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The inclusive electromagnetic responses in the quasi-elastic region are calculated with a model which considers the terms of the cluster expansion containinga single correlation line. The validity of this model is studied by comparing, in…
The results of Monte-Carlo simulations of electron-positron-photon cascades initiated by slow electrons in circularly polarized fields of ultra-high strength are presented and discussed. Our results confirm previous qualitative estimations…
The hemispherical Mueller matrix map for light reflected from a plane-parallel planetary atmosphere is shown to obey several symmetry properties that provide a straightforward method to check their physical realizability. The mirror…
Robbin and Salamon showed that attractor-repellor networks and Lyapunov maps are equivalent concepts and illustrate this with the example of linear flows on projective spaces. In these examples the fixed points are linearly ordered with…
We prove, under a certain representation theoretic assumption, that the set of real symmetric matrices, whose eigenvalues satisfy a linear matrix inequality, is itself a spectrahedron. The main application is that derivative relaxations of…
A scalar field obeying a Lorentz invariant higher order wave equation, is minimally coupled to the electromagnetic field. The propagator and vertex factors for the Feynman diagrams, are determined. As an example we write down the matrix…
Let $n \ge 3$ be an integer. Let $P_n = \{1, 2, 3, ..., n-1, n \}$ and let $S_n$ be the symmetric group of permutations on $P_n$. Motivated by the theory of discrete dynamical systems on the interval, we associate each permutation $\si_n$…
Expanding the results of [1], [2], [3], we demonstrate a network of algebraic connections between six well-known particle theories. These are the Spin(10) model, the Georgi-Glashow model, the Pati-Salam model, the Left-Right Symmetric…
The different types of orbits in the classical problem of two particles with equal masses and opposite charges on a plane under the influence of a constant orthogonal magnetic field are classified. The equations of the system are reduced to…
The new approach is developed for study of electron-positron pair production by a photon in oriented single crystal. It permits indivisible consideration of both coherent and incoherent mechanisms of pair creation and includes the action of…
For quantum groups at a root of unity, there is a web of theorems (due to Bezrukavnikov and Ostrik, and relying on work of Lusztig) connecting the following topics: (i) tilting modules; (ii) vector bundles on nilpotent orbits; and (iii)…
Toral automorphisms, represented by unimodular integer matrices, are investigated with respect to their symmetries and reversing symmetries. We characterize the symmetry groups of GL(n,Z) matrices with simple spectrum through their…
The electromagnetic analog of an elastic spring-mass network is constructed. These electromagnetic circuits offer the promise of manipulating electromagnetic fields in new ways, and linear electrical circuits correspond to a subclass of…
The probability-generating function of the number of electron-positron pairs produced in a uniform electric field is constructed. The mean and variance of the numbers of pairs are calculated, and analytical expressions for the probability…
Recently, there has been a revival of interest in mechanisms for changing the spin polarization of an electron beam on transmission through, or reflection from, a magnetic surface. An understanding of these mechanisms would allow the use of…
The effect of spontaneous breaking of chiral symmetry over the spectrum of highly excited hadrons is addressed in the framework of a microscopic chiral potential quark model (Generalised Nambu-Jona-Lasinio model) with a vectorial…
This paper introduces the class of "strongly endotactic networks", a subclass of the endotactic networks introduced by G. Craciun, F. Nazarov, and C. Pantea. The main result states that the global attractor conjecture holds for…
We present natural conjectural generalizations of the `positivity and integrality of mirror maps' phenomenon, encompassing the mirror maps appearing in the Batyrev--Borisov construction of mirror Calabi--Yau complete intersections in Fano…
The Lloyd model is extended to the exciton problem in quasi one-dimensional structures to study the interplay between the Coulomb attraction and disorder scattering. Within this model the averaging and resummation of the locator series can…
Nonlinear theories generalizing Maxwell's electromagnetism and arising from a Lagrangian formalism have dispersion relations in which propagation planes factor into null planes corresponding to two effective metrics which depend on the…