Chinese Quarterly Journal of Mathematics

A Generalization of Yamabe Equation on Complete Manifolds

WU San-xing

2010, 25(1): 1-7.

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This paper considers a semilinear elliptic equation on a n-dimensional complete noncompact Riemannian manifold, which is a generalization of the well known Yamabe equation. An existence result is proved.

A Rectangular Finite Element for Planar Elasticity and Stokes Problems

CHEN Shao-chun, ZHANG Bu-ying

2010, 25(1): 8-15.

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In this paper, a locking-free nonconforming rectangular finite element scheme is presented for the planar elasticity problem with pure displacement boundary condition. Meanwhile, we prove that this element is also convergent for stationary Stokes problem.

Some Remarks for the Relationships between the Generalized Bernoulli and Euler Polynomials

LUO Qiu-ming, GE Shu-mei

2010, 25(1): 16-22.

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In this paper, we prove the Srivastava-Pinter's addition theorems(see Applied Mathematic Lett.17(2004),375-380) by applying the another methods. We also provide some analoges of these addition theorems and deduce the corresponding special cases.

Value Distribution of a Class of Differential Polynomials

XU Jun-feng, ZHANG Zhan-liang

2010, 25(1): 23-29.

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Let f(z) be a transcendental meromorphic function in the complex plane and a = 0 be a constant, for any positive integer m,n,k, satisfy m ≥ nk+n+2, ψ = f^m+a(f^(k))ⁿhas infinitely many zeros. The corresponding normal criterion also is proved.

Two Classes of Solvable Subgroups of SL(3, C) and Application for Differential Equations in C

ZHANG Shao-fei, LI Hui-zhen

2010, 25(1): 30-36.

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Structures of two classes of solvable subgroups in SL(3,C) are given in this paper, and the integrability of the 3-order Fuchsian equation which is integrable in the sense that its monodromy group is solvable is discussed.

A Stage-structured Three-species Model with Intra-guild Predation and Disturbing Pulse

SHI Xiang-yun, CUI Xue-ying

2010, 25(1): 37-44.

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This paper considers a stage-structured three species model with intra-guild predation and disturbing pulse. Sufficient conditions which guarantee the global attractivity of boundary periodic solution and permanence of the system are obtained. Our results show that the pulse and time delay bring great effect on the dynamical behaviors of the model.

Mathematical Analysis of Immune Response of HIV-I Including Delay

WANG Zhan-wei, WANG Wen-di

2010, 25(1): 45-51.

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This paper considers a model of cell-to-cell spread of HIV-I with CTL immune response. By using a discrete delay to model the intracellular delay, it is shown that the uninfected equilibrium is globally asymptotical stable in some conditions and the sufficient condition to ensure the stability of the infected equilibrium does not change would be enlarged by Sturm sequence. Numerical simulations are presented to illustrate the results.

Relaxation-strategy-based Modification Branch-and-Bound Algorithm for Solving a Class of Transportation-production Problems

DU Ting-song, FEI Pu-sheng, JIAN Ji-gui

2010, 25(1): 52-59.

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In this paper, a new algorithm relaxation-strategy-based modification branch-and-bound algorithm is developed for a type of solving the minimum cost transportation production problem with concave production costs. The major improvement of the proposed new method is that modification algorithm reinforces the bounding operation using a Lagrangian relaxation, which is a concave minimization but obtains a tighter bound than the usual linear programming relaxation. Some computational results are included. Computation results indicate that the algorithm can solve fairly large scale problems.

Two Sums for a Class of Recurrence Sequences

PANG Jin-li, YE Xiao-li

2010, 25(1): 60-64.

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A conjecture posed by Melham for U_n^2k+U_n+1^2kin [2] is considered in this article. Several positive results on V_n+s^2k +...U_n+s^{2k ar}e achieved which generalize existed results on V_n+1²-...U_n+1².

The Upper Bound of the Moebius Scalar Curvature of Submanifolds in S^n+p

ZHONG Ding-xing, SUN Hong-an, MO Xiao-kai

2010, 25(1): 65-73.

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The most important Moebius invariants in the Moebius differential geometry of submanifolds in S^n+p are the Moebius metric g, the Moebius second fundamental form B, the Moebius form Φ and the Blaschke tensor A. In this paper, we obtain the upper bound of the Moebius scalar curvature of submanifolds with parallel Moebius form in S^n+p.

The Existence and Uniqueness of Periodic Solutions for a Kind of Lienard Equation with a Deviating Argument

WANG Na

2010, 25(1): 74-80.

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By means of Mawhin’s continuation theorem, we study a kind of lienard functional differential equations: x"(t)+f(x(t))x’(t)+g(t,x(t-τ(t)))=e(t). Some new results on the existence and uniqueness of periodic solutions are obtained.

The Backlund Transformation and Explicit Solution of Volterra Lattice Equation

WU Yong-qi

2010, 25(1): 81-85.

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The Backlund transformation and the generalized Miura transformation for the Volterra lattice equation are constructed by using point symmetry method. As an application, the explicit solution to the lattice equation is obtained.

Composition Operators From B₀ to Q_K and Q_K,0 Spaces

GUO Jian, LIU Yong-min

2010, 25(1): 86-91.

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When φ is an analytic map of the unit disk D into itself, and X is a Banach space of analytic functions on D, define the composition operator Cφ by Cφ(f) = f ο φ, for f ∈ X. In this paper, we study the boundedness and compactness of composition operators from the space B⁰ to Q_K and Q_K,0.

On the Location of Zeros of Higher Order Differential Equation

CHEN Yu-xian, WU Zhao-jun

2010, 25(1): 92-97.

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In this paper, by using the Nevanlinna Theory on angular domain, we establish a theorem which concerns the growth of entire function and his zero. As an application, we survey the location of zero of higher order differential equation, which can be regarded as an alternating but precise version of Wu^[6] and Yi^[7].

On Graphs with Equal Connected Domination and 2-connected Domination Numbers

CHEN Hong-yu, ZHU Zhe-li

2010, 25(1): 98-103.

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A subset S of V is called a k-connected dominating set if S is a dominating set and the induced subgraph S has at most k components. The k-connected domination number γ_c^k(G) of G is the minimum cardinality taken over all minimal k-connected dominating sets of G. In this paper, we characterize trees and unicyclic graphs with equal connected domination and 2-connected domination numbers.

ε-strongly Efficient Solutions for Vector Optimization with Set-valued Maps

WANG Qi-lin

2010, 25(1): 104-109.

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In locally convex Hausdorff topological vector spaces, ε-strongly efficient solutions for vector optimization with set-valued maps are discussed. Firstly, ε-strongly efficient point of set is introduced. Secondly, under the nearly cone-subconvex like set-valued maps, the theorem of scalarization for vector optimization is obtained. Finally, optimality conditions of ε-strongly efficient solutions for vector optimization with generalized inequality constraints and equality constraints are obtained.

Integral Operator Solving Process of the Boundary Value Problem of Abstract Kinetic Equation with the First Kind of Critical Parameter and Generalized Periodic Boundary Conditions

YU De-jian

2010, 25(1): 110-117.

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In this paper the concepts of the boundary value problem of abstract kinetic equation with the first kind of critical parameter λ = 0 and generalized periodic boundary conditions are introduced in a Lebesgue space which consists of functions with vector valued in a general Banach space, and then describe the solution of these abstract boundary value problem by the abstract linear integral operator of Volterra type. We call this process the integral operator solving process.

Partial Order and Extremes of Multivariate Extreme Value Distributions

DONG Yong-quan, XU Fu-xia

2010, 25(1): 118-123.

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This paper studies the dependence order among multivariate extreme value distributions with a fixed marginal distribution. Making use of copulas to prove that the set organized by multivariate extreme value distributions and the dependence order defined in it is a partial order set. Finally, the maximum and minimum values of the set is discussed.

Synchronization of a Class of Delayed Neural Networks with Sector Nonlinearity

HUANG You-liang

2010, 25(1): 124-131.

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In this paper, global synchronization is discussed for a general class of delayed neural networks with time-varying and distributed delays. Furthermore, the activation functions in the neural networks can be different type. Based on the drive-response concept and the Lyapunov stability theorem, some sufficient criteria are obtained to guarantee the global synchronization of the considered models even when input sector nonlinearity caused by physical limitations is presented in response systems. Finally, a typical example is also given to illustrate the effectiveness of the proposed synchronization scheme.

Connectedness of Cone-efficient Solution Set for Cone-quasiconvex Multiobjective Programming in Hausdorff Topological Vector Spaces

ZHOU Xuan-wei

2010, 25(1): 132-139.

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This paper deals with the connectedness of the cone-efficient solution set for vector optimization in locally convex Hausdorff topological vector spaces. The connectedness of the cone-efficient solution set is proved for multiobjective programming defined by a continuous one-to-one cone-quasiconvex mapping on a compact convex set of alternatives. During the proof, the generalized saddle theorem plays a key role.

The V-cycle Multigrid Method for a Hermite-type Rectangular Element

ZHAO Yan-min, SHI Dong-yang

2010, 25(1): 140-145.

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In this paper, a V-cycle multigrid method is presented for a Hermite rectangular element. By defining proper mesh-dependent inner product and transfer operator, we obtain its convergence property and the uniform convergence rate independent of mesh size and level are established.

A Property of Simple Groups

WANG Hui-qun, JI Xiao-long

2010, 25(1): 146-150.

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In this note, we use an elementary method to prove the fact: if G is a nonabelian simple group, then 2∈/cd_p(G),where p is a prime and p > 2.

Existence of Positive Solution for Superlinear Semipositone Singular Second-order m-point Boundary Value Problem

ZHANG Xing-qiu

2010, 25(1): 151-158.

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By applying fixed point theorem, the existence of positive solution is considered for superlinear semipositone singular m-point boundary value problem -(Lφ)(x) = ···, f ∈ C[(0,1) × R⁺,R⁺], f(x,φ) may be singular at x = 0 and x = 1, g(x):(0,1) → R is Lebesgue measurable, g may tend to negative infinity and have finitely many singularities.

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