Refraction of surface spin waves in spatially inhomogeneous ferrodielectrics with biaxial magnetic anisotropy

The refractive index of surface spin waves propagating in a ferromagnetic medium with a nonuniform distribution of the parameters of uniaxial and orthorhombic magnetic anisotropies and exchange coupling is determined within the spin-density formalism. The coefficients of reflection and transmission of spin waves at the interface between two homogeneous magnets with different constants of uniaxial and orthorhombic magnetic anisotropies, exchange coupling, and saturation magnetization are calculated. The dependences of the intensity of a reflected wave and the refractive index on the wave frequency and the strength of an external dc homogeneous magnetic field are determined.     

Sobolev-Type Classes of Functions with Values in a Metric Space. II

We prove equivalence of the definitions by the author and by Korevaar and Schoen of the Sobolev classes of mappings of a domain of an arithmetic n-dimensional space to a metric space.     

Mappings of Domains in Rn and Their Metric Tensors

We consider quasi-isometric mappings of domains in multidimensional Euclidean spaces. We establish that a mapping depends continuously in the sense of the topology of Sobolev classes on its metric tensor to within isometry of the space. In the space of metric tensors we take the topology determined by means of almost everywhere convergence. We show that if the metric tensor of a mapping is continuous then the length of the image of a rectifiable curve is determined by the same formula as in the case of mappings with continuous derivatives. (Continuity of the metric tensor of a mapping does not imply continuity of its derivatives.)     

Crystal and molecular structure of 3β-acetoxy-22S,25-epoxyholosta-7,9(11)-dien-17α-ol

A complete x-ray structural investigation has been made of 3-acetoxy-22S,25-epoxyholosta-7,9(11)-dien-17-ol. Important conformational differences between this compound and its 17-deoxy derivative have been found which show the mobility of the conformation of rings B and C of the holostane series and the tetrahydrofuran ring of the side chain of the molecule. It has been shown that the conformation of the side chain of the molecule is stabilized by an 017-H...022 intramolecular hydrogen bond, without excluding the possibility of the participation of the hydroxy group in the formation of intermolecular hydrogen bonds (bifurcated).Pacific Ocean Institute of Bioorganic Chemistry, Far Eastern Branch, Russian Academy of Sciences, Vladivostok. Translated from Khimiya Prirodnykh Soedinenii, Nos. 3,4, pp. 341–344, May–August, 1992.     

Crystal and molecular structures of 1,8-diacetyl-3-methyl-DL-allantoin

DL-Allantoin (I) has been isolated from an alcoholic extract of a marine spongeAxinellidae gen. sp., and derivatives of it have been obtained: 1, 8-diacetyl-DL-allantoin (II) and 1,8-diacetyl-3-methyl-DL-allantoin (III). The crystal and molecular structures of (III) have been established by X-ray structural analysis.Pacific Ocean Institute of Bioorganic Chemistry, Far Eastern Branch, USSR Academy of Sciences, Vladivostok. Translated from Khimiya Prirodnykh Soedinenii, No. 3, pp. 422–426, May–June, 1988.     

The anthropogenic transformation of the water bodies of the European North of Russia

Water bodies of the European North of Russia are classified according to the water contamination level. The high degree of contamination of particular river sections in the European North is shown to be caused by the accumulation of toxic heavy metal compounds and other pollutants. The values of the anthropogenicaltered natural background of water bodies were estimated. It was shown the content of phenol and of copper compounds, of iron and of nickel to exceed the maximum allowable concentrations dozens of times.     

Inhibition of explosive decomposition of acetylene

An experimental study of the inhibition of the exothermic decomposition of acetylene diluted with household propane+butane mixture and hydrogen was performed. Acetylene-inhibitor mixtures were heated behind reflected shock waves. The shock wave was generated by the detonation wave initiated in a stoichiometric acetylene-oxygen mixture. The minimum volumetric inhibitor concentrations capable of suppressing the self-decomposition of acetylene were determined.     

The effective action for superfield Lagrangian quantization in reducible hypergauges

The rules of local superfield Lagrangian quantization in reducible non-Abelian hypergauge functions are formulated for an arbitrary gauge theory. The generating functionals of standard and vertex Greens functions which depend on the Grassmann variable via super(anti)fields and sources are constructed. The difference between the local quantum and the gauge fixing action determines an almost Hamiltonian system such that translations with respect to along the solutions of this system define the superfield BRST transformations. The Ward identities are derived and the gauge independence of the S-matrix is proved.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 5966, October, 2004.