The long‐time behaviour of the thermoconvective flow in a porous medium

For the Boussinesq approximation of the equations of coupled heat and fluid flow in a porous medium we show that the corresponding system of partial differential equations possesses a global attractor. We give lower and upper bounds of the Hausdorff dimension of the attractor depending on a physical parameter of the system, namely the Rayleigh number of the flow. Numerical experiments confirm the theoretical findings and raise new questions on the structure of the solutions of the system. Copyright © 2004 John Wiley & Sons, Ltd.     

Monitoring genomic alterations with a panel of oligonucleotide probes specific for various simple repeat motifs

Germline and somatic instability of the human genome was studied, using synthetic oligonucleotides specific for simple repeat motifs. The following probes were used: (GTG)5, (GACA)4, (GATA)4, (CT)8, (TTAGGG)3, (GT)8, (GAA)6 and (GGAT)4. Each of them is unique with respect to the target regions recognized in the genome. Thus compilation of the various fingerprint data provides a complex map of the genome (and its deviations). While the fingerprints of differentiated somatic tissues never showed any alterations, in tumor tissues (namely gliomas) many changes could be detected. Most of the latter reflect secondary karyological aberrations. In nearly one third of the gliomas, drastically amplified and apparently monomorphic DNA fragments were identified. This marker should make it possible to deal with causal pathogenetic mechanisms as well as novel diagnostic strategies.     

Studies on pre-hump and main fractions of cellulose-2,5-acetate in acetone

Technical cellulose-2.5-acetates (CA 2.5) were characterized regarding their carbohydrate composition in comparison to the raw material. The association of the CA 2.5 samples in acetone was studied by size exclusion chromatography (SEC) using various acetone grades and styrene divinylbenzene copolymer columns. In HPLC grade acetone with and without addition of 1% water up to three different pre-humps eluted in front of the main fraction of the polymer. The evaluation of the main peak by light scattering measurements resulted in high molar masses indicating that for these technical CA 2.5 samples even the main fraction is not dissolved without association. No pre-humps or association phenomena were observed after addition of 1 ppm LiBr to HPLC grade acetone or with p.a. grade acetone. In addition pre-hump enriched and pre-hump free fractions were isolated by fractionated precipitation. The carbohydrate composition of these fractions was determined and correlated with their association pattern in SEC investigations.     

A decomposition result for a class of polling models

Boxma and Groenendijk have shown that the workload in polling models decomposes into two independent variables. This paper demonstrates a different type of decomposition that has an explicit multi-dimensional form. This decomposition does not apply to all polling models, but does, for example, apply to models with constant switch-over times and either exhaustive or gated service disciplines. For such models, we show that the population of customers present in the system (represented by a vector indicating the number of customers at each queue) at key time points breaks into two independent subpopulations: (1) the population of customers present in the related model with zero switch-over times; (2) another population, which is particularly easy to analyze. This result has a number of theoretical and applied implications.     

Zur Berechnung Stekloffscher Eigenwerte

Zusammenfassung Es wird ein neues Verfahren zur numerischen Berechnung des ersten nichttrivialen Stekloffschen Eigenwertes beschrieben. Dieses Verfahren arbeitet nur mit oberen Schranken.

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We describe a new procedure for the numerical evaluation of the first nontrivial Stekloff eigenvalue. This procedure works only with upper bounds.

     

Züchtung und röntgenographische Untersuchung von Einkristallen der Thiosilicate (Mn,Mg)2SiS4, (Mn,Fe)2SiS4 und (Mg,Fe)2SiS4 mit Olivinstruktur

Crystal Growth and Structure of Olivine Type Compounds (Mn, Mg)₂SiS₄, (Mn,Fe)₂SiS₄ and (Mg,Fe)₂SiS₄ Single crystals of (Mn, Mg)₂SiS₄, (Mn,Fe)₂SiS₄ and (Mg,Fe)₂SiS₄ were obtained by chemical transport reactions. Characterization of the crystals was done by electron microprobe analysis and X-ray methods. The compounds have the olivine structure with space group Pnma. Cell dimensions are a = 1267.6(1), b = 743.0(2), c = 592.7(2) pm for Mn_1,4Mg_0,6SiS₄, a = 1265.1(4), 736.1(2), c = 589.9(3) pm for Mn_1,4Fe_0,6SiS₄ and a = 1258.6(7), b = 732.9(3), c = 587.0(3) pm for Mg_1,14Fe_0,86SiS₄. Crystal structure refinement yielded different distributions of the two metal cations on the octahedral sites of the olivine structure: while Mn²⁺ and Mg²⁺ are evenly distributed over the M(1) and M(2) positions in Mn_1,4Mg_0,6SiS₄, the M(1) position is enriched in Fe²⁺ relative to M(2) in Mg_1,14Fe_0,86SiS₄.     

The vitamin D3 pathway in human skin and its role for regulation of biological processes

The skin is the only tissue yet known in which the complete ultraviolet-B (UV-B)-induced pathway from 7-dehydrocholesterol to hormonally active calcitriol (1alpha,25-dihydroxyvitamin D(3)) occurs under physiological conditions. Epidermal synthesis of calcitriol could be of fundamental relevance because calcitriol regulates important cellular functions in keratinocytes and immunocompetent cells. Because of their antiproliferative and prodifferentiating effects, calcitriol and other vitamin D analogs are highly efficient in the treatment of psoriasis vulgaris. The known antipsoriatic effect of UV-B light could, at least in part, be mediated via UV-B-induced synthesis of calcitriol. In addition, mounting evidence indicates that cutaneous vitamin D(3) synthesis is of high importance for the prevention of a broad variety of diseases, including various malignancies. New but controversially discussed sun-protection guidelines were established for the prevention of internal cancers. A better understanding of the metabolism of vitamin D in the skin opens new perspectives for therapeutic applications of vitamin D analogs.