非线性Schroeding方程Cauchy问题解的Blow—Up的质量集中

We prove in this paper the blow-up theorem of the generalized solution.and its L^2 mass concentration theorem on the set of blow-up points near the blow-up time of the Cauchy problem for nonlinear Schroedinger equations and give the structure of the set of the blow-up points and the estimates on the blow-up time.Furthermore we extend and improve some results in [2] and [5].     

A Cyclic Probabilistic C-Contraction Results using Hadzic and Lukasiewicz T-Norms in Menger Spaces

In this paper, we introduce generalized cyclic C-contractions through p num-ber of subsets of a probabilistic metric space and establish two fixed point results for such contractions. In our first theorem we use the Hadzic type t-norm. In our next theorem we use Lukasiewicz t-norm. Our results generalize the results of Choudhury and Bhandari [11]. A control function [3] has been utilized in our second theorem. The results are illustrated with some examples.     

Integral Formulas for Submanifolds in Euclidean Space and Their Applications to Uniqueness Theorem

In present paper we derived some integral formulas for two n-dimensional submanifolds in Euclidean Space of dimension n+p E~(n+p), by which we get some generalizations of the Christoffel theorem and the Hilbert-Liebmann theorem.     

从球面到欧几里得空间的连续映射的性质及其应用

In this paper, we study the property of continuous mappings from a sphere to the Euclidean space. By using the theory of the periodic transformation in algebraic topology, we obtain a generalized Borsuk-Ulam theorem and then give some applications of the theorem.     

ON-THE ALGORITHM TO REALIZE THEOREM PROVING AND SOLVING PROBLEM

This paper describes the algorithm and concrete process with BASIC program to realize theorem proving and solving some artificial intelligence problem. For theorem proving we introduce "subsumption test", "omiting method" and "programing technics" to speed up for finding proofs of theorem as the previous paper[1].     

The viability property of controlled jump diffusion processes

In this paper, we first give a comparison theorem of viscosity solution to some nonlinear second order integrodifferential equation. And then using the comparison theorem, we obtain a necessary and sufficient condition for the viability property of some controlled jump diffusion processes which can keep the solution within a constraint K.     

Complete bounded λ-hypersurfaces in the weighted volume-preserving mean curvature flow

In this paper, we study the complete bounded λ-hypersurfaces in the weighted volume-preserving mean curvature flow. Firstly, we investigate the volume comparison theorem of complete bounded λ-hypersurfaces with |A|≤α and get some applications of the volume comparison theorem. Secondly, we consider the relation among λ, extrinsic radius k, intrinsic diameter d, and dimension n of the complete λ-hypersurface,and we obtain some estimates for the intrinsic diameter and the extrinsic radius. At last, we get some topological properties of the bounded λ-hypersurface with some natural and general restrictions.     

Banach空间中增算子的不动点定理

In this paper,we give a fixed point theorem under the weak conditions and some corollaries,which generalize the results of [1]-[5].     

On an extension of the H k mean curvature flow

In this note,we generalize an extension theorem in [Le-Sesum] and [Xu-Ye-Zhao] of the mean curvature flow to the Hk mean curvature flow under some extra conditions.The main difficulty in proving the extension theorem is to find a suitable version of Michael-Simon inequality for the Hk mean curvature flow,and to do a suitable Moser iteration process.These two problems are overcome by imposing some extra conditions which may be weakened or removed in our forthcoming paper.On the other hand,we derive some estimates for the generalized mean curvature flow,which have their own interesting.     

EXISTENCE OF NON-OSCILLATORY SOLUTIONS OF A CLASS OF HIGHER-ORDER NONLINEAR NEUTRAL DIFFERENCE EQUATIONS WITH A FORCED TERM

In this paper, we consider a certain forced higher-order nonlinear neutral difference equation. By using Krasnoselskii's fixed point theorem and some new techniques, we obtain necessary and sufficient conditions for the existence of non-oscillatory solutions for the system. Our results extend the results of Zhang [5].     

On the Negative Extremums of Fundamental Functions of Lagrange Interpolation Based on Chebyshev Nodes

In this paper, we investigate the negative extremums of fundamental functions of Lagrange interpolation based on Chebyshev nodes. Moreover, we establish some companion results to the theorem of J. Szabados on the positive extremum.     

DECOMPOSITION, REPRESENTATION AND EXTENSION OF THE HARMONIC FUNCTIONS

In this paper, by using the probabilistic method, we obtained a decomposition theorem for the harmonic functions, generalized and strengthened some theorems: Doob's theorem on the limit behaviors of the superharmonic functions, Bocher's theorem on the representation of the harmonic functions and the extension theorem of the harmonic functions etc.     

Quasi-sure Limit Theorem of Parabolic Stochastic Partial Differential Equations

In this paper we prove a quasi-sure limit theorem of parabolic stochastic partial differentialequations with smooth coefficients and some initial conditions,by the way,we obtain the quasi-surecontinuity of the solution.     

THE EXISTENCE OF ALMOST PERIODIC SOLUTION TO A CLASS OF ALMOST PERIODIC DIFFERENTIAL SYSTEM

By means of the fixed point theorem and exponential dichotomy, in this paper we investigate the existence of almost periodic solutions to a class of n-dimensional almost periodic systems, which is more general than the systems in [1-2]. We generalize and improve some results in [3].     

弱Hopf群余代数的Maschke型定理（英文）

In this paper, we mainly generalize a Maschke type theorem to the setting of a weak Hopf group coalgebra. First we introduce the notion of a weak Hopf group coalgebra as a generalization of Hopf group coalgebra introduced in [7] and a weak Hopf algebra introduced in [2]. And we study some basic properties of weak Hopf group coalgebras. Next we aim at finding some sufficient conditions under which an epimorphism of weak(H, A)Hopf π-comodule splits if it splits as an A-module morphism and give an application of our results.     

2n阶微分方程反周期解的存在性与唯一性

In this paper, we study the anti-periodic solutions for 2n-th order differential equations. By using the Schauder＇s fixed point theorem, we present some new results about the existence and uniqueness of anti-periodic solutions for 2n-th order differential equations.     

Quasi-sure Limit Theorem of Parabolic Stochastic Partial Differential Equations

In this paper we prove a quasi-sure limit theorem of parabolic stochastic partial differential equations with smooth coefficients and some initial conditions, by the way, we obtain the quasi-sure continuity of the solution.     

中介逻辑的命题演算系统(Ⅱ)

This paper is a continuation of [1]、[2]、[4]. In this paper, we shall con-tinue to constitute the formal theorems and the important substituting theorem(see theorem 16 in this paper) of the propositional calculus system of mediumlogic MP. The order numbers of following formal theorems follow those in reference[4]     

An analogue of Beurling’s theorem for the Jacobi transform

In this paper, we prove Beurling＇s theorem for the Jacobi transform, from which we derive some other versions of uncertainty principles.     

Further Extension of a Theorem of Values Distribution of Meromorphic Function f^（k）f^n

In this paper we derive the fundamental inequality of the theorem of meromorphic functions. It extends some results of Yi Hong-xun et al. As one of its application, we then study the value distribution of f^（k）f^n-c（z）.