Entropy Numbers of Trudinger-Strichartz Embeddings of Radial Besov Spaces and Applications

The asymptotic behaviour of entropy numbers of Trudinger–Strichartzembeddings of radial Besov spaces on Rⁿ into exponential Orliczspaces is calculated. Estimates of the entropy numbers as wellas estimates of entropy numbers of Sobolev embeddings of radialBesov spaces are applied to spectral theory of certain pseudo-differentialoperators.     

Continuous embeddings of Besov-Morrey function spaces

We study embeddings of spaces of Besov-Morrey type, M Bp1,q1s1,r1(Rd ) → M Bp2 ,q2s2 ,r2 (R d ), and obtain necessary and sufficient conditions for this. Moreover, we can also characterise the special weighted situation Bp1 ,r1s1 (R d , w) → M Bp2 ,q2s2 ,r2 (Rd ) for a Muckenhoupt A ∞ weight w, with wα(x) = |x|α , α -d1, as a typical example.     

Radial subspaces of Besov and Lizorkin-Triebel classes: Extended strauss lemma and compactness of embeddings

In this article, subspaces of radial distributions of Besov-Lizorkin-Triebel type are investigated. We give sufficient and necessary conditions for the compactness of the Sobolev-type embeddings. It is also proved that smoothness of the radial function implies decay of the function at infinity. This extends the classical Strauss lemma. The main tool in our investigations consists of an adapted atomic decomposition.     

Rate constants for reaction of 1,2‐dimethylimidazole with benzyl bromide in ionic liquids and organic solvents

The rate constant for the Menschutkin reaction of 1,2‐dimethylimidazole with benzyl bromide to produce 3‐benzyl‐1,2‐dimethylimidazolium bromide was determined in a number of ionic liquids and molecular organic solvents. The rate constants in 12 ionic liquids are in the range of (1.0–3.2) × 10^?3 L mol^?1 s^?1 and vary with the solvent anion in the order (CF₃SO₂)₂ N^? < PF₆^? < BF₄^?. Variations with the solvent cation (butylmethylimidazolium, octylmethylimidazolium, butyldimethylimidazolium, octyldimethylimidazolium, butylmethylpyrrolidinium, and hexyltributylammonium) are minimal. The rate constants in the ionic liquids are comparable to those in polar aprotic molecular solvents (acetonitrile, propylene carbonate) but much higher than those in weakly polar organic solvents and in alcohols. Correlation of the rate constants with the solvatochromic parameter E _T(30) is reasonable within each group of similar solvents but very poor when all the solvents are correlated together. Better correlation is obtained for the organic solvents by using a combination of two parameters, π* (dipolarity/polarizibility) and α (hydrogen bond acidity), while additional parameters such as δ (cohesive energy density) do not provide any further improvement. © 2004 Wiley Periodicals, Inc. *

1 This article is a US Government work and, as such, is in the public domain of the United States of America.

Int J Chem Kinet 36: 253–258, 2004     

Subradial functions and compact embeddings

We investigate the compactness of embeddings of certain subsets of Nikol’skii-Besov spaces (defined on ? ^d ), consisting of essentially subradial functions, into Lebesgue spaces. Particular decay properties of radial functions are our main tool here.     

Characteristics of Λ andK 0 particles produced in central nucleus nucleus collisions at a 4.5 GeV/c momentum per incident nucleon

Data on Λ's andK ⁰'s, produced in central nucleus-nucleus collisions (C?C, C?Ne, O?Ne, C?Cu, C?Zr, C?Pb, O?Pb) at a 4.5 GeV/c momentum per incident nucleon obtained in the streamer chamber spectrometer SKM-200, are presented. Multiplicities, transverse momenta, rapidities and other characteristics are considered and compared with those for inelastic He?Li interactions. The polarization of Λ's was found to be consistent with zero. The upper limit of \(\bar \Lambda /\Lambda \) production ratio was estimated to be ≤10^?2 with a 90% confidence level. The results are compared with data of other experiments and some model calculations.     

Heat extensions,optimal atomic decompositions and Sobolev embeddings in presence of symmetries on manifolds

Our purpose is twofold. We give the heat semi-group characterization of spaces of Besov and Triebel-Lizorkin types defined on Riemannian manifolds of bounded geometry. Moreover we study boundedness and compactness of Sobolev embeddings of the spaces in presence of symmetries. To make it possible we first construct an optimal atomic decomposition for the above function spaces. Received: 4 October 2001; in final form: 13 March 2002 / Published online: 24 February 2003     

Convergence and pre-images of limit points for coding trees for iterations of holomorphic maps

Sections 1–3 contain the material of unpublished preprints [P4 and S]