Prox-regular functions in Hilbert spaces

This paper studies the prox-regularity concept for functions in the general context of Hilbert space. In particular, a subdifferential characterization is established as well as several other properties. It is also shown that the Moreau envelopes of such functions are continuously differentiable.     

Lim's theorems for multivalued mappings in CAT(0) spaces

Let X be a complete CAT(0) space. We prove that, if E is a nonempty bounded closed convex subset of X and a nonexpansive mapping satisfying the weakly inward condition, i.e., there exists p∈E such that ∀x∈E, ∀α∈[0,1], then T has a fixed point. In Banach spaces, this is a result of Lim [On asymptotic centers and fixed points of nonexpansive mappings, Canad. J. Math. 32 (1980) 421-430]. The related result for unbounded R-trees is given.     

Dilation equations and Markov operators

Using the theory of Markov operators, we give a new proof of the known fact saying that for every positive integers N and k>1, and for every nonnegative reals c₀,…,cN satisfying the first sum rule the dilation equation

     

HPLC-Bestimmung von S-Carboxymethyl-l-cystein in Haarwaschmitteln

Zusammenfassung S-Carboxymethyl-l-cystein läßt sich mit o-Phthaldialdehyd/Mercaptoethanol derivatisieren und mittels HPLC an einer LiChrosorb RP-8-Säule unter Verwendung eines Fluorescenzdetektors quantitativ bestimmen. Die Spezifität des Fluorescenzsignals und die gewählten chromatographischen Bedingungen gestatten, ohne spezielle Aufarbeitung der Proben zu arbeiten. Die Standardabweichung beträgt ± 1,1 mg/l bei einem mittleren Gehalt von 98 mg/l.

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Determination of S-carboxymethyl-l-cysteine in shampoo by HPLC

Summary S-Carboxymethyl-l-cysteine can be determined quantitatively by derivatisation with o-phthaldialdehyde/mercaptoethanol using HPLC with a LiChrosorb RP-8 column and a fluorescent detector. The specifity of the fluorescent signal and the Chromatographic conditions allow to work without any special preparation of the sample. The standard deviation is ± 1.1 mg/l for an average content of 98 mg/l.

     

Certain Ergodic Properties of a Differential System on a Compact Differentiable Manifold

Let M ⁿ be an n-dimensional compact C ^∞-differentiable manifold, n ≥ 2, and let S be a C ¹-differential system on M ⁿ . The system induces a one-parameter C ¹ transformation group φ _t (−∞ < t < ∞) over M ⁿ and, thus, naturally induces a one-parameter transformation group of the tangent bundle of M ⁿ . The aim of this paper, in essence, is to study certain ergodic properties of this latter transformation group. Among various results established in the paper, we mention here only the following, which might describe quite well the nature of our study. (A) Let M be the set of regular points in M ⁿ of the differential system S. With respect to a given C ^∞ Riemannian metric of M ⁿ , we consider the bundle of all (n−2) spheres Q _x ⁿ⁻², x∈M, where Q _x ⁿ⁻² for each x consists of all unit tangent vectors of M ⁿ orthogonal to the trajectory through x. Then, the differential system S gives rise naturally to a one-parameter transformation group ψ _t ^# (−∞<t<∞) of . For an l-frame α = (u ₁, u ₂,⋯, u _l ) of M ⁿ at a point x in M, 1 ≥ l ≥ n−1, each u _i being in , we shall denote the volume of the parallelotope in the tangent space of M ⁿ at x with edges u ₁, u ₂,⋯, u _l by υ(α), and let . This is a continuous real function of t. Let

Understanding the polarization signal of spherical particles for microwave limb radiances

This paper presents a simple conceptual model to explain that even spherical scatterers lead to a polarization difference signal for microwave limb radiances. The conceptual model relates the polarization difference measured by a limb-looking sensor situated inside a cloud with the anisotropy of the radiation. In the simulations, it was assumed that the cloud consists of spherical ice particles with a radius of which were situated between 10.6 and 12.3 km altitude. The frequencies 318 and 500 GHz were considered.The results of the conceptual model were compared to the results of the fully polarized scattering model ARTS-1-1. The comparison showed a good qualitative agreement. The polarization difference decreases inside the cloud with increasing height and changes sign. This behavior can be related to a different amount of radiation coming from the atmosphere above and below the cloud, compared to the amount of radiation coming from the sides. The sign of polarization difference of the scattered radiation is opposite for these two radiation sources.     

Recent developments in the line-by-line modeling of outgoing longwave radiation

High frequency resolution radiative transfer model calculations with the Atmospheric Radiative Transfer Simulator (ARTS) were used to simulate the clear-sky outgoing longwave radiative flux (OLR) at the top of the atmosphere. Compared to earlier calculations by Clough and coworkers the model used a spherical atmosphere instead of a plane parallel atmosphere, updated spectroscopic parameters from HITRAN, and updated continuum parameterizations from Mlawer and coworkers. These modifications lead to a reduction in simulated OLR by approximately 4.1%, the largest part, approximately 2.5%, being due to the absence of the plane parallel approximation. As a simple application of the new model, the sensitivity of OLR to changes in humidity, carbon dioxide concentration, and temperature were investigated for different cloud-free atmospheric scenarios. It was found that for the tropical scenario a 20% change in humidity has a larger impact than a doubling of the carbon dioxide concentration. The sensitive altitude region for temperature and humidity changes is the entire free troposphere, including the upper troposphere where humidity data quality is poor.     

On the modulus of -convexity

In this paper, we prove that the moduli of W^*-convexity, introduced by Ji Gao [J. Gao, The W^*-convexity and normal structure in Banach spaces, Appl. Math. Lett. 17 (2004) 1381–1386], of a Banach space X and of the ultrapower of X itself coincide whenever X is super-reflexive. Moreover, we improve a sufficient condition for uniform normal structure of the space and its dual. This generalizes and strengthens the main results of [J. Gao, The W^*-convexity and normal structure in Banach spaces, Appl. Math. Lett. 17 (2004) 1381–1386].     

On convergence of closed convex sets

In this paper we introduce a convergence concept for closed convex subsets of a finite-dimensional normed vector space. This convergence is called C-convergence. It is defined by appropriate notions of upper and lower limits. We compare this convergence with the well-known Painlevé-Kuratowski convergence and with scalar convergence. In fact, we show that a sequence (An)_n∈NC-converges to A if and only if the corresponding support functions converge pointwise, except at relative boundary points of the domain of the support function of A, to the support function of A.     

The range of united K-theory

We prove that the united K-theory functor is a surjective functor from the category of real simple separable purely infinite C^∗-algebras to the category of countable acyclic CRT-modules. As a consequence, we show that every complex Kirchberg algebra satisfying the universal coefficient theorem is the complexification of a real C^∗-algebra.