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2007年 第22卷 第2期    刊出日期：2007-06-30

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单位球Bⁿ上的Bohr不等式

王建飞, 刘太顺

2007, 22(2):  159-165. 

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Bohr’s type inequalities are studied in this paper: if f is a holomorphic mapping from the unit ball Bⁿ to Bⁿ, f(0)=p, then we have sum from ... and φ_P∈Aut(Bⁿ) such that φ_p=0. As corollaries of the above estimate, we obtain some sharp Bohr’s type modulus inequalities. In particular, when n=1 and |P|→1, then our theorem reduces to a classical result of Bohr. 


四个素数的平方及2的若干次幂和丢番图逼近

李伟平, 王天泽

2007, 22(2):  166-174. 

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Under certain condition, the inequality |λ₁p₁²+λ₂p₂²+λ₃p₃²+λ₄p₄²+μ₁2^x1+…+μ_s2^xs+γ|＜η has infinitely many solutions in primes p₁,p₂,p₃,p₄ and positive integers x₁,…,x_s.



非线性奇摄动系统的渐近性态

韩祥临

2007, 22(2):  175-178. 

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The asymptotic behavior of solution for a n-dimensional nonlinear singularly perturbed system is studied. Under the appropriate assumptions, the existence of solution for the system is proved and the estimation of the solution is given using the method of differential inequalities.



基于正交表的均匀Latin Hypercube设计及其构造

杨贵军

2007, 22(2):  179-186. 

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Orthogonal array-based uniform Latin hypercube design(uniform OALHD) is a class of orthogonal array-based Latin hypercube designs to have the best uniformity. In this paper, we provide a less computational algorithm to construct uniform OALHD in 2-dimensional space from Bundschuh and Zhu(1993). And some uniform OALHDs are con- structed by using our method.



乘积空间上的Calderón-Zygmund算子嵌套交换子

韩彦昌

2007, 22(2):  187-194. 

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Commutators of Calderon-Zygmund operators on product spaces to be study in the paper is the commutators of Sarah H Ferguson and Michael T Lacey. The LP boundedness of the nested commutators is proved on product spaces, where 1＜p＜∞.



非对称细胞神经网络的稳定性分析

李立平, 陈芳跃

2007, 22(2):  195-202. 

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This paper describes the problem of stability for one-dimensional Cellular Neural Networks(CNNs). A sufficient condition is presented to ensure complete stability for a class of special CNN’s with nonsymmetric templates, where the parameter in the output function is greater than or equal to zero. The main method is analysising the property of the equilibrium point of the CNNs system.





关于CPⁿ中共圆平坦全实极小子流形的一点注记

宋晓新, 粱宏伟

2007, 22(2):  203-206. 

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Let M be a concircularly flat totally real minimal submanifold in CP⁴. The infimum V_m of the volume V(M) of M is obtained, also the necessary and sufficient conditions of "V(M)=V_m" is given.

Volterra系统全局稳定、扇形稳定及关联稳定的一些新判据

刘锋, 葛照强

2007, 22(2):  207-211. 

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Stability of Volterra systems are discusses by subpositive definite matrix, and some new criterions for Volterra systems on overall situation stability, sector stability and connection stability are acquired. These results expand or improve some existing criterions.


奇异差分边值问题上下解方法的推广

胡卫敏, 韦俊

2007, 22(2):  212-219. 

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This paper presents new existence results for singular discrete boundary value problems. In particular our nonlinearity may be singular in its dependent variable and is allowed to change sign.


大型动态规划的分解算法

徐付霞, 史道济, 董永权, 王红丽

2007, 22(2):  220-224. 

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An approach about large dynamic programming based on discrete linear system with a quadratic index function is proposed by importing two Lagrange multipliers.


函数S-粗集及其规律特性

李东亚, 史开泉

2007, 22(2):  225-231. 

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Function S-rough sets(Function Singular rough sets) are defined by R-function equivalence class which has dynamic characteristic, and a function is s law, function S-rough sets have law characteristic. Function S-rough sets has these forms: function one direction S-rough sets, function two direction S-rough sets and dual of function one direction S-rough sets. This paper presents the law characteristic of function one direction S-rough sets and puts forward the theorems of law-chain-attribute and law-belt. Function S-rough sets is s new research direction of the rough sets theory. 


非协调元的各向异性插值误差估计

汪远征

2007, 22(2):  232-235. 

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The main aim of this paper is to study the local anisotropic interpolation error estimates. We show that the interpolation of a nonconforming element satisfy the anisotropic property for both the second and fourth order problems.


Manakov方程和导数Manakov方程的有限参数解

曹建莉

2007, 22(2):  236-244. 

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Finite-dimensional integrable Hamiltonian systems, obtained through the non- linearization of the 3×3 spectral problems associated with the Manakov and the derivative Manakov equations, are investigated. A generating function method is used to give a simple and effective way to prove the involutivity of integrals. Finite-parameter solutions of the Manakov and the derivative Manakov equations are calculated based on the commutative systems of ordinary differential equations with these integrals as Hamiltonians. 

格点上的非交换微分运算及其应用

刘震, 白永强, 李起升

2007, 22(2):  245-251. 

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By introducing the noncommutative differential calculus on the function space of the infinite/finite set and construct a homotopy operator, one prove the analogue of the Poincare lemma for the difference complex. As an application of the differential calculus, a two dimensional integral model can be derived from the noncommutative differential calculus.



欧氏空间上Co-regular集的表示式

邱玉文, 王莉萍, 赵希顺

2007, 22(2):  252-257. 

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For the computability of co-regular subsets in metric spaces, the properties of the co-regular subsets and several reasonable representations on co-regular sets have been suggested in this paper. As last, the ’weaker or stronger’ relations of these representations have been revealed.


广义Fibonacci数的一些求和公式

席高文, 刘麦学

2007, 22(2):  258-265. 

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This note provides the some sum formulas for generalized Fibonacci numbers. The results are proved using clever rearrangements, rather than using induction.



局部对称Lorentz空间中的具有常数量曲率的完备类空超曲面

张士诚, 吴报强

2007, 22(2):  266-275. 

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The complete space-like hypersurfaces with constant normal saclar curvature is discussed in a locally symmetric Lorentz space. A classified theorem is obtained by the operator L1 introduced by S Y Cheng and S T Yau [3].


一类带有未知控制方向的非线性系统的适应镇定问题

郑兆顺

2007, 22(2):  276-281. 

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The adaptive stabilization problem of nonlinear systems are studied. For a class of uncertain nonlinear systems with unknown control direction, we proposed a robust adaptive backstepping scheme withσ-modification by introducing Nussbaum function and Backstep- ping methods, and proved that all the signals of the closed-loop systems are bounded.


重尾随机变量和的大偏差

郭晓燕, 孔繁超

2007, 22(2):  282-289. 

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This paper is a further investigation of large deviations for sums of random variables Sn=sum form i=1 to n Xi and S(t)=sum form i=1 to N(t) Xi,(t≥0), where {X_n,n≥1) are independent identically distribution and non-negative random variables, and {N(t),t≥0} is a counting process of non-negative integer-valued random variables, independent of {X_n,n≥1}. In this paper, under the suppose F∈G, which is a bigger heavy-tailed class than C, proved large deviation results for sums of random variables. 

具有饱和项的捕食食饵系统正周期解的存在性

谢强军, 张花荣, 唐旭华

2007, 22(2):  290-295. 

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By the theory of periodic parabolic operators, Shauder estimates and bifurcation, the existence of positive periodic solutions for periodic prey-predator model with saturation is discussed. The necessary and sufficient conditions to coexistence of periodic system are obtained.


一维非单调流体模型在H²中解的整体存在性

吴中林, 徐娟娟

2007, 22(2):  296-304. 

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In this paper, we prove the existence in H₊², an incomplete metric subspace of H²×H²×H², of global solutions to the system for a one-dimensional non-monotone fluid in bounded domain Ω=(0,1). The results in this paper have improved those previously related results.



一类Hopf曲面上的全纯线丛的上同调

刘伟明, 苏简兵, 魏文斌

2007, 22(2):  305-311. 

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Let X be a non-primary Hopf Surface with Abelian fundamental groupπ, L_a line bundle on X, we give a formula for computing the dimension of cohomology H^q(X,Ω^P(L)) and the explicit results for non-primary exceptional Hopf surface.


一类微分差分方程的无穷守恒律及Backlund变换

杨潇, 王军民

2007, 22(2):  312-316. 

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In this paper, with the help of the Lax representation, we show the existence of infinitely many conservation laws for a differential-difference equation,which is one of the Ladic-Ablowitz hierarchy, and the conservation density and the associated flux are given for- mularlly. We also demonstrate the relation between a continuous partial differential equation and the differential-difference equation, and give Backlund transformation for the former.