一类随机流测度值过程的构造

张香伟, 王建平

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.

关于限制性m-位分拆函数

陈士超, 车颖涛

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 + m^a1 + ··· + m^aj with 0 ≤ a₀ ≤ a₁ ≤···≤ a_j<k. In this note, we obtain some congruences and distribution properties of b_m,k.

双诱导映射L集合范畴的L_b-余等值子和L_b-正则满态射

张红, 汤建钢, 李国华

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.

一类具多个偏差变元混合型p-Laplacian周期解

汪小明

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.

(2+1)维破裂孤子方程及Kadomtsev-Petviashvili方程的Stable-range解法

张颖, 李吉娜, 张江红, 宋晓倩

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.

K_n的H₂-cordiality性

曹向东, 刘峙山

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.

具时滞人机系统的稳定性与分支分析

杨纪华, 刘媚

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.

广义Besov空间到Zygmund空间的广义Cesàro算子与复合算子的积

欧阳小荣

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.

关于s-拟正规嵌人与c-可补子群的一个注记

李长稳, 胡滨

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.

欧氏空间En中Euler不等式的加强推广

王文, 杨世国

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.

广义2+1维变系数非线薛定愕方程新的准确解

蒋志萍

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.

大初值的抛物型守恒律方程解的大时间性态

王利娟

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.

非线性分数次边值问题改进的ADM解法

王洁

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.

Fuzzy蕴涵代数的素MP-滤子空间

刘春辉, 徐罗山

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).

时间测度上一类时滞半比率依赖扩散系统的周期解

刘振杰, 方小超, 李明, 高志英

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.

关于L_p-相交体的Busemann-Petty型问题

马统一

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 R_n, such that (R_n, ||·||K) embeds in L_p and I_pK I_pL, then vol_n(K) ≤ vol_n(L) for 0 < p < 1 and vol_n(K) ≥ vol_n(L) for p < 0.

Hirota-Satsuma方程的N-孤子解

魏含玉, 童艳春, 夏铁成

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.

加权Baouendi-Grushin型算子的基本解与一类加权Hardy不等式

狄艳媚, 金永阳, 沈守枫, 姜丽亚

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.

一类高阶差分方程非负解的全局行为

石启宏, 杨建伟, 王长有

2012, 27(2): 280-285.

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This paper is concerned with the following nonlinear difference equation: x_n+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.

一类新的单叶调和函数

李书海, 马丽娜

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.

非线性分数微分方程边值问题正解的存在性

宋利梅, 翁佩查

2012, 27(2): 293-300.

摘要 ( 7 )

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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.

一类脉冲时滞宿主一大寄生物系统周期解及全局吸引性

邵远夫, 唐国强

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.

Hosoya指标在一个闭区间的一类树的刻画

冶成福

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 S_n-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.

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一类随机流测度值过程的构造