Explicit Shimura's conjecture for Sp4

Shimura's conjectire (1963) concerns the rationality of the generating series for Hecke operators for the symplectic group of genus g. This conjecture wes proved by Andrianov for arbitrary genus g. For genus g=4, we explicify the rational fraction in this conjecture. Using formulas for images of double cosets, we first compute the sum of the generating series under the Satake spherical map, which is a rational fraction with polynomial coefficients. Then we recover the coefficients of this fraction as elements of the Hecke algebra using polynomial representation of basic Hecke operators under spherical map. Numerical examples of these fractions for special choice of Satake parameters are given

Elimination of High-Energy Divergence in Relativistic Lagrangean Formulation of Gravitating Particle Dynamics

The nonrenormalizable singularity of the gravitational 1/r potential at ralativistic and quantum levels is a longstanding problem of modern physics. The problem is discussed in Relativistic Lagrangean framework with the variable proper mass. It is shown that the so-called self-energy divergence for the 1/r graviational potntial can be eliminated within the variable proper mass concept. The problem has many aspects outlined, which should be further investigated before the final conclusion could be made

On neutrino family problem

The experiment conducted at the Brookhaven AGS at 1962 [1] on the interaction of high-energy neutrinos with matter is considered in literature the observation of electron and muon types of neutrinos. After analysis of the experiment we have concluded that the latter does not give direct evidence of the neutrino family existence.Comment: 5 page

On Problem of Mass Origin and Self-Energy Divergence in Relativistic Mechanics and Gravitational Physics

The classical problem of self-energy divergence was studied in the framework of Lagrangian formulation of Relativistic Mechanics. The conclusion was made that a revision of mass-energy concept is needed for the development of singularity-free gravitational and electromagnetic field theory. Perspectives of the development of unified field theory are discussed

On matter-antimatter separation in open relativistic material system

An open (having no physical boundaries) baryon symmetric system is considered in a flat space-time. We assume that a space is uniformly filled with electromagnetic radiation and material objects, and the system is isotropic in any inertial reference frame. It means that a coordinate-momentum distribution of radiation and material objects does not depend on a reference frame, and the system should be in a state of chaotic relativistic motion. The dominant interaction processes are like-matter merge, unlike-matter annihilation and pair production. In this approximation we came to the conclusion that matter and antimatter exist in a form of mix of material objects characterized by a stationary baryon symmetric mass distribution in a broad mass range. In other words, a matter-antimatter space separation takes place.Comment: 10 pages, 1 figur

Mass, Time, and Clock (Twin) Paradox in Relativity Theory

The paper is intended to clarify operational meaning of mass and time quantities as main characteristics of an atomic clock, which is considered a quantum oscillator in association with the de Broglie wave concept. The specification of the concept of clock in quantum terms reflects the idea of relativistic mass and time complementarity, which is important for avoiding ambiguity of such notions as ``time rate'', ``time record'', and ``elapsed time'' under relativistic conditions. We used this approach in SRT Kinematics to conduct a detailed analysis of the clock paradox; results are discussed. It is also shown that in SRT Dynamics the proper mass must be acted by Minkowski force, what results in a clock rate variation.Comment: 30 pages, 2 figure

On the Cosmological Aspects of Observed High Energy Cosmic Phenomena

Super-high energy corpuscular and gamma rays as well as cosmic high--power density sources are hard to explain in a galaxy model framework. Attempts to include some of those phenomena in the Standard Cosmological Model also encounter serious difficulties. In the present paper an alternative cosmological concept is discussed. There are several features in it. First of all, the whole Universe (Grand Universe) is a multitude of typical universes, like ours, evenly made of either matter or antimatter, hence, there is no violation of the baryon symmetry on the largest scale. Second, high-energy phenomena are the result of matter-antimatter annihilation processes in a typical universe evolution. Finally, the Ground Universe is a self-creating due to a balance of annihilation and pair creation in the inter-universe infinite space. This concept and its consistence with the major observational data are discussed in detail.Comment: submitted to the ANS Centennial Meeting, March 20 - 26, 1999, Atlanta, Georgi

Baryon Asymmetry of the Observed Universe as a Clue to a Resolution of Dark Matter, Galaxy Formation and Other Standard Model Problems

Baryon asymmetry of the observed universe as a clue to a resolution of dark matter, galaxy formation and other standard model problems

A Generalization of Redfield's Master Theorem

Generalizations of Redfield's master theorem and superposition theorem are proved by using decomposition of the tensor product of several induced monomial representations of the symmetric group $S_d$ into transitive constituents. As direct consequences, one obtains several graphical corollaries. Given graphs \Gamma_1,\hdots ,\Gamma_k, with $d$ vertices, together with their automorphism groups W_1\leq S_d,\hdots, W_k\leq S_d, one can find the number of superpositions of \Gamma_1,\hdots ,\Gamma_k, whose automorphism groups satisfy one of the following conditions: (1) the groups consist of even permutations; (2) the groups are trivial, in case at least one of $W_m$'s is cyclic; (3) the groups are of odd order, in case at least one of $W_m$'s is dihedral and its order is not divisible by 4; (4) the groups are of order dividing a natural number $r$, in case at least one of $W_m$'s has a normal solvable subgroup of order $r$, such that the corresponding factor-group is cyclic of order relatively prime to $r$; (5) the groups are $q$-groups ($q$ is a prime), in case at least one of $W_m$'s has a normal $q$-subgroup such that the corresponding factor-group is cyclic of order relatively prime to $q$.Comment: 9 pages, uses plain Te

Proper Mass Variation under Gravitational and Coulomb Force Action in Relativistic Mechanics of Point Particle

The problem studied is formulated in the title: proper mass variation under gravitational and Coulomb force action in Relativistic Mechanics of point particle. The novelty is that equations of motion are obtained in the relativistic Lagrangean framework for conservative force fields under assumption of field dependent proper mass. The dependence of proper mass on field strength is derived from the equations of particle motion. The result is the elimination of a classical 1/r divergence. It is shown that a photon in a gravitational field may be described in terms of a refracting massless medium. This makes the gravity phenomenon compatible with SR Dynamic framework. New results concerning gravitational properties of particle and photon, as well as an experimental test of predicted deviation from 1/r^2 classical Coulomb force law are discussed. The conclusion is made that the approach of field-dependent proper mass is perspective for better understanding GR problems and further studies on divergence-free field theory development. Key words: Relativity; gravity; Coulomb; particle; photon; speed of light; proper mass variation. PACS: 03.30.+p, 04.20.-gComment: 31 pages, 1 figur