RICE CONDITION NUMBERS OF CERTAIN CHARACTERISTIC SUBSPACES

This paper proposes the Rice condition numbers for invariant subspace, singular sub-spaces of a matrix and deflating subspaces of a regular matrix pair. The first-order perturbation estimations for these subspaces are derived by applying perturbation expansions of orthogonal projection operators.     

条形装箱问题的优化模型和增广Lagrange算法

This paper formulates a two-dimensional strip packing problem as a non-linear programming(NLP)problem and establishes the first-order optimality con-ditions for the NLP problem.A numerical algorithm for solving this NLP problemis given to find exact solutions to strip-packing problems involving up to 10 items.Approximate solutions can be found for big-sized problems by decomposing the setof items into small-sized blocks of which each block adopts the proposed numericalalgorithm.Numerical results show that the approximate solutions to big-sized prob-lems obtained by this method are superior to those by NFDH,FFDH and BFDHapproaches.     

Speedup estimates for some variants of the parallel implementations of the branch-and-bound method

The efficiency of parallel implementations of the branch-and-bound method in discrete optimization problems is considered. A theoretical analysis and comparison of two parallel implementations of this method is performed. A mathematical model of the computation process is constructed and used to obtain estimates of the maximum possible speedup. Examples of problems in which none of these two parallel implementations can speed up the computations are considered.     

A Joint Integral Test for the Locations of Extrema for Brownian Motion

Let μ⁺(t) and μ⁻(t) be the locations of the maximum and minimum, respectively, of a standard Brownian motion in the interval [0,t]. We establish a joint integral test for the lower functions of μ⁺(t) and μ⁻(t), in the sense of Paul Lévy. In particular, it yields the law of the iterated logarithm for max(μ⁺(t),μ⁻(t)) as a straightforward consequence. Our result is in agreement with well-known theorems of Chung and Erdős [(1952) Trans. Amer. Math. Soc. 72, 179–186.], and Csáki, F?ldes and Révész [(1987) Prob. Theory Relat. Fields 76, 477–497].      

A detailed analysis of the photoemission spectra of basic thioaromatic monolayers on noble metal substrates

Analysis of photoemission spectra of complex thioaromatic self-assembled monolayers (SAMs) requires the knowledge and understanding of such spectra for the basic systems. Keeping this goal in mind, synchrotron-based high-resolution X-ray photoelectron spectroscopy was used to characterize SAMs formed from the simplest thioaromatic compounds, namely thiophenol, 1,1′-biphenyl-4-thiol and 1,1′;4′,1″-terphenyl-4-thiol on evaporated Au(1 1 1) and Ag(1 1 1) substrates. The acquired S 2p and C 1s spectra were analyzed in terms of fine structure and initial and final state effects in the photoemission process. The assignment of the individual spectral features was considered in detail. Conclusions on quality and chemical and structural homogeneity of the investigated SAMs were derived.     

条件愈苦,意志愈坚 --记王淦昌早年的科研活动

文章介绍了中国物理学家王淦昌早期的科研工作，特别是在抗日战争时期的科研成绩．王淦昌早期的科研贡献并不是在先进的实验仪器上，在条件优裕的实验室内完成的，而是在实验设备缺乏，科学文献不足等极端困难的环境中完成的．从王淦昌身上，可以看到那个时代中国优秀科学家脚踏实地、执志若金的奋斗精神．     

Kuhn-Tucker条件与线性规划的对偶性

证明了线性规划的K uhn-Tucker条件蕴含着它的对偶问题,解释了L agrange乘子的意义.进而显示了K-T条件中的互补松驰性与对偶线性规划的互补松紧定理之间的联系.     

On the Lp–Lq maximal regularity for Stokes equations with Robin boundary condition in a bounded domain

We obtain the L_p–L_q maximal regularity of the Stokes equations with Robin boundary condition in a bounded domain in ?ⁿ (n?2). The Robin condition consists of two conditions: v ? u=0 and αu+β(T(u, p)v – 〈T(u, p)v, v〉v)=h on the boundary of the domain with α, β?0 and α+β=1, where u and p denote a velocity vector and a pressure, T(u, p) the stress tensor for the Stokes flow and v the unit outer normal to the boundary of the domain. It presents the slip condition when β=1 and non‐slip one when α=1, respectively. The slip condition is appropriate for problems that involve free boundaries. Copyright © 2006 John Wiley & Sons, Ltd.     

Hajek—Renyi不等式的推广及其应用

对Hajek-Renyi不等式进行了推广，利用推广的不等式给出了随机变量序列绝对平均意义下的强大数定律的一个条件．     

四次函数实零点的完全判据和正定条件

本文给出了四次函数实零点的完全判据和正定条件,这一结果在研究多项式系统的奇点分析和分支问题时给出了可以实用的判据．