The controllability and observability are of great importance in boththeory and applications. A plete theory haeen established for linearhyperbolic systems, in particular, for linear wave equations. There havealso been some results for semilinear wave equations. For quasilinearhyperbolic systems that have numerous applications in mechanics, physicsand other applied sciences, however, very few results are available evenwith space dimension one. This monograph iased mainly on the results obtained by the author andhis collaborators in recent years. By mea~s of the theory on the semi-globalclassical solution, a simple and direct constructive method is presentedin a systematic way to get both the controllability and observability in theframework of classical solutions for general first order 1-D quasilinearhyperbolic systems with general nonlinear boundary conditions.Corresponding applications are given for 1-D quasilinear wave equationsand for unsteady flows in a tree-like work of open canals, respectively.
空间与映射的分类设想是点集拓扑学的主要研究方向之一。本书利用映射方法系统论述广义度量空间的基本理论,总结了20世纪的年代以来空间与映射理论的重要研究成果,特别包含了学者的研究工作,内容包括广义度量空间的产生、度量空间的映象和广义度量空间类等3章和2个附录。第二版在版的基础上,对部分内容作了修饰,补充了广义度量空间理论的若干新进展,适当调整了附录和参考文献,列举了一些尚未解决的问题供有兴趣的读者研究。 本书可以作为广义度量空间理论学习或研究的参考书,可供大学数学系高年级学生、研究生及研究工作者使用。
偏微分方程是数学学科的一个重要分支,它与其他数学分支均有广泛的联系,而且在自然科学与工程技术中有广泛的应用.本书主要讲述偏微分方程的一般理论,广义函数与sob01ev空间,椭圆边值问题,能量方法,算子半群等内容,为提高读者的整体数学素质提供了必要的材料,也为部分读者进一步学习与研究偏微分方程理论做了准备。 本书可作为高等院校数学系(数学、应用数学、计算机数学等专业)与有关理工科的研究生教材,也可作为数学、工程等领域的青年教师或科研人员的参考书。
The controllability and observability are of great importance in boththeory and applications. A plete theory haeen established for linearhyperbolic systems, in particular, for linear wave equations. There havealso been some results for semilinear wave equations. For quasilinearhyperbolic systems that have numerous applications in mechanics, physicsand other applied sciences, however, very few results are available evenwith space dimension one. This monograph iased mainly on the results obtained by the author andhis collaborators in recent years. By mea~s of the theory on the semi-globalclassical solution, a simple and direct constructive method is presentedin a systematic way to get both the controllability and observability in theframework of classical solutions for general first order 1-D quasilinearhyperbolic systems with general nonlinear boundary conditions.Corresponding applications are given for 1-D quasilinear wave equationsand for unsteady flows in a tree-like work of open canals, respectively.
《测度论(第1卷)(影印版)》是作者在莫斯科国立大学数学力学系的讲稿基础上编写而成的。卷包括了通常测度论教材中的内容:测度的构造与延拓,Lebesgue积分的定义及基本性质,Jordan分解,Radon-Nikodym定理,Fourier变换,卷积,L空间,测度空间,Newton-Leibniz公式,极大函数,Henstock-Kurzweil积分等每章最后都附有非常丰富的补充与习题,其中包含许多有用的知识,例如:Whitney分解,Lebesgue-Stieltjes积分,Hausdorff度,Brunn-Minkowski不等式,Hellinger积分与Hellinger距离,BMO类,Calderon-Zygmund分解等。书的最后有详尽的参考文献及历史注记。这是一本很好的研究生教材和教学参考书。
美国萨奥尔编著的《数值分析》是一本的数值分析教材,书中不仅全面论述了数值分析的基本方法,还深入浅出地介绍了计算机和工程领域使用的一些高级数值方法,如压缩、前向和后向误差分析、求解方程组的迭代方法等。每章的“实例检验”部分结合数值分析在各领域的具体应用实例,进一步探究如何更好地应用数值分析方法解决实际问题。此外,书中含有一些算法的matlab实现代码,并且每章都配有大量难度适宜的习题和计算机问题,便于读者学习、巩固和提高。