数学季刊

贺福利

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.

具放牧率的非线性生态模型的正概周期解

倪华, 田立新

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.

个离散造血模型概周期解的吸引性和振动性

洪鹏花, 翁佩萱

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.

L-凸空间中新的不动点定理及其应用

文开庭

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.

组合模型在现实投资交易中的应用

王国欣, 柳静

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.

数学无穷与中介逻辑(上)——Leibniz的割线与切线问题在中介逻辑中的逻辑数学解释方法

朱梧槚, 宫宁生. 杜国平

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.

锥距离空间中压缩条件下的公共不动点定理

王云杰, 朱江

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.

弱次可加集值映射的可加选择映射的唯一存在性

朴勇杰, 石仁淑

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.

半线性双曲波动方程的H¹-Galerkin扩展混合元方法

王金凤, 刘洋, 李宏, 何斯日古愣

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.

Y-数值半径的范数性质

张晓燕

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_n is 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.

高维单形的等距共轭点性质初探

曾建国

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.

m-KdV-Sine-Gordon方程和m-KdV-Sinh-Gordon方程的行波解

李二强, 陈金兰

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.

与微分多项式分担值相关的正规定则

邓炳茂, 雷春林, 杨德贵

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.

一类差分方程性质的研究

肖倩, 石启宏

2013, 28(1): 93-98.

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This paper is concerned with the following rational difference equation x_n+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.

隔离-免疫-治疗模型的双重近似算法

王乐乐, 张昭

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.

Bloch型空间上广义Cesàro算子的本性模

赵弟

2013, 28(1): 105-110.

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The Bloch-type space B_ω 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) .

ψ-混合序列的若干收敛结果

潘婧, 朱业春, 邹委员, 王学军

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.

一类具有时滞和治疗的宿主-寄生虫交互动力学模型的研究

赵瑜

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 R₀, 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.

Bernstein算子迭代布尔和的点态逼近性质

霍晓燕, 李翠香, 姚秋妹

2013, 28(1): 129-138.

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In this paper, with the help of modulus of smoothness ω^2r(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.

闭算子Moore-Penrose逆的逆序律

杜法鹏, 薛以锋

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].

变系数迭代方程的集值解

米玉珍, 梁英

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.

新型的带自相溶源的变系数KP方程及其它的Grammian解

邢秀芝, 刘艳伟

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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