Randregularität des\bar \partial -Problems für die Halbkugel in ℂn

Let f be a -closed (0, q+1)-form defined on the half ball B₊ in ⁿ, which is of class C^k on ¯B. We prove the existence with C^k-estimates of a solution u of the equation .

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Die Anregung zu dieser Arbeit verdanke ich auch Herrn Piotr Jakóbczak aus Krakau, der sich eine gewisse Zeit am Max-Planck-Institut für Mathematik in Bonn aufhielt. Während dieser Zeit untersuchten wir die C⁰-Abschätzungen für die Halbkugel in ⁿ     

Attractors for a Three-Dimensional Thermo-Mechanical Model of Shape Memory Alloys

Abstract In this note, we consider a Frémond model of shape memory alloys. Let us imagine a piece of a shape memory alloy which is fixed on one part of its boundary, and assume that forcing terms, e.g., heat sources and external stress on the remaining part of its boundary, converge to some time-independent functions, in appropriate senses, as time goes to infinity. Under the above assumption, we shall discuss the asymptotic stability for the dynamical system from the viewpoint of the global attractor. More precisely, we generalize the paper [12] dealing with the one-dimensional case. First, we show the existence of the global attractor for the limiting autonomous dynamical system; then we characterize the asymptotic stability for the non-autonomous case by the limiting global attractor. * Project supported by the MIUR-COFIN 2004 research program on “Mathematical Modelling and Analysis of Free Boundary Problems”.     

Variable Charge-Densities in Hydrophilic Weak-Base Ion-Exchange Membranes. V. Equilibrium Properties with Pure 1-1 Electrolytes. Swelling and Ion-Exclusion

Abstract

The equilibrium distribution of chloride or nitrate counter-ions of K or NH₄ co-ions and of water is determined experimentally at different degrees of ionization X[xbar] of hydrophylic weak-base aminated polyvinyl-alcohol membranes. These data are analyzed and explained in terms of thermodynamics interrelating the molality of fixed-charge densities and of counter-ions to that of the amount of water and of diffused salt in the membrane.

Three domains have to be considered: the polyelectrolyte domain with small external concentration compared to the internal net fixed charge concentration (notion of “net-charge” densities), the domain of homogeneous interstitial liquid of the concentrated electrolyte type with sufficiently concentrated salt solution, and the intermediate domain.     

Vinyl Chloride-Vinyl Bromide Copolymers

Abstract

Radical copolymerization kinetics of vinyl chloride (VC) and vinyl bromide (VB) lead to the following reactivity ratios r_VC=0.825 r_VB=1.05 Vinyl bromide acts as a chain transfer agent, more powerful than vinyl chloride, the transfer constant for VC radicals being 8.5 × 10^?3 at 40° C. Neither thermal nor ionic degrad-ation produce controlled distribution of short diene sequences in the copolymer. In the ionic process initiated with LiCl or LiBr in dimethylformamide solution, substitution of halogen atoms as well as acid elimination takes place.     

Fiber crystal growth from the melt for non-linear optical applications

During several years, we have been involved in the growth and characterization of non-linear optical crystals by the two most common techniques for growing single-crystal fibers from the melt: laser-heated pedestal growth and micro-pulling down. Their specific features are presented in this study and their versatility is demonstrated through two typical examples of incongruently melting materials: K₃Li_2?xNb_5+xO_15+2x (solid solution of the ternary system K₂O–Li₂O–Nb₂O₅) and Ca₅(BO₃)₃F which can only be grown from a flux.     

Characterization of the structure of human skin substitutes by infrared microspectroscopy

The skin acts mainly as a protective barrier from the external environment, thanks to the stratum corneum which is the outermost layer of the skin. As in vitro tests on skin are essential to elaborate new drugs, the development of skin models closer to reality becomes essential. It is now possible to produce in vitro human skin substitutes through tissue engineering by using the self-assembly method developed by the Laboratoire d’Organogénèse Expérimentale. In the present work, infrared microspectroscopy imaging analyses were performed to get in-depth morpho-spectral characterization of the three characteristic layers of human skin substitutes and normal human skin, namely the stratum corneum, living epidermis, and dermis. An infrared spectral analysis of the skin is a powerful tool to gain information on the order and conformation of the lipid chains and the secondary structure of proteins. On one hand, the symmetric stretching mode of the lipid methylene groups (2,850 cm^?1) is sensitive to the acyl chain conformational order. The evolution profile of the frequency of this vibrational mode throughout the epidermis suggests that lipids in the stratum corneum are more ordered than those in the living epidermis. On the other hand, the frequencies of the infrared components underneath the envelop of the amide I band provide information about the overall protein conformation. The analysis of this mode establishes that the proteins essentially adopt an α-helix conformation in the epidermis, probably associated with the presence of keratin, while modifications of the protein content are observed in the dermis (extracellular matrix made of collagen). Finally, the lipid organization, as well as the protein composition in the different layers, is similar for human skin substitutes and normal human skin, confirming that the substitutes reproduce essential features of real skin and are appropriate biomimetics.     

Aluminum Chloride (Alcl3) Promotes Selective Oxidative Deprotection of Benzylic Trimethylsilyl and Tert- Butyldimethylsilyl Ethers to the Corresponding Carbonyl Compounds with Manganese Dioxide (Mno2)

Various types of trimethylsilyl and tert-butyldimethylsilyl ethers of primary and secondary benzylic alcohols could be selectively converted to their corresponding carbonyl compounds with MnO₂ in the presence of AlCl₃ in good to excellent yields.     

Preparation of the N-(2-Bromo-2-Nitroethenyl) Benzenamine: The First One-Pot Synthesis of a β-Halo-β-Nitroenamine

Bromonitromethane, triethyl orthoformate and aniline react together, in a one-flask procedure, to afford the title compound.