Kalorimetrische Messungen der thermischen Effekte bei Dehnung von Kautschuk

Ohne Zusammenfassung     

On a system of quasilinear parabolic functional differential equations

Summary We consider initial boundary value problems for a system of second order quasilinear parabolic equations where also the main part contains functional dependence on the unknown function. This system is of type, considered in [6], [7] by U. Hornung, W. J?ger and A. Mikelic.     

Hyperfunktionen und Sätze vom typ Edge of the Wedge

The theories of hyper- and microfunctions yelt powerful methods for general Edge- of the- Wedge theorems in the theory of analytic functions. Working out such theorems for sections in coherent analytic sheaves requests a new approach to the theory of generalised hyperfunctions in order to define the boundary value map for sheaves. This is done at the beginning of this paper. Moreover a theory of generalised microfunctions is worked out and as a first application an Edge- of the- Wedge theorem for sections in certain coherent analytic sheaves is proved.      

Fluorous‐Silica‐Supported Perfluoro‐Tagged Palladium Complexes Catalyze Suzuki Couplings in Water

Different Pd‐complexes (see 2a – d and 3 ) with and without perfluoroalkyl tags were deposited on fluorous reversed‐phase silica 1 and unmodified silica gel. These supported complexes were successfully used as precatalysts for the Suzuki reaction in H₂O. H₂O‐Soluble aryl bromides were easily converted to the corresponding biphenyls. Although none of the complexes is H₂O‐soluble, the active catalyst is most likely homogeneously dissolved. Nevertheless, the Pd‐leaching into the product was low.     

Complementary pivoting and the Hopf Degree Theorem

We describe a combinatorial process for the extension of triangulations and integer labeling functions. Together with a discussion of topological degree via completely labeled simplices our result yields an elementary proof of the Hopf Degree Theorem. A further application of our techniques will provide a regularization result, similar to theorems of H. Hopf and B. O'Neill.     

On spherical spline interpolation and approximation

Spherical spline functions are introduced by use of Green's surface functions with respect to the (Laplace-)Beltrami operator of the (unit) sphere. Natural (spherical) spline functions are used to interpolate data discretely given on the sphere. A method is presented that allows the smoothing of irregularities in measured values or experimental data. Extensions of Peano's theorem and Sard's theory of best approximation to the spherical case are given by integral formulas. Schoenberg's theorem is transcribed into spherical nomenclature.     

Euclidean Green's functions for Jaffe fields

We extend the axioms for Euclidean Green's functions recently proposed by Osterwalder and Schrader to Jaffe fields.     

A Simple Approximate Formula for the Aspect Ratio of Oblate Particles

A simple approximative formula is derived, which can be used to quantify the shape of oblate particles or an average shape of the corresponding particle system, when the results of sedimentation analysis (Stokes equivalent diameters) are known and results from either microscopic image analysis (assuming stable orientation, i.e., with the plane perpendicular to the direction of observation) or laser diffraction (assuming random orientation) are available for the same sample. In the latter case Cauchy's stereological theorem is applied to account for random orientation. Furthermore, it is shown that for sufficiently large aspect ratios, this formula is very close to the well‐known Jennings‐Parslow relation and can replace this more complicated expression in many practical cases, e.g., in the routine characterization of ceramic raw materials (kaolins and oxide or non‐oxide platelet powders).     

Investigation of Bis(Perfluoro-tert-Butoxy) Halogenates(I/III)

A systematic study of halogenate(I/III) anions with polyatomic ligands is presented. The bis(perfluoro-tert-butoxy) halogenates(I) [X(OC₄F₉)₂]⁻, X=Cl, Br, I, of chlorine, bromine, and iodine are prepared as their tetraethylammonium salts and characterized with IR, Raman, and NMR spectroscopic methods, as well as single-crystal X-ray diffraction analyses. Spectroscopical data are supported by quantum-chemical calculations. Additionally, the bonding situation of the species in question are analyzed and discussed. Furthermore, the oxidation to the corresponding halogenate(III) derivatives was studied. For [Br(OC₄F₉)₂]⁻, oxidation with elemental fluorine gave [BrF₂(OC₄F₉)₂]⁻. Iodide was directly oxidized by ClOC₄F₉ to the I^III species [I(OC₄F₉)₄]⁻, which is a surprisingly inert anion that might be used as a weakly coordinating anion (WCA) in the future. For [Cl(OC₄F₉)₂]⁻, the decomposition products of the synthetic approaches towards a chlorine(III) system were analyzed.