Vanishing Theorems for p-Harmonic Forms on Submanifolds in Spheres

In this paper,we present some vanishing theorems for p-harmonic forms on-super stable complete submanifold M immersed in sphere Sn+m.When 2≤1≤n-2,M has a flat normal bundle.Assuming that M is a minimal submanifold andδ>1(n-1)p2/4n[p-1+(p-1)2kp],we prove a vanishing theorem for p-harmonicℓ-forms.

DISTORTION THEOREMS FOR CLASSES OF g-PARAMETRIC STARLIKE MAPPINGS OF REAL ORDER IN C^(n)

In this paper,we define the class S_(g)^(BX)of g-parametric starlike mappings of real order γ on the unit ball BX in a complex Banach space X,where g is analytic and satisfies certain conditions.By establishing the distortion theorem of the Fr´echet-derivative type of S_(g)^(BX)with a weak restrictive condition,we further obtain the distortion results of the Jacobi-determinant type and the Fr´echet-derivative type for the corresponding classes(compared with S_(g)^(BX))defined on the unit polydisc(resp.unit ball with the arbitrary norm)in the space of n-dimensional complex variables,n≥2.Our results extend the classic distortion theorem of holomorphic functions from the case in one-dimensional complex space to the case in the higher dimensional complex space.The main theorems also generalize and improve some recent works.

REAL PALEY-WIENER THEOREMS FOR THE SPACE-TIME FOURIER TRANSFORM

This paper presents an extension of certain forms of the real Paley-Wiener theorems to the Minkowski space-time algebra. Our emphasis is dedicated to determining the space-time valued functions whose space-time Fourier transforms(SFT) have compact support using the partial derivatives operator and the Dirac operator of higher order.

GLOBAL RIGIDITY THEOREMS FOR SUBMANIFOLDS WITH PARALLEL MEAN CURVATURE

In this paper,we mainly study the global rigidity theorem of Riemannian submanifolds in space forms.Let Mn(n≥3)be a complete minimal submanifold in the unit sphere Sn+p(1).Forλ∈[0,n2−1/p),there is an explicit positive constant C(n,p,λ),depending only on n,p,λ,such that,if∫MSn/2dM<∞,∫M(S−λ)n/2+dM<C(n,p,λ),then Mn is a totally geodetic sphere,where S denotes the square of the second fundamental form of the submanifold and∫+=max{0,f}.Similar conclusions can be obtained for a complete submanifold with parallel mean curvature in the Euclidean space Rn+p.

CENTRAL LIMIT THEOREMS FOR A BRANCHING RANDOM WALK WITH A RANDOM ENVIRONMENT IN TIME

We consider a branching random walk with a random environment m time, in which the offspring distribution of a particle of generation n and the distribution of the displacements of its children depend on an environment indexed by the time n. The envi- ronment is supposed to be independent and identically distributed. For A C R, let Zn（A） be the number of particles of generation n located in A. We show central limit theorems for the counting measure Zn （-） with appropriate normalization.

NONSMOOTH CRITICAL POINT THEOREMS AND ITS APPLICATIONS TO QUASILINEAR SCHRDINGER EQUATIONS

In this paper, the existence and nonexistence of solutions to a class of quasilinear elliptic equations with nonsmooth functionals are discussed, and the results obtained are applied to quasilinear SchrSdinger equations with negative parameter which arose from the study of self-channeling of high-power ultrashort laser in matter.

TOPOLOGICAL DEGREE THEORY AND FIXED POINT THEOREMS IN PROBABILISTIC METRIC SPACES

The Leray-Schauder topological degree theory is established in the probabilistic linearnormed spaces.Based.on this theory,some fixed point theorems for mappings in theprobabilistic linear normed spaces are shown.

ON THE SHARP GROWTH,COVERING THEOREMS FOR NORMALIZED BIHOLOMORPHIC MAPPINGS IN C^n

In this article, a normalized biholomorphic mapping f defined on bounded starlike circular domain in Cn is considered, where z = 0 is a zero of order k ＋ 1 of f（z） - z. The sharp growth, covering theorems for almost starlike mappings of order α and starlike mappings of order α are established. Meanwhile, the construction of the above mappings on bounded starlike circular domain in Cn is also discussed, it provides the extremal mappings for the growth, covering theorems of the above mappings.

SYSTEM OF COINCIDENCE THEOREMS IN PRODUCT TOPOLOGICAL SPACES AND APPLICATIONS (Ⅰ)

A new notion of finite continuous topological space（in short, FC-space） with out convexity structure was introduced. A new continuous selection theorem was established in FC-spaces. By applying the continuous selection theorem, some new coincidence theorems for two families of set-valued mappings defined on product space of noncompact FC-spaces are proved under much weak assumptions. These results generalize many known results in recent literature. Some applications will be given in a follow-up paper.

FIXED POINT THEOREMS AND BEST APPROXIMATION IN CONVEX METRIC SPACES

Results regarding best approximation and best Simultaneous approximation on convex metric spaces are Obtained.Existence of fixed points for an ultimately nonexpansive semigroup of mappings is also shown.

EMBEDDING THEOREMS ON CAMPANATO-MORREY SPACES FOR VECTOR FIELDS OF HoRMANDER TYPE

This paper deals with embedding theorems on Campanato-Marrey spaces formed by degenerate vector fields, which include Honnander and Grushin type of vector fields. These embedding theorems are somewhat different from the known Poincare estimates. The main ingredients of the proofs rely on the fractional maximal functions. These results evidently have applications to the regularity of subelliptic PDE.

FREUD-BUTZER-HAHN TYPE QUANTITATIVE THEOREMS FOR PROBABILISTIC REPRESENTATIONS OF(C_0)OPERATOR SEMIGROUPS

In this paper,we shall exploit the Freud method in the Classical operator approximation theory to im- prove known quantitative estimalions with an emphasis on Calculah' on the generic constants.

AN HARMONIC ANALYSIS FOR OPERATORS IN THE CASE OF A LOCALLY COMPACT ABELIAN GROUP：F．AND M．RIESZ THEOREMS

Let G be a locally compact Abelian group, B a homogeneous Banach algebra without the order on G. at denotes the set of all integrable operators with respect to right translation on B(see [2]). Under some convenient conditions we obtain the following results:both the first F. and M. Riesz Theorem for operators in and the second F. and M. Riesz Theorem for operators in hold.

THE EXTENSION THEOREMS OF CONE LINEAR OPERATORS

A kind of cone separation theorems is established, by which the extension theorems for cone linear continuous operators are developed. As an application, the extension theorem for positive linear continuous operators is given.

TAUBERIAN THEOREMS FOR WEAK ALMOST CONVERGENT FUNCTIONS

The almost convergent function which was introduced by Raimi [6] and discussed by Ho [4], Das and Nanda [2, 3], is the continuous analogue of almost convergent sequences （see [5]）. In this paper, we establish the Tauberian conditions and the Cauchy criteria for weak almost convergent functions on R2＋ .

On Distortion Theorems for the n－th Order Derivative of Starlike and Convex Functions of Order α

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Calculation of multicentre nuclear attraction integrals over Slater-type orbitals using unsymmetrical one-range addition theorems

Using the unsymmetrical one-range addition theorems introduced by one of the authors with the help of complete orthonormal sets of $／varPsi ^／alpha $-exponential type orbitals （$／alpha = 1,0, - 1, - 2,...）$, this paper presents the sets of series expansion relations for multicentre nuclear attraction integrals over Slater-type orbitals arising in Hartree--Fock--Roothaan equations for molecules. The final results are expressed through multicentre charge density expansion coefficients and basic integrals. The convergence of the series is tested by calculating concrete cases for arbitrary values of parameters of orbitals.

THE BEST APPROXIMATION AND COINCIDENCE THEOREMS FOR COMPOSITES OF ACYCLIC MAPPINGS

Some new coincidence theorem s involving a new class of set_valued mappings containing composites of acyclic mappings defined in a contractible space are proved. For applications, some best approximation theorems and coincidence theorems for set-valued mappings are als o given. A number of known results in recent literature are improved and general ized by the theorems in this paper.

One-range addition theorems for generalized integer and noninteger μ Coulomb,and exponential type correlated interaction potentials with hyperbolic cosine in position,momentum,and four-dimensional spaces

The formulae are established in position,momentum,and four-dimensional spaces for the one-range addition theorems of generalized integer and noninteger μ Coulomb,and exponential type correlated interaction potentials with hyperbolic cosine（GCTCP and GETCP HC）.These formulae are expressed in terms of one-range addition theorems of complete orthonormal sets of Ψα-exponential type orbitals（Ψ α-ETO）,α-momentum space orbitals（α-MSO）,and zα-hyperspherical harmonics（zα-HSH） introduced.The one-range addition theorems obtained can be useful in the electronic structure calculations of atoms and molecules when the GCTCP and GETCP HC in position,momentum,and four-dimensional spaces are employed.

THE SPACES OF CESRO ALMOST CONVERGENT SEQUENCES AND CORE THEOREMS

As known, the method to obtain a sequence space by using convergence field of an infinite matrix is an old method in the theory of sequence spaces. However, the study of convergence field of an infinite matrix in the space of almost convergent sequences is so new （see [15]）. The purpose of this paper is to introduce the new spaces ^ ～f and fo consisting of all sequences whose Ceshro transforms of order one are in the spaces f and ^ ～ f0, respectively. Also, in this paper, we show that ^ ～f and ^ ～f0 are linearly isomorphic to the spaces f and f0, respectively. The β- and γ-duals of the spaces ^ ～f and 2% are computed. Furthermore, the classes （^ ～f： μ） and （μ ： f） of infinite matrices are characterized for any given sequence space μ, and determined the necessary and sufficient conditions on a matrix A to satisfy Bc-core（Ax） K-core（x）, K-core（Ax） Bg-core（x）, Bc-core（Ax） Be-core（x）, Bc-core（Ax） t-core（x） for all x ∈ t∞.