数学季刊

徐哲锋

2006, 21(1): 1-3.

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The main purpose of this paper is to introduce the general Smarandache multiplicative sequence based on the Smarandache multiplicative sequence, and calculate the value of some infinite series involving these sequences.

单纯形上积分型Stancu算子在L_p中的逼近逆定理

张春苟

2006, 21(1): 4-9.

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In this paper, the integral-type Stancu operators on a simplex is considered and its inverse theorem of approximation in L_p(1≤p<+∞)has been obtained.

二宽度CSL代数与套代数的因子分解

杨有龙, 吴艳

2006, 21(1): 10-14.

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In this paper, we show that the invertible operator T, which is a bounded linear functional on a separable Hilbert space H, could factor as T=US, where U is unitary and 5 belongs to width-two CSL algebra alg when nest M or N is a countable nest, or S belongs to alg when nests M and N are countable nests. For the factorization of nest,we obtain that T factors as T=US where S∈D^-1_N and U is unitary as N be a countable nest.

缺失数据场合Birnbaum-Saunders疲劳寿命分布的统计分布

王蓉华, 费鹤良

2006, 21(1): 15-27.

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n present paper, we derive the quasi-least squares estimation(QLSE) and approximate maximum likelihood estimation(AMLE) for the Birnbaum-Saunders fatigue life distribution under multiply Type-Ⅱcensoring. Furthermore, we get the variance and covariance of the approximate maximum likelihood estimation.

一类随机矩阵经验分布的强收敛性

梁庆文, 缪柏其, 王大鹏

2006, 21(1): 28-32.

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Let {v_ij}, i, j = 1, 2,…, be i.i.d. random variables with E_v11= 0, E²v11=1 and a_i= (a_i1,…,a_iM) be random vectors with {a_ij} being i.i.d. random variables. Define X_N=(x₁,…, X_K)and ... The spectral distribution of SN is proven to converge, with probability one, to a nonrandom distribution function under mild conditions.

椭圆方程Δu+K（x）e^2u=0的一个存在性结果

武三星

2006, 21(1): 33-37.

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This paper considers the existence problem of an elliptic equation, which is equivalent to solving the so called prescribing conformal Gaussian curvature problem on the hyperbolic disc H². An existence result is proved. In particular, K(x) is allowed to be unbounded above.

图的割宽极值问题

郝建修, 杨爱峰

2006, 21(1): 38-43.

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The problem studied in this paper is to determine e(p, C), the minimum size of a connected graph G with given vertex number p and cut-width C.

NURBS曲线保凸性质的几何证明

柳朝阳

2006, 21(1): 44-48.

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NURBS curves are convexity preserving, i.e. once the control polygon is convex, the associated NURBS curve will also be convex. In this paper this property is proved geometrically.

半线性波动方程解的低正则局部存在性

杨宁, 杨晗

2006, 21(1): 49-56.

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In this paper,we study how much regularity of initial data is needed to ensure existence of a local solution to the following semilinear wave equations …. We proved that the range of s is ,respectively,with if n=2, and δ>0 if n=3, and δ≥0 if n≥4. Which is consistent with Lindblad's counterexamples [3] for n=3, and the main ingredient is the use of the Strichartz estimates and the refinement of these.

关于乘积Borel概率测度的一点注记

马东魁, 徐志庭

2006, 21(1): 57-61.

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In this paper,a necessary and sufficient condition of a measure to be the product Borel probability measure on the product space of some compact metric spaces are given.

强正则自补图的一个注记

田方

2006, 21(1): 62-65.

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Kotzig put forward a question on strongly-regular self-complementary graphs, that is, for any natural number k, whether there exists a strongly-regular self- complementary graph whose order is 4k+1, where 4k+1=x2+y2, x and y are positive integers; what is the minimum number that made there exist at least two non-isomorphic strongly-regular self-complementary graphs. In this paper, we use two famous lemmas to generalize the existential conditions for strongly-regular self-complementary circular graphs with 4k+1 orders.

任意除环上一矩阵方程组的一般解与中心和反中心对称解

秦建国, 宋光艾

2006, 21(1): 66-70.

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Necessary and sufficient conditions are given for the existence of the general solution, the centrosymmetric solution, and the centroskewsymmetric solution to a system of linear matrix equations over an arbitrary skew field. The representations of such the solutions of the system are also derived.

在风险模型中一类重尾随机和的大偏差

孔繁超, 王金亮

2006, 21(1): 71-79.

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This paper is a further investigation into the large deviations for random sums of heavy-tailed,we extended and improved some results in ref. [1] and [2]. These results can applied to some questions in Insurance and Finance.

动力系统的稳定化问题

张志平, 王建平

2006, 21(1): 80-84.

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In this paper, we are concerned with the problem of stabilization for autonomous dynamical systems. We use theories in Liapunov stability and Lasalle stability theory and show that system (H) is stabilizable.

具有时滞的高阶Duffing型方程的2π周期解

林文贤

2006, 21(1): 85-89.

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In this paper, the high order delay Duffing equation ax⁽²ⁿ⁾+bx+g(x(t-τ)) =p(t) are considered,using the theory of coincidence degree, the sufficient condition for its there being at least a 2π-periodic solution is obtained.

具有边界摄动的拟线性Robin问题

陈雪东

2006, 21(1): 90-95.

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A class of quasilinear Robin problems with boundary perturbation are considered. Under suitable conditions, using theory of differential inequalities the asymptotic behavior of solution for the boundary value problem is studied.

一个推广的Hibert不等式及其应用

杨必成

2006, 21(1): 96-102.

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This paper gives a new generalization of Hilbert’s inequality with a best constant factor involving theβfunction. An applications, we consider the equivalent form and some particular results.

主次指标为最小化总完工时间和存储费用的带有准备时间的单机分批排序问题

李文华

2006, 21(1): 103-109.

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In this paper, the single machine scheduling problem with release dates and two hierarchical criteria is discussed. The first criterion is to minimize makespan, and the second criterion is to minimize stocking cost. We show that this problem is strongly NP-hard. We also give an O(n2) time algorithm for the special case that all stocking costs of jobs in unit time are 1.

二元二次函数逼近的存在性和局部性

郑成德

2006, 21(1): 110-114.

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This paper analysis the local behavior of the bivariate quadratic function approximation to a bivariate function which has a given power series expansion about the origin. It is shown that the bivariate quadratic Hermite-Pade form always defines a bivariate quadratic function and that this function is analytic in a neighborhood of the origin.

一类有界Reinhardt域上的函数论

李娴

2006, 21(1): 115-123.

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In this paper, we consider a class of bounded Reinhardt domains D_α(m, n₁,…,n_m). The Bergman kernel function K(z,z), the Bergman metric matrix T(z,z), the Cauchy-Szego kernel function S(z,ζ) are obtained. Then we prove that the formal Poisson kernel function is not a Poisson kernel function. At last, we prove that D_αis a quasiconvex domain and D_αis a stronger quasiconvex domain if and only if D_α is a hypersphere.

具有不同效用函数的最优投资组合分析

姚远, 史本山

2006, 21(1): 124-128.

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The question of optimal portfolio is that finds the trading strategy satisfying the maximal expected utility function subject to some constraints. There is the optimal trading strategy under the risk neutral probability measure (martingale measure) if and only if there is no-arbitrage opportunity in the market. This paper argues the optimal wealth and the optimal value of expected utility with different utility function.

关于给直径的(m,n)-树的最大谱半径

程伟, 谭尚旺

2006, 21(1): 129-137.

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Let (V, U) be the vertex-partition of tree T as a bipartite graph. T is called an (m,n)-tree if |V|=m and |U| = n. For given positive integers m,n and d, the maximum spectral radius of all (m,n)-trees on diameter d are obtained, and all extreme graphs are determined.

α次β型强螺旋映射的增长与掩盖定理

刘杰明, 王志军

2006, 21(1): 138-142.

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In this paper, we deduce growth and covering theorem for f(x) by the other means,where f(x) is strongly spirallike mapping of type β with orderαdefined on Unit Ball B of complex Banach space. and still give growth upper bound and distortion upper bound for subordinate mapping.

k-因子和图论中的扩张子图

王治国, 张驿

2006, 21(1): 143-147.

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In this paper, we discussed k-factors and spanning subgraph, and propose a conjecture which will lead to a series of important conclusion.

允许重新进货情况下单周期可替代产品的库存模型

李小申, 高克权

2006, 21(1): 148-158.

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In market, excess demands for many products can be met by reorder even during one period, and retailers usually adopt substitution strategy for more benefit. Under the retailer’s substitution strategy and permission of reorder, we develop the profits maximization model for the two-substitutable-product inventory problem with stochastic demands and proportional costs and revenues. We show that the objective function is concave and submodular, and therefore the optimal policy exists. We present the optimal conditions for order quantity and provide some properties of the optimal order quantities. Comparing our model with Netessine and Rudi’s, we prove that reorder and adoption of the substitution strategy can raise the general profits and adjust down the general stock level.

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