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中文
Table of Content
30 March 2009, Volume 24 Issue 1
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The Stability of Logistic Model with Random Impulse
LI Jun-ping, HOU Zhen-ting
2009, 24(1): 1-9.
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This paper is devoted to studying the stability of Logistic model with random impulse by using the theory of Markov skeleton processes and a convenient condition for Logistic model with random impulse to be stable is given.
Extended
Cesaàro
Operator between Bloch-type Spaces
LV Xiao-fen
2009, 24(1): 10-19.
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We characterize the symbol for which the induced extended Cesaàro operator T: Bω→ Bμ(respectively, Bω,0 → Bμ,0) is bounded or compact, where is a given holomorphic function on the unit disc D, ω and μ both are normal functions on [0,1).
Flexibility of Embeddings of a Halin Graph in the Torus
MA Deng-ju, REN Han
2009, 24(1): 20-26.
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In this paper we show that the face-width of any embedding of a Halin graph(a type of planar graph) in the torus is one, and give a formula for determining the number of all nonequivalent embeddings of a Halin graph in the torus.
The Equivalence Theorem of Appoximation for Two-dimensional Baskakov Operators
FENG Guo
2009, 24(1): 27-34.
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In this paper, we study the convergence rate of two-dimensional Baskakov operators with Jacobi-weights and the approximation equivalence theorem is obtained, making use of multivariate decompose skills and results of one-dimensional Baskakov operators.
A Convergence Theorem for Set-valued Eventual Supermartingle
LI Gao-ming
2009, 24(1): 35-39.
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In this paper, the properties of set-valued Eventual Supermartingle are discussed. The main result is that suppose {F
n
,n ≥ 1} be set-valued Eventual Supermartingle, if sup
T
E(d(0,F
τ
)) < ∞, then F
n
→F and S
F
1
= Φ, here T is the sets of all bounded stopping times.
Some Remarks On E'-matrices
LI Jian-ping
2009, 24(1): 40-45.
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The class of E -matrices introduced in [4] is a subclass of Q0-matrices whose proper principal submatrices are Q-matrices. In this paper, we investigate the relation of the class E to other known matrix classes and obtain a series of necessary and sufficient conditions for E -matrices.
Graph Description by the Chromatic Polynomials
MA Hai-cheng, LIU Hui-min, ZHANG Hai-liang
2009, 24(1): 46-52.
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By means of the chromatic polynomials, this paper provided a necessary and sufficient condition for the graph G being a mono-cycle graph(the Theorem 1), a first class bi-cycle graph and a second class bicycle graph(the Theorem 2), respectively.
Super-connected and Hyper-connected Cubic Bi-Cayley Graphs
CAO Ling, MENG Ji-xiang
2009, 24(1): 53-57.
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Let G be a finite group and let S(possibly, contains the identity element) be a subset of G. The Bi-Cayley graph BC(G, S) is a bipartite graph with vertex set G×{ 0,1} and edge set {(g,0) (sg,1) : g ∈ G, s ∈ S}. A graph is said to be super-connected if every minimum vertex cut isolates a vertex. A graph is said to be hyper-connected if every minimum vertex cut creates two components, one of which is an isolated vertex. In this paper, super-connected and/or hyper-connected cubic Bi-Cayley graphs are characterized.
Computation of Jordan Chains by Generalized Characteristic Matrices
LI Da-lin
2009, 24(1): 58-62.
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In this paper, we introduce a method to define generalized characteristic matrices of a defective matrix by the common form of Jordan chains. The generalized characteristic matrices can be obtained by solving a system of linear equations and they can be used to compute Jordan basis.
Commuting Dual Toeplitz Operators on the Polydisk
CHENG Guo-zheng, YU Tao
2009, 24(1): 63-68.
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We completely characterize commutativity of S and Sψ on L
a
2
(D
n
)⊥ for bounded pluriharmonic symbols and ψ on D
n
, and prove that SS
ψ
= S
ψ
if and only if is analytic or ψˉ is analytic.
A Remark on the Time Decay of Non-Newtonian Flows in R
3
YIN Gu-liang
2009, 24(1): 69-74.
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In the study of long time asymptotic behaviors of the solutions to a class system of the incompressible non-Newtonian fluid flows in R3, it is proved that the weak solutions decay in L2 norm at (1 + t)-34 and the error of difference between non-Newtonian fluid and linear equation is also investigated. The findings are mainly based on the classic Fourier splitting methods.
Zeros of Differential Polynomial f(z)f
(k)
(z) − a and Its Normality
LU Qian, GU Yong-xing
2009, 24(1): 75-80.
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Suppose that function f(z) is transcendental and meromorphic in the plane. The aim of this work is to investigate the conditions in which differential monomials f(z)f
(k)
(z) takes any non-zero finite complex number infinitely times and to consider the normality relation to differential monomials f(z)f
(k)
(z).
(Inco) Projective Modules of Relatively Hereditary Torsion Theroy
ZHANG Li-hong, XIN Da-wei
2009, 24(1): 81-86.
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In the paper, we define(inco) project modules of relatively hereditary torsion theory τ by intersection complement of module and study their properties; secondly, we define the(inco) τ-semisimple ring by(inco) τ-projective module and study their properties. When τ is a trivial torsion theory on R-mod, we prove that R is a semisimple ring if and only if R is a(inco) semisimple ring and satisfies(inco) condition.
Oscillation in a Variable Delay Logistic Difference Equation
TAN Qiong-hua, CHEN Ming
2009, 24(1): 87-93.
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Consider the nonautonomous delay logistic equation △y
n
= p
n
y
n
(1-(y
n
-l
n)
), n ≥ 0, (1)where {p
n
}n≥0 is a sequence of nonnegative real numbers, {l
n
}n≥0 is a sequence of positive integers satisfying lim n→∞(n - l
n
) = ∞, and k is a positive constant. Only solutions which are positive for n ≥ 0 are considered. We obtain a new sufficient for all positive solutions of (1) to oscillate about k which contains the corresponding result in [2] when i = 1.
An Estimation for the Average Error of the Quasi-
Grünwald
Interpolation in the Wiener Space
LIU Ying, XU Gui-qiao
2009, 24(1): 94-101.
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We obtain an upper bound for the average error of the quasi-Grünwald interpo-lation based on the zeros of Chebyshev polynomial of the second kind in the Wiener space.
Two Positive Periodic Solutions of Delay Functional Difference System with Feedback Control
GUO Peng-fei, ZHU Xian-yang, LI Yong-kun
2009, 24(1): 102-107.
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By using a fixed point theorem on a cone to investigate the existence of two positive periodic solutions for the following delay difference system with feedback control argument of the form △x(n) = -b(n)x(n) + f(n,x(n - τ1(n)),… ,x(n - τm(n)),u(n - δ(n))), △u(n) = -η(n)u(n) + a(n)x(n - σ(n)), n ∈ Z.
A Simple Proof of the Lower Bounds of Distortion Theorems on the Roper-Suffridge Operator
WANG Jian-fei, LIU Tai-shun
2009, 24(1): 108-111.
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Liczberski-Starkov first found a lower bound for ||D(f)|| near the origin, where f(z) = (F(z
1
), F (z
1
)z
2
,… , F (z
1
)z
n
) is the Roper-Suffridge operator on the unit ball Bn in Cn and F is a normalized convex function on the unit disk. Later, Liczberski-Starkov and Hamada-Kohr proved the lower bound holds on the whole unit ball using a complex computation. Here we provide a rather short and easy proof for the lower bound. Similarly, when F is a normalized starlike function on the unit disk, a lower bound of ||D(f)|| is obtained again.
A New Browder Fixed Point Theorem in Noncompact Hyperconvex Metric Spaces and Its Applications to Section Questions and Intersection Questions
WEN Kai-ting
2009, 24(1): 112-116.
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In this paper, a new Browder fixed point theorem is established in the noncompact sub-admissible subsets of noncompact hyperconvex metric spaces. As application, a Ky Fan section theorem and an intersection theorem are obtained.
Non-zero Solution for the Quasi-linear Elliptic Equation
RAO Ruo-feng, HE Qing-gao
2009, 24(1): 117-124.
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In this paper, the author has given an existence theorem for the resonant equation, -△
p
u = λ
1
|u|
p-2
u + f(u) + h(x), without any Landesman-Lazer conditions on h(x).
Loewner Chains Associated with the Generalized Roper-Suffridge Extension Operator on the Unit Ball in Hilbert Spaces
LIU Tao, FENG Shu-xia, YAN Chun-yan
2009, 24(1): 125-131.
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In this paper, we prove that the generalized Roper-Suffridge extension operator can be embeded in Loewner chains on the unit ball in Hibert spaces, and obtain the fact that the operator keeps the properties of almost spirallike mapping of type β and order α, almost starlikeness of order α, spirallikeness of type of β and starlikeness.
Optimal Batching Structures of Single Machine Scheduling
FENG Mi-luo
2009, 24(1): 132-137.
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A batch is a subset of jobs which must be processed jointly in either serial or parallel form. For the single machine, batching, total completion time scheduling problems, the algorithmic aspects have been extensively studied in the literature. This paper presents the optimal batching structures of the problems on the batching ways: all jobs in exactly N(arbitrary fix batch number and 1 < N < n) batches.
Existence for the Green-Lindsay Type Therm-elastic Problem of Nonhomogeneous Media
ZHANG Tong-bin, WAN Jian-jun
2009, 24(1): 138-144.
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We study a new model named the Green-Lindsay type therm-elastic model for nonhomogeneous media that consists of a system of dynamic thermoelasticity equations of displacement and dynamic heat conduction equation. We construct the model based on the classical GL-model for homogeneous material. This system is coupled dynamic problem and the displacement field and heat field must be solved at the same time. By using Fadeo-Galerkin method, we proved that the problem we proposed exist unique weak solution under some regular assumption.
Matlab Methods for Roots of Characteristic Equation of Cylindrical Bessel Equation Eigenvalue Problems on General Interval
2009, 24(1): 145-150.
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Root of characteristic equation for cylindrical Bessel equation eigenvalue prob- lems on general interval is of great real physical importance at engineering and physical. First, the characteristic equation of cylindrical Bessel equation eigenvalue problem on general interval is given, second, by mean of compared method, we obtaining roots of characteristic equation with Matlab program is discussed.
A Decision Model Based on Grey Rough Sets Integration with Incomplete Information
2009, 24(1): 151-158.
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In this paper, for multiple attribute decision-making problem in which attribute values are interval grey numbers and some of them are null values, a decision model based on grey rough sets integration with incomplete information is proposed. We put forward incidence degree coefficient formula for grey interval, by information entropy theory and analysis technique, the method and principle is presented to fill up null values. We also establish the method of grey interval incidence cluster. Because grey system theory and Rough set theory are complementary each other, decision table with preference information is obtained by the result of grey incidence cluster. An algorithm for inducing decision rules based on rough set theory and the dominance relationship is presented. In some extent, this algorithm can deal with decision-making problem in which the attribute values are interval grey numbers and some of them are null values. Contrasted with classical model of cluster decision-making, the algorithm has an advantage of flexibility and compatibility to new information. 还原
