New developments of functional differential equations combined with difference equations, and studies of related topics

与差分方程相结合的泛函微分方程的新进展及相关课题的研究

基本信息

批准号：
16540141
负责人：
NAITO Toshiki
金额：
$ 2.3万
依托单位：
The University of Electro-Communications
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2004
资助国家：
日本
起止时间：
2004 至 2006
项目状态：
已结题

项目摘要

Results about title of project : We considered a linear non-homogeneous difference equations with general matrix as a linear coefficient, and obtained a general formula representing its solutions with respect to discrete time and initial values by decomposing the solutions into the component of generalized eigen-spaces of the coefficient matrix. We followed up the detailed relation between this formula and the formula for the case that the coefficient matrix is an exponential function of a matrix. The new formula has three applications. Firstly, we obtained a formula determining by the initial values the asymptotic behavior of the solutions to the linear periodic differential equations. Secondary by transform of the results to the differential equations, we observed that the solutions are decomposed to the periodic functions and exponential functions. We made a difference equations which shows directly the relations of difference method and differential methods. As the third applicatio … More n, we observed that this new formula obtained by using difference methods is applicable to compute the Lyapunov numbers of solutions of linear differential equations. As a result, we succeeded to compute the Lyapunov numbers of solutions of non-homogeneous linear periodic differential equations. This number are not obtained by the classical methods.Results about differential equations and difference equations : The stability of solutions of Volterra difference equations on a Bamach space are obtained by using the summarbility of fundamental solutions and the characteristic operator. The asymptotic results of bounded and periodic property of solutions to functional differential equations are obtained by using Schawder fixed point theorem and contraction principle. Results about the existence of analytic solutions are obtained for the second order, non-homogeneous difference equations such that the eigen-values of the coefficient matrix are oneOther related researches : The Gevray well-posed property of initial values are obtained for a class of higher order, degenerated partial differential equations. Numerical methods for voice generation problems are constructed by using the finite element methods, and proposed an algorithm for the construction of the voice form. Finite element method and fundamental solution method are combined for the study of the reduced wave problem in the exterior region in two dimensional space. A homotopy theory are obtained about the space of singularity of energy functions of the space of smooth mappings from Riemann surface to complex projective spaces. Less

有关项目标题的结果：我们认为将一般矩阵的线性非均匀差方程作为线性系数，并获得了代表其解决方案相对于离散时间和初始值的通用公式，通过将溶液分解为核心基质的普通特征空间的组成部分。我们跟踪了此公式与公式之间的详细关系，即核心矩阵是矩阵的指数函数。新公式有三个应用程序。首先，我们获得了一个公式，该公式通过初始值确定的溶液对线性周期性微分方程的不对称行为。通过将结果转换为微分方程的次要，我们观察到解决方案分解为周期函数和指数函数。我们制作了一个差异方程式，该方程直接显示了差异方法和差异方法的关系。作为第三次应用……更多n，我们观察到，使用差异方法获得的这种新公式适用于计算线性微分方程的溶液的Lyapunov数量。结果，我们成功地计算了非均匀线性周期性微分方程的Lyapunov数量。这个数字不是通过经典方法获得的。关于微分方程和差方程的回报：通过使用基本解决方案的摘要和特征运算符，可以获得BAMACH空间上Volterra差异方程解决方案的稳定性。通过使用Schawder固定点定理和收缩原理，获得了界面对溶液对功能微分方程的不对称结果。有关二阶，非均匀差差方程的分析溶液的存在的结果，以使核心基质的特征值是一个相关的研究：获得一类高阶的初始值的Gevray拟及式特性，是一类较高级别的较高阶数值，退化的部分微分平等。语音生成问题的数值方法是通过使用有限元方法来构建的，并提出了用于构建语音形式的算法。将有限元方法和基本解决方案方法组合在一起，以研究二维空间中外部区域中的波浪问题。关于从黎曼表面到复杂的投影空间的平滑映射空间的能量函数奇异性的奇异性，获得了同一个理论。较少的

项目成果

期刊论文数量（204）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

New characterizations of exponential dichotomy and exponential stability of linear difference equations

DOI：
10.1080/00423110500211947
发表时间：
2005-09
期刊：
Journal of Difference Equations and Applications
影响因子：
1.1
作者：
Pham Huu Anh Ngoc;Toshiki Naito
通讯作者：
Pham Huu Anh Ngoc;Toshiki Naito

Massera's theorem for almost periodic solutions of functional differential equations

DOI：
10.2969/jmsj/1191418705
发表时间：
2004
期刊：
Journal of The Mathematical Society of Japan
影响因子：
0.7
作者：
S. Murakami;Toshiki Naito;N. Minh
通讯作者：
S. Murakami;Toshiki Naito;N. Minh

The homotopy of spaces of maps between real projective spaces

实射影空间之间的映射空间的同伦

DOI：
发表时间：
2006
期刊：
J. Math. Soc. Japan 58-4
影响因子：
0
作者：
小島定吉;糸川銚;酒井隆;戸田正人;小林治;二木昭人;浦川肇;十文字正樹;山口孝男;塩谷隆;小林亮一;T.Sakai;T. Sakai;Shingo Okuyama;Kazuhisa Shimakawa;Kohhei Yamaguchi
通讯作者：
Kohhei Yamaguchi

Holomorphic Solutions of a Functional Equation

函数方程的全纯解