On approximate properties of solutions of a nonlinear mixed-type equation

In the paper, we obtain sufficient solvability conditions of a certain boundary-value problem for a nonlinear mixed-type equation and find upper and lower estimates for Kolmogorov widths of the solution set. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 12, No. 5, pp. 95–107, 2005.     

Factorization properties of subdiagonal algebras

Let M be a von Neumann algebra equipped with a normal finite faithful normalized trace τ, and let A be a tracial subalgebra of M. Let E be a symmetric quasi-Banach space on [0, 1]. We show that A has an L_E(M)-factorization if and only if A is a subdiagonal algebra.     

Compounds of Acetamide and Its Analogs with Inorganic Acids: Synthesis and Properties

Quantum-chemical calculations with the MOPAC and HYPERCHEM programs and MNDO, AM1, and PM3 methods were used to identify the reaction center in the molecules of protonated acetamide and its analogs (alkylamides) and to determine the effect of their nature on reactivity. The results of calculations are supported by IR and UV data. The change in the reactivity of alkylamides during their reaction with inorganic acids is explained by the effect of the nature of a basic or acid partner.     

Holder-type inequalities of measurable operators

We proved Holder-type inequalities for measurable operators associated with a semi-finite von Neumann algebra, this results generalize some known Holder inequalities for matrix.     

Coercive solvability of a generalized Cauchy-Riemann system in the SpaceL p (E)

For an inhomogeneous generalized Cauchy-Riemann system with nonsmooth coefficients separated from zero, we establish conditions for the solvability and estimation of a weighted solution and its first-order derivatives.