a) Energy-momentum Based on Noether’s theorem, construct the energy-momentum tensor for classical electromagnetism from the above Lagrangian. Note that the usual procedure does not result in a symmetric tensor. To remedy that, we can add to T μν a term of the form ∂λK λμν , where K is antisymmetric in its first two indices. Such an object is automatically divergenceless, so T̂ μν = T μν + ∂λK λμ...

where g : R × R × R → R is a C function. Once we specify a parameter path u(t), t ≥ t1, in the parameter space we can solve (1.1) uniquely for x(t), t ≥ t1, with the given initial condition x(t1) = x0. Alternatively if we specify a parameter path u(t), t ≤ t1, in the parameter space we can solve (1.1) uniquely for x(t), t ≤ t1, with the given terminal condition x(t1) = x0. Suppose now that for ...

There are different finite element models in place for predicting the bending behavior of shear deformable beams and plates. Mostly, the literature abounds with traditional equi-spaced Langrange based low order finite element approximations using displacement formulations. However, the finite element models of Timoshenko beams and Mindlin plates with linear interpolation of all generalized disp...

this research intents to /explain the theory and practice of fascism in . italy an germany, and so it tries to recognise the ideology of classical fascism. studing the historical grounds of emerging of fascism, it explains the raising ideology of fascism in nature, resouce and contents of thought, and by looking to foundations of classical fascism's ideology, it studies natural history of ...

⋆ Suppose we have a certain message we want to transmit from location A to location B. What resources are needed to get it from here to there? How long will it take if we have a channel with a capacity of c bits per second? If transmission introduces errors, what do we do about them? These are the sorts of questions which are addressed by information theory as developed by Shannon and his succe...

Let SP2n(R) = SP2n = Sp be the real symplectic group of rank n. Let Sp denote the two-fold cover of Sp. There is a unitary representation, constructed by Shale [Sh] and Weil [WA], of Sp that is of considerable interest in the theory of automorphic forms. We denote this representation by wand call it the oscillator representation. The purpose of this paper is to establish about w a fact that sho...

In this paper we analyse a number of teaching paradoxes of classical electrodynamics, dealing with the relativistic transformation of energy and momentum for a fluid medium in an external electromagnetic field. In particular, we consider a moving parallel plate charged capacitor, where the electric attraction of its plates is balanced by the pressure of gas convicted between the plates.

This paper is a very brief introduction to knot theory. It describes knot coloring by quandles, the fundamental group of a knot complement, and handle-decompositions of knot complements.

D eflation, the opposite of inflation, is a situation of falling general prices. It should not be confused with disinflation, which refers to a declining inflation rate that nevertheless remains positive. It was the successful U.S. disinflation of the 1990s, a disinflation that lowered the inflation rate sufficiently to create concern that further downward pressure might push it into negative t...