Table of Content

30 June 2012, Volume 27 Issue 2

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The Construction of a Class of Measure-valued Processes of Stochastic Flows

ZHANG Xiang-wei, WANG Jian-ping

2012, 27(2):  159-164. 

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In this article, we give a description of measure-valued processes with interactive stochastic flows. It is a unified construction for superprocesses with dependent spatial motion constructed by Dawson, LI, Wang and superprocesses of stochastic flows constructed by Ma and Xiang.



On a Restrict m-ary Partition Function 

CHEN Shi-chao, CHE Ying-tao

2012, 27(2):  165-168. 

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Let n,m,k be positive integers and b_m,k be the number of representations of n as n = m^a0 + ma1 + ··· + m^aj with 0 ≤ a₀ ≤ a₁ ≤···≤ a_j<k. In this note, we obtain some congruences and distribution properties of b_m,k.

L_b-coequalizers and L_b-regular Epimorphisms in the Category of L-sets and Bi-induced Maps

ZHANG Hong, TANG Jian-gang, LI Guo-hua

2012, 27(2):  169-176. 

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In this paper, it gives the definition of the category of L-sets and bi-induced maps whose true value set is a Locale, a complete Heyting algebra. In this category it defines the L_b-monomorphisms and the L_b-epimorphisms. Especially, it gives the definition, the judgmental theorem of L_b-coequalizers. Furthermore, it defines L_b-regular epimorphisms and proves the judgmental theorem. At the end it concludes a result: the category of L-sets and bi-induced maps is finitely cocomplete. 

Periodic Solutions of Mixed Type p-Laplacian Equations with Deviating Arguments

WANG Xiao-ming

2012, 27(2):  177-182. 

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Based on Manasevich-Mawhin continuation theorem and some analysis skill, some sufficient conditions for the existence of periodic solutions for mixed type p-Laplacian equation with deviating arguments are established, which are complement of previously known results.

Stable-range Approach to the (2+1)-dimensional Breaking Soliton and Kadomtsev-Petviashvili Equations

ZHANG Ying, LI Ji-na, ZHANG Jiang-hong, SONG Xiao-qian

2012, 27(2):  183-190. 

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By using Xu’s stable-range method, families of explicit exact solutions with multiple parameter functions for the (2+1)-dimensional breaking soliton and Kadomtsev-Petviashvili equations. These parameter functions make our solutions more applicable to related practical models and boundary value problems.





The H₂-cordiality of K_n

CAO Xiang-dong, LIU Zhi-shan

2012, 27(2):  191-195. 

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In this paper, we correct a flaw for the H₂-cordiality of K_n appeared in M. Ghebleh and R Khoeilar’s paper, and give a necessary and suflcient condition for a complete graph K_n to be H₂-cordial.



Stability and Bifurcation Analysis of Man-machine System with Time Delay

YANG Ji-hua, LIU Mei

2012, 27(2):  196-203. 

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A mathematical model of man-machine system is considered. Based on the reference [4], the direction and stability of the Hopf bifurcation are determined using the normal form method and the center manifold theory. Furthermore, the existence of Hopf-zero bifurcation is discussed. In the end, some numerical simulations are carried out to illustrate the results found.



Products of Extended Ces`aro Operator and Composition Operator from Generalized Besov Spaces to Zygmund Spaces

OUYANG Xiao-rong

2012, 27(2):  204-212. 

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We characterize the boundedness and compactness of the product of extended Cesaro operator and composition operator T_gC_φ from generalized Besov spaces to Zygmund spaces, where g is a given holomorphic function in the unit disk D, φ is an analytic self-map of D and T_gC_φ is defined by T_gC_φf(z) = f(φ(t))g’(t)dt from t=0 to z.





A Note on s-quasinormally Embedded and c-supplemented Subgroups of Finite Groups

LI Chang-wen, HU Bin

2012, 27(2):  213-217. 

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In this paper the influence of s-quasinormally embedded and c-supplemented subgroups on the p-nilpotency of finite groups is investigate and some recent results are generalized.



Generalizations of Euler Inequality in the n-dimensional Euclidean Space

WANG Wen, YANG Shi-guo

2012, 27(2):  218-223. 

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The relation between the circum-radius and the in-radius of an n-dimensional simplex in En is studied. Two new generalizations of Euler inequality for the n-dimensional simplex are established. Besides, we obtain some stronger generalizations of Euler inequality for the n-dimensional simplex than previously known results.



New Exact Solutions for the Generalized (2+1)-dimensional Nonlinear Schrodinger Equation with Variable Coefficients

JIANG Zhi-ping

2012, 27(2):  224-231. 

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With the help of the variable-coefficient generalized projected Ricatti equation expansion method, we present exact solutions for the generalized (2+1)-dimensional nonlinear Schrdinger equation with variable coefficients. These solutions include solitary wave solutions, soliton-like solutions and trigonometric function solutions. Among these solutions, some are found for the first time.



Large-time Behavior of Solutions for Parabolic Conservation Laws with Large Initial Data

WANG Li-juan

2012, 27(2):  232-237. 

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In this paper, we study the large-time behavior of periodic solutions for parabolic conservation laws. There is no smallness assumption on the initial data. We firstly get the local existence of the solution by the iterative scheme, then we get the exponential decay estimates for the solution by energy method and maximum principle, and obtain the global solution in the same time.





The Modified Adomian Decomposition Method for Nonlinear Fractional Boundary Value Problems

WANG Jie

2012, 27(2):  238-245. 

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We use the modified Adomian decomposition method(ADM) for solving the nonlinear fractional boundary value problem {D(α0) + u(x) = f(x, u(x)), 0 < x < 1, 3 < α≤ 4 u(0) = α0, u’’ (0) = α2 u(1) = β0, u’’(1) = β2} (1) where D(0α)+u is Caputo fractional derivative and α0, α2, β0, β2 is not zero at all, and f:[0,1]×R→ R is continuous. The calculated numerical results show reliability and efficiency of the algorithm given. The numerical procedure is tested on linear and nonlinear problems. 





Prime MP-filter Spaces of Fuzzy Implication Algebras

LIU Chun-hui, XU Luo-shan

2012, 27(2):  246-253. 

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In this paper, the topological space (PFMP(X), T) based on prime MP-filters of a lattice FI-algebra X is constructed firstly and we proved that it is a compact T₀-space if X with condition (P). Secondly, we restricted T to the set of all maximal MP-filters MFMP(X) of X and concluded that (PFMP(X), T |(PFMP(X))) is a compact T₂ space if X with conditions (P) and (S).





Periodic Solutions to a Delayed Semi-ratio Dependent Diffusion System on Time Scales

LIU Zhen-jie, FANG Xiao-chao, LI Ming, GAO Zhi-ying

2012, 27(2):  254-258. 

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In this paper, we investigate the existence of periodic solutions of a semi-ratio-dependent predator-prey diffusion system with functional responses and time delays in a two-patch environment on time scales by using a continuation theorem based on coincidence degree theory.



On the Busemann-Petty’s Problem for L_p-intersection Body

MA Tong-yi

2012, 27(2):  259-269. 

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Haberl and Ludwig introduced the L_p-intersection body I_pK for an origin-symmetric star body K in R_n, where p < 1 and p ≠ 0. In this paper, we consider the Busemann-Petty’s problem for L_p-intersection bodies I_pK and I_pL. That is, whether I_pK  I_pL implies Vol_n(K) ≤ Vol_n(L). We obtain that for two origin-symmetric star bodies K and L in Rn, such that (Rn, ||·||K) embeds in L_p and I_pK  IpL, then vol_n(K) ≤ vol_n(L) for 0 < p < 1 and vol_n(K) ≥ vol_n(L) for p < 0. 

N-soliton Solution for Hirota-Satsuma Equation

WEI Han-yu, TONG Yan-chun, XIA Tie-cheng

2012, 27(2):  270-273. 

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In this work, using the Hirota bilinear method, N-soliton solution is obtained for Hirota-Satsuma nonlinear evolution equation: u_t- u_xxt-3u_xu_t+u_x= 0.





Fundamental Solution for Weighted Baouendi-Grushin Type Operators and a Class of Weighted Hardy Inequality

DI Yan-mei, JIN Yong-yang, SHEN Shou-feng, JIANG Li-ya

2012, 27(2):  274-279. 

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In this paper we obtain the fundamental solution for a class of weighted Baouendi-Grushin type operator L_p,γ,αu = ▽_γ·(|▽_γu|^p-2ρ^α▽_γu) on R^m+n with singularity at the origin, where ▽_γ is the gradient operator defined by ▽_γ =(▽_x,|x|^γ▽_y) and ρ is the distance function. As an application, we get some Hardy type inequalities associated with ▽_γ.





Global Behavior of Nonnegative Solutions to a Higher Order Difference Equation

SHI Qi-hong, YANG Jian-wei, WANG Chang-you

2012, 27(2):  280-285. 

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This paper is concerned with the following nonlinear difference equation: xn+1=… (1.1). The more simple suffcient conditions of asymptotic stability are obtained by using a smart technique, which extends and includes partially corresponding results obtained in the references [6-9]. The global behavior of the solutions is investigated. In addition, in order to support analytic results, some numerical simulations to the special equations are presented. 

A New Class of Harmonic Univalent Functions

LI Shu-hai, MA Li-na

2012, 27(2):  286-292. 

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A complex-valued harmonic function that is univalent and sense preserving in the unit disk U can be written in the form of f = h + g, where h and g are analytic in U. We define and investigate a new class LH_λ(α,β) by generalized Salagean operator of harmonic univalent functions. We give sufficient coefficient conditions for normalized harmonic functions in the class LH_λ(α,β). These conditions are also shown to be necessary when the coefficients are negative. This leads to distortion bounds and extreme points. 

Existence of Positive Solutions to Boundary Value Problem for a Nonlinear Fractional Differential Equation

SONG Li-mei, WENG Pei-xuan

2012, 27(2):  293-300. 

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In this paper, we study a Dirichlet-type boundary value problem (BVP) of nonlinear fractional differential equation with an order α∈(3,4], where the fractional derivative D^α_o+ is the standard Riemann-Liouville fractional derivative. By constructing the Green function and investigating its properties, we obtain some criteria for the existence of one positive solution and two positive solutions for the above BVP. The Krasnosel’skii fixed-point theorem in cones is used here. We also give an example to illustrate the applicability of our results. 

Periodic Solutions and Global Attractivity of an Impulsive Host-macroparasite Model with Delays

SHAO Yuan-fu, TANG Guo-qiang

2012, 27(2):  301-307. 

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By using Mawhin continuation theorem, an important lemma and some analysis techniques, sufficient conditions ensuring the existence and global attractivity of positive periodic solutions for an impulsive differential equation with time varying delay are investigated.



On the Trees Whose Hosoya Indices Belong to a Closed Interval

YE Cheng-fu

2012, 27(2):  308-316. 

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Let n and d be two positive integers. By B_n,d we denote the graph obtained by identifying an endvertex of path P_d with the center of star S_n-d+1, where n ≥ d + 1. By C_n,d we denote the graph obtained by identifying an endvertex of P_d-1 with the center of Stare S_n-d, and the other endvertex of P_d-1 with the center of S₃ where n ≥ d + 3. By E_n,d,k we denote the graph obtained by identifying the vertex v_k of P(v₁ - v₂ - ··· - v_d+1) with the center of Sn-d. In this paper, we completely characterize all trees T which have diameter at least d(d ≥ 3) and satisfy the following conditions: (i) Z(B_n,d) ≤ Z(T) ≤ Z(E_n,d,3) for n = d + 3; (ii) Z(B_n,d) ≤ Z(T) ≤ Z(C_n,d) for n ≥ d + 4.