Approximation of classesC_\infty ^{\bar \psi } by zygmund sumsby zygmund sums

We consider the approximation of functions of the classes of by Zygmund sums. In papticular, we present asymptotic equalities for the quantities under various conditions imposed on functions ψ₁(·) and ψ₂(·). Institute of Mathematics, Ukrainian Academy of Sciences, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 52, No. 6, pp. 856–860, June, 2000.     

Effect of the type of state of stress on the characteristics of the mechanical glass transition process in polymers

The effect of the type of state of stress on the activation energy and relaxation time is investigated with reference to the mechanical glass transition (softening) process in polymers. An expression relating the mechanical glass transition temperature with the structural glass transition temperature, the mean stress, and the stress intensity is obtained for isotropic homogeneous polymers. Experimental data obtained for polymethyl methacrylate in uniaxial tension and compression, pure bending, and shear are presented.All-Union Scientific Research Institute of Aviation Materials, Moscow. Translated from Mekhanika Polimerov, No. 2, pp. 195–199, March–April, 1971.     

Stability of the critical behavior of weakly disordered systems with respect to the introduction of an interaction potential breaking replica symmetry

The critical behavior of weakly disordered systems with a p-component order parameter is described using field-theoretic methods. A renormalization-group analysis of the effective model replica Hamiltonian with an interaction potential breaking replica symmetry is performed directly for three-dimensional systems in the two-loop approximation. For the case of a one-step replica symmetry breaking, fixed points of renormalization group equations are found using the Padé-Borel summation technique. It is established that the critical behavior of weakly disordered systems is stable with respect to replica symmetry breaking and that the former scenario of the influence of structural defects on the critical behavior of these systems is realized.     

Modeling process operations in the forming of parts made of flat metal-polymer composites

The forming of complex three-dimensional parts (tubular structures, sections, shells) from flat sheets of metal-polymer composites is examined. Results are reported from a series of experimental studies of the strain and strength characteristics of these composites, and features of the fabrication of shells of single and double curvature are analyzed. One method of solving the problem of bending shells of complex shape with large displacements (deflections) beyond the elastic limit of the material is proposed and substantiated empirically.Paper to be presented at the IX International Conference on the Mechanics of Composite Materials (Riga, October, 1995).Translated from Mekhanika Kompozitnykh Materialov, Vol. 31, No. 3, pp. 417–427, May–June, 1995.     

Positive solutions of quasilinear elliptic inequalities on noncompact Riemannian manifolds

In this paper, we consider the generalized solutions of the inequality $$ - div(A(x,u,\nabla u)\nabla u) \geqslant F(x,u,\nabla u)u^q , q > 1,$$ on noncompact Riemannian manifolds. We obtain sufficient conditions for the validity of Liouville’s theorem on the triviality of the positive solutions of the inequality under consideration. We also obtain sharp conditions for the existence of a positive solution of the inequality ? Δu ≥ u ^q, q > 1, on spherically symmetric noncompact Riemannian manifolds.     

Dearomative (3+2) cycloaddition of 2-substituted 3,5-dinitropyridines and N-methyl azomethine ylide

Chemistry of Heterocyclic Compounds - 1,3-Dipolar cycloaddition of various 2-substituted 3,5-dinitropyridines and unstabilized N-methyl azomethine ylide has been studied. It was found that,...     

On the problem of slow seismic waves

The use of vector eigenfunctions in the block method permits one one to simplify the construction of solutions of some boundary value problems and decrease the order of the systems of pseudodifferential equations. Because of this possibility, one can reveal some general properties of the stress-strain state of bounded deformable bodies. This result makes us closer to the explanation of certain behavior of block structures, including lithosphere plates, under seismic actions and allows one to study phenomena of the existence of slow seismic waves propagating in the Earth’s crust along the so-called “seismic traces.”     

Critical dynamics of slightly disordered spin systems

A new approach to the analysis of magnetic dipole motion in external magnetic field and fields generated by neighboring magnetic dipoles is suggested, and original general kinetic equations for the dipole density are derived. Special cases of these general equations are the Bloch, Redfield, and Provotorov equations, which are widely used in NMR theory. A comparison between NMR spectra calculated with the new theory and published experimental data also shows good agreement in regions to which the equations listed above do not apply. Zh. éksp. Teor. Fiz. 113, 967–980 (March 1998)