Chinese Quarterly Journal of Mathematics

Compound Boundary Value Problems for Hyperanalytic Functions

HE Fu-li

2013, 28(1): 1-10.

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In this paper, the so-called Riemann-Hilbert compound boundary value problems for hyperanalytic functions are considered, include the compound value problems for simply connected regions and open arcs, we get these solutions.

Positive Almost Periodic Solution on a Nonlinear Logistic Biological Model with Grazing Rates

NI Hua, TIAN Li-xin

2013, 28(1): 11-19.

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In this paper, we study the following nonlinear biological model dx(t)/dt = x(t)[a(t)-b(t)x^α(t)] + f(t, x_t), by using fixed pointed theorem, the sufficient conditions of the existence of unique positive almost periodic solution for the above system are obtained, by using the theories of stability, the sufficient conditions which guarantee the stability of the positive almost periodic solution are derived.

Attractivity and Oscillation of Almost-periodic Solution for a Discrete Model of Hematopoiesis

HONG Peng-hua, WENG Pei-xuan

2013, 28(1): 20-26.

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By using a new fixed point theorem, sufficientconditions are obtained for the existence of a positivealmost-periodic solution for an discrete model of hematopoiesis with almost-periodic coefficients. Its attractivity and oscillation are investigated.

A New Fixed Point Theorem in L-Convex Spaces with Applications

WEN Kai-ting

2013, 28(1): 27-32.

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In this paper, we present a new fixed point theorem in L-convex spaces and apply it to obtain a maximal element theorem, a variational inequality and a saddle point theorem in L-convex spaces.

Application of Portfolio Model in the Real Investment Transactions

WANG Guo-xin, LIU Jing

2013, 28(1): 33-40.

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This paper studies discrete investment portfolio model that the objective function is utility function. According to a hybrid branch-and-bound method based on Lagrangian relaxation and continuous relaxation, the paper analyzes the question using the real statistical data. The results indicate that discrete investment portfolio model really has its guidance in the actual investment.

Mathematical Infinity and Medium Logic (I) —Logical-mathematical Interpretation of Leibniz’s Secant and Tangent Lines Problem in Medium Logic

ZHU Wu-jia, GONG Ning-sheng, DU Guo-ping

2013, 28(1): 41-46.

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From the perspective of potential infinity (poi) and actual infinity, Ref [4] has confirmed that poi and aci are in ’unmediated opposition’ (P,﹁P ) whether in ZFC or not; it has further been proved that the manners in which a variable infinitely approaches its limit also satisfy the law of intermediate exclusion. With these results as theoretical bases, this paper attempts to provide an accurate and strict logical-mathematical interpretation of the incompatibility of Leibniz’s secant and tangent lines in the medium logic system from the perspective of logical mathematics.

Common Fixed Points under Contractive Conditions in Cone Metric Spaces

WANG Yun-jie, ZHU Jiang

2013, 28(1): 47-52.

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In order to develop and improve the fixed point theorems in cone metric spaces, some new fixed point theorems are presented for two mappings in cone metric spaces which satisfy contractive conditions, where the cone is not necessarily normal. Our results generalize fixed point theorems of Abbas, Jungck and Stojan Radenovic in cone metric spaces.

The Unique Existence of Additive Selection Maps for a Weak Subadditive Set-valued Map

PIAO Yong-jie, SHI Ren-shu

2013, 28(1): 53-59.

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In this paper, we discuss the unique existent problems of a additive selection map for the following map F:X→P0(Y):, ··· , r, where α_i and α_i(i = 1, ··· , r) are all non-negative real numbers.

An H¹-Galerkin Expanded Mixed Element Method for Semi-linear Hyperbolic Wave Equation

WANG Jin-feng, LIU Yang, LI Hong, HE Siriguleng

2013, 28(1): 60-68.

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An H¹-Galerkin expanded mixed finite element method is discussed for a class of second order semi-linear hyperbolic wave equations. By using the mixed formulation, we can get the optimal approximation for three variables: the scalar unknown, its gradient and its flux(coefficient times the gradient), simultaneously. We also prove the existence and uniqueness of semi-discrete solution. Finally, we obtain some numerical results to illustrate the efficiency of the method.

Norm Properties of Y-numerical Radii

ZHANG Xiao-yan

2013, 28(1): 69-76.

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Given an n×n complex matrix A and an n-dimensional complex vector y=(ν₁ , ··· , ν_n), the y-numerical radius of A is the nonnegative quantity r_y(A)=max{n∑_j=1,..., x_j∈C_n}. Here C_nis an n-dimensional linear space over the complex field C. For y = (1, 0, ··· , 0) it reduces to the classical radius r(A) =max {|x*Ax|: x*x=1}. We show that r_y is a generalized matrix norm if and only if n∑_j=1ν_j≠ 0. Next, we study some properties of the y-numerical radius of matrices and vectors with non-negative entries.

Preliminary Exploration on Properties of the Equidistant Conjugate Points of Higher Dimensional Simplex

ZENG Jian-guo

2013, 28(1): 77-81.

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In this paper, the concept of the equidistant conjugate points of a triangle to the n-dimensional Euclidean space is extended. The concept of equidistant conjugate point in high dimensional simplex is defined, and the property of the equidistant conjugate points of a triangle is generalized to high dimensional simplex.

Travelling Wave Solutions to the m-KdV-Sine-Gordon Equation and the m-KdV-Sinh-Gordon Equation

LI Er-qiang, CHEN Jin-lan

2013, 28(1): 82-86.

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By using the function transformation and proper Sub-ODE, exact travelling wave solutions of the m-KdV-Sine-Gordon and the m-KdV-Sinh-Gordon equation are obtained, from which exact travelling wave solutions of the m-KdV equation, the Sine-Gordon equation and the Sinh-Gordon equation are derived.

Normality and Shared Value Concerning Differential Polynomials

DENG Bing-mao, LEI Chun-lin, YANG De-gui

2013, 28(1): 87-92.

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Let F be a family of functions meromorphic in a domain D, let m, n_k, k be three positive integers and b be a finite nonzero complex number. Suppose that, (1) for each f∈F, all zeros of f have multiplicities at least k ; (2) for each pair of functions f, g ∈F, P(f)H(f) and P(g)H(g) share b, where P(f) and H(f) were defined as (1.1) and (1.2) and n_k≥max_1≤i≤k-1{n_i}; (3) m ≥ 2 or n_k≥ 2, k ≥ 2, then F is normal in D.

On the Qualitative Behavior of a Difference Equation

XIAO Qian, SHI Qi-hong

2013, 28(1): 93-98.

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This paper is concerned with the following rational difference equation xn+1=ax_n-bx_n-1+ex²_n/(cX_n+dx_n-1), with the initial conditions x_-1, x₀∈ (0, +∞) and a, b, c, d, e ∈ R⁺. Locally asymptotically stability, global attractively and boundedness character of the equilibrium point of the equation are investigated. Moreover, simulation is shown to support the results.

Bicriteria Approximation Algorithm for Quarantining-vaccination-cure Problem

WANG Le-le, ZHANG Zhao

2013, 28(1): 99-104.

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In this paper, we propose a model for the epidemic control problem, the goal of which is to minimize the total cost of quarantining, vaccination and cure under the constraint on the maximum number of infected people allowed. A (1+ε+ε3 , 1+ ε+1/ε )- bicriteria approximation algorithm is given.

Essential Norm of Extended Cesàro Operators between Bloch-type Spaces

ZHAO Di

2013, 28(1): 105-110.

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The Bloch-type space Bω consists of all functions f ∈ H(B) for which ||f||B_ω=sup_z∈Bω(z)|▽f(z)|< ∞. Let T be the extended Cesàro operator with holomorphic symbol. The essential norm of T as an operator from Bω to Bμ is denoted by ||T||_e,Bω→B_μ. The purpose of this paper is to prove that, for ω, μ normal and ...dt/ω(t) .

Some Convergence Results for Sequences of ψ-mixing Random Variables

PAN Jing, ZHU Ye-chun, ZOU Wei-yuan, WANG Xue-jun

2013, 28(1): 111-117.

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In this paper, we will present some strong convergence results for sequences of ψ-mixing random variables. The results for sequences of ψ-mixing random variables generalize the corresponding results for independent random variable sequences without any extra conditions.

Analysis of a Dynamic Model of Host-parasite Interaction with Delay and Treatment

ZHAO Yu

2013, 28(1): 118-128.

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In this paper, the dynamic behaviors of a host-parasite model with intracellular delay and drug treatment is investigated. we obtain the basic reproductive ratio R_0,which determined the behaviors of the system. If R₀<1, the infection-free equilibrium is globally asymptotic stability. If 1<R₀<3, the infection equilibrium is locally asymptotic stability. If R₀>3, by choosing the delay τ as a bifurcation parameter, the infection equilibrium bifurcate a family of periodic solution as τ crosses a critical value. Furthermore, we give some examples to verify our theoretical results and discuss the sensitivity of the drug efficacy and effect of the delay. In the finally, we give a brief discussion.

Pointwise Approximation for the Iterated Boolean Sums of Bernstein Operators

HUO Xiao-yan, LI Cui-xiang, YAO Qiu-mei

2013, 28(1): 129-138.

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In this paper, with the help of modulus of smoothness ω2r(f, t), we discuss the pointwise approximation properties for the iterated Boolean sums of Bernstein operator B_n and obtain direct and inverse theorems when 1-1/r ≤λ≤ 1, r ∈N.

The Reverse Order Law for Moore-Penrose Inverse of Closed Operators

DU Fa-peng, XUE Yi-feng

2013, 28(1): 139-146.

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In this paper, the reverse order law for the Moore-Penrose inverse of closed linear operators with closed range is investigated by virtue of the Norm-preserving extension of the bounded linear operators. The results generalize some results obtained by S Izumino in [12].

Multivalued Solutions of an Iterative Equation with Variable Coefficients

MI Yu-zhen, LIANG Ying

2013, 28(1): 147-151.

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In this paper, we consider a second order multivalued iterative equation with variable coefficients and the results on increasing solution and decreasing solution are obtained.

New Type of Variable-coefficient KP Equation with Self-consistent Sources and Its Grammian Solutions

XING Xiu-zhi, LIU Yan-wei

2013, 28(1): 152-158.

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New type of variable-coefficient KP equation with self-consistent sources and its Grammian solutions are obtained by using the source generation procedure.

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