Multi-avoidance of generalised patterns

Recently, Babson and Steingrímsson introduced generalised permutation patterns that allow the requirement that two adjacent letters in a pattern must be adjacent in the permutation. We investigate simultaneous avoidance of two or more 3-patterns without internal dashes, that is, where the pattern corresponds to a contiguous subword in a permutation.     

Quantum-mechanical simulation of the interaction of aluminum- and boron-containing zeolite clusters with molecules of water and ammonia

Quantum-mechanical computations of zeolite clusters with molecules of water and ammonia have been carried out. The clusters consisted of ten atoms of silicon and aluminum, where one atom of aluminum was also replaced with an atom of boron. Values of the bond length and bond angles have been obtained; the geometry of adsorption complexes and the bond energy for molecules of water and ammonia with atoms of aluminum and boron of a zeolite fragment have been determined. The computed values of bond energy for molecule probes yield the quantitative strength characteristic of zeolite aprotic acid centers.     

Evolution of the symmetry of intermediate phases and their phonon spectra during the topochemical conversion of silicon into silicon carbide

A symmetry analysis of the crystal structure and the phonon spectrum during continuous topochemical conversion of silicon into silicon carbide has been carried out. The transformation of the symmetry of phonons at high-symmetry points of the Brillouin zone upon the transition from the initial cubic structure of silicon (diamond) through an intermediate cubic structure of silicon carbide to the trigonal structure of SiC has been determined. The selection rules for the infrared and Raman spectra of all the three phases under investigation have been established.     

Isomonodromic deformations and self-similar solutions of the Einstein-Maxwell equations

It is shown that the self-similar solutions of the Einstein-Maxwell equations in the cylindrical case describe the isomonodromic deformations of ordinary linear differential equations with rational coefficients. New types of such solutions, expressed in terms of the fifth Painlevé transcendent, are found.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 181, pp. 65–92, 1990.The author is grateful to A. R. Its and V. V. Matveev for the discussion of the results and for support.     

Effect of surface state on shear stress anisotropy for muscovites

The magnitude of the shearing stress for mica was determined by Lashev [1] using a circular die. The characteristic obtained in this manner indicates the average value of the shearing stress withoug allowing for the crystallographic directions. In this article, anisotropy in the shearing stress is determined for Mamsk muscovites using a plane die; in addition, the effect of the crystal surface state on this quantity is considered.     

Double electron-nuclear resonance of free radical 1,3-diphenyl-1, 4-dihydro-1,2,4-benzotriazin-4-yl

Conclusions The HFS constants for the protons in positions 5–13 of the free radical 1,3-diphenyl-1, 4-dihydro-1,2,4-benzotriazin-4-yl were determined by the DENR method.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 3, pp. 698–699, March, 1984.