Boundary Limits for Bounded Quasiregular Mappings

In this paper we establish results on the existence of nontangential limits for weighted -harmonic functions in the weighted Sobolev space , for some q>1 and w in the Muckenhoupt A _q class, where is the unit ball in . These results generalize the ones in Sect. 3 of Koskela et al., Trans. Am. Math. Soc. 348(2), 755–766, 1996, where the weight was identically equal to one. Weighted -harmonic functions are weak solutions of the partial differential equation

Analysis of finite dimensional approximations to a class of partial differential equations

In this paper, a unified approach for analysing finite dimensional approximations to a class of partial differential equations boundary value problems (second‐kind Fredholm differential equations) is introduced. The approach is shown to be general despite of its extremely simple form. In particular, it is expected to be useful in the convergence analysis of finite element methods for solving PDE problems. Three specific examples are presented to illustrate the broad applicability of the approach. Copyright © 2004 John Wiley & Sons, Ltd.     

On Necessary Optimality Conditions with Higher-Order Complementarity Slackness for Set-Valued Optimization Problems

Set-Valued and Variational Analysis - We aim to establish Karush-Kuhn-Tucker multiplier rules involving higher-order complementarity slackness under Hölder metric subregularity. These rules...     

Feature Selection using Fuzzy Support Vector Machines

The feature selection consists of obtaining a subset of these features to optimally realize the task without the irrelevant ones. Since it can provide faster and cost-effective learning machines and also improve the prediction performance of the predictors, it is a crucial step in machine learning. The feature selection methods using support machines have obtained satisfactory results, but the noises and outliers often reduce the performance. In this paper, we propose a feature selection approach using fuzzy support vector machines and compare it with the previous work, the results of experiments on the UCI data sets show that feature selection using fuzzy SVM obtains better results than using SVM.     

DIRICHLET BOUNDARY VALUE PROBLEMS FOR SECOND-ORDER QUASI-LINEAR DIFFERENTIAL EQUATIONS WITH CHANGING SIGN NONLINEARITIES

This paper is concerned with the existence of positive solutions of two-point Dirichlet singular and nonsingular boundary problems for second-order quasi-linear differential equations with changing sign nonlinearities.     

A structure-preserving finite element approximation of surface diffusion for curve networks and surface clusters

We consider the evolution of curve networks in two dimensions (2d) and surface clusters in three dimensions (3d). The motion of the interfaces is described by surface diffusion, with boundary conditions at the triple junction points lines, where three interfaces meet, and at the boundary points lines, where an interface meets a fixed planar boundary. We propose a parametric finite element method based on a suitable variational formulation. The constructed method is semi-implicit and can be shown to satisfy the volume conservation of each enclosed bubble and the unconditional energy-stability, thus preserving the two fundamental geometric structures of the flow. Besides, the method has very good properties with respect to the distribution of mesh points, thus no mesh smoothing or regularization technique is required. A generalization of the introduced scheme to the case of anisotropic surface energies and non-neutral external boundaries is also considered. Numerical results are presented for the evolution of two-dimensional curve networks and three-dimensional surface clusters in the cases of both isotropic and anisotropic surface energies.     

Preparation and nonisothermal crystallization behavior of polyamide 6/montmorillonite nanocomposites

Polyamide 6 (PA6)/montmorillonite (MMT) nanocomposites were prepared via melt intercalation. The structure, mechanical properties, and nonisothermal crystallization kinetics of PA6/MMT nanocomposites were investigated by X‐ray diffraction (XRD), tensile and impact tests, and differential scanning calorimetry (DSC). Before melt compounding, MMT was treated with an organic surfactant agent. XRD traces showed that PA6 crystallizes exclusively in γ‐crystalline structure within the nanocomposites. Tensile measurements showed that the MMT additions are beneficial in improving the strength and the stiffness of PA6, at the expense of tensile ductility. Impact tests revealed that the impact strength of PA6/MMT nanocomposites tended to decrease with increasing MMT content. The nonisothermal crystallization DSC data were analyzed by Avrami, Ozawa, modified Avrami‐Ozawa, and Nedkov methods. The validity of these empirical equations on the nonisothermal crystallization process of PA6/MMT nanocomposites is discussed. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2878–2891, 2004     

用样条函数表示非球面方程式的光线追迹

提出用样条函数来表示非球面方程式,它优于一般的非球面方程式表示法,便于计算。     

Synthesis and properties of side chain liquid crystalline ionomers containing quaternary ammonium salt groups

New thermotropic side chain liquid crystalline ionomers (LCIs), containing 4-(4-allyloxybenzyloxy)-4'-alkoxybiphenyl (IM) as mesogenic unit and allyltriethylammonium bromide (ATAB) as non-mesogenic unit, were synthesized by graft copolymerization upon polymethylhydrosiloxane. The chemical structures of the polymers were confirmed by IR spectroscopy. Differential scanning calorimetry (DSC) was used to measure the thermal properties of these polymers; the mesogenic properties were characterized by polarizing optical micrography, DSC and X-ray diffraction. The influence of the alkoxy chain length on the clearing temperatures of the ionomers is clearly shown in an odd-even effect, similar to other side chain liquid crystal polymers. The mesomorphic behaviour of the ionomers is compared with that of isomeric ionomers synthesized in previous work. The results demonstrate that the phase behaviour of the two series of isomeric ionomers is similar, but with the difference that the melting temperature of ionomers with biphenyl located at the end of the mesogen is higher than for ionomers with biphenyl located at the middle of the mesogen. The latter are more useful for smectic orientational order than the former.