数学季刊

王卿文, 孙建华, 李尚志

2003, 18(2): 111-116.

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Let Ω be a finite dimensional central algebra and chart Ω≠2. The matrix equation AXB - CXD = E over Ω is considered. Necessary and sufficient conditions for the existence of centro(skew)symmetric solutions of the matrix equation are given. As a particular case, the matrix equation X - AXB = C over Ω is also considered.

一类强非线性奇摄动边值问题

唐荣荣

2003, 18(2): 117-120.

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In this paper,a class of strongly nonlinear singular perturbed boundary value problems are considered by the theory of differential inequalities and the correction of boundary layer,under which the existence of solution is proved and the uniformly valid asymptotic expansions is obtained as well.

一个具无穷时滞的动力系统模型平衡解的全局渐近稳定性

李想, 翁佩萱

2003, 18(2): 121-128.

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By using a criterion lur asymptotic stability in Banach space BC,a group of sufficient condi- tions for a dynamical model with infinite delay which is derived from hematology were cbtained,which refined the result in the reference [10]got by the second author herself.

一类Burgers-KPP方程新的显示精确行波解

夏铁成, 张鸿庆, 李佩春

2003, 18(2): 129-133.

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In this paper, many new explicit and exact travelling wave solutions for Burgers-Kolmogorov-Petrovskii-Piscounov(Burgers-KPP) equations are obtained by using hyperbola function method and Wu-elimination method, which include new singular solitary wave solutions and periodic solutions. Particular important cases of the equation, such as the generalized Burgers-Fisher equation, Burgers-Chaffee infante equation and KPP equation, the corresponding solutions can be obtained also. The method can also solve other nonlinear partial differential equations.

广义复合Poisson风险模型下的生存概率

龚日朝

2003, 18(2): 134-139.

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In this paper we generalize the aggregated premium income process from a constant rate pro- cees to a poisson process for the classical compound Poinsson risk modlel,then for the generalized moclel and the classical compound poisson risk model,we respectively get its survival probability in finite time period in case of exponential claim amounts.

一类LC¹规划问题的超线性收敛ODE信赖域算法

欧宜贵, 侯定丕

2003, 18(2): 140-145.

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In this paper,a new trust region algorithrn for unconstrained LC'optimization problems is given.Compare with those existing trust region methods,this algorithm has a different feature:it ob- tains a stepsize at each iteration not by soloving a quadratic subproblem with a trust region bound,but by solving a system of linear equations.Thus it reduces computational complexity and improves compu- tation efficlency.It is proven that this algorithm is globally convergent and locally superlinear under some conditions.

非线性互补问题的逐次逼近类Broyden算法

马昌凤, 梁国平

2003, 18(2): 146-153.

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In this paper,we present a new form of succesive approximation Broyden-like algorithm for nonlinear complementarity problem based on its equivalent nonsmooth equations.Under suitable condi- tions,we get the global convergence on the algorithms.Some numerical results are also reported.

求解无约束非线性规划问题的一个新的重开始共轭梯度算法的收敛性

孙清滢

2003, 18(2): 154-162.

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Conjugate gradient optimization algorithms depend on the search directions with different choices for the parameters in the search directions.In this note,by combining the nice numerical per- formance of PR and HS methods with the global convergence property of the class of conjugate gradient methods presented by HU and STOREY(1991),a class of new restarting conjugate gradient methods is presented.Global convergences of the new method with two kinds of common line searches,are proved.Firstly,it is shown that,using reverse modulus of continuity function and forcing function, the new method for solving unconstrained optimization can work for a continously differentiable function with Curry-Altman's step size rule and a bounded level set.Secondly,by using comparing technique, some general convergence propecties of the new method with other kind of step size rule are established. Numerical experiments show that the new method is efficient by comparing with FR conjugate gradient method

车多项式对Ferrers矩阵的刻画

马海成, 扈生彪

2003, 18(2): 163-167.

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In this paper,we show that there cxist preisely W(A)Ferrers matrices F(c₁,c₂,…,c_n) such that the rcok polynomials is equal to the nook palynomial of Ferrers matrix F(b₁,b₂,…,b_m), where A={b₁,b₂-1,…,b_m-m+1l is a rupeated set,W(A)is weight of A.

一类高阶中立型偏微分方程组解的振动性

林文贤

2003, 18(2): 168-174.

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In this paper,some sufficient conditions are obtained for the oscillation for solutions of sys- tems of high order partial differential equations of neutral type.

泛连通图的Faudree-Schelp定理和哈密尔顿连通图的Ore定理的注记

赵克文, 曾克扬

2003, 18(2): 175-177.

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In this note more short proofs are given for Faudree Schelp theorem and Ore theorem.

图式流形的分类方法

王予民, 李起升, 刘震

2003, 18(2): 178-181.

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In this paper,we give a kind of method which can easily be operated to classify the graphlike manifold with contraction.

具有S-WGHP性质的对偶对

李龙锁, 刘金霞, 赵玟亨

2003, 18(2): 182-185.

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In this paper,we introcuce the signed weak gliding hump property in a dual pair with the structure of a system of sections and show that if a dual pair [E,F]has the signed weak gliding hump property,then the β-dual space of E is a weak sequentially complete space if and only if for every n ∈N,(F(n),σ(F("),El))is sequentially complete.Furthermore,we also prove that if [E,F] has the signed weak gliding hump property,then(E,r(E,E())is an AK-space.

相应于随机自相似分形的记忆函数和分数次积分

梁洪亮, 刘孝书

2003, 18(2): 186-191.

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For a physics systerm which exhibits memory,if memory is preserved only at points of random self-similar fractals,we define random memory functions and give the connection between the expecta- tion of flux and the fractional integral.In particular,when memory sets degenerate to Cantor type frac- tals or non-random self-similar fractals our results coincide with that of Nigmatullin and Ren et al..

一类拟线性奇摄动方程的边值问题

韩祥临

2003, 18(2): 192-197.

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In this paper,the Nagumo theorem and the fixed-point theorem are used to prove the exist- ence and the uniqueness and to estimate the asyrmptotic expansion of the shock solutions of the boundary value problems for a class of quasilinear differential equations,the asymptotic expansion of solution of any orders including boundary is obtained.

具有逆断面的正规纯正半群

朱凤林

2003, 18(2): 198-204.

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A normal orthodox semigroup is an orthodox semigroup whose idempotent elements form a normal band.We deal with congruences on a normal orthodox semigroup with an inverse transversal.A structure theorem for such semigroup is obtained.Munn(1966)gave a fundamental inverse semigroup. Following Munn's idea,we give a fundamental normal orthodox semigroup with an inverse transversal.

Cⁿ中单位球上的Dirichlet空间和Q_p,0空间

胡鹏彦, 张文俊

2003, 18(2): 205-212.

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In this paper,we first give sxme new characterizations of Qu spaces by means of vanishing p-Carlexon muasure.Using these results,we can prove that Dirichlet space is a subset of Q,o for ...

基于特殊选择的抽象进化算法的收敛性

毕永青, 薛明志

2003, 18(2): 213-220.

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There has been a growing interest in mathematical models to character the evolutionary algo- rithms.The best-known one of such models is the axiomatic model colled the abstract evolutionary al- gorithm.In this paper,we first introduce the definitions of the abhstract selection and evolution opera- tors,and that of the abstract evolutionary algorithm,which describes the evolution as an abstract sto- chastic process composed of these two fundamental abstract operators.In particular,a kind of abstract evolutionary algorithms based on a special selection mechansim is discussed.According to the sorting for
the state space,the properties of the single step transition matrix for the algorithm are anaylzed.In the end,we prove that the limit probability distribution of the Markov chains exists.The present work provides a big step toward the establishment of a unified theory of evolutionary computation.

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