Chinese Quarterly Journal of Mathematics

The Spaces b^p with 0 < p < 1

HU Zhang-jian, LIU Tai-shun

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).

Remarks on Maximal Attractors for the Compressible Navier-Stokes Equations of Viscous and Heat Conductive Fluid

QIN Yu-ming, WANG Xiu-qin, CUI Guo-zhong

2004, 19(4): 338-345.

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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).

On a Boolean-valued Model of the Strict Implication System(Continuous)

LI Na, LIU Hua-ke

2004, 19(4): 346-349.

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The reference [4] proved the consistency of S₁and 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, S₄and 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^Bof the ZFC axiom system in set theory is also a Boolean-valued model of Lewis’ the strict implication system S³, S⁴ and S^5.

New Characterization of Two Generalized Frames are Duals to Each Other

YAO Xi-yan

2004, 19(4): 350-354.

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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.

Some Invariant Properties of Semi-symmetric Metric Recurrent Connections and Curvature Tensor Expressions

ZHAO Pei-biao, SONG Hong-zao, YANG Xiao-ping

2004, 19(4): 355-361.

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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.

Problems on Two-dimensional Bandwidth under Distance of L_∞-norm

HAO Jian-xiu, LI Xiang-lu

2004, 19(4): 362-367.

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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.

On a Class of Number Fields of Eisenstein Type

JIANG Jian-jun

2004, 19(4): 368-372.

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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.

Oscillations of the Solutions of Nonlinear Delay Hyperbolic Partial Differential Equations

LIU An-ping, GUO Yan-feng, YANG Xiang-hui

2004, 19(4): 373-378.

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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.

A Characterization of Pointwise Approximation for Linear Combinations of Szász-type Operators

FENG Guo

2004, 19(4): 379-384.

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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.

Subdirectly Irreducible and Directly Indecomposable Lattice Implication Algebras

WANG Xue-fang, XU Yang, SONG Zhen-ming

2004, 19(4): 385-392.

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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.

A Note on the BMO Space with Non-doubling Measure

CHU Ze-fu, LE Fu-long

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.

A Note for one of Inequality

ZHANG Zhi-ping, WANG Jian-ping

2004, 19(4): 399-400.

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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.

State Model and the Link Polynomial with Two Variables

HAN You-fa, FAN Xing, ZHAO Yan

2004, 19(4): 401-406.

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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.

The Oscillation of the Solutions of Higher-order Functional Differential Equations

BAI Shui-zhou

2004, 19(4): 407-411.

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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), ...

Equitable Coloring of Complete r-partite Graphs

WANG Xiu-mei

2004, 19(4): 412-415.

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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.

Uniqueness and Stability of Solution for Semi-liner Heat-conduction Equationin Higher Dimension

CAO Dian-li, LIANG Bao-song, YE Yao-jun

2004, 19(4): 416-421.

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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.

The Extremism of Two Variable Function Based on the Positive Definite Property

LU Bao-xian, LI Xiu-li

2004, 19(4): 422-425.

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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.

The Existence of Global Solution for a Class of Semilinear Equations on Heisenberg Group

ZHENG Zhu-jun, WANG Guo-an, LU Ke-ping, LUO Xue-bo

2004, 19(4): 426-435.

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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.

The Interior Layer Problem for the Strongly Nonlinear Singularly Perturbed System

HAN Xiang-lin

2004, 19(4): 436-440.

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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.

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