text:
\section{Introduction}
Topological quantum field theory (TQFT) \cite{w1,at}
has given
considerable insight into a number of unsolved
problems in theoretical
physics \cite{w3,w5}
and also provided an important research tool in pure mathematics
\cite{w2,rt,tv}.
Most work in this field has been devoted to studying particular examples
of such theories and uncovering their physical content as well as their
relation to low-dimensional topology.

The problem of classifying topological quantum field theories
is a hard one in more than two dimensions since
it is intimately tied up with the classification of
topological manifolds in these dimensions.  In two dimensions the
situation is radically different since a compact
orientable two-dimensional manifold is
characterized topologically
by its genus and the number of boundary components.  In \cite{w5} it was
shown that the two-dimensional theories have indeed a very simple structure.

The
classification problem for TQFT in two dimensions was addressed in
\cite{th1}, see also \cite{th2},
using triangulated surfaces and fields associated with
vertices.  In these papers topological
theories were constructed with the partition
function for a closed surface of genus $g$ given by
\begin{equation}
Z_g=\lambda ^{g-1}\label{partition}
\end{equation}
where $\lambda$ is an arbitrary
positive number.

In the present paper we prove
that the most general unitary
TQFT in two dimensions is in fact a direct sum of
theories of this type.
The proof is very simple.  It  uses the fact that
any two-dimensional surface can be constructed by gluing together
spheres with three or fewer boundary components and therefore
any unitary TQFT in two dimensions
is determined by the partition functions for a sphere
with three or fewer holes.  Unitarity implies that an associated
handle creation operator is hermitean and it follows that the
theory
is characterized up to equivalence by the values of partition functions
for closed surfaces.

The classification of unitary TQFT on triangulated surfaces with the fields
defined on links and taking values in a finite set
has been discussed in a number of recent papers
\cite{bachas,filk,fukuma}.   It was first shown in \cite{bachas} that the
weight factors for triangles can in this case
be regarded as structure constants
of a semisimple associative algebra and the physical Hilbert space can
be identified with the center of the algebra.  It follows that in these
theories the number $\lambda$ in \rf{partition} is always
the inverse square of
an integer.  This is also the case in two-dimensional topological gauge
theories \cite{jwtop,wtop}.
Theories with fields defined on links can easily be realized as
vertex theories.

In the next section we describe the Atiyah axioms for unitary
TQFT and point out
simplifications that occur in two dimensions.  We then proceed to
show that the theory is determined by the three loop function on the
sphere and use the gluing axiom
to show that the partition function for a closed surface is necessarily
a sum of exponentials as in \rf{partition}.  In section 4
we construct a lattice TQFT of the most general form. In the
final section we comment on the classification problem in higher
dimensions.

\section{The Atiyah axioms}
In this section we recall the axioms for a unitary TQFT \cite{at} as
they apply in two dimensions.  We assume that all manifolds are smooth,
oriented and
compact
unless otherwise is stated.  If $M$ is an oriented manifold,
we denote by $M^*$ the same manifold with the orientation reversed.

A unitary TQFT in two dimensions
comprises the following assignments: To each closed
1-dimensional manifold
$\Sigma$ there is assigned a finite dimensional Hilbert space ${\cal H}
_{\Sigma}$ with inner
product $<,>_{\Sigma}$.  To each surface $S$ (not necessarily closed)
there is assigned an element $Z(S)\in {\cal H} _{\Sigma}$, called
the partition function for $S$, where $\Sigma =\partial
S$ is the boundary of $S$.  The Hilbert space associated with the empty
1-dimensional manifold $\emptyset$ is ${\cal H} _{\emptyset}= {\bf C}$ so $Z(S)\in
{\bf C}$ if $S$ is closed.
These objects satisfy the following conditions:
\begin{enumerate}
\item If $f:\Sigma _1\mapsto \Sigma _2$ is an orientation preserving
diffeomorphism between 1-manifolds then there is an associated unitary mapping
\begin{equation}
U_f:{\cal H} _{\Sigma
_1} \mapsto {\cal H} _{\Sigma _2}
\end{equation}
 such that $U_{g\circ f}=U_gU_f$ if $g$ is
an orientation preserving diffeomorphism from $\Sigma _2$ to another
1-manifold $\Sigma
_3$.

If $f$ extends to an orientation preserving diffeomorphism between
surfaces, $S_1\mapsto
S_2$, where $\partial S_i=\Sigma _i$, $i=1,2$, then $U_f(Z(S_1))=Z(S_2)$.

\item For any 1-manifold $\Sigma$,
\begin{equation}
{\cal H} _{\Sigma ^*}={\cal H} _{\Sigma}^*
\end{equation}
i.e. we have an identification between these spaces, which
is equivalent to giving a
non-degenerate bilinear form
\begin{equation}
( , )_{\Sigma}:{\cal H} _{\Sigma}\times {\cal H} _{\Sigma ^*}\mapsto {\bf C}
\label{bil}
\end{equation}
such that
\begin{equation}
(x,y)_{\Sigma}=(y,x)_{\Sigma ^*}.\label{a}
\end{equation}
This form is preserved by diffeomorphisms, i.e.
for $f:\Sigma _1\mapsto\Sigma _2$ as in axiom 1,
\begin{equation}
(x,y)_{\Sigma _1}=(U_fx,U_{f^*}y)_{\Sigma _2} \label{b}
\end{equation}
for all $x\in{\cal H} _{\Sigma _1}$, $y\in {\cal H} _{\Sigma _1^*}$, where
$f^*:\mapsto\Sigma _1^*\mapsto \Sigma _2^*$ denotes $f$
regarded as an orientation preserving map between $\Sigma _1^*$
and $\Sigma _2^*$.

Defining the conjugate linear isomorphism $y\mapsto y^*$ from ${\cal H} _{\Sigma}$
to ${\cal H} _{\Sigma ^*}$
 by
\begin{equation}
(x,y^*)_{\Sigma}=<x,y>_{\Sigma}  \label{c}
\end{equation}
for $x,y\in {\cal H} _{\Sigma}$, we furthermore assume that
$x^{**}=x$ for all $x\in {\cal H} _{\Sigma}$ and
\begin{equation}
Z(S^*)=Z(S)^*  \label{con}
\end{equation}
for any surface $S$ with boundary $\Sigma$.

\item  If $\Sigma =\Sigma _1\cup \Sigma _2$ is a disjoint union of
1-manifolds then
${\cal H} _{\Sigma}={\cal H} _{\Sigma_1}\otimes {\cal H} _{\Sigma_2}$ and
we have a corresponding factorization of the bilinear forms
and unitary maps, i.e. $(,)_{\Sigma}=(,)_{\Sigma _1}
\otimes
(, )_{\Sigma _2}$, and if $f_1:\Sigma _1\mapsto
\Sigma _1'$ and $f_2:\Sigma _2\mapsto \Sigma _2'$ are orientation
preserving diffeomorphisms, then $U_f=U_{f_1}\otimes U_{f_2}$ where $f:
\Sigma \mapsto \Sigma _1'\cup \Sigma _2'$ denotes the diffeomorphism that
equals $f_1$ on $\Sigma _1$ and $f_2$ on $\Sigma _2$.

Let $S_1$ and $S_2$ be two surfaces such that $\partial S_1=\Sigma
_1\cup\Sigma _3$ and $\partial S_2=\Sigma _2\cup \Sigma _3^*$.  Let $S$ be the
surface obtained by gluing $S_1$ and $S_2$ together along their $\Sigma
_3$ boundary component,
\begin{equation}
S=S_1\cup _{\Sigma _3}S_2.
\end{equation}
Then $Z(S)=(Z(S_1),Z(S_2))_{\Sigma _3}$ where, by abuse of notation,
 $(\cdot ,\cdot )_{\Sigma _3}$
denotes the  pairing
\begin{equation}
{\cal H} _{\Sigma _1}\otimes {\cal H} _{\Sigma _3}\otimes {\cal H} _{\Sigma _2}
\otimes {\cal H} _{\Sigma
_3}^*\mapsto {\cal H} _{\Sigma _1}\otimes {\cal H} _{\Sigma _2}
\end{equation}
induced by \rf{bil}.

Concretely, if $\{ x_i\}$, $\{ y_j\}$, $\{ z_k\}$ are bases for ${\cal H}
_{\Sigma _1}$,  ${\cal H}
_{\Sigma _2}$, ${\cal H}
_{\Sigma _3}$, respectively, and $\{ z_k^*\}$ is the dual basis for ${\cal H}
_{\Sigma _3}^*$, then we can write
\begin{eqnarray}
Z(S_1)&=&\sum _{i,k}c_{ik}\, x_i\otimes z_k\\
Z(S_2)&=&\sum _{j,l}d_{jl}\, y_j\otimes z_l^*
\end{eqnarray}
for suitable constants $c_{ik}$, $d_{jl}$, and
\begin{equation}
Z(S)=\sum _{i,j,k}c_{ik}d_{jk}\, x_i\otimes y_j.
\end{equation}

\item Let $\Sigma$ be an oriented 1-manifold and orient the cylinder
$\Sigma\times [ 0,1] $ such that $x\mapsto (x,0)$ is an
orientation reversing map from $\Sigma$ onto $\Sigma\times \{ 0\}$
whereas $x\mapsto (x,1)$ is an
orientation preserving mapping from $\Sigma$ onto $\Sigma\times \{ 1\}$.
Using the canonical identification
${\cal H} _1^*\otimes {\cal H} _2\approx {\rm Hom} ({\cal H} _1,{\cal H} _2)$,  we may according to
axioms 2 and 3 regard $Z(\Sigma\times [ 0,1] )$ as a linear map from
${\cal H} _{\Sigma\times \{ 0\} }$ to ${\cal H} _{\Sigma\times \{ 1\} }$ and we
assume that
$
Z(\Sigma\times [ 0,1] )=U_f
$
where $f:\Sigma\times \{ 0\}\mapsto \Sigma\times \{ 1\} $ is defined
by $f((x,0))=(x,1)$.
Using the mapping $U_f$
to identify the spaces ${\cal H} _{\Sigma \times\{ 0\} }$ and
${\cal H} _{\Sigma\times \{ 1\} }$ we can
write
\begin{equation}
 Z(\Sigma\times [ 0,1])  =I
\end{equation}
where $I$ is the identity mappping.

\end{enumerate}

We refer to \cite{at} for a detailed discussion of the axioms.
Here we make a few comments that apply especially in the two-dimensional
case.

It is a standard consequence of the axioms that the unitary mapping
$U_f$ with $f$ as in axiom 1 only depends on the homotopy class of the
diffeomorphism $f$.  If $\Sigma _1$ and $\Sigma _2$ are connected, i.e.
circles, there is
only one homotopy class of orientation preserving diffeomorphisms and we can
write $U_f=U(\Sigma _1,\Sigma _2)$.  By axiom 1 it follows that
the mappings $U(\Sigma _1,\Sigma _2)$ yield a canonical identification of
all the Hilbert spaces ${\cal H} _{\Sigma}$ (where $\Sigma$ is
connected) with a single
Hilbert space which we denote by ${\cal H}$ with inner product $<,>$.  With these
identifications all the mappings $U(\Sigma _1,\Sigma _2)$
are of course the identity and by
\rf{a} and \rf{b} a unique symmetric bilinear form $(,)$ is defined on ${\cal H}$.
Similarly, by \rf{b} and \rf{c} the $*$-maps define a unique conjugate
linear involution $x\mapsto x^*$ on ${\cal H}$ given by
\begin{equation}
(x,y^*)=<x,y>. \label{nbil}
\end{equation}

It follows from the assumed factorization properties of the inner products,
bilinear forms and unitary mappings that the vectorspace associated to a
1-manifold with $n$ boundary components $\Sigma _1,\ldots ,\Sigma _n$ can
be identified with ${\cal H} ^{\otimes n}$.  If $f$ is a diffeomorphism
of $\Sigma _1\cup \ldots \cup \Sigma _n$ onto itself
which permutes the boundary components,
then the mapping induced by $U_f$ acts on ${\cal H} ^{\otimes n}$ by the
corresponding permutation of factors in the tensor product.  This implies that
if $S$ is a {\em connected} surface with $\partial S=\Sigma _1 \cup \ldots\cup
\Sigma _n$ then $Z(S)\in{\cal H} ^{\otimes n}$ is a symmetric tensor since there
exist orientation preserving
diffeomorphisms that permute the boundary components
of $S$ in any prescribed way.  Moreover, since any surface $S$ possesses an
orientation resversing diffeomorphism, we conclude that $Z(S^*) =Z(S)$ and
hence, by \rf{con}, that
\begin{equation}
Z(S)=Z(S)^*   \label{real}
\end{equation}
for any surface $S$.

Letting ${\cal H} _R$ denote the real subspace of ${\cal H}$ defined by
\begin{equation}
{\cal H} _R=\{ x\in{\cal H} : x=x^*\}
\end{equation}
we have a direct sum decomposition over ${\bf R}$,
\begin{equation}
{\cal H} ={\cal H} _R\oplus i{\cal H} _R.   \label{bas}
\end{equation}
According to \rf{nbil} and the symmetry of $(,)$ it follows that the
restriction of the inner product to ${\cal H} _R$ is a real inner product
on ${\cal H} _R$ which equals the restriction of the bilinear form to ${\cal H} _R$.
We thus conclude from \rf{real} that any two-dimensional unitary TQFT
is effectively real, i.e. we might have started from the outset with
real Hilbert spaces and partition functions satisfying the analogues
of axioms 1-4 without \rf{c} and \rf{con}.

\section{Classification} Let us assume that we are given a unitary
TQFT satisfying the axioms of the previous section.  Let us denote the
partition function for a connected surface of genus $g$ with $n$ boundary
components by $Z_{g,n}$ and write $Z_{g,0}=Z_g$.
We choose an orthonormal basis $\{ x_i\}$ for ${\cal H} _R$ which, according to
\rf{bas}, also constitutes an orthonormal basis for ${\cal H}$ with $x_i^*=x_i$.
 The one loop function on the sphere can
then be expressed as
\begin{equation}
Z_{0,1}=\sum_{i}d_i\,x_i.
\end{equation}
The two and three loop functions on the sphere can similarly be written as
\begin{equation}
Z_{0,2}=\sum_{ij}q_{ij}\,x_i\otimes x_j\label{q}
\end{equation}
and
\begin{equation}
Z_{0,3}=\sum _{ijk} C _{ijk}\, x_i\otimes x_j\otimes x_k,
\end{equation}
where $q_{ij}$ and $C_{ijk}$ are real and symmetric under interchange of the
indices.
By axioms 3 and 4 we have
\begin{equation}
\sum _iq_{ij}\,x_i=x_j^*
\end{equation}
so $q_{ij}=\delta _{ij}$ with respect to the chosen basis.

We define a handle operator
$H\in {\rm End }({\cal H} )$ by gluing together two three loop functions:
\begin{equation}
H=\sum _{il}H_{il}\, x_i\otimes x_l^*
\end{equation}
where
\begin{equation}
H_{il}=\sum _{jk}C_{ijk}C_{ljk}.
\end{equation}
This is the same as regarding $Z_{1,2}$ as an operator on ${\cal H}$.
Applying $H$ to the vector $Z_{g,1}$ clearly gives $Z_{g+1,1}$.  The
operator $H$ is hermitean by \rf{con} i.e. symmetric on ${\cal H} _R$.

We now choose the basis
$\{ x_i\}$ to consist of the eigenvectors of $H$ and let $\lambda _1, \ldots
\lambda _n$ denote the eigenvalues of $H$ (not necessarily distinct),
$n={\rm dim}\,{\cal H}$.  Then by axiom 3
\begin{eqnarray}
Z_g&=&<Z_{0,1},H^{g}Z_{0,1}>\\
   &=&\sum _{i}\lambda _i^{g} |d_i|^2 \label{spec}
\end{eqnarray}
for any $g\geq 0$.
Furthermore,
\begin{equation}
Z_{g+1}={\rm Tr} H^g=\sum _i\lambda _i^g\label{spec2}
\end{equation}
for all $g\geq 0$.
It follows that
\begin{equation}
\sum _i\lambda _i^g|d_i|^2=\sum _i\lambda _i^{g-1} \label{spec3}
\end{equation}
for all $g\geq 1$.

Eq. \rf{spec3} implies that
all the eigenvalues are nonegative.  In order
to prove this we order the eigenvalues according to their absolute value so
that $|\lambda _i|\geq |\lambda _j|$ if $i\leq j$ and assume $\lambda _1\neq
0$.
  Clearly
\rf{spec3} cannot hold for
all $g$ unless $\lambda _1$ is positive and
we conclude also that
\begin{equation}
\sum _{i=1}^{k}\lambda _i^g|d_i|^2=k\lambda _1^{g-1}  \label{sub}
\end{equation}
where $k$ is the multiplicity of $\lambda _1$.  Subtracting \rf{sub}
from \rf{spec3} and repeating the above argument we conclude that all
the eigenvalues are nonegative.
Below we show that a zero eigenvalue cannot occur and
we can choose a basis such that $d_i=\lambda _i^{-{1\over 2}}$.

Consider the operators $C_i$ on ${\cal H}_R$
defined by
\begin{equation}
C_i=\sum_{jk}C_{ijk}\,x_j\otimes x_k^*.
\end{equation}
By the symmetry of $C_{ijk}$ and the four loop
function these operators are mutually commuting
and symmetric so they can be simultaneously diagonalized
and we can choose a new self-dual basis such that
$C_{ijk}=\delta _{ij}\delta _{ik}C_{iii}$.
Using the definition of the handle operator we now find that
$
C_{iii}^2=\lambda _i
$
and $H$ is diagonal in this basis.
If $\lambda _i=0$, then $C_{iii}=0$.
This contradicts axiom 4 which states that
\begin{equation}
\sum _{ijk}C_{ijk}d_k\,x_i\otimes x_j^*=I
\end{equation}
and implies that all $C_{iii}\neq 0$ and $C_{iii}d_i=1$.

It is not hard
to convince oneself that any positive operator can arise as a handle
operator.  In fact we give an explicit construction in
the next section.

We conclude this section by showing that all the information
in a two-dimensional
unitary TQFT is contained in the
spectrum of $H$.  We begin by making precise what we mean by
the equivalence of two unitary TQFT in two dimensions.
Let $T$ be a theory satisfying the axioms of section 2
and let $T'$ be another one whose objects are distinguished from those of
$T$ by a prime.  We say that $T$ and $T'$ are equivalent if for
any 1-manifold $\Sigma$ there exists a unitary mapping
\begin{equation}
V_{\Sigma}:{\cal H} _{\Sigma}\mapsto {\cal H} _{\Sigma}'
\end{equation}
such that the following  conditions hold:
\begin{enumerate}
\item For any orientation preserving diffeomorphism
$f:\Sigma _1\mapsto\Sigma _2$ between 1-manifolds
\begin{equation}
U_f'=V_{\Sigma _2}U_fV_{\Sigma _1}^*.
\end{equation}
\item For any oriented surface $S$
\begin{equation}
Z'(S)=V_{\partial S}(Z(S))
\end{equation}
with the understanding that $Z'(S)=Z(S)$ if $S$ is closed.

\item For any 1-manifold $\Sigma$ we have
\begin{equation}
(V_{\Sigma}x,V_{\Sigma ^*}y)_{\Sigma}'=(x,y)_{\Sigma}.
\end{equation}
\end{enumerate}

Let $T,T'$ be a pair of unitary TQFT's whose handle operators have
the spectrum $\lambda _1, \ldots ,\lambda _n$.
Then, by previous arguments, they
are both equivalent to theories where
all Hilbert spaces for connected boundary components coincide and equal ${\cal H}$
and ${\cal H} '$, respectively.  We have seen that by a
suitable choice of bases the three loop functions then take the form
\begin{equation}
Z_{3,0}=\sum _i\sqrt{\lambda _i}\,x_i\otimes x_i\otimes x_i.
\end{equation}
Let us call such a basis a canonical basis.
Furthermore, $q_{ij}=\delta _{ij}$, $d_i=\lambda _i^{-{1\over 2}}$
with respect to
a canonical basis.  An equivalence between $T$ and
$T'$ is now obtained by mapping a canonical basis for ${\cal H}$ to a canonical
basis for ${\cal H} '$.

We finally remark that two unitary TQFT's whose partition functions
take the same value for all closed surfaces have handle operators
with identical spectra, in view of
\rf{spec2}, and are therefore equivalent.

\section{Construction}
In \cite{th1} a field theoretical construction was given of a TQFT on
triangulated surfaces, using fields defined on vertices, such that
$Z_g=N^{\chi}$, where $N$ could take any positive value and $\chi$ is the
Euler characteristic.
In order to obtain a theory whose partition functions for closed surfaces
are sums of
exponentials we can take a direct sum of theories of this type.

Let us explain what we mean by the
direct sum of two TQFT's.  Suppose we have two theories with loop functions
$Z_{g,n}$ and $Z_{g,n}'$ and Hilbert spaces ${\cal H}$ and ${\cal H} '$ for each
connected boundary component.
The direct sum is a TQFT with the Hilbert space $\tilde{{\cal H}}={\cal H}\oplus
{\cal H} '$ for each boundary component and loop functions $\tilde{Z}_{g,n}=
Z_{g,n}+Z_{g,n}'$ where we regard $Z_{g,n}+Z_{g,n}'$ in a natural
way as an element of $\tilde{{\cal H}}^{\otimes n}$, $n\neq 0$.
Unitary maps and bilinear forms are defined in the obvious way.
One can then
check that the direct sum satisfies the axioms if the original theories do so.

Here we give an alternative and more direct construction of a TQFT with
an arbitrary handle operator using triangulations and local weights.
Let $S$ be a triangulated surface
of genus $g$ and $N_1,\ldots ,N_n$ a sequence of $n$ not necessarily
distinct positive numbers.  Let $J=\{ 1, \ldots ,n\} $.  A colouring of $S$ is
a
mapping from the vertices of $S$, ${\cal V} (S)$, into $J$.  The image of a vertex
under a colouring is called
its colour.  Given a colouring $\phi$ of $S$ we define
the weight of the vertex $v$ to be $N_i$ where $i=\phi (v)$.  The weight
$w_{\Delta}$ of a triangle $\Delta$ in $S$ with corners whose colours are
$i,j,k$ is defined to be $N_i^{-{1\over 2}}$
if $i=j=k$ but zero otherwise.  The partition
function for a closed surface $S$ is now defined to be
\begin{equation}
Z(S)=\sum _{\phi}\prod _{v\in {\cal V} (S)} N_{\phi (v)}\prod _{\Delta \in
{\cal T} (S)}w_{\Delta},
\end{equation}
where the sum is over all colourings of $S$ and ${\cal T} (S)$ denotes the set of
all triangles in $S$.
It is easy to see that if $S$ is connected the only colourings which contribute
are those that assign the same colour to all vertices and
\begin{equation}
Z(S)=\sum _{i=1}^n N_i^{\chi}.
\end{equation}

Now let $S$ be a connected
triangulated surface with $b$ boundary components.
Let $|\partial S|$ be the number of verticies in $\partial S$ and define
\begin{equation}
\zeta _i(S)=N_i^{-{1\over 2}|\partial S|}
\sum _{\phi}\prod _{v\in {\cal V} (S)} N_{\phi (v)}\prod _{\Delta \in
{\cal T} (S)}w_{\Delta},
\end{equation}
where $\phi$ now runs over all colourings which are $i$ on the boundary.
Clearly $ \zeta _i(S)= N_i^{\chi (S)}$.
We define an $n$-dimensional
Hilbert space ${\cal H}$ by assigning a vector $x_i$ to each colour
and let $\{x_i\}$ be an orthonormal basis for ${\cal H}$ and
we set $x_i^*=x_i$.  The partition function for $S$ is now defined by
regarding $ \zeta _i(S)$ as a coordinate of $Z(S)$ with respect to
the chosen basis, i.e.
\begin{equation}
Z(S)=\sum _i \zeta _i(S)x_i^{\otimes b}.
\end{equation}
It is not hard to check that the theory so defined satisfies all the axioms
and $N_i^{-{1\over 2}}$ are the eigenvalues of the handle operator.

\section{Discussion}
In this paper we have classified all two-dimensional unitary TQFT's
and shown how they can be obtained using locally defined weights on
triangulated surfaces.  Obviously one would like to generalize some
of these results to higher dimensions.

The notions of equivalence and direct sums extend in a
straightforward fashion to
dimensions higher than 2.  As we have seen any two-dimensional
unitary TQFT can be written as a direct sum of theories for which the
space associated with the circle is 1-dimensional.  It is appropriate to
call such theories irreducible.  It seems to be of importance to
introduce a notion of irreducibility and to establish
associated decomposition properties for
TQFT's in general.
A large class of 3-dimensional TQFT's has been constructed
\cite{durhuus,durhuus2,felder,chung}
generalizing the
theory of Turaev and Viro \cite{tv} and these theories
serve as candidates for irreducible theories since the dimension of
the Hilbert space of the sphere is always 1 and thus they cannot
be decomposed.

A natural question to ask is whether it is true in higher dimensions that
the partition functions for closed manifolds determine a theory up to
equivalence as is the case in two dimensions.  If the partition functions
for manifolds $M$ with $\partial M=\Sigma$ span the Hilbert space associated to
$\Sigma$ for all boundaries $\Sigma$, then it is not hard to show
that this is the case.  However, this condition is in general not
fulfilled.  In the two-dimensional case it holds only if the spectrum of the
handle operator is non-degenerate.

redpajama_set_name: RedPajamaArXiv


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The board of directors of the Export-Import Bank of the United States voted today to grant preliminary approval for a $805.6 million direct loan to South Africa's state-owned electric power utility, Eskom, Limited. A final vote by the board is anticipated in approximately 35 days, following the mandatory Congressional notification period.
The financing, if finally approved, will support Eskom's purchase of engineering and construction management services from Black & Veatch International of Overland Park, Kansas which will be used to construct the Kusile power plant located in the Emalahleni area of the Mpumulanga Province . Hundreds of highly-skilled American senior engineers and support personnel in Ann Arbor, Mich., Raleigh, N.C. and Kansas City will be employed by Black & Veatch each year during a five year period.
South Africa is one of nine countries identified by Ex-Im Bank as offering the greatest export sales opportunities to U.S. companies. In winning this contract with the Bank's support, Black & Veatch overcame competition from several major European engineering companies. The Kusile plant will consist of six 800 MW units, for a total capacity of 4,800 MW. It is the second of two plants being constructed by Eskom in order to meet the country's increasing demand for electric power.
The Kusile plant is designed with advanced technology and equipment, including highly efficient supercritical boilers. Eskom undertook a comprehensive environmental assessment for the project, and a number of environmental safeguards, including scrubbers to control sulfur dioxide and equipment to minimize particulate emissions were included in the plant's design. Notably, Kusile will be the first coal-fired power plant in South Africa to include sulfur dioxide scrubbers. To help conserve water, the plant will use an air cooling system. The plant also is designed to be carbon capture and sequestration ready, which means it is configured in a way that will facilitate subsequent installation of equipment to capture and transport carbon emissions to a permanent storage location.
Ex-Im Bank financing supports hundreds of U.S. jobs, and also brings assurances of compliance with its environmental and social guidelines, including those for high intensity carbon projects. Throughout this process, Ex-Im Bank met on several occasions with officials of environmental non-governmental organizations (NGOs) and project stakeholders to address their concerns relating to the potential environmental and social impacts of the Kusile project. Ex-Im Bank took into account all of the information and comments it received from these meetings on the project's potential environmental and social impacts.
The application to finance the Kusile project underwent a review that focused on aspects related to its carbon dioxide production, and South Africa's long-range goals to reduce its carbon dioxide production. Eskom, as a state-owned energy enterprise, has announced its goal to significantly reduce its long-term dependence on coal by 2025.
Included in the Bank's Carbon Policy is enhanced due diligence and improved transparency in the tracking and reporting of CO2 emissions from projects that the Bank supports. No other export credit agency tracks or discloses this information to the public. The board took its vote today after considering the results of a complete financial, technical and environmental review of the project.
In fiscal year 2010, which ended September 30, 2010, Ex-Im Bank authorized a record $812 million to support exports to sub-Saharan Africa. The bank projects FY 2011 authorizations for the region may ultimately exceed $1.5 billion. Ex-Im Bank is an independent federal agency that helps create and maintain U.S. jobs by filling gaps in private export financing at no cost to American taxpayers. The Bank provides a variety of financing mechanisms, including working capital guarantees, export-credit insurance, and financing to help foreign buyers purchase U.S. goods and services. By charging fees and interest on all loan-related transactions, Ex-Im Bank is self-sustaining and is able to cover all operation costs and potential losses while also producing revenue. The Bank has generated $3.4 billion for U.S. taxpayers over the past five years.
In fiscal year 2010, Ex-Im Bank authorized a record high of approximately $24.5 billion in loans, guarantees and insurance (including more than $5 billion in authorizations for small businesses), supporting an estimated 230,000 American jobs.
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Phillies officially name Klentak as new General…
Phillies officially name Klentak as new General Manager
Phillies incoming general manager and vice president Matt Klentak speaks during a news conference, Monday, Oct. 26, 2015, in Philadelphia. The 35-year-old Klentak becomes the youngest GM in team history. He had been the Angels assistant GM since November 2011. (AP Photo/Matt Rourke)
By Jack McCaffery | jmccaffery@delcotimes.com | The Reporter
PUBLISHED: October 26, 2015 at 11:49 a.m. | UPDATED: September 24, 2021 at 1:28 a.m.
PHILADELPHIA >> Spreading confidence sprinkled with caution, Matt Klentak was officially introduced Monday as the Phillies' general manager.
At 35, the former assistant general manager of the Los Angeles Angels immediately announced his intention to succeed, though steadfastly refused to sturdy that with any timetable.
"Winning," he said, "is ultimately what this is all about. You know that and I know that. Philadelphia knows that. That's why I'm here. I would not have left Mike Trout in his prime to come here if I didn't believe that. I promise you that. I look forward to contributing and helping this franchise get back to its winning ways."
Aware that the Phillies last enjoyed a first-place finish in 2011 and just suffered a 99-loss season, the former Dartmouth shortstop and economics student, not necessarily in that order, clearly realized that his rebuilding task could take some time.
"I see a lot of talent and it's exciting," he said. "This industry and this game is about the players and I see a lot of good, solid if not better than that pitchers and athletes and good players in the system."
Yet asked about how far the Phillies are from contention, Klentak said, "The short answer is I don't know. The players will dictate that. Players will dictate when this team is ready to be as good as they can possibly be. And players, as you know, will develop at different speeds and different rates. Some will be better than we thought they would be. Some will underwhelm us. But overall, the players will dictate that. What I do know is at the first sign this team is ready and we are ready to be good and take that next step, and, God, I hope it's April, we will do everything we can to support that group and create a core that's going to last for a long, long time."
The process to replace Ruben Amaro Jr., who was fired Sept. 10, was, by design, long, long as well. Keeping his vow to undergo an exhaustive search, new president Andy MacPhail was reported to have reduced his list of candidates to three by last week. They included Klentak, Rays vice president of baseball operations Chaim Bloom and Dan Kantrovitz, an assistant general manager in Oakland.
In Klentak, MacPhail will reunite with a former protege of his in the Baltimore organization. The decision, MacPhail confirmed, was made Thursday.
"I'll tell you the truth," MacPhail said. "I know it's a natural assumption to make, 'Well, he ended up hiring the guy that was your assistant down in Baltimore.' But it really didn't feel that way. I don't know that we really lased-in on anybody. There are a lot of very talented people in the game. I actually got to a point where I was thinking, 'What a waste that the Americans are investing this much brain power in sports?' There are high-quality people. And it was not a foregone conclusion. And that's where I relied on ownership to make sure that we had everybody invested in this decision. They have a lot at stake. They need to be invested. So I don't think we lased-in on it until the final day or two."
Klentak was in the Angels front office from 2012 through 2015, most recently as assistant general manager. From 2008 through 2011, he was director of baseball operations in Baltimore, working under MacPhail. While he was in L.A., the Angels won the 2014 American League West championship. With MacPhail, he has been credited with helping the Baltimore organization acquire the talent to win the 2014 A.L. East championship.
Earlier, Klentak had spent four years in the labor-relations department of Major League Baseball. Prior to that, he worked in the Colorado Rockies' baseball operations department. Though Phillies ownership partner John Middleton made it clear that the organization has been and will continue to bolster its concentration on baseball analytics, Klentak was not hired only for his ability to process numbers at an Ivy League pace.
"In process of all areas of baseball operations, we will be connected," Klentak said. "We will work together. We will have a process for everything that we do. And we will not veer off course.
"Information is important. We want to be the best at everything that we do. We want to have the best scouts in the field, the best coaches, the best players. And we will. And we will use every form of technology and information available to us to be at the forefront of information in this industry. And how we manage that will be the key. We want to take the information from all the different people and marry that into our process. How we do that will determine our fate. If we have the best information, we will make the best decisions.
"One thing I know is that we can't force culture. But we can build an environment that allows our players to succeed. To play loose and play confidently. We will create an environment that allows our players to get better and allows the Phillies to win a lot of baseball games.
"And if we are successful in those first four points, we will do a lot of winning."
Jack McCaffery | Reporter


Add some sparkle to your career with this entry-level course and become a jeweller or jewellery designer.
Kick start your jewellery career with this entry-level course. Develop the skills and knowledge required to become a jeweller. With growing consumer demand for gold and silver jewellery, employment opportunities in this industry are increasing.
In this course you will learn about jewellery repair, stone and gem setting, metal casting, chain making, and technical drawing. You will also develop the ability to plan and interpret designs, use hand tools for precision work, and work safely with a wide range of materials.
Successful completion of this course will give you the skills and knowledge required to work as a jeweller or jewellery designer. You will also develop a solid foundation to continue onto further study.
If you can demonstrate substantial competency in this qualification, you may be able to access funding for recognition of prior learning and gap training through the Trade Skills and Assessment Gap Training (TSAGT) program. TAFE Queensland is a proud recipient of funding from the Queensland Government, Department of Employment, Small Business and Training (DESBT) for this program. Only eligible participants may receive funding for eligible courses. Learn more about eligibility criteria.
At TAFE Queensland we maintain strong and relevant industry connections. Our teachers have their finger on the pulse and are equipped to guide you through your education to give you the ability to meet and exceed expectations set within the business world.
The successful achievement of this qualification requires you to complete all core and elective units based on points from the list below.
This unit covers performing brazing (including braze welding) and silver soldering. It includes the preparation of materials and equipment and the inspection of the completed work.
This unit covers performing straight forward heating/quenching, tempering and annealing of ferrous and non-ferrous metals.
This unit covers finishing and polishing materials using a range of media and equipment.
This unit covers using personal protective equipment (PPEs), identifying the particular hazards and emergencyprocedures, and observing safe working practices in that environment.
This unit covers working safely with molten metals or glass including the appropriate using personal protectiveequipment (PPE), identifying and responding to emergency procedures, observing safe work practices, and identifying the hazardous conditions in a heavy engineering environment.
This unit covers inspecting products, keeping records and providing feedback on the conformance of product tospecifications.
This unit covers casting jewellery primarily by the 'lost wax' method of investment casting.
This unit covers producing jewellery illustrations using manual and electronic procedures and equipment.
This unit covers correct general handling and observing of gem materials through a basic understanding of gemology and gemstone terminology. Included in this unit is a basic understanding of gemology and gemstone types (including diamonds), nomenclature relative to gemstones and diamonds and the use of the basic equipment required to observe the condition and features of gemstones.
This unit covers performing most diamond and gem setting styles by manual methods.
This unit covers preparing jewellery designs and associated documentation with a view to producing the designed item/s. Pre-requisites apply - refer training package for details.
This unit covers producing one-off wax models in simple to moderate carved forms and simple to moderate structural forms.
This unit covers the manufacturing jewellery master pattern(s) for jewellery reproduction, mainly by hand held application of processes. It requires the application of precision measurement and hand-making/machine skills to a greater level than that required in MEM19005B (Produce three-dimensional precision items).
This unit covers constructing jewellery components or single-piece items of basic design.
This unit covers constructing jewellery components, single and multiple-piece items involving a range of fabrication processes and techniques.
This unit covers making common repairs to a range of jewellery items. It requires the application of skills and knowledge in jewellery manufacturing and finishing techniques.


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Get the equivalent to 8 hours of battery life on just 15 minutes with this new charger that also works for other mobiles than Motorola.
Motorola has in the United States launched their Turbo Charger which using Qualcomm's Quick Charge 2.0 technology can provide 8 hours of life on the new Moto X in just 15 minutes.
So far it cannot be purchased here at home, but is priced at 35 dollars (~ 200,-EUR). According to Android Central which has got his fingers in a charger, it is somewhat larger than the charger that comes with your phone at purchase.
It is also interesting that the charger should work for other phone models which are equipped with Qualcomm's Quick Charge 2.0 technology, this is, among other things, HTC One M8, Samsung Galaxy Note 4, Sony Xperia Z2 and Z3 and a number of other phones and tablets.
It of course requires that the hardware manufacturer enable this feature fully writes Qualcomm, while Motorola points out to let the speed decreases the more power there is in the battery, so you get the best performance if the battery is almost empty.
With a compatible phone, the Motorola charger can send a larger voltage which with the right orbit, can be converted into faster charging. You can, however, be fine to use the charger with phones which do not support Qualcomm's Quick Charge 2.0, then used a standard voltage and no bursting in the air.


When it comes to Corsair, we always know we're going to get a quality product, we just don't know how high the quality is going to be or what kind of new bar they're going to set this time compared to the last Corsair Road Warrior gaming chair they had made.
The Corsair T1 gaming chair was an absolute winner. Corsair, seemingly inspired by the roaring success of the T1, decided to grab their research team and hunker down for another shot at recreating a masterpiece. The T2 is given an updated body that is less 'FIA GT' and more 'Road sport'. From looks alone, it's obvious that the T2 is aimed at a more mature crowd who still want a little bit of that racing culture. It certainly looks the part, but will it give you that racing edge like its predecessor did? Let's see if Corsair has actually managed to outdo the T1 by striving for peak performance or if they've gone a little too wide and missed the corner with the Corsair T2 Road Warrior gaming chair.
The Corsair T2 Road Warrior gaming chair is another industry standard setter and the whole flow of the chair is a little bit different than we're used to seeing as well. Something we don't commonly see is the more narrow body to head ratio on these chairs and it's kind of refreshing to see one honestly. How does the Corsair Road Warrior chair hold up to its competition and does Corsair have a chance in the world of PC gaming chairs?
The design of Corsair T2 Road Warrior isn't as blatant or as obvious as some other gaming chairs out on the market as the design of this chair is complemented by the narrow long base. Most chairs have curves or try to be shaped much like an hourglass but we're glad to see something trying to break out of the meta and do something different, not just go with the flow. This is a pretty unique design and the color scheme can be changed but for the most part, the colors are pretty bland. The seam stitching job seems well done but there's nothing too special about that.
Wide base chairs often come with great durability as they have the capacity to support more weight than usual and there's not usually any problems when it comes to maximum capacity or worrying about wear and tear on the chair due to being overused. the Corsair Road Warrior chair is solid and you won't have to worry about the overall durability of the chair. It comes with an extremely strong skeleton steel type infrastructure that runs all way up to the head of the chair.
Steel Construction – The chair is made purely with steel construction material and is guaranteed not to fold or break under any pressure. You can rest assured that no matter how much weight you put on the chair or how long it's going to be used, the frame of the chair will ultimately be solid. Not only on the base of the chair, but the construction of the back is also made of steel, giving it that added extra durability.
Style – The finish of the chair is glossy and finished with high-quality PU leather material. While the overall design is basically some of the same from many of the chairs that we review, it's the glossy PU leather finish that really lets this chair shine above their competition. While this Corsair Road Warrior chair does find itself with a lot of hand-me-downs from its older sibling (the T1 Road Warrior), it's got enough character by itself to let it step out of the T1's shadow. The T2 zeroes in on comfort, making it a priority with levels of dedication that are usually seen on expensive luxury office chairs. While the T1 had bold red accents that ran down the length of its body, the T2 foregoes the loud visuals for something a little more subtle. The most noticeable visual feature is the red racing stripe that runs down a quilted section of the seat, which is hidden almost entirely when you're seated. Another rather interesting tidbit on the T2 is the 4D armrest paddles. They look like they're designed after miniature automotive paddle shifters.
Smooth Roller Wheels – Thankfully, for those of us who have wood flooring that constantly worries about leaving scuff marks, you don't have to worry about that with this chair. These wheels were made to last and they were made to roll without leaving any kind of significant markings behind.
Similar to rollerblade wheels, they are sturdy, yet soft. Incredibly quiet in addition to being scratch proof, you won't bother anybody downstairs, or even in the same room as you for that matter.
Comfort First – The whole design of this chair wasn't to draw attention to the look of the chair, it was designed to be comfortable for the consumer first and foremost. This is why they've created a deep seat design and gave it a tall back, to help relax and stimulate the nerves in your back for ultimate comfort and relaxation.
The extra-wide seat is perfect for big and tall gamers that need a little bit of wiggle room in their gaming chair.
Cushions made of mesh-like PU leather are comfortable and breathable. if you tend to overheat when sitting in leather chairs, then you will love how cool your back stays in this one.
4D armrests can be adjusted up and down, side to side giving even more room in the seat, tilt to different angles, or be lifted up out of the way.
How far does this chair lean back?
This Corsair Road Warrior chair can be tilted back up to 180 degrees when it's fully reclined. You could even take a nap in it when fully reclined.
The base is heavy enough to balance the chair and provide rock-solid support when you recline the T2 to its 180-degree recline. It's actually rather comfortable when you tilt it all the way and kick your feet up on your desk. We do agree that a footstool or something to keep your legs up at a comfortable height is an absolute requirement when you're using the more extreme recline angles. The waterfall edge on the seat is most accommodating to a more relaxed position, but it still isn't as comfortable as we'd like it to be.
How easy is the chair to assemble?
From our experience and the experience of other customers, the chair can be put up in just a few minutes without any assembly tools but it's a little tricky at the start figuring it out. Make sure you build the chair where you will be using it as it is quite heavy once assembled so moving it to where you will use it could be tricky.
Corsair Road Warrior chair was built for comfort and it shows when you sit down. The Corsair gaming chair is an excellent gaming chair and it's something that you'll cherish for a while. This should complete your gaming setup and serve as a great backbone while you game and slay your enemies. We recommend this chair highly and advise you give it a shot. It's highly customizable and will last you a lifetime.
If you are a big and tall gamer, then you will definitely see a lot of value in this gaming chair.
It's got everything you need for a long night of gaming, streaming or working. It looks good as a gaming chair yet you can also have it parked in an office without drawing too much attention from your boss.


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Lee Johnson talks about the Bailey Wright suspension and how the Bristol City squad reacted
Robins boss explains the effect on his squad before victory over the Bluebirds
Bristol City made it three wins in a row by defeating rivals Cardiff City at Ashton Gate on Saturday afternoon in the Severnside derby.
And that was despite having their pre-match preparation thrown into confusion when a late FA charge was handed out to club captain Bailey Wright for 'successful deception of a match official'.
And after the game the Bristol Post asked head coach Lee Johnson about the effect that the suspension had on his team.
Dispute between Bristol City fans and club over attempts at St George's Cross display during Cardiff City game
"Well I think you have to use any situation to your advantage and that siege mentality - you need only look at Sir Alex Ferguson and he was amazing like that," explained Johnson on Saturday afternoon.
"You make sure you reference it because it can bring a group together.
"We did reference it and we made sure that everybody knew that we're fighting for a cause here. Not applause. And making sure that we're a unit together.
"Because if you get stretched against Cardiff they've got enough players to be able to hurt you. We had to win this game in a slightly different way and we did."
Aden Flint celebrates his goal for Bristol City
The Bristol Post also asked how the squad had reacted to the bad news the day before the crucial match against Neil Warnock's side.
Neil Warnock left incensed by referee Mike Jones' display in defeat for Cardiff City against Bristol City
"To be honest, they just have to get on with it. Some players will feel bad for him but we know we've got a job to do.
"You saw the hashtag [#winitforbails], which was quite interesting if you like, if not a little bit cringey, but important because it shows the players actually care about their teammates."
"The first thing they did when they won was come in and give Bailey a big hug and made sure he knew he was as big a part of the win as the lads that played."
Aden Flint celebrates after scoring his goal
Bristol City beat Cardiff City for first time since 2012 thanks to goals from Flint and O'Dowda
As for the club stance and whether they will look to try and shorten the suspension, Johnson was unsure.
"The honest answer is I don't know. Obviously I'm disappointed to lose Bailey because he's our captain, but the club have made their statement, which is fine, but my focus has got to be the minute I know we haven't got Bailey I have to make sure every single player knows their job.
"It's like a Rubik's Cube, I have to move everybody about - we put Magnusson in and we moved Joe Bryan up today [Saturday].
"It's disappointing for Bailey and disappointing for the team but what can I do?" asked Johnson.
Callum O'Dowda
So is there any chance of a further appeal?
"At the moment it doesn't seem like there's an appeal and I don't feel that that will be the case and I'll be without him for Sheffield Wednesday."
The best fan reaction from Bristol City's first win against Cardiff City in five years
"The statement says it all. To go into that depth shows that we felt it was a bit of an injustice."
Bristol City next head to Sheffield Wednesday on 18 November.


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PHOTOS | Record Snowfall in Japan's Northern Regions, First Snow in Kyoto
Record breaking snowfall has hit several parts of northern Japan since December 15, and is wreaking havoc on transportation and daily life in the affected parts of the country.
The heaviest snowfall, as of December 17 at 6 P.M. JST, was found in the area around Gunma Prefecture. The city of Fujihara, in the district of Minamikami has seen more than two meters of snowーa recordー206 centimeters to be exact.
Local authorities are urging everyone to exercise caution when venturing outside for snow removal, after several incidents of injuries were reported.
For example, a man his 70s in Uonuma City, Niigata, was reported to have injured his leg by falling from a ladder on December 16, when he was trying to remove snow from his roof.
Inconvenience to Travelers
Areas especially near mountain ranges in Hokuriku, Niigata, Aomori, Fukushima, and Hokkaido have all registered over a meter of snow in less than three days.
As a consequence, transportation and traffic have been affected.
The national highway around Niigata was basically blocked by snow through the night of December 16, with up to a thousand vehicles unable to move, causing major traffic jams for tens of kilometers.
The Japan Self-Defense Force was dispatched on December 17 to provide food, water, and portable toilets to drivers that had braved conditions through the night.
About 70 people who were stuck near Yuzawa, a famous ski resort in Niigata, were lucky enough to be evacuated to nearby hotels where they could spend the night safely and avoid driving in the fierce conditions.
A man who was stuck on the Kan-Etsu expressway, which runs from northern Tokyo through Saitama and Gunma Prefectures to Niigata, called into the NHK broadcasting network on the afternoon of December 16 to report that his car hadn't moved in more than 9 hours.
Beautiful Winter Scenery Dusts Kyoto
Although the northern regions of the country have been seriously affected by the sudden snowfall, the whole of the Japanese archipelago has been hit by winter cold since December 15. The change in atmospheric conditions brought light snow to other parts of the country.
One example is Kyoto, which saw its first dusting of snow on December 17, with temperatures three degrees colder than the average year, at 0.2 degrees celsius.
Those who could afford to take time off work on a weekday could admire Kinkakuji's Golden Pavilion covered in a thin layer of white snow. Although the building is currently undergoing renovation, it was nonetheless a lovely sight to behold.
Visitors could find other impressive winter scenery to admire in Kyoto as well, including Kiyomizudera Temple brushed with snow. The temple, which just unveiled its recent restoration, showed off its beautiful lines in all the splendor of the crisp winter air.
An early morning visitor from Sagamihara City in Kanagawa had come from the Kanto region especially to take pictures of the scenery.
Twenty six year old Kazuho Kanzawa told The Sankei Shimbun and JAPAN Forward: "I saw the news forecast that it was going to snow in Kyoto, so I took the Shinkansen last night and came here. I didn't think it was going to be this much snow. It was so beautifulーI was really moved."
(Read a report used for part of this article here, in Japanese.)
Author: JAPAN Forward
Related Topics:aomoriGinkakujiHokkaidoIwatejapanKiyomizuderakyotoNiigataNorthern Regionsnowtravel


Iron ore mines are to open up again in Sweden.
The 350 percent rise in the world market price of iron ore in the last four years has prompted mines that have been closed for up to 16 years to start digging again.
The increasing demand for steel is behind the move.
New businesses are to mine for the ore and other minerals in mines in just north of Stockholm.
The mines are to be up and running by next year.


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The pandemic more than just a disruption to education
Early reports one year after COVID-19 point to measurable learning loss, as well as racial and socioeconomic disparities. Kaaren Tamm, whose four-year-old daughter struggled with virtual learning, says, "There was no learning going on at all." Professor says, "We need to mobilize more — everything we can — to help teachers deal with this crisis." "The real wave will be that we'll wake up in two, three years and see that we have more social inequality," he predicts. According to the professor, the pandemic has had numerous negative effects on emotional, physical, social, and mental health.
Early readers in Grades 1, 2, and 3 are struggling to read at grade level, according to Alberta researcher George Georgiou. He claims that many students are still performing six to eight months below grade level. It's possible that those who struggled have improved and will finish the school year on par with their peers. But, as Georgiu points out, this is contingent on timely, targeted interventions. According to Sarah Barrett of York University, this puts enormous pressure on teachers, many of whom are already burned out. She claims that teachers are unsure how children will ever catch up on pandemic-prohibited social skills.
Teachers were most concerned about students with special needs, those who were poor, students who were racialized or Indigenous, and English-language learners. According to Julie Garlen, benchmarks are socially constructed targets that can be changed. Changing academic requirements, however, carries risks, according to Peter D'Angiulli. Prachi Srivastava, an education expert, would like to see efforts focused on high-risk neighborhoods and schools. However, according to a Western Ontario education expert, structural barriers make widespread reform difficult. "It actually demonstrates how myopic we have been in terms of understanding in Canada."
When seeking solutions, Garlen advises policymakers to consult with families and students. The pandemic exposed long-standing educational inequities, which were exacerbated by the threat of COVID-19. Some families are more likely than others to live in overcrowded housing or have intermittent access to the internet.
News and picture source: The Canadian Press
30 people trying to enter Canada with fake COVID results nabbed by border control
Minister of Foreign Affairs denounces attacks on protestors in Myanmar


Leave a lasting legacy and include the museum in your estate planning. Including a charitable gift within your overall estate and financial plans will ensure that future generations experience a promising future full of creativity and life-long learning. An estate planning attorney can assist with arrangements and will ensure your wishes are carried out.


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Justia › US Law › Case Law › Federal Courts › District Courts › Maryland › District of Maryland › 1937 › The Losmar
The Losmar, 20 F. Supp. 887 (D. Md. 1937)
US District Court for the District of Maryland - 20 F. Supp. 887 (D. Md. 1937)
20 F. Supp. 887 (1937)
THE LOSMAR.
No. 2225.
District Court, D. Maryland.
*888 Venable, Baetjer & Howard, Joseph France, and George W. P. Whip, all of Baltimore, Md., for libelant.
I. Duke Avnet and Wilfred T. McQuaid, both of Baltimore, Md., for respondents.
WILLIAM C. COLEMAN, District Judge.
It seems to the court, under the present circumstances, that its position should be made entirely clear with relation to the facts in the present case, since it has been contended that they are so different from the facts in the Oakmar Case, 20 F. Supp. 650 as to raise some different questions of law. As has been pointed out, the hearing today arose originally upon a show-cause order, an order requiring these men to show why they should not leave the Losmar. Now, it is explained to the court that through misunderstanding of the court's order they have actually left, and being no longer on the boat, and counsel having stated in open court today that they will not advise them to return, the question presented by the show-cause order, in effect, becomes moot. That is true. But lest there be any future misunderstanding with respect to the position of this court in a case of this kind, and its bearing upon the former decision of this court in the Oakmar Case, 20 F. Supp. 650, it seems desirable for the court to express an opinion, looking back to the situation that did exist until this morning, and from which the vessel owner asked for relief.
As to the other question with respect to which counsel for these men are seeking advice, and an opportunity to file a separate libel, namely, the right, as they claim, to have this court pass upon the validity of the discharge of these men, coupled with the question as to whether or not this court can or should, if the discharge is found to have been improper, reinstate these men, the court now announces that it, of course, has no disposition to deny to these men an opportunity to be heard on that question, if they see fit. However, and without, of course, now attempting to decide that question, because all the facts involved may not be before the court, it is only proper for the court to say that it believes that the statute referred to, section 594 of title 46 of the U. S. Code Annotated, affords the only available remedy in a court of admiralty. That is to say, it provides a measure of damages which this court believes to be in lieu of any other damages that might otherwise be obtained, in the event that an improper discharge is proved. The court believes *889 such has, in effect, been decided by the Supreme Court (see The Steel Trader, 275 U.S. 388, 48 S. Ct. 162, 72 L.Ed. 326), and, therefore, this court is bound by that ruling.
In short, this court finds nowhere in that section or any other section governing this court sitting as an admiralty court, any warrant for saying that these men, or any other men under like circumstances, may obtain specific performance of their contract of employment, and may require that their employer, the master or the owner of the vessel, reinstate them. It is fundamental in the law that ordinarily private contracts of employment, if breached, for whatever cause, do not carry with them the right to compel the employer to take the employee back, if the discharge is found to have been wrongful. This court is not attempting to pass upon what may be the extension of that doctrine, by virtue of the National Labor Relations Act, 29 U.S.C.A. § 151 et seq., because, as the court understands, what has just been asked for by counsel for these men in the present case is a hearing at a future time by this court sitting as an admiralty court. Therefore, this court is not now attempting to say what, if any, additional rights these men might have by claiming that this situation presents a labor dispute referable by them to the Labor Relations Board, or to some other channel. That is a question that is not now before this court. And, as already explained, this court, at any future hearing, will so construe the admiralty statute as to exclude a consideration of those questions.
What has just been said is by way of further explanation of the jurisdiction of this court sitting in admiralty. It is not a final announcement with respect to the propriety or impropriety of the discharge of these men as such, but is simply a restatement for the benefit of counsel, in order that they may know what the court believes to be the limitations of the law, in the event that that matter is heard.
We return now to the original question which, as explained, although having become moot, does seem to require that it be dealt with, lest there be any misunderstanding in the future. The court will endeavor to deal with that major question on the facts as they were presented up to the moment when the men actually left the vessel. On September 17th, this court, sitting in admiralty, had before it the case of the steamship Oakmar, in which certain persons who had formerly been members of the crew of that vessel and who, contrary to the orders of her master, refused to leave her, endeavored by thus engaging in what is generally known as a sympathetic sit-down strike to extort from the master and owner of the vessel certain additional advantages with respect to terms of future employment.
In the Oakmar Case it was admitted by counsel for these men that they were trespassers upon the vessel; but it was argued that nevertheless they could not be required to leave the vessel, because they were engaged in a labor dispute which was, under the circumstances, only justiciable in the first instance by the Labor Board, created by the National Labor Relations Act, enacted July 5, 1935, and that this act of Congress superseded any power which the courts of admiralty might previously have had with respect to possessory libels. But this court dismissed these contentions, because totally without merit, and subversive of every principle of the law of trespass and of the correlative fundamental principles of admiralty, that the courts of admiralty have the right to secure to the lawful owners of a vessel on navigable waters of the United States complete and uninterrupted possession and use of such vessel in lawful commerce. Accordingly, this court directed the marshal forthwith to seize the vessel and to remove forthwith any persons who might be found upon her contrary to the ruling of the court, and to hold the vessel subject to the further order of this court, in the interest of her owner, all of which was immediately accomplished.
In spite of the recent action of this court, as just explained, thirteen members of the crew of the steamship Losmar, owned by the same company, the Calmar Steamship Corporation, as was the steamship Oakmar, asserted their right to remain on the Losmar ever since September 15th last, although on that day they refused to perform any of the duties which they had contracted to perform on the vessel pursuant to their shipping articles, and although, because of such refusal, the master of the Losmar, on September 17th, discharged them, tendering them their earned wages, and ordered them to leave the vessel. The same tender of wages and order to leave the vessel was repeated on September 24th, but again ignored.
*890 The reason which was given for the lapse of some seven days between the first and last order from the master to the men to leave the vessel is that on or about the 16th of September, the master had preferred, before the local maritime board of inspectors at Baltimore, charges of insubordination against these men, and desired to have their certificates of service taken away. At the suggestion of that board the men were allowed, without prejudice to the rights of the master or owner of the vessel, to remain aboard her until the hearing before that board was terminated, which I understand occurred on or about September 23d, when the board took under advisement the matter that had been referred to it, and I assume announced that it would render a decision in due course, disclaiming, as has been announced in court today, any power to adjudicate the question of the legality of the so-called sit-down strike, in which these thirteen members of the vessel's crew had been engaged since September 15th, and had given as their basic reason the employment by the master of certain other members of the crew of the Losmar who are not members of the National Maritime Union, of which the respondents are members.
Numerous other reasons were also advanced, most of which need not be discussed here, because believed to be foreign to the question now before this court. The claim that these men are entitled to one month's wages in addition to the wages actually earned, which the master tendered them upon their discharge, is based upon section 4527 of the Revised Statutes (46 U.S.C.A. § 594) already referred to, and which is as follows: "Any seaman who has signed an agreement and is afterwards discharged before the commencement of the voyage or before one month's wages are earned, without fault on his part justifying such discharge, and without his consent, shall be entitled to receive from the master or owner, in addition to any wages he may have earned, a sum equal in amount to one month's wages as compensation, and may, on adducing evidence satisfactory to the court hearing the case, of having been improperly discharged, recover such compensation as if it were wages duly earned."
It is clear from the language of this statute that the master or owner of a vessel owes no seamen upon their discharge any wages in addition to those actually earned, unless and until they have proved in a court hearing that they were improperly discharged. The owner of the Losmar claims that the right to complete and immediate possession of her is a substantive right entirely independent of the question of what, if any, additional wages the present respondents may ultimately be found to be entitled to under this statute, if their claim for same is properly prosecuted here or in some other appropriate court, and entirely apart from any just grounds which may have been or may hereafter be advanced by them for their refusal to obey the master's order to leave the vessel. In short, the owner claims that the present case is no different in principle from that involving the steamship Oakmar, recently heard by this court, and that the admitted differences in facts do not call for the application of any different legal principles. In this we believe the owner of the Losmar is unquestionably correct. What this court decided in the Oakmar Case must necessarily be equally applicable to the facts in the present case, in spite of some existing differences.
What are the material factual differences? That here the men's contracts of employment, namely, their shipping articles, were still subsisting when they were discharged, whereas in the Oakmar Case the crew's term of employment was completed, and, second, that unlike the situation in the Oakmar Case, these men later on offered to resume work, and that offer was refused on the part of the Losmar's master.
But these differences can have no material bearing upon the single, clear-cut question of law raised by the present possessory libel, which is precisely the same, and the only question raised by the possessory libel brought in the Oakmar Case, namely, may the owner's possession and use of his vessel lawfully be taken away or interfered with by mere trespassers, because of some claim which they may have against the master or the owner of the vessel for wages, or for anything else?
As this court said in its opinion in the Oakmar Case, the mere statement of such a theory so obviously untenable is its best refutation. Shorn of its deceptive coloration, it is simply this, that any means will be justified to obtain a given end, even the destruction of personal and property rights; that the mere assertion of some human need is sufficient to overthrow and to render obsolete any legal principle that may stand as a barrier to the more prompt *891 fulfillment of that need. That, as this court said in the Oakmar Case, "is but another and less shocking way of saying, `If the law does not give us what we want, we will make the law over.' Such theories are the hand-maid of crime and anarchy; they emanate from those persons who lack that self-control which enables men to abide the slower processes of orderly government instead of yielding to that impatience which, if not restrained, will ultimately destroy the fundamental rules for human freedom, upon which our form of government is based. The law is, of course, progressive. It must be, because the law represents rules of human conduct of life. And life is progress. The child progresses, grows into manhood or womanhood, but not into an animal, with attributes of the beast displacing human ones. Similarly, our law must always keep inviolate certain basic rights inherent in any free people. And one of those rights is the right to use one's property without molestation from mere trespassers. Such rights will be protected by this Court as long as it sits, without fear or favor."
With just as much, or as little, plausibility could it be argued that a litigant before this court, having pleaded his cause, which we will assume was based upon an alleged debt due him by another, and having been told by this court that it would take the matter under advisement and render a decision in due course, would be justified in saying, "No, I must have my money at once or I personally shall dispossess my debtor of his home and hold it until he pays me." No, the law of this admiralty court, which protects the owners of a vessel in the lawful use of it, is not dead. The law of trespass is not dead on the law side of this court. The two principles are fundamentally the same, and will be enforced without fear or favor as long as this court sits, or until these principles are changed by those higher tribunals whose decisions control this court.
It may be assumed, but, of course without actually deciding for the purpose of the present case, that these so-called sit-down strikers may prove that their discharge was arbitrary and unwarranted and that, therefore, they should be paid the extra statutory wage penalty that they are claiming. It likewise may be assumed, but again without actually deciding, that this statutory penalty has been supplemented, or even entirely displaced by the more recently enacted remedies afforded to those engaged in labor disputes, and that the federal Labor Relations Board has jurisdiction to hear the alleged grievances of these men, and afford them every additional compensation or advantage, monetary or otherwise, which they are seeking, including an order requiring the master and owner of the Losmar to reinstate them in employment, and still these men would not have shown the slightest justification for refusing to leave the vessel when ordered so to do by her master. Nowhere in the labor acts does the court find any provision, express or implied, which gives any support to the contentions of these men. The power to discharge his crew as and when he sees fit is of necessity inherent in the master of a vessel. Such must be the prerogative of the master, for it is the corollary of his responsibility for the adequate protection of life and property aboard his vessel. It is just as idle to say, therefore, that the master should not be able to hire and to discharge members of his crew as and when he chooses, as to say that, when in the face of imminent peril of collision or other dangers of the sea, he could not use his own judgment with respect to the actual navigation of his vessel. "To discharge" means "to dismiss," "to get rid of." Such dismissal or riddance may ultimately be proved to have been unwarranted, but pending such proof in the manner that the law provides, and pending lawful reinstatement, any member of the crew becomes a trespasser if he does not obey unqualifiedly the master's command to leave.
No order is necessary to be issued in this case, in view of the changed status, as admitted, of the men against whom the show-cause order was directed. But let the court finally say that although the changed facts did not actually require the rendition of an opinion in this case such as has been rendered, nevertheless, the court has deemed it appropriate, if not necessary, to cover all of the various points that are or may be involved, in order that there may be no misunderstanding in the future as to the intended scope of the court's action and order in the previous case.
If these men, respondents in this case, or in any other like case, see fit to bring an appropriate action, in order that the question of the legality of their discharge can be heard by this court, and an interpretation placed by this court upon the other questions that have been referred to in the *892 opinion just rendered, that is their right, and the court will entertain such in due course.
Permission is given to file a cross-libel, for the purpose of raising the question of the discharge. But let me again make it clear, that any men who do go back on these vessels, in violation of the opinion just rendered, and of the terms of the announcements in both of these cases, will be treated as though they were in contempt of the ruling of the court, and will be cited to show cause why they should not be punished for such contempt. Of course, I am not attempting to pass upon the rights of parties who are not before me in either of these cases, but I am referring, when I say "any person," to any person who has been affected by these cases. If other men have a different state of facts, they are entitled to be heard on them. But let me say this in conclusion, if counsel for any one has any doubt as to the meaning or the extent of the ruling respecting the situation on both of these vessels, now is the time for them to ask the court for further clarification. The court has endeavored to make its decision entirely clear, and it is their duty now to ask the court for further clarification, if they are still in doubt, and to obey the orders of the court, unless and until an appeal is taken, and the orders of this court are changed. This court sees no necessity for any further ruling being asked of it with respect to either of the cases. The only order that would be appropriate at this time would be an order in effect dismissing these proceedings, were it not for the fact that permission has just been granted to counsel for these men to file a cross-libel with respect to the question of discharge, to be heard at a later date.


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Until recently, many schools largely adhere to this format but the focus on vocational of other trade schools began to shift in the 1990s toward a curriculum that offers academic as well as technical skills to their students.
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Ever since I purchased the Humble Mobile Bundle, I have been slightly obsessed with one game in particular: The Room.
The Room is your typical point and click cryptic puzzle game that most people have probably played before. This isn't a new formula. Find hidden objects, use those objects and solve puzzles to unlock more items and secret areas.
The story that unfolds as you progress through the game and this story is delivered through a series of notes hidden throughout the game. While these notes don't actually help you solve the puzzles they help to keep you engaged in the story which adds to the entertainment value.
I knew your curiosity would get the better of you.
The answers you seek are inside this box; along with something else. Something they said could never be built. It is the only one in existence, and it is the key to incomprehensible power. This safe was constructed to keep it from lesser minds. I have every faith in you solving its mysteries. You always were the smart one.
With the enclosed key I gift you one parting favour. Keep this eyepiece with you always. Without it, you are as blind as the rest.
Some of the puzzles are obvious, even as you get towards the end of the game, but others will have you wanting to throw your phone or tablet across the room or searching for a walkthrough as I did on a couple of occasions. If you do resort to walkthroughs, you will soon realize how obvious the answer really was, and I would certainly recommend taking a very brief look to see if you can get a hint and then putting the walkthrough away. You will get more satisfaction from solving the problem yourself.
The visuals are very dark which adds to the atmosphere but everything is lit up just enough so you won't have any problems seeing what needs to be done. The controls are intuitive and you are given a nice tutorial to get you started.
The Room is currently available on the Play Store for AU $1.87 which is well worth the money even if the game is quite short. It is also still available on the Humble Mobile Bundle if you pay more than the average which at the time of writing is $5.56 which is excellent value for 9 games.
Next Want to wear some Ausdroid gear? You can.
The game needs to be longer, I want more spoooooky puzzles!
Agreed! Was a GREAT game..great graphics, great sound, great pizzles…but NOT long enough!


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Q: How to sort numpy array by absolute value of a column? What I have now:
import numpy as np
# 1) Read CSV with headers
data = np.genfromtxt("big.csv", delimiter=',', names=True)
# 2) Get absolute values for column in a new ndarray
new_ndarray = np.absolute(data["target_column_name"])
# 3) Append column in new_ndarray to data
# I'm having trouble here. Can't get hstack, concatenate, append, etc; to work
# 4) Sort by new column and obtain a new ndarray
data.sort(order="target_column_name_abs")

I would like:

*

*A solution for 3): To be able to add this new "abs" column to the original ndarray or

*Another approach to be able to sort a csv file by the absolute values of a column.

A: Here is a way to do it.
First, let's create a sample array:
In [39]: a = (np.arange(12).reshape(4, 3) - 6)

In [40]: a
Out[40]:
array([[-6, -5, -4],
       [-3, -2, -1],
       [ 0,  1,  2],
       [ 3,  4,  5]])

Ok, lets say
In [41]: col = 1

which is the column we want to sort by,
and here is the sorting code - using Python's sorted:
In [42]: b = sorted(a, key=lambda row: np.abs(row[col]))

Let's convert b from list to array, and we have:
In [43]: np.array(b)
Out[43]:
array([[ 0,  1,  2],
       [-3, -2, -1],
       [ 3,  4,  5],
       [-6, -5, -4]])

Which is the array with the rows sorted according to
the absolute value of column 1.

A: Here's a solution using pandas:
In [117]: import pandas as pd

In [118]: df = pd.read_csv('test.csv')

In [119]: df
Out[119]:
   a  b
0  1 -3
1  2  2
2  3 -1
3  4  4

In [120]: df['c'] = abs(df['b'])

In [121]: df
Out[121]:
   a  b  c
0  1 -3  3
1  2  2  2
2  3 -1  1
3  4  4  4

In [122]: df.sort_values(by='c')
Out[122]:
   a  b  c
2  3 -1  1
1  2  2  2
0  1 -3  3
3  4  4  4

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text:
Edison Field may refer to:

 Edison Field (Anaheim), now Angel Stadium
 Edison Oil Field, Kern County, California

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A girl named Maggie Wagner has decided to not shave her legs until the NHL lockout is over, and she's now a faux-celebrity because of it. Yes, you read that right. Today, Yahoo's "Puck Daddy" blog has posted an interview with Wagner, and she is now certain to become a minor footnote in internet history over the course of the next 48 hours.
Why are we posting this? Because the lockout needs to end. Now. When Yahoo is stuck paying Greg Wyshynski to interview a girl who hasn't shaved in 100 plus days and calling it "news" then it's time to re-think one of two things: either the lockout, or Yahoo continuing to host an NHL page on their sports site.
Yes, that's her legs. The kicker is that they're not even that hairy.
Your move, NHL - it's you or the Yahoo.