The Convergence and Stability of Splitting Finite-Difference Schemes for Nonlinear Evolutionary Equations

We consider a splitting finite-difference scheme for an initial-boundary value problem for a two-dimensional nonlinear evolutionary equation. The problem is split into nonlinear and linear parts. The linear part is also split into locally one-dimensional equations. We prove the convergence and stability of the scheme in L ₂ and C norms. Printed in Lietuvos Matematikos Rinkinys, Vol. 45, No. 3, pp. 413–434, July–September, 2005.     

Stress State of Multilayer Thin-Walled Elements with Interfacial Defects of Structure

Based on the discrete-structural theory of thin plates and shells, a calculation model for thin-walled elements consisting of a number of rigid anisotropic layers is put forward. It is assumed that the transverse shear and compression stresses are equal on the interfaces. Elastic slippage is allowed over the interfaces between adjacent layers. The solution to the problem is obtained in a geometrically nonlinear statement with account of the influence of transverse shear and compression strains. The stress-strain state of circular two-layer transversely isotropic plates, both without defects and with a local area of adhesion failure at their center, is investigated numerically and experimentally. It is found that the kinematic and static contact conditions on the interfaces of layered thin-walled structural members greatly affect the magnitude of stresses and strains. With the use of three variants of calculation models, in the cases of perfect and weakened contact conditions between layers, the calculation results for circular plates are compared. It is revealed that the variant suggested in this paper adequately reflects the behavior of layered thin-walled structural elements under large deformations. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 41, No. 6, pp. 761–772, November–December, 2005.     

On the Convenience to Form Coalitions or Partnerships in Simple Games

A partnership in a cooperative game is a coalition that possesses an internal structure and, simultaneously, behaves as an individual member. Forming partnerships leads to a modification of the original game which differs from the quotient game that arises when one or more coalitions are actually formed. In this paper, the Shapley value is used to discuss the convenience to form either coalitions or partnerships. To this end, the difference between the additive Shapley value of the partnership in the partnership game and the Shapley alliance value of the coalition, and also between the corresponding value of the internal and external players, are analysed. Simple games are especially considered. Research partially supported by Grant BFM 2003-01314 of the Science and Technology Spanish Ministry and the European Regional Development Fund.     

On rank-perfect subclasses of near-bipartite graphs

Shepherd95 proved that the stable set polytopes of near-bipartite graphs are given by constraints associated with the complete join of antiwebs only. For antiwebs, the facet set reduces to rank constraints associated with single antiwebs by Wagler2004. We extend this result to a larger graph class, the complements of fuzzy circular interval graphs, recently introduced in ChudnovskySeymour2004. Received: November 2004 / Revised version: June 2005     

Electron-Optical System of a High-Power Gyrotron with Nonadiabatic Electron Gun

We describe a nonadiabatic electron gun operated in the mode of a currentconfined by spatial charge and intended for producing helical electron beams for high-power gyroresonantdevices.Results of numerical simulation of electron trajectories and electron-beam parameters arepresented. It is shown that for a high operating current, the pitch factor and the electronvelocity spread can be significantly better than in the conventional adiabatic systems. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 48,No. 6, pp. 517–522, June 2005     

Magnetic and martensitic transitions in Ni-Fe-Ga alloy

The ferromagnetic shape memory alloy with nominal composition Ni₅₄Fe₁₉Ga₂₇ is investigated by Ac susceptibility and resistivity measurements. The alloy shows long-range ferromagnetic order below 290 K. The anomaly due to the martensitic transition is observed in the susceptibility and resistivity data in the temperature range around 220 K, which is associated with clear thermal hysteresis. Minor hysteresis loop technique was used to investigate the phase coexistence across the martensitic transition, and our analysis indicate that both martensite and austenite phases mutually coexist in the region of hysteresis.     

Validation of a computer-program for the interpretation of infrared spectra

The capability of a modern interpretation system for IR spectra has been tested, in which the process of structural assignment is modelled by methods of fuzzy logic. Figures of merit were generated for different interpretation algorithms. These figures of merit permit the validation as well as a comparison of independent interpretation systems. The influence of the sample preparation practice onto the information content of the resulting spectrum has been evaluated as well. Automatically generated band tables show only restricted reliability. Received: 13 February 1997 / Revised: 1 April 1997 / Accepted: 3 April 1997