Classical solution of a problem with an integral condition for the one-dimensional wave equation

We find a closed-form classical solution of the homogeneous wave equation with Cauchy conditions, a boundary condition on the lateral boundary, and a nonlocal integral condition involving the values of the solution at interior points of the domain. A classical solution is understood as a function that is defined everywhere in the closure of the domain and has all classical derivatives occurring in the equation and conditions of the problem. The derivatives are defined via the limit values of finite-difference ratios of the function and corresponding increments of the arguments.     

Thermolysis of binuclear heterometallic pivalate with Pd(II)-Ce(III) metal core in dibenzyl ether

A reaction between palladium(II) acetate and aqueous cerium(III) acetate in acetic acid with subsequent boiling in benzene with excess pivalic acid is found to yield the complex Pd(μ-OOCBu^t)₄Ce(OOCBu^t)(HOOCBu^t)₃ (1). The liquid-phase thermolysis of complex 1 in dibenzyl ether (190°C) leads to the formation of the tetranuclear complex [Pd(μ-OOCBu^t)₄Ce(HOOCBu^t)]₂(μ-OOCBu^t)(μ-OH₂) (2). The structure of the synthesized complexes is established by X-ray diffraction.     

The nature of permeability anisotropy and catalytic activity

The phenomena of permeability anisotropy and an increase in the rates of catalytic reactions in porous membranes modified with highly dispersed catalytic systems were analyzed. A model of stochastic gas motions was proposed; this model is based on the hypothesis of the specific interaction of molecules with the inner surface of pores resulting in a nonisotropic distribution of molecules over traveling directions. The effects of asymmetric gas transfer in porous and gradient-porous membranes were considered to explain differences in the rates of heterogeneous catalytic reactions in a nanoporous membrane reactor under changes in the direction of supplying a reaction mixture. From the model proposed, it follows that the transversal diffusion of gas molecules is most probable in the porous medium of a ceramic membrane with a pore-size distribution gradient from large to small pores along the flow direction. This diffusion results in an increase in the frequency of molecular collisions with the wall of a microchannel and, correspondingly, in an increase in the contact time. The model proposed explains the intensification of a number of heterogeneous catalytic reactions performed in the porous media of catalytic porous membranes.     

The completeness of the eigenfunctions of the Tricomi problem for the Lavrent'ev–Bitsadze equation with the Frankl gluing condition

The Tricomi and Tricomi–Neumann problems for the Lavrent'ev-Bitsadze equation. It is proved in this work that when the Frankl gluing condition is fulfilled, the system of eigenfunctions can either be: a Riesz basis; not complete; not minimal; complete and minimal, but not a basis.     

Charge transfer features and ferromagnetic order in semiconductor heterostructures δ-doped with manganese

The temperature and field dependences of the specific magnetization and magnetoresistance in heterostructures with a GaAs/Ga_0.84In_0.16As/GaAs quantum well and a δ-layer of atomic Mn in the barrier layer near the quantum well filled with holes are studied. A change in the resistance and magnetization behavior upon ordering of localized magnetic moments in the cap layer due to a change in the manganese ion distribution topology is detected.     

Synthesis and electrochemical characterization of complexes of 1,2-bis[2-(pyridylmethylideneamino)phenylthio]ethanes with transition metals (CoII, NiII, CuII)

Transition metal (Ni^II, Co^II, and Cu^II) complexes with 1,2-bis[2-(3-pyridylmethylideneamino)phenylthio]ethane (1) and 1,2-bis[2-(4-pyridylmethylideneamino)phenylthio]ethane (2) were synthesized for the first time by slow diffusion of solutions of compounds 1 or 2 in CH₂Cl₂ into solutions of MX₂ · nH₂O (M = Ni, Co, or Cu; X = Cl or NO₃; n = 2 or 6) in ethanol. The reactions with Co^II and Cu^II chlorides afford complexes of composition M(L)Cl₂ (L = 1 or 2). The reactions of compound 1 with Ni^II salts produce complexes with 1,2-bis(2-aminophenylthio)ethane. The molecular structure of dinitrato[1,2-bis(2-aminophenylthio)ethane]nickel(ii) was confirmed by X-ray diffraction. The ligands and the complexes were investigated by cyclic voltammetry and rotating disk electrode voltammetry. The initial reduction of the complexes proceeds at the metal atom. The oxidation of the chlorine-containing complexes proceeds at the coordinated chloride anion. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 2, pp. 350–355, February, 2008.     

Maximizing field-effect mobility and solid-state luminescence in organic semiconductors

Conductive and emissive: organic transistors made from a simple styrylanthracene derivative have high charge mobility and high luminescence quantum yields. These properties are attributed to the lack of singlet fission, and challenge the idea that the efficient π interactions required for high mobility always lead to quenching of emission. The transistors emit blue electroluminescence and are stable during operation and storage.     

On the solution of the Gellerstedt problem for the Lavrent’ev-Bitsadze equation

We study the solvability of the Gellerstedt problem for the Lavrent??ev-Bitsadze equation under an inhomogeneous boundary condition on the half-circle of the ellipticity domain of the equation, homogeneous boundary conditions on external, internal, and parallel side characteristics of the hyperbolicity domain of the equation, and the transmission conditions on the type change line of the equation.     

Oxidative dimerization of methane: Kinetics,mathematical modeling,and optimization with La/Ce catalysts

Kinetic features of oxidative dimerization of methane to ethane and ethylene, catalyzed by a mixture of lanthanum and cerium oxides deposited onto a magnesium oxide support, were examined. A kinetic model was proposed, and the process optimization was performed for a plug-flow reactor in the quasi-homogeneous approximation.