Functionals strictly subjected to convergent series and search for singularities of mappings

This paper is a continuation of the author’s previous works where the concepts of search functionals were introduced and used to develop methods of cascade search for singularities of mappings between metric spaces. Such singularities of mappings were considered as coincidences, common preimages, common fixed points and common roots of finite sets of mappings. In this paper, a new class of functionals strictly subjected to convergent series is introduced. With the help of such functionals the problems of local search for the above-mentioned singularities of mappings between metric spaces are investigated. Some new iteration schemes are suggested. Generalizations of several known results are obtained.     

Algebraic properties of certain cohomological invariants of equivariant mappings

Translated from Matematicheskie Zametki, Vol. 50, No. 1, pp. 108–117, July, 1991.     

New approach to the synthesis of dihydrothiopyrans using cobalt complexes

Institute of Organic Chemistry, Bashkir Science Center, Urals Branch, Russian Academy of Sciences, 450054 Ufa, Bashkortostan, Russia. Translated fromIzvestiya Akademii Nauk, Seriya Khimicheskaya, No. 12, pp. 2813–2814, December, 1992.     

The behavior of Riesz means of the coefficients of a symmetric square L-function

Let f(z) be a holomorphic Hecke eigencuspform of even weight k with respect to SL(2, Z) and let L(s, sym ² f) = ∑ _n=1 ^∞ c_nn^−s, Re s > 1, be the symmetric square L-function associated with f. Represent the Riesz mean (ρ ≥ 0)

Fixed-point and coincidence theorems in ordered sets

The paper is devoted to the problem of the existence of common fixed points and coincidence points of a family of set-valued maps of ordered sets. Fixed-point and coincidence theorems for families of set-values maps are presented, which generalize some of the known results. The presented theorems, unlike previous ones, do not assume the maps to be isotone or coverable. They require only the existence of special chains having lower bounds with certain properties in the ordered set.     

The influence of radiation on the temperature profile of an induced discharge in argon at atmospheric pressure

This study presents a quantitative evaluation of the influence of radiation upon the parameters of a long induced discharge in argon at atmospheric pressure. Radiation heat transfer in the optically transparent tin plasma layers with thickness of the order of several centimeters) and reabsorption spectral intervals is examined. Experimental error produced by inaccurate knowledge of the transfer and optical characteristics of the plasma is evaluated. The effect of convection on radial temperature profile is evaluated.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiztki, No. 6, pp. 35–43, November–December, 1971.     

Recyclization reactions of heterocycles

2-Thioxo-4-oxazolidone and thiazolidines containing heteroatom substituants (O, S, and NH) in the 2 and 4 positions are converted to benzimidazole derivatives on reaction with o-phenylenediamine. The direction of these recyclizations depends on the nature of the heteroatom substituents in the 2 and 4 positions of the heteroring.See [1] for communication XX.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 5, pp. 666–668, May, 1978.     

Recyclization reactions of heterocyles. XVII. Hydrazination of 1, 3, 4-oxadiazolium salts

2, 5-Diaryl-3-alkyl-1, 3, 4-oxadiazolium salts react with hydrazine to give acyclic hydrazinolysis products or products of recyclization with participation of the carbon atom in the 2 position of the oxadiazole ring, i.e., dihydro-sym-tetrazines and N-amino-sym-triazoles (with hydrazine) and 2-phenyl-5-aryl-1, 3, 4-oxadiazoles (with benzoylhydrazine) or formazans (with phenylhydrazine).See [1] for communication XVI.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 5, pp. 629–634, May, 1976.     

Number of the representations of integers by certain ternary quadratic forms

Exact formulas are derived for the number of the representations of positive integers by certain positive ternary quadratic forms, belonging to multiclass genera. The Fourier coefficients of the corresponding cusp forms (on the basis of the known results of Waldspurger and Tunnell) are expressed in terms of the values of the Hasse-Weil L-functions of certain elliptic curves at the center of the critical strip.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 154, pp. 154–162, 1986.