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2012年 第27卷 第1期    刊出日期：2012-03-30

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一类高阶非线性微分方程解的存在问题

唐林山, 江成顺

2012, 27(1):  1-10. 

摘要 ( 36 )   PDF (413KB) ( 14 )  

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This paper is concerned with the following n-th ordinary differential equation: {u⁽ⁿ⁾(t) = ...=0, where a, c ∈ R, ≥, such that a²+b² >0 and c²+d²>0, n ≥ 2, f: [0,1] × R → R is a continuous function. Assume that f satisfies one-sided Nagumo condition, the existence theorems of solutions of the boundary value problem for the n-th-order nonlinear differential equations above are established by using Leray-Schauder degree theory, lower and upper solutions, a priori estimate technique. 


平面不可压缩的Navier-Stokes方程的一个新七模截断

王贺元, 崔妍, 黄敏

2012, 27(1):  11-17. 

摘要 ( 28 )   PDF (626KB) ( 25 )  

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A new seven-modes truncation of Fourier series of Navier-Stokes equations for a two-dimensional incompressible fluid on a torus is obtained. And its stationary solutions, the existence of attractor and the global stability of the equations are firmly proved. At the same time, several issues such as some basic dynamical behaviors and routs to chaos are shown numerically by changing Reynolds number. The system exhibits a stochastic behavior approached through an involved sequence of bifurcations.



慢变线性切换系统的镇定

张兵, 梁童

2012, 27(1):  18-23. 

摘要 ( 31 )   PDF (307KB) ( 20 )  

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The stabilization problem of systems that switch among a finite set of slowly varying linear systems with arbitrary switching frequency is discussed. It is shown that if the entries of the pointwise stabilizing feedback gain matrix are continuously differentiable functions of the entries of the system coefficient matrices, then the closed-loop system is uniformly asymptotically stable if the rate of time variation of the system coefficient matrices is sufficiently small.



半无穷区间上二阶三点边值问题的多个正解的存在性

孙艳梅

2012, 27(1):  24-28. 

摘要 ( 35 )   PDF (271KB) ( 15 )  

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In this paper, we are concerned with the existence of multiple positive solutions to a second-order three-point boundary value problem on the half-line. The results are obtained by the Leggett-Williams fixed point theorem.



椭圆方程在Orlicz类中的正则估计

陶祥兴, 方益

2012, 27(1):  29-35. 

摘要 ( 36 )   PDF (341KB) ( 61 )  

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The purpose of this paper is to give the element proof of the regularity estimates in Orlicz classes for the second order derivatives of the solutions to the general second order elliptic equations. The global regularities in Orlicz for the second order derivatives of the solutions of the Dirichlet problems are also given.



完全多部图的无符号Laplacian特征多项式

卢世芳, 赵海兴

2012, 27(1):  36-40. 

摘要 ( 44 )   PDF (268KB) ( 40 )  

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For a simple graph G, let matrix Q(G)=D(G) + A(G) be it’s signless Laplacian matrix and Q_G(λ)=det(λI Q) it’s signless Laplacian characteristic polynomial, where D(G) denotes the diagonal matrix of vertex degrees of G, A(G) denotes its adjacency matrix of G. If all eigenvalues of Q_G(λ) are integral, then the graph G is called Q-integral. In this paper, we obtain that the signless Laplacian characteristic polynomials of the complete multi-partite graphs G=K_{n1,n2,···,nt}. We prove that the complete t-partite graphs K_{(n,n,···,n)}t are Q-integral and give a necessary and sufficient condition for the complete multipartite graphs K_{(m,···,m)s(n,···,n)}t to be Q-integral. We also obtain that the signless Laplacian characteristic polynomials of the complete multipartite graphs K_{(m,···,m,)}s_{1(n,···,n,)}s_{2(l,···,l)}s₃. 


量子Yang-Baxter方程的1/2旋子的奇异上三角型解(Ⅱ)

王轲, 王欣, 李娴

2012, 27(1):  41-53. 

摘要 ( 31 )   PDF (424KB) ( 27 )  

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In these two papers (Ⅰ) and (Ⅱ), the singular upper triangle type solutions with spin 1/2 of quantum Yang-Baxter equation are given. In the Paper (Ⅱ), we give the general solutions of the Yang-Baxter equation in this case.



两参数指数分布经验贝叶斯检验:定数截尾情形

王亮, 师义民, 常萍

2012, 27(1):  54-58. 

摘要 ( 34 )   PDF (270KB) ( 15 )  

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The empirical Bayes test problem is considered for scale parameter of two-parameter exponential distribution under type-II censored data. By using wavelets estimation method, the EB test function is constructed, of which the asymptotic optimality and convergence rates are obtained. Finally, an example concerning the main result is given.





一类Sierpinski垫片的Hausdorff测度的估计

张云秀, 顾惠

2012, 27(1):  59-62. 

摘要 ( 30 )   PDF (242KB) ( 39 )  

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Suppose F₀ is an arbitrary triangle and F is a kind of Sierpinski carpet generated by F₀. We construct a projection mapping to obtain the lower bound of the Hausdorff measure of F; meanwhile the upper bound of the Hausdorff measure of F is calculated by the general covering.



一个新的GLKKM定理及其对抽象经济的应用

文开庭

2012, 27(1):  63-67. 

摘要 ( 34 )   PDF (252KB) ( 33 )  

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In this paper, a new GLKKM theorem in L-convex spaces is established. As applications, a new fixed point theorem and a maximal element theorem are obtained in Lconvex spaces. Finally, equilibrium existence theorems for economies and qualitative games in L-convex spaces are yielded.



有变量核的分数次积分算子交换子的CBMO估计

王立伟, 束立生, 瞿萌

2012, 27(1):  68-73. 

摘要 ( 39 )   PDF (327KB) ( 42 )  

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In this paper, the authors introduce the central bounded oscillation space CBMOq(Rⁿ), let [b,T_α] be the commutator generated by fractional integral operators with variable kernels and CBMO function, we establish the boundedness of [b,T_α] on homogeneous Morrey-Herz spaces.



内点同伦方法求解更一般非凸集上的不动点问题

苏孟龙, 刘麦学

2012, 27(1):  74-78. 

摘要 ( 31 )   PDF (247KB) ( 19 )  

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In this paper, we are mainly devoted to solving fixed point problems in more general nonconvex sets via an interior point homotopy method. Under suitable conditions, a constructive proof is given to prove the existence of fixed points, which can lead to an implementable globally convergent algorithm.



尖点形式L函数的广义零点密度估计

李英杰

2012, 27(1):  79-86. 

摘要 ( 30 )   PDF (380KB) ( 39 )  

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In this paper a zero-density estimate of the large sieve type is given for the automorphic L-function L_f(s,χ), where f is a holomorphic cusp form and χ a Dirichlet character of mod q.



着色的琼斯函数

韩友发, 阎昕明, 吕丽莉

2012, 27(1):  87-91. 

摘要 ( 25 )   PDF (1069KB) ( 21 )  

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In this paper, we discuss the properties of the colored Jones function of knots. Particularly, we calculate the colored Jones function of some knots(3₁,4₁,5₁,5₂). Furthermore, one can compute the Kashaev’s invariants and study some properties of the Kashaev’s conjecture.



圈和完全图的点可区别VE-全染色

辛小青, 陈祥恩, 王志文

2012, 27(1):  92-97. 

摘要 ( 37 )   PDF (297KB) ( 29 )  

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Let G be a simple graph of order at least 2. A VE-total-coloring using k colors of a graph G is a mapping f from V (G) E(G) into {1,2,···,k} such that no edge receives the same color as one of its endpoints. Let C(u)={f(u)} {f(uv) | uv ∈ E(G)} be the color-set of u. If C(u)=C(v) for any two vertices u and v of V (G), then f is called a k-vertex-distinguishing VE-total coloring of G or a k-VDVET coloring of G for short. The minimum number of colors required for a VDVET coloring of G is denoted by χ^ve_vt(G) and it is called the VDVET chromatic number of G. In this paper we get cycle C_n, path P_n and complete graph K_n of their VDVET chromatic numbers and propose a related conjecture. 


U(4,Z)的自同构群

王玉雷, 孙大为, 王志俊

2012, 27(1):  98-103. 

摘要 ( 61 )   PDF (306KB) ( 17 )  

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In this paper, the automorphism group of G is determined, where G is a 4 × 4 upper unitriangular matrix group over Z. Let K be the subgroup of AutG consisting of all elements of AutG which act trivially on G/G, G /ζG and ζG, then (i) InnG K AutG; (ii) AutG/K≌=G₁×D₈×Z₂, where G₁=(a,b,c|a⁴=b²=c²=1, a^b=a^-1, [a,c]= [b,c]=1; (iii) K/InnG≌=Z×Z×Z.



非交换的Kolmogorov不等式和Zygmund不等式 

吴田峰, 周佳, 王运霞

2012, 27(1):  104-109. 

摘要 ( 39 )   PDF (296KB) ( 30 )  

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In this paper, we discuss some properties of distribution functions of τ-measurable operators and obtain non-commutative analogue of Kolmogorov inequality and Zygmund inequality.



权分担三个公共值的亚纯函数的唯一性定理

王新利, 曹璋龙

2012, 27(1):  110-116. 

摘要 ( 35 )   PDF (301KB) ( 23 )  

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In this paper, with the idea of weighted sharing values, we deal with the problem of uniqueness of mesomorphic functions sharing three weighted values. We obtain some theorems which improve the results of H X Yi and W R Lu.



分数阶时滞微分系统的滑模控制

司家芳, 蒋威

2012, 27(1):  117-122. 

摘要 ( 24 )   PDF (271KB) ( 9 )  

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The problem of sliding mode control for fractional differential systems with statedelay is considered. A novel sliding surface is proposed and a controller is designed correspondingly, such that the state starting from any initial value will move toward the switching surface and reach the sliding surface in finite time and the state variables on the sliding surface will converge to equilibrium point. And the stability of the proposed control design is discussed.



模糊粗糙群中的同态映射

秦克云, 张晓华

2012, 27(1):  123-127. 

摘要 ( 35 )   PDF (267KB) ( 27 )  

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This paper is devoted to the discussion of homomorphic properties of fuzzy rough groups. The fuzzy approximation space was generated by fuzzy normal subgroups and the fuzzy rough approximation operators were discussed in the frame of fuzzy rough set model. The basic properties of fuzzy rough approximation operators were obtained.



环的Extensions扩张与余纯维数

卢博

2012, 27(1):  128-132. 

摘要 ( 24 )   PDF (240KB) ( 28 )  

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Let R be a noetherian ring and S an excellent extension of R. cid(M) denotes the copure injective dimension of M and cfd(M) denotes the copure flat dimension of M. We prove that if M S is a right S-module then cid(M S)=cid(M R) and if S M is a left S-module then cfd(S M)=cfd(R M). Moreover, cid-D(S)=cid-D(R) and cfd-D(S)=cfdD(R).



向量优化问题的对偶性

黄龙光

2012, 27(1):  133-138. 

摘要 ( 40 )   PDF (273KB) ( 43 )  

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Duality framework on vector optimization problems in a locally convex topological vector space are established by using scalarization with a cone-strongly increasing function. The dualities for the scalar convex composed optimization problems and for general vector optimization problems are studied. A general approach for studying duality in vector optimization problems is presented.



关于Wrpp半群上的Lawson偏序

刘海军, 郭小江

2012, 27(1):  139-144. 

摘要 ( 34 )   PDF (268KB) ( 20 )  

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In this paper, we introduce Lawson partial order ≤w on wrpp semigroups. After obtaining some properties of ≤w, we determine when ≤w is (left; right) compatible with the multiplication. These results extend and enrich the related results of Lawson and GuoLuo on abundant semigroups, of Guo-Shum on rpp semigroups and of Liu-Guo on wrpp semigroups.



具有连续分布偏差变元的双曲型微分方程振动准则的进一步结果

张蒙, 宋国华

2012, 27(1):  145-151. 

摘要 ( 28 )   PDF (331KB) ( 18 )  

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A class of hyperbolic equations with continuous distributed deviating arguments is considered and its oscillation theorems are discussed. These theorems are of higher degree of generality and deal with the cases which are not covered by the known criteria. Particularly,these criteria extend and unify a number of existing results.



盒子型区域上变分不等式的一个光滑牛顿法

谢亚君, 马昌凤

2012, 27(1):  152-158. 

摘要 ( 29 )   PDF (317KB) ( 20 )  

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The box constrained variational inequality problem can be reformulated as a nonsmooth equation by using median operator. In this paper, we present a smoothing Newton method for solving the box constrained variational inequality problem based on a new smoothing approximation function. The proposed algorithm is proved to be well defined and convergent globally under weaker conditions.