Buchbesprechungen

Ohne Zusammenfassung     

Optical and conductive properties of AlSi-alloy/SiCp composites: application in modelling CO2 laser processing of composites

The optical properties—reflectivity, real part of the refractive index, absorption coefficient as well as the thermal and electrical conductivity of AlSi-alloy/SiC_p composite were measured. The optical parameters and both conductivities decreased with the increase of SiC_p particles volume in AlSi-alloy matrix. This decrease was almost linear for the volume fraction of SiC_p particle up to 10 vol% of the total mass of the composite. For the 15 vol% of SiC_p particles, the departure from linearity is connected with the presence of additional phases in AlSi-alloy/SiC_p composite materials. The measured temperature dependencies of optical reflectivity and electrical conductivity for AlSi-alloy/SiC_p 15 vol% are of metallic character. Modelling of the interaction of the CO₂ laser radiation with AlSi-alloy/SiC_p 15 vol% composite should allow to estimate the initiation time at which the surface composite reaches melting temperature.     

Unions and Intersections of Families of Lp-Spaces

Let L^Ψ and E^Ψ be the ORLICZ space and the space of finite elements respectively, on a measure space (Ω, Σ, μ), and let T ? (0, ∞). It is proved that if inf {p: p ? T} ? T or sup {p: p ? T} ? T and μ is an infinite atomless measure, then there is no ORLICZ function Ψ such that: \documentclass{article}\pagestyle{empty}\begin{document}$ L^\varphi = Lin\mathop { \cup L^p }\limits_{p\varepsilon T} $\end{document} or \documentclass{article}\pagestyle{empty}\begin{document}$ E^\varphi = Lin\mathop { \cup L^p }\limits_{p\varepsilon T} $\end{document} and moreover, there is no ORLICZ function Ψ such that: \documentclass{article}\pagestyle{empty}\begin{document}$ L^\varphi = Lin\mathop { \cap L^p }\limits_{p\varepsilon T} $\end{document} or \documentclass{article}\pagestyle{empty}\begin{document}$ E^\varphi = Lin\mathop { \cap L^p }\limits_{p\varepsilon T} $\end{document}.     

On Calderón-Toeplitz operators

We discuss boundedness and Schatten ideal criteria for a class of Toeplitz style operators based on the Calderón reproducing formula. These operators are a variation on Calderón-Zygmund operators but our results also apply to classical Toeplitz operators acting on the weighted Bergman space of the upper half plane.     

Alkoxy/siloxy group exchange in the system vinyltrialkoxysilane-iridium(I) siloxide complex

A study of reactions of dimeric siloxide iridium complex, [[(cod)Ir(mu-OSiMe3)]2] (1) with vinyltriethoxysilane and vinyltrimethoxysilane has revealed a new type of the reation--alkoxy group transfer from silicon to iridium with a simultaneous transfer of a siloxy group from iridium to silicon--as a result of which vinyldialkoxytrimethyldisiloxane and dimeric alkoxide iridium complex [[(cod)Ir(mu-OR)]2] (3) are formed. The structure of [[(cod)Ir(mu-OEt)]2] (3a) has been solved by X-ray diffraction.     

An analogue to a conjecture of S. Chowla and H. Walum

It is proved that (for every ε > 0)

$\text{∑}\text{n?T}{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}\text{∑n<}\text{T}\text{n}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{n}{}^{\mathrm{a}}\text{m}{}^{\mathrm{b}}\text{B}{}_{\mathrm{k}}\text{({}\text{T}\text{nm}\text{}) = O(T}{}^{\mathrm{<mtext>(a+b+1)</mtext><mtext>3?</mtext>}}\text{)}$

(where {·} denotes the fractional part and B_k the Bernoulli polynomial of order k) under the suppositions that k ≥ 2 and 2a ? 1 ≥ b ≥ 1. If (1) were true for k = 1, a = b = 0, then Piltz' divisor problem (for n = 3) would be readily solved. This is an analog to a conjecture formulated by S. Chowla and H. Walum in 1963 and settled in the affirmative (under suitable suppositions) quite recently by S. Kanemitsu and R. Sita Rama Chandra Rao.     

A biosensor for monitoring formaldehyde using a new lipophilic tetrathiafulvalene-tetracyanoquinodimethane salt and a polyurethane membrane

The fabrication and application of an end-column amperometric detection (AD) system with a carbon electrode for capillary-column liquid chromatography (CLC) were described. This new amperometric detector showed good sensitivity and stability in detecting the thiocompounds and other analytes with CLC. In order to obtain the better separation and detection performance for analytes, several operational parameters had been investigated: the working potentials, pH and flow rate. Under the optimum conditions, the method could effectively separate and determine cysteine (Cys), glutathione (GSH), dopamine (DA) and 6-thiopurine (6-TP). Good repeatability for retention time was obtained with a relative standard deviation (R.S.D.) value of 0.5%. The linear range covered over three orders of magnitude and the limits of detection were 8 fmol for cysteine, 20 fmol for glutathione, 8 fmol for dopamine and 20 fmol for 6-thiopurine. This method was successfully applied in determination of urinary sample with characteristics of simplicity, high sensitivity and good repeatability.