Synthesis and Characterization of Zn(II) Complexes of 2-(7-Bromo-2-oxo-5-phenyl-2,3-dihydro-1<Emphasis Type="Italic">H</Emphasis>-1,4-benzodiazepin-1-yl)acetohydrazide and Its Condensation Products with Pyruvic Acid and Isatin

The systems ZnCl₂–2-(7-bromo-2-oxo-5-phenyl-2,3-dihydro-1H-1,4-benzodiazepin-1-yl)acetohydrazide (Hydr)–propan-2-ol, ZnCl₂–Hydr–pyruvic acid (HPv), and Zn(CH₃COO)₂–Hydr–isatin(HIz)–propan-2-ol were studied. Optimal synthesis conditions were determined, and the complexes [Zn(Hydr)₂Cl₂], [Zn(HydrHPv)₂Cl₂], and [Zn(HydrIz)₂] were isolated. The complexes were characterized by elemental analysis, thermogravimetry, IR spectroscopy, and mass spectrometry. The electrical conductivities of the complexes were measured. The local environment of the central atom in the coordination entity was determined by X-ray absorption spectroscopy.     

Synthesis,structure, and photoluminescence properties of molecular complexes of bis(4-formyl-3-methyl-1-phenyl-1<Emphasis Type="Italic">H</Emphasis>-pyrazol-5-olato)cadmium(II) with aminoquinolines and 1-aminoisoquinoline

Molecular complexes of bis(4-formyl-3-methyl-1-phenyl-1H-pyrazol-5-olato)cadmium(II) with isoquinolin-1-amine, quinolin-3-amine, 4,6-dimethylquinolin-5-amine, and quinolin-6-amine have been synthesized, and their structure was studied by IR, UV, ¹H NMR, and X-ray absorption spectroscopy. Photoluminescence properties of the complexes have also been examined.     

Approximation of Smooth Functions and Constants by Polynomials with Integer and Natural Coefficients

Direct theorems on the approximation of smooth functions by polynomials with integer coefficients are strengthened. First theorems on approximation by polynomials with natural coefficients are obtained.     

Contribution to the asymptotic theory of quasisteady viscous flows

The aim of this paper is to obtain equations which, as Re , describe quasisteady viscous incompressible flows with stream surfaces that are closed only in the limit as Re , and also to examine the simpler consequences of these equations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 46–51, July–August, 1985.The author wishes to thank V. Ya. Neiland for taking an interest in his work and discussing the results.     

The banach algebra A and its properties

Beurling’s algebra is considered. A* arises quite naturally in problems of summability of the Fourier series at Lebesgue points, whereas Wiener’s algebra A of functions with absolutely convergent Fourier series arises when studying the norm convergence of linear means. Certainly, both algebras are used in some other areas. A* has many properties similar to those of A, but there are certain essential distinctions. A* is a regular Banach algebra, its space of maximal ideals coincides with[−π, π], and its dual space is indicated. Analogs of Herz’s and Wiener-Ditkin’s theorems hold. Quantitative parameters in an analog of the Beurling-Pollard theorem differ from those for A. Several inclusion results comparing the algebra A* with certain Banach spaces of smooth functions are given. Some special properties of the analogous space for Fourier transforms on the real axis are presented. The paper ends with a summary of some open problems.     

Estimation of electromagnetic energy accumulation time in a water drop exposed to infrared laser radiation

The time of accumulation of electromagnetic energy in a water drop exposed to infrared laser radiation is estimated numerically taking into account the energy of interaction of water molecules and optical parameters of the water drop. The calculated value of electromagnetic energy accumulation time is in good agreement with the experimental value.     

Approximation of functions by polynomials with various constraints

The pointwise approximations of functions with a given modulus of continuity of their r-th derivatives on a closed interval of the real axis are done with various additional constraints. The paper attempts to review such constraints.