Improved linear multi-step methods for stochastic ordinary differential equations

We consider linear multi-step methods for stochastic ordinary differential equations and study their convergence properties for problems with small noise or additive noise. We present schemes where the drift part is approximated by well-known methods for deterministic ordinary differential equations. In previous work, we considered Maruyama-type schemes, where only the increments of the driving Wiener process are used to discretize the diffusion part. Here, we suggest the improvement of the discretization of the diffusion part by also taking into account mixed classical-stochastic integrals. We show that the relation of the applied step sizes to the smallness of the noise is essential in deciding whether the new methods are worthwhile. Simulation results illustrate the theoretical findings.     

The efficient solution of electromagnetic scattering for inhomogeneous media

We consider an electromagnetic scattering problem for inhomogeneous media. In particular, we focus on the numerical computation of the electromagnetic scattered wave generated by the interaction of an electromagnetic plane wave and an inhomogeneity in the corresponding propagation medium. This problem is studied in the VV polarization case, where some special symmetry requirements for the incident wave and for the inhomogeneity are assumed. This problem is reformulated as a Fredholm integral equation of second kind, which is discretized by a linear system having a special form. This allows to compute efficiently an approximate solution of the scattering problem by using iterative techniques for linear systems. Some numerical examples are reported.     

Quadruple systems of the projective special linear group PSL(2,q), q ≡ 1 (mod 4)

We determine the distribution of quadruple systems among the orbits of 4‐element subsets under the action of PSL(2,q) on the projective line when q ≡ 1 (mod 4). © 2003 Wiley Periodicals, Inc. J Combin Designs 11: 339–351, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/jcd.10043     

Optimization model of recrystallization hot rolling of titanium-vanadium steels

An optimization model was built based on the data of a pilot-scale (4.5 MN load, 225 KW power capacity) rolling mill to minimize the austenite grain sizes of Ti–V steels, which prevail at the instant of completion of the static recrystallization during hot rolling. A computer program developed for this optimization model was run for the rolling schedule, which is designed according to the complete recrystallization case. An energy optimization model developed previously was applied to different rolling schedules. The grain size optimization results demonstrate the effectiveness of these modelling approaches in terms of final grain size, final plate thickness, measured and computed roll force and torque values for both the design of the thermomechanical schedules which produce plate with fine-grained microstructures, high strength, and notch toughness and the temperature-reduction schedules of conventional controlled rolling.     

An Infeasible Point Method for Minimizing the Lennard-Jones Potential

Minimizing the Lennard-Jones potential, the most-studied modelproblem for molecular conformation, is an unconstrained globaloptimization problem with a large number of local minima. In thispaper, the problem is reformulated as an equality constrainednonlinear programming problem with only linear constraints. Thisformulation allows the solution to approached through infeasibleconfigurations, increasing the basin of attraction of the globalsolution. In this way the likelihood of finding a global minimizeris increased. An algorithm for solving this nonlinear program isdiscussed, and results of numerical tests are presented.     

Directions of Coaxiality between Pure Strain and Stress in Linear Elasticity

For a linear anisotropic hyperelastic body subjected to a state of pure strain it is shown that there are at least three directions such that the stress and strain tensors are coaxial.     

金属线性热膨胀系数的研究

 从温度T时的压强表达式出发，结合普适状态方程（UEOS）、Debye模型和热力学关系式，给出了计算金属线性热膨胀系数的普遍公式。并对Al、Cu、Pb的这一物理量进行了具体计算。结果表明，理论与实验符合较好。     

增长曲线模型中UMRE估计的存在性

对于设计矩阵不满秩，协方差阵任意或具有均匀结构或序列结构的正态增长曲线模型，本文讨论参数矩阵的一致最小风险同变（UMng）估计的存在性．在仿射变换群GI和转移交换群、二次损失和矩阵损失下本文分别获得存在回归系数矩阵的线性可估函数矩阵的UMRE估计的充要条件，推广了由[21]给出的在设计矩阵满秩下估计回归系数矩阵的结果．本文还首次证明了在群G1和二次损失下不存在协方差阵V和trV的UMRE估计．     

Linear Phase Shift Response with High Dynamic Range for Holographic Recording in As2S3

Amorphous As₂S₃ films are real-time photographic materials for phase holograms. This work focuses on the phase shift in As₂S₃ films as a function of the exposure. A method for measuring the phase shift response and the exposure simultaneously is presented. A relative displacement determination of interferometric patterns allows precise measurements insensitive to changes of experimental conditions. The phase shift dependence on the intensity of the writing beam is evaluated for two different films. As a result, a linear phase shift response is obtained with a dynamic range of nearly n. It is independent of the intensity over four orders of magnitude. The results are proofed by diffraction efficiency measurements.     

关于资源影子价格问题的讨论

本就资源影子价格所存在的问题，重点阐述了我们自己的看法和研究结果。