数学季刊

冶成福, 王波, 刘儒英

2009, 24(3): 317-324.

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The parameter R(G) is the function about the front three coefficients of the adjoint polynomial of graph G. In the paper, the range of R(G) is given when β(G)<β(D_n), where β(G) is the minimum root of the adjoint polynomial of graph G and the chromatically equivalent classification of tD_n is completely depicted. Furthermore,a sufficient and necessary condition for the class of graphs to be chromatically unique is obtained.

带干扰Cox模型的渐近性质

王慧丽, 史忠科, 任志平

2009, 24(3): 325-332.

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In this paper, the asymptotic behavior on the Cox risk model perturbed by diffusion is studied. The sufficient and necessary conditions for the process when it weakly convergence to Normal distribution and the rate of weakly convergence are received. Finally discuses the exponential upper bound for ruin probability of this risk model.

树的线图的P₃-因子

李晓娟, 张昭

2009, 24(3): 333-337.

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In this paper, we give a necessary and sufficient condition for the existence of P₃-factors in the line graph of a tree. Then we present an algorithm to determine whether the line graph of a tree has a P₃-factor.

Baskakov-Kantorovich算子的完全渐进展开

王全娥, 张春苟

2009, 24(3): 338-342.

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In this paper, we derive the Baskakov-Kantorovich operators V_n(f;x) the complete asymptotic expansion in the form of all coefficients of n^-k_,k = 0,1… being calculated explicitly. As a corollary, we also get the Voronovskaja-type result for the operators.

关于L_ρ2[-a,a]中G.G.Lorentz型的四个猜想

王元恒, 杨文善

2009, 24(3): 343-348.

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In the space C[-1,1], G G Lorentz proposed four conjectures on the properties of the polynomials of the best approximation in 1977,1978 and 1980. The present paper transplants the four conjectures in the space L_ρ²[-a,a] and proves them being all right in only one theorem under the corresponding conditions, although each of the original conjectures is very difficulty.

两个目标的重新排序问题

慕运动

2009, 24(3): 349-356.

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In the rescheduling on a single machine, a set of original jobs has already been scheduled to minimize some cost objective, when a new set of jobs arrives and creates a disruption. The decision maker needs to insert the new jobs into the existing schedule without excessively disrupting it. In this paper, we consider hierarchical optimization between the scheduling cost of all the jobs and the degree of this disruption. For every problem, we provide either a polynomial time algorithm or an intractable result.

de Sitter空间中具有常数量曲率的完备类空子流形

刘建成, 张德燕

2009, 24(3): 357-364.

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In this paper, we study the complete space-like submanifold Mⁿwith constant scalar curvature R≤c in the de Sitter space S_p^n+p(c) and obtain a pinching condition for Mn to be totally umbilical ones. The result generalizes that in [5,Main Theorem] to higher codimension and give a complement for n=2 there.

具动力边界条件椭圆方程解的衰减性

呼青英, 朱碧, 张宏伟

2009, 24(3): 365-369.

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The decay estimations of the solution to an elliptic equation with dynamical boundary condition is considered. We proved that, for suitable initial datum, the energy of the solution decays "in time" exponentially if p=0,whereas the decay is polynomial order if p>0.

非线性抛物型积分-微分方程的向后Euler差分有限体积元方法

王波, 王强

2009, 24(3): 370-377.

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The Finite volume backward Euler difference method is established to discuss two-dimensional parabolic integro-differential equations. These results are new for finite volume element methods for parabolic integro-differential equations.

在抽象框架理论中刻画R-对偶序列

吴国昌, 王澜峰, 李登峰

2009, 24(3): 378-383.

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In this paper, two operators are defined, and their underlying properties are found, then the R-dual relationship is classified from the aspect of the operators defined. Furthermore, the commutability of the bases of constructing R-dual sequence is discussed. In particular, SR-dual sequence is defined and is clarified. At last an example is given.

反双曲正弦函数的单调性和不等式

张士勤, 郭白妮

2009, 24(3): 384-388.

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In this paper, we present monotonicity results of a function involving the inverse hyperbolic sine. From these, we obtain some lower bounds for the inverse hyperbolic sine.

一类Holling Ⅲ型强耦合捕食模型的共存解

黄优良, 张来, 房少梅

2009, 24(3): 389-393.

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In this paper, the two-species prey-predator Lotka-Volterra model with the Holling’s type Ⅲ is discussed. By the method of coupled upper and lower solutions and its associated monotone iterations, the existence of solutions for a strongly coupled elliptic system with homogeneous of Dirchlet boundary conditions is derived. These results show that this model admits at least one coexistence state if across-diffusions are weak.

一类非线性偏微分方程的有限差分格式的稳定性研究

王秀琴, 徐琛梅

2009, 24(3): 394-399.

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The main purpose of this paper is to set up the finite difference scheme with incremental unknowns for the nonlinear differential equation by means of introducing incremental unknowns method and discuss the stability of the scheme. Through the stability analyzing for the scheme, it was shown that the stability of the finite difference scheme with the incremental unknowns is improved when compared with the stability of the corresponding classic difference scheme.

Fibonacci数积的平方倒数的求和公式

席高文, 王淑玉

2009, 24(3): 400-406.

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By applying the method of on summation by parts, the purpose of this paper is to give several reciprocal summations related to squares of products of the Fibonacci numbers.

当试验没有观察到失效时产品可靠度的E-Bayes估计

韩明

2009, 24(3): 407-414.

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This paper develops a new method, named E-Bayesian estimation method, to estimate the reliability parameters. The E-Bayesian estimation method of the reliability are derived for the zero-failure data from the product with Binomial distribution. Firstly, for the product reliability, the definitions of E-Bayesian estimation were given, and on the base, expressions of the E-Bayesian estimation and hierarchical Bayesian estimation of the products reliability was given. Secondly, discuss properties of the E-Bayesian estimation. Finally, the new method is applied to a real zero-failure data set, and as can be seen, it is both efficient and easy to operate.

双循环半群的ω扩张

朱雯, 詹亮

2009, 24(3): 415-419.

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In this paper, we discussed ω-extension of bicyclic semigroups. Two types of this extension are proposed. In §2 we discussed strong semilattice extension and the structure of the extension is well presented. In §3 we discussed another order extension. We proved that congruence lattice of this extension semigroups is union set of two sublattice. One is the group congruence semilattice, the other is the pure idempotent congruence semilattice.

Loewner链与推广的Roper-Suffridge算子

成金环, 刘涛

2009, 24(3): 420-425.

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In this paper, we prove that the generalized Roper-Suffridge extension operator can be embedded 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 other α,almost starlikeness of order α, spirallikeness of type β and starlikeness.

希尔伯特空间上松弛强变分不等式组的广义映射法

杨峻, 吴忠林

2009, 24(3): 426-431.

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In this paper, we consider a new algorithm for a generalized system for relaxed coercive nonlinear inequalities involving three different operators in Hilbert spaces by the convergence of projection methods. Our results include the previous results as special cases extend and improve the main results obtained by many others.

非线性Sobolev-Galpern型方程解的Blow-up性质

张恩彪, 江成顺

2009, 24(3): 432-438.

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In this paper, the initial boundary value problems of the nonlinear Sobolev-Galpern equation are studied. The existence, uniqueness of local solution for the problem are obtained by means of a special Green’s function and the contraction mapping principle. Finally, the blow-up of solution in finite time under some assumed conditions is proved with the aid of Jensen’s inequality.

非线性脉冲时滞双曲型偏微分方程的振动性

罗李平, 彭白玉, 欧阳自根

2009, 24(3): 439-444.

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In this paper, by making use of the calculous technique and some results of the impulsive differential inequality, oscillatory properties of the solutions of certain nonlinear impulsive delay hyperbolic partial differential equations with nonlinear diffusion coefficient are investigated. Sufficient conditions for oscillations of such equations are obtained.

二维全平面上具线性阻尼Navier-Stokes方程组的整体吸引子和渐近光滑效应

赵才地, 李用声, 周盛凡

2009, 24(3): 445-452.

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This paper studies the long time behavior of solutions to the Navier-Stokes equations with linear damping on R². The authors prove the existence of L²-global attractor and H¹-global attractor by showing that the corresponding semigroup is asymptotically compact. Thereafter, they establish that the two attractors are the same and thus reveal the asymptotic smoothing effect of the solutions.

参数的两自由度陀螺系统的一致有效解

欧阳成

2009, 24(3): 453-457.

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A general top system of two free dimensions with parameter is studied and the four cases satisfied by the frequency of the system are discussed. Using the multiple scale method, its uniformly valid asymptotic solution, which is expressed by complex amplitudes, of the first order is obtained. And solvable conditions satisfied by the complex amplitudes are given, and then the relative result is generalized.

一类并联冗余可修复系统解的线性稳定性

王鸿燕, 赵占锋, 亓正申

2009, 24(3): 458-463.

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In this paper, the solution of a parallel redundant repairable system is investigated.by using the method of functional analysis. Especially, the linear semigroups of operator theory on Banach space, we prove the existence of the strictly dominant eigenvalue, and show the linear stability of solution.

有限群的分解

闫杰生, 杨丽华

2009, 24(3): 464-468.

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In this paper, we investigate the conditions under which a finite group can be decomposed, and present several sufficient conditions for it decompose.

不等式约束最优化问题的可行SQP下降算法及其收敛性

张和平, 叶留青

2009, 24(3): 469-474.

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In this paper, the new SQP feasible descent algorithm for nonlinear constrained optimization problems presented, and under weaker conditions of relative, we proofed the new method still possesses global convergence and its strong convergence. The

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