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.     

Collaborative Curriculum Investigation as a Vehicle for Teacher Enhancement and Mathematics Curriculum Reform

The Missouri Middle Mathematics (M³) Project is an NSF-funded 3-year professional development project involving teacher/administrator teams from districts statewide. Project activities focus on collaborative investigation of emerging reform-based middle school mathematics curricula to support individual and systemic reform. Collaborative review and field-testing of material facilitates awareness and exploration of alternative instructional and assessment strategies and informed decision making. Early indicators of the model's success are reflected in participants’ enthusiasm and professional growth. Project activities stimulate discussions of critical topics including questioning appropriateness of various teaching practices, research about teaching and learning, tracking policies, appropriate assessment models for gauging student learning and the importance of calculators and manipulatives as teaching and learning tools. These discussions transcend curriculum materials being reviewed and serve as a powerful vehicle for professional growth and development for individual teachers and districts.     

Majority judgment over a convex candidate space

Most voting methods can only deal with a finite number of candidates. In practice, there are important voting applications where the candidate space is continuous. We describe a new voting method by extending the Majority Judgment voting and ranking method to handle a continuous candidate space which is modeled as a convex set. We characterize the structure of the winner determination problem and present a practical iterative voting procedure for finding a (or the) winner when voter preferences are unknown.     

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.     

Investigation of a Phase Field Model for Elasto-plastic Fracture

Phase field modelling of brittle fracture is very well understood today. However, the attempts of investigation of elasto-plastic fracture by the phase field approach are limited. This contribution deals with the investigation of a phase field model for elasto-plastic fracture. Based on a free energy density comprising elastic, fracture and plastic contributions, the model describes an extension of the linear elastic model towards von Mises plasticity. In this work it is analyzed numerically to which extend analytical findings concerning the interpretation of the model parameters in 1D are transferable to 2D scenarios. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

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 “X is F,” where X is a variable taking values in U, induces a possibility distribution ∏X which equates the possibility of X taking the value u to μF(u)—the compatibility of u with F. In this way, X becomes a fuzzy variable which is associated with the possibility distribution ∏_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 “X is F is α-possible,” where α is a number in the interval [0, 1], is formulated and illustrated by examples.     

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.