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中文
Table of Content
30 June 2008, Volume 23 Issue 2
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Auxiliary Equation Method and New Exact Solutions of BKP Equation
MA Hong-cai , ZHANG Ya-li , DENG Ai-ping
2008, 23(2): 159-164.
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In this paper, auxiliary equation method is proposed for constructing more general exact solutions of nonlinear partial differential equation with the aid of symbolic computation. We study the (2+1)-dimensional BKP equation and get a series of new types of traveling wave solutions. The method used here can be also extended to other nonlinear partial differential equations.
A Class of Third-order Convergence Variants of Newton’s Method
ZHAO Ling-ling, WANG Xia
2008, 23(2): 165-170.
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A class of third-order convergence methods of solving roots for non-linear equation,which are variant Newton’s method, are given. Their convergence properties are proved. They are at least third order convergence near simple root and one order convergence near multiple roots. In the end, numerical tests are given and compared with other known Newton’s methods. The results show that the proposed methods have some more advantages than others. They enrich the methods to find the roots of non-linear equations and they are important in both theory and application.
P-kernel Normal Systems in Weakly P-inversive Semigroups
CHEN Qian-hua, FAN Xing-kui
2008, 23(2): 171-177.
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In this paper, we first give the concept of weakly P-inversive semigroup S(P). Then we describe the strong P-congruences on S(P) in terms of their P-kernel normal systems. It is proved that there is a bijection between the strong P-congruences and the P-kernel normal systems. Finally, it is also prove that the lattice of strong P-congruences and the lattice of P-kernel normal systems on S(P) are isomorphic.
Interacting Super-Brownian Motions Depending on Population Size
CHEN Li, YAN Guo-jun
2008, 23(2): 178-187.
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In this paper, we investigate the interacting super-Brownian motion depending on population size. This process can be viewed as the high density limit of a sequence of particle systems with branching mechanism depending on their population size. We will construct a limit function-valued dual process.
Upper Bound and Lower Bound Estimate of Monotone Increasing Fractal Function
MA Guan-zhong, YUAN Gui-xia, CUI Zhen-wen
2008, 23(2): 188-194.
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Mass distribution principle is one of important tools in studying Hausdorff dimension and Hausdorff measure. In this paper we will give a numerical approximate method of upper bound and lower bound of mass distribution function f(x)(it is a monotone increasing fractal function) and its some applications.
Several Properties of p-w-hyponormal Operators
LI Hai-ying , YANG Chang-sen
2008, 23(2): 195-201.
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In this paper, let T be a bounded linear operator on a complex Hilbert H. We give and prove that every p-w-hyponormal operator has Bishop’s property(β) and spectral properties; Quasi-similar p-w-hyponormal operators have equal spectra and equal essential spectra. Finally, for p-w-hyponormal operators, we give a kind of proof of its normality by use of properties of partial isometry.
Some Results on Position Restriction Scheduling Problems
CHEN You-jun, LIN Yi-xun
2008, 23(2): 202-206.
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In this paper, we first consider the position restriction scheduling problems on a single machine. The problems have been solved in certain special cases, especially for those obtained by restricting the processing time pj=1. We introduce the bipartite matching algorithm to provide some polynomial-time algorithms to solve them. Then we further consider a problem on unrelated processors.
Markov Chain Induced by Random Dynamical System on Graph
ZHENG Jie, LIU Chao-yang
2008, 23(2): 207-214.
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In this paper, we define a model of random dynamical systems(RDS) on graphs and prove that they are actually homogeneous discrete-time Markov chains. Moreover, a necessary and suffcient condition is obtained for that two state vectors can communicate with each other in a random dynamical system(RDS).
On Matrix Γ
α
-group Inverse and Γα-sharp Ordering
ZHANG Jin-ou, CEN Jian-miao
2008, 23(2): 215-221.
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The Γ
α
-group inverse and the Γ
α
-sharp ordering in matrix set are introduced. Some characterizations and properties of the Γ
α
-sharp ordering are given. The relations between the Γ
α
-sharp ordering and the Γ
α
-minus ordering are discussed.
The Stability Research for the Finite Difference Scheme of a Nonlinear Reaction-diffusion Equation
XU Chen-mei
2008, 23(2): 222-227.
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In the article, the fully discrete finite difference scheme for a type of nonlinear reaction-diffusion equation is established. Then the new function space is introduced and the stability problem for the finite difference scheme is discussed by means of variational approximation method in this function space. The approach used is of a simple characteristic in gaining the stability condition of the scheme.
Boundedness of Marcinkiewicz Integral on Weighted Herz Spaces
XIE Ru-long, SHU Li-sheng
2008, 23(2): 228-234.
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In this paper, it is proved that the Marcinkiewicz integral operator μΩ is bounded on K
q
α,p
(ω
1
;ω
2
).
The Scattering Theory of Nonlinear Schrodinger Equations with Interaction Terms
YUAN Jia
2008, 23(2): 235-239.
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In this paper, we give a simplified proof on the energy scattering for the nonlinear Schrodinger equations with interaction terems by use of the interaction Morawetz estimate, which is originally introduced in [4].
Existence and Uniqueness of Solution of Some Increasing Operators and Applications
HAO Jian-li
2008, 23(2): 240-244.
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By using the cone theory and the monotone succession skills, it is studied the existence uniqueness of fixed point for a class of increasing operators without continuity and compactness and concave or convex conditions in Banach spaces. The results presented here improve and generalize some corresponding results for increasing operator.
Knowledge Law and Attribute Disturbance of Law
ZHANG Guan-yu , DU Ying-ling , QIU Yu-feng
2008, 23(2): 245-251.
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By employing the knowledge(R-element equivalence class) in one direction S- rough sets and dual of one direction S-rough sets, the concept of knowledge law is given; the generation theorem of knowledge law, the excursion theorem of knowledge law, and the attribute disturbance discernible theorem of knowledge law are proposed. Knowledge law is a new characteristic of S-rough sets.
On the Acceleration Problem of q-Bernstein Polynomials
YUN Lian-ying, XIANG Xue-yan, WANG Hui
2008, 23(2): 252-259.
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In this paper, we investigate not only the acceleration problem of the q-Bernstein polynomials Bn(f,q;x) to B∞(f,q;x) but also the convergence of their iterated Boolean sum. Using the methods of exact estimate and theories of modulus of smoothness, we get the respective estimates of the convergence rate, which suggest that q-Bernstein polynomials have the similar answer with the classical Bernstein polynomials to these two problems.
Exact Solutions for the Generalized KdV Equation: Modified Homogeneous Balance Method
WANG Xiu-mei, ZHU Yue-feng
2008, 23(2): 260-269.
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In this paper, we present a solution methodology to obtain exact solutions of some nonlinear evolution equation by modifying the homogeneous balance method. Based on the modified homogeneous balance method, several kinds of exact(new) solutions of the generalized KdV equation are obtained.
Error Analysis on Corrector Formula for Rectangular Rule
XIAO Ze-chang, DU Yue-peng
2008, 23(2): 270-275.
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This paper presents truncation errors among Corrector Formula for left Rectangular rule and Corrector Formula for middle Rectangular rule respectively. It also displays an analysis on convergence order of compound corrector formulas for rectangular rule. Examples of numerical calculation have validated theoretical analysis.
Quenching for Degenerate Semilinear Reaction-diffusion Systems
LI Mei
2008, 23(2): 276-283.
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In this paper, the initial boundary value problem of semilinear degenerate reaction-diffusion systems is studied. The regularization method and upper and lower solutions technique are employed to show the existence and continuation of a positive classical solution. The location of quenching points is found. The critical length is estimated by the eigenvalue method.
Singular Hybrid Boundary Node Method for Solving Poisson Equation
SIMA Yu-zhou, ZHU Hong-ping, MIAO Yu
2008, 23(2): 284-291.
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As a boundary-type meshless method, the singular hybrid boundary node method(SHBNM) is based on the modified variational principle and the moving least square(MLS) approximation, so it has the advantages of both boundary element method(BEM) and meshless method. In this paper, the dual reciprocity method(DRM) is combined with SHBNM to solve Poisson equation in which the solution is divided into particular solution and general solution. The general solution is achieved by means of SHBNM, and the particular solution is approximated by using the radial basis function(RBF). Only randomly distributed nodes on the bounding surface of the domain are required and it doesn’t need extra equations to compute internal parameters in the domain. The postprocess is very simple. Numerical examples for the solution of Poisson equation show that high convergence rates and high accuracy with a small node number are achievable. 还原
Exponential Stability of Periodic Solution for Delayed Hopfield Networks
XIANG Hong-jun, WANG Jin-hua
2008, 23(2): 292-300.
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The paper is devoted to periodic attractor of delayed Hopfield neural networks with time-varying. By constructing Lyapunov functionals and using inequality techniques, some new suffcient criteria are obtained to guarantee the existence and global exponential stability of periodic attractor. Our results improve and extend some existing ones in [13～14]. One example is also worked out to demonstrate the advantages of our results.
Existence, Uniqueness and Blow-up of Generalized Solutions to General Nonlinear Filtration Equations
HUO Zhen-hong, LI Hai-feng
2008, 23(2): 301-308.
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In this paper, we consider nonnegative solutions to Cauchy problem for the general nonlinear filtration equations u
t
-D
j
(a
ij
(x,t,u)D
i
+(u))+b
i
(t,u)D
i
u+C(x,t,u)=0, and obtain the existence, uniqueness and blow-up in finite time of these solutions under some structure conditions.
A New Kind of Conjugate-nested Central Configurations in Consisted of One Regular Tetrahedron and One Regular Octahedron
LIU Xue-fei, XIANG Yi-hua
2008, 23(2): 309-316.
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A new case configuration in R
3
, the conjugate-nest consisted of one regular tetrahedron and one regular octahedron is discussed. If the configuration is a central configuration, then all masses of outside layer are equivalent, the masses of inside layer are also equivalent. At the same time the following relation between ρ(r = √3/3 ρ is the radius ratio of the sizes) and mass ratio τ = m~/m must be satisfied τ = ...
and for any mass ratio τ, when mass ratio τ is in the open interval (0,0.03871633950 ···), there exist three central configuration solutions(the initial configuration conditions who im- ply hamagraphic solutions) corresponding radius ratios are r
1
,r
2
, and r
3
, two of them in the interval (2.639300779··· ,+∞) and one is in the interval (0.7379549890···, 1.490942703···). when mass ratio τ is in the open interval (130.8164950··· ,+∞), in the same way there have three corresponding radius ratios, two of them in the interval (0,0.4211584789···) and one is in the interval (0.7379549890···, 1.490942703···). When mass ratio τ is in the open interval (0.03871633950···, 130.8164950···), there has only one solution r in the interval (0.7379549890···, 1.490942703···).
