On a non-abelian invariant on complex surfaces of general type

In this paper, we give certain homotopy and diffeomorphism versions as a generalization to an earlier result due to W.S. Cheung, Bun Wong and Stephen S. T. Yau concerning a local rigidity problem of the tangent bundle over compact surfaces of general type.     

关于二维球面上的Ricci流的一个注记

给出Hamilton和Chow关于二维球面上的Ricci流的一个定理的新证明．这个证明结合了Hamilton关于Ricci流的紧性定理和二维ancientp解的分类和Perelman的非塌缩定理．     

On Faltings' annihilator theorem

In the present article, the author shows that Faltings' annihilator theorem holds for any Noetherian ring if is universally catenary; all the formal fibers of all the localizations of  are Cohen-Macaulay; and the Cohen-Macaulay locus of each finitely generated -algebra is open.

     

Another note on Weyl's theorem

``Weyl's theorem holds" for an operator on a Banach space when the complement in the spectrum of the ``Weyl spectrum" coincides with the isolated points of spectrum which are eigenvalues of finite multiplicity. This is close to, but not quite the same as, equality between the Weyl spectrum and the ``Browder spectrum", which in turn ought to, but does not, guarantee the spectral mapping theorem for the Weyl spectrum of polynomials in . In this note we try to explore these distinctions.

     

关于非紧流形上的Ricci流的一个注记

设（M^3,90）是非紧三维Riemann流形,其Ricci曲率非负,单射半径有正的下界,且当x→∞时数量曲率R（x）→0。则以（M^3,go）为初始值的Ricci流在M^3×[0,∞）上有长期解。这推广了马和朱最近的一个结果．在高维情形我们也有相应的结果,并且我们给Chau,Tam和Yu在Ktihler情形的类似定理一个新的证明。     

Fixed point sets of deformations of polyhedra with local cut points

A locally finite simplicial complex is said to be 2-dimensionally connected if is connected. Such spaces exhibit ``classical' behavior in that they all admit deformations with one fixed point, and they admit fixed point free deformations if and only if the Euler characteristic is zero. A result of G.-H. Shi implies that, for non 2-dimensionally connected spaces, the fixed point sets of deformations are equivalent to the fixed point sets of certain combinatorial maps which he calls good displacements. U. K. Scholz combined Shi's results with a theorem of P. Hall to obtain a characterization of all finite simplicial complexes which admit fixed point free deformations. In this paper we begin by explicitly capturing the combinatorial structure of a non 2-dimensionally connected polyhedron in a bipartite graph. We then apply an extended version of Hall's theorem to this graph to get a realization theorem which gives necessary and sufficient conditions for the existence of a deformation with a prescribed finite fixed point set. Scholz's result, and a characterization of all finite simplicial complexes without fixed point free deformations that admit deformations with a single fixed point follow immediately from this realization theorem.

     

Growth Theorem and Distortion Theorem for a Sub class of Parab olic Starlike Mappings

In this article, we firstly introduce a subclass of parabolic starlike mappings writen as P S (β;ρ). Secondly, the growth theorem for P S (β;ρ) on the unit ball in complex Banach space is obtained. Finaly, as the application of the growth theorem of P S (β;ρ), the distortion theorem along a unit direction is also established.     

A Note on Class Field Theory for Two-Dimensional Local Rings

The class field theory for the fraction field of a two-dimensional complete normal local ring with finite residue field is established by S. Saito. In this paper, we investigate the index of the norm group in the K ₂-idele class group for a finite Abelian extension of such fields and deduce that the existence theorem does not hold for almost fields in this case.     

模型论在代数上的应用

给出了模型论在代数上的两个应用,得到了下列定理：定理A：如环R的任何有限生成子环均是局部环,则R是局部环.定理B：存在自然数的真扩张R使其具有下列特征：（1）虽然R有无限多零因子,但R中有无限多零因子,但R中的首1多项式的根的个数可以得到很好的控制.（2）R不仅将自然数的素数特征保留下来,而且还可在其上定义指数函数。     

Modal extension of ideal paraconsistent four-valued logic and its subsystem

This study aims to introduce a modal extension M4CC of Arieli, Avron, and Zamansky's ideal paraconsistent four-valued logic 4CC as a Gentzen-type sequent calculus and prove the Kripke-completeness and cut-elimination theorems for M4CC. The logic M4CC is also shown to be decidable and embeddable into the normal modal logic S4. Furthermore, a subsystem of M4CC, which has some characteristic properties that do not hold for M4CC, is introduced and the Kripke-completeness and cut-elimination theorems for this subsystem are proved. This subsystem is also shown to be decidable and embeddable into S4.     

A class of strong limit theorems for countable nonhomogeneous Markov chains on the generalized gambling system

In this paper, we study the limit properties of countable nonhomogeneous Markov chains in the generalized gambling system by means of constructing compatible distributions and martingales. By allowing random selection functions to take values in arbitrary intervals, the concept of random selection is generalized. As corollaries, some strong limit theorems and the asymptotic equipartition property (AEP) theorems for countable nonhomogeneous Markov chains in the generalized gambling system are established. Some results obtained are extended.      

Some compactness theorems via m-Bakry–Émery and m-modified Ricci curvatures with negative m

Stimulated by S. Ohta and W. Wylie, we establish some compactness theorems for complete Riemannian manifolds via m-Bakry–Émery and m-modified Ricci curvatures with negative m. Our results may be considered as generalizations of the classical compactness theorems via Ricci curvature due to S.B. Myers, W. Ambrose, G.J. Galloway, and J. Cheeger, M. Gromov, and M. Taylor, and relax some previous compactness criteria for complete Riemannian manifolds via m-Bakry–Émery and m-modified Ricci curvatures obtained when m is a positive constant or infinity.     

Extension of the local maximum principle to abnormal optimal control problems

In this paper, an optimal control problem with terminal data is considered in the so-called abnormal case, i.e., when the classical Pontryagin-type maximum principle has a degenerate form which does not depend on the functional being minimized. An extension of the Dubovitskii-Milyutin method to the nonregular case, obtained by applying Avakov's generalization of the Lusternik theorem, is presented. By using this extension, a local maximum principle which has a nondegenerate form also in the abnormal case is proved. An example which supports the theory is given.The author would like to thank Professors S. Walczak and W. Kotarski for fruitful discussions in the process of writing this paper.This research was supported by a SIUE Research Scholar Award and by NSF Grant DMS-91-009324.     

A converse to a theorem of Adamyan, Arov and Krein

A well known theorem of Akhiezer, Adamyan, Arov and Krein gives a criterion (in terms of the signature of a certain Hermitian matrix) for interpolation by a meromorphic function in the unit disc with at most poles subject to an -norm bound on the unit circle. One can view this theorem as an assertion about the Hardy space of analytic functions on the disc and its reproducing kernel. A similar assertion makes sense (though it is not usually true) for an arbitrary Hilbert space of functions. One can therefore ask for which spaces the assertion is true. We answer this question by showing that it holds precisely for a class of spaces closely related to .

     

Remarks on sphere-type theorems

We prove if is a complete Riemannian manifold with an embedded totally geodesic compact hypersurface such that has nonnegative sectional curvature, and the sectional curvature of is strictly positive in a neighborhood of , then the pair is diffeomorphic to the pair . This result gives an affirmative answer to a question of H. Wu in the case when is compact and simply connected.

     

The Chevalley-Warning theorem and a combinatorial question on finite groups

Recently, W. D. Gao (1996) proved the following theorem: For a cyclic group of prime order, and any element in it, and an arbitrary sequence of elements from , the number of ways of writing as a sum of exactly of the 's is or modulo according as is zero or not. The dual purpose of this note is (i) to give an entirely different type of proof of this theorem; and (ii) to solve a conjecture of J. E. Olson (1976) by answering an analogous question affirmatively for solvable groups.

     

B值随机变量序列的局部收敛定理

本文的目的是研究B值随机变量序列的局部收敛定理。作为推论，得到了一类B值鞅差序列的极限定理和若干经典的独立随机变量序列的极限定理。     

Intersection of sets with -connected unions

We show that if sets in a topological space are given so that all the sets are closed or all are open, and for each every of the sets have a -connected union, then the sets have a point in common. As a consequence, we obtain the following starshaped version of Helly's theorem: If every or fewer members of a finite family of closed sets in have a starshaped union, then all the members of the family have a point in common. The proof relies on a topological KKM-type intersection theorem.

     

Banach空间积分双半群的生成条件

研究Banach空间中积分双半群的生成条件.利用算子A的豫解算子,给出了积分双半群T(t)的生成定理.结果表明:如果对任意的x∈X,f∈X*,以及A|λ]<δ,λ∈ρ(A),有∈Lp(R),则存在算子族S(t),t∈R,S(t)强连续且满足积分双半群的定义.     

Tauberian theorems and stability of solutions of the Cauchy problem

Let be a bounded, strongly measurable function with values in a Banach space , and let be the singular set of the Laplace transform in . Suppose that is countable and uniformly for , as , for each in . It is shown that

as , for each in ; in particular, if is uniformly continuous. This result is similar to a Tauberian theorem of Arendt and Batty. It is obtained by applying a result of the authors concerning local stability of bounded semigroups to the translation semigroup on , and it implies several results concerning stability of solutions of Cauchy problems.