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出版者:广西人民出版社

作者:定光桂

出品人:

页数:123

译者:

出版时间:1986.06

价格:68.00元

装帧:

isbn号码:9780007113705

丛书系列:

图书标签:

泛函分析
次加泛函
数学分析
优化
变分法
非线性分析
拓扑学
泛函不等式
应用数学
理论基础

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具体描述

This is the story of Ayna and Ceri, who both had Gifts, and of Gair, who thought he was ordinary. Gair spent his time gazing out onto the Moor and brooding. Ayna could answer questions about the future, Ceri could find things which were lost. Gair seems to have no Gift and knew he was a disappointment to his jovial, heroic father -- who is Chief. Perhaps his feelings of not fitting in was what made him so curious about these other different sorts of beings who lived on the Moor -- the Giants and the Dorig. Certainly it was because he believed he was ordinary that he did his best to become wise, and to learn as much as he could abou the three great Powers of Sun, Moon and Earth. And when the crisis came, Gair found the knowledge he had gained was to help save not only his own life but those of all his people.

《次加泛函引论》是一本专注于探索数学领域中“次加泛函”这一重要概念的学术专著。本书系统地介绍了次加泛函的基本定义、性质及其在不同数学分支中的应用，旨在为相关领域的研究者、高年级本科生和研究生提供一套严谨而全面的理论框架。全书围绕次加泛函的核心展开，首先从集合函数这一基础概念出发，逐步引入次加性、次可加性等关键属性，并在此基础上定义了次加泛函。随后，本书深入剖析了次加泛函的内在结构，探讨了其与单调性、下半连续性、Lipschitz连续性等重要性质之间的联系与区别。作者通过大量清晰的数学证明和严谨的逻辑推理，展现了次加泛函的丰富理论体系。在理论建构的同时，本书高度重视次加泛函在实际问题中的应用价值。书中详细阐述了次加泛函在凸分析、度量空间理论、优化理论、概率论以及博弈论等多个数学分支中的具体应用实例。例如，在凸分析中，次加泛函可以用来刻画某些非凸函数的性质，为非凸优化问题的研究提供了新的视角；在度量空间中，次加泛函的概念与距离函数的性质紧密相连，有助于深入理解度量空间的结构和性质；在概率论中，次加泛函与风险测度等概念有着密切的联系，在金融数学和保险数学等领域具有重要的理论意义。为了帮助读者更好地理解和掌握次加泛函的知识，本书在每个章节末都精心设计了练习题，涵盖了基础概念的巩固、理论性质的推导以及应用问题的分析等多个层面。这些习题旨在检验读者的理解程度，并激发其独立思考和解决问题的能力。此外，书中还提供了丰富的参考文献列表，方便读者进一步深入研究相关领域的最新进展。《次加泛函引论》的编写风格严谨而清晰，语言简洁明了，力求做到既有深度又不失可读性。本书的理论体系完整，论证严密，图文并茂，是数学专业领域内一本不可多得的参考书籍。无论是希望系统学习次加泛函理论的研究者，还是希望将其应用于实际问题的实践者，都能从本书中获益匪浅。