SOME PROPERTIES OF (A)ρω(X,μ)

In this paper, we shall give a necessary and sufficient condition for which the dual of (A)pω(X, M,μ)(0 ＜ p ＜∞) is zero , and a necessary and sufficient condition for which (A)pω(X,M,μ) (0 ＜ p ＜1) is normable.     

SOME PROPERTIES OF Λ_ω~P(X,μ)

In this paper, we shall give a necessary and sufficient condition for which the dual of ΛAωP(X,μ) (0 < p < ∞) is zero , and a necessary and sufficient condition for which ΛAωP(X,μ) (0 < p < 1) is normable.     

THE STRUCTURE OF Ⅱ SPACE(Ⅱ)

This paper continues the study of.In this paper,the author discusses when asubspace of Ⅱ space is a complete subspace,and gives the structure of general linearsubspaces(in particular,that of closed linear subspaces).     

SOME PROPERTIES OF THE l_2-VALUED LONG JAMES BANACH SPACE J(η, l_2)

The main result of this paper is to show that the bidual J(η, l_2)~(**) of the long James type l_2-valued Banach space J(η, l_2) can be identified with transfinite matrices of scalars [(b_(α, i)i∈[0,ω)]_(α∈[0,n)) with some conditions and the norm of the element x~(**) in J(η, l_2)~(**) equals ■‖■b_(α,i)φ_(α,i)‖_(J(η_2)~(**)).     

SOME PROPERTIES OF Λω^p（X,μ）

In this paper, we shall give a necessary and sufficient condition for which the dual of Λ _ω ^p (X, M, μ) (0<p<∞) is zero, and a necessary and sufficient condition for which Λ _ω ^p (X, M, μ), (0<p<1) is normable. Supported by 973 project (G1999075105), RFDP (20030335019) and ZJNSF(RC97017).     

THE TRANSFINITE BASIS OF THE BIDUAL SPACE OF THE LONG JAMES SPACE

A transfinite basis of the bidual space of the long James space is presented in this paper. Moreover, we prove that the space J(w+r) has the approximation property, where J (ω) is the James space, r is any finite integer.     

A SURVEY OF SOME ASPECTS ON THE RESEARCH WORK OF FUZZY TOPOLOGY IN CHINA

The fundamental concept of a fuzzy set,introduced by Zadeh in 1965 [34] provides a natural foundation for treating mathematically the fuzzy phenomena which exist prevasively in our real world and for building new branches of fuzzy mathematics.In the area of fuzzy topology much research has been carried out since 1968 [1].     

SOME TOPOLOGICAL AND GEOMETRICAL PROPERTIES OF THE SEQUENCE SPACE e^r（u, p）

In this paper, we introduce the sequence space er (u, p) and investigate its some topological and geometrical properties such as basis, α-, β-, γ- duals and the uniform Opial property.     

A FORMULA OF THE KINEMATIC MEASURE IN NONEUCLIDEAN SPACE AND SOME PROBLEMS ON THE GEOMETRIC PROBABILITIES

Let P_n, be the n-dimensional projective space. Let x_0,x_1,…,x_n be the homogeneous coordinates of point x. Consider the quadric φ(x) =x_0~2+x_1~2+…x_(n-1)~2+εx_n~2, where ε can take the value of +1 or -1. We assume the homogeneous coordinates of the points x that do not belong to φ = 0 are normalized, such that     

μ-AVERAGE N-WIDTHS ON THE WIENER SPACE

In this paper we investigate the asymptotic bebaviour of μ-average n-widths of integral operator Kon the Wiener space. where K is the inverse operator of an ordinary linear differential operator L of orderm. For 1≤p.q<∞ C_n~a(K,W)_(p,q)a_n~a(K,W)_(p,q)n~(-(m)-(1/2)and for p∈(1,∞), q∈(2,∞) d_n~a(K; W)_(p.q)n~(-(m)-(1/2)).     

THE PATCH PROPERTY OF SELF-DUAL YANG-MILLS FIELD

SDYM-field is a holomorphic vector bandles over twistor Euclidean Space covered by two patches U_1 and U_2. In this paper, the property of the field on each patch and relationship between them are found. We point out that if the field on one patch correspond to the left SDYM-J equation, then on the other patch will be right SDYM-J equation. The Lagrangian form of the field is also found, which has relation to H_n=SL(n, c)/SU(n) nonlinear sigma model with Wess-Zumino terms.     

THE FUNCTIONAL DIMENSION OF SOME CLASSES OF SPACES

The functional dimension of countable Hilbert spaces has been discussed by some authors. They showed that every countable Hilbert space with finite functional dimension is nuclear. In this paper the authors do further research on the functional dimension, and obtain the following results: (1) They construct a countable Hilbert space, which is nuclear, but its functional dimension is infinite. (2) The functional dimension of a Banach space is finite if and only if this space is finite dimensional. (3) Let B be a Banach space, B* be its dual, and denote the weak * topology of B* by σ(B*,B). Then the functional dimension of (B*,σ(B*,B)) is 1. By the third result, a class of topological linear spaces with finite functional dimension is presented.     

THE HOMOTOPY TYPES OF THE DELETED PRODUCTS OF SOME VECTOR BUNDLES

In this paper it is shown that if W is an m-vector bundle over an n-manifold M with some conditions, then the W~k—ΔW, k-deleted product of W, and M~k ∪ΔM×S~((k-1×m+n)-1) are homotopy equivalent.     

THE LIMITING DISTRIBUTIONS OF SOME SUBCLASSES OF THE GENERALIZED NON-CENTRAL t-DISTRIBUTION

A general theorem on the limiting distribution of the generalized t-distribution is obtained,many applications of this theorem to some subclasses of elliptically contoured distributions in cluding multivariate normal and multivariate t distributions are discussed.Further,their limiting distributions by density function are derived.     

SOME SUBGROUPS OF THE EXTENDED HECKE GROUPS (λ_q)

The authors consider the extended Hecke groups H(λq) generated by T(z) = -1 / z, S(z) = -1/(z + λq,) and R(z) = 1 / z with A, = 2 cos(π/q) for q≥3 an integer. In this paper, the even subgroup He(λq), the second commutator subgroup H (λq) and the principal congruence subgroups Hp(λq) of the extended Hecke groups H(λq) are studied. Also, relations between them are given.     

ON THE HEAT KERNEL OF THE RIEMANNIAN SYMMETRIC SPACE SU(6)/SP(3)

ＯＮＴＨＥＨＥＡＴＫＥＲＮＥＬＯＦＴＨＥＲＩＥＭＡＮＮＩＡＮＳＹＭＭＥＴＲＩＣＳＰＡＣＥＳＵ（６）／ＳＰ（３）ＺｈｕＦｕｌｉｕ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ．ＷｕｈａｎＵｎｉｖｅｒｓｉｔｙ，Ｗｕｈａｎ４３００７２，Ｃｈｉｎａ．）Ａｂ...     

DUAL ASPECTS OF THE QUASITRIANGULAR BIALGEBRAS AND THE BRAIDED BIALGEBRAS

ＤＵＡＬＡＳＰＥＣＴＳＯＦＴＨＥＱＵＡＳＩＴＲＩＡＮＧＵＬＡＲＢＩＡＬＧＥＢＲＡＳＡＮＤＴＨＥＢＲＡＩＤＥＤＢＩＡＬＧＥＢＲＡＳＬＵＤＩＭＩＮＧＡｂｓｔｒａｃｔＩｔｉｓｓｈｏｗｎｔｈａｔｔｈｅｄｕａｌｂｉａｌｇｅｂｒａｏｆａｎｙｑｕａｓｉｔｒｉ...     

THE CHARACTERISTICS OF HYPERSPHERES IN MINKOWSKI SPACE

Y-Riemannian metric gY is an important tool in Finsler geometry, where Y is a smooth non-zero vector field on Finsler manifold. If Y is a geodesic field, it is very effective to study flag curvature using Y-Riemann metric. In this paper, using a special Y-Riemann metric ( that is, so called v-Riemann metric ), we study hyperspheres in a Minkowski space and give some characteristics of hyperspheres in a Minkowski space.     

THE LSRS PROPERTY AND THE CONVERGENCE THEOREM OF HENSTOCK-KURZWEIL INTEGRAL

1Introducti0nandPreliminariesIn19571958,J.KurzweilandR.Henst0ckindependentlygaveaRiemannc0mpletetypeintegral,calledtl1eKurzweil-Henstockintegral(0rKH-integral/H-integral)['].Itisan0n-absoluteinterga1anditsdefinitiondoesn0tneedthemeasuretlieory.lthasbeenprovedthatthisintegralisequivalenttothespecialDenjoyilltegral['].Theref0retlieH-integralc0ntainstl1eNewton,ffiemann,Improper-fuemannandLebesgueintegrals.In1985,P.Y.LeeandT.S.ChewgavetheC0ntr0lledC0nvergenceTheorem,andmadetheH-integraJ…     

ON THE APPROXIMATION OF TCHEBYCHEFF-FOURIER SERIES IN THE C SPACE AND L_p~ω SPACE

The degree of approximation to a function f(x)∈C[-1,1] by (U, λ) means and f(x) ∈ Lpw by (Jr) means are discussed, some results in the literatures [1],[2],[3] have been improved.