Symbolic Dynamics Methods and Simulation of Internet Search

The self-consistent choice theory is applied to solve the problem of ranking Internet pages given the link matrix. The damping factor introduced in the Google search engine distorts the initial information. A binary weak-order relation is constructed for ranking Internet pages and sites without the damping factor.__________Translated from Prikladnaya Matematika i Informatika, No. 16, pp. 74–89, 2004.     

Dynamic approach to solving bargaining games

The article examines the solution of bargaining games on the basis of the previously proposed paradigm of stationary strategies in supergames. The value of axiomatic bargaining theory for choosing the unique solution in agreement games is considered. The “splitting the dollar” game for two and three players is discussed as an application. __________ Translated from Prikladnaya Matematika i Informatika, No. 22, pp. 91–104, 2005.     

Influence of non-bridging donor atoms on the value of exchange interaction in binuclear Cu<Superscript>II</Superscript> complexes with bis-hydrazones based on 2,6-diformylphenol

The quantum chemical simulation of exchange interaction according to the broken symmetry approach was performed for a series of binuclear Cu^II complexes containing the asymmetric exchange moiety based on bis-hydrazones of 2,6-diformylphenol. The calculated values were compared between themselves and with the experimental values of the exchange parameter 2J for the binuclear copper(II) complexes with bis-hydrazones based on 2,6-diformylphenol in order to reveal the influence pattern of the nature of nonbridging donor atoms X (O, N, S, and Se) onto the exchange interaction. The strength of exchange interaction of the antiferromagnetic type depends significantly on the nature of nonbridging donor atoms, increasing in the series of X = O, NH, S, and Se.     

Characterization of Cu(II) coordination compounds with 2-(7-bromo-2-oxo-5-phenyl-2,3-dihydro-1<Emphasis Type="Italic">Н</Emphasis>-1,4-benzodiazepin-1-yl)acetohydrazide and a product of its condensation with pyruvic acid

[Cu(HydrHPv)(H₂O)Cl₂] complex has been prepared and characterized by elemental analysis, IR spectroscopy, electrical conductivity, and magnetic susceptibility data. Structure of the coordination sphere and exact parameters of nearest surrounding of Cu²⁺ ions have been determined by X-ray absorption spectroscopy.     

Crystal structure of bis-Isonicotinoyl hydrazone of 2,5-diformylpyrrole

bis-Isonicotinoyl hydrazone of 2,5-diformylpyrrole existing in the crystal in the form of a tetrahydrate of the hydrazone tautomeric form is synthesized and its structure is described. In the crystal, an infinite three-dimensional network of hydrogen bonds is formed by hydrazone molecules. The neighboring hydrazone molecules are bonded by intermolecular π stacking interactions. A quantum chemical calculation of the geometry and total energy of possible tautomers in vacuum and an aqueous solution is performed.     

Boolean equations with many unknowns

The method of constructing general analytical solutions of Boolean equations previously developed for equations with a single unknown is generalized to the case of many unknowns. The efficiency of the method is demonstrated using several examples. In particular, we establish the integrability conditions and the general form of the solution of a “Boolean partial differential equation”; we consider the design of anRS-flipflop circuit and determine the general form of the corresponding family of functionsR andS. Translated from Nelineinaya Dinamika i Upravlenie, pp. 105–118, 1999.     

Atomic structure of the copper bromide complex based on benzoin 1′-phthalazinylhydrazone: DFT and X-ray absorption spectroscopy analysis

A copper bromide complex based on benzoin 1′-phthalazinylhydrazone is synthesized. Within density functional theory (OPBE/TZP) the optimal structural parameters of the complex are determined. X-ray Absorption Near-Edge Structure (XANES) spectra above the K absorption edge of copper are measured in the copper bromide complex. Theoretical XANES spectra of the K absorption edge of copper are calculated based on the full multiple scattering method and in the full potential of the finite difference method. Good agreement between the theoretical XANES spectrum and the experimental data is obtained.     

Crystal structure and magnetic properties of binuclear copper(II) complex with 2-<Emphasis Type="Italic">N</Emphasis>-(phenylhydrazono)-3-((ethyl-2-olato)imino)-1-phenyl-1,2,3-butanetrione

The binuclear copper(II) complex based on azomethine, being a condensation product of 2-aminoethanol with 1-phenyl-1,2,3-butanetrione phenylhydrazone, is structurally characterized (CIF file CCDC 1059996). The structure is compared with the structure of an analog containing the axially coordinated pyridine molecule. The influence of the axial coordination of pyridine on the magnetic exchange interaction is studied by the DFT method in the broken symmetry approach.