Affine-scaling for linear programs with free variables

The affine-scaling modification of Karmarkar's algorithm is extended to solve problems with free variables. This extended primal algorithm is used to prove two important results. First the geometrically elegant feasibility algorithm proposed by Chandru and Kochar is the same algorithm as the one obtained by appending a single column of residuals to the constraint matrix. Second the dual algorithm as first described by Adler et al., is the same as the extended primal algorithm applied to the dual.     

Piecewise-linearized methods for oscillators with limit cycles

A piecewise linearization method based on the linearization of nonlinear ordinary differential equations in small intervals, that provides piecewise analytical solutions in each interval and smooth solutions everywhere, is developed for the study of the limit cycles of smooth and non-smooth, conservative and non-conservative, nonlinear oscillators. It is shown that this method provides nonlinear maps for the displacement and velocity which depend on the previous values through the nonlinearity and its partial derivatives with respect to time, displacement and velocity, and yields non-standard finite difference formulae. It is also shown by means of five examples that the piecewise linearization method presented here is more robust and yields more accurate (in terms of displacement, energy and frequency) solutions than the harmonic balance procedure, the method of slowly varying amplitude and phase, and other non-standard finite difference equations.     

Dependence of the Phase Transition Temperature on the Domain Size

Dependence of the phase transition temperature on the domain size is investigated for a double-well quadratic potential. It is shown that for a domain whose boundary is subjected to a hydrostatical pressure, the temperature of phase transitions is independent of the domain and the surface tension coefficient and depends exclusively on the properties of the elastic media. If the displacement field vanishes on the boundary, then for sufficiently small domains, the temperature also does not depend on the surface tension and domain size and is determined by properties of the elastic media only. Bibliography: 8 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 310, 2004, pp. 98–113.     

Automated proving and analysis of geometric theorems in coordinate-free form by using the anticommutative Gröbner basis method

Some geometric theorems can be stated in coordinate-free form as polynomials in Grassman algebra and can be proven by the anticommutative Gröbner basis method. In this article, we analyze some properties of both sets of hypotheses and conclusions of the theorem.     

Energy losses of dipoles traveling relative to a moving medium

We consider the radiation from nonoscillating dipoles traveling with constant velocity directed parallel or antiparallel to the velocity of a homogeneous transparent moving medium. It is assumed that the medium in its rest frame is isotropic and has no spatial dispersion. We obtain expressions for the radiative energy losses and estimate the polarization energy losses of electric and magnetic dipoles of different orientations. In particular, it is shown that the energy loss of a source is negative if it moves in the direction of the medium motion and the source velocity is less than the medium velocity. Estimates for the energy losses of dipoles in the cases of an electron beam and a flow of a weakly dispersive medium are given. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 49, No. 6, pp. 502–512, June 2006.     

Dependence of the H2-H2 Interaction on the Monomer Bond Lengths: Steps Toward an Accurate ab initio Estimate

We compute the vibrational coupling between two H₂ molecules from ab initio quantum chemical calculations of the H₂-H₂ potential carried out at the full configuration interaction level of theory using the atom-centered aug-cc-pVTZ basis set for hydrogen. We compare the full configuration interaction results with those obtained using two variants of coupled cluster theory and find that a fully iterative treatment of connected triples may be required to estimate the H₂-H₂ vibrational coupling accurately using coupled cluster theory.     

Influence of Azimuthal Structure of Surface Waves on Efficiency of their Excitation by Tubular Electron Beams

The excitation of eigen surface waves by tubular electron beams in cylindrical discharge devices is studied. The influence of the wave‐field azimuthal structure on the excitation efficiency and nonlinear stage of the plasmabeam instability is investigated both numerically and analytically. Analytical expressions for the saturation amplitude and excitation efficiency of the wave under study are derived. They are found to agree well with results obtained by numerical modelling of the plasma‐beam interaction presented in this paper. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Periodic Integrable Systems with Delta-Potentials

In this paper we study root system generalizations of the quantum Bose-gas on the circle with pair-wise delta-function interactions. The underlying symmetry structures are shown to be governed by the associated graded algebra of Cherednik's (suitably filtered) degenerate double affine Hecke algebra, acting by Dunkl-type differential-reflection operators. We use Gutkin's generalization of the equivalence between the impenetrable Bose-gas and the free Fermi-gas to derive the Bethe ansatz equations and the Bethe ansatz eigenfunctions.     

Chaos and hyperchaos in a gyrotron

We study oscillation in a gyrotron with allowance for reflections from an output horn. Regions with different system behaviors, such as stationary oscillation, self-modulation, and complex-dynamics regimes are found in the parameter plane. The scenarios of appearance of chaotic oscillations are considered. It is shown that they can emerge via either a sequence of period-doubling bifurcations or destruction of quasiperiodic motion. For chaotic attractors, Lyapunov exponents are calculated and their dimensions are estimated on the basis of the Kaplan-Yorke formula. The dimension values turn out to be anomalously large, which is stipulated by the presence of a large number of high-Q eigenmodes in the gyrotron cavity due to operation near the cutoff frequency of an electrodynamic system. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 49, No. 10, pp. 887–899, October 2006.