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 ...

Test theories can be divided roughly into two categories. The first is classical test theory, which dates back to Spearman’s conception of the observed test score as a composite of true and error components, and which was introduced to psychologists at the beginning of this century. Important milestones in its long and venerable tradition are Gulliksen’s Theory of Mental Tests (1950) and Lord a...

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...

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...

We consider classical Yang-Mills theory with point sources and derive equations of motion for the coupled particle-field system. As an example, we discuss the special case of Yang-Mills theory coupled to point particles in (1þ 1) dimensions. We formulate the initial value problem for the system and describe several example solutions. VC 2011 American Association of Physics Teachers. [DOI: 10.11...

Current advances in test development theory have mostly been influenced by item response theory. Notwithstanding this, classical test theory still plays a major part in the development of tests for applied educational and behavioral research. This article describes ViSta-CITA, a computer program that implements a set of classical item and test analysis methods that incorporate innovative graphi...