An almost fourth order uniformly convergent difference scheme for a semilinear singularly perturbed reaction-diffusion problem

Summary. This paper is concerned with a high order convergent discretization for the semilinear reaction-diffusion problem: , for , subject to , where . We assume that on , which guarantees uniqueness of a solution to the problem. Asymptotic properties of this solution are discussed. We consider a polynomial-based three-point difference scheme on a simple piecewise equidistant mesh of Shishkin type. Existence and local uniqueness of a solution to the scheme are analysed. We prove that the scheme is almost fourth order accurate in the discrete maximum norm, uniformly in the perturbation parameter . We present numerical results in support of this result. Received February 25, 1994     

A robust and efficient adaptive reweighted estimator of multivariate location and scatter

This article proposes a reweighted estimator of multivariate location and scatter, with weights adaptively computed from the data. Its breakdown point and asymptotic behavior under elliptical distributions are established. This adaptive estimator is able to attain simultaneously the maximum possible breakdown point for affine equivariant estimators and full asymptotic efficiency at the multivariate normal distribution. For the special case of hard-rejection weights and the MCD as initial estimator, it is shown to be more efficient than its non-adaptive counterpart for a broad range of heavy-tailed elliptical distributions. A Monte Carlo study shows that the adaptive estimator is as robust as its non-adaptive relative for several types of bias-inducing contaminations, while it is remarkably more efficient under normality for sample sizes as small as 200.     

关于限制李超代数的分解

代数$A$ 称为不可分解的,如果 $A$ 不能分解成理想的直和.文中将证明满足$C(L_{\bar{0}})=C(L)=\{0\}$的限制李超代数能够分解成不可分解限制理想的直和,这种分解在不计理想次序的前提下是唯一的.而且还证明了限制李超代数的一些结果.     

Temperature‐modulated differential scanning calorimetry studies on the origin of double melting peaks in isothermally melt‐crystallized poly(L‐lactic acid)

In this work, the melting behaviors of nonisothermally and isothermally melt‐crystallized poly(L ‐lactic acid) (PLLA) from the melt were investigated with differential scanning calorimetry (DSC) and temperature‐modulated differential scanning calorimetry (TMDSC). The isothermal melt crystallizations of PLLA at a temperature in the range of 100–110 °C for 120 min or at 110 °C for a time in the range of 10–180 min appeared to exhibit double melting peaks in the DSC heating curves of 10 °C/min. TMDSC analysis revealed that the melting–recrystallization mechanism dominated the formation of the double melting peaks in PLLA samples following melt crystallizations at 110 °C for a shorter time (≤30 min) or at a lower temperature (100, 103, or 105 °C) for 120 min, whereas the double lamellar thickness model dominated the formation of the double melting peaks in those PLLA samples crystallized at a higher temperature (108 or 110 °C) for 120 min or at 110 °C for a longer time (≥45 min). © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 466–474, 2007     

Fonctions qui opèrent sur les espaces de Besov

Sans résumé

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Runge–Kutta convolution quadrature methods for well-posed equations with memory

Runge–Kutta based convolution quadrature methods for abstract, well-posed, linear, and homogeneous Volterra equations, non necessarily of sectorial type, are developed. A general representation of the numerical solution in terms of the continuous one is given. The error and stability analysis is based on this representation, which, for the particular case of the backward Euler method, also shows that the numerical solution inherits some interesting qualitative properties, such as positivity, of the exact solution. Numerical illustrations are provided.     

On the bidirectional vortex and other similarity solutions in spherical coordinates

The bidirectional vortex refers to the bipolar, coaxial swirling motion that can be triggered, for example, in cyclone separators and some liquid rocket engines with tangential aft-end injectors. In this study, we present an exact solution to describe the corresponding bulk motion in spherical coordinates. To do so, we examine both linear and nonlinear solutions of the momentum and vorticity transport equations in spherical coordinates. The assumption will be that of steady, incompressible, inviscid, rotational, and axisymmetric flow. We further relate the vorticity to some power of the stream function. At the outset, three possible types of similarity solutions are shown to fulfill the momentum equation. While the first type is incapable of satisfying the conditions for the bidirectional vortex, it can be used to accommodate other physical settings such as Hill’s vortex. This case is illustrated in the context of inviscid flow over a sphere. The second leads to a closed-form analytical expression that satisfies the boundary conditions for the bidirectional vortex in a straight cylinder. The third type is more general and provides multiple solutions. The spherical bidirectional vortex is derived using separation of variables and the method of variation of parameters. The three-pronged analysis presented here increases our repertoire of general mean flow solutions that rarely appear in spherical geometry. It is hoped that these special forms will permit extending the current approach to other complex fluid motions that are easier to capture using spherical coordinates.     

热传导型半导体瞬态问题特征变网格有限元法及其分析

热传导型半导体器件的瞬时状态由四个方程的非线性偏微分方程组的初边值问题所决定，其中电子位势方程是椭圆型的，电子和空穴浓度方程是对流扩散型的，温度方程为热传导型的。本文提出解这类问题的特征变网格有限元法，并进行了理论分析，在一定条件下，得到了某种意义下的最佳L^2误差估计结果。