Parametric resonance in the problem of a heavy rigid body rolling along a straight line on a plane

The problem of the stability of a heavy rigid body, bounded by the surface of an ellipsoid and with a cavity in the form of a coaxial ellipsoid, rolling along a straight line on a horizontal rough plane is investigated. It is shown that in the case of a body that is close to being dynamically symmetrical, parametric resonance always occurs leading to instability of the rolling. Each ellipsoid has its own “individual” resonance angular velocity. In the general case, regions in which the necessary stability conditions are satisfied can be distinguished in parameter space. The problem of calculating the resonance coefficient corresponding to instability for parametric resonance in a reversible third-order system is solved.     

Proof of a conjecture on irredundance perfect graphs

Let ir(G) and γ(G) be the irredundance number and the domination number of a graph G, respectively. A graph G is called irredundance perfect if ir(H)=γ(H), for every induced subgraph H of G. In this article we present a result which immediately implies three known conjectures on irredundance perfect graphs. © 2002 Wiley Periodicals, Inc. J Graph Theory 41: 292–306, 2002     

Unconditional Bases, the Matrix Muckenhoupt Condition, and Carleson Series in a Spectrum

Two families of functions constructed by a system of n scalar Muckenhoupt weights are studied. Criteria are given under which these families are unconditional bases. From the point of view of the spectral operator theory, the problem is reduced to the study of the structure of n-dimensional perturbations of the integration operator. Weighted estimates for the Hilbert transform in the spaces of vector-functions are applied to construct an operator mapping functions of the studied families to vector-valued rational functions. The concept of the Carleson series is used in the study of the following problem: when do vector-valued rational functions form an unconditional basis? Bibliography: 8 titles.     

Numerical solutions of the shallow water equations with discontinuous bed topography

A simple scheme is developed for treatment of vertical bed topography in shallow water flows. The effect of the vertical step on flows is modelled with the shallow water equations including local energy loss terms. The bed elevation is denoted with z_b^‐ for the left and z_b⁺ for the right values at each grid point, hence exactly representing a discontinuity in the bed topography. The surface gradient method (SGM) is generalized to reconstruct water depths at cell interfaces involving a vertical step so that the fluxes at the cell interfaces can accurately be calculated with a Riemann solver. The scheme is verified by predicting a surge crossing a step, a tidal flow over a step and dam‐break flows on wet/dry beds. The results have shown good agreements compared with analytical solutions and available experimental data. The scheme is efficient, robust, and may be used for practical flow calculations. Copyright © 2002 John Wiley & Sons, Ltd.     

An evolution operator in semiclassical electrodynamics

An evolution operatior is described, which acts on the operators of a problem to take it into the solutions of the corresponding problem of semiclassical electrodynamics.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 66–69, November, 1981.     

Systematic investigations of the multi-element preconcentration from copper by precipitation of the matrix as copper(I) oxide and copper(I) thiocyanate

Two methods for multi-element preconcentration from copper by reductive matrix precipitation are presented. In systematic investigations on the coprecipitation behaviour of Ag, Al, Au, Bi, Cd, Co, Cr, Fe, Ga, In, Mn, Mo, NJ, Pb, Sb, Se, Sn, Te and Zn during precipitation of the copper matrix as Cu₂O or CuSCN, the separation parameters were optimized. By combination with a hexamethyleneammonium hexamethylenedithiocarbamate collector precipitation, a concentration of 8 elements (Cu₂O precipitation) or 13 elements (CuSCN precipitation) in a small volume was achieved. The limits of detection of the procedures are, depending on the element, 0.1–5 μg g^?1 for flame atomic absorption spectrometry (AAS) and 0.01–0.1 μg g^?1 for graphite furnace AAS. The relative standard deviations are about 3%. The analytical performance of the procedures is compared with that of an electrolytic copper separation.     

Reaction of methyl bromopropiolate with diamines as a method of synthesis of imidazolidine derivatives

A convenient method of synthesis of 2-(methoxycarbonylmethylene)-substituted imidazolidines and imidazolidinium bromides, and also of bicyclic diazo compounds has been developed starting from methyl bromopropiolate and ethylenediamine and its derivatives.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 9, pp. 1205–1208, September, 1991.     

Numerical analysis of near electromagnetic fields of a parabolic cylinder and a paraboloid of revolution

Translated from Chislennye Metody Resheniya Obratnykh Zadach Matematicheskoi Fiziki, pp. 119–127.