The Neumann problem,cylindrical outlets and Sobolev spaces

The Neumann problem is crucial in mathematical physics. Nevertheless, as far as cylindrical domains are concerned there is still the open question how to construct solutions to data in usual Sobolev spaces since the standard Kondratiev theory does not apply. In this paper that unsatisfactory gap is filled and moreover, data with polynomial asymptotic behaviour are considered. As interesting special case we find solutions with bounded Dirichlet integral. Copyright © 2002 John Wiley & Sons, Ltd.     

Orientation and relaxation of polymer–clay solutions studied by rheology and small-angle neutron scattering

The influence of shear on viscoelastic solutions of poly(ethylene oxide) (PEO) and clay [montmorillonite, i.e., Cloisite NA+ (CNA)] was investigated with rheology and small-angle neutron scattering (SANS). The steady-state viscosity and SANS were used to measure the shear-induced orientation and relaxation of the polymer and clay platelets. Anisotropic scattering patterns developed at much lower shear rates than in pure clay solutions. The scattering anisotropy saturated at low shear rates, and the CNA clay platelets aligned with the flow, with the surface normal parallel to the gradient direction. The cessation of shear led to partial and slow randomization of the CNA platelets, whereas extremely fast relaxation was observed for laponite (LRD) platelets. These PEO–CNA networklike solutions were compared with previously reported PEO–LRD networks, and the differences and similarities, with respect to the shear orientation, relaxation, and polymer–clay interactions, were examined. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3102–3112, 2004     

4-Amino-imidazole durchThorpe-Cyclisierung

The alkylation of arylaminomethylenecyanamides1 or cyano-imidothiocarbamates2 with -halogen carbonyl compounds followed by base catalysed cyclization yields substituted 4-amino-imidazoles4. Imidazo[4,5-d]pyrimidones5, 6 and imidazo[4,5-b]pyridines7 can be obtained from4.     

UVA-INDUCED AUTOCRINE STIMULATION OF FIBROBLAST-DERIVED COLLAGENASE/MMP-1 BY INTERRELATED LOOPS OFINTERLEUKIN–1 andINTERLEUKIN–6

Abstract— Previous work has shown that fibroblast-derived collagenase/matrix-metalloproteinase-1(MMP–1), responsible for the breakdown of dermal interstitial collagen, was dose-dependently induced in vitro and in vivo by UVA irradiation and this induction was at least partly mediated byinterleukin–6(IL–6). We here provide evidence that UVA-inducedIL–1α andIL–1β play a central role in the induction of the synthesis both ofIL–6 and collagenase/MMP–1. In contrast to the late increase ofIL–1α andIL–1β mRNA levels at 6 h postirradiation, bioactivity ofIL–1 is already detectable at 1 h postirradiation. This early peak ofIL–1 bioactivity appears to be responsible for the induction ofIL–6 synthesis and together withIL–6 lead to an increase of the steady-state mRNA level of collagenase/MMP–1 as deduced from studies usingIL–1α andIL–1β antisense oligonucleotides or neutralizing antibodies againstIL–1α andIL–1β Besides the early posttranslationally controlled release of intracellularIL–1, a latter pretranslationally controlled synthesis and release ofIL–1 perpetuates the UV response. From these data we suggest a UV-induced cytokine network consisting ofIL–1α,IL–1β andIL–6, which via interrelated autocrine loops induce collagenase/MMP–1 and thus may contribute to the loss of interstitial collagen in cutaneous photoaging.     

Eine Bemerkung zum Satz von Ivory

In 1809 J. IVORY found a distance relation between any two confocal ellipsoids in Euclidean space E³. After that, the theorem of IVORY has been formulated for any two nondegenerate confocal quadrics of the same type. In this paper we succeed in completing these results and in formulating and proving them uniformly for any two quadrics of the same type belonging to a general system of confocal quadrics.

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Herrn Prof. Dr. Oswald Giering zum 60. Geburtstag gewidmet     

Fractal dimension,attractors, and the boussinesq approximation in three dimensions

The Boussinesq approximation, where the viscosity depends polynomially on the shear rate, finds more and more frequent use in geological practice. In the paper, this modified Boussinesq approximation is investigated as a dynamical system for which the existence of a global attractor is proved. Finally, a new criterion for estimating the fractal dimension of invariant sets is formulated and its application to the problem under consideration is illustrated.     

Solution and X-Ray Crystal Structures of the Di- and Tetra-allyl Ether of tert- utylcalix[4]arene

The di- and tetra-allyl ethers of tert-butylcalix[4]arene 1 and 2 have been prepared by alkylation of tert-butylcalix[4]arene with allyl bromide and K₂CO₃ using different reaction times. Solution ¹H NMR measurement of the di-allyl ether 1 and X-ray crystal structures of the complexes of 1 with chloroform (1a) or methanol (1b) indicate the cone conformation of 1 in which intramolecular hydrogen bonding can be maximized. The crystalline state conformers 1a and 1b are distorted in different grades depending on the solvent. While methanol is incorporated in the macrocycle, chloroform molecules do not occupy the cage. The solution ¹H NMR spectra of tetra-allyl ether 2 show the co-existence of the cone and partial cone conformation. The partial cone conformer of 2 was investigated by X-ray crystallography. In this compound hydrogen bonding is not existent. The conformer distribution is likely affected by steric and template effects.