基于指数分布的进化策略

典型的进化策略受自然进化过程的启发而成为求解全局优化问题的重要方法。传统的ES变异算子作为一个主要的进化技术是建立在正态分布的随机变量基础上的，本文提出了基于指数分布的进化策略由于采用了新的变异算子有效地减少了产生探试解的成本，从而优于传统的进化策略。     

基于增广Lagrange函数的RQP方法

Recursive quadratic programming is a family of techniques developd by Bartholomew-Biggs and other authors for solving nonlinear programming problems.This paperdescribes a new method for constrained optimization which obtains its search di-rections from a quadratic programming subproblem based on the well-known aug-mented Lagrangian function.It avoids the penalty parameter to tend to infinity.We employ the Fletcher‘s exact penalty function as a merit function and the use of an approximate directional derivative of the function that avoids the need toevaluate the second order derivatives of the problem functions.We prove that thealgorithm possesses global and superlinear convergence properties.At the sametime, numerical results are reported.     

Efficient algorithms for solving certain nonconvex programs dealing with the product of two affine fractional functions

Two algorithms for finding a global minimum of the product of two affine fractional functions over a compact convex set and solving linear fractional programs with an additional constraint defined by the product of two affine fractional functions are proposed. The algorithms are based on branch and bound techniques using an adaptive branching operation which takes place in one-dimensional intervals. Results from numerical experiments show that large scale problems can be efficiently solved by the proposed methods.     

高阶非线性差分方程的全局吸引性

研究了差分方程 xn 1 =a - bxn- k A - xn( a≥ 0 ,A≥ b≥ 0 )的全局稳定性和正解的周期性质 .证明了方程的一个正平衡点是一个全局吸引子 ,并给出了相应的吸引域     

Global stabilization of a Lorenz system

In this paper,using feedback linearizing technique,we show that a Lorenz system can be considered as a cascade system.Moreover,this system satisfies the assumptions of global stabilization of casecade systems.Thus coninuous state feedback control laws are proposed to globally stabilize the Lorenz system at the equilibrium point.Simulation results are presented to verify our method.This method can be further generalized to other chaotic systems such as Chen system,coupled dynamos system,etc.     

Unipotent Algebraic Affine Supergroups and Nilpotent Lie Superalgebras

We characterize hereditary (as coalgebras) Hopf algebras by the property of ‘equivariant smoothness’, and apply the result to generalize to the super-context, the category equivalence, due to Hochschild, between the unipotent algebraic affine groups and the finite-dimensional nilpotent Lie algebras, in characteristic zero. The global dimension of commutative Hopf algebras, regarded as coalgebras, is also discussed. Presented by S. Montgomery Mathematics Subject Classification (2000) 16W30.     

杨振宁学术成就——量子不可积相位因子和规范场的积分表示

简要介绍杨振宁的一项重要学术贡献。一般物理学界人士都熟悉杨振宁在现代物理学中的三项伟大贡献：（1）非阿贝尔规范场理论；（2）杨－Baxter方程；（3）弱互作用宇称不守恒。文章介绍的是在这三大贡献之外的一项较少为人知的重要贡献：量子不可积相位因子和规范场的积分表示。     

GLOBAL BEHAVIOR IN A RATIONAL RECURSIVE SEQUENCE

In this paper, we study the global stability, and the periodic character of the rational recursive sequence. We show that the positive equilibrium of the sequence is a global attractor with a basin which depends on certain conditions posed on the coefficients.     

Global Existence for a Parabolic-hyperbolic Free Boundary Problem Modelling Tumor Growth

In this paper we study a free boundary problem modelling tumor growth, proposed by A. Friedman in 2004. This free boundary problem involves a nonlinear second-order parabolic equation describing the diffusion of nutrient in the tumor, and three nonlinear first-order hyperbolic equations describing the evolution of proliferative cells, quiescent cells and dead cells, respectively. By applying Lp theory of parabolic equations, the characteristic theory of hyperbolic equations, and the Banach fixed point theorem, we prove that this problem has a unique global classical solution.     

Monitoring of the ducting by a ground-based GPS receiver

In this paper, we describe the estimation of low-altitude refractivity structure from simulation and real ground-based GPS delays. The vertical structure of the refractive environment is modeled using three parameters, i.e., duct height, duct thickness, and duct slope. The refractivity model is implemented with a priori constraints on the duct height, thickness, and strength, which might be derived from soundings or numerical weather-prediction models. A ray propagation model maps the refractivity structure into a replica field. Replica fields are compared with the simulation observed data using a squared-error objective function. A global search for the three environmental parameters is performed using genetic algorithm. The inversion is assessed by comparing the refractivity profiles from the radiosondes to those estimated. This technique could provide near-real-time estimation of ducting effect. The results suggest that ground-based GPS provides significant atmospheric refractivity information, despite certain fundamental limitations of ground-based measurements. Radiosondes typically are launched just a few times daily. Consequently, estimates of temporally and spatially varying refractivity that assimilate GPS delays could substantially improve over-estimates using radiosonde data alone.