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Table of Content
30 March 2011, Volume 26 Issue 1
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Symmetry Function Induced by a Convex Body
Long-guang
2011, 26(1): 1-6.
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This paper shows some properties of symmetry function induced by a convex body in a normal linear space. Some relationships between symmetry function induced by a convex body and Minkowski functional of the convex body are presented.
On the Counting Functions of Meromorphic Solutions of Systems of Higher-order Algebraic Differential Equations
CHEN Miao-ling, GAO Ling-yun
2011, 26(1): 7-10.
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Using Nevanlinna theory and value distribution of meromorphic functions and the other techniques, we investigate the counting functions of meromorphic solutions of systems of higher-order algebraic differential equations and obtain some results.
The Integrable in Liouville Sense of a Finite-dimensional Hamilton System
ZHU Yun, YIN Li
2011, 26(1): 11-15.
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Based on a 2 × 2 eigenvalue problem, a set of (1 + 1)-dimensional soliton equations are proposed. Moreover, we obtain a finite dimensional Hamilton system with the help of nonlinearization approach. Then the generating function approach and the way to straighten out of Fm-flow are used to prove the involutivity and the functional independence of conserved integrals for the finite-dimensional Hamilton system, hence, we can verify it is completely integrable in Liouville sense.
Global Existence of Solutions to the Prey-predator System of Three Species with Cross-diffusion
CHEN Zhi-hui, CHEN Xia
2011, 26(1): 16-20.
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The prey-predator system of three species with cross-diffusion pressure is known to possess a local solution with the maximal existence time T ≤∞. By obtaining the bounds of W21-norms of the local solution independent of T, it is established the global existence of the solution.
Natural Mappings on Set-valued Mapping Spaces
LI Zu-quan, WANG Jiu-jing
2011, 26(1): 21-25.
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In this paper, we discuss the continuities of some natural mappings on point compact continuous set-valued mapping spaces with compact-open topology and obtain the properties of set-valued injective mappings, set-valued diagonal mappings, induced mappings, set-valued evaluation mappings, set-valued topological sum mappings and set-valued topological product mappings.
ε-super Efficient Solutions of Optimization Problems with Set-valued Maps in Locally Convex Space
WANG Shu-yu, LIU Wan-li
2011, 26(1): 26-31.
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In this paper, the ε-super effcient solution for set-valued map vector optimization in locally convex space is introduced. And under the assumption of the nearly generalized cone-subconvexlikeness for set-valued maps, used new methods, the scalarization theorem and Lagrange multiplier theorem for ε-super effcient solution are established.
The Probability Model of the Multi-valued KM1M2 Clock Controlled Generator
DU Yi-bin, HUANG Xiao-ying, LI Zheng-chao, TENG Ji-hong
2011, 26(1): 32-38.
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This paper constructs the probability model of the multi-valued KM1M2 clock controlled generator, and discusses the probability distributing, homogeneous Markov property, ergodic property, strict placidity, numeral character and the property of large numbers of the random variables with this kind of output sequence. It gets the probability formula of the coincidence of the output sequence with the input sequence, and gives important reference to the design and analysis of the multi-valued key stream clock controlled generator in cryptography.
Weak Solution of Generalized KdV Equation with High Order Perturbation Terms
CHENG Jun-xiang, WANG Yan-hong
2011, 26(1): 39-45.
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By using the theory of compensated compactness, we prove that there exists a sequence {u
ε
δ
} converges nearly everywhere to the solution of the initial-value problem of generalized KdV equation with high order perturbation terms, namely we prove the existence of the weak solution.
A Remark on the Pullback Attractors for the Non-autonomous Benjamin-Bona-Mahony Equation
QIN Jia
2011, 26(1): 46-50.
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In this paper, we show the existence of pullback attractors for the nonautonomous Benjamin-Bona-Mahony equations by establishing the pullback uniform asymptotically compactness.
The Moments of First Entrance Time Distributions of Markov Chains in Random Environments
LI Shou-wei, ZHU Dong-jin
2011, 26(1): 51-55.
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After defining generating functions, this paper discusses their properties, and then provides a suffcient and necessary condition for a finite property of the moments of first entrance time distributions of Markov chains in random environments by generating functions. Finally, the paper obtains relevant conclusions of the moments of first entrance time distributions.
Periodic Solutions of Singular Neutral Differential Systems with Infinite Delay
ZHOU Gui-fang, ZHANG Hai, JIANG Wei
2011, 26(1): 56-60.
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In this paper, we discuss the periodic solutions of the nonlinear singular neutral differential systems with infinite delay. By using matrix measure and Krasnoselskii’s fixed point theorem, we obtained the sufficient conditions of the existence of periodic solutions.
L
p
loc
-solutions of Nonlinear Impulsive Volterra Integral Equation in Abstract Space
2011, 26(1): 61-68.
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In this paper, we discuss L
p
loc
-solutions of a kind of nonlinear impulsive Volterra integral equation and present an existence theorem of solutions in Banach space.
Global Convergence of a New Restarting Three Terms Conjugate Gradient Method for Non-linear Optimizations
SUN Qing-ying, SANG Zhao-yang, TIAN Feng-ting
2011, 26(1): 69-76.
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In this note, by combining the nice numerical performance of PR and HS methods with the global convergence property of FR method, a class of new restarting three terms conjugate gradient methods is presented. Global convergence properties of the new method with two kinds of common line searches are proved.
Picard Boundary Value Problems of Second Order p-Laplacian Differential Equations
LIU Yu-ji
2011, 26(1): 77-84.
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Sufficient conditions for the existence of at least one solution of two-point boundary value problems for second order nonlinear differential equations [φ(x(t))] + kx(t) + g(t,x(t)) = p(t),t ∈(0,π) x(0) = x(π) = 0 are established, where [φ(x)] =(|x |p-2x) with p > 1. Our result is new even when [φ(x)] = x in above problem, i.e. p = 2. Examples are presented to illustrate the efficiency of the theorem in this paper.
The Structure Theorem for Module Coalgebras
WANG Yong, ZHANG Liang-yun, CAI Zhi-min
2011, 26(1): 85-92.
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This paper, mainly gives the structure theorem for module coalgebras by a kind of new method, and deletes the condition that the antipode S of the Hopf algebra H is bijective.
Factorisable Quasi-adequate Semigroups
PENG Ting-ting, GUO Xiao-jiang
2011, 26(1): 93-99.
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In this paper, we investigate a class of factorisable IC quasi-adequate semigroups, so-called, factorisable IC quasi-adequate semigroups of type-(H,I). Some characterizations of factorisable IC quasi-adequate semigroups of type-(H,I) are obtained. In particular, we prove that any IC quasi-adequate semigroup has a factorisable IC quasi-adequate subsemigroups of type-(H,I) and a band of cancellative monoids.
The Solvable Lie Algebras with Filiform Rn Nilradicals
WU Ming-zhong
2011, 26(1): 100-107.
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In this paper we explicitly determine automorphism group of filiform Lie algebra Rn to find the indecomposable solvable Lie algebras with filiform Lie algebra Rn nilradicals. We also prove that the indecomposable solvable Lie algebras with filiform Rn nilradicals is complete.
Alternative Error Bounds for Some Numerical Quadrature Rules
LU Jian-fang, FENG Ping-hua
2011, 26(1): 108-113.
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Similar to having done for the mid-point and trapezoid quadrature rules, we obtain alternative estimations of error bounds for the Simpson’s quadrature rule involving n-time(1 ≤ n ≤ 4) differentiable mappings and then to the estimations of error bounds for the adaptive Simpson’s quadrature rule.
Inequalities of Maximum of Partial Sums and Convergence Rates in the Strong Laws for ρ
-
-mixing Random Variables
TAN Cheng-liang, WU Qun-ying, HE Yan-mei
2011, 26(1): 114-119.
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In this paper, we establish a Rosenthal-type inequality of partial sums for ρ
-
-
mixing random variables. As its applications, we get the complete convergence rates in the strong laws for ρ
-
-mixing random variables. The result obtained extends the corresponding result.
Tests for Parameter Changes in Time Series
JIN Hao, YANG Yun-feng
2011, 26(1): 120-124.
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The paper considers the problem of testing for a change point in the parameters of AR(p) models. It is shown that the asymptotically limiting distribution of the residual CUSUM of squares test(RCUSQ) is still the sup of a standard Brownian bridge under null hypothesis. We also show via simulations that our asymptotic results provide good approximations in finite samples.
Ideal-based Zero-divisor Graphs of Non-commutative Rings
LI Yun-hui, TANG Gao-hua
2011, 26(1): 125-130.
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This paper introduces an ideal-boyed zero-divisor graph of non-commutative rings, denoted ΓI(R).ΓI(R) is a directed graph. The properties and possible structures of the graph is studied.
Error Estimates of H
1
-Galerkin Mixed Methods for the Viscoelasticity Wave Equation
WANG Jin-feng, LIU Yang, LI Hong
2011, 26(1): 131-137.
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H
1
-Galerkin mixed methods are proposed for viscoelasticity wave equation. Depending on the physical quantities of interest, two methods are discussed. The optimal error estimates and the proof of the existence and uniqueness of semidiscrete solutions are derived for problems in one space dimension. And the methods don’t require the LBB condition.
Existence of Solutions for a Multi-point Boundary Value Problems with Three Dimension Kernal at Resonance
LIANG Ju-hua, REN Li-shun, ZHAO Zhi-liang
2011, 26(1): 138-143.
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In this paper, a multi-point boundary value problems for a three order nonlinear deferential equation is considered. With the help of coincidence theorem due to Mawhin, a existence theorem is obtained.
The Number and Distributions of Limit Cycles of a Cubic Hamiltonian System with Z
2
-symmetry Perturbation
ZHOU Hong-xian, ZHANG Yan
2011, 26(1): 144-151.
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This paper is concerned with the number and distributions of limit cycles of a cubic Z
2
-symmetry Hamiltonian system under quintic perturbation. By using qualitative analysis of differential equation, bifurcation theory of dynamical systems and the method of detection function, we obtain that this system exists at least 14 limit cycles with the distribution C
1
9...
C
1
2
)].
Strong Converse Inequalities for Certain Mixed Szasz-Beta Operators
QI Qiu-lan, ZHANG Yu-ping
2011, 26(1): 152-158.
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In this paper, a strong converse inequality of type B in terms of a new K-functional K
λ
α
(f, t
2)
(0 < α < 2, 0 ≤λ≤ 1) for certain mixed Szász-Beta operators is given. By this inequality, the converse theorem can be obtained for the operators.
