Rationally trivial hermitian spaces are locally trivial

Let R be a regular local ring, K its field of fractions and A an Azumaya algebra with involution over R. Let h be an -hermitian space over A. We show that if is hyperbolic over , then h is hyperbolic over A. Received September 28, 1998; in final form December 6, 1999 / Published online March 12, 2001     

Phenomenological model of the inhomogeneous state of a material under a pulse effect

A model is proposed that takes account of features of the material state under a pulse effect. The characteristic inhomogeneous states for an unstable medium are analyzed. Their correspondence with experimentally detected effects is noted.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 50–55, June, 1990.     

Relaxation mechanism of rotational type in fracture of weld joints for austenic steels

Studied is the mesoscale behavior of plastic deformation and fracture of weld joints for austenic steels. Large-scale rotational modes of deformation in heat affected zones are identified with the first stage of formation of band structures; it is related to the “traveling neck” phenomenon in the base metal. The second stage is connected with crack generation and the state of affairs in the heart-affected zone.     

Electronic Fock space as associative superalgebra

A new algebraic structure on a finite dimensional electronic Fock space is studied in detail. This structure is defined in terms of a certain multiplication of many electron wave functions and has close interrelation with coupled cluster and similar approaches. Its study simplifies the mathematical backgrounds of these approaches. Even more, it leads to relations that would be very difficult to derive using conventional technique. Formulas for action of the creation‐annihilation operators on products of state vectors are derived. Explicit expressions for action of simplest particle‐conserving products of the creation‐annihilation operators on powers of state vectors are given. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

CASSCF optimization problem for a group of excited states

A second-order version of the CASSCF approach to the optimization problem for a single (ground or excited) state and a group of excited states (involving, if necessary, also the ground state) is proposed. In contrast to the already existing methods, in the frameworks of our approach, there arises no need in completing the set of states to be optimized to the full basis set of configuration function space. Generation of secondary orbitals in the course of orbital optimization is also not required. All necessary integral transformations are performed only with active orbitals. These certainly attractive features of our approach appear due to employing the Gauss parametrization of average electronic energy domain, which is nonstandard in quantum chemistry. © 1992 John Wiley & Sons, Inc.     

Overview on mesomechanics of plastic deformation and fracture of solids

Mesomechanics involves analyzing the deformation and/or fracture of solids at the micro-, meso- and macro-scale level. Base elements for each scale level are chosen such that the behavior of the solid would be described by a combination of these elements. Special attention is given to the fragmentation of solid which is the main character of plastic flow at the mesoscale level. The final stage of fragmentation corresponds to fracture as the changes from the meso- to the macro-scale level.     

Index Reduction Formulas for Twisted Flag Varieties, II

This is a continuation of the determination begun in K-Theory 10 (1996), 517–596, of explicit index reduction formulas for function fields of twisted flag varieties of adjoint semisimple algebraic groups. We give index reduction formulas for the varieties associated to the classical simple groups of outer type A _n-1 and D _n, and the exceptional simple groups of type E ₆ and E ₇. We also give formulas for the varieties associated to transfers and direct products of algebraic groups. This allows one to compute recursively the index reduction formulas for the twisted flag varieties of any semi-simple algebraic group.     

Luminescence of ZnO nanocrystals capped with an organic dye

ZnO nanocrystals capped with an organic dye Rhodamine 6G (Rh6G) were investigated by photoluminescence (PL) and cathodoluminescence (CL) techniques. PL and CL spectra showed a remarkable decrease in visible emission intensity after ZnO nanocrystals were capped with Rh6G, indicating that dangling bonds and defect states existing at the surface of ZnO nanocrystals were significantly passivated. Rh6G on the ZnO surface exhibited a monomer-like emission, and the intensity and the position of the emission were dependent on the dye concentration.     

Effect of the hardened layer thickness of the formation of mesostructures during extension of surface hardened samples

We have made a systematic experimental study of the effect of the thickness of the surface hardened layer in planar samples of 65X13 steel on the geometric parameters of the quasiperiodic mesobustructures which are formed in the surface layer and the bulk of the sample during its plastic extension. The observed dependence of the dimensions of the fragments of mesosubstructure on the thickness of the surface hardened layer correlates well with theoretical calculations [1, 2] of the mechanical or thermal stress at the interface of two media in an external field. Institute of the Physics of Strength and Materials Science, Siberian Section, Russian Academy of Sciences. Tomsk Polytechnic University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 63–69, June, 1998.     

Statistical theory of the microdeformations of polycrystals. I

A model of microdeformations in a polycrystal which takes into account the inhomogeneity due to grain reorientation in its stressed state is considered. Using the apparatus of the theory of random functions, theoretical calculations are made of the true and macroscopic elastic limits of the polycrystal. It is shown that the limits depend on the functional form of the grain distribution density as a function of the stresses, composition, and state of the alloy, and the nature of the dislocation sources.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 96–101, August, 1971.