A selection theorem in metric trees

In this paper, we show that nonempty closed convex subsets of a metric tree enjoy many properties shared by convex subsets of Hilbert spaces and admissible subsets of hyperconvex spaces. Furthermore, we prove that a set-valued mapping of a metric tree with convex values has a selection for which for each . Here by we mean the Hausdroff distance. Many applications of this result are given.

     

The invertibility of adapted perturbations of identity on the Wiener space

Let $(W,H,\mu )$ be the classical Wiener space. Assume that $U=I_W+u$ is an adapted perturbation of identity, i.e., $u:W\to H$ is adapted to the canonical filtration of W. We give some sufficient analytic conditions on u which imply the invertibility of the map U. To cite this article: A.S. Üstünel, M. Zakai, C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

The Picard Theorem on S-metric spaces

Recently, the notion of an S-metric space is defined and extensively studied as a generalization of a metric space. In this paper, we define the notion of the S∞-space and prove its completeness. We obtain a new generalization of the classical "Picard Theorem".     

Polyelectrolytes in thin liquid films

The review addresses the influence of polyelectrolytes on the statics and dynamics of thin liquid films. Both, changes of interfacial and bulk properties, contribute to the overall behaviour of thin films formed from aqueous polyelectrolyte solutions. Therefore, the chapter is separated into two parts: polyelectrolytes at film interfaces and polymers in film bulk.     

Spectroscopy and dynamics of the isolated sp2 CH chromophore in trideuteroacetaldehyde CD3CHO as derived from extrapolated SDCI ab initio calculations

Ab initio CI potential energy (PES) and dipole moment (DMS) surfaces have been calculated with singles and doubles excitation configuration interaction (SDCI) for the 2-dimensional isolated sp² CH chromophore subspace of trideuteroacetaldehyde (CD₃CHO). Different extrapolation schemes to full-CI have been applied after the extrapolation to full-SDCI. Vibrational band centres and absolute intensities are determined variationally on six extrapolated surfaces. The band centres are analysed within the effective Hamiltonian model for isolated CH chromophores and the effective spectroscopic parameters are compared for the different extrapolation schemes. Time dependent population evolution for vibrational quantum motion with a pure CH stretching state being initially populated is calculated for some of the extrapolated surfaces within the effective Hamiltonian model.     

Molecular dynamics simulation of liquid tetrahydrofuran: on the uniqueness of force fields

Molecular dynamics simulations of liquid tetrahydrofuran have been performed with different force fields to illustrate that there is no unique way to model a given system of molecules. Parameters for the force fields have been taken from existing force fields and have been used as starting guesses for a simplex optimization. In spite of the very different final parameter values, all optimized force fields reproduce properly the physical properties for which they have been optimized, but not necessarily other ones.     

On the purely irregular fundamental group

Based on the (not yet fully understood analogy) between irregular connections and wild ramification, we define a purely irregular fundamental group for complex algebraic varieties and prove some results about this fundamental group which are analogous to the p‐adic étale fundamental group of algebraic varieties over fields of characteristic p (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Algorithmic computation of generalized symmetries of nonlinear evolution and lattice equations

A straightforward algorithm for the symbolic computation of generalized (higher‐order) symmetries of nonlinear evolution equations and lattice equations is presented. The scaling properties of the evolution or lattice equations are used to determine the polynomial form of the generalized symmetries. The coefficients of the symmetry can be found by solving a linear system. The method applies to polynomial systems of PDEs of first order in time and arbitrary order in one space variable. Likewise, lattices must be of first order in time but may involve arbitrary shifts in the discretized space variable. The algorithm is implemented in Mathematica and can be used to test the integrability of both nonlinear evolution equations and semi‐discrete lattice equations. With our Integrability Package, generalized symmetries are obtained for several well‐known systems of evolution and lattice equations. For PDEs and lattices with parameters, the code allows one to determine the conditions on these parameters so that a sequence of generalized symmetries exists. The existence of a sequence of such symmetries is a predictor for integrability. This revised version was published online in June 2006 with corrections to the Cover Date.     

99mTc-Exorphin-glucuronide in tumor diagnosis: Preparation and biodistribution studies in rats

Summary  Elérh