Inverse problem for Euler-Poisson-Darboux abstract differential equation

For the nonhomogeneous Euler-Poisson-Darboux equation in a Banach space, we consider the problem of determination of a parameter on the right-hand side of the equation by the excessive final condition. This problem can be reduced to the inversion of some operator represented in a suitable form and related to the operator solving the Cauchy problem for the homogeneous Euler-Poisson-Darboux equation. As the final result, we show that the solvability of the problem considered depends on the distribution of zeroes of some analytic function. In addition, we give a simple sufficient condition ensuring the unique solvability of the problem. __________ Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 15, Differential and Functional Differential Equations. Part 1, 2006.     

Group of automorphisms of the ring ℤA4

The structure of the group of automorphisms of the integer group ring of the group A₄ is studied in terms of a semidirect product. We show that the Zassenhaus conjecture on the structure of automorphisms of integer group rings of finite groups for the group Aut ?A₄ holds.     

Yurii Pavlovich Popov February 13, 1928–February 24, 2005 (On the 80th anniversary of his birth)

The scientific biography of the distinguished physicist experimentalist and prominent expert in the field of neutron nuclear physics Yurii Pavlovich Popov (13.02.1928–24.02.2005) is presented, including his work at Lebedev Physical Institute, AS USSR and the Joint Institute for Nuclear Research. Yu.P. Popov was a member of the editorial board of the journal Physics of Particles and Nuclei from 1971 to the end of his life.     

A new electrochemical procedure for preparing 2,4,6-triphenylselenopyran from 1,5-diketones under conditions of acid catalysis

A new electrochemical procedure was developed for preparing 2,4,6-triphenylselenopyran from 1,5-diketones under conditions of acid catalysis at oxidative electrochemical activation of hydrogen selenide in the presence of a one-electron oxidizing agent in a nonaqueous solution. The electrolysis products were analyzed by gas chromatography with a mass-selective detector.     

Determination of C<Subscript>1</Subscript>-C<Subscript>3</Subscript> carboxylic acids in air using a sensor

The adsorption of C₁-C₃ carboxylic acids on modified films of different natures and polarities is studied in exposuring piezoelectric sensors to acid vapors. The method of film fabrication and the ratio of components in the mixed films are optimized; the sensitivity and selectivity of films are calculated; piezoelectric sensors are proposed for the separate determination of acids in air; and equations for calculating their concentrations are derived.     

Problems of Thin Inclusions in a Two-Dimensional Viscoelastic Body

Under study are the equilibrium problems for a two-dimensional viscoelastic body with delaminated thin inclusions in the cases of elastic and rigid inclusions. Both variational and differential formulations of the problems with nonlinear boundary conditions are presented; their unique solvability is substantiated. For the case of a thin elastic inclusion modelled as a Bernoulli–Euler beam, we consider the passage to the limit as the rigidity parameter of the inclusion tends to infinity. In the limit it is the problem about a thin rigid inclusion. Relationship is established between the problems about thin rigid inclusions and the previously considered problems about volume rigid inclusions. The corresponding passage to the limit is justified in the case of inclusions without delamination.     

Fragmented substructure and crack formation in low-alloy steel

In the work we studied the substructure of 30KhGSA steel after rolling. A relation has been established between the macrofracture of the specimen and its dislocation substructure. The formation and completion of a fragmented substructure with precipitation of carbides at the junctions of fragments during rolling indicate that the lifetime is close to exhaustion. Annealing that partially or completely destroys the fragmented substructure causes microcracks to collapse and heal, eliminates the microcrack nucleation sites, eliminates trajectories of facilitated microcrack growth, which follow subboundaries, and restores the plasticity of the steel.Tomsk State Architectural and Civil Engineering Academy. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 73–82, August, 1994.