王牟江山, 原军, 林上为等

2010, 25(3): 317-326.

摘要 ( 10 )

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A digraph D is k-ordered if for every sequence S : v₁, v_2,· · · , v_k of k distinct vertices, there exists a cycle C such that C encounters the vertices of S in the specified order. In particular, we say that D is k-ordered hamiltonian if for every sequence S : v_1, v_2,· · · , v_k of k distinct vertices, there exists a hamiltonian cycle C such that the vertices of S are encountered on C in the specified order. In this paper, sufficient conditions for digraphs to be ordered and ordered hamiltonian have been given.

若干Rogers-Ramanujan-Bailey型恒等式

张之正, 张颖

2010, 25(3): 327-334.

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By introducing multiparameter generalization of Bailey pair, the purpose of this paper is to find a number of new Rogers-Ramanujan-Bailey type identities.

一类非线性拟抛物方程的初边值问题

郭红霞, 韩献军

2010, 25(3): 335-343.

摘要 ( 20 )

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In this paper, the existence, the uniqueness, the asymptotic behavior and the non-existence of the global generalized solutions of the initial boundary value problems for the non-linear pseudo-parabolic equation u_t-αu_xx-βu_xxt=F(u)-βF (u)_xx are proved, where α, β > 0 are constants, F(s) is a given function.

带小参数的非线性倒向随机微分议程在局部Lipschitz条件下解的存在唯一性

谢臻赟, 夏宁茂

2010, 25(3): 344-351.

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In this paper we study the following nonlinear BSDE: y(t) +... , t ∈ [0,1], where ε is a small parameter. The coefficient f is locally Lipschitz in y and z, the coefficient g 1 is locally Lipschitz in y, and the coefficient g 2 is uniformly Lipschitz in y and z. Let L N be the locally Lipschitz constant of the coefficients on the ball B(0,N) of R^d×R^d×r. We prove the existence and uniqueness of the solution when L_N ～√ logN and the parameter ε is small.

一类具非局部源的退化反应扩散方程的爆破性质

崔国忠, 高艳玲, 郭从洲

2010, 25(3): 352-359.

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This paper deals with the properties of the solution to a class of nonlocal degenerate reaction-diffusion equation with nonlocal source, subject to the null Dirichlet boundary condition. We first give sufficient conditions for that the solution exists globally or blows up in the finite time. Then the blow-up time is also given. At last, we obtain a property differing from the local source which the blow-up set is the entire interval.

de Sitter空间中类空子流形的刚性定理

陈伟, 郭震

2010, 25(3): 360-365.

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In this paper, we study the compact spacelike submanifolds in the de Sitter space, under the assumption that the normalized mean curvature vector is parallel in the normal bundle. Using the generalized Cheng-Yau’s differential operator, we obtain some general rigidity theorems which naturally generalize some existing results.

FGM随机序列极值的极限分布

张建, 张玲

2010, 25(3): 366-371.

摘要 ( 11 )

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This paper mainly study extreme values of FGM random sequences. We prove a technique theorem by the dependence structure of FGM sequences, and further obtain the limiting distributions of maxima and k-th largest for stationary FGM random sequences.

PA样本下刻度指数族参数的渐近最优的经验Bayes估计

范国良, 凌能祥, 徐红霞

2010, 25(3): 372-378.

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The Bayes estimator of the parameter is obtained for the scale exponential family in the case of identically distributed and positively associated(PA) samples under weighted square loss function. We construct the empirical Bayes(EB) estimator and prove it is asymptotic optimal.

一类p-Laplacian算子多点边值问题在共振条件下解的存在性

李丽芳, 葛渭高

2010, 25(3): 379-384.

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This paper is concerned with the existence of solutions for the following multipoint boundary value problem at resonance {(Φp (x’))’ + f(t,x)=0,0 < t < 1,...,0 < ξ < 1. An existence theorem is obtained by using the extension of Mawhin’s continuation theorem. Since almost all the multi-point boundary value problem at resonance in previous papers are for the linear operator without p-Laplacian by the use of Mawhin’s continuation theorem, our method is new.

一个新的GMλ-KKM定理及其鞍点的应用

文开庭

2010, 25(3): 385-389.

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In this paper, a new GMλ-KKM theorem is established for noncompact λ-hyperconvex metric spaces. As applications, the properties of the solution set of the variational inequality is shown and an existence theorem for saddle points is obtained.

推广的l*-模

牛裕琪, 孟晓然, 袁俭

2010, 25(3): 390-398.

摘要 ( 14 )

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Theory of uncertainty reasoning base on l-module of true value field, in this paper, an extended l-module was proposed, some properties and lattice measure were discussed, then the lattice integral on l-module was gained.

一类推广更新风险模型的大偏差

高珊

2010, 25(3): 399-406.

摘要 ( 15 )

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This paper extends the ordinary renewal risk model to the case where the premium income process, based on a renewal counting process, is no longer a linear function; and the total claim amount process is described by a compound renewal process. For this realistic risk model, the large deviations for the claim surplus process is investigated.

具有反馈控制和收获项的时滞单物种模型两个周期解的存在性

田德生, 蔡光兴, 杨策平

2010, 25(3): 407-413.

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By means of the continuation theorem of the coincidence degree theory, the existence of two periodic solutions of a delayed single species model with feedback regulation and harvest term is obtained.

一类复阶解析函数

李书海, 杨静宇

2010, 25(3): 414-421.

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In this paper, the integral expression, coefficient inequality and distortion theorems are given for the class of analytic functions L(λ,b,A,B) which defined by making use of Ruscheweyh derivatives. This paper spreads the result of [6].

条件非线性最优扰动方法在理论草原生态模型中的应用

王波, 王建平, 霍振华等

2010, 25(3): 422-429.

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Using a simplified nonlinearly theoretical grassland ecosystem proposed by Zeng et al., we study the sensitivity and nonlinear instability of the grassland ecosystem to finite amplitude initial perturbations with the approach of conditional nonlinear optimal perturbation (CNOP). The results show that the linearly stable grassland (desert or latent desert) states can turn to be nonlinearly unstable with finite amplitude initial perturbations. When the precipitation is between the two bifurcation points, a large enough finite amplitude initial perturbation can induce a transition between the grassland state the desert state or the latent desert.

基-中紧空间

曹金文, 宋际平, 刘徽

2010, 25(3): 430-435.

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In this paper the notation of base-mesocompactness is introduced and the following results are mainly obtained: (1) Let X be base-mesocompact and X’ an F σ subset of X. If X is normal, then X’ is base-mesocompact relative to X. (2) Let f: X → Y be a base-mesocompact mapping, ω(X) be a regular cardinality of X and ω(X) ≥ω(Y). If Y is base-mesocompact and regular, then X is base-mesocompact. (3) Let f: X → Y be a closed lindel of mapping with regular domain and regular range. If Y is base-mesocompact, then X is base-mesocompact. (4) Let X be base-mesocompact. If Y is locally compact and base-esocompact, then X × Y is base-mesocompact.

半E预不变凸函数的性质和应用

全靖, 龙宪军, 彭再云, 谭英双

2010, 25(3): 436-443.

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A class of sets called E-invex sets and a class of functions called E-preinvex functions, semi-E-preinvex functions and generalized semi-E-preinvex functions are introduced. They are the generalizations of E-convex sets, E-convex functions and semi-E-convex functions respectively, also the generalizations of invex sets and preinvex functions. Furthermore some optimality results of mathematical programming problems involved semi-E-preinvex functions and generalized semi-E-preinvex functions are obtained.

求解无约束优化问题的一种新的非线性共轭梯度法

刘金魁, 王开荣, 宋晓倩, 杜祥林

2010, 25(3): 444-450.

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In this paper, an efficient conjugate gradient method is given to solve the general unconstrained optimization problems, which can guarantee the sufficient descent property and the global convergence with the strong Wolfe line search conditions. Numerical results show that the new method is efficient and stationary by comparing with PRP+ method, so it can be widely used in scientific computation.

一类灰色随机分布时滞系统的均方指数鲁棒稳定性

李景杰, 苏春华

2010, 25(3): 451-458.

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Two easily verified delay-dependent criteria of mean-square exponential robust stability are obtained by constructing Lyapunov-Krasovskii functional and employing the decomposition technique of the continuous matrix-discovered set of grey matrix and Ito formula. A numerical example shows the validity and practicality of the criteria presented in this paper.

门限代理门限签名方案的密码学分析

韩金广, 亢保元

2010, 25(3): 459-463.

摘要 ( 16 )

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Recently, Hwang et al proposed a (t,n) threshold-proxy (c,m) threshold-signature schemes, in which only any t or more original signers of n original signers can authorize a proxy group of m proxy signers and then only c or more proxy signers can cooperatively generate threshold-proxy threshold-signature. In this scheme, they claimed that original signers cannot forge the proxy signature and the proxy signers cannot forge signature on behalf of the original signers. However, in this paper, we will give a attack to show that their scheme can not resist impersonation attacks.

B值鞅的Hàjek-Rèniy型不等式及其应用

龚小兵

2010, 25(3): 464-469.

摘要 ( 12 )

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In this paper, we establish the Hàjek-Rèniy type inequality for Banach space valued martingales generalizing the recent results of Tómcs and L’ibor [1]. Then p-uniformly smoothable Banach space is characterized in terms of the Hàjek-Rèniy type inequality for Banach space valued martingales. Those results generalize the recent results of Gan Shixin [2].

ρ^-混合序列的不变原理

刘筱萍, 鄢寒, 吴群英

2010, 25(3): 470-474.

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In this paper, we establish an invariance principle for ρ^-mixing random sequences under some moment condition. The result improve and extend the relevant result of Wu(2003).

当期目录

一类非线性拟抛物方程的初边值问题