对称向量拟均衡问题有效解的存在性

利用标量化方法建立对称向量拟均衡问题有效解的存在性定理。作为标量化方法的应用，利用这一方法得到向量变分不等式和拟向量变分不等式有效解的存在性定理。     

激光水下扫描成像系统的图像修正机理

同步扫描系统可以克服后向散射，但同时也产生了两种非线性，一是扫描线速度的非线性，一是由于距离对光能衰减造成的非线性，两种非线性都需要修正，本文从原理上讨论水下激光成像时能量衰减的修正原理与修正方法，并给出仿真结果。     

KrF准分子激光激发掺锗光纤折射率扰动的非线性过程

本文采用了一种简单的功率监测法,观察了KrF准分子激光对掺锗光纤折射率影响的非线性过程。观察到子纤芯折射率扰动过程中非稳定现象、饱和现象和折射率扰动的非线性。     

Co-Orthogonal Codes

We define, construct and sketch possible applications of a new class of non-linear codes: co-orthogonal codes, with possible applications in cryptography and parallel processing. We also describe a fast and general method for generating (non-linear) codes with prescribed dot-products with the help of multi-linear polynomials.     

On the topological representation of catalytic cycles with nonlinear steps

Reaction route analysis is applied to visualize reaction networks in several heterogeneous catalytic reactions. Combination of the theory of complex reactions with the notion of catalytic cycles results in a topological representation of complex mechanisms with the nodes comprising all possible surface species including free sites and branches indicating interconnections between reactions.     

The mathematics of playing golf, or: a new class of difficult non-linear mixed integer programs

We consider a class of non-linear mixed integer programs with n integer variables and k continuous variables. Solving instances from this class to optimality is an NP-hard problem. We show that for the cases with k=1 and k=2, every optimal solution is integral. In contrast to this, for every k≥3 there exist instances where every optimal solution takes non-integral values. Received: August 2001 / Accepted: January 2002?Published online March 27, 2002     

求解准确的表面张力—重力波方程的新方法

本文提供一个求解重力和表面张力同时作用的周期前进二维非线性波的新方法.自由表面在计算域转入单位圆后用有限项Fourier级数表示.动力学边界条件用的是完整的非线性形式.Fourier级数的系数用Newton-Raphson方法迭代求解.这是一个精巧的方法.所用计算工作量小而结果精度高.     

Heat conductivity of three periodic Hard Disks via nonequilibrium molecular dynamics

We use a driving field, of the type first suggested by Evans, to generate a steady heat current in the simplest possible system, a two-dimensional periodic fluid of three hard disks. Hard-disk motion equations can be conveniently derived from repulsive constant-force or linear-force potentials by considering the infinitely repulsive limit of these potentials. We show that the isoenergetic and isokinetic forms of the nonequilibrium equations of motion generate steady-state heat conductivities differing by terms of order 1/N, whereN is the number of particles. The resulting conductivities appear to vary as the logarithm of the driving field strength. Even at low fields, the three-body periodic-system results lie well below Enskog's infinite-system prediction.     

Syntheses, structures and third-order non-linear optical properties of homometal clusters containing molybdenum

Both the homometal cluster [P(ph₄)]₂[Mo₂O₂(μ-S)₂(S₂)₂] (1) and [Mo₂O₂(μ-S)₂(Et₂dtc)₂] (2) (Et₂dtc=diethyl-dithiocarbamate) were successfully synthesized by low-temperature solid-state reactions. X-ray single-crystal diffraction studies suggest that compound (1) is a dinuclear anion cluster, and compound (2) is a dinuclear neutral cluster. The two compounds were characterized by elemental analyses, IR spectra and UV-Vis spectra. The third-order non-linear optical (NLO) properties of the clusters were also investigated and all exhibited nice non-linear absorption and self-defocusing performance with moduli of the hyperpolarizabilities 5.145×10⁻³⁰ esu for (1) and 5.428×10⁻³⁰ esu for (2).     

几个金属卤素簇的合成与性能研究

The hydrothermal reaction of CuBr2 and CuBr with phen·H2O （phen= 1,10-phenanthroline） in a molar ratio of 1：1：1.5 gave birth to the first copper-halo cationic cluster [Cu2^Ⅱ Cu2^Br4 （phen）4 ] ^2＋（1） with tetranuclear anionic cluster [Cu4Br6]^2-. Changing the precursors or their molar ratios, two mononuclear complexes [Cu（phen）2Br]Br·H2O （2） and [Ni（phen）3][CuCl2]2 （3） as well as two unusual copper-halo chains found in polymers [Cu2Br2（phen）]∞ （4） and [Cu^ⅡCu3^ⅠBr2Ⅰ3 （phen）2 ]∞ （5） were obtained. The （Cu2Br2）∞ chain of 4 looks like a linearar ray of hexagons based on fused Cu3Br3 units, and the linear （Cu3Ⅰ3Br^-）∞ chain of 5 is an alternate combination of the rhombic Cu2I2 cores and the Cu4I4Br2^2- units. In addition, the hydrothermal reaction of CuBr2 with NA（NA=nicotinic acid） or INA （INA =isonicotinic acid） resulted in the syntheses of two compounds [CuBr（NA）] （6） and [CuBr（INA）]∞（7） containing staircase chain. Among them the third-order non-linear optical properties of 2, 5, 6 and 7 were investigated and all exhibit the reverse saturable absorption （α2〉0） and self-defocusing performance （n2〈0）.