To the Jubilee of Vsevolod Alekseevich Solonnikov

Bibliography: 42 titles.__________Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 306, 2003, pp. 7–15.     

Correlation between the Mechanical Properties and the Amount of Desorbed Water for Composites Based on Low-Density Polyethylene and Linen Yarn Production Waste

The effect of the amount of desorbed water on the mechanical properties of composites based on low-density polyethylene and linen yarn production waste (LW) is analyzed by statistical methods. It is shown that the amount of absorbed water decreases during the desorption process at room temperature both for specimens modified and unmodified with diphenylmethane diisocyanate (DIC.) The most sensitive to the action of water is the elastic modulus, which decreases considerably under the effect of water and is fully restored in the desorption process. The tensile strain also increases with the amount of absorbed water. It is found that the elastic modulus of the unmodified composite correlates linearly with the amount of desorbed water. Between the amount of desorbed water and the tensile strain, as well the specific work of deformation, a negative linear correlation is revealed. After water desorption, all strength and deformation characteristics of both the modified and unmodified composites are fully recovered.__________Translated from Mekhanika Kompozitnykh Materialov, Vol. 41, No. 4, pp. 515–524, July–August, 2005.     

Restrictions of Quadratic Forms to Lagrangian Planes,Quadratic Matrix Equations,and Gyroscopic Stabilization

We discuss the symplectic geometry of linear Hamiltonian systems with nondegenerate Hamiltonians. These systems can be reduced to linear second-order differential equations characteristic of linear oscillation theory. This reduction is related to the problem on the signatures of restrictions of quadratic forms to Lagrangian planes. We study vortex symplectic planes invariant with respect to linear Hamiltonian systems. These planes are determined by the solutions of quadratic matrix equations of a special form. New conditions for gyroscopic stabilization are found.     

Quantum diffusion

Basic ideas and results which characterize quantum diffusion of defects in quantum crystals like solid helium as a new phenomenon are presented. Quantum effects in such media lead to a delocalization of point defects (vacancies, impurities etc.) and they turn into quasiparticles of a new type—defectons, which are characterized not by their position in the crystal lattice but by their quasimomentum and dispersion law. Defecton-defecton and defecton-phonon scattering are considered and an interpolation formula for the diffusion coefficient valid in all interesting temperature and concentration regions is presented. A comparison with the experimental data is made. Some alternative points of view are discussed in detail and the inconsistency of the Kisvarsanyi-Sullivan theory is shown.     

Analysis and prediction of primary structures of proteins using a computer

On the basis of a computer analysis of four classes of toxic polypeptides, generalized primary structures of each class have been obtained which can be used for planning the synthesis of biologically active compounds.     

Coset extensions of <Emphasis Type=”Italic”>S</Emphasis>-sets

Summary Three weak variants of compactness which lie strictly between compactness and quasicompactness, are introduced. Their basic properties are studied. The interplay with mapping and their direct and inverse preservation under mappings are investigated. In the process three decompositions of compactness are observed.     

Inverse Problem for a Mathematical Model of Adsorption Dynamics

A mixed problem is considered for a system of partial differential equations modeling the process of adsorption dynamics. An existence and uniqueness theorem is proved for this problem, and the solution properties are investigated. The inverse problem is posed, involving the determination of the system coefficient given additional information about the solution. A uniqueness theorem is proved for the solution of the inverse problem.__________Translated from Prikladnaya Matematika i Informatika, No. 16, pp. 5 – 14, 2004.     

Representations of Positive Projections II

In this paper we obtain a number of Maharam-type slice integral representations, with respect to scalar measures, for positive projections in Dedekind complete vector lattices and f-algebras. AMS Classification: 47B65, 46A40, 06F25