黎曼积分的几个等价定义

本文给出了定积分的几个较简单的定义，并证明这些定义均与黎曼积分定义等价。     

关于概率空间与次线性期望空间中的随机变量一致可积性的一个注记（英文）

在这篇注记中我们讨论随机变量的一致可积性.在概率空间中,我们引进了随机变量一致可积性的两个新的定义,并证明了他们与经典定义等价.在次线性期望空间中,我们给出了随机变量一致可积性的德拉瓦利普桑准则,并作了一些其它讨论.     

关于定积分概念的数列化

讨论定积分概念的数列化及其相关问题．使用经典的精确分析方法,得到一个数列化的可积的充要条件．探索微元法表述后续相关概念与证明相关结果．同时举例说明定积分概念数列化的优越性与微元法处理后续相关问题的可行性．     

积分型Cauchy中值函数若干分析性质

给出"积分型Cauchy中值函数"的定义,对"积分型Cauchy中值函数"的分析性质进行了系统讨论,证明了"积分型Cauchy中值函数"的单调性、可积性、连续性、可微性等分析性质.作为"积分型Cauchy中值函数"的特例,给出了"第一积分中值函数"的定义及"第一积分中值函数"相应的分析性质.     

关于Taylor中值函数若干分析性质的讨论

给出了"Taylor中值函数"的定义,对Taylor中值函数的分析性质进行了系统的综合讨论,证明了Taylor中值函数的单调性、可积性、连续性、可微性等分析性质.     

R^n中Banaeh值函数的MeShane积分（I）

R．A．Gordon在[1]中定义了从R^1到Banach空间抽象函数的McShane积分，证明了当X不含C0时，如果，在[a，b]上MeShane f可积，则在[a．b]上Pettis可积．在这篇文章中，我们定义了从R^n到Banaach空间抽象函数的Mcshane积分。证明了f McShane可积，则f是Pettis可积．于是我们推广了[1]的结果。     

广义达芬振子的广义李对称和完全可积性

本文考虑了广义达芬振子的广义李对称及完全可积性。证明了当达芬振子具无穷多个对称时变系数所满足的条件等价于当达芬振子被变换为可积达芬振子时变系数所满足的条件，同时文章给出了这些对称代数的结构。     

关于模糊集值平方可积鞅的随机积分

给出了模糊集值平方可积鞅的定义以及简单实值可料过程关于模糊集值平方可积鞅的随机积分的定义;证明了该积分仍具有模糊集值平方可积鞅的性质。     

紧致黎曼面上具有可积伸张及指定界值的拟共形同胚的极值映照

设S是亏格大于1的紧致黎曼面，本文对S上的拟共形ID—同胚定义了一种极值，证明了在每一个S到另外一紧致字文面S’的保向同胚同伦类中，如果存在一个广义的Teichmuller映照，那么在这种新定义的极值意义下，它是唯一最小的极值映照．     

第一积分中值函数

通过上下确界,给出了"第一积分中值函数"的定义,对"第一积分中值函数"的分析性质进行了系统的讨论,证明了"第一积分中值函数"的单调性、可积性、连续性、可导性等分析性质.     

导数Manakov方程的Darboux变换及其精确解

本文给出了导数Manakov方程新的Darboux变换.利用此Darboux变换得到了导数Manakov方程的精确解.最后,通过选择适当的参数,作出了孤子解的图形.     

Darboux integrability of a Mathieu-van der Pol-Duffing oscillator

In this paper, we characterize all the Darboux polynomials of a Mathieu-van der Pol-Duffing oscillator by transforming from the original system into a three dimensional system. We also provide a complete classification of the rational first integrals and of the Darboux first integrals through the analysis of its Darboux polynomials and its exponential factors.     

The Fundamental and Rigidity Theorems for Pseudohermitian Submanifolds in the Heisenberg Groups

In this paper, we study some basic geometric properties of pseudohermitian submanifolds of the Heisenberg groups. In particular, we obtain the uniqueness and existence theorems, and some rigidity theorems.     

On Darboux helices in Euclidean 4‐space

The notion of Darboux helix in Euclidean 3‐space was introduced and studied by Yayl? et al. 2012. They show that the class of Darboux helices coincide with the class of slant helices. In a special case, if the curvature functions satisfy the equality κ² + τ² = constant, then these curves are curve of the constant precession. In this paper, we study Darboux helices in Euclidean 4‐space, and we give a characterization for a curve to be a Darboux helix. We also prove that Darboux helices coincide with the general helices. In a special case, if the first and third curvatures of the curve are equal, then Darboux helix, general helix, and V₄‐slant helix are the same concepts.     

Darboux integrability and algebraic limit cycles for a class of polynomial differential systems

This paper deals with the existence of Darboux first integrals for the planar polynomial differential systems x=x-y+P n+1(x,y)+xF2n(x,y),y=x+y+Q n+1(x,y)+yF2n(x,y),where P i(x,y),Q i(x,y)and F i(x,y)are homogeneous polynomials of degree i.Within this class,we identify some new Darboux integrable systems having either a focus or a center at the origin.For such Darboux integrable systems having degrees 5and 9 we give the explicit expressions of their algebraic limit cycles.For the systems having degrees 3,5,7 and 9and restricted to a certain subclass we present necessary and sufficient conditions for being Darboux integrable.     

On the linearization of isochronous centre of a modified Emden equation with linear external forcing

In this work, we carry out a detailed study on the linearization of isochronous centre of a modified Emden equation with linear external forcing. We construct inverse integrating factor and time independent first integral for this system through Darboux method. To linearize the isochronous centre we explore a transverse commuting dynamical system and its first integral. With the help of first integrals of the original dynamical system and its transverse commuting system we derive the linearizing transformation and reduce the nonlinear system into linear isochronous one. We also point out certain mathematical structures associated with this dynamical system.     

Slant helix of order n and sequence of Darboux developables of principal-directional curves

In this paper, we consider the sequence of the principal-directional curves of a curve γ and define the slant helix of order n (n-SLH) of the curve in Euclidean 3-space. The notion is an extension of the notion of slant helix. We present an important formula that determines if the nth principal-directional curve of γ can be the slant helix of order n (n ≥ 1). As an application of singularity theory, we study the singularities classifications of the Darboux developable of nth principal-directional curve of γ . It is demonstrated that the formula plays a key role in characterizing the singularities of the Darboux developables of the nth principal-directional curve of a curve γ .     

Planar polynomial vector fields having first integrals and algebraic limit cycles

With the help of Abel differential equations we obtain a new class of Darboux integrable planar polynomial differential systems, which have degenerate infinity. Moreover such integrable systems may have algebraic limit cycles. Also we present the explicit expressions of these algebraic limit cycles for quintic systems.