Investigation of a solid body rotary motion as a whole

Behavior of rotary motions of a solid body with a fixed point is investigated throughout the whole of phase space (as a whole). The system of equations that determines the relation between the configuration space topology and the global properties of solid body motions is derived.     

Investigation of velocity dependence of rolling frictions as a means of studying adhesion

Investigation of the rolling of two cylinders on the device described in this paper has shown that a study of the rolling friction of bodies coated with polymer films offers a means of investigating adhesion processes. It has been found that the resistance to rolling of bodies coated with nonadhesive polymers has a tendency to increase with increase in velocity, in accordance with the electrical theory of adhesion. The resistance to rolling of bodies coated with adhesive polymers passes through a maximum as the velocity increases and then decreases, in accordance with the diffusion theory of adhesion.Mekhanika Polimerov, Vol. 1, No. 4 pp. 117–122, 1965     

A mathematical model for estimating the potential margin of state undecided voters for a candidate in a US Federal election

A US Federal election in which candidates from two major political parties compete for the votes of those undecided voters in a state who usually do not vote in US elections is considered. A mathematical model for evaluating the expectation of the margin of votes to be received from such voters by either candidate as a result of the election campaigns of all the competing candidates is proposed. On the basis of this model, finding the estimation under consideration is reducible to finding the minimum of the maximin function of the difference of two bilinear functions with one and the same first vector argument whose second vector arguments belong to a polyhedron of connected variables (strategies of the candidates), and this minimum is sought on another polyhedron.     

Regularity criterion for a mathematical model of the laser

There exists a deep relationship between the nonexplosion conditions for Markov evolution in classical and quantum probability theories. Both of these conditions are equivalent to the preservation of the unit operator (total probability) by a minimal Markov semigroup. In this work, we study the Heisenberg evolution describing an interaction between the chain ofN two-level atoms andn-mode external Bose field, which was considered recently by J. Alli and J. Sewell. The unbounded generator of the Markov evolution of observables acts in the von Neumann algebra. For the generator of a Markov semigroup, we prove a nonexplosion condition, which is the operator analog of a similar condition suggested by R. Z. Khas’minski and later by T. Taniguchi for classical stochastic processes. For the operator algebra situation, this condition ensures the uniqueness and conservativity of the quantum dynamical semigroup describing the Markov evolution of a quantum system. In the regular case, the nonexplosion condition establishes a one-to-one relation between the formal generator and the infinitesimal operator of the Markov semigroup. Translated fromMatematicheskie Zemetki, Vol. 67, No. 5, pp. 788–796, May, 2000.     

Quasienergy basis for multielectron system in a strong laser field

The second-quantization procedure is performed in the basis of quasienergy states, and an expression is obtained for the Green's function of a finite Fermi system. A nonstationary effective potential is constructed in the Hartree-Fock and local-density approximations, and possibilities for using it are discussed.Voronezh Constructional Engineering Institute. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 97, No. 1, pp. 121–132, October, 1993.     

Kinetic theory of a super-radiating laser

Statistical properties of the radiation of a super-radiating laser are studied on the basis of the kinetic equation for the density matrix of the generating field. An original derivation of this equation is proposed. Statistical properties of the laser medium are investigated in the stationary generating regime. We analyze the role played by the decay rate of intracavity photon fluctuations and by the statistical properties of the active medium in the suppression of the photocurrent shot noise. We consider the external pump to be weak, which is physically the most interesting case. It is shown that if the active medium is weakly excited, then only a 50% depression of the shot noise is possible. In the case of a strongly excited medium, depression can reach 100%. The spectrum of optical generation is obtained for conditions far from the instability zone.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 109, No. 2, pp. 250–269, November, 1996.     

Fuzzy sets as a basis for a theory of possibility

The theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable. More specifically, if F is a fuzzy subset of a universe of discourse U = {u} which is characterized by its membership function μ_F, then a proposition of the form $\text{“X}\text{is}\text{F”}$, where X is a variable taking values in U, induces a possibility distribution $\text{t}\text{?}{}_{\mathrm{x}}$ which equates the possibility of X taking the value u to μ_F(u)—the compatibility of u with F. In this way, X becomes a fuzzy variable which is associated with the possibility distribution $\text{t}\text{?}{}_{\mathrm{x}}$ in much the same way as a random variable is associated with a probability distribution. In general, a variable may be associated both with a possibility distribution and a probability distribution, with the weak connection between the two expressed as the possibility/probability consistency principle.A thesis advanced in this paper is that the imprecision that is intrinsic in natural languages is, in the main, possibilistic rather than probabilistic in nature. Thus, by employing the concept of a possibility distribution, a proposition, p, in a natural language may be translated into a procedure which computes the probability distribution of a set of attributes which are implied by p. Several types of conditional translation rules are discussed and, in particular, a translation rule for propositions of the form $\text{“X}\text{is}\text{F}$ is α-possible”, where α is a number in the interval [0,1], is formulated and illustrated by examples.     

An Investigation of a Pair of Integral Equations for the Biharmonic Problem

The paper contains an elementary investigation of the questionof uniqueness of a pair of integral equations connected withthe plane biharmonic problem. It is shown that for two particularexceptional geometries of the boundary curve the pair of integralequations does not have a unique solution. This defect can beremoved by adding two supplementary integral conditions whichthe solution of the integral equations must satisfy. As an illustrationthe integral equations are solved numerically with and withoutthese extra conditions.     

Theoretical analysis and numerical solution of laser pulse transformation for satellite laser ranging

The processes of the pulse transformation in satellite laser ranging (SLR) are analyzed, the analytical expressions of the transformation are deduced, and the effects of the transformation on Center-of-Mass corrections of satellite and ranging precision are discussed. The numerical solution of the transformation and its effects are also given. The results reveal the rules of pulse transformation affected by different kinds of factors. These are significant for designing the SLR system with millimeter accuracy.     

Investigation of the dispersion equation for an acoustics problem in a borehole

One gives the results of the analytic and numerical analysis of the roots of the dispersion equation for a model of a log borehole. One investigates the effect of the elastic parameters and of the densities on the dispersion and the damping of the waves in the case of radial oscillations.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 128, pp. 89–94, 1983.     

The truncatedSVD as a method for regularization

The truncated singular value decomposition (SVD) is considered as a method for regularization of ill-posed linear least squares problems. In particular, the truncated SVD solution is compared with the usual regularized solution. Necessary conditions are defined in which the two methods will yield similar results. This investigation suggests the truncated SVD as a favorable alternative to standard-form regularization in cases of ill-conditioned matrices with well-determined numerical rank.This work was carried out while the author visited the Dept. of Computer Science, Stanford University, California, U.S.A., and was supported in part by National Science Foundation Grant Number DCR 8412314, by a Fulbright Supplementary Grant, and by the Danish Space Board.