ON A KHLER VERSION OF CHEEGER-GROMOLL-PERELMAN'S SOUL THEOREM

In this note, we will prove a Khler version of Cheeger-Gromoll-Perelman's soul theorem, only assuming the sectional curvature is nonnegative and bisectional curvature is positive at one point.     

A HEAT KERNEL VERSION OF HARDY’S THEOREM FOR THE LAGUERRE HYPERGROUP

In this article, we prove a heat kernel version of Hardy’s theorem for the Laguerre hypergroup.     

GENERALIZATIONS OF KY FAN＇S THEOREM ON BEST APPROXIMATIONS

In 1969, Ky Fan[3] proved that for any continuous function f from a compact convex subset M of a normed linear space X into X, there exists x ∈ M such that f (x) - x = dist( f (x), M). Since then, there have appeared several generalizations, extensions and applications of this result. This paper also deals with some extensions and generalizations of this result when the underlying spaces are convex metric spaces.     

A GENERALIZATION OF CLARKE＇S FIXED POINT THEOREM

This paper proposes a formally stronger set-valued Claxke‘s fixed point theorem. By this-theorem we can improve a fixed point theorem for weakly inward contraction set-valued mapping of D. Dowing and W.A. Kirk.     

AN ADAPTIVE VERSION OF GLIMM＇S SCHEME

This article describes a local error estimator for Glimm＇s scheme for hyperbolic systems of conservation laws and uses it to replace the usual random choice in Glimm＇s scheme by an optimal choice. As a by-product of the local error estimator, the procedure provides a global error estimator that is shown numerically to be a very accurate estimate of the error in L1 （R） for all times. Although there is partial mathematical evidence for the error estimator proposed, at this stage the error estimator must be considered ad- hoc. Nonetheless, the error estimator is simple to compute, relatively inexpensive, without adjustable parameters and at least as accurate as other existing error estimators. Numerical experiments in 1-D for Burgers＇ equation and for Euler＇s system are performed to measure the asymptotic accuracy of the resulting scheme and of the error estimator.     

THEOREMS OF BARTH-LEFSCHETZ TYPE ON KAHLER MANIFOLDS WITH PARTIALLY POSITIVE CURVATURE

The author obtains the theorems of Barth-Lefschetz type on Kahler manifolds with partially positive bisectional curvature without the assumption of nonnegative bisectional curvature. Some applications of the results to holomorphic mappings are given.     

SOME GENERALIZATIONS OF KY FAN＇S BEST APPROXIMATION THEOREM

We pressent new Ky Fan type best approximation theorems for a discontinuous multivalued map onmetrizable topological vector spaces and hyperconvex spaces. In addition, fixed point results are derivedfor the map studied. Our work generalizes severl results in approximation theory.     

A GENERAL VERSION OF KALTON'S CLOSED GRAPH THEOREM

ＡＧＥＮＥＲＡＬＶＥＲＳＩＯＮＯＦＫＡＬＴＯＮ＇ＳＣＬＯＳＥＤＧＲＡＰＨＴＨＥＯＲＥＭＱｉｕＪｉｎｇｈｕｉ（丘京辉）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＳｕｚｈｏｕＵｎｉｖｅｒｓｔｉｙ，Ｓｕｚｈｏｕ２１５００６，Ｃｈｉｎａ．）Ａｂｓｔｒ...     

A SIMPLIFIED BRAUER＇S THEOREM ON MATRIX EIGENVALUES

Let A=(a _ij)∈C ^n×n and . Suppose that for each row of A there is at least one nonzero off-diagonal entry. It is proved that all eigenvalues of A are contained in . The result reduces the number of ovals in original Brauer’s theorem in many cases. Eigenvalues (and associated eigenvectors) that locate in the boundary of are discussed. The project is supported in part by Natural Science Foundation of Guangdong.     

ON A THEOREM OF CHUI

Let f∈C_(2π) and let α_0/2+sum from k=1 to ∞ (a_k coskx+b_k sinkx) (1)be its Fourier series. Denote by S_n(f, x) the n-th partial sumof series (1) and by ω(f,δ) the modulus of continuity of functionf(x). For each q0, the Euler (E, q)-mean of series (1) is     

ON A GENERALIZATION OF A THEOREM OF ERDŐS AND FUCHS

Sárközy generalized a theorem of Erds and Fuchs by considering sums of.....     

ON THE WILLMORE’S THEOREM FOR CONVEX HYPERSURFACES

Let M be a compact convex hypersurface of class C2, which is assumed to bound a nonempty convex body K in the Euclidean space Rn and H be the mean curvature of M. We obtain a lower bound of the total square of mean curvature M H2dA. The bound is the Minkowski quermassintegral of the convex body K. The total square of mean curvature attains the lower bound when M is an (n-1)-sphere.     

GIRSANOV＇S THEOREM ON ABSTRACT WIENER SPACES

ＴＨＥＰＥＲＴＵＲＢＡＴＩＯＮＴＨＥＯＲＹＦＯＲＴＨＥＳＵＭＭＡＢＩＬＩＴＹＯＦＳＥＬＦＡＤＪＯＩＮＴＯＰＥＲＡＴＯＲＳＣ．Ｗ．ＬＥＵＮＧＭａｎｕｓｃｒｉｐｔｒｅｃｅｉｖｅｄＮｏｖｅｍｂｅｒ１４，１９９４．ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍ...     

A NOTE ON A CHARACTERIZATION THEOREM OF STRAUSS

Assume that B is a compact subset on the real axis containing at least n+1 points,C(B) the normed linear space of all continuous functions defined on B,with Chebyshevnorm‖·‖,and G=span(g_1,…,g_n) an n-dimensional subspace of C(B).LetG_R={g=sum from j=1 to n a_jg_j:v(x)≤g(x)≤u(x),q_i≤sum from j=1 to n d_(ij)a_j≤p_i for i=1,…,l}where u,v are extended real-valued functions on B subject to -∞≤v(x)相似文献   

A NOTE ON TB THEOREM OF DAVID-JOURNE-SEMMES

David, Journe and Semmes proved the Tb theorem for para-accreclive funclions and showed this theo-rem is optimal in certain sense. In this note, we give a technical proof of Tb theorem for pseado-accretivefunctions. Our result still holds for para-accreting functions.     

A NOTE ON A STRONG UNIQUENESS THEOREM OF SITRAUSS

In this paper we present a correction of the proof of u strong uniqueness theorem given by H. Struuss [1] in 1992 on approximation by reciprocals of functions uf an n-dimensional space (u,…un) satisfying coefficient constraints.     

ON A CONJECTURE OF K. OGIUE FOR KAEHLER HYPERSURFACES

ＯＮ Ａ ＣＯＮＪＥＣＴＵＲＥ ＯＦ Ｋ． ＯＧＩＵＥ ＦＯＲ ＫＡＥＨＬＥＲ ＨＹＰＥＲＳＵＲＦＡＣＥＳ￥ＳＨＡＮＧＷＥＩＭＩＮＧＡｂｓｔｒａｃｔ：ＡｎａｆｆｉｒｍａｔｉｖｅａｎｓｗｅｒｔｏａｃｏｎｊｅｃｔｕｒｅｏｆＫ．Ｏｇｉｕｅｆｏｒｍｕｌａｔｅ...     

REMARKS ON BRUALDI＇S THEOREM FOR SPECTRUM INCLUSION REGION OF AN IRREDUCIBLE MATRIX

This paper obtains a necessary and sufficient condition for an irreducible complex matrix whose comparison matrix is a singular M-matrix to be singular. This is used to establish a necessary and sufficient condition for a boundary point of Brualdi‘s inclusion region of the eigenvalues of an irreducible complex matrix to be an eigenvalue.     

A THEOREM ON THE CONTINUITIES OF STOCHASTIC PROCESSES

If a stochastic process X_t is continuous in probability,then the points of discontinuityin γ-th mean constitute a set of lst category.     

A NOTE ON A STRONG UNIQUENESS THEOREM OF STRAUSS

In this paper we present a correction of the proofofa strong uniqueness theorem given by H.Strauss in1992 on approximation by reciprocals of functions of an n-dimensional space span (u_1,…,u_n) satisfyingcoefficient constraints.