Reduced synthesis in harmonic analysis and compact synthesis in operator theory

The notion of reduced synthesis in the context of harmonic analysis on general locally compact groups is introduced; in the classical situation of commutative groups, this notion means that a function f in the Fourier algebra is annihilated by any pseudofunction supported on f ^?1(0). A relationship between reduced synthesis and compact synthesis (i.e., the possibility of approximating compact operators by pseudointegral ones without increasing the support) is determined, which makes it possible to obtain new results both in operator theory and in harmonic analysis. Applications to the theory of linear operator equations are also given.     

RHEOKINETICS EFFECT ON FLOW AND CONVECTIVE HEAT TRANSFER OF POLYMERIZING FLUIDS

A method is proposed for space-time separation and subsequent coincidence of the parameters for kinetic and convective stages of a process. It is implemented in a constant pressure device with independent thermostating thermal chemical (reservoir) and thermal hydraulic (channel) units. Based on the macrokinetic model, numerical calculations are made of thermal and kinetic characteristics of amine-curing-agent polymerization of epoxy resin. The viscosity of a partially cured composition is found as a function of temperature and conversion β. The technique is developed to calculate, to a one-dimensional approximation, integral hydraulic and thermal characteristics of nonisothermal pressure flow of partially cured fluid in the thermal entrance section of a tube. To evaluate its applicability, the two-dimensional problem on developing nonisothermal flow of thermo-sensitive fluid is considered to a boundary-layer approximation     

Reversible sorption in the crystalline microporous semiconductor Rb-CTH-1

The sorption capacity of the recently reported crystalline microporous semiconductor Rb-CTH-1 was investigated, revealing that the structure demonstrates heat-induced reversible sorption of 3 wt% water and hydrocarbons. The Rb-CTH-1 structure maintains its crystallinity and semiconducting properties when heated to 150 °C. The treatment causes desorption induced irreversible rearrangements of the remaining guest species with a response in the semiconductive properties of the material.     

Invariant Subspaces of Subgraded Lie Algebras of Compact Operators

We show that finitely subgraded Lie algebras of compact operators have invariant subspaces when conditions of quasinilpotence are imposed on certain components of the subgrading. This allows us to obtain some useful information about the structure of such algebras. As an application, we prove a number of results on the existence of invariant subspaces for algebraic structures of compact operators, in particular for Jordan algebras and Lie triple systems of Volterra operators. Along the way we obtain new criteria for the triangularizability of a Lie algebra of compact operators. The support received from INTAS project No 06-1000017-8609 is gratefully acknowledged by the third author.     

Oxidation mechanism of 6-methyl-2,4-dioxopyrimidine with selenium oxide and selenous acid

Analysis of the oxidation mechanism of 6-methyl-2,4-dioxopyrimidine with selenium oxide and selenous acid with the formation of orotic aldehyde has been carried out by the ab initio quantum-chemical method on the 6-31G** basis. The mixed anhydride of acetic and selenous acids is formed with a gain of energy. It possesses high activity and steric accessibility in electrophilic attack on position 5 of the pyrimidine ring. The three-stage mechanism of the oxidation of the methyl group in 6-methyluracil by the mixed anhydride of selenous and acetic acids has been analyzed.     

Stability under Small Hilbert–Schmidt Perturbations for <Emphasis Type="Italic">C</Emphasis><Superscript>*</Superscript>-Algebras

This paper studies the tracial stability of C^*-algebras, which is a general property of stability of relations in a Hilbert–Schmidt-type norm defined by a trace on a C^*-algebra. Precise definitions are formulated in terms of tracial ultraproducts. For nuclear C^*-algebras, a characterization of matricial tracial stability in terms of approximation of tracial states by traces of finite-dimensional representations is obtained. For the nonnuclear case, new obstructions and counterexamples are constructed in terms of free entropy theory.