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

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

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

Analysis of the results of different treatment methods for patellar dislocation

The aim of the study was the analysis of domestic and foreign medical literature of different time periods, which describes the basic methods of surgical and conservative treatment of congenital or habitual dislocation of patella, as well as statistical analysis of the results of treatment. Due to the existence of a large number of options of surgical treatment for this pathology (more than 150 methods were developed) and high variability of its manifestations, it is necessary to know the basic methods and their results for planning tactics of treatment with individual approach to each patient. Based on this review, analysis was performed for the results of using different options for invasive treatment of congenital or habitual dislocation of patella. Also, the paper contains the indications and efficacy of conservative therapy for this disease. A comparative analysis was made on the results of surgical and conservative methods of treatment of patellar dislocation, which were used in different time periods, from the initial description of the first results of treatment of this pathology to modern surgical techniques that are currently used. It is shown that all methods of surgical treatment of the pathology are divided into three main groups: myofascioplastic surgeries, osteoplastic and combined surgical interventions. It is underlined that the diseases requires individual approach to the choice of correction method in each certain case to achieve positive outcomes