WANGMU Jiang-shan, YUAN Jun, LIN Shang-wei, WANG Shi-ying

2010, 25(3): 317-326.

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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.

Some Rogers-Ramanujan-Bailey Type Identities

ZHANG Zhi-zheng, ZHANG Ying

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.

Initial Boundary Value Problems for a Class of Non-linear Pseudo-parabolic Equation

GUO Hong-xia, HAN Xian-jun

2010, 25(3): 335-343.

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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.

Existence and Uniqueness of the Nonlinear BSDEs with a Small Parameter under Locally Lipschitz Condition

XIE Zhen-yun, XIA Ning-mao

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.

Blow-up for a Class of Degenerate Reaction-diffusion Equation with Nonlocal Source

CUI Guo-zhong, GAO Yan-ling, GUO Cong-zhou

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.

Rigidity Theorems of Spacelike Submanifolds in de Sitter Spaces

CHEN Wei, GUO Zhen

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.

Limiting Distribution of Extreme Values for FGM Random Sequences

ZHANG Jian, ZHANG Ling

2010, 25(3): 366-371.

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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.

Asymptotically Optimal Empirical Bayes Estimation of Parameter for Scale-exponential Family under PA Samples

FAN Guo-liang, LING Neng-xiang, XU Hong-xia

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.

Existence of Solutions to Multi-point BVP with p-Laplacian at Resonance

LI Li-fang, GE Wei-gao

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.

A New GMλ-KKM Theorem and Its Application to Saddle Points

WEN Kai-ting

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.

Extended l∗-Module

NIU Yu-qi, MENG Xiao-ran, YUAN Jian

2010, 25(3): 390-398.

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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.

Large Deviations for a Generalized Compound Renewal Risk Model

GAO Shan

2010, 25(3): 399-406.

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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.

Existence of Two Periodic Solutions of a Delayed Single Species Model with Feedback Regulation and Harvest Term

TIAN De-sheng, CAI Guang-xing, YANG Ce-ping

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.

A Class of Analytic Functions of Complex Order

LI Shu-hai, YANG Jing-yu

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].

Application of the Conditional Nonlinear Optimal Perturbations Method in a Theoretical Grassland Ecosystem

WANG Bo, WANG Jian-ping, HUO Zhen-hua, ZHANG Pei-jun, WANG Qiang

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.

Base-mesocompact Spaces

CAO Jin-wen, SONG Ji-ping, LIU Hui

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.

Characterization and Applications of Semi-E-preinvex Functions

QUAN Jing, LONG Xian-jun, PENG Zai-yun, TAN Ying-shuang

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.

A New Nonlinear Conjugate Gradient Method for Unconstrained Optimization Problems

LIU Jin-kui, WANG Kai-rong, SONG Xiao-qian, DU Xiang-lin

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.

Mean-square Exponential Robust Stability for a Class of Grey Stochastic Systems with Distributed Delays

LI Jing-jie, SU Chun-hua

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.

Cryptanalysis of Threshold-proxy Threshold-signature Schemes

HAN Jin-guang, KANG Bao-yuan

2010, 25(3): 459-463.

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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.

Hàjek-Rèniy Type Inequality for Banach Space Valued Martingales and Its Applications

GONG Xiao-bing

2010, 25(3): 464-469.

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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].

An Invariance Principle for ρ^-Mixing Random Sequences

LIU Xiao-ping, YAN Han, WU Qun-ying

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).

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