Weighted pseudo almost periodic solutions of N-th order neutral differential equations with piecewise constant arguments

In this work, we present some existence theorems of weighted pseudo almost periodic solutions for N-th order neutral differential equations with piecewise constant argument by means of weighted pseudo almost periodic solutions of relevant difference equations.     

Square-mean almost periodic solutions to some stochastic evolution equations

This paper concerns the square-mean almost periodic mild solutions to a class of abstract nonautonomous functional integro-differential stochastic evolution equations in a real separable Hilbert space. By using the so-called "Acquistapace–Terreni" conditions and the Banach fixed point theorem, we establish the existence, uniqueness and the asymptotical stability of square-mean almost periodic solutions to such nonautonomous stochastic differential equations. As an application, almost periodic solution to a concrete nonautonomous stochastic integro-differential equation is considered to illustrate the applicability of our abstract results.     

Landesman–Lazer Type Conditions and Multiplicity Results for Nonlinear Elliptic Problems with Neumann Boundary Values

We establish the existence and multiplicity of solutions for Steklov problems under non- resonance or resonance conditions using variational methods. In our main theorems, we consider a weighted eigenvalue problem of Steklov type.     

Existence and Uniqueness of Renormalized Solution of Nonlinear Degenerated Elliptic Problems

In this paper, We study a general class of nonlinear degenerated elliptic problems associated with the differential inclusion β(u)-div(a(x, Du)+ F(u)) ■ f in Ω, where f ∈ L1 Ω. A vector field a(·,·) is a Carath′eodory function. Using truncation techniques and the generalized monotonicity method in the functional spaces we prove the existence of renormalized solutions for general L1-data. Under an additional strict monotonicity assumption uniqueness of the renormalized solution is established.     

Generalized area operators on L^p（R^n）

We introduce the generalized area operators by using nonnegative measures defined on upper half-spaces R＋^n＋1. The characterization of the boundedness and compactness of the generalized area operator from LP（]Rn） to Lq（IRn） is investigated in terms of s-Carleson measures with 1 〈 p, q 〈 ＋∞. In the case of p = q = 1, the weak type estimate is also obtained.     

《微分方程数值解》课程教学改革的探索和实践

结合近几年数学学院信息与计算科学专业微分方程数值解课程的教学实践,本文对该课程的教学内容、教学方法和手段,及以科研促教学等方面进行了探讨.     

基于单纯形分布的比例数据的回归分析

很多应用领域中的实验结果都表达成连续比例型数据,这类数据通常度量成为百分比、比率或比例,并取值于单位区间.为了采用弥散模型中的单纯形分布来模拟此类实验结果,本文首先研究单纯形分布的部分重要性质,在回归分析中参数估计和统计推断需要运用这些性质.模拟研究表明,当所研究情形不满足分布假设时,单纯形回归模型比Beta回归和分对数-正态回归模型更为稳健.通过对体外造血干细胞移植技术的真实数据分析,本文阐释这种方法和它针对异常值的稳健性.在R软件中,单纯形回归可以由程序包"simplexreg"实现,读者可以自行下载这个程序包,地址为http://my.zju.edu.cn/share/2466293(验证码:7919).     

连串反应中控制火焰的耦合GKS-CGL方程组解的极限行为

本文考虑连串反应中控制火焰的耦合广义Kuramoto Sivashinsky-Ginzburg Landau(GKS-CGL)方程组的周期初值问题,主要研究其解在系数g→0和δ→0时的极限行为.首先,采用Galerkin方法,通过构造一系列精细的先验估计,得到GKS-CGL方程组周期初值问题整体光滑解的存在唯一性.其次,利用一致有界估计证得GKS-CGL方程组极限解收敛,并给出解的收敛率估计.     

广义幂级数代数的滤链维数

In this paper, we study the properties of generalized power series modules and the filtration dimensions of generalized power series algebras. We obtain that [[△S,≤]]- gfd([[AS,≤]]) =△-gfd(A) if A is an R-module where R is a perfect and coherent commutative algebra, and(R, ≤) is standardly stratified.     

一道错解例题引发的探究性教学

南方出版社出版的高中学业水平考试达标测评丛书《系统集成》（2014年湖南省专用）第64页有这么一道例题： 题目设函数f（x）=a·b,其中向量a=（cos2x＋1,1）,b=（1,3（1/2）sin 2x＋m）.（1）求f（x）的最小正周期;（2）当x∈[0,π6]时,-4〈f（x）〈4恒成立,求实数m的取值范围．