On Instability of Equilibrium Figures of Rotating Viscous Incompressible Liquid

We prove that non-axially symmetric equilibrium figures of uniformly rotating viscous incompressible liquid are unstable when the second variation of the energy functional can take negative values. Bibliography: 8 titles.__________Translated from Problemy Matematicheskogo Analiza, No. 30, 2005, pp. 69–85.     

Higher order optimality conditions with an arbitrary non-differentiable function

In this paper, we introduce a higher order directional derivative and higher order subdifferential of Hadamard type of a given proper extended real function. We obtain necessary and sufficient optimality conditions of order n (n is a positive integer) for unconstrained problems in terms of them. We do not require any restrictions on the function in our results. In contrast to the most known directional derivatives, our derivative is harmonized with the classical higher order Fréchet directional derivative of the same order in the sense that both of them coincide, provided that the last one exists. A notion of a higher order critical direction is introduced. It is applied in the characterizations of the isolated local minimum of order n. Higher order invex functions are defined. They are the largest class such that the necessary conditions for a local minimum are sufficient for global one. We compare our results with some previous ones. As an application, we improve a result due to V. F. Demyanov, showing that the condition introduced by this author is a complete characterization of isolated local minimizers of order n.     

Discovery of small molecule inhibitors of ubiquitin-like poxvirus proteinase I7L using homology modeling and covalent docking approaches

Essential for viral replication and highly conserved among poxviridae, the vaccinia virus I7L ubiquitin-like proteinase (ULP) is an attractive target for development of smallpox antiviral drugs. At the same time, the I7L proteinase exemplifies several interesting challenges from the rational drug design perspective. In the absence of a published I7L X-ray structure, we have built a detailed 3D model of the I7L ligand binding site (S2-S2' pocket) based on exceptionally high structural conservation of this site in proteases of the ULP family. The accuracy and limitations of this model were assessed through comparative analysis of available X-ray structures of ULPs, as well as energy based conformational modeling. The 3D model of the I7L ligand binding site was used to perform covalent docking and VLS of a comprehensive library of about 230,000 available ketone and aldehyde compounds. Out of 456 predicted ligands, 97 inhibitors of I7L proteinase activity were confirmed in biochemical assays ( approximately 20% overall hit rate). These experimental results both validate our I7L ligand binding model and provide initial leads for rational optimization of poxvirus I7L proteinase inhibitors. Thus, fragments predicted to bind in the prime portion of the active site can be combined with fragments on non-prime side to yield compounds with improved activity and specificity.     

Tetrasubstituted 2-imidazolones via Ag(I)-catalyzed cycloisomerization of propargylic ureas

A one-pot protocol based on a Ag(I)-catalyzed cycloisomerization of propargylic ureas, derived from secondary propargylamines and isocyanates, was developed for the generation of the 2-imidazolone core.     

Radical cations of branched alkanes in solutions: time-resolved magnetic field effect and quantum chemical studies

Radical cations of heptane and octane isomers, as well as several longer branched alkanes, were detected in irradiated n-hexane solutions at room temperature by the method of time-resolved magnetic field effect (TR MFE). To identify radical cations, the hyperfine coupling constants as determined by simulation of the TR MFE curves were compared to the constants calculated using the density functional theory (DFT) approach. The g-values of the observed radical cations were close to that of the 2,2,3,3-tetramethylbutane radical cation studied earlier by optically detected electron spin resonance (ESR) and TR MFE techniques. No evidence of the decay of the radical cations of branched alkanes to produce olefin radical cations was found, which was further supported by the observation of positive charge transfer from the observed radical cations to cycloalkane molecules. The lifetimes of the radical cations of the branched alkanes were found to be longer than tens of nanoseconds.     

Characterizations of pseudoconvex functions and semistrictly quasiconvex ones

In this paper, we provide some new necessary and sufficient conditions for pseudoconvexity and semistrict quasiconvexity of a given proper extended real-valued function in terms of the Clarke–Rockafellar subdifferential. Further, we extend to programs with pseudoconvex objective function two earlier characterizations of the solutions set of a set constrained nonlinear programming problem due to Mangasarian (Oper Res Lett 7:21–26, 1988). A positive function p appears in the most results. It is replaced by the number 1 if the function is convex and its domain of definition is convex, too.     

Solvability of some two-dimensional quasistationary free boundary problems for the Navier-Stokes equations with moving contact points

The paper is concerned with some quasistationary two-dimensional free boundary problems of viscous flow with moving contact points and with contact angle equal to π. A typical example of such a flow is filling a capillary tube in the presence of surface tension. The proof of the solvability of these problems is based on the analysis (made by the author and V. V. Pukhnachëv about 10 years ago) of the asymptotic formulas for the solutions of the Navier-Stokes equations in a neigborhood of contact points. Bibliography: 10 titles.