text:
\section{Introduction}

In September 1908, Minkowski \cite{CologneAddress} presented a
4-dimensional geometrical version of special relativity theory; for
the historical context, one may compare Walter \cite{ScottWalter}. A
bit earlier \cite{Grundgleichungen}, in December 1907, he gave a
preliminary version, and he expressed Maxwell's theory of
electrodynamics in a 4-dimensional form. For the Maxwell equations he
found, as pointed out by Damour \cite{Thibault} in his historical
analysis, the very compact representation
\begin{equation}\label{MinMax}
\boxed{\text{lor}\, f=-s\qquad\text{and}\qquad \text{lor}\, F^*=0\,.}
\end{equation}
Here lor$_h:=\partial/\partial x_h$ are the components of the
4-dimensional differential operator. The excitation $f$ and the field
strength $F$ are represented in Maxwell's nomenclature
by\footnote{Minkowski took $D\!=\!e$, $H\!=\!m$; $E\!=\!E$, $B\!=\!M$,
  that is, for the excitation $f\sim(e,m)$ and for the field strength
  $F\sim(E,M)$. Even though this seems logical and appropriate ($e,E$
  correspond to electric and $m,M$ to magnetic), the Maxwellian
  notation is so deeply ingrained in our subconsciousness that any
  competing notation seems to have no chance.}
\begin{equation}\label{fF}
( { f}_{hk})= \left(\begin{array}{cccc}
      0\hspace{5pt} &H_z & -H_y & -iD_x\\ -H_z &0\hspace{5pt} & H_x &
      -iD_y\\ H_y & -H_x &0\hspace{5pt} &-iD_z\\ iD_x & iD_y & iD_z
      &0\hspace{5pt}
  \end{array}\right),\quad
(F_{hk})=\left(\begin{array}{cccc}0 &
    B_z & -B_y & -iE_x\\-B_z &0\hspace{5pt} & B_x & -iE_y\\ B_y & -B_x
    &0\hspace{5pt} & -iE_z\\ iE_x & iE_y & iE_z &0\hspace{5pt}
  \end{array}\right),
\end{equation}
with the imaginary unit $i:=\sqrt{-1}$. The rows and columns of the
matrices in (\ref{fF}) are numbered from 1 to 4. The 4-dimensional
electric current is denoted by $s$. The star $^{*}$ used in
(\ref{MinMax})$_2$ is a duality operator, that is,
$F^*_{hk}:=\frac{1}{2}\hat{\epsilon}_{hklm} F_{lm}$, with
$\hat{\epsilon}_{hklm}=\pm 1,0$ as the totally antisymmetric
Levi-Civita symbol and $\hat{\epsilon}_{1234}=+1$; moreover, the
summation convention is applied.  Minkowski demonstrated
\cite{Grundgleichungen} that the equations in (\ref{MinMax}) are
covariant under arbitrary Poincar\'e (inhomogeneous Lorentz)
transformations.

For vacuum (in the ``aether'', as Minkowski said), excitation and field
strength, in suitable units, are related by
\begin{equation}\label{fF0}f=F\qquad\text{or}\qquad
  (f_{hk})=(F_{hk})\,.
\end{equation}
Accordingly, Minkowski found the correct 4-dimensional representation of the
Maxwell equations in the context of special relativity theory.

Later it became clear, perhaps for the first time to Einstein
\cite{Einstein1916}, that the Maxwell-Minkowski equations
(\ref{MinMax}) can be generalized such that they become covariant
under general coordinate transformations (diffeomorphisms) and metric
independent. Then, only the generalization of the constitutive
relation (\ref{fF0}) remains metric dependent.

In the calculus of exterior forms, the 4-dimensional Maxwell equations
for the excitation $H$ and the field strength $\cal F$ eventually
read\footnote{We take the notation of our book \cite{Birkbook}. The
  only exception is that we denote the field strength by $\cal F$ in
  order not to mix it up with Minkowksi's $F$. For other presentations
  of Maxwell's equations in exterior calculus, see, e.g., Bamberg \&
  Sternberg \cite{Bamberg}, Choquet-Bruhat et al.\ \cite{3ladies},
  Delphenich \cite{Dave1,Dave2}, Frankel \cite{Ted}, Jancewicz
  \cite{Bernard}, Lindell \cite{IsmoBook}, Misner, Thorne \& Wheeler
  \cite{MTW}, Russer \cite{Russer}, Thirring \cite{Thirring}, and
  Trautman \cite{Trautman}.}
\begin{equation}\label{MaxExt}
\boxed{dH=J\qquad\text{and}\qquad d{\cal F}=0\,.}
\end{equation}
Here $d$ is the exterior differential. The Minkowskian scheme
(\ref{MinMax}) foreshadows in its compactness the exterior calculus
version in (\ref{MaxExt}). This point was stressed by Damour
\cite{Thibault}. The equations in (\ref{MaxExt}) are
premetric\footnote{We call a structure {\it premetric}, if it can be
  defined ``before'' a metric is available (or a metric exists, but it
  is not used).} and, accordingly, also valid in this form in general
relativity and in general relativistic field theories with torsion and
curvature \cite{Puntigam}. The 2-forms of the excitation $H=\frac
12\,H_{ij}dx^i\wedge dx^j$ and of the field strength ${\cal F}=\frac
12\,{\cal F}_{ij}dx^i\wedge dx^j$, with $i,j=0,1,2,3$, decompose in
1+3 according to \cite{Birkbook}
\begin{equation}\label{HFdecomp}
H=-{\cal H}\wedge dt+{\cal D}\qquad\text{and}\qquad {\cal F}=E\wedge dt +B\,.
\end{equation}
The signs in (\ref{HFdecomp}) are {\it not} conventional. They are
rather dictated by the Lenz rule, see Itin et al.\
\cite{ItinAdP,ItinHehl}. If we put the latter two equations into
matrix form in order to be able to compare them later with the results
of Minkowski, we find
\begin{equation}\label{Gtwiddle}
\hspace{-30pt}H=  (H_{ij})=\left(\begin{array}{cccc
      0\hspace{5pt} & {\cal H}_1 & {\cal H}_2 & {\cal H}_3\\ -{\cal
        H}_1 &0\hspace{5pt} & {\cal D}^3 &
      -{\cal D}^2\\ -{\cal H}_2 & -{\cal D}^3 &0\hspace{5pt} &
      {\cal D}^1\\ -{\cal H}_3 & {\cal D}^2 & -{\cal D}^1
      &0\hspace{5pt}
  \end{array}\right),\quad
{\cal F}=({\cal F}_{ij})=\left(\begin{array}{cccc}0 &
    -E_1 & -E_2 & -E_3\\ E_1 &0\hspace{5pt} & B^3 & -B^2\\ E_2 & -B^3
    &0\hspace{5pt} & B^1\\ E_3 & B^2 & -B^1 &0\hspace{5pt}
  \end{array}\right).
\end{equation}
Here ${\cal D}^a:=\frac 12\epsilon^{abc}{\cal D}_{bc}$ and
${B}^a:=\frac 12\epsilon^{abc}{B}_{bc}$, with the 3-dimensional
Levi-Civita symbol $\epsilon^{123}=+1$, that is, $\cal D$ and $B$, as
required by their definitions in physics, are 3-dimensional 2-forms,
whereas $E$ and $\cal H$ are 1-forms. Note that ${\cal D}^a$ and
${B}^a$ are vector {\it densities}.  We stress that the
identifications in (\ref{Gtwiddle}) are premetric, they are valid on
any (well-behaved) differential manifold that can be split locally
into time and space.

The excitation $H$ is a 2-form {\it with} twist (sometimes called odd
2-form) and the field strength $\cal F$ a 2-form without twist
(sometimes called even form 2-form). These are consequences of the
definitions of $H$ and $\cal F$ via charge conservation and the
Lorentz force density, respectively. For this reason, in exterior
calculus, the constitutive law for vacuum (``the spacetime relation'')
reads
\begin{equation}\label{constitext}
H=\lambda_0 \,^\star {\cal F}\,.
\end{equation}
Here $\lambda_0=\sqrt{\varepsilon_0/\mu_0}\approx 1/377\,\Omega$ is
the vacuum admittance; in the units Minkowski chose,
$\lambda_0=1$. The metric-dependent Hodge star operator $^\star$ in
(\ref{constitext}) maps a 2-form without twist into a form with twist, and
vice versa.

In this paper we want to trace the way from Minkowski's system
(\ref{MinMax}) and (\ref{fF}) with (\ref{fF0}) to the premetric
framework (\ref{MaxExt}) and (\ref{Gtwiddle}) with the
metric-dependent spacetime relation (\ref{constitext}). Subsequently,
we analyze Minkowski's discovery of the energy-momentum tensor of the
electromagnetic field and display its modern premetric version.

\section{Minkowski's way to:\; lor $\mathbf{f=-s},$\;
  lor $\mathbf{F^*=0}$}

Minkowski first introduced the fields $f$ and $F$ in Cartesian
coordinates $x,y,z$ and with an imaginary time coordinate $it$ (he put
$c=1$), see (\ref{fF}). Afterwards he changed to the numbering of
coordinates in the following way: $x_1:=x$, $x_2:=y$, $x_3:=z$,
$x_4:=it$. His metric is Euclidean
$ds^2=dx_1^2+dx_2^2+dx_3^2+dx_4^2=g_{hk}dx_h dx_k$, with
$g_{hk}=\text{diag}(1,1,1,1)$. Sometimes he also seems to use the
signature $(-1,-1,-1,-1)$. In any case, as long as Minkowski sticks to
Cartesian coordinates---and this is what he was doing---there is no
need to distinguish contravariant (upper) from covariant (lower)
indices. He displays the conventional Maxwell equations in component
form. The inhomogeneous Maxwell equation reads
\begin{eqnarray}\label{inhom} \nonumber
  \hspace{30pt}\frac{\partial f_{12}}{\partial x_2}
  +\frac{\partial f_{13}}{\partial x_3}
  +\frac{\partial f_{14}}{\partial x_4}&=&s_1\,,\\ \nonumber
  \frac{\partial f_{21}}{\partial x_1}
  +\hspace{30pt}\frac{\partial f_{23}}{\partial x_3}
  +\frac{\partial f_{24}}{\partial x_4}&=&s_2\,,\\
  \frac{\partial f_{31}}{\partial x_1}
  +\frac{\partial f_{32}}{\partial x_2}\hspace{30pt}
  +\frac{\partial f_{34}}{\partial x_4}&=&s_3\,,\\ \nonumber
  \frac{\partial f_{41}}{\partial x_1}
  +\frac{\partial f_{42}}{\partial x_2}
  +\frac{\partial f_{43}}{\partial x_3}\hspace{30pt}&=&s_4\,, \nonumber
\end{eqnarray}
and the homogeneous one
\begin{eqnarray}\label{hom} \nonumber
  \hspace{30pt}\frac{\partial F_{34}}{\partial x_2}
  +\frac{\partial F_{42}}{\partial x_3}
  +\frac{\partial F_{23}}{\partial x_4}&=&0\,,\\ \nonumber
  \frac{\partial F_{43}}{\partial x_1}
  +\hspace{30pt}\frac{\partial F_{14}}{\partial x_3}
  +\frac{\partial F_{31}}{\partial x_4}&=&0\,,\\
  \frac{\partial F_{24}}{\partial x_1}
  +\frac{\partial F_{41}}{\partial x_2}\hspace{30pt}
  +\frac{\partial F_{12}}{\partial x_4}&=&0\,,\\ \nonumber
  \frac{\partial F_{32}}{\partial x_1}
  +\frac{\partial F_{13}}{\partial x_2}
  +\frac{\partial F_{21}}{\partial x_3}\hspace{30pt}&=&0\,. \nonumber
\end{eqnarray}
Using modern notation, including the summation convention, see Schouten
\cite{Schouten}, we can rewrite (\ref{inhom})
 and (\ref{hom}) as
\begin{equation}\label{MinMax'}
  \frac{\partial f_{hk}}{\partial x_k}=s_h\qquad\text{and}\qquad
   \frac{\partial F_{hk}}{\partial x_l}
  +\frac{\partial F_{kl}}{\partial x_h}
  +\frac{\partial F_{lh}}{\partial x_k}=0\,.
\end{equation}
Here $h,k,...=1,2,3,4$. Minkowski also introduced the dual of $F_{hk}$
according to $F^*_{hk}:=\frac 12\hat{\epsilon}_{hklm}F_{lm}$, with the
Levi-Civita symbol $\hat{\epsilon}_{hklm}=\pm 1,0$ and
$\hat{\epsilon}_{1234}=+1$. Explicitly, we have
\begin{equation}\label{fF"}
  F^*=(F^*_{hk})=\left(\begin{array}{cccc}0 &-iE_z & iE_y & B_x\\iE_z
      &0\hspace{5pt} &
      -iE_x & B_y\\ -iE_y & iE_x
      &0\hspace{5pt} & B_z\\ -B_x &-B_y & -B_z &0\hspace{5pt}
  \end{array}\right).
\end{equation}
Then we can put the homogeneous equation in a form reminiscent of the
inhomogeneous one (apart from the sources):
\begin{equation}\label{MinMax''}
\frac{\partial F^{*}_{hk}}{\partial x_k}=0\,.
\end{equation}

Subsequently Minkowski develops a type of Cartesian tensor calculus
with a 4-dimensional differential operator called `lor' (abbreviation
of Lorentz). He introduces ordinary (co)vectors (space-time vectors of
the 1st kind), like $x_h$ and lor$_h:=\frac{\partial}{\partial x_h}$,
and antisymmetric 2nd rank tensors (space-time vectors of the 2nd
kind), like $f_{hk}$ and $F_{hk}$. Then, he can represent
(\ref{MinMax'})$_1$ and (\ref{MinMax''}) symbolically as
\begin{equation}\label{MinMax'''}
\text{lor}\,f=-s\qquad\text{and}\qquad\text{lor} \,F^*=0\,,
\end{equation}
respectively, see (\ref{MinMax}). Using his Cartesian tensor calculus,
Minkowski showed that equations (\ref{MinMax'''}) are covariant
under Poincar\'e transformations.

Einstein and Laub \cite{EL08} thought that Minkowski's presentation of
electrodynamics was very demanding from the point of view of the
mathematics involved. Therefore, they essentially rederived
Minkowski's results in a purely 3-dimensional formalism.

\section{Premetric electrodynamics in tensor calculus}

The next step in the development of the Maxwell equations occurred
immediately after Einstein's fundamental 1915 paper on general
relativity and even before his big survey paper on general relativity
would appear. Now Einstein was in command of tensor calculus in
arbitrary coordinate systems. Einstein \cite{Einstein1916} observed
that Maxwell's equations in vacuum can be put in a generally covariant
form by picking suitable field variables.

Einstein used the metric $ds^2=g_{\mu\nu}dx^\mu dx^\nu$ with signature
$(1,-1,-1,-1)$, here $\mu,\nu,...=0,1,2,3$. Einstein
\cite{Einstein1916} wrote Maxwell's equations as\footnote{Einstein
  used subscripts for denoting the coordinates $x$, i.e., $x_\tau$
  etc.  Moreover, we dropped twice the summation symbols
  $\Sigma$. Einstein's identifications, which were only worked out for
  vacuum, read \begin{equation}\label{Einstein} {\mathfrak F}=(
    {\mathfrak F}^{\mu\nu})= \left(\begin{array}{cccc} 0\hspace{5pt}
      &E_x & E_y & E_z\\ -E_x &0\hspace{5pt} & H_z & - H_y\\-E_y& -H_z
      &0\hspace{5pt} &H_x\\-E_z & H_y & -H_x &0\hspace{5pt}
  \end{array}\right),\quad
{F}=({F}_{\rho\sigma})=\left(\begin{array}{cccc}0 &
    -E_x & -E_y & -E_z\\E_x &0\hspace{5pt} & H_z & -H_y\\ E_y & -H_z
    &0\hspace{5pt} &H_x\\ E_z & H_y & -H_x &0\hspace{5pt}
  \end{array}\right).
\end{equation} Einstein discussed already earlier the general
covariant form of Maxwell's equations, see
\cite{Einstein1914}. However, the presentation was a bit different
from (\ref{akademie}) and also by far not as transparent as the one
in \cite{Einstein1916}. Probably for this reason Einstein
republished these ideas.}
\begin{equation}\label{akademie}
  \frac{ \partial F_{\rho\sigma}}{\partial x^\tau}+ \frac{ \partial
    F_{\sigma\tau}}{\partial x^\rho}+ \frac{ \partial
    F_{\tau\rho}}{\partial x^\sigma}=0\,,\quad {\frak
    F}^{\mu\nu}=\sqrt{-g}g^{\mu\alpha}
  g^{\nu\beta}F_{\alpha\beta}\,,\quad \frac{\partial{\frak
      F}^{\mu\nu}}{\partial x^\nu}={\cal J}^\mu\,.
\end{equation}
The field strength $F_{\rho\sigma}$ is a tensor, the excitation ${\frak
  F}^{\mu\nu}$ a tensor density. In his ``Meaning of Relativity''
\cite{meaning}, in the part on general relativity, he even picked the
letter $\phi$ for the field strength (instead of $F$) apparently in
order to stress the different nature of $\phi$ and ${\frak F}$.

The Maxwell equations (\ref{akademie})$_1$ and (\ref{akademie})$_3$
are generally covariant {\em and\/} metric independent. Since in
general relativity the metric $g$ is recognized as the gravitational
potential, it is quite fitting that the fundamental field equations of
electromagnetism do {\em not\/} contain the gravitational
potential. The equations in (\ref{akademie}) are specifically valid in
Minkowskian spacetime. Then, of course, the metric occurring in
(\ref{akademie})$_2$ is flat, i.e., its curvature vanishes. Hence by
transforming Minkowski's \,lor $f=-s$ and \,lor $F^*=0$ to curvilinear
coordinates, one can equally well arrive at (\ref{akademie}).

The gravitational potential only enters equation
(\ref{akademie})$_2$. We call this equation the spacetime
relation---it is the ``constitutive law'' of the vacuum. Needless to
say that having understood that there exists a way to formulate
Maxwell's equations in a generally covariant and metric-independent
manner, going back to (\ref{MinMax'}) would appear to be an
anachronism.  Einstein's argument in favor of his formalism, which is
similar to the Minkowski version (\ref{MinMax'}), and not following
(\ref{MinMax'})$_1$ and (\ref{MinMax''}), was that with his formalism
one can derive the energy-momentum tensor of the electromagnetic field
in a much more transparent way. This is certainly true. Still, it was
Minkowski who discovered the energy-momentum expression
\cite{Grundgleichungen} by performing products between the two
space-time vectors of the 2nd kind $f$ and $F$.

But the real decisive step was left to Kottler \cite{Kottler}. He
derived the Maxwell equations from the conservation laws of electric
charge and magnetic flux. The charges in a 3-dimensional volume and the flux
lines piercing a 2-dimensional area are conserved. These two independent
conservation laws are related to counting procedures and thus are
independent of any length or time standard. It is for this reason that
the two Maxwell equations (\ref{akademie})$_1$ and
(\ref{akademie})$_3$ emerge as a priori independent structures and
free of a metric. It is then left to the constitutive law to link the
excitation ${\frak F}^{\mu\nu}$ with the field strength $F_{\alpha\beta}$.

In (\ref{akademie}) we displayed the Maxwellian system in the way
Einstein wrote it. Changing now to modern notation, see Schouten
\cite{Schouten} and Post \cite{Post}, and using the conventions of
\cite{Birkbook}, the premetric Maxwell equations read\footnote{Post
  \cite{Post} denotes $\check{H}^{ij}$ by $\mathfrak{ G}^{\mu\nu}$. In
  Obukhov's investigations on the energy-momentum tensor
  \cite{YuriAnnalen}, the $\check{H}^{ij}$ is simply named ${H}^{ij}$,
  that is, the $\;\check{\null}\;$ is dropped.} ($i,j,...=0,1,2,3$)
\begin{equation}\label{MaxPost}
 \partial_j \check{H}^{ij}=\check{J}^i\,
\qquad\text{and}\qquad \partial_{[i}{\cal F}_{jk]}=0\,.
\end{equation}
The antisymmetrization bracket is defined according to $[ijk] :=\frac
16(ijk-jik+jki-+...)$ i.e., a plus (minus) sign occurs before even
(odd) permutations of the indices $ijk$. Here $\check{H}^{ij}$ are
components of a tensor density, whereas ${\cal F}_{ij}$ are those of a
tensor. For ${\cal F}_{ij}$ we have the identification
(\ref{Gtwiddle})$_2$ and for $\check{H}^{ij}:=\frac
12\epsilon^{ijkl}H_{kl}$, with $H_{kl}$ identified according to
(\ref{Gtwiddle})$_1$. Thus, explicitly,\footnote{If we abandon Minkowski's
  imaginary time coordinate and go over to $x^i$, with $i=0,1,2,3$,
  then excitation and field strength in Minkwowski's framework read
\begin{equation}\label{fF1}
 \tilde { f}=(\tilde { f}_{hk})= \left(\begin{array}{cccc}
      0\hspace{5pt} &D_x & D_y & D_z\\ -D_x &0\hspace{5pt} & H_z &
      - H_y\\-D_y& -H_z &0\hspace{5pt} &H_x\\-D_z & H_y & -H_x
      &0\hspace{5pt}
  \end{array}\right),\quad
\tilde{F}=(\tilde{F}_{hk})=\left(\begin{array}{cccc}0 &
    E_x & E_y & E_z\\-E_x &0\hspace{5pt} & B_z & -B_y\\ -E_y & -B_z
    &0\hspace{5pt} &B_x\\ -E_z & B_y & -B_x &0\hspace{5pt}
  \end{array}\right).
\end{equation}}
\begin{equation}
\label{checkH}
\check{H}=(\check{H}^{ij})= \left(\begin{array}{cccc}
    0\hspace{5pt} & {\cal D}^1 & {\cal D}^2 & {\cal D}^3\\
    -{\cal D}^1 &0\hspace{5pt} & {\cal H}_3 &
    -{\cal H}_2\\ -{\cal D}^2 & -{\cal H}_3 &0\hspace{5pt} &
    {\cal H}_1\\ -{\cal D}^3 & {\cal H}_2 & -{\cal H}_1
    &0\hspace{5pt}
  \end{array}\right).
\end{equation}
If we substitute $\check{H}^{ij}$ into (\ref{MaxPost})$_1$ and use
$J_{ijk}:=\frac 16\hat{\epsilon}_{ijkl}\check{J}^l$, then
(\ref{MaxPost}) can be displayed in the more symmetric form of
\begin{equation}\label{MaxPost'}
 \partial_{[i}H_{jk]}={J}_{ijk}\,
\qquad\text{and}\qquad \partial_{[i}{\cal F}_{jk]}=0\,.
\end{equation}

Today it is not only of academic interest to put Maxwell's equations
in a general covariant form. On the surface of a neutron star, for
example, where we might have strong magnetic fields of some $10^{10}$
tesla and a huge curvature of spacetime---we are, after all, not
too far outside the Schwarzschild radius of the neutron star of some 3
km---the Maxwell equations keep their form (\ref{MaxPost}). The
metric of spacetime enters the vacuum relation, see
(\ref{akademie})$_2$. There is no longer place for only a Poincar\'e
covariant formulation of Maxwell's equations \`a la (\ref{MinMax'}). A
less extreme case is the Global Positioning System. Nevertheless, also
the GPS rules out Poincar\'e covariant electrodynamics, see Ashby
\cite{Ashby}.

\subsection{Constitutive relation}

The system of the $4+4$ Maxwell equations (\ref{MaxPost}) for the
$6+6$ independent components of the electromagnetic field
$\check{H}^{ij}$ and ${\cal F}_{kl}$ is evidently underdetermined. To
complete this system, a constitutive relation of the form
 \begin{equation}\label{Pconst0}
   \check{H}^{ij}= \check{H}^{ij}({\cal F}_{kl})
 \end{equation}
 has to be assumed. The constitutive relation (\ref{Pconst0}) is
 independent of the Maxwell equations and its form can be determined
 by using experimental results. For general {\it magnetoelectric}
 media, including the vacuum as special case, we assume with Tamm
 \cite{Tamm2,Tamm3}, v.~Laue \cite{Laue}, and Post \cite{Post} the
 {\it local}\footnote{A nonlocal generalization of this law is being
   investigated by Mashhoon, see his review \cite{Bahram}.}  and {\it
   linear} premetric relation
\begin{equation}\label{Tamm}
  \check{H}^{ij}=\frac
  12\,\chi^{ijkl}{\cal F}_{kl}\,,
\end{equation}
where $\chi^{ijkl}$ is a {\it constitutive tensor density} of rank 4
and weight $+1$, with the dimension $[\chi]=1/$resistance. Since both
$ \check{H}^{ij}$ and ${\cal F}_{kl}$ are antisymmetric in their
indices, we have $\chi^{ijkl}= -\chi^{jikl}=-\chi^{ijlk}$. An
antisymmetric pair of indices corresponds, in four dimensions, to six
independent components. Thus, the constitutive tensor can be
considered as a $6\times 6$ matrix with 36 independent components.

One can take the premetric Maxwell equations (\ref{MaxPost}) together
with the premetric ansatz (\ref{Tamm}) as an electrodynamic framework
(``local and linear premetric electrodynamics''), see also Matagne
\cite{Matagne}. Therein one can study the propagation of
electromagnetic waves in the geometrical optics approximation. It
turns out, see \cite{Rubilar,Birkbook}, that the premetric, totally
symmetric {\it Tamm-Rubilar tensor}\footnote{Parentheses around
  indices denote total symmetrization, that is,
  $(ijkl):=\frac{1}{24}\{ijkl+jikl+jkil+\cdots\}$. The covariant
  epsilon-system is marked by a hat: $\hat{\epsilon}_{ijkl}=\pm 1,0;\;
  \hat{\epsilon}_{0123}=+1$.}
\begin{equation}\label{G4}
  {{\cal G}^{ijkl}(\chi):=\frac{1}{4!}\,\hat{\epsilon}_{mnpq}\,
    \hat{\epsilon}_{rstu}\, {\chi}^{mnr(i}\, {\chi}^{j|ps|k}\,
    {\chi}^{l)qtu }}
\end{equation}
---a new structural element in theoretical physics---controls the
light propagation via a generalized Fresnel equation ${\cal
  G}^{ijkl}q_iq_jq_kq_l=0$. The $q_i$ are the components of the wave
vector of the light.\footnote{This scheme was generalized to Abelian
  gauge and string theory by Schuller, Wohlfahrt, et al., see the
  articles \cite{Schuller,Punzi} and the references given there. Also in
  these generalized schemes a Tamm-Rubilar type tensor plays a
  decisive role.} If birefringence is forbidden, then the light cone
emerges \cite{LammerH}, that is, the metric $g_{ij}$ up to a
(dilation) factor \cite{HOPotsdam}.

Let us come back to $\chi^{ijkl}$. As a $6\times 6$ matrix, it can be
decomposed in its tracefree symmetric part (20 independent
components), its antisymmetric part (15 components), and its trace (1
component). On the level of $\chi^{ijkl}$, this {\it
  decomposition} is reflected in
\begin{eqnarray}\label{chidec}
  \chi^{ijkl}&=&\,^{(1)}\chi^{ijkl}+
  \,^{(2)}\chi^{ijkl}+
  \,^{(3)}\chi^{ijkl}\,.\\ \nonumber 36
  &=&\hspace{11pt} 20\hspace{11pt}\oplus \hspace{11pt}15\hspace{12pt}
  \oplus \hspace{18pt}1\,.
\end{eqnarray}
The third part, the {\it axion} part, is totally antisymmetric and as
such proportional to the Levi-Civita symbol, $ ^{(3)}\chi^{ijkl}:=
\chi^{[ijkl]} ={\alpha}\, {\epsilon}^{ijkl}$. Note that ${\alpha}$ is a
pseudoscalar since ${\epsilon}^{ijkl}$ has weight $-1$.  Therefore,
the weight of ${\epsilon}^{ijkl}$ is essential information. The second
part, the {\it skewon} part, is defined according to $
^{(2)}\chi^{ijkl}:=\frac 12(\chi^{ijkl}- \chi^{klij})$.  If the
constitutive equation can be derived from a Lagrangian, which is the
case as long as only reversible processes are considered, then
$^{(2)}\chi^{ijkl}=0$. The {\it principal} part $^{(1)}\chi^{ijkl}$
fulfills the symmetries $ ^{(1)}\chi^{ijkl}= {}^{(1)}\chi^{klij}$ and
$^{(1)}\chi^{[ijkl]}=0$.  The premetric constitutive relation now reads
\begin{equation}\label{constit7}
  { \check{H}^{ij}=\frac
    12\left({}^{(1)}{\chi}^{ijkl}+ {}^{(2)}{\chi}^{ijkl} +{\alpha}\,
      {\epsilon}^{ijkl}\right){\cal F}_{kl}\,.}
\end{equation}

If we assume the existence of a metric $g_{ij}$, then {\it in vacuum}
the constitutive tensor reduces to
\begin{equation}
\chi{}^{ijkl} = \lambda_0\sqrt{-g}\left(g^{ik}g^{jl}
- g^{il}g^{jk}\right).\label{chi0}
\end{equation}
This formula is, up to a factor, determined uniquely by the symmetries
of the principal part. On substitution of (\ref{chi0}) into
(\ref{Tamm}), we find the vacuum relation
\begin{equation}\label{Kottler}
  \check{H}^{ij}=\lambda_0\,\sqrt{-g}g^{ik}g^{jl}\,F_{kl}\,,\qquad
  \text{or}\qquad H_{ij}=\frac{\lambda_0}{2}\hat{\epsilon}_{ijmn}
  \sqrt{-g}g^{mk}g^{nl}F_{kl}\,,
\end{equation}
compare (\ref{akademie})$_2$. Note that (\ref{chi0}) belongs to the
principal part $^{(1)}{\chi}^{ijkl}$.

In order to compare (\ref{constit7}) with experiments, we have to
split it into time and space parts. As shown in
\cite{Birkbook,Postconstraint} in detail, we can parameterize the {\it
  principal} part by the 6 permittivities $\varepsilon^{ab}=
\varepsilon^{ba}$, the 6 permeabilities $\mu_{ab}=\mu_{ba}$, and the 8
magnetoelectric pieces $\gamma^a{}_b$ (the trace vanishes, $\gamma^c{}_c=0$)
and the {\it skewon} part by the 3 permittivities $n_a$, the 3
permeabilities $m^a$, and the 9 magnetoelectric pieces
$s_a{}^b$. Then, the premetric constitutive relation (\ref{constit7})
can be rewritten as
\begin{eqnarray}\label{explicit'}\nonumber
  {\cal D}^a\!&=\!&\left( \varepsilon^{ab}\hspace{4pt} - \,
    \epsilon^{abc}\,n_c \right)E_b\,+\left(\hspace{9pt} \gamma^a{}_b +
    s_b{}^a - \delta_b^a s_c{}^c\right) {B}^b +
  {\alpha}\,B^a \,, \\ {\cal H}_a\!&=\!&\left( \mu_{ab}^{-1}
    - \hat{\epsilon}_{abc}m^c \right) {B}^b\hspace{2pt} +\left(- \gamma^b{}_a +
    s_a{}^b - \delta_a^b s_c{}^c\right)E_b\hspace{1pt} -
  {\alpha}\,E_a\,.\label{explicit''}
\end{eqnarray}
Here $\epsilon^{abc}= \hat{\epsilon}_{abc}=\pm 1,0$ are the
3-dimensional Levi-Civita symbols, with
$\epsilon^{123}=\hat{\epsilon}_{123}=+1$. As can be seen from our
derivation, ${\alpha}$ is a 4-dimensional pseudo (or axial) scalar,
whereas $s_c{}^c$ is only a 3-dimensional scalar. The cross-term
$\gamma^a{}_b$ is related to the Fresnel-Fizeau effects.  The skewon
contributions $m^c,n_c$ are responsible for electric and magnetic
Faraday effects, respectively, whereas the skewon terms $s_a{}^b$
describe optical activity. Equivalent constitutive relations were
formulated by Serdyukov et al.\ \cite{Serdyukov}, p.86, and studied in
quite some detail.

\subsection{Some applications of premetric structures}

The theory of a possible {\it skewon} part of (\ref{constit7}) lies in
its infancy, see \cite{SkewonPLA,SkewonPRD}.
The {\it axion} part was widely neglected in the literature, if not
even put to zero right away \cite{Post}. As we can see from
(\ref{constit7}) and (\ref{explicit'}), the axion piece obeys
\begin{equation}\label{axion}
  ^{(3)}\!\check{H}^{ij}=\frac 12\alpha\,\epsilon^{ijkl}{\cal F}_{kl}\,
  \qquad\text{or}\qquad\left\{\begin{array}{l}
      {\cal D}=\hspace{8pt} \alpha B \\{\cal H}=-\alpha E
    \end{array}\right\}.
\end{equation}

\noindent$\bullet$ Tellegen \cite{Tellegen1,Tellegen2} introduced the
{\it gyrator}, with $\alpha=const$, as a new device in the theory of
two-port networks that ``rotates'' the field strength $(B,E)$ into the
excitation $({\cal D},{\cal H})$---that is, ``voltages'' into
``currents''---and vice versa, see \cite{Postconstraint}.\medskip

\noindent$\bullet$ In the {\it axion-electrodynamics} of Wilczek
\cite{Wilczek}, the axion piece as a field is added to
(\ref{Kottler}),
\begin{equation}\label{Kottler'}
  \check{H}^{ij}=\left(\lambda_0\,\sqrt{-g}g^{ik}g^{jl}
+\frac{1}{2}\alpha(x)\epsilon^{ijkl}\right)F_{kl}\,,
\end{equation}
see also Itin \cite{YakovAxion}. Moreover, kinetic terms for the axion
are added in order to make the axion a propagating field.\medskip

\noindent$\bullet$ Lindell \& Sihvola \cite{PEMC,PEMCAdP}, again for
$\alpha=const$, defined the {\it perfect electromagnetic conductor} (PEMC)
via (\ref{axion}). Hopefully the PEMC can be realized by suitable
metamaterials, see Sihvola \cite{metaAri}. Lindell \& Sihvola arrived
at the PEMC when studying electrodynamics in its 4-dimensional
version. Then the minus sign in ${\cal H}=-\alpha E$ emerges naturally.
Note, ${\cal D}=-sB$ and ${\cal H}=-sE$, with $s:=s_c{}^c$, see
(\ref{explicit'}), represent a (spatially) isotropic skewon that is
only a 3-dimensional scalar. Thus, the relative sign in the second
column of (\ref{axion}) is decisive.\medskip

\noindent$\bullet$ On the basis of experiments in solid state physics,
we were able to show \cite{PRA} that in Cr$_2$O$_3$ a phase can occur
(below the Curie temperature) that obeys the relation (written in
terms of exterior forms) $ ^{(3)}\!H=\alpha {\cal F}$, with $\alpha\approx
10^{-4}\lambda_0$. This proves that $H$ is a form with twist and $\cal
F$ one without twist thereby demonstrating the consistency of the
system $dH=J,\; d{\cal F}=0\, \text{and}\, ^{(3)}\!H=\alpha {\cal F}$.

\section{Premetric electrodynamics in exterior calculus}

One of the principal goals of exterior calculus is to put equations,
in the case under consideration, Maxwell's equations and the
constitutive law, into a manifestly coordinate independent form. In a
way, in exterior calculus, the principle of coordinate covariance is
built-in. If we handle the 2-form $H$, we handle a geometrical quantity
which does not depend on coordinates at all. Only if we are interested
in its components $H_{ij}$, with $H=\frac 12\,H_{ij}dx^i\wedge dx^j$,
then these components are, of course, coordinate dependent. Thus, the
Maxwell equations as such, namely $dH=J$ and $d{\cal F}=0$ are just
relations between forms, coordinates do not play a role. Naturally,
such a calculus expresses the universality of Maxwell's equations in a
particular impressive way.

Let us derive the Maxwell equations in modern language {\it ab ovo} in
order to liberate the physics of Maxwell's equations from historical
ballast, see \cite{Birkbook} for details. Electrodynamics is based on
two conservation laws. First, we have {\it electric charge
  conservation} (first axiom). The charge-current density 3-form $J$
is closed $dJ=0$ and, by de Rham's theorem, also
exact, \begin{equation}\label{Maxinh}dH=J,\end{equation} with the
excitation 2-form $H$ as ``charge-current potential'' \cite{TT}. This
is already the inhomogeneous Maxwell equation.

The current $J$ is a 3-form {\it with} twist ``since an electric
charge has no screw-sense,'' cf.\ Schouten \cite{Schouten}. As a
consequence, the excitation $H$ also carries twist or, in the words of
Perlick \cite{Perlick} (my translation), ``...one {\it must}
understand the excitation as a form with twist if one wants that the
charge contained in a volume always has the same sign, independent of
the orientation chosen.''

We decompose the 4-dimensional excitation $H$ into two pieces: one
along the 1-dimensional time $t$ and another one embedded in
3-dimensional space ($a,b=1,2,3$). We find (see \cite{Birkbook})
\begin{equation}\label{cutexcitation}
  H=-{\cal H}\wedge dt + {\cal D}=-{\cal H}_adx^a\wedge dt+\frac
  12{\cal D}_{ab}dx^a\wedge dx^b
\end{equation}
which, if put in matrix form, yields the identification
(\ref{Gtwiddle})$_1$. Substitution of (\ref{cutexcitation}) into
(\ref{Maxinh}) leads to the 3-dimensional inhomogeneous Maxwell
equations,
\begin{equation}\label{dH}
   \underline{d}\,{\cal D}=\rho\,,\qquad
   \underline{d}\,{\cal H}-\dot{{\cal D}}=j\,,
\end{equation}
i.e., to the Coulomb-Gauss and the Oersted-Amp\`ere-Maxwell laws,
respectively.  The underline denotes the 3-dimensional exterior
differential and the dot differentiation with respect to time.

With charge conservation alone, we arrived at the inhomogeneous
Maxwell equations (\ref{Maxinh}). Now we need some more input for deriving
the homogeneous Maxwell equations. The force on a charge density is
encoded into the axiom of the {\em Lorentz force density\/} (second
axiom)
\begin{equation}\label{Lorentz}
  f_\alpha =(e_\alpha\rfloor {\cal F})\wedge J\,.
\end{equation}
Here $e_\alpha$ is an arbitrary (or anholonomic) frame or tetrad, a
basis of the tangent space, with $\alpha=0,1,2,3$, and $\rfloor$
denotes the interior product (contraction). In tensor language, we can
express (\ref{Lorentz}) as $\check{f}_i={\cal F}_{ik}
\,\check{J}^k$. The axiom (\ref{Lorentz}) should be read as an
operational procedure for defining the electromagnetic field strength
2-form ${\cal F}$ in terms of the force density $f_\alpha$, known
{}from mechanics, and the current density $J$, known {}from charge
conservation. According to (\ref{Lorentz}), the field strength $\cal
F$ turns out to be a 2-form without twist. Its 1+3 decomposition reads
\begin{equation}\label{Fdecomp}
  {\cal F}=E\wedge d\sigma+B=E_adx^a\wedge dt +\frac 12
  B_{ab}dx^a\wedge dx^b\,,
\end{equation}
which yields the identification (\ref{Gtwiddle})$_2$.

{\em Magnetic flux conservation\/} is our third axiom.  The field
strength $\cal F$ is closed, \begin{equation}\label{Maxhom}d{\cal
    F}=0\,.\end{equation} This is the homogeneous Maxwell
equation. Split into 1+3, we find
\begin{equation}\label{dB}
\underline{d}\,E+\dot{B}=0\,,\qquad \underline{d}\,B=0\,,
\end{equation}
that is, Faraday's induction law and the sourcelessness of $B$. The
laws (\ref{dB}) are also premetric. The Lenz rule, as the reason for
the relative sign difference between the time derivatives in
(\ref{dH})$_2$ and (\ref{dB})$_1$, is discussed in
\cite{ItinAdP,ItinHehl}.

We have then the Maxwellian set\footnote{Damour \cite{Thibault}
  discussed Maxwell's equations in exterior calculus in his footnote
  1. He found $\delta f=s$ and $\delta\star F=0$. The codifferential is defined
  according to $\delta:=\star d\star$. For a p-form $\psi$ we have
  ${\star\star}\psi=(-1)^{p-1}\psi$. For the homogeneous equation we
  find $\star d{\star\star}F=-\star dF=0$ or $dF=0$, which coincides
  with (\ref{qaz})$_2$. Thus $F$ can be identified with the field
  strength $\cal F$. We apply the star to Damour's inhomogeneous
  Maxwell equation and find $\star\left(\delta
    f\right)={\star\star}d{\star}f=d\star f=S :=\star s$ or $d\star
  f=S$. This equation only agrees with (\ref{qaz})$_1$, provided we
  put $H=\star f$. Consequently, in Damour's exterior calculus, $f$
  loses its operational interpretation as electromagnetic
  excitation. Of course, the codifferential $\delta$ is not required for the
  formulation of the Maxwell equations (\ref{qaz}). The exterior
  differential $d$ is sufficient.}
\begin{equation}\label{qaz} dH=J \qquad\text{and}\qquad d{\cal
    F}=0\,.\end{equation} If decomposed into components, we recover
the tensor calculus formulas in (\ref{MaxPost'}). This closes our
considerations on the appropriate form of Maxwell's equations in
4-dimensional spacetime. For vacuum, the Hodge star maps the 2-form
$\cal F$ without twist into the 2-form $H$ with twist according to
\begin{equation}\label{qaz1}
H=\lambda_0\,^\star{\cal F}
\end{equation}
---this is equivalent to (\ref{Kottler}). The Hodge star, as applied
to 2-forms in 4 dimensions, depends only on the conformally invariant
part of the metric, see, e.g., Frankel \cite{Ted} and Kastrup
\cite{Kastrup}. The constitutive relation for axion-electrodynamics
simply reads
\begin{equation}\label{qaz1'}
H=\lambda_0\,^\star{\cal F}+\alpha{\cal F}\,,
\end{equation}
that is, for the PEMC we have simply $H=\alpha{\cal F}$. For matter we
have the relation
\begin{equation}\label{qaz2}
H=\kappa({\cal F})
\end{equation}
as analog of (\ref{Pconst0}). If the operator $\kappa$ is local and
linear, we find for its components
\begin{equation}\label{qaz3}
  \kappa_{ij}{}^{kl}=\frac 12\hat{\epsilon}_{ijmn}\chi^{mnkl}\,.
\end{equation}

\section{Minkowski's discovery of the energy-momentum tensor}

Minkowski's ``greatest discovery was that at any point in the
  electromagnetic field {\em in vacuo} there exists a tensor of rank 2
  of outstanding physical importance. \ldots{\em each component of the
    tensor} $E_p{}^q$ {\em has a physical interpretation,} which in
  every case had been discovered many years before Minkowski showed
  that these 16 components constitute a tensor of rank 2. The tensor
  $E_p{}^q$ is called the {\em energy tensor} of the electromagnetic
  field.''

  These words of Whittaker \cite{Whittaker}, Vol.\ 2, pp.\ 66 and 67,
  stress the central importance of this discovery. Einstein wouldn't
  have been able to derive the field equations of gravity of general
  relativity without being aware of this important quantity that
  figures as source of his (and Hilbert's) field equation of
  gravity. Einstein's reason for picking the scheme (\ref{akademie}),
  and thus (\ref{MaxPost}) with (\ref{Kottler})$_1$, was that this
  allowed him to derive the energy-momentum tensor of the
  electromagnetic field in a more transparent way than Minkowski.

  Minkowski starts with his ``field vectors'' $f$ and $F$, as
  specified in (\ref{fF}), and multiplies them as matrices according
  to $fF$. The product matrix he decomposes, without giving any
  motivation, into a tracefree piece ${S}$ (that is, with
  $\text{tr}\,{S}=0$), which he calls a spacetime matrix of the 2nd
  kind, and a trace piece ${\cal L}\,\mathbf{1}$, with the unit matrix
  $\mathbf{1}$ and with ${\cal L}:=-\frac 14\text{tr}(fF)$, which
  Minkowski identifies correctly as the Lagrangian density $\frac 12(
  H\!\cdot\! B-D\!\cdot\! E)$ of the electromagnetic field. He wrote,
  if we formulate it compactly in the notation of Cartesian tensor
  calculus,
\begin{equation}\label{matrix}
  S_{hk}=f_{hl}F_{lk}-\frac 14\delta_{hk}f_{lm}F_{ml}\,,\qquad\text{that is,}
  \qquad S_{hh}=0\,.
\end{equation}

In order to display the reality relations appropriately, he wrote his
spacetime matrix as
\begin{equation}
  {S}=\left(S_{hk}\right)=\left(\begin{array}{cccc}
      S_{11}&S_{12}&S_{13}&S_{14}\\
      S_{21}&S_{22}&S_{23}&S_{24}\\
      S_{31}&S_{32}&S_{33}&S_{34}\\S_{41}&S_{42}&S_{43}&S_{44}\end{array}
  \right)=\left(\begin{array}{cccc}X_x&Y_x&Z_x&-iT_x\\
      X_y&Y_y&Z_y&-iT_y\\X_z&Y_z&Z_z&-iT_z\\-iX_t&-iY_t&-iZ_t&T_t
   \end{array} \right).
\end{equation}
With the help of (\ref{matrix}), Minkowski identifies explicitly the
Maxwell stress (momentum flux density)
\begin{eqnarray}\label{MaxStress}
X_x&=&\frac 12\left(D_xE_x-D_yE_y-D_zE_z+H_xB_x-H_yB_y-H_zB_z
 \right)\,,\nonumber\\
X_y&=&D_yE_x+H_xB_y\,,\\
Y_x&=&D_xE_y+H_yB_x\,\quad\text{etc.}\,,\nonumber
\end{eqnarray}
the Poynting vector (energy flux density)
\begin{eqnarray}\label{Poynting}
T_x=H_zE_y-H_yE_z\,\quad\text{etc.}\,,
\end{eqnarray}
and the electromagnetic energy density
\begin{eqnarray}\label{energy}
  T_t=\frac 12\left(D_xE_x+D_yE_y+D_zE_z+H_xB_x+H_yB_y+H_zB_z \right)\,.
\end{eqnarray}
He did not name the electromagnetic momentum density
$X_t,Y_t,Z_t$---which, by Lebedev \cite{Lebedew}, had already been
discovered experimentally in 1901. Note that Minkowski's
energy-momentum tensor is asymmetric in general and thus, because of
its tracelessness, has 15 independent components (for the algebraic
properties of energy-momentum currents, see Itin
\cite{YakovAlgebraic}).

We leave this historical track and turn first to {\it tensor
  calculus:} Starting with the Lorentz force density
$\check{f}_i={\cal F}_{ij}\check{J}^k$, substituting the inhomogeneous
Maxwell equation (\ref{MaxPost})$_1$, and using (\ref{MaxPost})$_2$,
we arrive at the Minkowski energy-momentum tensor density\footnote{If
  we use $\check{H}^{ij}=\frac 12\epsilon^{ijkl}H_{kl}$, then
  ${\cal T}_i{}^j=\frac{1}{4}\,\epsilon^{jklm}\left(H_{ik}{\cal
      F}_{lm} -{\cal F}_{ik}H_{lm}\right)$.  It is remarkable that
  Ishiwara \cite{Ishiwara} in 1913, inspired by Minkowski's formalism,
  displayed the energy-momentum tensor as $\mathbf{T}=-\frac
  12\left\{\left[\left[\mathbf{H}^*\mathbf{F}^* \right]\right]-
    \left[\left[\mathbf{F}\,\mathbf{H} \right]\right]\right\}$.}
\begin{equation}\label{ff}
  {\cal T}_i{}^{j}=\frac{1}{4}\delta_i^j {\cal F}_{kl}\check{{H}}^{kl}
  -{\cal F}_{ik}\check{{H}}^{jk}\,,\qquad {\cal T}_k{}^k=0\,,
\end{equation}
together with $ \check{f}_i=\partial_j {\cal T}_i{}^{j}+{\cal X}_i$
and the auxiliary force density $ {\cal X}_i= \frac{1}{4}
\left[\left( \partial_i {\cal F}_{jk}\right)\check{{H}}^{jk}- {\cal
    F}_{jk} \,\partial_i\check{{H}}^{jk}\right]$. Incidentally,
already Minkowski proved \cite{Grundgleichungen} that $ {\cal
  T}_i{}^j\,{\cal T}_j{}^k = \frac{1}{4 }\,\delta_i^k\,{\cal T}^2$,
with ${\cal T}^2:={\cal T}_l{}^m{\cal T}_m{}^l$, a formula
that was repeatedly rediscovered.

For {\it vacuum,} $ \check{H}^{ij}=\lambda_0\, \sqrt{-g}g^{ik}g^{jl}\,
F_{kl}$, and thus, in {\it Cartesian coordinates}
[$g_{ij}=\text{diag}(1,-1,-1,-1$)], the auxiliary force density ${\cal
  X}_i=0$. Then ${\cal T}_{ik}:=g_{kj} {\cal T}_i{}^j={\cal T}_{ki}$
is symmetric and conserved, see \cite{Birkbook} for details---and we
recover the result of Einstein \cite{Einstein1916}. At the same time,
under those two conditions (vacuum and Cartesian coordinates),
Minkowski's formula $K=$ lor $S\,$ re-emerges, where $K$ is the
4-dimensional Lorentz force density and $S$ Minkowski's
energy-momentum matrix.

In {\it exterior calculus} we can apply an analogous procedure and
find the energy-momentum 3-form as
\begin{equation}\label{Sigma}
  \Sigma_\alpha :={\frac 1 2}\left[{\cal F}\wedge(e_\alpha\rfloor
    H) - H\wedge (e_\alpha\rfloor {\cal F})\right]\,,\qquad
  \vartheta^\alpha\wedge\Sigma_\alpha=0\,,
\end{equation}
where $e_\alpha$ denotes the frame (tetrad) and $\vartheta^\alpha$ the coframe, with
$e_\alpha\rfloor\vartheta^\beta=\delta_\alpha^\beta$. The expression (\ref{Sigma})$_1$
translates into (\ref{ff})$_1$ via $\Sigma_\alpha={\cal
  T}_\alpha{}^\beta\,^\star\!\vartheta_\beta$. Accordingly, the formulas (\ref{ff})
and (\ref{Sigma}) incorporate Minkowski's energy-momentum of the
electromagnetic field in a modern notation.

Apparently Minkowski's energy-momentum tensor is defined for matter,
in particular also for {\it moving matter}. Abraham
\cite{Abraham1,Abraham2,Abraham3} introduced a symmetric tensor
instead, since the symmetry was believed to be important from the
point of view of angular momentum conservation, amongst other
reasons. The dispute between the supporters of the Minkowski and the
Abraham tensor is lingering on till today. Obukhov \cite{YuriAnnalen}
reviewed this problem, partly following
\cite{energy-m1,Birkbook,energy-m2}. Obukhov \cite{YuriAnnalen} based
his discussion on a general Lagrange-Noether framework. He recovers
the Minkowski tensor as the {\it canonical} energy-momentum and shows
that the balance equations of energy-momentum and angular momentum are
always satisfied for an open electromagnetic system because of the
asymmetry of the canonical tensor. Moreover, Obukhov is able to
formulate an ``abrahamization'' prescription for symmetrizing a given
asymmetric energy-momentum tensor, provided a timelike vector is
available (a velocity of a medium, for example). Obukhov considers an
ideal fluid with isotropic electric and magnetic properties
interacting with the electromagnetic field. Thereby Obukhov resolves
the perennial Abraham-Minkowski controversy and assigns the
appropriate places for the Minkowski as well as for the Abraham
tensor.

\section{Discussion}

Compare, in vacuum, Minkowski's system
\begin{eqnarray}\label{Minkowski}
  \left\{\text{lor}\right.\! f=\left.\!\!-s,\quad\text{lor}\,F^*=0;
    \quad f=F\right\},
\end{eqnarray}
with the system in exterior calculus
\begin{eqnarray}\label{Exterior}
  \left\{\right.\!\! dH=J,\left.\hspace{-4pt}\qquad d{\cal F}=0;
\hspace{-4pt}\qquad H={}^\star {\cal F}\right\}.
\end{eqnarray}
The first system is Poincar\'e covariant, the second one generally covariant.

Equation (\ref{Minkowski}) is a special case of
(\ref{Exterior}). Since in Minkowski's formalism \,lor $F^*=0$ in its
version (\ref{MinMax'})$_2$ is already generally covariant, we rewrite
it tentatively as $\,(\text{lor}^*)\,F=0$ and identify
$\text{lor}^*\rightarrow d$. Then, the inhomogeneous equation becomes
$(\text{lor}^*)\,f^*=s\>$ or $\>d\, f^*=s$, and we arrive at
$  \left\{d\,f^*=s,\> dF=0; \
    f=F\right\}$,
  or at (\ref{Exterior}), provided we identify $H\rightarrow{} f^*$
  and ${\cal F}\rightarrow -F$. Roughly we could say that in the
  transition from (\ref{Minkowski}) to (\ref{Exterior}) the star
  migrated from the Maxwell equations to the constitutive relation for
  the vacuum. Of course, the system (\ref{Minkowski}) is now
  history. The set (\ref{Exterior}), which was derived from a
  reasonable axiomatics of Maxwell's theory, has superseded it. Still,
  we find it remarkable how powerful Minkowski's formalism is and how
  closely (\ref{Exterior}) resembles (\ref{Minkowski}).

And in exterior calculus Minkowski's energy-momentum matrix $S_{hk}$
finds its particular compact expression as energy-momentum 3-form
\begin{equation}\label{XXX}
  \Sigma_\alpha :={\frac 1 2}\left[{\cal F}\wedge(e_\alpha\rfloor H) -
    H\wedge (e_\alpha\rfloor {\cal F})\right]\,.
\end{equation}
Summing up: The Maxwell equations $dH=J$, $d{\cal F}=0$, the Lorentz
force density $f_\alpha=(e_\alpha\rfloor{\cal F})\wedge J$, and Minkowski's
energy momentum `tensor' (\ref{XXX}) represent the framework of
premetric electrodynamics. As such, they are a modern generally
covariant expression of Minkowski's 4-dimensional Poincar\'e covariant
theory of electromagnetism.

\begin{acknowledgement}
  I am very grateful to Yuri Obukhov (Moscow) for thorough and
  detailed discussions on the subject of this article. Moreover, I
  would like to thank the following colleagues and friends for reading
  my article and for coming up with numerous suggestions and
  corrections: Gerhard Bruhn (Darmstadt), Hubert Goenner
  (G\"ottingen), Yakov Itin (Jerusalem), Bernard Jancewicz
  (Wroc{\l}aw), Florian Loebbert (Golm), Bahram Mashhoon (Columbia,
  Missouri), G\"unter Nimtz (K\"oln), Dirk P\"utzfeld (Golm),
  Guillermo Rubilar (Concepci\'on), Tilman Sauer (Pasadena), Gerhard
  Sch\"afer (Jena), Engelbert Sch\"ucking (New York), Ari Sihvola
  (Helsinki), and Yosef Verbin (Tel Aviv). At an earlier stage, this
  work was supported partly by the Deutsche Forschungsgemeinschaft
  (Bonn) with the grant HE 528/21-1.
\end{acknowledgement}

redpajama_set_name: RedPajamaArXiv


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text:
DC mayor closes Wharf fish markets after patrons fail to follow social distancing guidelines
People who were at the Wharf fish markets did not appear to be practicing social distancing, so they were shut down. A strong police presence is now in the area.
Author: Nick Boykin (WUSA9), Sarah Konsmo
Published: 5:08 PM CDT April 4, 2020
Updated: 4:56 PM CDT April 6, 2020
WASHINGTON — The vendors at the Municipal Fish Market in D.C.'s Wharf community are closed after it was clear that many of the people there on Saturday were not practicing social distancing guidelines to help mitigate the spread of COVID-19, D.C. Mayor Muriel Bowser said Sunday.
"The notice shall remain in effect until April 24 which is the last day of the public health emergency (subject to change)," Bowser said. "Since food is essential, the operators will be able to present a plan for social distancing to DCRA. If the plan allows for safe operations, the venue will be allowed to reopen, and DCRA and D.C. Health would continue to monitor compliance."
Bowser on Monday said that she's food policy team to look at all options on how to make sure people can get in and out of the market, while also enforcing the social distancing policies that have been put in place.
Many employees arrived Sunday morning for work not knowing about the closure.
Captain Billy White owns three stalls at the market. He said he spent $1,800 on private security to keep social distancing in check Saturday. But, crowds were bigger than they anticipated, White said.
White said he was working with D.C. police Saturday night on a better social distancing plan, but learned about the emergency closure late last night.
According to officials, the rest of The Wharf neighborhood remains open for essential needs to members of the community, including carryout and delivery.
While some patrons to the fish market on Saturday were wearing gloves and masks on, many were not following the Centers for Disease Control and Prevention guidelines to limit the spread of the virus.
A merchant at the fish market was captured by WUSA9, even telling a customer to stay six-feet away, or that they would be "shut down."
The Wharf Community Association released the following statement Sunday about the closure.
"The health and safety of our community and the general public is of paramount importance to everyone at The Wharf.
At the request of the District of Columbia, we urged the Fish Market vendors to implement and enforce distancing guidelines to reinforce the Mayor's Order during the COVID-19 public health emergency. In an effort to further reduce crowds, the vendors at the Municipal Fish Market have been temporarily closed by the District of Columbia. We respect the decision of the Department of Consumer and Regulatory Affairs (DCRA) to shut down the sale of seafood from barges at the Municipal Fish Market. If the Fish Market vendors can satisfy DCRA that sufficient measures will be taken so that they can operate safely, we likewise will respect a future decision of DCRA to allow the Fish Market vendors to reopen. The Wharf neighborhood remains open only for essential access to peoples' homes, offices, hotels, and businesses—including groceries, carryout and delivery food service, in accordance with the Mayor's Order. All of us at The Wharf will continue to encourage complete compliance with the Mayor's mandate in this most challenging time." - The Wharf Community Association
D.C. police said that tickets were given out by city parking enforcement on cars that surrounded the fish market, but other types of enforcement of the stay-at-home order were not discussed by the department with WUSA9.
D.C.'s stay-at-home order, which went into effect on Monday, essentially made it law to practice social distancing. It also gave police the authority to enforce the order handed down by Bowser.
D.C. was the last in the DMV to implement a stay-at-home order and came after Gov. Larry Hogan of Maryland and Gov. Ralph Northam of Virginia sent down similar orders in their states.
Places like fish markets, meat markets and other types of food markets can be labeled as essential businesses under the stay-at-home order issued for the District.
The Wharf is home to multiple fish markets, seafood eateries and a variety of bars and restaurants. It is also a popular gathering spot for D.C. residents year-round and is also home to the popular music venue "The Anthem."
There are about 150 people who work at the fish market-plus the fishermen they buy from, White said. During the closures, he said his 50 employees would receive a full day's wage, despite the closure.
RELATED: 'This is the moment to not be going to the grocery store' | White House coronavirus expert suggests DC's a potential virus hot spot
RELATED: At funerals in virus outbreak, mourning is from a distance
RELATED: How to make your own face mask without a sewing machine
RELATED: Olympian Dominique Dawes offers creative ways to stay fit during pandemic
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redpajama_set_name: RedPajamaCommonCrawl


text:
Home » Why conservatorship of Fannie and Freddie must end
From HW Magazine
Why conservatorship of Fannie and Freddie must end
Working people need access to responsible and sustainable mortgage loans
KEYWORDS Fannie Mae Freddie Mac National Community Reinvestment Coalition
Recently, in the pages of HousingWire and elsewhere, housing policy consultant Barry Zigas has called into question the motives of affordable housing and civil rights groups advocating for ending the conservatorship of Fannie Mae and Freddie Mac and suggested that ending their conservatorship is Wall Street's preferred solution.
This is deeply ironic given the fact that the Johnson-Crapo framework for housing finance reform Zigas supports is favored and backed by Wall Street banks. Those who live in glass houses shouldn't throw stones, especially when they are just wrong.
Let's first address why the National Community Reinvestment Coalition has been so deeply engaged in this conversation and debate about the fate of Fannie Mae and Freddie Mac.
NCRC's sole purpose in the housing finance reform debate, from which we have never wavered, is to make sure that working people have access to responsible and sustainable mortgage loans. It is nonsense and disingenuous to suggest that the hedge funds involved in this debate have any influence on us whatsoever.
The fate of the Fannie and Freddie investors is not our concern. We are concerned about what happens to communities. And what is happening right now is that the future ability of working class families to obtain responsible home loans is in serious jeopardy.
The stakes are high.
The best option for communities at this juncture is to recapitalize Fannie and Freddie, end their conservatorship, and continue the reforms of the entities begun with the Housing and Economic Act. It's essential that this administration act now to begin to undertake these steps.
There seems to be the notion, coming from Zigas and others, that the GSEs can just sit in conservatorship until "the stars align" for the passage of a perfect comprehensive legislative solution.
This is a deeply flawed assumption, for several reasons. Even Federal Housing Finance Agency Director Mel Watt, who oversees the conservatorship, has conceded that "…staying in conservatorship is just not sustainable."
Advocates for an indefinite conservatorship don't acknowledge that Fannie and Freddie are on a path to being dismantled. They are literally winding down.
The Federal Housing Finance Agency's Office of the Inspector General observed that the GSEs may not be able to sustain profitability as they wind down their investment portfolios, eliminate their capital cushion, and so on. Mel Watt has also opined that the GSEs may not be able to attract qualified staff moving forward. As Fannie and Freddie wind down, the risk that they will have to draw on government funds, which could create a shock to the market, increases precipitously.
As Josh Rosner, Glen Corso and others have pointed out (see Industry Pulse, page 64), the conservatorship is having a real chilling effect on the activities of the GSEs, and has resulted in an excessive tightening of credit.
There is also the simple fact that for most of their history, when Fannie and Freddie were not under conservatorship, they did a significantly better job securitizing responsible loans to working Americans, including families of modest means.
The GSEs would also be operating in a much-improved regulatory environment and a more safe and sound financial system by virtue of the Dodd-Frank reforms.
The GSEs have been reformed themselves as well: HERA included significant reforms to the GSEs' regulator, their capital standards, their portfolio limits and their prudential management and operations.
It's worth noting that all of the uncertainties that Zigas raises about liquidity, cost, and so on, are uncertainties that would also exist, and indeed would be even greater in the case of a brand new system in the form of the Johnson-Crapo framework.
Zigas himself has acknowledged that the cost of mortgages would rise under the Johnson-Crapo model.
In the case of Fannie and Freddie, they have a proven track record of doing a very good job at creating broad access to responsible loans for most of their history. That's a lot more to go on than a nebulous hope for comprehensive legislative reform down the road that would put in place something that's completely untried and untested.
Fannie and Freddie also already have critically important affordable housing goals, which have not been included in any of the legislation to replace the GSEs. The goals
help to make sure that all creditworthy borrowers have access to responsible mortgage credit – whether they are in urban or rural communities, or moderate-income or low-income communities.
None of the legislative proposals to gain serious congressional consideration have included affordable housing goals. The proposal that was the foundation for the Johnson-Crapo legislation stated that "Neither the Public Guarantor nor MBS issuers should be subject to numerical housing goals or quotas."
In that way alone, all of these legislative proposals have been inferior to our existing system.
Gretchen Morgenson of The New York Times recently put a spotlight on Wall Street banks' efforts to "muscle out" Fannie and Freddie.
She noted that there has been a considerable revolving door between the industry and Obama administration housing posts. It's clear that there is a well-organized, orchestrated effort to reconstitute the housing finance system in a new shape that mainly benefits Wall Street banks and doesn't do nearly enough to help working communities.
Does handing over Fannie and Freddie's role to Wall Street institutions, whose reckless and abusive practices included securitizing millions of unsafe, unsound unsustainable predatory mortgages, sound like a good idea to you?
For all of these reasons, at this juncture, many affordable housing advocates look at this picture and see the need for immediate action to preserve Fannie, Freddie, the public mission in their charters, and their affordable housing goals.
While some seem content to kick the can down the road and hope it turns to gold, we are not. The big question: is the Obama Administration?
Inaction on the conservatorship could be remembered in the annals of history as a very bad decision.Homeownership is the single most common way working-class Americans build equity and wealth. Let's not unwittingly undermine this proven system by eliminating Fannie and Freddie and the affordable housing goals.
The end of Fannie, Freddie conservatorship? Trump reportedly picking Mark Calabria to lead FHFA
End of conservatorship? Trump administration proposes privatizing Fannie Mae, Freddie Mac
Investors Unite forges ahead with plan to end Fannie, Freddie conservatorship
John Taylor is president and CEO of the National Community Reinvestment Coalition and has more than 25 years experience in the field.


Inter House Competitions are conducted to tap the talents and to develop the true competitive spirit. Students get to participate in events like Elocution, Theatre/Drama, Debates, Quiz Sessions, Dance, Exhibitions and many more. The school has a robust Students' Council both at both the branches.
The following are the portfolios.
The House guardian of each group guides the students' Council to keep order in the school, and in conducting competitions.
We have an NCC wing that provides opportunities to the students for their all round development with a sense of Duty, Commitment, Dedication, Discipline and Moral Values, so that, they become able leaders and useful citizens.
The mission of Scouting is to contribute to the education of young people, through a value system based on the Scout Promise and Law to help build a better world where people are self-fulfilled as individuals and play a constructive role in the society.


Marc Viera, LMHC is a counselor in New Bedford, MA. He specializes in counseling and addiction and substance abuse counseling.
He truly cares about my son. His advice does help my son do better in school and at home. And he is a great positive role model for him as well. He's also very easy to talk to.
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I've been thinking about this a little bit with the bad market. In talking to many other advisors, it seems some advisors are more concerned with getting the best returns or outperforming the benchmark by as much as they can. I understand the fun in that and also the fact that some clients seek that out.
But, having ACAT'd in numerous accounts, it is very apparent that the conservative portion of a portfolio is way overlooked. For whatever reason, possibly the fact that it pays less to implement or that it isn't as exciting as being "long and strong". That being said, do you feel you properly have addressed or do address this portion of clients' money? If not, why don't you spend more time on the conservative money portion? And after this market wreck, I don't consider the 40% bond allocation in a 60/40 portfolio to be safe.
And after this market wreck, I don't consider the 40% bond allocation in a 60/40 portfolio to be safe. Why? [/quote] Ice, I should've have excluded you from this thread. I know you're ok and somewhat legit. ;) I just feel with some bond values way way way down, even they aren't as conservative (in this environment) as some clients would like. And most bond portfolios aren't even diversified like they should be.
I put more time than before with the fixed income portion of my clients allocation this year when bonds started behaving badly. True, it was hard to look for bond funds that were supposed to go up when equities went down. That's why I'm short corporate bonds for now. However, there are (or were) good funds in intermediate to long term government bonds in the past two to three months. I've been more selective with the bond allocation rather than more diversified.
Snags, it's apparent you're leaning toward "safe money alternatives," i.e. annuities.
I've thought many times about finding a relatively conservative area in which to specialize (Munis, VAs, Fixed annuities) and doing nothing but that. I just have a hard time walking away from helping people create balanced portfolios via a variety of asset classes. I still have to believe that they'll benefit most from that approach over the long run. I've also grown suspicious about just how "safe" anything is these days. Insurance companies are changing and/or suspending their VA guarantees, fixed annuities are subject to all claims, munis are getting pounded, etc.
[quote=Borker Boy]Snags, it's apparent you're leaning toward "safe money alternatives," i.e. annuities.
I've thought many times about finding a relatively conservative area in which to specialize (Munis, VAs, Fixed annuities) and doing nothing but that. I just have a hard time walking away from helping people create balanced portfolios via a variety of asset classes. I still have to believe that they'll benefit most from that approach over the long run. I've also grown suspicious about just how "safe" anything is these days. Insurance companies are changing and/or suspending their VA guarantees, fixed annuities are subject to all claims, munis are getting pounded, etc.[/quote] I'm not walking away from long-term riskier investing. Quite the contrary. I'm just not going to seek it out. This is about sales. It's the time to build a substantial book of business. When the market has plummeted, people are scared. I want to sell to that fear in 2009. With my foot in the door, I can earn the riskier stuff later. Ultimately, I want to do what other advisors aren't doing. Let's face it. Most investors only hear about the "let's make money" side of things. Sure, some of you guys do more than that, but how many accounts have you ACAT'd in that have too much risk? Many advisors simply don't get excited over the safe stuff. What are you going to say on the phone that makes you sound different than everyone else? How many advisors call up and say, "I've got this yield, or I help plan for retirement, or I'll do a complimentary review"? That's what people hear every day. I ask myself, what's the easiest way to get all of a client's assets? I figure by going after what others aren't, getting it and servicing the heck out of them, my foot will be in the door and I'll be there when someone F's their other stuff up or doesn't service them as well.
I'm convinced that being market neutral is the way of the future to be conservative. I've been toying with some convertable arbitrage models. It's nothing new and almost all the hedge funds still alive are doing it. I think I can do just as well and get 7 to 9 % return reagardless of what the market does. I'm thinking that's the future of being conservative. That ans having 5 years in cash to ride out a business cycle without cashing in securities for pennies on the dollar.
Sounds familiar (Madoff) - I wouldnt say those words to any clients or prospects in this environment.!!
The idea of having sufficient reserves(perhaps even excess) makes a LOT of sense, and I think many advisors are hurting right now because they didn't follow that advice.
As for convert arb, it would be my understanding that lots of the hedgies got hurt in that strategy when normal interrelationships blew up…so might want to check into that carefully.
I sell a lot of whole life insurance because it's the best vehicle for someone's long-term savings dollars. Tax-free, creditor-protected (in my state), dividends that can't be wiped out by a downswing in the market, liquid. Plus, it's great to have a permanent death benefit when you are planning for retirement income.
But, having ACAT'd in numerous accounts, it is very apparent that the conservative portion of a portfolio is way overlooked. For whatever reason, possibly the fact that it pays less to implement or that it isn't as exciting as being "long and strong".
That being said, do you feel you properly have addressed or do address this portion of clients' money? If not, why don't you spend more time on the conservative money portion?
I don't think that brokers have overlooked the "conservative" portion of a client's portfolio, rather that the opinion of what "conservative" means from the clients perspective. It's one thing for the client to say they can stomach a 40% drop in the equity portion of their portfolio and a whole other to see a $200k (or whatever) cut in their net worth.
As far as going after that portion of a prospects account, I'd say take whatever piece they're willing to give you and as you said later, service the hell out of them to gather the rest.


Welcome to the 16th edition of the newsletter of the LAW&ICT Shared Virtual Campus project.
The registration in the LAW&ICT Shared Virtual Campus e-learning offer (LEFIS Master, LEFIS Specialization Certificates and LEFIS Courses of Professional Specialization) is open. The brochure that provides information about the courses is here.
Zaragoza, 4-5 Mayo de 2009. La invitación para enviar comunicaciones y participar en las Jornadas se encuentra AQUÍ.
Beja (Portugal, 7 May), Belfast (United Kingdom, 8-9 June), Istambul (Turkey, 29 June-10 July), La Laguna (Spain, May), Lisbon (Portugal, 8 May), Münster (Germany), Rovaniemi (Finnland, 27 April), Santa Catarina (Brasil, November), Vaasa (Finnland, 23-24 April), Vilnius (Lithuania, 2 March) and Zaragoza (Spain, 4-5 May).
LEFIS. This Newsletter will report about the celebration of the meetings.
e-Government", of the International Journal of Electronic Governance (IJEG) is here.
The Special Issue on Developments in Information Technology Law in South Africa JILT 2008 (2) is here.
News on the Free Knowledge Institute can be read here.
The published volumes of the LEFIS Series list is here. The content of the LEFIS Series, part of the LEFIS Digital Library, can be searched here.


Are you wondering if energy management is something for you? And if so, how to get started? Discover some of the basic functions of EnergyID and try it out for free.
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We try to represent everything as simple as possible. Energy monitoring is a complex thing, but we want the end user (that's you!) to be at the centre of it all.
With only a few meter readings we can already start to visualise your energy consumption.
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Groups give you access to the services of our partners. All services aim to increase your energy efficiency and reduce your CO2 impact.
As soon as you complete the registration, you are asked to create a record. In a record you can enter meter readings or consumption numbers of all meters in your home or building. Next, your consumption profile is calculated and you gain insight into your consumption via our graphs.
Groups are a way for local initiatives and organisations to follow the performance of multiple records. This enables them to provide the owners of those records with specific advice, or to set up actions that can benefit the whole group, like a group purchase. Check out the group overview and find groups in your neighbourhood.


text:
import { RowNode } from "../../entities/rowNode";
import { GridOptionsWrapper } from "../../gridOptionsWrapper";
import { Context } from "../../context/context";
import { EventService } from "../../eventService";
import { RowDataTransaction, RowNodeTransaction } from "./clientSideRowModel";
import { ColumnController } from "../../columnController/columnController";
import { GridApi } from "../../gridApi";
import { ColumnApi } from "../../columnController/columnApi";
import { SelectionController } from "../../selectionController";
export declare class ClientSideNodeManager {
    private static TOP_LEVEL;
    private rootNode;
    private gridOptionsWrapper;
    private context;
    private eventService;
    private columnController;
    private selectionController;
    private nextId;
    private static ROOT_NODE_ID;
    private getNodeChildDetails;
    private doesDataFlower;
    private isRowMasterFunc;
    private suppressParentsInRowNodes;
    private doingLegacyTreeData;
    private doingMasterDetail;
    private allNodesMap;
    private columnApi;
    private gridApi;
    constructor(rootNode: RowNode, gridOptionsWrapper: GridOptionsWrapper, context: Context, eventService: EventService, columnController: ColumnController, gridApi: GridApi, columnApi: ColumnApi, selectionController: SelectionController);
    postConstruct(): void;
    getCopyOfNodesMap(): {
        [id: string]: RowNode;
    };
    getRowNode(id: string): RowNode;
    setRowData(rowData: any[]): RowNode[];
    updateRowData(rowDataTran: RowDataTransaction, rowNodeOrder: {
        [id: string]: number;
    } | null | undefined): RowNodeTransaction | null;
    private executeAdd;
    private executeRemove;
    private executeUpdate;
    private addRowNode;
    private lookupRowNode;
    private recursiveFunction;
    private createNode;
    private isExpanded;
    private setLeafChildren;
    isLegacyTreeData(): boolean;
}

redpajama_set_name: RedPajamaGithub


Prime Minister Narendra Modi said on Saturday that "bitter medicine" might be needed to rescue the economy and restore the country's fiscal health even if the measures dent his popularity and hurt BJP in the short run.
The PM's blunt message after his vigorous `acche din aane waale hain' campaign is seen as an attempt to temper expectations over any dra matic turnaround of the economic situation while preparing the ground for unpopular measures.
"Tough decisions and strong measures in the com ing one or two years are needed to bring financial discipline that will restore and boost the country's self-confidence," Modi told party cadres.
"I need to take some harsh decisions and administer some bitter medicine in order to resuscitate this patient.
The medicine may hurt some of you but I ask for your support at this time," he added later at a separate event.
The prime minister's plainspeak follows the assessment in the government of the state of the economy being much worse than feared. The comments, coming weeks ahead of the Union Budget, are seen as an indication of austerity and a check on sops.
"I have taken over the reins of the country in circumstances when there is nothing left behind by the previous government. They left everything empty." he said.
PM Narendra Modi's emphasis on fiscal prudence — clear from his message to party cadres in Panaji on Saturday that he might have to administer "bitter medicine" to nurse the economy to good health — is driven by sluggish growth in tax collections in the wake of sub-5% growth, which has put the spotlight in curbing wasteful expenditure.
Modi's "no gain without pain" message is intended to put a lid on runaway government spending which will help curb borrowing and reduce pressure on interest rates. Lower rates should help households reduce mortage burdens and spur consumption. It will also result in higher investment by companies which can borrow more at reasonable rates.
The comments preparing BJP for a dip in popularity indicate that the PM will not be deterred by political considerations due to approaching polls in Maharashtra, Haryana, Jharkhand and possibly Delhi. This is the first time since taking over on May 26 that Modi has talked about the health of the economy and seems to be preparing the country for some short term pain.
"We won't be helping the country by praising Modi and praising BJP.
There is no guarantee that just singing praise of Modi would improve the situation. We need to take harsh measures to improve the financial situation," the PM said.
Later addressing around 150 special invitees at an event convened by Goa chief minister Manohar Parrikar, Modi said, "The nation's economy is in very bad shape and I have come to realize the huge quantum of work to be done." The PMO later put out a Twitter messages on its website. "Time has come to take tough decisions in the interest of the nation. Whatever decisions we take will be solely guided by national interest," the PM said in the message.


When ill.Gates waxes poetic on music production processes, it's clear that he's spent uncountable hours in the studio. In today's video, he shares some of his most valuable tips for anyone taking on the creative process of producing. Learn why "it's not over until someone kills a puppy" is reasonable music writing advice – watch the full video inside.
Prep/Nighttime: Shorter amount of time, good for sound design, plugins, making sounds and kits, organizing library, practicing finger drumming (essentially anything isn't writing music). This is more about exploring and experimentation.
Writing/Daytime: Treat this like you would a job – wake up early, focus entirely on writing the music for a long period. Get as much writing done as possible in one session!
Phase 1: Saying Yes – This is when you're creating new ideas, jamming. Putting down as many ideas as possible. Add as many things as you want to your project.
Phase 2: Saying No – Arrange the above ideas into a track "by subtracting, not by adding". Delete stuff from the first stage – you can't incorporate all of your ideas into one song.
Phase 3: Finishing Up – Finalize everything – flatten it down to audio stems. Mix rendered audio instead of live instruments (for the sake of processing power). Correct timing, and tidy things up. Mix again with fancy plugins and make small edits to your stems where needed (reverse things, pitch shift, etc).
ill.Gates likes to stand up for phase 1 – when jamming – not be sitting down. This is common in a lot of creative practices.
Buy monitor arms / trees and attach your various gear to. There are a number of low-cost options on Amazon – which tilt and rotate fully. Many pieces of gear won't have VESA mounts on the back of them, so try using heavy-duty Velcro instead!
You can also use your phone – ill.Gates recommends interval timers – he specifically uses Seconds Pro ($4.99 on the App Store) which allows you to allocate specific amounts of time for different studio tasks.
Find more ill.Gates' studio advice on ProducerDJ.com – including his Ill Methodology tutorial series.
Want to own some of ill.Gates' original finger drumming soundpacks? Check out the packs he released with DJ Techtools here.


text:
Salyan (), is a city and the capital of the Salyan District of Azerbaijan. The city of Salyan is industrialized and known for processing caviar.

History
The city has been a continuous settlement of sal tribe, after whom the city named and occupied by Kura river. Salyan was part of Quba Khanate during 1680 to 1782 and ruled by various khans. Salyan was the administrative center of the Javad Uyezd of the Baku Governorate.

Throughout its history, Salyan has suffered from floods because of its proximity to the river and the relatively low elevation of most of the town.

Geography

Demographics

Administrative divisions
The municipality of Salyan consists of the city of Salyan. The mayor, presently Sevindik Hatamov, embodies the executive power of the city.

List of City's mayors

Salyan Khanate
(1729–1748) Hasanbay Khan
(1748–1757) Ibrahim Khan Rudbary
(1757–1768) Kalb Ali Khan
(1768–1782) Qubad Khan

Azerbaijani SSR
(1920) Yusif Gasimov
(1961–1966) Huseyn Huseynov

Azerbaijan Republic
(1993) A.Yusubov
(1993–2004) Valihat Azizov
(2004) Yusif Alakbarov
(2004–2009) Rasim Bashirov
(2009–2011) Aliagha Huseynov
(2011–2016) Tahir Karimov
(2016–present) Sevindik Hatamov

Economy

Culture

Sport
Salyan was home to former football teams Plastik Salyan and Mughan. Mughan through its history played in the Azerbaijan Premier League.

Transport

Public transport
Salyan has a large urban transport system, mostly managed by the Ministry of Transportation.

Education

Notable residents

Some of the city's many prestigious residents include: philosopher Ali bey Huseynzade, mathematician Vagif Guliyev, lieutenant general Rail Rzayev, poet Khalil Rza Uluturk and footballer Samadagha Shikhlarov.

References

External links

World Gazetteer: Azerbaijan – World-Gazetteer.com
The ministry of Culture and Tourism of Azerbaijan Republic: Azerbaijan

Populated places in Salyan District (Azerbaijan)

redpajama_set_name: RedPajamaWikipedia


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I just read two articles, one pro toads in the garden, one con. I could use the toads for pest control, but one article said the the toad could be toxic for my dog if it drinks from her water bowl. I keep the water bowl in the garage for when my canine is on her tie out in the backyard, or in the grass or sidewalk when she is tethered in the front yard. Will this pose a problem if I try to attract the beneficial toads to control slugs and pests destroying my garden?
You should be ok. For the most part, toads will avoid water bowls just because of the fact that there is a large mammal (i.e. you dog) nearby. Could it happen, yes, but is it likely to happen, no. They are shy animals and are happiest hidden. If you provide enough moist areas, they will avoid more populated areas like waterbowls. They would have to be desperate to go near one.
On top of that, dogs normally learn their lesson really quick with toads. Just biting a toad can be an unpleasant and horrible tasting experience for a dog. They may do it once, but will learn very quickly what a toad tastes like and will avoid them thereafter.


The annual "WOMB PRESENTS NEW YEAR COUNTDOWN" will be held again this year. This year's guest is NIC FANCIULLI, who was nominated for a Grammy as a producer and has performed at ULTRA JAPAN, the major festival in Japan, for 2 years in a row.
Keep an eye on his future activities, as he went beyond the boundaries of a musical artist this year and announced his collaboration with Marc Jacques Burton, the famous fashion designer.
What makes this even more exciting is WOMB's uniquely extravagant countdown, which will include a sparkly confetti shower using a cannon! Bring in the new year with everybody!


text:
Comcast's wireless service dips toe into 5G waters with new Samsung Galaxy devices
By Michelle Caffrey Philadelphia Business Journal
With the arrival of ultra-fast 5G networks looming on the horizon in recent years, executives at Comcast have remained cautious, saying they're still evaluating its capabilities and, by extension, its potential to disrupt traditional broadband services.
Comcast's wireless service is now dipping its toe into the 5G waters, saying it will carry the 5G-capable Samsung Galaxy S20+ 5G and Galaxy S20 Ultra 5G when they're released nationwide. How the 5G wave will affect Comcast's broadband business, however, remains unclear.
The company first confirmed it will participate in the 5G market during last month's earnings call, saying Xfinity Mobile will resell Verizon's 5G service just as it resells capacity on Verizon's LTE network via a mobile virtual network operator agreement.
"One of the great things about our existing relationship
Xfinity Mobile, offered only to Comcast customers, was rolled out in 2017 and has since amassed more than 2 million lines. Executives have said customers are drawn to the ability to have both unlimited and pay-by-the-gig lines under one family plan, although it's not clear how 5G options will be priced moving forward.
"We continue to differentiate by delivering a better wireless experience for less money on the most popular devices – and we're excited to be able to bring the Samsung Galaxy S20+ 5G and S20 Ultra 5G to our customers, with plans to launch 5G data options soon so our customers can take full advantage of all these devices have to offer," Billy Stephens, senior vice president of wireless devices for Xfinity Mobile, said in a statement.


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text:
Mekong Region Legal Studies
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Scholarship Support for Students
Cambodia - Guangxi - Laos - Myanmar - Thailand - Vietnam - Yunnan
CMLC's Mekong Region Legal Studies Program (MRLSP) brings together students from throughout the Greater Mekong Subregion (GMS) for collaborative study of subjects of domestic and international public law, as well as other courses designed to prepare future lawyers to serve vulnerable or disadvantaged communities in Southeast Asia. The MRLSP endeavors to cultivate a cadre of professionals who will work in government, for civil society organizations, or as private lawyers protecting and supporting weaker segments of society.
CMLC launched its first experimental implementation of the MRLSP during spring semester 2016 (in cooperation with Thammasat University, Faculty of Law, Lampang Campus). This initial pilot was attended by two students from China, two students from Myanmar, two students from Thailand and two students from Vietnam. The program was praised by the attending students, who remain in contact and represent our first cadre of connected professionals working in the GMS. Our second pilot was completed at Thailand's Khon Kaen University, Faculty of Integrated Social Sciences, Nongkhai Campus (autumn semester 2018), with 15 students: Three Cambodians, two Chinese, two Lao, two Myanmar, two Thai and four Vietnamese. All students attending the MRLSP experiment pilots have at least three-years legal training in their home countries, most already at graduate level, positioning the students to gain the most from MRLSP's curriculum.
Currently, the MRLSP serves as the first semester of a future LL.M. degree program in Mekong Region Legal Studies, with an expected Masters degree launch date of autumn 2021. Students that demonstrated superior performance in the preliminary semester programs will be invited back to complete the LL.M. degree. Two of our best performing students in the 2018 MRLSP are currently under consideration for scholarship support to study in the U.S. starting August 2020.
The Faculty of Integrated Social Science at Khon Kaen University, Nongkhai Campus is a supportive and eager partner for the MRLSP, and provides an excellent location and platform for transforming the Mekong Region Legal Studies Program into a unique, comprehensive graduate level legal studies program. Related initiatives include annual symposia on subjects of law relevant to the GMS, a Mekong Region research paper series and a consortium of supporting regional law schools.
Students in the MRLSP currently attend four courses as follows:
Introduction to the Chinese Legal System (3 credits)
This course explores the fundamental structure and operation of the Chinese legal system, offering a critical perspective on the development of law in China and providing students with the basic training necessary to work with Chinese law on a deeper and practical level. The course covers the historical development of the Chinese legal system, the relevant institutions responsible for the formation and application of law in China (and associated legislative and judicial processes) and issues of Chinese law, society, and culture. Subjects also include constitutionalism in China, Chinese administrative law, Chinese overseas direct investment, Chinese family law, women and the law, and lawyering in China.
Comparative Study of Mekong Region Legal Systems (3 Credits)
This course introduces the legal systems of Cambodia, Laos, Myanmar, Thailand and Vietnam, offering a comparative perspective on the various ways that legal systems develop. Students will learn the sources of law for each country and each country's institutional framework for both the formation and implementation of law. Emphasis is on common problems affecting all these countries and different methods for solving social conflict.
Comparative Government Procurement Law (3 Credits)
On average, government procurement represents 20% of a country's economic activity. This course employs case law analysis to demonstrate the similar legislative frameworks, but very different operating environments, for public contracting in the U.S., China, Myanmar, Thailand, Vietnam and other countries. Students not only learn the basics of government procurement law, but also explore very different administrative systems. Topics include coverage of government procurement law, authority of government agents, ethical rules and counter-corruption in government procurement, social policies in government procurement, choice of procurement procedures, bid challenges, contractor debarment, and issues of public contract performance.
Project Design and Grant Proposal Writing (3 Credits)
Lawyers are expected to contribute to the public good. Some lawyers meet this obligation by simply representing underprivileged groups at no charge (pro bono). Others prefer to work for NGOs on law related projects or other public service initiatives. Some lawyers even develop their own projects to better society. This course introduces the student to the process of developing law-related projects that provide benefits to disadvantaged individuals and communities. Students will learn how to identify social problems in need of resolution and how to develop effective and sustainable strategies to solve or mitigate the impact of such social problems. Importantly, students will also learn the basics of drafting a grant proposal for funding to successfully implement their designed projects, including drafting a compelling mission statement, creating a realistic budget, reporting back to funders, and measuring project outcomes.
Teaching Law in Context
All MRLSP course stress law in context; teaching students to serve as lawyers for disadvantaged individuals/groups and vulnerable populations with respect to how law actually operates in the various Greater Mekong Subregion countries, identifying, but not relying, on the aspirational components of how law should be, as taught in many Asian law school curricula. A comparative and cross-border focus underlays all MRLSP courses.
Students attending the MRLSP do so at no expense to the student. CMLC provides all funding for their participation, including housing and a very humble living stipend, so that students are not denied this innovative learning opportunity just because they lack adequate funds. CMLC hopes to continue this scholarship support as the MRLSP transforms into a two-year degree program, targeting 20 students for full scholarship, and reasonable tuition fees for another 20 students who otherwise do not qualify for assistance. Outside financial support for this initiative is thus indispensable, so please donate.
The next step for the MRLSP is further curriculum development with a focus on specialized course offerings relevant to the GMS (and not readily available in Asian law schools). These include:
Migrant Labor Law;
Microcredit and Financial Inclusiveness;
Riparian Law and Managing Shared Water Resources;
Civil Society Organizations and Public Participation in Development (course design already completed pursuant to a generous grant from the International Center for Not-For-Profit Law);
Land Use and Environmental/Wildlife Protection;
Border Trade;
Human Trafficking, Stateless Persons and Refugee Law; and
Agriculture Law: Everything You Need to Know to Represent Rural Communities
The MRLSP appreciates any support, financial or in-kind, for developing course materials and identifying and/or sponsoring legal experts to come teach in the MRLSP. Finding qualified professionals to teach the above enumerated courses is obviously a challenge, but one worth overcoming to train a new era of lawyers who can adequately and ethically represent disadvantaged communities, solving or mitigating impacts from the extraordinary problems facing the peoples of the GMS. Providing support for curriculum development and visiting faculty eases pressures on China-Mekong Law Center, sustaining student scholarships for worthy Mekong Region law students. Over time, local faculty will develop the skills to teach these high-level courses reducing reliance on visiting experts.
We hope you agree that the Mekong Region Legal Studies Program is a unique and valuable learning opportunity for the future stewards of the Greater Mekong Subregion. Please help us bring this opportunity to as many GMS students as possible. Thank you.
Please help us bring this opportunity to as many GMS students as possible
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About McCarthyism includes key readings that trace the rise, fall, and ongoing legacy of Senator Joseph McCarthy, one of the most infamous personalities of the 1950s.
Transcripts of significant Cold War documents, arranged by topic. Each transcription includes a citation to the original document. Site maintained by Yale Law School.
In 1948 the USSR blockaded West Berlin to force the Allies to handover the city to Russia. The U.S. and Britain responded with a daily airlift of supplies that eventually compelled Stalin to lift the blockade. The Truman Presidential Library retells the story with photographs, narratives, and important documents.
Focused on integrating voices from former communist countries into the historical study of the Cold War. An initiative of the Woodrow Wilson International Center for scholars.
Includes a vast array of readings focusing on key people and events of the 1950s. Edited by Al Filreis, an author and professor affiliated with the University of Pennsylvania.
Transcripts published by the U.S. Senate. See the right sidebar for three articles that provide further context.
Online exhibits and timeline information published by the organization behind the planned Cold War Museum.
Image-rich exhibit that divides the Cold War chronologically according to the sitting President. Explanatory text accompanies each image. from the National Portrait Gallery, Smithsonian Institution.
Primary and secondary sources from the Cold War era, many focused on the Vietnam War. Maintained by the Institute for Advanced Technology in the Humanities at the University of Virginia, Charlottesville.
The Washington Post revisits Watergate in a multimedia study encompassing documents, a timeline, cartoons, biographies of key individuals, and the Post's award winning reporting.


An Ezra Jack Keats Book Award Winner A New York Times Best Illustrated Book An NPR Best Book of the Year A Bulletin Blue Ribbon Book A Parents Choice Gold Award WinnerA picture book celebration of the indomitable Muddy Waters, a blues musician whose fierce and electric sound laid the groundwork for what would become rock and roll.Muddy Waters was never good at doing whatAn Ezra Jack Keats Book Award Winner A New York Times Best Illustrated Book An NPR Best Book of the Year A Bulletin Blue Ribbon Book A Parents Choice Gold Award WinnerA picture book celebration of the indomitable Muddy Waters, a blues musician whose fierce and electric sound laid the groundwork for what would become rock and roll.Muddy Waters was never good at doing what he was told When Grandma Della said the blues wouldn t put food on the table, Muddy didn t listen And when record producers told him no one wanted to listen to a country boy playing country blues, Muddy ignored them as well This tenacious streak carried Muddy from the hardscrabble fields of Mississippi to the smoky juke joints of Chicago and finally to a recording studio where a landmark record was made.Soon the world fell in love with the tough spirit of Muddy Waters In blues infused prose and soulful illustrations, Michael Mahin and award winning artist Evan Turk tell Muddy s fascinating and inspiring story of struggle, determination, and hope.
I am going to have to come back later to form words for this title. Right night all I can say is it is simply glorious. The story and the illustrations. There is no illustrator today quite like Evan Turk. In a perfect world his name would be as popular and widely known as Mo Willems. Different art techniques for sure but just as creative and wonderful.
I had the pleasure of accessing an Advanced Reader Copy. This book fires on all cylinders. The writing is lyrical and emotional. The artwork is stunning. I was not surprised to learn that it was nominated for the "Mock Caldecott" award. A great non-fiction story about the blues, perseverance and overcoming adversity.
Beautiful picture book about the life of Muddy Waters (born McKinley Morganfield--now that's a cool name too!). His grandma gave him his nickname for always playing in the mud. Gorgeous artwork illustrates the book, with vibrant colors, abstract images. Author's note gives full details that aren't spelled out in the simple picturebook text.
The perfect storytelling and illustrations. Introduced my daughter to a blues legend then we spent the next morning listening to his music.
Apr 23, 2019 - 17:55 PM J.