Flächenabbildungen mit gemeinsamem Invariantensystem

Zusammenfassung und Ausblick Unsere Betrachtungen zeigen, daß die Differentialinvarianten, die zu einem Paar aufeinander abgebildeter Flächen gehören, dieses, auch wenn man triviale Verschiedenheiten nicht als Unterschiede rechnet, durchaus nicht immer eindeutig zu bestimmen brauchen, trotzdem sie die affine Beziehung zwischen den Umgebungen je zweier entsprechender Flächenpunkte vollkommen im Raume festlegen.Beispiele, die dies näher belegen, sollen in einer besonderen Arbeït mitgeteilt werden.Naturgemäß stellt sich uns nun als nächstes Problem das folgende:Welche Bedingungen müssen vier Funktionen i₁,i₂,i,j von zwei Veränderlichenu, v erfüllen, damit zwei Vektoren und (u, v) die den Gleichungen (1) und (1) genügen, existieren?Herrn Geheimrat Prof. Dr.C. Carathéodory gewidmet.     

Zum Auswaschen von Niederschl?gen mit heissem Wasser

Ohne Zusammenfassung     

Random homogeneous sodium sulfonate polysulfone ionomers: Preparation,characterization, and blend studies

The sodium salts of randomly sulfonated polysulfone (Na-SPSF), derived from 1,1′-sulfonylbis-[4-chlorobenzene] with 4,4′-(1-methylethylidene)-bis-[phenol], were prepared over the composition range of 3–30 mol% sodium sulfonate, using improved procedures in which the sulfonating complex was introduced into an intensely agitated polymer solution. In contrast to earlier work, T_g was found to increase nonlinearly with sodium sulfonate content. A SAXS study provided no evidence of ionic clustering in these polymers. Binary blends of Na-SPSFs differing only in composition were prepared by casting films from solution, and their phase behavior was studied by dynamic mechanical analysis after annealing at 250°C. It was found that the blends were miscible up to a composition difference of about 9–10 mol% sodium sulfonate. Using this fact it was possible to calculate a value for χ_ABn of 200–250, where χ_AB represents the segmental interaction parameter between unmodified and modified repeat units, and n is the degree of polymerization. Uncertainty in the degree of ionic association places a degree of uncertainty on the effective value of n and therefore on χ_AB. The product, however, is independent of any assumptions regarding molecular associations.     

Magnetic hyperfine fields of119Sn in vacancy-associated defect structures in 3d ferromagnets

Hyperfine Interactions - Defect structures associated with Sb or In impurity atoms in iron, cobalt, and nickel hosts have been detected by Sn-119 Mössbauer spectroscopy. With substitutional...     

Kinetics of the reactions of the hydroxyl radical with dimethyl ether and diethyl ether

Absolute rate coefficients for the reactions of the hydroxyl radical with dimethyl ether (k₁) and diethyl ether (k₂) were measured over the temperature range 295–442 K. The rate coefficient data, in the units cm³ molecule^?1 s^?1, were fitted to the Arrhenius equations k₁ (T) = (1.04 ± 0.10) × 10^?11 exp[?(739 ± 67 cal mol^?1)/RT] and k₂(T) = (9.13 ± 0.35) × 10^?12 exp[+(228 ± 27 kcal mol^?1)/RT], respectively, in which the stated error limits are 2σ values. Our results are compared with those of previous studies of hydrogen-atom abstraction from saturated hydrocarbons by OH. Correlations between measured reaction-rate coefficients and C? H bond-dissociation energies are discussed.     

One-Parameter Groups Arising from Real Subspaces of Self-Dual Hilbert W*-Moduli

The purpose of this paper is to generalize the results of M. A. Rieffel and A. van Daele [8, §§ 1, 2, 3] for Hilbert W^*-moduli over commutative W^*-Algebras. Some special real subspaces of such Hilbert W^*-moduli and the related operators are investigated. Particularly, the relation is established between ^*weakly continuous unitary one-parameter groups of operators arising from them and the generalized K.M.S. condition. All key definitions are formulated without any commutativity supposition for the underlying W^*-algebra. The interpretation of these results is given for sets of continuous sections of “self-dual” locally trivial Hilbert bundles over hyperstonian compact spaces. At the end of this paper some aspects of the general noncommutative case are discussed.