On sets which are removable for quasiconformal space mappings

Siberian Mathematical Journal -     

Structure effects on reactivity of coordinated NO

Quantum-chemical calculations have been made on the atomic charges in 3d-metal pentacyanonitrosyl complexes, as well as in porphine and tetraazoporphine nitroso complexes, which represent simplified structural analogs for porphyrins and phthalocyanines. The charge qN on the nitrogen atom in the coordinated NO is an indicator in reactions with rigid nucleophilic reagents. In the reduction of nitric oxide by ammonia, one finds high electrophilic reactivity for the complexes formed by Mn, Fe, Co, Ni, and Cu with porphyrins and phthalocyanins, which is due to the large -electron systems in the equatorial ligands.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 25, No. 5, pp. 586–590, September–October, 1989.     

Calculations of electronic structure of molecules and complexes by the modified horn-murrel method

We describe the characteristic features of the VAI and VSAI calculation schemes, designed for nonempirical valence-basis calculations of the electronic structure of molecules and complexes and carried out using the program KOMPLEKS-2. The calculation results presented demonstrate good agreement with all-electron calculations. We show that the approximate VSAI method reproduces sufficiently satisfactorily the Hartree-Fock-Roothaan calculations.Translated from Teoreticheskaya i Eksperimental'naya Khimiya, Vol. 25, No. 4, pp. 427–432, July–August, 1989.     

Effect of the initial pressure of multicomponent bubble media on the characteristics of detonation waves

The effect of the initial pressure of multicomponent bubble media on the conditions of initiation, the structure, the velocity, and the pressure of detonation waves is experimentally studied. The variation of the initial pressure of a bubble medium is found to be an effective method to control the parameters of bubble detonation waves.     

A method of analysis of distributions of local electric fields in composites

A method of prediction of distributions of local electric fields in composite media based on analysis of the tensor operators of the concentration of intensity and induction is proposed. Both general expressions and the relations for calculating these operators are obtained in various approximations. The analytical expressions are presented for the operators of the concentration of electric fields in various types of inhomogeneous structures obtained in the generalized singular approximation.     

Regularity theory for one-dimensional variational problems with singular ellipticity

In this paper we develop regularity theory for one-dimensional variational problems with singular ellipticity. As is known the classical indirect methods can not be applied in this case since the Euler equation is not defined. However it is still possible to suggest certain direct methods. Such a theory is the content of this paper.     

Collisions of Detonation Waves in Bubbly Media

Technical Physics - The oncoming collisions of detonation waves, generated in bubbly media, is studied in the present paper while determining the critical conditions of collisions initiated in...     

Attainment and relaxation results in special classes of deformations

In this paper we deal with the attainment and relaxation issues in variational problems of mathematical theory of elasticity. We consider minimization of energy functionals in certain classes of deformations which render the problem essentially scalar. It turns out that in those cases the relaxation theorem holds for integrands that are bounded from below by a power function, with power exceeding the dimension of the space of independent variables. The bound from below can be improved in the homogeneous case. The mathematical fact behind the results is that relaxation holds at those Sobolev functions that are a.e. differentiable in the classical sense, independently of growth of Carathéodory integrands. In the homogeneous case we can also indicate a condition which is both necessary and sufficient for solvability of all boundary value minimization problems of the Dirichlet type.Received: 16 June 2000, Accepted: 12 March 2003, Published online: 6 June 2003M. A. Sychev: This research was partially supported by the grant N 00-01-00912 of the Russian Foundation for Basic Research     

Young measure approach to characterization of behaviour of integral functionals on weakly convergent sequences by means of their integrands

It is known that sequential weak lower semicontinuity and weak-strong convergence (in the scalar case) properties of integral functionals may be characterized by means of their integrands. In this paper we introduce a Young measure approach obtaining both these results and the characterization for the second property in the vector-valued case. We discuss also motivations for the definition of strict quasiconvexity, and point out that the characterization of the classes of functionals having weak-strong convergence property everywhere is not a trivial problem in the general case.