New exact solutions to the (2 + 1)-dimensional Ito equation: Extended homoclinic test technique

Exact soliton solutions to the (2 + 1)-dimensional Ito equation are studied based on the idea of extended homoclinic test and bilinear method. Some explicit solutions, such as triangle function solutions, soliton solutions, doubly-periodic wave solutions and periodic solitary wave solutions, are obtained. It shows that the (2 + 1)-dimensional Ito equation has richer solutions. Besides, the elastic interactions of the solutions and their corresponding physical meaning are discussed.     

半素环的(1,σ)导子扩张

本文给出了半素环的自同构和（ １,σ）导子的扩张命题,这推广了［１］中的一些结论,然后借助半素环的广义中心里的幂等元在（１,σ）导子扩张模上建立起拓扑空间,从拓扑学角度给出（１,σ）导子扩张模的结构定理．     

New explicit traveling wave solutions for three nonlinear evolution equations

In this paper, using the extended tanh-function method, new explicit traveling wave solutions including rational solutions for three nonlinear evolution equations are obtained with the aid of Mathematica.     

New Bounds for the Inhomogenous Burgers and the Kuramoto-Sivashinsky Equations

We give a substantially simplified proof of the near-optimal estimate on the Kuramoto-Sivashinsky equation from a previous paper of the third author, at the same time slightly improving the result. That result relied on two ingredients: a regularity estimate for capillary Burgers and an a novel priori estimate for the inhomogeneous inviscid Burgers equation, which works out that in many ways the conservative transport nonlinearity acts as a coercive term. It is the proof of the second ingredient that we substantially simplify by proving a modified Kármán-Howarth-Monin identity for solutions of the inhomogeneous inviscid Burgers equation. We show that this provides a new interpretation of recent results obtained by Golse and Perthame.     

Forelli-Rudin积分的帐篷嵌入与Qp到α-Bloch空间上的积分算子——纪念李国平院士吴新谋教授诞辰100周年

该文借助关于帐篷空间的嵌入定理与Carleson型测度特征刻画了复单位球上从Q_p空间到α-Bloch空间的广义Cesàro算子的有界性与紧性.     

同伦分析法求解Burgers方程的初边值问题

采用同伦分析法求解了Burgers方程的一初边值问题,得到了它的近似解析解.在不同粘性系数情形下,对近似解与精确解进行了比较,发现在粘性系数不是非常小的情况下,用此方法得到的解析解与精确解符合地很好.     

Recovering a source term in the time-fractional Burgers equation by an energy boundary functional equation

An inverse source problem for the recovery of an unknown space–time dependent source term of a time-fractional Burgers equation is solved in the paper. By using the prescribed boundary data, a sequence of boundary functions is derived, which together with the zero element constitute a linear space. An energy boundary functional equation is derived in the linear space, of which the time-dependent energy is preserved for each energy boundary function. The iterative algorithm used to recover the unknown source with energy boundary functions as the bases is developed, which is robust and convergent fast.     

Complete Convergence and Complete Moment Convergence for Maximal Weighted Sums of Extended Negatively Dependent Random Variables

In this paper,the complete convergence and complete moment convergence for maximal weighted sums of extended negatively dependent random variables are investigated.Some sufficient conditions for the convergence are provided.In addition,the Marcinkiewicz–Zygmund type strong law of large numbers for weighted sums of extended negatively dependent random variables is obtained.The results obtained in the article extend the corresponding ones for independent random variables and some dependent random variables.     

An Initial Boundary-Value Problem in a Half-Strip for the Korteweg–De Vries Equation in Fractional-Order Sobolev Spaces

Abstract

An initial boundary-value problem in a half-strip with one boundary condition for the Korteweg–de Vries equation is considered and results on global well-posedness of this problem are established in Sobolev spaces of various orders, including fractional. Initial and boundary data satisfy natural (or close to natural) conditions, originating from properties of solutions of a corresponding initial-value problem for a linearized KdV equation. An essential part of the study is the investigation of special solutions of a “boundary potential” type for this linearized KdV equation.     

Burgers方程的小波精细积分算法

求解偏微分方程的常用方法包括有限差分法、有限元法等。近年来,小波分析在偏微分方程数值求解中的应用已引起很多学者的关注,例如采用Daubechies小波或shannon小波构造的小波配置方法已经取得较好的结果。钟万勰院士提出的偏微分方程的子域精细积分方法是一种半解析方法,方法简单,精度高。将小波方法和精细积分方法相结合应用于偏微分方程的数值求解中将有利于提高算法的精度和稳定性,为此本文以Burgers方程为例,提出了一种求解一维非线性抛物型偏微分方程的小波精积分方法。该方法用拟小波配点法对空间域进行离散,建立起对时间的常微分方程组,然后采用精细时程积分方法对该方程组求解。数值计算结果表明,该方法同其它方法相比,具有计算格式简单,数值稳定性和精度较高的优点。