扩展的Boussinesq系统Lax对的Backlund变换和递推求解公式的导出

本文研究2+1维的扩展经典Boussinesq系统.首先,研究了系统的Lax对,找出了一个形式十分新颖的带有一个任意函数的Backlund变换.然后,又导出了Lax对的特征函数的生成公式.最后,利用Backlund变换和Lax对特征函数生成公式相结合得出了Lax对的递推求解公式.利用此递推公式,求出了一些Lax对的解.     

扩展的Boussinesq系统Lax对的Bäcklund变换和递推求解公式的导出

本文研究2+1维的扩展经典Boussinesq系统.首先,研究了系统的Lax对,找出了一个形式十分新颖的带有一个任意函数的Backlund变换.然后,又导出了Lax对的特征函数的生成公式.最后,利用Backlund变换和Lax对特征函数生成公式相结合得出了Lax对的递推求解公式.利用此递推公式,求出了一些Lax对的解.     

关于Strichartz的一个谱对准则

研究了与压缩迭代函数系和扩张迭代函数系相关的自仿测度的谱性质.在和谐对的条件下,分别确定了谱对形成的一些充分条件和必要条件.首先,给出了Strichartz谱对准则的几个等价形式.其次,得到了这个谱对成立的两个必要条件.最后,提供了Strichartz谱对准则的一个严格而详细的证明.     

基于动力学模型的人口数量预测和政策评估

随着单独二胎政策的放开,计划生育政策再次引起了人们的关注.为评估生育胎次对中国人口数量的影响,本文建立了关于人口增长的动力学模型.首先,分别对辽宁省和新疆自治区的人口数据进行了拟合,评估了"二胎"政策对两地区人口的影响.其次,对全国人口数据和抚养比进行了拟合和预测.最后,通过参数敏感性分析,评估各因素对总人口增长的影响.     

下部有常热通量加热作用时非均匀温度梯度和磁场对Marangoni对流作用的影响

在一个水平流体层中,下部加热和上部致冷,热通量为常数时,研究磁场和非均匀温度梯度对Marangoni对流作用的影响.对线性稳定分析进行了详细的研究.分析了各种参数对对流作用的影响.考虑了6种基本的温度分布曲线,给出了造成失稳影响的一些普遍结论.     

一类复三次样条

J. H. Ahlberg, E. N. Nilson和J. L. Walsh研究了复三次样条的存在唯一性,特别是对复三次样条的收敛性作了比较细致的讨论。另外,还考虑了解析样条以及复三次样条的两个基本积分关系式(参看文[1])。J. H. Ahlberg在论述复样条已有成果的基础上,对复样条作了进一步的推广和研究(参看[2])。文[3]对Hermite插值问题研究了亏数为     

具有对合的自反环（英文）

本文研究了具有对合的环的自反性质.称环R的一个对合*是自反的,如果对任意a,b∈R,由aRb=0可推出bRa~*=0.若环R具有自反的对合*,则称R为*-自反环.我们对*-自反环的性质进行了刻画,并给出了一些具体的例子.作为应用,我们主要研究了与*-自反环相关的广义逆.对*-自反环R,我们证明了Moore-Penrose可逆元未必是群可逆元.     

集值映象的某些重合定理

Browder[1]已得到了Schauder不动点定理的加强形式.许多作者从不同方向推广了Browder的结果.最近H.M.Ko;K.K.Tan[2]在放松紧性条件下得到了Browder定理的改进,K.K.Tan[3]将Browder定理推广到了集值映象对的重合定理,在本文中我们得到了集值映象对的某些重合定理,它们分别改进和推广了[1,2,3]中主要结果.     

栅格翼空化干扰水动力建模研究

对水下超空泡栅格翼水动力进行了研究.分析了叶片数、叶片间距、叶片厚度、叶片攻角和空化数对栅格翼水动力的影响.揭示了叶片间隙中的空泡流动对水动力的干扰机理.建立了超空泡栅格翼水动力数学模型,并用实验结果进行了验证.最后基于模型解释了实验中发现的栅格翼水动力变化规律.     

单物种人口模型指数隐式Euler方法的振动性

本文研究了用以描述单物种人口模型的延迟Logistic方程的数值振动性.对方程应用隐式Euler方法进行求解,针对离散格式定义了指数隐式Euler方法,证明了该方法的收敛阶为1.根据线性振动性理论获得了数值解振动的充分条件.进而还对非振动数值解的性质作了讨论.最后用数值算例对理论结果进行了验证.     

基于梯度的Sylvester共轭矩阵方程的迭代解

本文提出了一种基于梯度的Sylvester共轭矩阵方程的迭代算法.通过引入一个松弛参数和采用递阶辨识原理,构造一个迭代算法求解Sylvester矩阵方程.通过应用复矩阵的实数表达以及实数表示的一些性质,收敛性分析表明在一定假设条件下,对于任意初始值,迭代方法均收敛到精确解,数值算例也表明了所给方法的有效性.     

Real polynomial iterative roots in the case of nonmonotonicity height ≥ 2

It is known that a strictly piecewise monotone function with nonmonotonicity height ≥ 2 on a compact interval has no iterative roots of order greater than the number of forts. An open question is: Does it have iterative roots of order less than or equal to the number of forts? An answer was given recently in the case of "equal to". Since many theories of resultant and algebraic varieties can be applied to computation of polynomials, a special class of strictly piecewise monotone functions, in this paper we investigate the question in the case of "less than" for polynomials. For this purpose we extend the question from a compact interval to the whole real line and give a procedure of computation for real polynomial iterative roots. Applying the procedure together with the theory of discriminants, we find all real quartic polynomials of non-monotonicity height 2 which have quadratic polynomial iterative roots of order 2 and answer the question.     

Strong Convergence Theorems for Quasi-Nonexpansive Mappings and Uniformly L-Lipschitzian Asymptotically Pseudo-Contractive Mappings in Banach Spaces

A new 𝒮-generated Ishikawa iteration with errors is proposed for a pair of quasi-nonexpansive mapping and uniformly L-Lipschitzian asymptotically pseudo-contractive mapping in real Banach spaces. We show that the proposed iterative scheme converges strongly to a common solution of quasi-nonexpansive mapping and uniformly L-Lipschitzian asymptotically pseudo-contractive mapping in real Banach spaces. A comparison table is prepared using a numeric example which shows that the proposed iterative algorithm is faster than some known iterative algorithms.     

关于变分包含问题和不动点问题的一些结果及应用

基于一个广义迭代算法,考虑了逼近一类拟变分包含问题解集与一族无限多个非扩张映象公共不动点集的某一公共元问题.在实Hilbert空间的框架下,证明了由次广义迭代算法产生的迭代序列强收敛到某一公共元.     

实规范矩阵的特征值问题

实对称矩阵的特征值问题,无论是低阶稠密矩阵的全部特征值问题,或高阶稀疏矩阵的部分特征值问题,都已有许多有效的计算方法,迄今最重要的一些成果已总结在[5]中。本文利用规范矩阵的一些重要性质将对于Hermite矩阵(特别是对弥矩阵)特征值问题的一些有效算法推广到规范矩阵的特征值问题,由于对复规范阵的推广是简单的,而且实际上常遇到的是实矩阵(这时常要求只用实运算),因此我们着重讨论实规范矩阵的特征值问题。     

Iterative solutions to the extended Sylvester-conjugate matrix equations

This paper is concerned with iterative solutions to a class of complex matrix equations. By applying the hierarchical identification principle, an iterative algorithm is constructed to solve this class of complex matrix equations. The range of the convergence factor is given to guarantee that the proposed algorithm is convergent for arbitrary initial matrix by applying a real representation of a complex matrix as a tool. By using some properties of the real representation, a sufficient convergence condition that is easier to compute is also given by original coefficient matrices. Two numerical examples are given to illustrate the effectiveness of the proposed methods.     

Iterative algorithms for solving a class of complex conjugate and transpose matrix equations

This paper is concerned with iterative solutions to a class of complex matrix equations, which include some previously investigated matrix equations as special cases. By applying the hierarchical identification principle, an iterative algorithm is constructed to solve this class of matrix equations. A sufficient condition is presented to guarantee that the proposed algorithm is convergent for an arbitrary initial matrix with a real representation of a complex matrix as tools. By using some properties of the real representation, a convergence condition that is easier to compute is also given in terms of original coefficient matrices. A numerical example is employed to illustrate the effectiveness of the proposed methods.     

Strong Convergence Theorem for Multiple Sets Split Feasibility Problems in Banach Spaces

The purpose of this article is to study the iterative approximation of solution to multiple sets split feasibility problems in p-uniformly convex real Banach spaces that are also uniformly smooth. We propose an iterative algorithm for solving multiple sets split feasibility problems and prove a strong convergence theorem of the sequence generated by our algorithm under some appropriate conditions in p-uniformly convex real Banach spaces that are also uniformly smooth.     

A convergence analysis result for constrained convex minimization problem

Abstract

Our purpose in this paper is to obtain strong convergence result for approximation of solution to constrained convex minimization problem using a new iterative scheme in a real Hilbert space. Furthermore, we give numerical analysis of our iterative scheme.     

Convergence of hybrid viscosity and steepest-descent methods for pseudocontractive mappings and nonlinear Hammerstein equations

In this article, we first introduce an iterative method based on the hybrid viscosity approximation method and the hybrid steepest-descent method for finding a fixed point of a Lipschitz pseudocontractive mapping (assuming existence) and prove that our proposed scheme has strong convergence under some mild conditions imposed on algorithm parameters in real Hilbert spaces. Next, we introduce a new iterative method for a solution of a nonlinear integral equation of Hammerstein type and obtain strong convergence in real Hilbert spaces. Our results presented in this article generalize and extend the corresponding results on Lipschitz pseudocontractive mapping and nonlinear integral equation of Hammerstein type reported by some authors recently. We compare our iterative scheme numerically with other iterative scheme for solving non-linear integral equation of Hammerstein type to verify the efficiency and implementation of our new method.