Convex composite minimization withC 1,1 functions

In this paper, we present second-order optimality conditions for convex composite minimization problems in which the objective function is a composition of a finite-valued or a nonfinite-valued lower semicontinuous convex function and aC ^1,1 function. The results provide optimality conditions for composite problems under reduced differentiability requirements.This paper is a revised version of the Departmental Preliminary Report AM92/32, School of Mathematics, University of New South Wales, Kensington, NSW, Australia.Research of this author was supported in part by an Australian Research Council Grant.     

一种高效的等参有限元逆变换算法

采用Ｔａｙｌｏｒ展开技术构造了一种具有线性迭代格式的等参有限元逆变换算法，对算法的收敛性和收敛速度分别给出了理论证明和数值检验。该算法不仅形式简单、便于程序实现，且适合于任何类型的等参单元，是一种高效实用的逆变换算法。文中还给出了算法的实施框图。     

非理想1/4波片对泵浦光偏振态的影响

为了研究调整架角度误差以及波片与光源波长不匹配对线偏振光经过1/4波片之后偏振态的影响,本文利用坐标变换法得到1/4波片的琼斯矩阵,并用琼斯矩阵表示各偏振态。推导出波片与光源不匹配时对偏振态的影响理论模型。当考虑到调整架的角度误差时,对入射光偏振态以及波片的琼斯矩阵表达式做引入角度误差的泰勒展开,最后得到和实验结果匹配的仿真曲线。仿真结果表明,当采用808 nm 1/4波片对795 nm波长的线偏振光作用时,在不考虑调整误差的理想情况下出射光椭圆度最高为0.9746,考虑调整误差时,对应理想情况下椭圆度最高为0.96,椭圆度最高点偏移1.72°。仿真和实验结果为进一步分析泵浦光椭圆度对原子参数的影响提供了依据。     

TC4动态力学性能研究

材料的本构模型参量是结构冲击动力响应数值模拟的基础。本文运用静态实验机和SHB装置,对TC4在常温~750C°、应变率10-4~103s-1下的力学行为进行了研究,得到了相应的塑性本构模型参量。通过Taylor撞击实验及其数值模拟对本构模型参量进行了验证,表明所得参量可较好描述冲击载荷作用下材料的塑性力学行为。     

Taylor dispersion analysis discloses the impairment of Aβ peptide aggregation by the presence of a fluorescent tag

The use of fluorescently tagged amyloid peptides, implicated in Alzheimer's disease, to study their aggregation at low concentrations is a common method; however, the fluorescent tag should not introduce a bias in the aggregation process. In this work, native amyloid peptides Aβ(1–40) and Aβ(1–42) and fluorescein-5-isothiocyanate (FITC), tagged ones, were studied using Taylor dispersion analysis coupled with a simultaneous UV and light-emitting diode-induced fluorescence detection, to unravel the effect of FITC on the aggregation process. For that, a total concentration of 100 µM of peptides consisting of a mixture of native and tagged ones (up to 10% in moles) was applied. Results demonstrated that FITC had a strong inhibition effect upon the aggregation behaviour of Aβ(1–42), whereas for Aβ(1–40), only a retardation in kinetics was observed. It was also shown that when mixed solutions of Aβ(1–40) and Aβ(1–42) are used, the Aβ(1–42) alloform was the leading peptide in the aggregation process, and when the latter was tagged, the aggregation kinetics decreased but the lifetime of potentially toxic oligomers was drastically increased. These results confirmed that the hydrophilicity of the N-terminus part of the peptide plays a major role in the aggregation process.     

A Collocation Method for Solving Fractional Riccati Differential Equation

In this article, we have introduced a Taylor collocation method, which is based on collocation method for solving fractional Riccati differential equation. The fractional derivatives are described in the Caputo sense. This method is based on first taking the truncated Taylor expansions of the solution function in the fractional Riccati differential equation and then substituting their matrix forms into the equation. Using collocation points, the systems of nonlinear algebraic equation are derived. We further solve the system of nonlinear algebraic equation using Maple 13 and thus obtain the coefficients of the generalized Taylor expansion. Illustrative examples are presented to demonstrate the effectiveness of the proposed method.     

45钢动态塑性本构参量与验证

运用静态实验机和SHPB装置,对45钢在常温～750C、应变率为10-4～103 s-1下的力学行为进行了研究,拟合得到了Johnson-Cook本构模型参量。开展了Taylor圆柱撞击的火炮实验,运用LS-DYNA进行了相应的数值模拟,通过二者的比较对本构模型参量进行了验证,表明所得模型参量可以较好地描述材料在高速变形下的大应变力学行为。     

On Taylor-series expansion methods for the second kind integral equations

In this paper, we comment on the recent papers by Yuhe Ren et al. (1999) [1] and Maleknejad et al. (2006) [7] concerning the use of the Taylor series to approximate a solution of the Fredholm integral equation of the second kind as well as a solution of a system of Fredholm equations. The technique presented in Yuhe Ren et al. (1999) [1] takes advantage of a rapidly decaying convolution kernel k(|s−t|) as |s−t| increases. However, it does not apply to equations having other types of kernels. We present in this paper a more general Taylor expansion method which can be applied to approximate a solution of the Fredholm equation having a smooth kernel. Also, it is shown that when the new method is applied to the Fredholm equation with a rapidly decaying kernel, it provides more accurate results than the method in Yuhe Ren et al. (1999) [1]. We also discuss an application of the new Taylor-series method to a system of Fredholm integral equations of the second kind.     

A higher order lattice BGK model for simulating some nonlinear partial differential equations

In this paper, we consider a one-dimensional nonlinear partial differential equation that has the form ut + αuux + βunux - γuxx + δuxxx = F(u). A higher order lattice Bhatnager-Gross-Krook (BGK) model with an amending-function is proposed. With the Chapman-Enskog expansion, different kinds of nonlinear partial differential equations are recovered correctly from the continuous Boltzmann equation. The numerical results show that this method is very effective.     

On Taylor and other joint spectra for commuting n-tuples of operators

Let R and S be commuting n-tuples of operators. We will give some spectral relations between RS and SR that extend the case of single operators. We connect the Taylor spectrum, the Fredholm spectrum and some other joint spectra of RS and SR. Applications to Aluthge transforms of commuting n-tuples are also provided.