Notions of Local Compactness and Smallest Compactifications of Biframes

The category of coherent biframes is shown to be equivalent to that of the coupled lattices, and dually equivalent to the spectral bispaces. Stably continuous biframes arise as the retracts of the coherent biframes. The coherent and the stably continuous biframes are coreflective in all biframes. Weak local compactness is introduced, and in conjunction with regularity, is shown to be sufficient for the construction of smallest compactifications.     

Efficient Light‐Induced pKa Modulation Coupled to Base‐Catalyzed Photochromism

Photoswitchable acid–base pairs, whose pK_a values can be reversibly altered, are attractive molecular tools to control chemical and biological processes with light. A significant, light‐induced pK_a change of three units in aqueous medium has been realized for two thermally stable states, which can be interconverted using UV and green light. The light‐induced pK_a modulation is based on incorporating a 3‐H‐thiazol‐2‐one moiety into the framework of a diarylethene photoswitch, which loses the heteroaromatic stabilization of the negatively charged conjugate base upon photochemical ring closure, and hence becomes significantly less acidic. In addition, the efficiency of the photoreactions is drastically increased in the deprotonated state, giving rise to catalytically enhanced photochromism. It appears that protonation has a significant influence on the shape of the ground‐ and excited‐state potential energy surfaces, as indicated by quantum‐chemical calculations.     

A simple explanation of unexpected efg's in19F-TDPAD measurements

In our¹⁹F — TDPAD experiments often efg's are appearing, which are due to bonds of the probe nucleus that do not exist in the target substance. A simple mechanism is proposed to explain these unexpected coupling constants in molecular crystals.     

The electric hyperfine interaction in group VI-a hexafluorides

The electric hyperfine interaction in group VI-a hexafluorides SF₆, SeF₆ and TeF₆ has been studied in the temperature range from 10 K to about 110K by means of the TDPAD method. The temperature dependence can be explained by Bayer — Kushida theory. The coupling constants decrease with increasing temperature. The strength of the temperature dependence diminishes from SF₆ to TeF₆, indicating an increase of ionicity of the bonds. If the coupling constants are plotted versus the elements of the fluorine compounds, characteristic trends can be seen. Therefore we predict the coupling constant of OF₂ to be about 100 MHzThis work was supported by the Bundesministerium für Forshung und Technologie     

A characterization ofC 1-convex sets in Sobolev spaces

In this paper we prove that, ifK is a closed subset ofW ₀ ^1,p (Ω,R ^m ) with 1<p<+∞ andm≥1, thenK is stable under convex combinations withC ¹ coefficients if and only if there exists a closed and convex valued multifunction from Ω toR ^m such that The casem=1 has already been studied by using truncation arguments which rely on the order structure ofR (see [2]). In the casem>1 a different approach is needed, and new techniques involving suitable Lipschitz projections onto convex sets are developed. Our results are used to prove the stability, with respect to the convergence in the sense of Mosco, of the class of convex sets of the form (*); this property may be useful in the study of the limit behaviour of a sequence of variational problems of obstacle type. This article was processed by the author using the Springer-Verlag TEX mamath macro package 1990     

Homogenization of quasi-linear equations with natural growth terms

In this paper we deal with the limit behaviour of the bounded solutions u_ε of quasi-linear equations of the form of Ω with Dirichlet boundary conditions on σΩ. The map a=a(x,ϕ) is periodic in x, monotone in ϕ, and satisfies suitable coerciveness and growth conditions. The function H=H(x,s,ϕ) is assumed to be periodic in x, continuous in [s,ϕ] and to grow at most like |ξ|^p. Under these assumptions on a and H we prove that there exists a function H⁰=H⁰(s,ϕ) with the same behaviour of H, such that, up to a subsequence, (u_ε) converges to a solution u of the homogenized problem -div(b(Du)) + γ|u|^p-2u = H⁰(u,Du) + h(x) on Ω, where b depends only on a and has analogous qualitative properties.     

Anf?rbung von Aminos?uren mit Metallsalz-Ninhydrin-Gemischen

Zusammenfassung Der Einfluß verschiedener Metallionen auf die Anfärbbarkeit einer Reihe von Aminosäuren mit Ninhydrin wurde überprüft. Es ergab sich, daß die Farben des gesamten Spektrums, von blau über grün und gelb bis rot entstehen.

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Summary The influence of different metal ions on the colour produced by action of ninhydrin on several amino acids has been investigated. It has been shown that colours of the whole spectrum are formed, from blue via green and yellow to red.

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Auszugsweise vorgetragen auf dem V. Internationalen Symposium des Quedlinburger Arbeitskreises für Eiweißanalytik vom 27.–29. Oktober 1966.