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本书旨在向数学工作者介绍大气/海洋科学（AOS）这一引人入胜且重要的领域。本书适合对偏微分方程及其在大气/海洋科学（AOS）中的应用感兴趣的研究生以及数学研究人员阅读参考。Written by a leading specialist in the area of atmosphere/ocean science （AOS）， the book presents an excellent introduction to this important topic. The goals of these lecture notes， based on courses presented by the author at the Courant Institute of Mathematical Sciences， are to introduce mathematicians to the fascinating and important area of AOS and， conversely， to develop a mathematical viewpoint on basic topics in AOS of interest to the disciplinary AOS community， ranging from graduate students to researchers. The lecture notes emphasize the serendipitous connections between applied mathematics and geophysical flows in the style of modern applied mathematics， where rigorous mathematical analysis as well as asymptotic， qualitative， and numerical modeling all interact to ease the understanding of physical phenomena. Reading these lecture notes does not require a previous course in fluid dynamics， although a serious reader should supplement them with additional information on geophysical flows， as suggested in the preface.The book is intended for graduate students and researchers working in interdisciplinary areas between mathematics and AOS. It is excellent for supplementary course reading or independent study.

本书是作者在莫斯科大学力学数学系多遍讲授数学分析课程的基础上写成的，自1981年第1版出版以来，到2015年已经修订、增补至第7版。作者加强了分析学、代数学和几何学等现代数学课程之间的联系，重点关注一般数学中最有本质意义的概念和方法，采用适当接近现代数学文献的语言进行叙述，在保持数学一般理论叙述严谨性的同时，也尽量体现数学在自然科学中的各种应用。全书共两卷，第一卷内容包括：集合、逻辑符号的运用、实数理论、极限和连续性、一元函数微分学、积分、多元函数及其极限与连续性、多元函数微分学。本书观点较高，内容丰富新颖，所选习题极具特色，是教材理论部分的有益补充。本书可作为综合大学和师范大学数学、物理、力学及相关专业的教师和学生的教材或主要参考书，也可供工科大学应用数学专业的教师和学生参考使用。

Ramsey理论是对数学对象的结构的研究，这本创新的书提供了Ramsey理论对整数的第一个有凝聚力的研究。它可能包含了这个蓬勃发展的学科中已解决和未解决问题的最实质性的说明。本书适合对组合学、数论和Ramsey理论感兴趣的研究生和数学研究人员阅读参考。Ramsey theory is the study of the structure of mathematical objects that is preserved under partitions. In its full generality， Ramsey theory is quite powerful， but can quickly become complicated. By limiting the focus of this book to Ramsey theory applied to the set of integers， the authors have produced a gentle， but meaningful， introduction to an important and enticing branch of modern mathematics. Ramsey Theory on the Integers offers students a glimpse into the world of mathematical research and the opportunity for them to begin pondering unsolved problems.For this new edition， several sections have been added and others have been significantly updated. Among the newly introduced topics are： rainbow Ramsey theory， an “inequality” version of Schur's theorem， monochromatic solutions of recurrence relations， Ramsey results involving both sums and products， monochromatic sets avoiding certain differences， Ramsey properties for polynomial progressions， generalizations of the Erd？s-Ginzberg-Ziv theorem， and the number of arithmetic progressions under arbitrary colorings.

本书是作者在莫斯科大学力学数学系多遍讲授数学分析课程的基础上写成的，自1981年第1版出版以来，到2015年已经修订、增补至第7版。作者加强了分析学、代数学和几何学等现代数学课程之间的联系，重点关注一般数学中最有本质意义的概念和方法，采用适当接近现代数学文献的语言进行叙述，在保持数学一般理论叙述严谨性的同时，也尽量体现数学在自然科学中的各种应用。全书共两卷，第一卷内容包括：集合、逻辑符号的运用、实数理论、极限和连续性、一元函数微分学、积分、多元函数及其极限与连续性、多元函数微分学。本书观点较高，内容丰富新颖，所选习题极具特色，是教材理论部分的有益补充。本书可作为综合大学和师范大学数学、物理、力学及相关专业的教师和学生的教材或主要参考书，也可供工科大学应用数学专业的教师和学生参考使用。

本书发展了处理非线性常微分方程和偏微分方程的拓扑和解析方法。本书适合对泛函分析感兴趣的研究生和数学研究人员阅读参考。Since its first appearance as a set of lecture notes published by the Courant Institute in 1974， this book has served as an introduction to various subjects in nonlinear functional analysis. The current edition is a reprint of these notes， with added bibliographic references.Topological and analytic methods are developed for treating nonlinear ordinary and partial differential equations. The first two chapters of the book introduce the notion of topological degree and develop its basic properties. These properties are used in later chapters in the discussion of bifurcation theory （the possible branching of solutions as parameters vary）， including the proof of Rabinowitz's global bifurcation theorem. Stability of the branches is also studied. The book concludes with a presentation of some generalized implicit function theorems of Nash-Moser type with applications to Kolmogorov-Arnold-Moser theory and to conjugacy problems.After more than 20 years， this book continues to be an excellent graduate level textbook and a useful supplementary course text.

测地流是现代动力系统理论体系中最重要的研究课题之一，其动力学理论已发展成为融合黎曼几何、芬斯勒几何、微分动力系统、哈密顿系统、辛几何、拓扑学等多个领域的前沿交叉学科。本书着重介绍了双曲流形的几何性质；在此基础上，研究了双曲流形上测地流的一致双曲性、拓扑动力学和遍历性等动力学性质。在内容上，本书十分强调几何直观，兼顾表述的启发性和论证的严密性，力求揭示概念和定理的数学本质。本书可供高等院校数学及相关专业的广大师生教学参考，亦适合作为硕士生和博士生一学期课程或讨论班的参考书。

From the earliest days of measure theory， invariant measures have held the interests of geometers and analysts alike， with the Haar measure playing an especially delightful role. The aim of this book is to present invariant measures on topological groups， progressing from special cases to the more general. Presenting existence proofs inspecial cases， such as compact metrizable groups， highlights how the added assumptions give insight into just what the Haar measure is like; tools from different aspects of analysis and/or combinatorics demonstrate the diverse views afforded the subject. After presenting the compact case， applications indicate how these tools can find use. The generalization to locally compact groups is then presented and applied to show relations between metric and measure theoretic invariance. Steinlage’s approach to the general problem of homogeneous action in the locally compact setting shows how Banach’s approach and that of Cartan and Weil can be unified with good effect. Finally， the situation of a nonlocally compact Polish group is discussed briefly with the surprisingly unsettling consequences indicated.The book is accessible to graduate and advanced undergraduate students who have been exposed to a basic course in real variables， although the authors do review the development of the Lebesgue measure. It will be a stimulating reference for students and professors who use the Haar measure in their studies and research.

《区间函数型数据评价理论、方法及其应用研究》是作者对近几年在区间函数型数据评价方面所取得的研究成果进行的系统整理与归类。《区间函数型数据评价理论、方法及其应用研究》共九章内容，可以分为四部分：第1部分为区间函数型数据评价理论体系构建，主要讲述区间函数型数据评价的基本步骤、赋权方法、评价结果处理等；第2部分为区间函数型主成分评价方法研究，主要阐述单变量和多变量区间函数型主成分评价方法、一般分布下的区间函数型主成分评价方法以及案例研究；第3部分为区间函数型聚类评价方法研究，主要阐述单变量和多变量区间函数型聚类评价方法、一般分布下的区间函数型聚类评价方法以及案例研究。第4部分为《区间函数型数据评价理论、方法及其应用研究》总结与展望。《区间函数型数据评价理论、方法及其应用研究》是关于综合评价理论在数据形式方向拓展与应用的一本学术著作，理论联系实际，内容新颖，研究方法具有前沿性。

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