A convenient semicarbazide resin for the solid-phase synthesis of peptide ketones and aldehydes

Use of a semicarbazide resin for the solid-phase preparation of peptide ketones and aldehyde led to optimal results in terms of both purity of the final product and overall yield. This resin was prepared without complication by activation of the commercial available aminomethyl polystyrene with CDI at room temperature, followed by treatment with tert-butyl carbazate. Furthermore, the TNBSA colorimetric assay has been adapted for checking the incorporation of the carbonyl moiety onto hydrazine-based resins.     

Laguerre expansion on the Heisenberg group and Fourier-Bessel transform on C~n Dedicated to Professor Sheng GONG on the occasion of his 75th birthday

Given a principal value convolution on the Heisenberg group Hn = Cn×R, we study the relation between its Laguerre expansion and the Fourier-Bessel expansion of its limit on Cn. We also calculate the Dirichlet kernel for the Laguerre expansion on the group Hn.     

Unavoidable Traces Of Set Systems

Sauer, Shelah, Vapnik and Chervonenkis proved that if a set system on n vertices contains many sets, then the set system has full trace on a large set. Although the restriction on the size of the groundset cannot be lifted, Frankl and Pach found a trace structure that is guaranteed to occur in uniform set systems even if we do not bound the size of the groundset. In this note we shall give three sequences of structures such that every set system consisting of sufficiently many sets contains at least one of these structures with many sets.     

Enclosure results for second-order relative spectra by elementary means

Motivated by the general approach due to Shargorodsky we derive enclosure results for the second-order relative spectrum of bounded selfadjoint operators by studying quadratic operator pencils. The quality of the results is discussed by means of a simple example.

     

Synthesis and properties of the nanocomposite of zink oxide and poly(amic acid)

The composite comprised of zinc oxide quantum dots and poly(amic acid) (PAAc) was prepared and studied by X-rays diffraction, X-ray photoelectron spectroscopy, light scattering, UV absorbance and UV fluorescence. The UV absorbance of the ZnO/PAAc composite was found to be much larger than that of its components taken separately. The fluorescence of the ZnO/PAAc composite was found to be shifted to longer wavelengthes in comparison with pure ZnO. The presence of the dopant dodecylbenzenesulfonic acid was found to affect the observed fluorescence.     

Approximation of multi-scale elliptic problems using patches of finite elements

In this paper we present a method to solve numerically elliptic problems with multi-scale data using multiple levels of not necessarily nested grids. The method consists in calculating successive corrections to the solution in patches whose discretizations are not necessarily conforming. It resembles the FAC method (see Math. Comp. 46 (174) (1986) 439–456) and its convergence is obtained by a domain decomposition technique (see Math. Comp. 57 (195) (1991) 1–21). However it is of much more flexible use in comparison to the latter. To cite this article: R. Glowinski et al., C. R. Acad. Sci. Paris, Ser. I 337 (2003).     

Tribute to Endre Csáki and Pál Révész

Summary This article provides a glimpse of some of the highlights of the joint work of Endre Csáki and Pál Révész since 1979. The topics of this short exploration of the rich stochastic milieu of this inspiring collaboration revolve around Brownian motion, random walks and their long excursions, local times and additive functionals, iterated processes, almost sure local and global central limit theorems, integral functionals of geometric stochastic processes, favourite sites--favourite values and jump sizes for random walk and Brownian motion, random walking in a random scenery, and large void zones and occupation times for coalescing random walks.