New Horizons in Mathematical Physics

5

Authors: Vasiliy K. Balkhanov, Yuriy B. Bashkuev, Ludmila Kh. Angarkhaeva

This paper derives the analytical formula for impedance two-layer media “dielectricconductor”. In the winter on the Northern sea route and the salt lakes of Eurasia for demanding radio paths you can model two-layer media, where the first media (ice) is a dielectric layer and the second (sea, salt water) over a wide frequency range of radio waves is underlying conductive media. Two-layer media under consideration with real physical and geometrical parameters has strongly inductive impedance, which is calculated from a transcendental equation. The article shows that a large contrast between the electrophysical properties of the layers of ice and water allows you to set an approximate analytical formula for impedance, which is within the applicability of the impedance definition practically coincides with the decision of the transcendental equation. It was established that for the two-layer media impedance phase lies within -45.10 - -89.90, that is the criterion for heavily inductive surface.

3

Authors: Vasiliy K. Balkhanov

The article found that quasi-classic quantum approach allows to calculate temperature and entropy of black holes. Installed border applicability of quasi classical approximation: the mass of the black hole must be greater than the Planck mass.

7

Authors: V.G.Mete, V.D.Elkar, Poonam P. Kadu

An attempt has been taken to study the minimally interacting fields, dark matter and holographic dark energy in scalar tensor theory formulated by Saez and Ballester. The exact solution of the field equations is obtained by using the fact that the scalar expansion of the universe is proportional to the shear scalar. Some physical and geometrical aspects of the model are also discussed.

12

Authors: Maria F. Correia, Christopher Cox, Hong-Kun Zhang

We investigate a three-parameter family of billiard tables with circular arc boundaries. These umbrella-shaped billiards may be viewed as a generalization of two-parameter moon and asymmetric lemon billiards, in which the latter classes comprise instances where the new parameter is 0. Like those two previously studied classes, for certain parameters umbrella billiards exhibit evidence of chaotic behavior despite failing to meet certain criteria for defocusing or dispersing, the two most well understood mechanisms for generating ergodicity and hyperbolicity. For some parameters corresponding to non-ergodic lemon and moon billiards, small increases in the new parameter transform elliptic 2-periodic points into a cascade of higher order elliptic points. These may either stabilize or dissipate as the new parameter is increased. We characterize the periodic points and present evidence of new ergodic examples.

4

Authors: M.A. Grado-Caffaro, M. Grado-Caffaro

After presenting a lemma, two theorems on negative energy density associated with a quantum free scalar field are established. The first theorem provides a lower bound for a non-negative weight function whose existence is guaranteed by the lemma. The above energy density is evaluated over an inertial world line of the Minkowski space-time. The second theorem provides an upper bound for the averaged (with respect to the sampling function) absolute expectation value of the negative energy-density function. In particular, a complex-valued sampling function is introduced by the first time so a more generalized formulation is proposed.

7

Authors: Mark D. Roberts

In a certain sense Riemannian geometry can be thought of as geometry built up from the Finslerian properties of point particles. The string and membrane generalization of this to a geometry similar but not the same as Finslerian geometry is investigated. Solely classical arguments suggest a physical interpretation in which microscopic strings are directly related to macroscopic geometry; alternatively the resulting geometry can be interpreted as that describing microscopic spacetime. The construction presented can be thought of as providing a mechanism for oxidization.

13

Authors: Huili Liu, Seoung Dal Jung

In this paper we give a kind of representation formula for a null curve with null arc length parameter in three dimensional Minkowski spacetime E3 1 and define structure function of such null curve. Using this representation formula and relations between the null curvature function and structure function of null curve, especially by solving certain differential equations, we obtain some characterizations and classifications of some special null curves.