Stability of a Steady Viscous Incompressible Flow Past an Obstacle

We derive a sufficient condition for stability of a steady solution of the Navier–Stokes equation in a 3D exterior domain Ω. The condition is formulated as a requirement on integrability on the time interval (0, +∞) of a semigroup generated by the linearized problem for perturbations, applied to a finite family of certain functions. The norm of the semigroup is measured in a bounded sub-domain of Ω. We do not use any condition on “smallness” of the basic steady solution.      

Existence of Solutions with the Prescribed Flux of the Navier–Stokes System in an Infinite Cylinder

The existence and uniqueness of a solution to the nonstationary Navier–Stokes system having a prescribed flux in an infinite cylinder is proved. We assume that the initial data and the external forces do not depend on x₃ and find the solution (u, p) having the following form

Stereoselective Synthesis of (Z)‐ and (E)‐Allyl Aryl Sulfides and Selenides from Baylis?Hillman Acetates under Neutral Conditions Using β‐Cyclodextrin in Water

The first example of the stereoselective synthesis of (Z)‐ and (E)‐allyl aryl sulfides and selenides from Baylis? Hillman acetates under neutral conditions in H₂O by supramolecular catalysis involving β‐cyclodextrin is reported. β‐Cyclodextrin can be recovered and reused. The reaction is very efficient in providing allyl aryl sulfides and selenides in good‐to‐excellent yields with clean reaction profiles under mild reaction conditions.     

Kinetics and mechanism of catalytic oxidation of alcohols to carbonyl compounds with dioxygen in the Pd-containing aqua system

The oxidation of lower aliphatic alcohols C₁–C₄ with dioxygen to form the corresponding carbonyl compounds in the presence of the PdII tetraaqua complexes and Fe^II-Fe^III aqua ions in an aqueous medium was studied at 40–80 °C. The introduction of an aromatic compound (acetophenone, benzonitrile, phenylacetonitrile, o-cyanotoluene, nitrobenzene) and Fe^II aqua ion instead of the Fe^III aqua ion into the reaction system increases substantially the catalytic activity and the yield of the carbonyl compound. The key role of the Pd species in the intermediate oxidation state stabilized by the aromatic additive in the catalytic cycle of alcohol oxidation with dioxygen to the carbonyl compound was shown. An increase in the kinetic isotope effect with an increase in the temperature of methanol oxidation indicates a change in the rate-determining step of alcohol oxidation with dioxygen in the presence of Pd^II-Fe^II-Fe^III and the aromatic compound. At temperatures below 60 °C, the catalytically active palladium species are mainly formed upon the reduction of the Pd^II tetraaqua complex with the Fe^II aqua ion, whereas at higher temperatures the reaction between the alcohol and Pd^II predominates. The mechanism and kinetic equation of the process were proposed. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 5, pp. 842–848, May, 2007.     

Luminescence Study of ZnS Quantum Dots Prepared by Chemical Method

We report synthesis of ZnS quantum dots by chemical method at room temperature. In this technique, ZnS quantum dots are produced by simple chemical reactions where zeolite, acts as matrix, plays the key role in controlling particle growth during synthesis. Quantum dots exhibit luminescence properties such as Zn²⁺ related emission, efficient low voltage electroluminescence, and super linear voltage-brightness EL characteristics. This study demonstrates the technological importance of semiconductor nanosystems prepared by low cost chemical route.     

A remark on a maximal function over a Cantor set of directions

LetM _e ⁰ be the maximal operator over segments of length 1 with directions belonging to a Cantor set. It has been conjectured that this operator is bounded onL ². We consider a sequence of operators over finite sets of directions converging toM _e ⁰ . We improve the previous estimate for the (L ²,L ²)-norm of these particular operators. We also prove thatM _e ⁰ is bounded from some subsets ofL ² toL ². These subsets are composed of positive functions whose Fourier transforms have a very weak decay or are supported in a vertical strip. Partially supported by Spanish DGICYT grant no. PB90-0187.     

Relativistic mean-field parametrization of effective interaction in nuclear matter

The results of the modern relativistic Dirac-Brueckner calculations of nuclear matter are parametrized in terms of the relativistic- mean-field theory with scalar and vector nonlinear selfinteractions. It is shown that the inclusion of the isoscalar vector-meson quartic selfinteraction is essential for obtaining a proper density dependence of the vector potential in the mean-field model. The obtained mean-field parameters represent a simple parametrization of effective interaction in nuclear matter. This interaction may be used in the mean-field studies of the structure of finite nuclei without the introduction of additional free parameters.This work was supported in part by the Grant Agency of the Slovak Academy of Sciences under Grant No. GA SAV-517/1991.     

Increasing Self-Described Sequences

We proceed with our study of increasing self-described sequences F, beginning with 1 and defined by a functional equation In [1] we exhibited the simple solution f (t)=Ct, for some (0,1), of the associated functional-differential equation and we proved that provided <2/(2+d()), where we have the asymtotic equivalence F(m)~ Cm.In the present paper we show that this last result is optimal, in the sense that the self-described sequence defined by |F^–1(m)|=F(m)², that is