text:
\section{Introduction}
\label{sec:intro}
Let $\mathbb{F}_q$ be the finite field of size $q$
and $\mathbb{F}^N_q$ denotes the vector space of
$N$-tuples over $\mathbb{F}_q$.
For a positive integer $n$ and a non-negative integer $l$,
we fix an $l$-dimensional subspace
$\mathfrak{e}$ of $\mathbb{F}^{n+l}_q$.
The corresponding {\it attenuated space} associated with
$\mathbb{F}^{n+l}_q$ and $\mathfrak{e}$ is the collection of
all subspaces of $\mathbb{F}^{n+l}_q$ intersecting trivially
with $\mathfrak{e}$.
For non-negative integers $m$ and $k$, an $m$-dimensional subspace
$\mathfrak{p}$ of $\mathbb{F}^{n+l}_q$ is called a subspace of
{\it type $(m,k)$} with respect to $\mathfrak{e}$
if $\dim \mathfrak{p}\cap \mathfrak{e}=k$,
and especially a subspace $\mathfrak{p}$ of type $(m,0)$ is
an element of the attenuated space associated with
$\mathbb{F}^{n+l}_q$ and $\mathfrak{e}$.
Denote the set of all subspaces of
type $(m,k)$ in $\mathbb{F}^{n+l}_q$ by $\mathcal{M}_q(m,k;n+l,n)$.
The cardinality of $\mathcal{M}_q(m,k;n+l,n)$ is
\[q^{(m-k)(l-k)}\qbinom{n}{m-k}_q\qbinom{l}{k}_q,\]
where $\qbinom{n}{k}_q=\prod ^{k-1}_{i=0}\frac{q^n-q^i}{q^k-q^i}$,
i.e., the {\it Gaussian coefficient}.
The subscript $q$ will be omitted
when there is no possibility of confusion.

In 2009, Wang, Guo and Li proved that $\mathcal{M}_q(m,0;n+l,n)$ has
a structure of a symmetric association scheme
$\mathfrak{X}(\mathcal{M}_q(m,0;n+l,n))$ and
they computed intersection numbers of
$\mathfrak{X}(\mathcal{M}_q(m,0;n+l,n))$~\cite{Wang2009asb}.
In their paper, the relation $R_{(i,j)}$ on
$\mathcal{M}_q(m,0;n+l,n)$ is defined to be the set of pairs
$(\mathfrak{p},\mathfrak{q})$ satisfying
\[
\dim ((\mathfrak{p}+\mathfrak{e})/\mathfrak{e}
\cap (\mathfrak{q}+\mathfrak{e})/\mathfrak{e})
=m-i\
\text{and}\
\dim \mathfrak{p}\cap \mathfrak{q}=(m-i)-j,\]
for $(i,j)\in K=\set{(i,j)\in {\mathbb{Z}_{\ge 0}}^2}
{i\le m\wedge (n-m),
\ j\le (m-i)\wedge l}$,
where for integers $a$ and $b$,
the value $a\wedge b$ denotes
$\min\{a,b \}$ for short.
Then $(\mathcal{M}_q(m,0;n+l,n), \{R_{(i,j)}\}_{(i,j)\in K})$ is
a symmetric association scheme
and called an
{\it association scheme based on
an attenuated space}.
In this paper,
we denote it by $\mathfrak{X}(\mathcal{M}_q(m,0;n+l,n))$.

The association scheme $\mathfrak{X}(\mathcal{M}_q(m,0;n+l,n))$
is a common generalization of the Grassmann scheme $J_q(n,m)$
and the bilinear forms scheme $H_q(n,l)$.
In fact, if $l=0$, then the association scheme
$\mathfrak{X}(\mathcal{M}_q(m,0;n,n))$ is isomorphic to
the Grassmann scheme $J_q(n,m)$ and if $m=n$,
then the association scheme $\mathfrak{X}(\mathcal{M}_q(n,0;n+l,n))$
is isomorphic to the bilinear forms scheme $H_q(n,l)$.
Moreover the association scheme
$\mathfrak{X}(\mathcal{M}_q(m,0;n+l,n))$ is also a $q$-analogue of
the non-binary Johnson scheme (cf.~\cite{Tarnanen1985njs}).

The aim of this paper is to determine the character tables of
association schemes based on attenuated spaces.
To determine the character tables, we use the method of Tarnanen,
Aaltonen and Goethals~\cite{Tarnanen1985njs}.

Determining the character table of an association scheme corresponds
to determining the spherical functions of a compact symmetric space.
In~\cite{Bannai1984aci}, Bannai and Ito referred to an analogy
between compact symmetric spaces of rank one and  a family of
association schemes which are called ($P$ and $Q$)-polynomial
association schemes.
In fact, zonal spherical functions of compact symmetric spaces of
rank one and eigenmatrices of ($P$ and $Q$)-polynomial association
schemes are described by certain orthogonal polynomials.
Moreover Bannai~\cite{Bannai1990ctoa} had the assurance that there
exists an analogy between general compact symmetric spaces and
most of commutative association schemes, and he observed relations
between spherical functions of some compact symmetric spaces and
character tables of some commutative association schemes.
In order to study relations between compact symmetric spaces and
commutative association schemes,
it is useful to know many examples of character tables of
commutative association schemes.

In Section~\ref{sec:main_sec},
the main result of this paper will be described after giving
some definitions and basic facts about association schemes.
In Section~\ref{sec:proof_of_main}, we prove Lemma~\ref{prop:prod_c},
which is a key lemma of the proof of the main result.
In Section~\ref{sec:m-flat},
a relation between association schemes based on attenuated spaces and
$m$-flat association schemes will be found.
Namely, we prove that association schemes
based on attenuated spaces include as a special case
the $m$-flat association scheme,
which is defined on the set of
cosets of subspaces of a constant dimension in a vector space over
a finite field.
Finally in Appendix~\ref{sec:formula}
we describe some useful formulas about the number of
subspaces of a vector space over a finite field
and equations related to the $q$-Gaussian coefficient,
the generalized Eberlein polynomials and
the generalized Krawtchouk polynomials,
which are used in this paper.

\section{Character tables of association schemes based on attenuated
spaces}
\label{sec:main_sec}
We begin with a review of basic definitions concerning
association schemes.
The reader is referred to Bannai-Ito~\cite{Bannai1984aci} for the
background material.

A {\it symmetric association scheme}
$\mathfrak{X}=(X,\{R_i\}_{0\le i\le d})$
consists of a finite set $X$ and a set $\{R_i\}_{0\le i\le d}$
of binary relations on $X$ satisfying:
\begin{enumerate}
\item $R_0=\set{(x,x)}{x\in X}$;
\item $\{R_i\}_{0\le i\le d}$ is a partition of $X\times X$;
\item $\trans{R_i}=R_i$ for each $i\in \{0,1,\ldots ,d\}$,
where $\trans{R_i}=\set{(y,x)}{(x,y)\in R_i}$;
\item the numbers $|\set{z\in X}{\text{$(x,z)\in R_i$ and $(z,y)\in
R_j$}}|$ are constant whenever $(x,y)\in R_k$, for each $i,j,k\in
\{0,1,\ldots ,d\}$.
\end{enumerate}
Note that the numbers $|\set{z\in X}{\text{$(x,z)\in R_i$ and
$(z,y) \in R_j$}}|$ are called the {\it intersection numbers}
and denoted by $p^{k}_{i,j}$.
Let $M_X(\mathbb{C})$ denote the algebra of matrices over the complex
field $\mathbb{C}$ with rows and columns indexed by $X$.
The $i$-th {\it adjacency matrix} $A_i$ in $M_X(\mathbb{C})$ of
$\mathfrak{X}$ is defined by
\[A_i(x,y)=
\begin{cases}
1 & \text{if $(x,y)\in R_i$,}\\
0 & \text{otherwise.}
\end{cases}\]
The vector space
$\mathfrak{A}=\langle A_0,A_1,\ldots, A_d\rangle_\mathbb{C}$
spanned by $A_i$'s ($i=0,1,\ldots ,d$) forms a commutative algebra
and called the {\it Bose-Mesner algebra} of
$\mathfrak{X}=(X,\{R_i\}_{0\le i\le d})$.
It is well known that $\mathfrak{A}$ is semi-simple,
hence $\mathfrak{A}$ has a basis
consisting of the primitive
idempotents $E_0=1/|X|J, E_1,\ldots ,E_d$,
i.e., $E_i E_j=\delta_{i,j}E_i$, $\sum^{d}_{i=0}E_i=I$, where $J$ is
the all-one matrix and
the notation $\delta _{i,j}$ stands for the value 1 if $i=j$,
0 otherwise.
The {\it first eigenmatrix} $P=(P_i(j))_{0\le j,i\le d}$
and the {\it second eigenmatrix} $Q=(Q_i(j))_{0\le j,i\le d}$
of $\mathfrak{X}$ are defined by
\[A_i=\sum^{d}_{j=0}P_i(j)E_j\
\text{and}\
E_i=\frac{1}{|X|}\sum^{d}_{j=0}Q_i(j)A_j,\]
respectively.
In particular, the first eigenmatrix $P$ is also called the
{\it character table} of $\mathfrak{X}$.
Note that $P$ and $Q$ satisfy $P Q=Q P=|X| I$,
and it is well known that
\begin{equation}
\label{eq:P-Q-valency-multi}
\frac{Q_j(i)}{m_j}
=
\frac{P_i(j)}{v_i},
\end{equation}
where
$v_i=p^0_{i,i}$ is called the $i$-th {\it valency}
and
$m_j=\tr (E_j)$ is called the $j$-th {\it multiplicity}.

Next we give two examples of association schemes.
The eigenmatrices of association schemes based on
attenuated spaces will be given using
the entries of
the eigenmatrices of these association schemes.
Let $V$ and $E$ be $n$-dimensional and $l$-dimensional vector spaces
over $\mathbb{F}_q$, respectively,
and let $L(V,E)$ denote the set of all linear maps from $V$ to $E$.
For a subspace $\mathfrak{p}$ of $V$, the set of all $r$-dimensional
subspaces of $\mathfrak{p}$ is denoted by $\qbinom{\mathfrak{p}}{r}$.

The set $\qbinom{V}{m}$ together with the nonempty relations
\[
R_i=\set{(\mathfrak{x},\mathfrak{y})\in {\textstyle \qbinom{V}{m}^2}}
{\dim \mathfrak{x}\cap \mathfrak{y}=m-i}
\]
is an
$m\wedge (n-m)$-class symmetric association scheme called the
{\it Grassmann scheme} $J_q(n,m)$.
The first eigenmatrix $P^G=(P^G_k(x))_{0\le x,k\le m\wedge (n-m)}$
of the Grassmann scheme
$J_q(n,m)$ is given by the {\it generalized Eberlein polynomials}
$E_k(n,m;q;x)$
\cite{Delsarte1976paa}, namely
\begin{eqnarray*}
P^G_k(x)&=&E_k(n,m;q;x)\\
&=&\sum^{k}_{j=0}(-1)^{k-j}q^{j x+\binom{k-j}{2}}\qbinom{m-j}{m-k}
\qbinom{m-x}{j}\qbinom{n-m+j-x}{j}.
\end{eqnarray*}
Furthermore, since the valencies $v_i$ and the multiplicities $m_j$
of the Grassmann scheme $J_q(n,m)$ are given as
$v_i=q^{i^2}\qbinom{n-m}{i}\qbinom{m}{i}$
and
$m_j=\qbinom{n}{j}-\qbinom{n}{j-1}$,
respectively (cf.~\cite[p.~269]{Brouwer1989dg}),
by (\ref{eq:P-Q-valency-multi})
we obtain the second eigenmatrix
$Q^G=(Q^G_k(x))_{0\le x,k\le m\wedge (n-m)}$
of the Grassmann scheme
$J_q(n,m)$
as follows;
\begin{eqnarray*}
\lefteqn{Q^G_k(x)}\\
&=&\frac{\qbinom{n}{k}-\qbinom{n}{k-1}}
{q^{x^2}\qbinom{n-m}{x}\qbinom{m}{x}}
\sum^{x}_{j=0}(-1)^{x-j}q^{j k+\binom{x-j}{2}}\qbinom{m-j}{m-x}
\qbinom{m-k}{j}\qbinom{n-m+j-k}{j}.
\end{eqnarray*}
We denote this value by $Q_k(n,m;q;x)$.

The set $L(V,E)$ together with the nonempty relations
\[R_i=\set{(f,g)\in L(V,E)^2}{\rank (f-g)=i}\]
is an $n\wedge l$-class symmetric association scheme called the
{\it bilinear forms scheme} $H_q(n,l)$~\cite{Delsarte1978bfo}.
The first eigenmatrix $P^B=(P^B_k(x))_{0\le x,k\le n\wedge l}$
of the bilinear forms scheme
$H_q(n,l)$ is given by the {\it generalized Krawtchouk polynomials}
$K_k(n,l;q;x)$
\cite{Delsarte1976paa}, namely
\begin{eqnarray*}
P^B_k(x)&=&K_k(n,l;q;x)\\
&=&\sum^{k}_{j=0}(-1)^{k-j}q^{j l+\binom{k-j}{2}}\qbinom{n-j}{n-k}
\qbinom{n-x}{j}.
\end{eqnarray*}
Note that bilinear forms schemes are self-dual, i.e., $P^B=Q^B$,
where $Q^B$ is the second eigenmatrix of $H_q(n,l)$
(see~\cite{Delsarte1978bfo}).
Hence, by $P^B Q^B =|L(V,E)| I$, we obtain
\begin{equation}
\label{eq:orth_Krawtchouk}
\sum^{n \wedge l}_{k=0}
K_k(n,l;q;i)
K_j(n,l;q;k)
=q^{n l} \delta _{i,j}.
\end{equation}

In order to calculate the character table of the association scheme
$\mathfrak{X}(\mathcal{M}_q(m,0;n+l,n))$,
we deal with another realization of
$\mathfrak{X}(\mathcal{M}_q(m,0;n+l,n))$.
Let $\X$ be the set of all pairs of a subspace $\mathfrak{x}$ in $V$
and a linear map $\xi$ in $L(\mathfrak{x}, E)$ and let
$\X_m =\set{(\mathfrak{x},\xi)\in \X}{\mathfrak{x}\in \qbinom{V}{m}}$.
The set $\X_m$ has cardinality $q^{ml} \qbinom{n}{m}$.
Then there is the following one-to-one correspondence between
$\X_m$ and $\mathcal{M}_q(m,0;n+l,n)$:
we regard $V\oplus E$ as $\mathbb{F}_q ^{n+l}$
and also regard $\{0\} \oplus E$ as $\mathfrak{e}$.
For $(\mathfrak{x},\xi)$ in $\X _m$,
we set $\mathfrak{x}_\xi =\set{(x, \xi (x))}{x\in \mathfrak{x}}$
in $\mathbb{F}_q ^{n+l}$.
Then we immediately check that
$\mathfrak{x}_\xi$ is type $(m,0)$ with respect to
$\mathfrak{e}$,
i.e., $\mathfrak{x}_\xi \in \mathcal{M}_q(m,0;n+l,n)$,
and
the map $(\mathfrak{x},\xi) \mapsto \mathfrak{x}_\xi$
from $\X _m$ to $\mathcal{M}_q(m,0;n+l,n)$
is injective.
On the other hand, we have
$|\X _m|=|\mathcal{M}_q(m,0;n+l,n)| =q^{ml} \qbinom{n}{m}$.
This means that the map from $\X _m$ to $\mathcal{M}_q(m,0;n+l,n)$
is bijective.
Next, we define the relation $S_{(i,j)}$ on $\X_m$
to be the set of pairs
$((\mathfrak{x},\xi), (\mathfrak{y},\eta))$ satisfying
\[
\dim \mathfrak{x}\cap \mathfrak{y}=m-i\ \text{and}\
\rank (\xi |_{\mathfrak{x}\cap \mathfrak{y}}-\eta |_{\mathfrak{x}
\cap \mathfrak{y}})=j.
\]
Then, by the two equalities
\begin{eqnarray*}
\dim
(\mathfrak{x}_\xi +\mathfrak{e})/\mathfrak{e}
\cap
(\mathfrak{y}_\eta +\mathfrak{e})/\mathfrak{e}
&=&
\dim
(\mathfrak{x} \cap \mathfrak{y}\oplus E)/
(\{0\}\oplus E)\\
&=&\dim \mathfrak{x} \cap \mathfrak{y}
\end{eqnarray*}
and
\begin{eqnarray*}
\dim \mathfrak{x}_\xi \cap \mathfrak{y}_\eta
&=&
\dim \set{(x, \xi(x))}{x \in \ker
(\xi |_{\mathfrak{x}\cap \mathfrak{y}}-\eta |_{\mathfrak{x}
\cap \mathfrak{y}})}\\
&=&\dim \ker
(\xi |_{\mathfrak{x}\cap \mathfrak{y}}-\eta |_{\mathfrak{x}
\cap \mathfrak{y}})\\
&=&\dim \mathfrak{x} \cap \mathfrak{y}-
\rank
(\xi |_{\mathfrak{x}\cap \mathfrak{y}}-\eta |_{\mathfrak{x}
\cap \mathfrak{y}}),
\end{eqnarray*}
it follows that
$((\mathfrak{x},\xi), (\mathfrak{y},\eta)) \in S_{(i,j)}$
if and only if $(\mathfrak{x}_\xi, \mathfrak{y}_\eta) \in R_{(i,j)}$.
Consequently, we obtain another representation of
$\mathfrak{X}(\mathcal{M}_q(m,0;n+l,n))$,
and we denote
the association scheme
$(\X_m, \{S_{(i,j)}\}_{(i,j)\in K})$ by
$\mathfrak{X}(\mathcal{M}_q(m,0;n+l,n))$.

We calculate the character table of this association scheme
using the following theorem
proved by Tarnanen, Aaltonen and Goethals~\cite{Tarnanen1985njs}:
\begin{thm}
\label{thm:chara_thm}
Let $X$ be a non-empty finite set.
Assume that $\{R_i\}_{0\le i\le d}$ is a partition of $X\times X$,
each $R_i$ is a symmetric relation,
that is $\trans{R_i}=R_i$,
and $R_0=\set{(x,x)}{x\in X}$.
Let $\mathfrak{A}=\langle A_0,A_1,\ldots, A_d\rangle_\mathbb{C}$
be the complex linear space generated by the adjacency matrices
$A_i$ of $R_i$ $(i\in \{0,1,\ldots ,d\})$.
If there exist matrices $C_0=J, C_1,\ldots ,C_d$ of $\mathfrak{A}$
such that
\[A_i=\sum^{d}_{j=0}\alpha_i(j)C_j\ \text{and }\  C_k C_s=
\sum^{k\wedge s}_{j=0} \beta_{k;s}(j)C_j,\quad k,s\in
\{0,1,\ldots ,d\},\]
where $\alpha_i(j)$and $\beta_{k;s}(j)$ are complex numbers,
then $(X,\{R_i\}_{0\le i\le d})$ is a symmetric association scheme
and its first eigenmatrix $P=(P_i(s))_{0\le s, i\le d}$
is given by
\[P_i(s)=\sum^{d}_{k=s}\alpha_i(k)\beta_{k;s}(s),
\quad i,s\in \{0,1,\ldots ,d\}.\]
\end{thm}
For the rest of this paper, let $d=m\wedge (n-m)$.
Let $A_{(i,j)}$ denote
the adjacency matrix of the relation
$S_{(i,j)}$.
We define $L=\set{(r,s)\in {\mathbb{Z}_{\ge 0}}^2}{s\le m\wedge l,
r\le m, \ 0\le r-s\le d}$.
Since $(i,j)\mapsto (r,s)=(i+j,j)$ is a bijection from
$K$ to $L$, we have $|L|=|K|$.
For $(r,s)\in L$, a matrix $C_{(r,s)}$ is defined as follows,
which serves as $C_i$ in Theorem \ref{thm:chara_thm}:
for $0\le i\le d$ and $0\le s\le m\wedge l$,
\[B_{(i,s)}=\sum^{(m-i) \wedge l}_{j=0}K_s(m-i,l;q;j)A_{(i,j)}\]
and for $(r,s)\in L$,
\[C_{(r,s)}=\sum^{d\wedge (m-s)}_{i=0}\qbinom{m-i-s}{r-s}B_{(i,s)}.\]
Namely,
for $((\mathfrak{x},\xi),(\mathfrak{y},\eta))\in S_{(m-u,u-v)}$,
the $((\mathfrak{x},\xi), (\mathfrak{y},\eta))$-entry of $C_{(r,s)}$
is as follows:
\begin{equation}
\label{eq:C_rs}
C_{(r,s)}((\mathfrak{x},\xi),(\mathfrak{y},\eta))=
\qbinom{u-s}{r-s}K_s(u,l;q;u-v).
\end{equation}
By using (\ref{eq:orth_Krawtchouk})
for the bilinear forms scheme $H_q(m-i,l)$,
for $(i,j)\in K$,
we obtain
\begin{align*}
A_{(i,j)}&=
q^{-(m-i)l}\sum^{(m-i)\wedge l}_{h=0}K_{j}(m-i,l;q;h)B_{(i,h)}
\\ &=
q^{-(m-i)l}\sum^{m \wedge l}_{h=0}K_{j}(m-i,l;q;h)B_{(i,h)},
\end{align*}
since $K_{j}(m-i,l;q;h)=0$ if $h>m-i$.
We claim that the square matrix
\[
M^s=
\left(\qbinom{m-i-s}{r-s}\right)
_{\substack{0\le i\le d\wedge (m-s),\\ s\le r\le (d+s)\wedge m}}
\]
is nonsingular. Indeed,
since $\qbinom{m-i-s}{r-s}$ is a polynomial of degree $r-s$
in $q^{-i}$,
$M^s$ can be converted into a Vandermonde matrix
$((q^{-i})^{r'})_{0\le i,r'\le d\wedge (m-s)}$
by a sequence of elementary transformations.
Thus the inverse matrix $N^s$
of $M^s$ satisfies
\begin{equation}
\label{eq:N^s}
\sum^{(d+s)\wedge m}_{k=s}
\qbinom{m-i-s}{k-s}N^s (k,j)
=\delta_{i,j}
\end{equation}
for $0\le i,j\le d\wedge (m-s)$.
By (\ref{eq:N^s}),
for $0\le i\le d$ and $0\le h \le m \wedge l$,
we obtain
\[B_{(i,h)}=\sum^{(d+h)\wedge m}_{k=h}
N^h (k,i) C_{(k,h)}.\]
Therefore we have
$A_{(i,j)}=\sum_{(k,h)\in L}\alpha _{(i,j)}(k,h)C_{(k,h)}$, where
\begin{equation}
\label{eq:alpha}
\alpha _{(i,j)}(k,h)=q^{-(m-i)l}
K_{j}(m-i,l;q;h) N^h (k,i).
\end{equation}

The following lemma gives the expansion of $C_{(r,s)}C_{(k,h)}$
in terms of $C_{(i,j)}$,
which serves as the expansion of $C_k C_s$ in terms of $C_j$
in Theorem \ref{thm:chara_thm}.
\begin{lem}
\label{prop:prod_c}
The matrices $\{C_{(r,s)}\}_{(r,s)\in L}$ satisfy
\[C_{(r,s)}C_{(k,h)}=\sum^{r\wedge k}_{i=s}
\beta_{(r,s;k,h)}(i,s) C_{(i,s)},\]
where
\[\beta_{(r,s;k,h)}(i,s)=\delta_{s,h}q^{ml+(i-s)(m-r-k+i)}
\qbinom{m-i}{m-r}\qbinom{m-i}{m-k}\qbinom{n-r-k+s}{m-r-k+i}.\]
\end{lem}
We will prove Lemma \ref{prop:prod_c} in Section
\ref{sec:proof_of_main}.
Using Lemma \ref{prop:prod_c},
we obtain the main theorem of this paper.
\begin{thm}
\label{thm:main}
Let $P=(P_{(i,j)}(r,s))_{(r,s)\in L, (i,j)\in K}$
and $Q=(Q_{(r,s)}(i,j))_{(i,j)\in K, (r,s)\in L}$
be the first and second eigenmatrices of the association scheme based
on attenuated space $\mathfrak{X}(\mathcal{M}_q(m,0;n+l,n))$,
respectively.
Then the following hold.
\begin{equation}
\label{eq:main_thm_P}
P_{(i,j)}(r,s)=
q^{i l}K_{j}(m-i,l;q;s)E_i(n-s,m-s;q;r-s)
\end{equation}
and
\begin{equation}
\label{eq:main_thm_Q}
Q_{(r,s)}(i,j)=
\frac{\qbinom{n}{m}}{\qbinom{n-s}{m-s}}K_s(m-i,l;q;j)
Q_{r-s}(n-s,m-s;q;i).
\end{equation}
\end{thm}
\begin{proof}
Let $\succeq$ be the lexicographical order of $L$ so that the
relation $(k,h)\succeq (r,s)$ means that $h> s$ or that $k\ge r$
if $h=s$.
By Theorem \ref{thm:chara_thm}, the eigenvalue $P_{(i,j)}(r,s)$ of
$\mathfrak{X}(\mathcal{M}_q(m,0;n+l,n))
=(\X_m, \{S_{(i,j)}\}_{(i,j)\in K})$ is calculated
as follows.
For $(i,j)\in K$ and $(r,s)\in L$,
we have
\begin{eqnarray*}
P_{(i,j)}(r,s) &=&\sum_{(k,h)\succeq (r,s)}\alpha_{(i,j)}(k,h)
\beta_{(k,h;r,s)}(r,s)\\
&=&\sum^{m\wedge (d+s)}_{k=r}q^{-(m-i)l}
K_{j}(m-i,l;q;s) N^s (k,i)\\
&&\times q^{ml}q^{(r-s)(m-k)}\qbinom{m-r}{m-k}\qbinom{n-k-r+s}{m-k}\\
&=&q^{il}K_{j}(m-i,l;q;s)\sum^{m\wedge (d+s)}_{k=s} N^s (k,i)\\
&&\times q^{(m-k)(r-s)}\qbinom{m-r}{m-k}\qbinom{n-k-r+s}{m-k},
\end{eqnarray*}
since $\qbinom{m-r}{m-k}=0$ if $k<r$.
Moreover using Lemma \ref{lem:eberlein}
and (\ref{eq:N^s}),
we obtain
\begin{eqnarray*}
P_{(i,j)}(r,s)
&=&q^{i l}K_{j}(m-i,l;q;s)\sum^{m\wedge (d+s)}_{k=s}N^s (k,i)\\
&&\times \sum^{m-s}_{t=0}\qbinom{m-s-t}{k-s}E_t(n-s,m-s;q;r-s)\\
&=&q^{i l}K_{j}(m-i,l;q;s)E_i(n-s,m-s;q;r-s).
\end{eqnarray*}

To verify
(\ref{eq:main_thm_Q}),
it is sufficient to show that
\[\sum_{(i,j)\in K}
\frac{\qbinom{n}{m}}{\qbinom{n-s}{m-s}}K_s(m-i,l;q;j)
Q_{r-s}(n-s,m-s;q;i)P_{(i,j)}(k,h)
=q^{ml}\qbinom{n}{m}\delta_{r,k}\delta_{s,h}\]
for all $(r,s)$ and $(k,h)$ in $L$.
Substituting (\ref{eq:main_thm_P}) for $P_{(i,j)}(k,h)$ and
using the orthogonality of
eigenmatrices of Grassmann schemes
$J_q(n-s,m-s)$
and bilinear forms schemes $H_q(m-i,l)$,
this orthogonality relation is verified.
\end{proof}

\section{Proof of Lemma \ref{prop:prod_c}}
\label{sec:proof_of_main}
Let $\Y$ be the set of all pairs of a subspace $\mathfrak{a}$ in $V$
and a linear map $f$ from $E$ to $\mathfrak{a}$, and
$\Y_r=\set{(\mathfrak{a},f)\in \Y}{\dim \mathfrak{a}=r}$.
For a subspace $\mathfrak{x}$ of $V$,
let $\Y^\mathfrak{x}_r=\set{(\mathfrak{a},f)\in \Y_r}{\mathfrak{a}
\subset \mathfrak{x}}$ and
$\Y^\mathfrak{x}_{r,s}=\set{(\mathfrak{a},f)\in
\Y^\mathfrak{x}_r}{\rank f=s}$.
We shall define a complex-valued function
$\xprod{\cdot}{\cdot}$
over $\Y\times \X$ needed in the proof of Lemma \ref{prop:prod_c}.
Consider a pair $((\mathfrak{a},f),(\mathfrak{x},\xi))\in \Y\times\X$
satisfying $\mathfrak{a}\subset \mathfrak{x}$.
When $\dim \mathfrak{x}=r$, the linear map
$f\circ \xi:\mathfrak{x}\rightarrow \mathfrak{a}\subset \mathfrak{x}$
is regarded as a square matrix $T_{f\circ \xi}$ of degree $r$ for
some basis of $\mathfrak{x}$.
Note that the trace $\tr (T_{f\circ \xi})$ of $T_{f\circ \xi}$
is independent of the chosen basis of $\mathfrak{x}$,
so that $\tr (T_{f\circ \xi})$ only depends on the pair
$((\mathfrak{a},f),(\mathfrak{x},\xi))$.
\begin{df}
Let $p$ be the prime divisor of $q$ and let
$\epsilon$ be a primitive $p$-th root of unity.
We take $\chi : \mathbb{F}_q \rightarrow \mathbb{Z}[\epsilon]$ to be a
non-principal character of the elementary abelian $p$-group
$(\mathbb{F}_q, +)$.
The function
$\Y\times \X\ni ((\mathfrak{a},f),(\mathfrak{x},\xi))\mapsto
\xprod{(\mathfrak{a},f)}{(\mathfrak{x},\xi)}\in \mathbb{C}$
is defined as
\[\xprod{(\mathfrak{a},f)}{(\mathfrak{x},\xi)}=
\begin{cases}
\chi (\tr (T_{f\circ \xi})) &
\text{if $\mathfrak{a}\subset \mathfrak{x}$,}\\
0& \text{otherwise.}
\end{cases}\]
\end{df}
Fix an element $\mathfrak{x}$ in $\qbinom{V}{r}$.
For $f\in L(E, \mathfrak{x})$,
we define the function
$\Lambda _f : L(\mathfrak{x},E)\rightarrow \mathbb{C}$
by
$\Lambda _f(\xi)=\xprod{(\mathfrak{x},f)}{(\mathfrak{x},\xi)}$.
Then
$\set{\Lambda _f}{f\in L(E, \mathfrak{x})}$
is the character group of $L(\mathfrak{x},E)$
and we denote it by $L(\mathfrak{x},E)^\ast$.
There is the orthogonality relation of
$L(\mathfrak{x},E)^\ast$:
\begin{equation}
\label{eq:krawtchouk}
\sum_{\xi \in L(\mathfrak{x},E)}
\overline{\xprod{(\mathfrak{x},f)}{(\mathfrak{x},\xi)}}
\xprod{(\mathfrak{x},g)}{(\mathfrak{x},\xi)}=
\begin{cases}
q^{r l} & \text{if $f =g$,}\\
0 & \text{otherwise,}
\end{cases}
\end{equation}
and there is the following equation
(cf.~\cite{Delsarte1978bfo}):
\begin{equation}
\label{eq:krawtchouk_rank_s}
\sum_{\substack{f\in L(E,\mathfrak{x})\\
\rank f=s}}
\xprod{(\mathfrak{x},f)}{(\mathfrak{x},\xi)}
\overline{\xprod{(\mathfrak{x},f)}{(\mathfrak{x},\eta)}}
=K_s(r,l;q;\rank(\xi-\eta)).
\end{equation}

For $(\mathfrak{a},f)$ and $(\mathfrak{b},g)$ in $\Y$,
if $f(x)=g(x)$ for any $x\in E$,
then we call the pair $(\mathfrak{a},f)$ and $(\mathfrak{b},g)$
{\it almost equal} and denote this by
$(\mathfrak{a},f)\approx (\mathfrak{b},g)$.
When $(\mathfrak{a},f)\approx (\mathfrak{b},g)$,
it can be easily seen that
$\im f=\im g\subset \mathfrak{a}\cap \mathfrak{b}$ and
$\xprod{(\mathfrak{a},f)}{(\mathfrak{x},\xi)} =
\xprod{(\mathfrak{b},g)}{(\mathfrak{x},\xi)}$
for any $(\mathfrak{x},\xi)\in \X$ with
$\mathfrak{a}+\mathfrak{b}\subset \mathfrak{x}$.

\begin{lem}
\label{clm:chara_and_krawtchouk}
For $(\mathfrak{x},\xi)$ and $(\mathfrak{y},\eta)$ in $\X_m$,
\begin{equation}
\label{eq:vipeq}
\sum_{(\mathfrak{a},f)\in \Y^V_{r,s}}\xprod{(\mathfrak{a},f)}
{(\mathfrak{x},\xi)}\overline{\xprod{(\mathfrak{a},f)}
{(\mathfrak{y},\eta)}}
=C_{(r,s)}((\mathfrak{x},\xi), (\mathfrak{y},\eta)).
\end{equation}
\end{lem}

\begin{proof}
By the definition of $\xprod{\cdot}{\cdot}$,
the range of the summation of $(\mathfrak{a},f)$
in the left hand side of (\ref{eq:vipeq}) is restricted within
$\Y^{\mathfrak{x}\cap \mathfrak{y}}_{r,s}$.
Since $f\circ \xi$ has a matrix representation
of the following form
\[T_{f\circ \xi} =\left(
\begin{array}{cc}
T &\ast \\
0 &0 \\
\end{array}\right),\]
where $T$ is a matrix representation of
$f\circ \xi |_\mathfrak{a} \in L(\mathfrak{a},\mathfrak{a})$,
we obtain
\[\xprod{(\mathfrak{a},f)}{(\mathfrak{x},\xi)}=
\xprod{(\mathfrak{a},f)}{(\mathfrak{a},\xi |_{\mathfrak{a}})}.\]
Similarly, we obtain
\[\xprod{(\mathfrak{a},f)}{(\mathfrak{y},\eta)}=
\xprod{(\mathfrak{a},f)}{(\mathfrak{a},\eta |_{\mathfrak{a}})}.\]
Therefore by (\ref{eq:krawtchouk_rank_s}), we obtain
\begin{eqnarray*}
\sum_{(\mathfrak{a},f)\in \Y^V_{r,s}}\xprod{(\mathfrak{a},f)}
{(\mathfrak{x},\xi)}\overline{\xprod{(\mathfrak{a},f)}
{(\mathfrak{y},\eta)}}&=&
\sum_{(\mathfrak{a},f)\in \Y^{\mathfrak{x}\cap \mathfrak{y}}_{r,s}}
\xprod{(\mathfrak{a},f)}{(\mathfrak{a},\xi |_{\mathfrak{a}})}
\overline{\xprod{(\mathfrak{a},f)}
{(\mathfrak{a},\eta |_{\mathfrak{a}})}}\\
&=&\sum_{\mathfrak{a}\in \qbinom{\mathfrak{x}\cap \mathfrak{y}}{r}}
K_s(r,l;q;\rank (\xi |_{\mathfrak{a}}-\eta |_{\mathfrak{a}})).\\
\end{eqnarray*}
Let us remark that
$\rank(\xi |_{\mathfrak{a}}-\eta |_{\mathfrak{a}})=\dim \mathfrak{a}
-\dim \ker (\xi |_{\mathfrak{a}}-\eta |_{\mathfrak{a}})$
and
$\ker (\xi |_{\mathfrak{a}}-\eta |_{\mathfrak{a}})=\ker (\xi |_
{\mathfrak{x}\cap \mathfrak{y}}-\eta |_{\mathfrak{x}\cap
\mathfrak{y}})\cap \mathfrak{a}$.
Thus when $\dim \mathfrak{x}\cap
\mathfrak{y}=u$ and
$\dim \ker (\xi |_
{\mathfrak{x}\cap \mathfrak{y}}-\eta |_{\mathfrak{x}\cap
\mathfrak{y}})=v$
(i.e., $((\mathfrak{x},\xi), (\mathfrak{y},\eta)) \in S_{(m-u,u-v)}$),
by Corollary \ref{lem:BCN},
the number of
$\mathfrak{a}\in \qbinom{\mathfrak{x}\cap \mathfrak{y}}{r}$
with
$\dim \ker (\xi |_{\mathfrak{x}\cap \mathfrak{y}}-\eta |
_{\mathfrak{x}\cap \mathfrak{y}})\cap \mathfrak{a}=r-j$
is equal to
\[q^{j(v-r+j)}\qbinom{u-v}{j}\qbinom{v}{r-j}.\]
Hence it follows that
\begin{eqnarray*}
\sum_{\mathfrak{a}\in \qbinom{\mathfrak{x}\cap \mathfrak{y}}{r}}
K_s(r,l;q;\rank (\xi |_{\mathfrak{a}}-\eta |_{\mathfrak{a}}))
&=&\sum^{r\wedge (u-v)}_{j=0\vee (v-r)}q^{j(v-r+j)}\qbinom{u-v}{j}
\qbinom{v}{r-j}K_s(r,l;q;j)\\
&=&\qbinom{u-s}{r-s}K_s(u,l;q;u-v)\\
&=&C_{(r,s)}((\mathfrak{x},\xi), (\mathfrak{y},\eta)),
\end{eqnarray*}
where for integers $a$ and $b$,
the value $a\vee b$ denotes
$\max\{a,b \}$ for short.
In the second line,
we used Lemma \ref{lem:relation_of_krawtchouk}.
\end{proof}
\begin{proof}[Proof of Lemma \ref{prop:prod_c}]
Since $\mathfrak{X}(\mathcal{M}_q(m,0;n+l,n))$ is symmetric,
without loss of generality,
we may suppose $r\le k$.
By Lemma \ref{clm:chara_and_krawtchouk},
for $((\mathfrak{x},\xi), (\mathfrak{y},\eta))\in S_{(m-u,u-v)}$,
we obtain
\begin{eqnarray*}
C_{(r,s)}C_{(k,h)}((\mathfrak{x},\xi), (\mathfrak{y},\eta)) &=&
\sum_{(\mathfrak{z},\zeta)\in \X_m}C_{(r,s)}((\mathfrak{x},\xi),
(\mathfrak{z},\zeta))\cdot C_{(k,h)}((\mathfrak{z},\zeta),
(\mathfrak{y},\eta))\\
&=&\sum_{(\mathfrak{a},f)\in \Y^V_{r,s}}\sum_{(\mathfrak{b},g)\in
\Y^V_{k,h}}\xprod{(\mathfrak{a},f)}{(\mathfrak{x},\xi)}
\overline{\xprod{(\mathfrak{b},g)}{(\mathfrak{y},\eta)}}\\
&&\times \sum_{(\mathfrak{z},\zeta)\in \X_m}\overline{\xprod{(
\mathfrak{a},f)}{(\mathfrak{z},\zeta)}}\xprod{(\mathfrak{b},g)}
{(\mathfrak{z},\zeta)}.
\end{eqnarray*}
By the definition of $\xprod{\cdot}{\cdot}$, we may restrict the range of
the summation to be those
$(\mathfrak{z},\zeta)\in \X_m$ satisfying
$\mathfrak{z}\supset \mathfrak{a+b}$.
Thus we obtain
\begin{eqnarray*}
\sum_{(\mathfrak{z},\zeta)\in \X_m}\overline{\xprod{(\mathfrak{a},f)}
{(\mathfrak{z},\zeta)}}\xprod{(\mathfrak{b},g)}{(\mathfrak{z},\zeta)}
&=&\sum_{\substack{\mathfrak{z}\in \qbinom{V}{m}\\
\mathfrak{z}\supset \mathfrak{a}+\mathfrak{b}}}
\sum_{\zeta\in L(\mathfrak{z},E)}\overline{\xprod{(\mathfrak{a},f)}
{(\mathfrak{z},\zeta)}}\xprod{(\mathfrak{b},g)}{(\mathfrak{z},\zeta)}
\\
&=&\sum_{\substack{\mathfrak{z}\in \qbinom{V}{m}\\
\mathfrak{z}\supset \mathfrak{a}+\mathfrak{b}}}
\sum_{\zeta\in L(\mathfrak{z},E)}\overline{\xprod{(\mathfrak{z},f)}
{(\mathfrak{z},\zeta)}}\xprod{(\mathfrak{z},g)}{(\mathfrak{z},\zeta)}
\end{eqnarray*}
and, by (\ref{eq:krawtchouk}),
the value
$\sum_{\zeta\in L(\mathfrak{z},E)}\overline{\xprod{(\mathfrak{z},f)}
{(\mathfrak{z},\zeta)}}\xprod{(\mathfrak{z},g)}
{(\mathfrak{z},\zeta)}$
is equal to $q^{ml}$ if $(\mathfrak{a},f)\approx (\mathfrak{b},g)$
or vanishes otherwise.
Hence, if $h \neq s$, then $C_{(r,s)}C_{(k,h)}=0$
and we will henceforth assume that $h=s$.
The number of $\mathfrak{z}\in \qbinom{V}{m}$
satisfying
$\mathfrak{z}\supset \mathfrak{a}+\mathfrak{b}$ is equal to
$
\qbinom{n-\dim (\mathfrak{a}+\mathfrak{b})}
{m-\dim (\mathfrak{a}+\mathfrak{b})}
$.
Thus we obtain
\begin{eqnarray}
\label{eq:C_rs*C_ks}
\lefteqn{C_{(r,s)}C_{(k,s)}
((\mathfrak{x},\xi), (\mathfrak{y},\eta))}\\
\notag&=&
\sum_{\substack{(\mathfrak{a},f)\in \Y^\mathfrak{x}_{r,s}\\
(\mathfrak{b},g)\in \Y^\mathfrak{y}_{k,s}\\
(\mathfrak{a},f)\approx (\mathfrak{b},g)}}
\xprod{(\mathfrak{a},f)}{(\mathfrak{x},\xi)}
\overline{\xprod{(\mathfrak{b},g)}{(\mathfrak{y},\eta)}}
q^{ml}\qbinom{n-\dim (\mathfrak{a}+\mathfrak{b})}
{m-\dim (\mathfrak{a}+\mathfrak{b})}.
\end{eqnarray}

Let us impose the additional constraints:
$\dim\mathfrak{a}\cap \mathfrak{b}=e$,
$\dim\mathfrak{a}\cap \mathfrak{y}=r-t$ and
$\dim\mathfrak{b}\cap \mathfrak{x}=k-j$.
Since $(\mathfrak{a},f)\approx (\mathfrak{b},g)$,
i.e., $\im f=\im g\subset \mathfrak{a} \cap \mathfrak{b}$,
it follows that $e \ge s$ and
that $C_{(r,s)}C_{(k,h)}((\mathfrak{x},\xi), (\mathfrak{y},\eta))$
is equal to
\[
q^{ml}\sum^{r}_{e=s}\qbinom{n-r-k+e}{m-r-k+e}
\sum^{r-e}_{t=0}\sum^{k-e}_{j=0}\sum_{(\mathfrak{a},f)\in T_1}
\sum_{\mathfrak{b}\in T_2}
\xprod{(\mathfrak{a},f)}{(\mathfrak{x},\xi)}
\overline{
\xprod{(\mathfrak{b},f)}{(\mathfrak{y},\eta)}},
\]
where
$T_1=\set{(\mathfrak{a},f)\in \Y^{\mathfrak{x}}_{r,s}}
{\dim\mathfrak{a}\cap \mathfrak{y}=r-t,
\ \im f\subset \mathfrak{a}\cap \mathfrak{y}}$
and
$T_2=
\set{\mathfrak{b}\in \qbinom{\mathfrak{y}}{k}}{
\dim\mathfrak{b}\cap \mathfrak{x}=k-j,
\ \dim\mathfrak{a}\cap \mathfrak{b}=e,\ \mathfrak{b}\supset \im f}$.
Since
$\xprod{(\mathfrak{b},f)}{(\mathfrak{y},\eta)}
=
\xprod{(\mathfrak{a}\cap \mathfrak{y},f)}{(\mathfrak{y},\eta)}$
is independent of $\mathfrak{b}$,
it follows that
\begin{eqnarray}
\label{eq:(a,f)_and_b}
\lefteqn{
\sum_{(\mathfrak{a},f)\in T_1}
\sum_{\mathfrak{b}\in T_2}
\xprod{(\mathfrak{a},f)}{(\mathfrak{x},\xi)}
\overline{
\xprod{(\mathfrak{b},f)}{(\mathfrak{y},\eta)}}
}\\
&=&\notag
\sum_{(\mathfrak{a},f)\in T_1}|T_2|
\xprod{(\mathfrak{a},f)}{(\mathfrak{x},\xi)}
\overline{
\xprod{(\mathfrak{a} \cap \mathfrak{y},f)}{(\mathfrak{y},\eta)}}.
\end{eqnarray}
We shall count the number of elements in $T_2$.
By Proposition \ref{prop:dunkl},
the number of
$\mathfrak{b'}\in \qbinom{\mathfrak{x}\cap \mathfrak{y}}{k-j}$
satisfying $\mathfrak{b}'\supset \im f$ and
$\dim\mathfrak{a}\cap \mathfrak{b}'=e$ is
\[q^{(r-t-e)(k-j-e)}\qbinom{r-t-s}{e-s}\qbinom{u-r+t}{k-j-e}\]
and the number of $\mathfrak{b}\in \qbinom{\mathfrak{y}}{k}$
satisfying $\mathfrak{b}\cap \mathfrak{x}=\mathfrak{b}'$ is
\[q^{j(u-k+j)}\qbinom{m-u}{j},\]
that is,
\begin{equation}
\label{eq:T_2}
|T_2|=q^{(r-t-e)(k-j-e)+j(u-k+j)}
\qbinom{r-t-s}{e-s}\qbinom{u-r+t}{k-j-e}\qbinom{m-u}{j}.
\end{equation}
This means that
$|T_2|$ is independent of the choice of $(\mathfrak{a},f)$.
Note that, for
$(\mathfrak{a}',f')\in \Y^{\mathfrak{x}\cap \mathfrak{y}}_{r-t,s}$,
all $(\mathfrak{a},f)\in T_1$ with
$\mathfrak{a} \cap \mathfrak{y}=\mathfrak{a}'$ and
$f(x)= f'(x)$ for any
$x\in E$ satisfy $\xprod{(\mathfrak{a},f)}{(\mathfrak{x},\xi)}
\overline{
\xprod{(\mathfrak{a} \cap \mathfrak{y},f)}{(\mathfrak{y},\eta)}}=
\xprod{(\mathfrak{a}',f')}{(\mathfrak{x},\xi)}
\overline{\xprod{(\mathfrak{a}',f')}{(\mathfrak{y},\eta)}}$.
On the other hand, by Proposition \ref{prop:dunkl},
it follows that the number of $(\mathfrak{a},f)\in T_1$ with
$\mathfrak{a} \cap \mathfrak{y}=\mathfrak{a}'$ and
$f(x)= f'(x)$ for any $x\in E$ is
\[q^{t(u-r+t)}\qbinom{m-u}{t}.\]
Therefore we obtain
\begin{eqnarray}
\label{eq:a_and_f}
\lefteqn{\sum_{(\mathfrak{a},f)\in T_1}
\xprod{(\mathfrak{a},f)}{(\mathfrak{x},\xi)}
\overline{
\xprod{(\mathfrak{a} \cap \mathfrak{y},f)}{(\mathfrak{y},\eta)}}}\\
&=&q^{t(u-r+t)}\qbinom{m-u}{t}
\sum_{(\mathfrak{a}',f')\in \Y^{\mathfrak{x}\cap
\mathfrak{y}}_{r-t,s}}
\xprod{(\mathfrak{a}',f')}{(\mathfrak{x},\xi)}
\overline{\xprod{(\mathfrak{a}',f')}{(\mathfrak{y},\eta)}}\notag.
\end{eqnarray}
By (\ref{eq:(a,f)_and_b}), (\ref{eq:T_2}) and
(\ref{eq:a_and_f}) and Lemma \ref{clm:chara_and_krawtchouk},
it follows that
$C_{(r,s)}C_{(k,h)}((\mathfrak{x},\xi), (\mathfrak{y},\eta))$
is equal to
\begin{eqnarray*}
\lefteqn{q^{ml}\sum^{r}_{e=s}
\qbinom{n-r-k+e}{m-r-k+e}\sum^{r-e}_{t=0}
\sum^{k-e}_{j=0}q^{(u-r+t)t+(u-k+j)j+(r-t-e)(k-j-e)}}\\
&&\times\qbinom{m-u}{t}\qbinom{m-u}{j}\qbinom{r-t-s}{e-s}
\qbinom{u-r+t}{k-j-e}
C_{(r-t,s)}((\mathfrak{x},\xi), (\mathfrak{y},\eta)).
\end{eqnarray*}
Substituting (\ref{eq:C_rs}) for
$C_{(r-t,s)}((\mathfrak{x},\xi), (\mathfrak{y},\eta))$ and
using Proposition \ref{thm:q-bino} (\ref{eq:most_important}) (a) as
$(k,x,r,t)=(m-s,u-s,r-s,r-t-s)$, i.e.,
\[
\qbinom{u-s}{r-t-s}\qbinom{m-u}{t}
=
\sum^{r}_{i=s}
(-1)^{i-r+t}q^{-t(u-r+t)+\binom{i-r+t}{2}}
\qbinom{i-s}{r-t-s}\qbinom{m-i}{r-i}\qbinom{u-s}{i-s},
\]
and
substituting (\ref{eq:C_rs}) for
$C_{(i,s)}((\mathfrak{x},\xi), (\mathfrak{y},\eta))$ again,
$C_{(r,s)}C_{(k,h)}((\mathfrak{x},\xi), (\mathfrak{y},\eta))$
is equal to
\begin{eqnarray*}
\lefteqn{q^{ml}\sum^{r}_{i=s}\sum^{r}_{e=s}
\qbinom{n-r-k+e}{m-r-k+e}\sum^{r-e}_{t=0}(-1)^{i-r+t}
\qbinom{r-t-s}{e-s}\qbinom{i-s}{r-t-s}\qbinom{m-i}{r-i}}\\
&&\times q^{(r-t-e)(k-e)+\binom{i-r+t}{2}}\sum^{k-e}_{j=0}
q^{j(u-r+t-k+j+e)}\qbinom{m-u}{j}\qbinom{u-r+t}{k-j-e}
C_{(i,s)}((\mathfrak{x},\xi), (\mathfrak{y},\eta)).
\end{eqnarray*}
Using Proposition \ref{thm:q-bino} (\ref{eq:q-Vandermonde}) (b)
for the summation of $j$, i.e.,
\[
\sum^{k-e}_{j=0}
q^{j(u-r+t-k+j+e)}\qbinom{m-u}{j}\qbinom{u-r+t}{k-j-e}
=
\qbinom{m-r+t}{k-e},
\]
using Proposition \ref{thm:q-bino}
(\ref{eq:most_important}) (b) as
$(k,x,r,t)=(m-s,i-s,m-s-k+e,e-s)$,
i.e.,
\begin{eqnarray*}
&&\sum^{r-e}_{t=0}(-1)^{i-r+t}
q^{(r-t-e)(k-e)+\binom{i-r+t}{2}}
\qbinom{r-t-s}{e-s}\qbinom{i-s}{r-t-s}
\qbinom{m-r+t}{k-e}\\
&&=
(-1)^{i-e}q^{\binom{i-e}{2}}
\qbinom{i-s}{e-s}\qbinom{m-i}{m-k},
\end{eqnarray*}
and using Proposition \ref{thm:q-bino}
(\ref{eq:most_important}) (a) as
$(k,x,r,t)=(n-r-k+i,i-s,m-r-k+i,0)$,
i.e.,
\[
\sum^{r}_{e=s}(-1)^{i-e}q^{\binom{i-e}{2}}
\qbinom{n-r-k+e}{m-r-k+e}\qbinom{i-s}{e-s}
=
\qbinom{n-r-k+s}{m-r-k+i}q^{(m-r-k+i)(i-s)},
\]
we have
\begin{eqnarray*}
&&\sum^{r}_{e=s}
\qbinom{n-r-k+e}{m-r-k+e}\sum^{r-e}_{t=0}(-1)^{i-r+t}
\qbinom{r-t-s}{e-s}\qbinom{i-s}{r-t-s}\\
&&\times q^{(r-t-e)(k-e)+\binom{i-r+t}{2}}\sum^{k-e}_{j=0}
q^{j(u-r+t-k+j+e)}\qbinom{m-u}{j}\qbinom{u-r+t}{k-j-e}\\
&&=
\qbinom{m-i}{m-k}
\qbinom{n-r-k+s}{m-r-k+i}q^{(m-r-k+i)(i-s)}.
\end{eqnarray*}
Therefore the desired result follows.
\end{proof}

\section{Relations between association schemes based on attenuated
spaces and $m$-flat association schemes}
\label{sec:m-flat}
Assume that integers $n$ and $m$ satisfy $0 < m < n$.
First in this section,
we describe the definition of $m$-flat association schemes.
The cosets of $\mathbb{F}_q^n$ relative to any $m$-dimensional vector
subspace are called {\it $m$-flats}.
Let $X_n(m)$ be the set of all $m$-flats of $\mathbb{F}_q^n$.
Then the cardinality of $X_n(m)$ is $q^{n-m}\qbinom{n}{m}$.
We define the relation $T_{(i,j)}$ on $X_n(m)$
to be the set of pairs
$(\mathfrak{p} + x, \mathfrak{q} + y)$ satisfying
$\dim \mathfrak{p} \cap \mathfrak{q}=m-i$,
for $0\le i\le d$,
and $x-y \in \mathfrak{p}+\mathfrak{q}$ if $j=0$,
$x-y \notin \mathfrak{p}+\mathfrak{q}$ if $j=1$.
Then the pair
$\tilde{J}_q(n,m)=
(X_n(m),\{T_{(i,j)}\}_{0\le i\le d, 0\le j \le (n-m-i)\wedge 1})$
is a symmetric association scheme and called an
{\it $m$-flat association scheme}.
Zhu and Li computed all intersection numbers of $m$-flat association
schemes~\cite{Zhu1997coa} and the author gave the character table
of $m$-flat association schemes~\cite{Kurihara2009cto}.

There are relations between $m$-flat association
schemes and association schemes based on attenuated spaces
as follows:
\begin{thm}
\label{thm:m-flat}
The $m$-flat association scheme $\tilde{J}_q(n,m)$ is isomorphic to
the association scheme based on attenuated space
$\mathfrak{X}(\mathcal{M}_q(n-m,0;n+1,n))$.
\end{thm}
We note that
if $l=1$, the attenuated space is just an affine space,
and
Theorem \ref{thm:m-flat} implies that
Theorem \ref{thm:main} contains the main result of the
paper \cite{Kurihara2009cto} as a special case.

\begin{proof}[Proof of Theorem \ref{thm:m-flat}]
Let $\mathscr{L}(x_1,x_2,\ldots ,x_r)$ denote the subspace
of $\mathbb{F}_q^{n}$ spanned by
vectors $x_1,x_2,\ldots ,x_r\in \mathbb{F}_q^{n}$.
Let $e_i$ be the $i$-th standard base of $\mathbb{F}_q^n$ with $1$
in the $i$-th component and $0$ elsewhere,
and $(\cdot ,\cdot )$ be the standard non-degenerate symmetric
bilinear form on $\mathbb{F}_q^{n}$
(i.e., $(\sum^{n}_{i=1}c_i e_i,\sum^{n}_{i=1}c'_i e_i)
=\sum^{n}_{i=1}c_i c'_i$).
For a subspace $\mathfrak{p}$ of $\mathbb{F}_q^n$, we define
$\mathfrak{p}^{\bot }=\set{\beta \in \mathbb{F}_q^n}
{(\alpha ,\beta )=0\ (\forall \alpha \in \mathfrak{x})}$.
We regard $\mathbb{F}_q^n\oplus \mathbb{F}_q$
as $\mathbb{F}_q ^{n+1}$
and also regard $\{0\} \oplus \mathbb{F}_q$ as $\mathfrak{e}$.
For $\mathfrak{p}+x$ in $X_n(m)$,
we set $\mathfrak{p}_{x} =\set{(v, (x,v))}
{v\in \mathfrak{p}^{\bot}}$
in $\mathbb{F}_q ^{n+1}$.
Since any $x$ and $x'$ in $\mathfrak{p}+x$ satisfy
$(x,v)=(x',v)$,
the map
$\Phi : \mathfrak{p}+x \mapsto \mathfrak{p}_{x}$
from $X_n(m)$ to $\mathbb{F}_q ^{n+1}$
is well-defined.
Then we immediately check that
$\dim \mathfrak{p}_{x}
=\dim \mathfrak{p}^{\bot }
=n-m$
and
$\mathfrak{p}_{x} \cap \mathfrak{e} =\{(0,0)\}$,
i.e., $\mathfrak{p}_{x} \in \mathcal{M}_q(n-m,0;n+1,n)$,
and
$\Phi$ is an injective map
from $X_n(m)$ to $\mathcal{M}_q(n-m,0;n+1,n)$.
On the other hand, we have
$|X_n(m)|=|\mathcal{M}_q(n-m,0;n+1,n)| =q^{n-m}\qbinom{n}{m}$.
This means that $\Phi$ is bijective.

Finally, we check that
for each $\mathfrak{p}+x,\mathfrak{q}+y \in X_n(m)$,
$(\mathfrak{p}+x,\mathfrak{q}+y) \in T_{(i,j)}$ if and only if
$(\mathfrak{p}_x,\mathfrak{q}_y) \in R_{(i,j)}$.
By
\begin{eqnarray*}
\dim
(\mathfrak{p}_{x} +\mathfrak{e})/\mathfrak{e}
\cap
(\mathfrak{q}_{y} +\mathfrak{e})/\mathfrak{e}
&=&
\dim
\mathfrak{p}^{\bot} \cap \mathfrak{q}^{\bot}\\
&=&n-\dim (\mathfrak{p} + \mathfrak{q}),
\end{eqnarray*}
it follows that
$\dim \mathfrak{p} \cap \mathfrak{q}=m-i$
if and only if $\dim
(\mathfrak{p}_{x} +\mathfrak{e})/\mathfrak{e}
\cap
(\mathfrak{q}_{y} +\mathfrak{e})/\mathfrak{e}
=n-m-i$.
Moreover, we have
\begin{eqnarray*}
\dim \mathfrak{p}_{x} \cap \mathfrak{q}_{y}
&=&
\dim \set{(v, (x,v))}{v\in
\mathfrak{p}^{\bot} \cap \mathfrak{q}^{\bot}
\ \text{and}\
(x,v)=(y,v)}\\
&=&
\begin{cases}
\dim\fp^\bot\cap\fq^\bot&\text{if $\fp^\bot\cap\fq^\bot\subset
\mathscr{L}(x-y)^\bot$,}\\
\dim\fp^\bot\cap\fq^\bot-1&\text{otherwise}
\end{cases}
\\ &=&
\begin{cases}
n-m-i&\text{if $x-y\in\fp+\fq$,}\\
n-m-i-1&\text{otherwise.}
\end{cases}
\end{eqnarray*}
Therefore the desired result follows.
\end{proof}

redpajama_set_name: RedPajamaArXiv


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Should we flash our lumias to an Indian CV?
Re: Should we flash our lumias to an Indian CV?
Should you? If you want.
not saying you'll run into trouble, (I didn't care for LTE and turned it off anyway, so it worked out perfectly for me) but just be careful and know what you're doing.


These were the release notes for the TIBCO StreamBase® component of TIBCO® Spotfire Data Streams 10.4.0.
TIBCO Streaming is the full set of streaming technologies, and includes TIBCO StreamBase®, TIBCO LiveView™, and the TIBCO StreamBase Studio™ development environment. See What is TIBCO Streaming for a complete list of included technologies.
TIBCO Spotfire Data Streams is a subset of the TIBCO® Streaming package, configured as an add-on for TIBCO Spotfire® users, and licensed for the sole purpose of serving live data to TIBCO Spotfire. See What is TIBCO Spotfire Data Streams for the contents of this package.
A summary of the license term changes for these new product packages is found on the License Considerations page.
Initial work has begun to separately brand the Welcome screens in StreamBase Studio and some of the documentation. Whichever new product you have licensed, you can expect to see unchanged former names and terminology throughout Studio menus and dialogs, and in the documentation. This branding work is expected to proceed over the next several releases.
The TIBCO StreamBase® and TIBCO® Live Datamart independent products still exist for licensees of those products. Version updates and maintenance releases for StreamBase and Live Datamart will be fulfilled with installers branded as TIBCO Streaming. However, your Licenses for those products are not automatically upgraded to a TIBCO Streaming license. Contact your TIBCO Sales Engineer for further information.
To add fragment dependencies for an application project.
To add fragment-to-fragment or fragment-to-Java dependencies for a fragment project.
Opens the POM Editor for the selected project's pom.xml file.
See Add a Dependency for instructions on the application project case.
You can now stop, remove, and forcefully remove multiple running nodes using the context menu by Ctrl+clicking nodes in the Clusters view.
A new StreamBase Expression Language Function was added, getResourceAbsolutePath(). This function returns the absolute file system path for a specified resource in a Studio project's src/main/resources folder.
By default, attempting to override the transaction isolation of a parent module in a child module generates a typecheck warning, because transaction isolation cannot be overridden by child modules. This warning can now be optionally disabled, as described on the Typechecking preferences page.
Include debugging messages in the log output.
Save packaging steps logs to a directory.
Run tests during fragment and archive packaging.
If Studio fails to connect to a fragment during a launch because the fragment has authentication requirements, a new error dialog notifies you that Studio does not currently support such attachments.
A (commented out) example of how to load a configuration file is now included in generated unit test cases.
The TIBCO StreamBase® Input Adapter for Google Protocol Buffers parses the protobuf typed byte array based on a custom-formatted descriptor.
The TIBCO StreamBase® Output Protobuf Adapter converts the input tuple into a protobuf typed byte array.
See the Protobuf page for adapter details and the sample page for the adapter sample.
The TIBCO StreamBase® Web Input Response Adapter allows a StreamBase application to respond to a REST call that was handled by a linked Web Input Adapter.
Three new WITSML operators were added that allow for generic operations on any parent-child object structure such as logs, log rigs, rig wells, well, and so on. See The WITSML operator documentation for details regarding the new WITSML read, write, and delete operators.
In addition, the WITSML operator suite now includes an option to specify which WITSML version is used when performing operations against the server.
The eFTL Input Subscribe and Output Publish adapters now include new properties, including a Unique Id property that appends a unique ID to a client ID. See the links above for additional property details.
The TIBCO StreamBase® Database Change Data Capture Input adapter now includes options to disable the startup of the SQL Server agent, as well as to disable the adapter on a table, at startup, if not already enabled.
The Oracle JDK version bundled with StreamBase and Live Datamart is now JDK 1.8.0_u181.
Starting with TIBCO Streaming release 10.4.0, StreamBase Studio detects and prefers a system-installed Oracle JDK 8 over its own bundled JDK. Using a system-installed JDK allows you to take advantage of cryptography features of the JDK that TIBCO is not licensed to include with TIBCO Spotfire Data Streams, and allows you to manage your JDK installation independent of StreamBase. See Installing a JDK for details on this new feature.
StreamBase Studio, StreamBase Manager, and LiveView Desktop are now based on Eclipse 4.9 (2018-09). This version includes changes to the Eclipse workspace format.
StreamBase Studio silently updates the workspace format. However, TIBCO strongly recommends importing your projects from previous releases into a new, unused Studio 10.4 workspace rather than trying to reuse a previous release's workspace.
LiveView Desktop users may be prompted to upgrade their workspaces.
See the Eclipse documentation for additional details on Eclipse 4.9 capabilities.
The Maven version bundled with StreamBase is now 3.5.4.
The RPM installer for the streambase-server-*.rpm now includes the RPM Requires clause that works on all supported Linux operating systems. Also, if you unpack the RPMs and use the client and server RPMs independently with yum install, the required dependencies are installed.
In StreamBase Studio, the Jetty web server version was upgraded to 9.3.25. The upgrade applies to, for example, the TIBCO StreamBase® Web Server Request adapter and the TIBCO StreamBase® Web Server Response adapter, as well as for developing your own applications that require Jetty.
A new epadmin command target, dynvar, was added to set and get dynamic variables. See this page for epadmin command guidance.
A suspend command was added to the engine administration target to support stopping an engine in a suspended state for debugging. See this page for an overview of the engine lifecycle.
A reset authentication command was added to restore the initial authentication characteristics of a node.
The epadmin generate and list commands were added to generate and list HOCON configuration files, respectively. See this page for details.
The epadmin display container command now includes a --detailed option. When set to true, the command output includes container content details.
See this page for more information regarding security management.
The epadmin display cluster command now displays addresses of all distribution instances on the node.
The display stream command adds the --detailed option to display additional input and output stream information. Also, the command's --schema option is now deprecated.
For the epadmin display adapter command, the output has a new field named Adapter, which contains the full output name of the adapter.
The export artifact command now requires a file parameter, which specifies a client-side file for the exported data. The file is overwritten if it already exists.
Multiple independent TrustedHosts configuration files are now supported within a node's security configuration (with one active at a time still enforced).
TrustedHosts configuration files configuration files now support IPv6 CIDR block notation.
If a StreamBase client connection does not specify the username, a default username is obtained by calling System.getProperty("user.name"). This is used as a convenience, albeit a potentially unsafe one. For default security information, see this page.
The API was updated for service discovery and publishing. This API is used to support service discovery in existing Java APIs and also to allow applications to publish their own service records.
remoteQuorumLost — provides notification when a quorum lost state occurs.
partitionActive and partitionNotActive — provides notification when state changes occur for each partition; multiple PartitionNotifiers for each Partition are supported (for example, one Notifier for each Partition on each engine).
Improved handling of large model files by providing a file cache option in lieu of model storage via transactional memory.
Artifact replication across multiple nodes in the cluster. This ensures that the artifacts remain available in the cluster if nodes are removed from the cluster. Artifact replication is always enabled. You can use ADS to configure the number of replica nodes used (defaults to two) and the nodes used as replica nodes (defaults to all nodes in the cluster).
The streambase.codegen.broken-method-names system property, used for refactoring all or individually generated methods, now supports simple (as well as fully qualified) method names. See this page for use-cases and details.
An engine.shutdownTimerSeconds parameter was added, which you can apply to StreamBase, LiveView, and Java engines.
See this page for the default availability zone and data distribution policy settings.
The File>New>StreamBase Project wizard is more streamlined, with fewer decisions to make when creating a Docker image to contain your StreamBase or LiveView application. When creating a project for a StreamBase Application, a single check box now selects the option to create your application as a Docker image. See Creating and Running Docker Images for newly written instructions for this procedure.
See Creating and Running Docker Images for updated Docker image creation instructions.
In previous releases, the StreamBase Studio Configuration Directory was named with a three-position version number, such as 10.2.0. This meant that every maintenance release, such as 10.2.1, got a separate configuration directory. For customers who added Eclipse plug-ins to Studio, this convention required them to reinstall those plug-ins with each maintenance release.
Starting with release 10.4.0, the configuration directory is named with a two-position version number such as 10.4. This means that all maintenance releases for each major.minor release can share the same Studio configuration settings, including Eclipse plug-ins added to Studio.
This change does not refer to the Studio workspace directory, whose default location naming syntax has not changed. TIBCO does still recommend using a new, empty workspace for each major.minor release, and importing your projects from the previous release to the new workspace.
Generation of LiveView projects using the Maven archetype now, by default, now includes the LiveView Web WAR file as a dependency. You can disable this by setting the archetype property lvweb to false.
The Node is not running message that is returned when a node is started, but no target engines are available was improved to distinguish between the node that has not been started, compared to when there are no running engines.
Logging Now Supports Transaction ID as a Pattern Element in Logs. The keyword %transaction in a Logback configuration file places the current transaction ID, if any, into the log record for the current event. If no transaction is active, none is inserted; if there is an active transaction, but the identifier cannot be determined, unavailable is inserted. See StreamBase Logback Extensions for further information.
Additionally, when the default duplicate suppression filter is in place, the suppressed-message log event uses the same category and level as that of the suppressed messages. See Default Logging for default logging information.
Also note that duplicate message filtering is always in place. If you specify a filter, the filter is used. Otherwise the default is used.
Legacy log level integer settings used in StreamBase releases before 10.2.0 were removed in the Advanced tab of the EventFlow Fragment launch configuration.
Docker container logging is now supported.
Round-robin data mappers specified in StreamBase Runtime Application configuration files now support dynamic data distribution policies, in addition to static ones.
The HOCON Configuration File Editor now includes the option to search by HOCON property name to assist in locating the configuration file type to use.
The TIBCO StreamBase® Web Input adapter's ResponseId field is renamed to SB_ResponseId. For more about the property, see Web Input Adapter.
Additionally, the adapter now handles HTTP metadata such as headers and cookies.
This release removes the forcelocal option from the load configuration command. Providing a configuration file to the configuration target is always local to where the administration client is running, which may or may not be the same as the node.
Also removed from the command is the debug option. Use normal logging support to enable debug tracing in HOCON.
StreamBase 10.4.0 had the following deprecations.
The XML Normalizer operator is now deprecated. Applications that use the operator continue to compile and run, but the operator no longer appears in the Operators and Adapters dialog. Documentation for the operator and its sample were removed.
StreamBase 10 does not support custom functions written in C++, but references to the callcpp() expression language function were still present in Studio function assistance. Those references were removed in this release.
The deploy parameter mirrorclient for Run Configurations is deprecated and removed in this release, including its documentation.
The epadmin display security --type hosts command is deprecated. Use epadmin display trusted instead.
The SecureCommunicationServerProfile and SecureCommunicationClientProfile root objects' excludedProtocolPatterns property is now deprecated and still supported for backward compatabilty.
The Timestamp.INTERVAL_FORMAT public object was changed. Instead of com.ibm.icu.text.DecimalFormat, the API now uses java.text.DecimalFormat. If you are using the old INTERVAL_FORMAT object, you must change your import dependency to java.text.DecimalFormat.
If the ICU enhancement methods were used with the INTERVAL_FORMAT, you must find an alternative way of realizing similar functionalities, as the new API does not support the ICU enhancement methods. See this link for specific ICU enhancement methods.
This section provides a list of errors corrected in release 10.4.0 of the TIBCO StreamBase® component of TIBCO® Spotfire Data Streams.
TIBCO StreamBase® 10.4.0 incorporates all fixes resolved in the release 10.0 series through 10.4.0 and all fixes resolved in the release 7.7 series through 7.7.5.
SB‑44922 The Query operator was incorrectly failing to return all rows when a query was executed, and when the rows only differed in tuple sub-field values. This was resolved.
SB‑44907 Studio inadvertently swapped the cluster and node names in the service name, when launching a Java fragment. This was fixed.
SB‑44748 This release fixes an issue that caused the Diameter adapter message types CEA and CER to incorrectly report the Auth_Application_Id list, when a vendor was not linked.
SB‑44740 This release fixes premature failover when one engine of a multi-engine application is stopped.
SB‑44739 The WITSML Trajectory Write operator was not inserting trajectory stations due to lack of UID being passed. The operator now properly uses the UID field.
SB‑44718 In Studio, right-clicking on a package and selecting New>Module would incorrectly select the top-level package for the application. This was fixed.
SB‑44635 If an orphaned node directory exists during a fragment launch, a subsequent launch would fail with an error in a (node install) line in the Console view.
A node directory is the directory used to store the state information for a node used a fragment. Such a directory can become orphaned if the processes managing somehow die or are terminated abnormally, and therefore the node directory is not cleaned up as it normally would be.
The problem is now fixed. A subsequent launch detects the orphaned directory and prompts whether it should be removed. When confirmed, the orphaned node directory is removed and the launch continues successfully.
SB‑44589 When there is an exception during the start of the LiveView fragment, the dialog displayed after the launch is started did not dismiss itself. That problem is now fixed. The dialog now dismisses itself and the output from the failed launch is displayed in a separate dialog.
SB‑44575 An issue prevented epadmin logging commands from working when a node was stopped. This was fixed.
SB‑44458 This release fixes an exception error from the eFTL adapter that could occur when the adapter tried to subscribe when not connected to the server. The adapter no longer reports an exception if not connected when trying to subscribe. It now reports an error status message that you are not connected and must connect first.
SB‑44327 In some circumstances, running the display partition command on a node failed with an NPE after an application was deployed. This was fixed.
SB‑44310 The Web Input and Web Output adapters can now set a defined context path.
SB‑44306 The epadmin enqueue stream command Help incorrectly reported input as a required parameter. This was fixed; input is now listed as optional.
SB‑44240 An issue caused the H2O adapter to fail loading an unsupervised classification model. This was fixed.
SB‑43910 This release fixes an issue that prevented the HOCON editor from automatically generating sample EventFlowDeployment configurations.
SB‑43061 The TIBCO BusinessEvents Fraud Detection sample was upgraded. The sample no longer requires you to convert it from StreamBase 7 to StreamBase 10 format.
SB‑42408 Using dynamic partitioning for the Artifact Distribution Service (ADS) caused duplicate key errors when loading artifacts, if the artifacts were not replicated to all nodes in a cluster. This was fixed; ADS now supports artifact replication.
SB‑42407 The Artifact Distribution Service (ADS) could incorrectly report existing artifacts as missing and create duplicate artifacts after a node is added or removed from a cluster, if high availability is not configured. This was fixed; ADS now supports artifact replication.
CQS‑4583 In some cases, the StreamBase HOCON editor's auto-complete function would fail to suggest the appropriate HOCON property. This was fixed.


Hope Everyone one is enjoying their summer.
We have a sales promo on our rubber stamps. For August, ARF is featuring Morning Sunshine. It's now on SALE FOR $7. It's first come first serve so stop by our shop to snag this stamp before it's gone (sales end 8/26).
Check out the wonderful finished version of Morning Sunshine by our design team.
Gorgeous cards ladies, super cute image Sherry!!


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Why do we sit in the Succah (Tabernacles Feast booth)? What do the four varieties mean? What is the connection between Yom Kippur (the Day of Atonement) and Simchat Torah (Rejoicing of the Torah)? The wisdom of Kabbalah describes the sequence of situations we experience in the intricate relationship between ourselves and our Maker. These situations evolve one after the other because they lead us from one degree to the next, just like a chemical or a physical process that must evolve gradually, step by step.
This complex relationship is experienced by us in a very tangible manner, no less than the reality we live in. It is not about fantasy or delusions, but about the discovery of a beautiful world where changes that occur follow strict and well-defined laws. These laws are discovered by anyone who climbs the spiritual ladder, and arrives at the same places that Kabbalists describe in the holy books.
There is nothing new under the sun. Each of us is different and unique, but we all comply with the same rules, and advance from darkness and confusion to clarity and vision through the same degrees. These degrees are described by the great Kabbalists in the holy books, and it is by them that we set the sequence of holidays in our world.
We must point out that the names of all the holidays mentioned here describe internal situations that a person undergoes in the process of correction, and that the holidays we celebrate simply mark the sequence of corrections. This means that a Kabbalist can experience the holidays internally on a regular day as well.
Let us remember the sequence of the holidays: the Jewish New Year starts the holidays of Israel. After ten days we come to Yom Kippur (Day of Atonement) and after that we celebrate Succoth for seven days. Finally we come to Simchat Torah.
If you ask yourself what the meaning of these holidays is, Kabbalah explains that they describe the sequence of revelation and correction of one complete degree.
At the beginning of the spiritual revelation we feel that the Creator is giving us perfect bliss, but that we are incapable of giving anything back. More than anything, we want to overcome the shame that we feel toward the Creator, and bring Him some sort of pleasure.
It is like a person who is suffering from an illness. First we must discover how ill we are and that we cannot heal ourselves without turning to a physician. Once we have done that, we are given medicine and begin to heal, until we attain health and happiness. Only then can we appreciate the greatness and the kindness of the physician.
On the Jewish New Year we begin to understand our situation as opposed to the Creator. Over the course of the next ten days, until the Day of Atonement we realize more and more how incapable we are of equalizing with His degree and bringing Him delight (that is our illness).
The process lasts ten days because each spiritual vessel is revealed in ten degrees called Sefirot.
On the Day of Atonement, which is the tenth day of the inquiries, when it is clear to us that we haven't any power of bestowal toward the Creator, we can pray, fast and ask from the bottom of our heart to be endowed with life. The meaning of spiritual life is the ability to resemble the Creator and delight Him, but in order to receive that life we need to be corrected.
At that point we begin to receive the lights that are called the "surrounding lights". These lights enable us to gradually correct ourselves and acquire the ability to bestow. During the four days between the Day of Atonement and Succoth we get a chance to begin the correction.
The building of the Succah is a crucial stage in the correction because the Succah symbolizes one's faith. Its thatch defends from the heat of the sun, but it is made of waste, of leaves and stalks that have no other use to man. The meaning is that precisely those desires that we have decided are superfluous and useless now form a shield from the intensity of the pleasure that comes to us. By giving up those wishes we defend ourselves from excessive greed for self-indulgence. After we have discovered our inability to bestow, we now receive the strength to protect ourselves from our egoistical desires. The danger is that if we are enslaved by those desires, we will forget who provides them and will take the pleasure for ourselves. The defense that we get renders us the strength to believe in the Creator and see His greatness, despite the tempting pleasures we are faced with. For that reason we try to spend as much time as possible inside the Succah during the holiday and even sleep in it.
The fact that we build and decorate the Succah by ourselves gives us the confidence that we can protect ourselves from our excessive desires. That defense is the light of faith that fills us with endless bliss.
But that defense is not enough to bring contentment to our Maker. We must not forget that the Creator loves us and wants to render us with pleasure and not prevent it from us. Therefore we need to learn how to receive pleasure, in order to please the Creator. Now we need a means by which we can receive the pleasure. That means is the connection that we make between the citron, the palm branch, the myrtle and the willow.
The four varieties mark the four degrees of the will that one discovers in the course of our spiritual work. Sometimes we find in it a good taste and a good scent, and we call it a citron; sometimes it has taste, but no scent, so we call it a palm branch; sometimes it is fragrant but tasteless and is thus called myrtle, and when it has no taste and no scent we call it willow.
The ability to join all types of work in one direction, in order to delight the Creator, gives us the ability to receive genuine delight under any condition and under any circumstances, because under any situation we remember what we live and who we work for. It is marked in Succoth by rocking the palm branch and the encircling of the altar.
The seven days of Succoth mark the correction of our seven lower sefirot, which must be unified and connected, until on the eighth day the corrections are finished. That is why that day is called Shmini Atzeret (the stopping eighth).
On that day, after we have completed the corrections, we get to unite with our Creator and receive from Him the true pleasure called Torah. The Torah is a means that gives us the ability to bring endless delight to our Maker, just as our Maker delights us, and unite with Him in everlasting love.


text:
A Colleague Lost, and the Unknown Devastation of Attacks on Health Care
Margarite Nathe
We know very little about what happened to our dear colleague Sister Veronika Rackova, a physician and Catholic nun who was loved by her community in Yei, South Sudan.
We know she was driving the St. Bakhita Medical Centre's ambulance on May 16. We know she was on her way back from the neighboring Harvester's Health Centre, to which she had rushed a pregnant woman in the midst of a medical emergency. And we know it was late at night, about 1am.
Most people in the region know the roads aren't safe at that hour. Checkpoints that may be benign in the daylight grow more and more volatile as the night goes on and the soldiers manning them get rowdier or drunker. People get hurt.
But of course, medical emergencies are not restricted to safe hours or safe places.
We know that someone shot at Sister Veronika's ambulance, and that she was hit in the stomach. We know she was evacuated from Yei to a hospital in Nairobi, Kenya.
And we know that four days later, she died.
But so many details are still missing. Who shot her? Was it one of the four members of the security forces now in custody? But why? Was it because she was driving an ambulance or was that just a coincidence?
And what will become of the many people who relied on Sister Veronika's care?
Health care under attack
Sister Veronika was one of more than a thousand people killed in the last 15 months as a result of attacks on health care. According to the Safeguarding Health in Conflict Coalition's new report, No Protection, No Respect: Health Workers and Health Facilities Under Attack, 19 countries have seen continuous assaults on ambulances, frontline health workers, patients, and health facilities.
Hospitals are being looted, burned, and bombed. Ambulances are being attacked. Infants in incubators are dying as hospital generators are destroyed or run out of fuel.
Like many of the other 18 countries in the report, South Sudan is in the midst terrible violence and warfare, which the United Nations estimates have killed at least 50,000 people there since the fighting began in 2013 (and among those, Sister Veronika was the fifty-fourth aid worker killed). Both sides of the conflict have taken to obstructing access to medical facilities, stealing medical supplies, and kidnapping or murdering health and humanitarian workers.
Sister Veronika's death is a tragic microcosm of the ongoing assault on health care in war-torn regions around the world—all are marked by unanswered questions, impunity for perpetrators, and health consequences that will echo within affected communities for generations to come.
Here is one of the most striking revelations within the report's pages: No one knows exactly how many attacks like the one that killed our colleague occur. No one knows how many health workers have died, how many people are left without care as a result, or who is responsible for many of the attacks.
Usually, there is no prosecution, because there are little or no data.
For years, the Safeguarding Health in Conflict Coalition has been calling on the United Nations and the World Health Organization to change this by putting in place a mechanism to monitor attacks and punish perpetrators.
And the agencies have begun to respond. Last month, the UN Security Council unanimously passed a resolution condemning attacks on health workers and facilities. And now for the first time, the WHO is calling for an information hub on health care attacks and gathering data to quantify the scope of the problem.
So far, WHO officials say they have found that between 2014 and 2015, attacks on health workers and facilities killed 959 people and injured 1,561. But the coalition believes this is a gross underestimate and is based on insufficient data. It continues to advocate for the WHO to refine its methodology to reach a more comprehensive calculation of what—and whom—we've lost in ongoing conflicts throughout the world.
Sister Veronika's death is a tragic microcosm of the ongoing assault on health care in war-torn regions around the world.
The night she was shot, Sister Veronika had just transported a pregnant woman from St. Bakhita to Harvester's Medical Centre for the specialized care the woman needed during her medical emergency. Without Sister Veronika's quick action and devotion to her clients, the woman and her baby might have died that night. But instead, the mother safely delivered a healthy baby boy, and both are alive today.
"I worked with Sister Veronika very closely at St. Bakhita Medical Centre," says Patrick Buruga, HIV prevention deputy manager at IntraHealth International in South Sudan. "I knew her as a joyous and welcoming person, loved by her staff. She was dedicated to her work, and met her death while in service taking a mother to deliver where there were better facilities. Her death is a big loss for us and for the people she served in Yei."
As director of St. Bakhita, Sister Veronika worked with IntraHealth's South Sudan office as they trained and supported her team of health workers. She helped many HIV-positive mothers in and around Yei to deliver their babies free of the virus. She was an invaluable health worker, neighbor, and friend.
And no amount of data will bring her back.
But knowing what happened matters. It affects how we move forward, how we prevent future attacks, and how—or if—anyone is held accountable for these ongoing atrocities.
IntraHealth has partnered with St. Bakhita Medical Centre in South Sudan since 2007. Our work in South Sudan is funded by the US Centers for Disease Control and Prevention and by the US Agency for International Development. IntraHealth serves as the secretariat for the Safeguarding Health in Conflict Coalition.
This post originally appeared in the Huffington Post at http://www.huffingtonpost.com/entry/a-colleague-lost-and-the-unknown-devastation-of-attacks_us_575aca91e4b052f656ef75bb.
Photo by Trevor Snapp for IntraHealth International
Advocacy, Health Workers, IntraHealth International, South Sudan, Safeguarding Health in Conflict Coalition -

redpajama_set_name: RedPajamaCommonCrawl


Let me start this off by saying, that A and I usually go to bed early. And by early I mean 9pm. We force ourselves to stay up at least until 9pm. But after 9pm both of us literally fall apart.
But when A asked me to lay down next to him yesterday (16th of October 2012) around 8pm, even I was surprised and a bit taken aback. That's early, even for our standards. In retrospect though, best decision ever.
I crawled up into our loft bed and laid down next to A. As I laid my head on my pillow I realized that there was something hard underneath it. I immediately sat up again, almost bumping my head on the ceiling, and pulled out the object underneath my pillow. It was a book: The book of Love – Vol 2.
Volume 1 of the Book of Love was a birthday-gift from Anthony about a year and a half ago. The first book was about how we first met and how we stayed together, even through the distance and that eventually we both will be able to live together. Back then, neither of us knew that only a few months later we would move to Oslo together.
As I opened the book, A told me to carefully read every page. He was very clear that I was not allowed to flip through the pages WITHOUT reading it. So I did just that. I basically was reliving our first year together as I was looking through the pages.
I then came to a blue page with a poem of my most favorite German author: Johann W. Goethe.
Goethe writes about, how even through distance you can still be together. Forever. To be honest, I thought it was pretty awesome that A picked this particular poem. It sums up our relationship so well and as I was reminiscing about the time, we were apart, being happy that we will never have to live like that anymore, I turned the page once more.
As I read through the first few lines (and yes, I am tearing up again as I write this), I was wondering what ring A was talking about. I didn't see a ring. Ultimately the lord of the rings came to my mind but then I read about the diamond, the hands, the lives together and I was wondering… could it be? Is it true? This must have been A's longest minutes in his life. Since I started to choke up, he took it upon himself to read out loud the last few lines of the page.
I then looked onto the next page and there it was.
A was on his knees, helping me to get the ring out of the self-made pouch in the book (and yes, he cut the hole in himself too, I imagine that only took forever), and he asked me the one question, that did not require an answer, because in his heart he already knew the answer, the day we first met.
I immediately started crying and laughing and hugged A and of course, the answer was and is and always will be – yes. I will.
I then looked closely at the engraving of the ring, and it said, like in the poem, 'Ich bin bei dir' (I am with you). And that A will be, for the rest of my life.
I didn't sleep all night, because the feeling, the happiness, the excitement is so overwhelming. I can't even begin to describe it. Knowing that you have found your significant other, is one thing, knowing that you will be with him for the rest of your life, is an entirely different situation. I am lost for words.
All I can say is, that I too, will be with A.


Fedor Emelianenko and Ryan Bader have cleared the final hurdle for the Bellator 214 main event, as both men made weight earlier today.
The promotion's light-heavyweight champ Bader will face Emelianenko in the finals of Bellator's heavyweight grand-prix tomorrow. The winner will secure the heavyweight belt.
* Almeida missed weight and will forfeit 10% of show money to opponent and 10% to the commission. If he wins, 20% of win bonus will go to opponent.
Bellator 214 will be hosted by the Forum in Inglewood, California.


Like most other big name artists Alkaline is branching out into merchandising. The dancehall hitmaker has launch a new clothing named after his group Vendetta.
A rep for the deejay told Urban Islandz that they have launched a line of Vendetta T-Shirts and are gearing up to launch other gears like caps and and possibly a shoe line. The shirts are currently available for sale on Alkalinemusic.com.
Alkaline is still enjoying some success from his debut album "New Level Unlocked" which peaked at No. 1 on the Billboard Reggae Chart. There are also talks that the deejay could be working on his sophomore album.
Looks like a good sleep shirt.?


Anaheim, California, January 22, 2015 - Apogee Electronics, industry leader in digital audio recording technology since 1985, is pleased to introduce Groove – a new portable USB DAC and headphone amp for listening to music on your Mac or PC. Built upon Apogee's 30-year history of award-winning digital audio technology for music creation, Groove unlocks the highest possible quality of any headphones or powered speakers you have, allowing you to listen to the music you love with incredible lifelike clarity.
Apogee's digital audio technology has been trusted by professional recording artists, producers and engineers from around the world to create countless GRAMMY® and OSCAR® winning recordings since 1985. For the first time, Groove puts this same technology into a compact, durable, easy to use interface for consumers, providing a music listening experience of unparalleled quality, as it was originally captured in the recording studio.
Groove's innovative circuit design provides an even distribution of output power across the audible frequency spectrum, correcting impedance imperfections often found in entry-level headphones and powering even the most demanding high impedance headphones. Setup is easy - simply connect Groove to your Mac or PC with the included USB 2.0 cable and plug your headphones or speakers into Groove's ⅛" analog output. The result is smooth, detailed analog warmth that will impress even the most discerning audiophile.
To commemorate Apogee's 30 years of digital audio excellence, a limited edition anniversary model of Groove will also be available. The Groove 30th Anniversary Edition will feature a custom machined aluminum body, performance enhancements and will be available in silver and gold.
Apogee Groove and Groove 30th Anniversary Edition will be available Spring 2015. Visit apogeedigital.com for more info and sign up for product updates.
See Groove and other Apogee products at the 2015 NAMM show, booth #6500.


A little bit about Mike!
I am a Colorado native and I have lived in north-west Denver for the last ten years. I went to school at the University of Northern Colorado in Greeley and after graduating I started working in restaurants. I have been working for an independent bar owner for over ten years and I am now the general manager of Hopper's Sports Grill. CrossFit Vantage is right down the block from where I live and after checking it out, it seemed like a perfect fit for what I needed. I needed a change and CrossFit was the beginning to a bunch of changes!
Bar life takes its toll long days and late nights start to add up and after a couple of years of dating I decided to ask my girlfriend, Kari to be my wife. She deserves more than an out of shape bar tender. When I have some spare time I enjoy the mountains as much as I can. The bar I work at has volleyball leagues in the summer so I try to get involved with at least one team. In the winter Kari and I usually hit up a few concerts around Denver.
It takes a lot of self-control for me to avoid all the bar food that I am around pretty much all day every day. When I cheat it usually has something to do with fried food. CrossFit works great for me because of the class structure and the easy schedule. I appreciate the group motivation and constant coaching help from the great staff at Vantage. CrossFit has helped me get out of the day to day grind at work. A more active, healthier lifestyle has become a habit as opposed to the exception that it used to be.
Our June Female Athlete can be found in the evening classes as well as the mid-day classes. Her name is Anna, come spend a few minutes getting to know her.
Today as you sit at your desk and are surfing from site to site counting the hours till the weekend, pause for a few minutes and get to know Shaelen.


I am upgrading http://hartmannantiques.com to use marketpress. Is there a 3 column theme you could recommend that would look similar to their existing site? ie widget with Random Featured products on the left.
I do not have a WP site online, I am developing and testing locally. But I like the layout of the existing site.
I do not have trouble changing/modifying CSS.
we have many themes that are 3 column, many can be adjusted in the theme options too. there's also some good themes over at themeforest too.


Follower is an app that lets you request your own real-time shadow, who will invisibly track you for a day. How will you act when you know someone is watching?
That's the notification you'll get one morning after signing up for a new app called Follower. A real-life human will follow you around, unseen, for a single day.
Artist Lauren McCarthy created the app-as-performance-art after spending a week looking at a thousand different social media accounts. "I was thinking a lot about why we want followers, and what does that attention do for us," she says. If we have a desire to be seen, she wondered, is being seen in real life even better?
The app is simple. If you want to be followed, you answer two questions–why you want to do it, and why someone should follow you. If chosen to be followed, you download the app. You don't know when it will start, but one morning, you'll get the notification, and another at the end of the day letting you know you're no longer being followed. The follower–McCarthy–sends you a single picture from the day.
The app took weeks to get approval at the App Store, and someone at Apple asked if it was a stalker app. McCarthy says it's the opposite: A stalker gives you unwanted attention; in this case, you're requesting it. She imagines it as part of the gig economy; if you can hire a Taskrabbit to help you build your Ikea furniture or someone from Lyft to give you a ride, why not hire someone to follow you around?
It's meant to raise questions about the lines we draw between privacy and the desire to broadcast every part of our lives online. "It feels like people have such gut reactions to surveillance, and I was just interested in trying to complicate that a little bit," McCarthy says.
Follower is currently available in New York City. Apply here if you want to be followed (or to be a follower).


text:
Memorial History USA
Abolition A History Of Slavery And Antislavery
This fight is about much more than who owns our history and who gets to write it. Wilentz cites many blistering critiques of the proposed charter that came from antislavery opponents of.
Mar 3, 2018. Slavery and the History of Abolition: An Interview with Manisha Sinha. The Slavery and Antislavery collection also contains abolitionist.
Was Christopher Columbus Portuguese Christopher went to sea at the age of 14. In 1476, the ship on which he was aboard was attacked off the coast of Portugal. He managed to swim the six miles to Lisbon. He settled there and married the daughter of a Portuguese nobleman. A museum in Toronto wants to recognize the Portuguese presence
Rather, it reveals the deadly reason for Saint-Domingue's prosperity: perhaps the most horrific system of slavery ever seen.
Feb 28, 2017. Follow the timeline to learn more about the history of slavery in the. It becomes one of the most influential works to stir anti-slavery sentiments.
But the history of the racist roots of gun control go back much. party pushing gun control is the same political party.
'From any historical perspective', writes the pre-eminent historian of slavery, and the Puritan Samuel Sewall published America's first antislavery tract, The.
The Music of Black America in Migration" as a way to memorialize the Great Migration out of the rural South after the.
In his publication 'The history of the British West Indies' (published 1819), The anti-slavery society countered the claims of the pro-slavery lobby by providing.
What City Was The Constitutional Convention Held In A Constitutional Convention is an event where members of the public can get involved in making decisions about the. Conventions and assemblies on constitutional issues have been held in a number of countries and regions, including. John Quincy Adams Biografia 28 Fev 2004. John Quincy Adams, o sexto presidente norte-americano, é filho do segundo presidente,
Christopher L. Brown, professor, specializes in the history of eighteenth. and the comparative history of slavery and abolition, with secondary interests in. " Slavery and Antislavery, 1760-1820," in Oxford Handbook on the Atlantic World, c.
United States Abolition and Anti-Slavery Timeline. and milestones in American history, including major milestones in the history of slavery in North America.
Story Continued Below Ostensibly focused on Buchanan's extralegal machinations to secure slavery in the new state of Kansas.
The abolition movement sought to end the practice of slavery in the United States. evolved into the formation of antislavery societies in the early nineteenth century. one of the most influential memoirs of an enslaved person in US history.
For example, go back to arguably the country's finest moment – the abolition of slavery in 1865 – and the assassination.
An introduction to various anti-slavery historical sources. transatlantic slave trade and, after 1807, for the complete abolition of slavery in the British colonies.
Feb 28, 2016. In "The Slave's Cause: A History of Abolition," she turns her attention from. suggests how she links antislavery not only with the women's rights.
Aug 18, 2018. Slavery represents one of the greatest tragedies in American history, but. She helped organize the Boston Female Anti-Slavery Society and.
putting transmigrated Blacks to work as slaves. The guilt here must be shared. Jefferson's anti-slavery passage, we know, was excised by Congress, and so it did not appear in the Declaration of.
Origins: Current Events in Historical Perspective; In each issue of Origins, Finally in 1807, thanks to the impassioned efforts of the Anti-Slavery Society, the.
Jefferson had assumed that the abolition of the slave trade would weaken. a transcription are available online courtesy of the Massachusetts Historical Society.
because the nation's pro-slavery and anti-slavery tendencies are so closely intertwined. The letter is rooted in a vision of.
John Quincy Adams Biografia 28 Fev 2004. John Quincy Adams, o sexto presidente norte-americano, é filho do segundo presidente, John Adams, que governou o país entre 1797 e 1800. Pai e filho são os únicos presidentes norte-americanos que não nasceram no. John Quincy Adams (Braintree (Massachusetts), 11 de julio de 1767 – Washington D. C., 23 de febrero de
This meeting was a natural continuation, to explore further, our area roots and racial relationships to set the tone for a.
Her mother's family owned a plantation where black servants abounded long after the abolition of slavery. Elizabeth grew up.
The Knot Worldwide, which operates the Knot and WeddingWire, already has started working on guidelines to ensure wedding.
Mar 22, 2007. 1807 – Britain passes Abolition of the Slave Trade Act, outlawing. High Commissioner for Human Rights: here; Anti-Slavery Society: here.
Sep 9, 2019. Slavery and Anti-Slavery: A Transnational Archive. Includes:. Slavery in America and the World: History, Culture & Law. Brings together.
Sep 13, 2013. Elsewhere in the country, antislavery measures progressed rapidly. The vote tipped in favor of abolition only after the absentee ballots of soldiers. for the history of slavery in Maryland in the Maryland State Archives.
This of course was almost a full century before the abolition of slavery in 1865, and almost two centuries before the removal.
Malcolm X Quotes On Life 6 Sep 2013. 42 Quotes from The Autobiography of Malcolm X. The Honorable Elijah Muhammad teaches us that segregation is when your life and liberty. 19 Feb 2019. The subject was a quote from Barry Goldwater, the alt-right. As a result, the debate took place and is now part of Malcolm X's history: two books
In 1780, when the Massachusetts Constitution went into effect, slavery was legal. Justice William Cushing: "[S]lavery is in my judgment as effectively abolished as. "Quock Walker Case," 5 The American Journal of Legal History 118 (1961).
On Feb. 3, the program will be "Abolition and Slavery in Montgomery County," presented. "SorryCharlieDay," a general.
What Is Usa History "Our children and their children may ask us: what did you do? What did you say?" he says. "We have a mission, and a mandate, to be on the right side of history." 3:52 p.m. Rep. Adam Schiff takes over. Many universities in the United States require students to take at least one, if not
History Book Review: Women's Rights Emerges within the Anti-Slavery Movement, 1830-1870: A Brief History with Documents (The.
Feb 4, 2012. Celebrating Black History Month, Part I: Slavery and Abolition. one of the largest in the entire history of the American antislavery movement,
A. Yes. As an undergraduate at Oxford in the 1960s I was aware of work that brought a fresh and deeper understanding of African-American history. This was an era of breakthrough studies on slavery and.
The women's suffrage movement has a history that is complicated and fascinating. notably the temperance and anti-slavery.
I scratched the surface of Oglethorpe's purposeful life and pivotal times in the Dec. 14 History column. Craig's paper, "Slavery and Antislavery in the founding of Georgia and New.
Advocate Khirod Rout filed the PIL on behalf of the petitioner – Anti-Slavery India, a Public Charitable Trust. of the.
Jun 21, 2019. In 1833, the same year Britain outlawed slavery, the American Anti-Slavery Society was established. It came under the leadership of William.
This history perfectly illustrates the intention of the college. How do we involve the people of the university as well as.
Unlike science and math, history is taught differently in every state. In the District of Columbia, students in younger grades learn about slavery through holidays and historical figures.
Understanding History
Martin Van Buren Dollar Value
Christmas Markets In Usa History
Ageod American Civil War 2
James A Garfield Political Philosophy
Christopher Columbus Statue Arecibo Puerto Rico
Who Were The Four Main Founding Fathers
Thomas Jefferson Tyranny Quotes
Founding Fathers Of Ghana
Boston Tea Party Description
President Grover Cleveland Facts
Usa History Of Tariffs
Virtues Of Benjamin Franklin
Thomas Jefferson Apartments Denver
Four Founding Fathers Of Tau Gamma Phi
Who Is Christopher Columbus And What Did He Do
History On Texas A&m
First Person To Die In American Revolution
History Of Usa Agriculture
Public Education History Usa
History Of Slavery Different Cultures
American Presidents A Dark History
Christopher Columbus High School Ny
German Pow In Usa History Channel
Alexander Hamilton Did All Of The Following Except
History Of Slavery In Ny


text:
namespace xla {
namespace util {

void MultiWait::Done() {
  bool notify = false;
  {
    std::lock_guard<std::mutex> lock(mutex_);
    completed_count_ += 1;
    notify = completed_count_ >= count_;
  }
  if (notify) {
    cv_.notify_all();
  }
}

void MultiWait::Wait() {
  std::unique_lock<std::mutex> lock(mutex_);
  cv_.wait(lock, [this] { return completed_count_ >= count_; });
  if (exptr_ != nullptr) {
    std::rethrow_exception(exptr_);
  }
}

void MultiWait::Wait(double wait_seconds) {
  std::unique_lock<std::mutex> lock(mutex_);
  if (!cv_.wait_for(lock, std::chrono::duration<double>(wait_seconds),
                    [this] { return completed_count_ >= count_; })) {
    TF_LOG(FATAL) << "Hit timeout";
  }
  if (exptr_ != nullptr) {
    std::rethrow_exception(exptr_);
  }
}

void MultiWait::Reset(size_t count) {
  std::lock_guard<std::mutex> lock(mutex_);
  count_ = count;
  completed_count_ = 0;
  exptr_ = nullptr;
}

std::function<void()> MultiWait::Completer(std::function<void()> func) {
  auto completer = [this, func = std::move(func)]() {
    try {
      func();
    } catch (...) {
      std::lock_guard<std::mutex> lock(mutex_);
      exptr_ = std::current_exception();
    }
    Done();
  };
  return completer;
}

}  // namespace util
}  // namespace xla

redpajama_set_name: RedPajamaGithub


text:
More Job Descriptions
Tom Streissguth - Updated July 05, 2017
The Highest Ranked Navy SEALs & How Much They Make
Heavy Vehicle and ... $47,460/year /> 2012-2016 +3.1%
Physicians and ... $204,950/year /> 2012-2016 +0.8%
Jupiterimages/Goodshoot/Getty Images
The U.S. Navy's Sea, Air and Land squads form an elite commando force that undergoes the toughest training in the military. If they survive the rigorous physical demands of training, SEAL team members must be ready to take on hazardous missions anywhere in the world. Navy ranks and pay apply to SEALs, who can also earn special allowances, bonuses and other benefits for their service.
Basic Pay and Allowances
The members of the Navy SEALs volunteer for this special forces branch of the military, but draw standard Navy pay and allowances. The higher your rank, the higher your monthly pay, while a full military pension is available to all team members who put in 20 years of service. SEALs are also eligible for a full range of standard Navy bonuses, including dive pay at the rate of $375 per month, jump pay of $225 per month, and special duty pay of $110 per month. The military also offers special monthly bonuses for team members who operate the customized aquatic transports known as SEAL Delivery Vehicles or SDVs.
Officer Ranks
The highest pay grade a Navy officer can reach is 0-10, a rank attained by Admiral Eric T. Olson. A graduate of the rigorous BUD/S training in 1976, Olson served as commander of the U.S. Special Operations Command from 2008 until 2011, and was the first Navy SEAL to reach three-star and, subsequently, four-star admiral rank. By 2013, there were about 2,500 active-duty Navy SEALS, with most serving in enlisted ranks from E4 to E9, a smaller number as warrant officers and approximately 500 with officer rank. The SEALs also honor their longest-serving active-duty veteran with the informal title of Bull Frog.
In the Navy, monthly pay and allowances increase with rank and experience, with the latter scale ranging for less than two to 40 years of service. As of January 2013, an O-9 or O-10 admiral with between 20 and 40 years of service earned $14,975.10 per month in base pay. In addition, all Navy personnel earn a Basic Allowance for Housing, which varies with the assignment location, as well as a Basic Allowance for Subsistence.
Benefits and Bonuses
Benefits available to SEAL officers and all other Navy personnel include vacation pay of up to 30 days per year, medical and dental insurance, and retirement benefits after 20 years of service. The Navy also pays bonuses for specialized training, such as advanced marksmanship, intelligence analysis, communications, combat medicine, and languages. Within the Navy Special Warfare Command, a selective re-enlistment bonus and a critical skills retention bonus is available for re-enlistment.
The Average Salary of an E5 Army Sergeant→
Military Dentist Salary→
The Average Salary of Army Rangers→
How Much Does a Marine Get Paid After Getting Married?→
Army National Guard Helicopter Pilot Jobs→
How Much Do Navy SEALs Get Paid a Year?→
NavySEALS.com: Benefits
NavySEALS.com: Learn About the Navy SEALs
Official Naval Special Warfare Website
Military.com: SEAL Training
Founder/president of the innovative reference publisher The Archive LLC, Tom Streissguth has been a self-employed business owner, independent bookseller and freelance author in the school/library market. Holding a bachelor's degree from Yale, Streissguth has published more than 100 works of history, biography, current affairs and geography for young readers.


That's why Rev. Bethune of the American Baptist Church is joining a growing chorus of faith leaders in Texas who are speaking out against discrimination—and in favor of protecting gay and transgender people under the law.
Rev. Bethune, who grew up in Pearland, a small city outside of Houston, is now the Senior Pastor of the University Baptist Church in Austin, Texas. He lives with his wife Gina, also an ordained Baptist clergyperson, and they just celebrated their 20th anniversary together.
As a lifelong Texan, Rev. Bethune grew up immersed in a culture where faith and hard work were valued above all else. Both his family and his faith community taught him the importance of treating others as he wishes to be treated..
Bethune describes further how his faith has led him to believe that discrimination in any form is wrong—and that all Texans should have the opportunity to work hard and make a living.
That's why Rev. Bethune is particularly incensed with attempts to treat gay and transgender Texans unfairly.
That some people in Texas would justify discrimination doesn't just offend Rev. Bethune from a religious standpoint, it offends him as a proud Texan as well.
He contends the mere fact that LGBT Texans experience high levels of discrimination underscores the urgent need to ensure that no Texan is discriminated against.


UPDATE: You can in fact now have your wedding at The Versace Mansion. Read our updated wedding venue listing for the Versace Mansion, now known as The Villa.
Miami Beach's Versace Mansion, as it is still fondly remembered as, is currently off the market as a potential wedding venue but is back on the real estate market. And a famous couple reportedly has their eye on it.
The former home of fashion designer Gianni Versace, who lived there until he was tragically killed in 1997, is going up for auction on September 17, with a starting bid of $25 million. Think it might be fun to go and check out? Think again. Only interested buyers are allowed to attend, and they must make a deposit of $3 million to even get in the door. That shouldn't be a problem for David Beckham and wife Victoria (a.k.a. Posh Spice), who are rumored to be interested in the property. David Beckham is thought to be seriously considering a move to Miami, where he would bring his MLS soccer team.
The location of the mansion would put Posh and Becks smack dab in the middle of Ocean Drive in Miami Beach, which would be kind of nuts. When Versace lived there the area was not nearly as developed, and he could casually walk down for his morning breakfast at The News Cafe (as he so often did) without many people noticing. The scene is a bit different today, and has become way more commercialized. However, as a Miami native who grew up near the famed house, I still think it would be an amazing place to live.
In the past few years (before the owners filed for bankruptcy) couples were able to rent the property for weddings. At last check the cost to have your wedding at the Versace Mansion (formerly known as Casa Casuarina and The Villa By Barton G) was $10,000 for the facility rental fee, and a $35,000 food and beverage minimum. We'll have to wait and see if couples will be able to get married there again, or if Posh and Becks will end up calling the Versace Mansion home sweet home.
Update on the venue for wedding??
Do you know if weddings are still held at the Mension?
Hi! Do you have updated information for this venue? Thanks!