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2004年 第19卷 第4期    刊出日期：2004-12-30

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关于b^p空间（0 < p < 1）

胡璋剑, 刘太顺

2004, 19(4):  331-337. 

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 Let 0 < p < 1. In this paper we prove that the Bergman norm on the p-th Bergman space bp(H) is equivalent to certain "normal direction norm" as well as certain "tangential direction norm", where H = R^n-1 × R₊ is the upper half space. As an application, we get the boundedness of harmonic conjugation operators on b^p(H).

关于粘性热传导流体可压缩Navier-Stokes方程的最大吸引子的注记

秦玉明, 王秀琴, 崔国忠

2004, 19(4):  338-345. 

摘要 ( 6 )   PDF (478KB) ( 3 )  

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This paper is concerned with the existence of maximal attractors in Hⁱ (i = 1, 2,4) for the compressible Navier-Stokes equations for a polytropic viscous heat conductive ideal gas in bounded annular domains Ωn in Rⁿ(n = 2,3).



关于严格蕴含系统的布尔值模型（续）

李娜, 刘华珂

2004, 19(4):  346-349. 

摘要 ( 4 )   PDF (218KB) ( 3 )  

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The reference [4] proved the consistency of S₁ and S₂ among Lewis’ five strict implication systems in the modal logic by using the method of the Boolean-valued model. But, in this method, the consistency of S₃, S₄ and S₅ in Lewis’ five strict implication systems is not decided. This paper makes use of the properties: (1) the equivalence of the modal systems S₃ and P₃, S₄ and P₄; (2) the modal systems P₃ and P4 all contained the modal axiom T(□p → p); (3) the modal axiom T is correspondence to the reflexive property in V^B. Hence, the paper proves: (a) ‖As₃1‖ = 1; (b) ‖AS₄1‖ = 1; (c) ‖AS₅l‖ = 1 in the model <V^B, R, ‖ ‖>(where B is a complete Boolean algebra, R is reflexive property in VB). Therefore, the paper finally proves that the Boolean-valued model V^B of the ZFC axiom system in set theory is also a Boolean-valued model of Lewis’ the strict implication system S³, S⁴ and S^5. 


两个广义框架互为对偶的新刻画

姚喜研

2004, 19(4):  350-354. 

摘要 ( 4 )   PDF (256KB) ( 5 )  

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In the paper, we introduce Bessel sets in a Hilbert space H, and give an equivalent condition that two Generalized Frames are duals to each other.


半对称度量循环联络的某些特征及曲率张量表示

赵培标, 宋鸿藻, 杨孝平

2004, 19(4):  355-361. 

摘要 ( 5 )   PDF (291KB) ( 3 )  

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The projective transformation of the special semi-symmetric metric recurrent connection is studied in this paper. First of all, an invariant under this transformation is granted; Secondly, by inducing of the invariant and making use of the properties that the corresponding covariant derivative keeps being fixed under the distinctness connection, the curvature tensor expression of the Riemannian manifold is posed at the same time.



L_∞模下的二维带宽问题

郝建修, 李湘露

2004, 19(4):  362-367. 

摘要 ( 7 )   PDF (208KB) ( 4 )  

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The two-dimensional bandwidth problem is to determine an embedding of graph G in a grid graph in the plane such that the longest edges are as short as possible. In this paper we study the problem under the distance of L_∞-norm.


关于一类Eisenstein数域

蒋剑军

2004, 19(4):  368-372. 

摘要 ( 5 )   PDF (188KB) ( 3 )  

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In this paper the author determine the factorization of p and the number of p-th subfields of the splitting field K of the irreducible binomial x^p-m(m is p-th powerfree and p | m) and obtain that all p-th subfields of K have power integral bases and the same discriminant.



非线性双曲型时滞偏微分方程解的振动性质

刘安平, 郭艳凤, 杨向辉

2004, 19(4):  373-378. 

摘要 ( 7 )   PDF (195KB) ( 2 )  

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In this paper, oscillatory properties of solutions of certain hyperbolic partial differential equations with multi-delays are investigated and a series of sufficient conditions for oscillations of the equations are established. The results fully indicate that the oscillations are caused by delays.



Szás型算子线性组合点态逼近的特征刻画

冯国

2004, 19(4):  379-384. 

摘要 ( 4 )   PDF (294KB) ( 2 )  

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In this paper, we use Ditzian-Totik modulus to study the pointwise approximation for the linear combinations of Szasz-type operators, and obtain the direct and converse theorem and the characterization of the pointwise approximation for the linear combinations of Szasz-type operators.



次直既约和不直可分解的格蕴涵代数

王学芳, 徐扬, 宋振明

2004, 19(4):  385-392. 

摘要 ( 5 )   PDF (400KB) ( 2 )  

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Lattice implication algebra is an algebraic structure that is established by combining lattice and implicative algebra. It originated from the study on lattice-valued logic. In this paper, we characterize two special classes of lattice implication algebra, namely, subdi-rectly irreducible and directly indecomposable lattice implication algebras. Some important results are obtained.



带非双倍测度的BMO空间的一个注记

楚泽甫, 勒孚龙

2004, 19(4):  393-398. 

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Let μ be a positive Radon measure which only satisfies an appropriate growth condition, and RBMO(μ) be the BMO space associated with μ which was introduced by Tolsa. In this paper, it is proved that the definition of RBMO(ρ) can be weakened sufficiently.



一个不等式的注记

张志平, 王建平

2004, 19(4):  399-400. 

摘要 ( 6 )   PDF (102KB) ( 2 )  

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In this paper, we find the largest contant C such that sin2 x + xtanx > 2x2 + cx5tan x 0<x<2/π.



状态模和两个变量的环链多项式

韩友发, 樊星, 赵岩

2004, 19(4):  401-406. 

摘要 ( 5 )   PDF (339KB) ( 2 )  

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State representation is used to discuss the link with two variables, and the estimation of breadth of the two variables(say l and m) is given for 5-links.



高阶泛函微分方程解的振动性

白水周

2004, 19(4):  407-411. 

摘要 ( 7 )   PDF (243KB) ( 2 )  

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In this paper we study the oscillation of the solutions of higher-order functional differential equations, and have given the new integral conditions when equation (1) is oscillatory and extended some known results.x⁽ⁿ⁾(t)+p(t)x(g(t)) = 0, (1)where n is even number, p(t) ∈ C(R, [0, +∞)), g(t) ∈ C(R; R), ...



完全r-部图的均匀着色

王秀梅

2004, 19(4):  412-415. 

摘要 ( 5 )   PDF (212KB) ( 3 )  

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A graph is equitably k-colorable if its vertices can be partitioned into k inde- pendent sets of as near equal sizes as possible.In this paper,we determine a suficient and necessary condition for which a complete r-parite graph is equitably k-colorable.From this result,we can provide another way to prove some previous results.


一类高维半线性热传导方程的唯一性与稳定性

曹殿立, 梁保松, 叶耀军

2004, 19(4):  416-421. 

摘要 ( 8 )   PDF (267KB) ( 4 )  

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This paper deals with the uniqueness of solution to a class of semi-linear heat-conduction equation in higher dimension on the basis of references [1] and [2]. The main results in this paper are as follows: the solution of problem (A) is unique and stable if it exists.





正定性与二次函数的极值

吕保献, 李秀丽

2004, 19(4):  422-425. 

摘要 ( 5 )   PDF (207KB) ( 3 )  

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In this paper we give out a sufficient and solution of quadratic function’s maximum with theory of quadratic form and give out the definition of the positive definite property of the following homogeneous polynomials of degree In two variables function, based on the definite of local maximum of two variables function.





Heisenberg群上一类半线性方程全局解的存在性

郑驻军, 汪国安, 卢克平, 罗学波

2004, 19(4):  426-435. 

摘要 ( 6 )   PDF (514KB) ( 5 )  

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Based on the concepts of a generalized critical point and the corresponding generalized P.S. condition introduced by Duong Minh Duc [1], we have proved a new Z2 index theorem and get a result on multiplicity of generalized critical points. Using the result and a quite standard variational method, it is found that the equation-ΔH^nu = |u|^p-1u,x∈H has infinite positive solutions. Our approach can also be applied to study more general nonlinear problems.



强非线性系统的内层问题

韩祥临

2004, 19(4):  436-440. 

摘要 ( 3 )   PDF (240KB) ( 3 )  

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The nonlinear strongly singularly perturbed systemε , …, are considered. Under suitable conditions, using the theory of differential inequalities the existence and asymptotic behavior of interior solution for the problems are studied.