Helmholtz theorem and the v-gauge in the problem of superluminal and instantaneous signals in classical electrodynamics

In this work we substantiate the applying of the Helmholtz vector decomposition theorem (H-theorem) to vector fields in classical electrodynamics. Using the H-theorem, within the framework of the two-parameter Lorentz-like gauge (so called v-gauge), we show that two kinds of magnetic vector potentials exist: one of them (solenoidal) can act exclusively with the velocity of light c and the other one (irrotational) with an arbitrary finite velocity $v$ (including a velocity more than c . We show also that the irrotational component of the electric field has a physical meaning and can propagate exclusively instantaneously.Comment: This variant has been accepted for publication in Found. Phys. Letter

Applications of M.G. Krein's Theory of Regular Symmetric Operators to Sampling Theory

The classical Kramer sampling theorem establishes general conditions that allow the reconstruction of functions by mean of orthogonal sampling formulae. One major task in sampling theory is to find concrete, non trivial realizations of this theorem. In this paper we provide a new approach to this subject on the basis of the M. G. Krein's theory of representation of simple regular symmetric operators having deficiency indices (1,1). We show that the resulting sampling formulae have the form of Lagrange interpolation series. We also characterize the space of functions reconstructible by our sampling formulae. Our construction allows a rigorous treatment of certain ideas proposed recently in quantum gravity.Comment: 15 pages; v2: minor changes in abstract, addition of PACS numbers, changes in some keywords, some few changes in the introduction, correction of the proof of the last theorem, and addition of some comments at the end of the fourth sectio

Investigation of Light Nucleus Clustering in Relativistic Multifragmentation Processes

The use of emulsions for studying nuclear clustering in light nucleus fragmentation processes at energies higher than 1A GeV is discussed. New results on the topologies of relativistic Li-7 and B-10 nucleus fragmentation in peripheral interactions are given. A program of research of the cluster structure in stable and radioactive nuclei is suggested.Comment: 4 pages, 1 figure. Presented at Conference on Fundamental Interactions, 2-6 December 2002, ITEP, Moscow, Russia (misprints are removed

Measurement of the ββ2ν decay of 76Ge

Abstract From the data taken with one of the enriched detectors of the Heidelberg-Moscow ββ experiment a half-life of T 1 2 2v = (1.42 ± 0.03 ( stat ) ± 0.13 ( syst )) × 10 12 yr for the two-neutrino double-beta ( ββ 2 ν ) decay of 76 Ge is derived. The 76 Ge exposure is 19.3 mol yr. This result represents the first high statistics measurement and probably the first undoubtable evidence of this extremely rare nuclear decay mode. The measured decay rate is in good agreement with the theoretical predictions