Calderón constants of finite-dimensional couples

The Calderón constant æ( $\bar X$ ) is a numerical invariant of finite-dimensional Banach couple $\bar X = (X_0 ,X_1 )$ measuring its interpolation property with respect to linear operators acting in $\bar X$ . In the paper we prove the duality relation æ( $\bar X$ )≈ æ( $\bar X$ ^*)and calculate the asymptotic behavior of æ( $\bar X$ ) as dim $\bar X \to \infty $ for a few “classical” Banach couples.     

Geodesic flows and Neumann systems on Stiefel varieties: geometry and integrability

We study integrable geodesic flows on Stiefel varieties V _n,r ?=?SO(n)/SO(n?r) given by the Euclidean, normal (standard), Manakov-type, and Einstein metrics. We also consider natural generalizations of the Neumann systems on V _n,r with the above metrics and proves their integrability in the non-commutative sense by presenting compatible Poisson brackets on (T ^* V _n,r )/SO(r). Various reductions of the latter systems are described, in particular, the generalized Neumann system on an oriented Grassmannian G _n,r and on a sphere S ^n?1 in presence of Yang–Mills fields or a magnetic monopole field. Apart from the known Lax pair for generalized Neumann systems, an alternative (dual) Lax pair is presented, which enables one to formulate a generalization of the Chasles theorem relating the trajectories of the systems and common linear spaces tangent to confocal quadrics. Additionally, several extensions are considered: the generalized Neumann system on the complex Stiefel variety W _n,r ?=?U(n)/U(n?r), the matrix analogs of the double and coupled Neumann systems.     

More on sonolytic and sonocatalytic decomposition of Diclofenac using zero-valent iron

The study is an extension of our previous work on sonolytic and sonocatalytic decomposition of Diclofenac-Na (DCF) to depict and highlight further operation parameters of significance, and to assess the effect of a novel home-made catalyst made of magnetic nanoparticles of zero-valent iron (ZVI). It was found that high-frequency was more effective than power ultrasound (20 kHz), and the efficiency was a maximum at 861 kHz, acetate-buffered pH 3.0 and air bubbling provided that samples were prepared from a pre-heated stock solution to enhance solubility of the compound. As such, 40-min sonication rendered nearly complete transformation of DCF to intermediate products that were more biodegradable than itself, but with little mineralization of organic carbon. Catalytic sono-treatment showed that the effect of the catalyst was largest in a non-buffered acidic solution and the rate of DCF elimination increased with increasing concentrations of solids up to a “critical” mass, above which it declined via the coalescence of particles and bubbles. Sonocatalysis using the “effective” solid mass also enhanced the overall degradation or mineralization of the compound as portrayed by the accumulation of chloride and nitrate ions in solution after prolonged contact. The production of excess H₂O₂ during catalysis with ZVI was attributed to the presence of additional and major routes of OH and/or H₂O₂ formation (other than water pyrolysis). The initial rate of DCF degradation in the presence of nanoparticles was found highly sensitive to the mass of solids in solution, declining sharply as the mass exceeded a “critical” effective level. A catalyst efficacy factor was defined as a function of the initial mass ratio of Fe⁰ to DCF and found to be one order of magnitude larger than that obtained by using commercial microparticles with a threefold larger Fe content. The result signifies that the role of aqueous Advanced Fenton reactions (Fe⁰/H₂O₂) was less significant in the presence of nanoparticles relative to that of heterogeneous reactions with reactive Fe and oxygen species on the massive surface areas with enriched reaction/adsorption and nucleation sites.     

Preparative synthesis and pharmacological activity of Albicar racemate and enantiomers

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Synthesis and antihypotensive properties of 2-amino-2-thiazoline analogues with enhanced lipophilicity

In a search of nitric oxide synthase inhibitors with prolonged vasoconstrictive activity, a series of lipophilic cyclohexafused 2-amino-2-thiazolines was obtained via cyclization of tert-butyl- or benzoyl-substituted N-(cyclohex-2-en-1-yl)thioureas. The crystal structure of intermediate N-[(3aRS,7aSR)- 3a,4,5,6,7,7a-hexahydro-1,3-benzothiazol-2-yl]benzamide hydrobromide was determined by X-ray analysis. One compound was found to cause pronounced and prolonged vasoconstrictive effect after single injection to the Wystar rats with lipopolysaccharide induced acute endotoxic (vasodilatation) shock.     

Cationic polymerization of 3-azidomethyl-3-methyloxetane in the presence of the boron fluoride etherate—ethylene glycol system

The kinetics of oligomerization of 3-azidomethyl-3-methyloxetane in the presence of the boron fluoride etherate—ethylene glycol initiating system is studied by gel-permeation chromatography and IR spectroscopy methods. It is found that the molecular-mass distribution of the resulting oligooxetanediol depends on the concentration of ethylene glycol, while its molecular mass remains practically unchanged throughout the reaction. In other words, ethylene glycol serves as a chain-transfer agent. The relative chaintransfer constant is 0.5. The schemes of polymerization reactions are proposed.     

Synthesis,Crystal Structure,and Colloidal Dispersions of Vanadium Tetrasulfide (VS4)

Although many of the layered metal chalcogenides, such as MoS₂, are well‐studied, some other chalcogenides have received less attention by comparison. In particular, there has been an emerging interest in vanadium tetrasulfide (VS₄), which displays useful properties as a component of hybrids. However, the synthetic methods and characteristics of individual VS₄ are not yet well defined, and there is no report on its solution processability. Here we have synthesized VS₄ by a simple and fast direct reaction between elements. Reinvestigation of the VS₄ crystal structure yielded more precise atomic coordinates and interatomic distances, thereby confirming the crystallization of VS₄ in the monoclinic C2/c group and its quasi‐1D chainlike structure. As the chains in VS₄ are only bonded by weak van der Waals forces, we further demonstrate that bulk VS₄ may be ultrasonically dispersed in appropriate solvents to form colloids, similarly to the layered chalcogenides. VS₄ particles in colloids retain their phase identity and rod‐shaped morphology with lengths in the range of hundreds of nanometers. Isopropanol dispersion exhibited the highest concentration and stability, which was achieved owing to the repulsion caused by high negative charges on the edges of the particles.