Stability results for Mountain Pass and Linking type solutions of semilinear problems involving Dirichlet forms

Some stability results for Mountain Pass and Linking type solutions of semilinear problems involving a very general class of Dirichlet forms are stated. The non linear terms are supposed to have a suitable superlinear growth and the family of Dirichlet forms is required to be dominated from below and from above by a fixed diffusion type form. Some concrete examples are also given.     

Expected Reflection Distance in G(r, 1, n) after a Fixed Number of Reflections

Extending to r > 1 a formula of the authors, we compute the expected reflection distance of a product of t random reflections in the complex reflection group G(r, 1, n). The result relies on an explicit decomposition of the reflection distance function into irreducible G(r, 1, n)-characters and on the eigenvalues of certain adjacency matrices.Received December 8, 2003     

Exact controllability of infinite dimensional systems persists under small perturbations

This paper studies the concept of controllability for infinite-dimensional linear control systems in Banach spaces. First, we prove that the set of admissible control operators for the semigroup generator is unchanged if we perturb the generator by the Desch–Schappacher perturbations. Second we show that exact controllability is not changed by such perturbations.     

Preparation and characterization of acrylic‐based black particles of poly(methyl methacrylate‐co‐ethylene glycol dimethacrylate) by dispersion polymerization for electrophoretic displays

Ultrafine black particles, ranging in diameter from 1 to 3 μm, were prepared by dispersion polymerization in a methanol/water mixture with vinyl monomers, nonpolymerizable Sudan black B dyes, and fluorescein isothiocyanate labeled charge control additives. Both the ratio of the methanol to the water dispersion medium and the polymeric stabilizer concentration had significant effects on the particle size. The important role of the stabilizer concentration lay in the particle formation step, during which it determined the particle stability and final particle size. These could affect the extent of the aggregation of nuclei by changing the adsorption rate of the stabilizer and the viscosity of the dispersion medium, resulting in smaller particles. The fluorescent‐labeled charge control additives strongly affected the electrophoretic mobility. A small concentration of fluorescent‐labeled charge control additives increased the electrophoretic mobility. However, a further addition reduced the electrophoretic mobility of the polymer particles. The concentration dependence of the fluorescent‐labeled charge control additives on the deposition behavior in the polymer particles was successfully imaged and thereafter quantified by image analysis. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 5608–5616, 2004     

Thermal behavior of metallodendrimers possessing bis(terpyridinyl)Ru(II) connectivity and different surface functionality

A series of metallodendrimers, assembled by means of bis(terpyridinyl)Ru^(II) connectivity on poly(propylene imine) dendrimer scaffolds, with homogeneous or heterogeneous surfaces, were prepared. Differential scanning calorimetry and thermogravimetric analysis were used to determine their thermal behavior, glass‐transition temperatures, and the decomposition kinetics and temperatures; no synergy effects for these properties were observed for the heterogeneously surfaced constructs in contrast to the corresponding homogeneously coated materials, which exhibited different values depending on their surface functionalities. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1487–1495, 2004     

类钙钛矿化合物Ca(Mn2 Cu1)Mn4 O12的磁性与磁电阻效应

利用固相反应法制备了名义成分为Ca(Mn2 Cu1 )Mn4 O1 2 的类钙钛矿锰氧化物 .x射线衍射表明 ,为了获得较为致密的样品和减小杂相含量 ,可以采用高温烧结再在 10 73K长时间空气中退火的制备方法 .样品在低温下同时存在铁磁相和反铁磁相 ,由于反铁磁相的存在导致样品在 4 5K时的磁化强度显著降低 ,并在 8T的高磁场下仍未达到饱和 .样品呈半导体导电性质 ,在 85K和 6T磁场下磁电阻比的最大值可达 - 4 6 % .     

Kinetic Studies on the Reaction of Sodium Hexa-cyanoferrate(II) Complex with Peroxydisulfate Anion

Introduction In the previous studies on the oxidation reaction,peroxydisulfate was widely used as an oxidizingagent.1-5 One of the advantages of this oxidant lies in itsstability in a wide range of pH values. The reaction be-tween Fe(CN)5L3- (L=N-aromatic heterocyclic li-gands) and S2O8 2- has been proved to proceed throughan outer-sphere electron transfer mechanism.5 For a re-action [(Eq. (1)] to be under an outer-sphere mechanismthe steps involved are the formation of a reactant …     

Synthesis of New 13-O-Acylavermectin Bl Aglycones

Six new 13-O-acylavermectin Bl aglycones(3-8) were synthesized from avermectin B1 aglycone and their bioactivities were evaluated against Spodoptera exigua, Spodoptera eridania, Tetranychus urticae and Aphis fabae.     

Kinetic Models for Chemotaxis and their Drift-Diffusion Limits

Kinetic models for chemotaxis, nonlinearly coupled to a Poisson equation for the chemo-attractant density, are considered. Under suitable assumptions on the turning kernel (including models introduced by Othmer, Dunbar and Alt), convergence in the macroscopic limit to a drift-diffusion model is proven. The drift-diffusion models derived in this way include the classical Keller-Segel model. Furthermore, sufficient conditions for kinetic models are given such that finite-time-blow-up does not occur. Examples are given satisfying these conditions, whereas the macroscopic limit problem is known to exhibit finite-time-blow-up. The main analytical tools are entropy techniques for the macroscopic limit as well as results from potential theory for the control of the chemo-attractant density.Present address: Centro de Matemática e Aplicações Fundamentais, Universidade de Lisboa, Av. Prof. Gama Pinto 2, 1649-003, Lisboa, Portugal     

On the Long-Time Behavior of the Quantum Fokker-Planck Equation

We analyze the long-time behavior of transport equations for a class of dissipative quantum systems with Fokker-planck type diffusion operator, subject to confining potentials of harmonic oscillator type. We establish the existence and uniqueness of a non-equilibrium steady state for the corresponding dynamics. Further, using a (classical) convex Sobolev inequality, we prove an optimal exponential rate of decay towards this state and additionally give precise dispersion estimates in those cases, where no stationary state exists.