On some Hasse principles for homogeneous spaces of algebraic groups over global fields of positive characteristic

We extend to global function fields some Hasse principles for homogeneous spaces of connected linear algebraic groups proved earlier by several authors in the case of number fields. We also give some applications.     

Total synthesis and proof of structure of mycothiol bimane

Mycothiol is a low-molecular weight thiol produced by actinomycetes that serves to protect these organisms from oxidative stress and alkylating agents. We report the total synthesis of mycothiol bimane (1) which is a commonly isolated derivative of mycothiol. The synthesis confirms the original structure assignment and unambiguously establishes the absolute stereochemistry of mycothiol to be 1-d-myo-inosityl 2-deoxy-2-(N-acetamido-l-cysteinamido)-alpha-d-glucopyranoside.     

Tracer studies on f-actin fluctuations

We present a study on the fluctuations of semiflexible actin filaments using fluorescence videomicroscopy, focusing on the end-to-end fluctuations of single filaments. In order to specifically measure the position of the polymer's ends, we developed a novel noninvasive method that consists of annealing short end tags to the filaments. This allows us to probe polymer fluctuations to a very high accuracy. We compared the distribution of the end-to-end distance with recent theoretical results, and found excellent agreement. We also studied the dynamics of the mean-square end-to-end distance deltaR2(t) and orientation of the ends, deltaTheta(2)(t), finding power laws t(3/4) and t(1/4), respectively. Scaling behavior for deltaR2(t) is observed over several decades in relaxation time in agreement with theoretical results.     

Quasi-solitonic behavior of self-written waveguides created by photopolymerization

We investigated the condition of unique self-written channel and multichannel propagation inside bulk photopolymerizable materials. Light was introduced in the medium by a single-mode optical fiber. At a very low beam power of 5 muW , a unique uniform-channel waveguide without any broadening was obtained by polymerization. When the input power is increased to 100 muW , the guide becomes chaotic and multichannel. We connected two fibers separated by a 1-cm distance. The results open the door to studies of the optical and electro-optical properties of photopolymerized guides doped by nonlinear optical chromophores and to possible applications in integrated optical devices.     

Inclusion of Enantiomeric Carvones in β-Cyclodextrin: a Variable Temperature 1H NMR Study in Aqueous Solution

In aqueous solution, the apparent association constant at room temperature for the 1 : 1 inclusion of S-(+)-carvone in c="/content/l30350746x027836/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">- cyclodextrin is double of that for R-(-)-carvone, whereas, at 45 °C, both enantiomers have association constants two orders of magnitude smaller, with the S-(+) inclusion being then slightly weaker than the R-(-) encapsulation. Calculations carried out at the molecular mechanics, AM1 and STO-3G levels confirm the preferential inclusion of the S-enantiomer and provide important clues for understanding chiral discrimination by c="/content/l30350746x027836/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-cyclodextrin.     

On list primitive recursion and the complexity of computinginf

We present a primitive recursive programinf_with_lists computing the minimum of two natural numbersn andp (written in unary notation) and using primitive recursion on lists. This program has at first sight the required property of visiting simultaneously its inputs, so it is a counterexample to a theorem showing that such a program cannot be written in the language of primitive recursion on natural numbers, in the more general framework of primitive recursion on term algebras. However, its complexity is at leastinf(n,p)² so it does not implement the algorithm we have in mind to computeinf(n,p).     

Vollständigkeitsbeweis des Dreifunktionenansatzes der linearen Elastizitätstheorie

Übersicht Der unabhängig voneinander durch Papkovich [1] und den Verfasser [2, 3] aufgestellte Ansatz zur Lösung dreidimensionaler Elastizitätsprobleme enthält 4 harmonische Funktionen, von denen in der Regel nur drei benötigt werden. Für die Vollständigkeit dieses Ansatzes wird nachstehend ein einfacher Beweis angegeben, der sich aus der Theorie der linearen Differentialgleichungen mit konstanten Koeffizienten ergibt.

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ckquote>Summary The three-functions-set of Papkovich and the author for the solution of three-dimensional problems of the linear theory of elasticity contains four harmonic functions, only three of which are generally used. A proof for the completeness of this set is given in this paper based on the theory of linear differential equations with constant coefficients.ckquote>

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Udo Wegner zum 70. Geburtstag.