An algorithm for the constrained extremum problem

An algorithm is proposed to find the constrained minimum of a function. The algorithm uses differential equations that incorporate the problem constraints as singular manifolds. Translated from Obratnye Zadachi Estestvoznaniya, Published by Moscow University, Moscow, 1997, pp. 48–51.     

Copper complexes with polydentate hetarylformazanylcelluloses

Copper complexes with polydentate irregular 1-aryl-5-heterylformazan-6-celluloses were synthesized (aryl is phenyl, 2-hydroxy-4-nitrophenyl, 2-hydroxy-5-nitrophenyl, 2-hydroxy-4-chloro-5-nitrophenyl, 2-hydroxy-4-nitro-5-chlorophenyl, 2-carboxyphenyl, 4-sulfophenyl; heteryl is 4-methyl-6-methoxypyrimidin-2-yl, 4,6-dimethylpyrimidin-2-yl, 4-methyl-1,6-dihydro-1H-6-oxopyrimidin-2-yl, benzoxazol-2-yl, benzothiazol-2-yl). The structures of the complexes were determined by EPR. The relationship between the static exchange capacity in terms of Cu²⁺ and the number of formazan groups in the matrix, which is 0.1–0.3 mM/g for hetarylformazancelluloses, was established.     

Equations of <Emphasis Type="Italic">G</Emphasis>-minimal conic bundles with degree 4

We consider the first nontrivial case of relatively G-minimal conic bundles which are G-minimal and have r = 4 singular fibers. Classification obtained gives explicit equations of minimal conic bundles (S, G) and an explicit action of the group G on the Picard group Pic(S) and on the surface S.     

Multipurpose Cyclotron System for Research Works and Applied Use

Physics of Particles and Nuclei Letters - A cyclotron system based on the updated MCC-30/15 cyclotron has been developed and manufactured at JSC Efremov Institute of Electrophysical Apparatus...     

Kinetic models for mechanoenzymes: structural aspects under large loads

A broad class of chemical kinetic model for mechanoenzymes is analyzed theoretically in order to uncover structural aspects of the underlying free-energy landscape that determine the behavior under large resisting and assisting loads, specifically the turnover rate or, for a translocatory motor protein, the mean velocity, say, V. A systematic graphical reduction algorithm is presented that provides explicit analytical expressions for mean occupation times in individual biomechanochemical states, for the splitting or backward/forward fractions, for the overall mean dwell time, and for the turnover rate. Application to the previously studied N-state sequential and (N alpha,N beta)-parallel-chain models provides explicit structural criteria (independent of the zero-load transition rates) that determine whether mid /V/ diverges to large values or, conversely, exhibits extrema and converges to a vanishing value as the externally imposed load grows. Closed-form analytical extensions accommodate side-chain and looped side-chain reaction sequences in the enzymatic cycle. A general divided-pathway model is analyzed in detail.