A Finite Difference Scheme for Blow-Up Solutions of Nonlinear Wave Equations

<正>We consider a finite difference scheme for a nonlinear wave equation,whose solutions may lose their smoothness in finite time,i.e.,blow up in finite time.In order to numerically reproduce blow-up solutions,we propose a rule for a time-stepping, which is a variant of what was successfully used in the case of nonlinear parabolic equations.A numerical blow-up time is defined and is proved to converge,under a certain hypothesis,to the real blow-up time as the grid size tends to zero.     

KAM Theory for Partial Differential Equations

In the last years much progress has been achieved in KAM theory concerning bifurcation of quasi-periodic solutions of Hamiltonian or reversible partial differential equations.We provide an overview of the state of the art in this field.     

Implicit Shape Reconstruction of Unorganized Points Using PDE-Based Deformable 3D Manifolds

<正>In this work we consider the problem of shape reconstruction from an unorganized data set which has many important applications in medical imaging,scientific computing,reverse engineering and geometric modelling.The reconstructed surface is obtained by continuously deforming an initial surface following the Partial Differential Equation(PDE)-based diffusion model derived by a minimal volume-like variational formulation.The evolution is driven both by the distance from the data set and by the curvature analytically computed by it.The distance function is computed by implicit local interpolants defined in terms of radial basis functions.Space discretization of the PDE model is obtained by finite co-volume schemes and semi-implicit approach is used in time/scale.The use of a level set method for the numerical computation of the surface reconstruction allows us to handle complex geometry and even changing topology, without the need of user-interaction.Numerical examples demonstrate the ability of the proposed method to produce high quality reconstructions.Moreover,we show the effectiveness of the new approach to solve hole filling problems and Boolean operations between different data sets.     

傅种孙先生在北京师大附中

1 傅种孙先生简介 1.1 傅先生基本情况介绍 傅种孙先生(1898～1962)1898年2月27日生于江西省高安县.1920年在北京高等师范学校数理部毕业,留母校附中(即现北京师大附中)任教;1921年任母校数理部的讲师;1928年任教授:抗日战争以前,曾先后兼任北京女子师范大学,北平大学女子文理学院,北京大学,辅仁大学教授;1933年当选北平(北京)市数学会理事长秘书;1935年当选中国数学会评议委员兼<数学杂志>编辑;1945年11月至1946年8月在牛津大学、1946年9月至1947年11月在剑桥大学考察;1947～1962年任北京师范大学数学系教授,1956年前曾兼系主任;在1949～1957年间,曾任北京师范大学教务长(3年)及副校长(5年);1952～1957年任北京市人民代表大会代表,中国数学会及其北京市分会常务理事,<中国数学杂志>及其后身<数学通报>总编辑;1962年1月18日病逝于北京.     

Local Unstable Entropy and Local Unstable Pressure for Partially Hyperbolic Endomorphisms*

In this paper, local unstable metric entropy, local unstable topological entropy and local unstable pressure for partially hyperbolic endomorphisms are introduced and investigated. Specially, two variational principles concerning relationships among the above mentioned numbers are formulated.     

Nonconforming Finite Element Methods for the Constrained Optimal Control Problems Governed by Nonsmooth Elliptic Equations

In this paper,nonconforming finite element methods(FEMs)are proposed for the constrained optimal control problems(OCPs)governed by the nonsmooth elliptic equations,in which the popular EQr1 ot element is employed to approximate the state and adjoint state,and the piecewise constant element is used to approximate the control.Firstly,the convergence and superconvergence properties for the nonsmooth elliptic equation are obtained by introducing an auxiliary problem.Secondly,the goal-oriented error estimates are obtained for the objective function through establishing the negative norm error estimate.Lastly,the methods are extended to some other well-known nonconforming elements.     

A Direct Method of Moving Planes to Fractional Power SubLaplace Equations on the Heisenberg Group

We give the direct method of moving planes for solutions to the conformally invariant fractional power sub Laplace equation on the Heisenberg group.The method is based on four maximum principles derived here.Then symmetry and nonexistence of positive cylindrical solutions are proved.     

Multivariate quasi-tight framelets with high balancing orders derived from any compactly supported refinable vector functions

Generalizing wavelets by adding desired redundancy and flexibility,framelets(i.e.,wavelet frames)are of interest and importance in many applications such as image processing and numerical algorithms.Several key properties of framelets are high vanishing moments for sparse multiscale representation,fast framelet transforms for numerical efficiency,and redundancy for robustness.However,it is a challenging problem to study and construct multivariate nonseparable framelets,mainly due to their intrinsic connections to factorization and syzygy modules of multivariate polynomial matrices.Moreover,all the known multivariate tight framelets derived from spline refinable scalar functions have only one vanishing moment,and framelets derived from refinable vector functions are barely studied yet in the literature.In this paper,we circumvent the above difficulties through the approach of quasi-tight framelets,which behave almost identically to tight framelets.Employing the popular oblique extension principle(OEP),from an arbitrary compactly supported M-refinable vector functionφwith multiplicity greater than one,we prove that we can always derive fromφa compactly supported multivariate quasi-tight framelet such that:(i)all the framelet generators have the highest possible order of vanishing moments;(ii)its associated fast framelet transform has the highest balancing order and is compact.For a refinable scalar functionφ(i.e.,its multiplicity is one),the above item(ii)often cannot be achieved intrinsically but we show that we can always construct a compactly supported OEP-based multivariate quasi-tight framelet derived fromφsatisfying item(i).We point out that constructing OEP-based quasi-tight framelets is closely related to the generalized spectral factorization of Hermitian trigonometric polynomial matrices.Our proof is critically built on a newly developed result on the normal form of a matrix-valued filter,which is of interest and importance in itself for greatly facilitating the study of refinable vector functions and multiwavelets/multiframelets.This paper provides a comprehensive investigation on OEP-based multivariate quasi-tight multiframelets and their associated framelet transforms with high balancing orders.This deepens our theoretical understanding of multivariate quasi-tight multiframelets and their associated fast multiframelet transforms.     

Singular integral operators on product domains along twisted surfaces

We introduce a class of singular integral operators on product domains along twisted surfaces.We prove that the operators are bounded on L^p provided that the kernels satisfy weak conditions.     

智慧窗

1 趣解等式七个文字与三个拼音字头组成了一道加法等式,你能否把它们分别换成0～9的数字. (相同文字、字母必须要换相同的数字)使其等式成立吗? (上海市长宁路476弄8号1602室(200042) 张刘福) 2 质数趣题请将5～20各数分别填入圆圈内,使每相邻的两个数之和都是质数.试试看,你能填出     

遗传群体的代数系统

根据生物遗传的内在规律,在多基因座配子中构造了一类运算,阐明了生物遗传具有交换的R-代数的数学结构,从而使遗传问题可用代数方法解决.文中利用这种代数所得到的因子频率定理,具有比Hardy-Weinberg平衡定律更为广泛的意义.同时,作为这种代数应用的例子,讨论了在连锁条件下群体基因型频率的计算问题,得到了一系列有意义的结果.     

基于最优保存和自适应性的混合遗传算法

1 引 言遗传算法（Genetic Algorithm,GA）是由Michigan大学Holland等创立的.常用的遗传算法一般有以下三种:简单遗传算法（Simple Genetic Algorithm,SGA）或称标准遗传算法（Canonical Genetic Algorithm,CGA）、最优保存简单遗传算法（Optimum MaintainingSimple Genetric Algorithm,OMSGA）和自适应遗传算法（Adaptive Genetic Algorithm,AGA）.     

Crossing Over Genetic Algorithms: The Sugal Generalised GA

Sugal is a major new public-domain software package designed to support experimentation with, and implementation of, Genetic Algorithms. Sugal includes a generalised Genetic Algorithm, which supports the major popular versions of the GA as special cases. Sugal also has integrated support for various datatypes, including real numbers, and features to make hybridisation simple. This paper discusses the Sugal GA, showing how recombining the features of the popular algorithms results in the creation of a number of useful hybrid algorithms.     

基于遗传算法的生产批量优化问题

本文针对生产费用、生产准备费用和库存费用综合指标最小的最优的能力约束生产批量问题,建立基于遗传算法的数学模型,通过模拟试验及实际问题的计算验证了算法的可行性。     

Theoretical analysis of steady state genetic algorithms

Evolutionary Algorithms, also known as Genetic Algorithms in a former terminology, are probabilistic algorithms for optimization, which mimic operators from natural selection and genetics. The paper analyses the convergence of the heuristic associated to a special type of Genetic Algorithm, namely the Steady State Genetic Algorithm (SSGA), considered as a discrete-time dynamical system non-generational model. Inspired by the Markov chain results in finite Evolutionary Algorithms, conditions are given under which the SSGA heuristic converges to the population consisting of copies of the best chromosome.     

基于遗传算法的装备维修费用优化分配理论及优化方法研究

在美国工业界武器系统咨询委员会提出的郊能公式基础上 ,建立了武器装备效能与维修费用函数关系 ,为武器装备维修费用的优化分配提供了一个标准 .针对多种武器装备维修费用优化 ,建立了一个维修费用分配模型 ,用遗传算法进行了优化 ,并对优化过程进行了详细阐述 .在此基础上开发了装备维修经费优化与管理辅助决策支持系统 .     

基于遗传算法的多目标可靠性优化

在元件的体积、重量和造价的共同约束下的多级串并联系统的可靠性优化问题是一个具有多局部极值的、非线性的、同时具有整数和实数变量的混合优化问题.将遗传算法和多目标可靠性分配问题相结合,对可靠性分配问题进行求解,得到较好效果,从而得出结论,遗传算法在求解多目标可靠性优化问题中是一种行之有效的方法.     

Search heuristics and the influence of non-perfect randomness: examining Genetic Algorithms and Simulated Annealing

Simulated Annealing and Genetic Algorithms are important methods to solve discrete optimization problems and are often used to find approximate solutions for diverse NP-complete problems. They depend on randomness to change their current configuration and transition to a new state. In Simulated Annealing, the random choice influences the construction of the new state as well as the acceptance of that new state. In Genetic Algorithms, selection, mutation and crossover depend on random choices. We experimentally investigate the robustness of the two generic search heuristics when using pseudorandom numbers of limited quality. To this end, we conducted experiments with linear congruential generators of various period lengths, a Mersenne Twister with artificially reduced period lengths as well as quasi-random numbers as the source of randomness. Both heuristics were used to solve several instances of the Traveling Salesman Problem in order to compare optimization results. Our experiments show that both Simulated Annealing and the Genetic Algorithm produce inferior solutions when using random numbers with small period lengths or quasi-random numbers of inappropriate dimension. The influence on Simulated Annealing, however, is more severe than on Genetic Algorithms. Interestingly, we found that when using diverse quasi-random sequences, the Genetic Algorithm outperforms its own results using quantum random numbers.     

Optimization of Mechanically Coupled Composite Pipes by Genetic Algorithms

The optimization of composite components with regard to minimum weight and maximum load bearing capacity in consideration of multiple constraints is an optimization problem of rather high complexity. Genetic Algorithms are a good choice for solving such problems. In this paper the formulation of a Genetic Algorithm for the simultaneous optimization of two thin walled, mechanically coupled composite pipes subjected to a combination of thermal and mechanical loads is presented. The optimization goal is the minimization of the total mass of the pipe arrangement taking into account multiple design constraints. It is shown that Genetic Algorithms are valueable tools for solving optimization problems with a large number of parameters. Furthermore, it is possible to find additional, perhaps practicable, close‐to‐optimal configurations as a byproduct of the optimization process. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Advanced Genetic Programming Based Machine Learning

A Genetic Programming based approach for solving classification problems is presented in this paper. Classification is understood as the act of placing an object into a set of categories, based on the object’s properties; classification algorithms are designed to learn a function which maps a vector of object features into one of several classes. This is done by analyzing a set of input-output examples (“training samples”) of the function. Here we present a method based on the theory of Genetic Algorithms and Genetic Programming that interprets classification problems as optimization problems: Each presented instance of the classification problem is interpreted as an instance of an optimization problem, and a solution is found by a heuristic optimization algorithm. The major new aspects presented in this paper are advanced algorithmic concepts as well as suitable genetic operators for this problem class (mainly the creation of new hypotheses by merging already existing ones and their detailed evaluation). The experimental part of the paper documents the results produced using new hybrid variants of Genetic Algorithms as well as investigated parameter settings. Graphical analysis is done using a novel multiclass classifier analysis concept based on the theory of Receiver Operating Characteristic curves. The work described in this paper was done within the Translational Research Project L282 “GP-Based Techniques for the Design of Virtual Sensors” sponsored by the Austrian Science Fund (FWF).