Spinor norms of local autometries of generalized quadratic lattices

It is proved that the group of spinor norms of autometries of a generalized quadratic lattice ℒ over the ring of integral elements v _p of a local field k _p , in the case wherep∤2 and ℒ is a generalized translation, is generated by the spinor norms of symmetries contained in the group of autometries of ℒ. As a corollary, an extension to the case of generalized quadratic lattices is given for known sufficient conditions of coincidence of the genus and the spinor genus of a quadratic lattice. Bibliography: 9 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 211, 1994, pp. 161–173. Translated by Yu. G. Teterin.     

Molecular electric field mapping of some anions and cations of 2- aminopurine and 6- thioguanine

Electric fields of the anions, cations and neutral forms of 2-aminopurine and 6-thioguanine have been mapped. Certain important features of the maps are similar to those found earlier in the neutral and ionic forms of adenine and guanine. The computed electric field patterns satisfactorily explain reactive sites and biological activity of the molecules.     

Formation of the structure and effective properties of composite material in the manufacture of shells with cross-ply reinforcement

Conclusion The proposed model of formation of the reinforcing framework in the manufacture of an axisymmetric shell by the CPW method makes it possible to numerically determine the thicknesses and rates of filling the layers, reinforcement angles as a function of the main parameters of the technological process, geometry of the mandrel, and characteristics of the reinforcing filament. It was established that the thicknesses of the layers, reinforcement rates and angles, and, as a consequence, the effective stiffness characteristics of the composite are substantially variable both along the meridian and over the thickness of the shell.Translated from Mekhanika Kompozitnykh Materialov, No. 5, pp. 609–617, September–October, 1992.The authors thank V. A. Frolov for the experimental results.     

To the problem of energy recuperation in gyrotrons

A relatively high level of the minimal electron energy at the gyrotron output even at very large spread in pitch factor is explained. An estimation of the recuperation efficiency, which can be obtained due to this effect, is given.     

Gravity in non-commutative geometry

We study general relativity in the framework of non-commutative differential geometry. As a prerequisite we develop the basic notions of non-commutative Riemannian geometry, including analogues of Riemannian metric, curvature and scalar curvature. This enables us to introduce a generalized Einstein-Hilbert action for non-commutative Riemannian spaces. As an example we study a space-time which is the product of a four dimensional manifold by a two-point space, using the tools of non-commutative Riemannian geometry, and derive its generalized Einstein-Hilbert action. In the simplest situation, where the Riemannian metric is taken to be the same on the two copies of the manifold, one obtains a model of a scalar field coupled to Einstein gravity. This field is geometrically interpreted as describing the distance between the two points in the internal space.Dedicated to H. ArakiSupported in part by the Swiss National Foundation (SNF)     

Reactions of 1,4-dihydropyridines (review)

The literature published over the period 1986–1990 on the chemical properties (oxidation, addition, substitution, reactions of the functional groups, etc.) of 1,4-dihydropyridines is correlated.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 5, No. 5, pp. 579–612, May, 1993.     

Fast algorithms for discrete Chebyshev-Vandermonde transforms and applications

Applying orthogonal polynomials, the discrete Chebyshev-Vandermonde transform (DCVT) is introduced as a special almost orthogonal transform. An important example of DCVT is the discrete cosine transform (DCT). Using the divide-and-conquer technique and the d'Alembert functional equation, fast DCT-algorithms are described. By the help of these results we present for the first time fast, numerically stable algorithms for simultaneous polynomial approximation and for collocation method for the airfoil equation, a special Cauchytype singular integral equation.     

On the Causes and Effects of Contaminations during rf Diode Deposition of Cr-Si Alloys

Investigations to the causes and effects of contaminants at the rf diode deposition of CrSi films in a non-heated high vacuum apparatus were carried out comparing an oxygen-free fusion target with an oxygen-containing cermet target. The films of the fusion target contained considerable amounts of oxygen; analogously the oxygen concentration in the films was increased in the case of the cermet target. Moreover, hydrogen was found. The concentration of the contaminants decreased with the sputtering power, however the rate of incorporation increased. For high sputtering rates the contamination process was reproducible and independent of the plant conditioning; the deposited films were depth-homogeneous. The reasons for this behaviour lie in water sources which are activated first of all by the discharge itself. The electrical properties found are explained by the contaminants and the deposition conditions.     

Approximate sine-Gordon solitons

We look at the recently proposed scheme of approximating a sine-Gordon soliton by an expression derived from two dimensional instantons. We point out that the scheme of Sutcliffe in which he uses two dimensional instantons can be generalised to higher dimensions and that these generalisations produce even better approximations than the original approximation. We also comment on generalisations to other models.