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中文
Table of Content
30 June 2003, Volume 18 Issue 2
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On the Centrosymmetric and Centroskewsymmetric Solutions to a Matrix Equation over a Central Algebra
WANG Qing-wen , SUN Jian-hua, LI Shang-zhi
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.
A Class of Strongly Nonlinear Singular Perturbed Boundary Value Problems
TANG Rong-rong
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.
Globally Asymptotic Stability of Equilibrium of a Dynamical Model with Infinite Delay
LI Xiang, WENG Pei-xuan
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.
New Explicit and Exact Travelling Wave Solutions for Burgers-Kolmogorov-Petrovskii-Piscounov Equations
XIA Tie-cheng, ZHANG Hong-qing, LI Pei-chun
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.
The Survival Probability in Generalized Poisson Risk Mode
GONG Ri-zhao
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.
A Superlinerly Convergent ODE-type Trust Region Algorithm for LC
1
Optimization Problems
OU Yi-gui , HOU Ding-pi
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.
The Successive Approximation Broyden-like Algorithm for Nonlinear Complementarity Problems
MA Chang-feng, LIANG Guo-ping
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.
Global Convergence of a New Restarting Conjugate Gradient Method for Nonlinear Optimizations
SUN Qing-ying
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
Ferrers Matrices Characterized by the Rook Polynomials
MA Hai-cheng, HU Sheng-biao
2003, 18(2): 163-167.
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In this paper,we show that there cxist preisely W(A)Ferrers matrices F(c
1
,c
2
,…,c
n
) such that the rcok polynomials is equal to the nook palynomial of Ferrers matrix F(b
1
,b₂,…,b
m
), where A={b₁,b₂-1,…,b
m
-m+1l is a rupeated set,W(A)is weight of A.
Oscillation for Solutions of Systems of High Order Partial Differential Equations of Neutral Type
LIN Wen-xian
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.
Note on Faudree-Schelp Theorem in Path Connected Graphs and Ore Theorem in Hamilton Connected Graphs
ZHAO Ke-wen, ZENG Ke-yang
2003, 18(2): 175-177.
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In this note more short proofs are given for Faudree Schelp theorem and Ore theorem.
Classification Method of Graphlike Manifold
WANG Yu-min, LI Qi-sheng, LIU Zhen
2003, 18(2): 178-181.
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The Dual Pair with the Signed-weak Gliding Hump Property
LI Long-suo , LIU Jin-xia , CHO Min-hyung
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.
Memory Function and Fractional Intergral Associated to the Random Self-similar Fracta
lLIANG Hong-liang, LIU Xiao-shu
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..
Singular Perturbations of Boundary Value Problems for a Class of Quasilinear Differential Equations
HAN Xiang-lin
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.
Normal Orthodox Semigroups with Inverse Transversals
ZHU Feng-lin
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.
Dirichlet and Q
p,0
Spaces on the Unit Ball of C
n
HU Peng-yan, ZHANG Wen-juna
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 ...
The Convergence of the Abstract Evolutionary Algorithm Based on a Special Selection Mechanism
BI Yong-qing , XUE Ming-zhi
2003, 18(2): 213-220.
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