by some strong high shrieks that weren't always on mike.
Lake has cited Oliver Nelson and Duke Ellington as influences and "Sometimes" bore that out. The horn voices sounded rich, slowly moving into a more soulful mood before moving into some heavy swinging by the end. The contrast between this more traditional backdrop and soloists like Lake and Jones made the whole thing sound more unique. Lake's World Saxophone bandmate David Murray also leads a big band too, but when they brought on Macy Gray as a singer (seen last year at the Detroit Jazz Fest) the band sort of reduced to a large scale vamp band. Lake did nothing of the sort.
Even when the band covered OutKast's "The Whole World," and the backbeat got a little rigid, the heat was still there. The same goes for "Is It Real," where everyone was taking a few bars to stand up and wail.
After the band played those four tunes, they took a break so some of the poets could get up and do their thing. It was about an hour into the show and by then the kid's mind was gone. Actually his focus never made it into the tent after he saw a playground a few feet away. While he's getting to be old enough to leave unattended at a playground, I wasn't ready to do that on the North Side.
So we took our leave, via that playground, as the sponsors was saying their thing and as the poets got ready to do theirs.


text:
Welcome to Downtown Vancouver
Downtown Vancouver is a favourite spot for locals and visitors alike, with something for everyone. Across the many unique neighbourhoods of the downtown area, you'll find an eclectic blend of historic and modern architecture.
No matter what area you find yourself in, there is always something to see, do, eat and drink:
Walk the historic cobbled streets of Gastown to see the Victorian architecture, fashion boutiques and souvenir shops - don't forget to get a selfie in front of the Steam Clock
Hit up Yaletown to shop (or window shop) at the quirky shops and boutiques, then stop for a meal in a trendy restaurant and a stroll in one of the waterfront parks
Hop on a ship for a cruise of the harbour, take a virtual flight over Canada get some Instagram-worthy pics of the views in Coal Harbour
Take in the colourful flags and rainbow crosswalks of Davie Village in the West End, known for its diverse community of LGBTQ+ residents and visitors. Shop the local independent stores and cafes, grab dinner at one of the multiple ethnic cuisines and then stay for the thriving nightlife.
Break out your credit cards on Robson Street, Vancouver's premier shopping district. Robson Street is also home to BC Place Stadium, the Vancouver Public Library and the Vancouver Art Gallery.
Get entertained on Granville Street by going to a show - from a classical performance at the Orpheum to a rock concert at the Commodore Ballroom - or hit the dance floor at one of the many bars and clubs.
Meet friends for dim sum and then spend a relaxing afternoon in Chinatown's Dr. Sun Yat-Sen Classical Chinese Garden.
Total Private Homes(2016)
Average value of home
The beach at English Bay is one of the most popular spots in Vancouver. Hang out on the beach, grab a bite at one of the many nearby restaurants or take in a fireworks display.
Vancouver's historic Chinatown is the 3rd largest in North America. Find Asian speciality shops, dim sum and other cuisines.
Visit the Art Gallery to take a tour through the ground-breaking exhibitions at one of North America's most innovative visual arts institutes.
Walk the cobbled streets of Vancouver's most historic area. Visit stylish boutiques and the neighbourhood's most established bars.
Downtown Vancouver Map
Downtown Vancouver Listings
205 189 NATIONAL Avenue
Downtown VE Vancouver V6A 4L8
The Sussex by Bosa - Well designed open floorplan with 2 bedrooms, 2 bathrooms, 980 sf, SW corner unit. Complete & thorough renovation includes, new kitchen w/updated cabinets, quartz countertops, undermounted sink, s/s appliances; bthrm finished w/stylish vanity & faucets, new lighting+ designer paint colors & laminate flooring through-out. Mstr bdrm w/large walk-in closet! Spacious 9x8 private outdoor covered balcony, 2 secured underground parking, storage locker & bike storage. Amenities include a well-equipped gym and billiards room. Quality constructed building that is well maintained by the strata. Steps to Olympic Village, seawall, parks and Skytrain. Pets & rentals allowed. Offers, if any, to be presented on Wednesday, January 13th at 7PM.
BCS1644
Clothes Washer/Dryer/Fridge/Stove/DW
Central Location, Marina Nearby, Recreation Nearby, Shopping Nearby
Bike Room, Exercise Centre, In Suite Laundry, Storage
Reno / Year:
Completely / 2020
These statistics are generated based on the current listing's property type and located in Downtown VE. Average values are derived using median calculations.