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。

暂缺简介...

Applications in modern biotechnology and molecular medicine often require simulation of biomolecular systems in atomic representation with immense length and timescales that are far beyond the capacity of computer power currently available. As a consequence， there is an increasing need for reduced models that describe the relevant dynamical properties while at the same time being less complex. In this book the authors exploit the existence of metastable sets for constructing such a reduced molecular dynamics model， the so-called Markov state model （MSM）， with good approximation properties on the long timescales. With its many examples and illustrations， this book is addressed to graduate students， mathematicians， and practical computational scientists wanting an overview of the mathematical background for the ever-increasing research activity on how to construct MSMs for very different molecular systems ranging from peptides to proteins， from RNA to DNA， and via molecular sensors to molecular aggregation. This book bridges the gap between mathematical research on molecular dynamics and its practical use for realistic molecular systems by providing readers with tools for performing in-depth analysis of simulation and data-analysis methods.

2022版课标特别关注代数推理，用代数推理发展数学逻辑，实现数学证明。书稿主要基于代数本质，以符号为载体，感受算术到代数的演变历程；基于代数推理教学，感悟代数推理的内容产生和方式表达，分化研究代数推理的具体呈现，整体建构代数推理的知识体系；基于代数推理应用，翻译代数问题，推理代数过程，表达代数逻辑，外显抽象的代数推理过程，感受代数推理的价值，体会代数推理的必要性、逻辑性与严谨性，实现从算术思维走向代数思维。

这本书以悠闲的方式涵盖了一个完整学年概率课程的所有标准内容，重点是在研究生或高年级本科生高级课程中的金融分析应用。它融入了相当多的测度论和实分析，但以特别简单和直观的方式介绍了σ-域、测度论和期望。每章都包含大量的例子和练习，丰富了教材的呈现。Walsh是这个学科的一位大师，他写了一本关于概率的精彩书籍，恰好适合这个水平。他以悠闲的步调覆盖了学生需要了解的所有重要主题，并提供了优秀的例子。我很遗憾，几年前我教授这门课程时，他的书还没有问世。—Ioannis Karatzas， Columbia University在这本精彩的书中，John Walsh呈现了概率论的全景图，从关于均值、中位数和众数的基本事实开始，继而对马尔可夫链和鞅进行了优秀的描述，并以布朗运动为高潮。作者的个人风格贯穿全书；他成功地将严谨性与对关键思想的强调结合起来，使读者在被太多细节围绕时也不会忘记森林的全貌。正如前言所述，“要愉快地教授一门课程，同时也应该在学习过程中获得乐趣。”事实上，几乎所有的教师都将从这本书中学到一些新知识（例如，Skorokhod嵌入的潜在理论证明），同时它对学生来说既有吸引力又易于理解。—Yuval Peres， Microsoft

本书介绍了相对论的数学基础的相关理论知识。目标读者是数学、其他科学和工程专业的高年级本科生和研究生。读者应了解高等微积分的基础知识、一些解微分方程的技巧、一些线性代数知识以及集合论和群论的基础知识。本书适合对相对论的数学方面感兴趣的高年级本科生、研究生以及数学研究人员阅读参考。This book has three main goals. First， it explores a selection of topics from the early period of the theory of relativity， focusing on particular aspects that are interesting or unusual. These include the twin paradox; relativistic mechanics and its interaction with Maxwell's laws; the earliest triumphs of general relativity relating to the orbit of Mercury and the deflection of light passing near the sun; and the surprising bizarre metric of Kurt G？del， in which time travel is possible. Second， it provides an exposition of the differential geometry needed to understand these topics on a level that is intended to be accessible to those with just two years of university-level mathematics as background. Third， it reflects on the historical development of the subject and its significance for our understanding of what reality is and how we can know about the physical universe. The book also takes note of historical prefigurations of relativity， such as Euler's 1744 result that a particle moving on a surface and subject to no tangential acceleration will move along a geodesic， and the work of Lorentz and Poincaré on space-time coordinate transformations between two observers in motion at constant relative velocity.The book is aimed at advanced undergraduate mathematics， science， and engineering majors （and， of course， at any interested person who knows a little university-level mathematics）. The reader is assumed to know the rudiments of advanced calculus， a few techniques for solving differential equations， some linear algebra， and basics of set theory and groups.

本书介绍了非线性色散方程理论的最新进展，主要是非线性薛定谔方程。本书适合对偏微分方程及其相关领域感兴趣的研究生和数学研究人员阅读参考。This volume presents recent progress in the theory of nonlinear dispersive equations， primarily the nonlinear Schr？dinger （NLS） equation. The Cauchy problem for defocusing NLS with critical nonlinearity is discussed. New techniques and results are described on global existence and properties of solutions with large Cauchy data. Current research in harmonic analysis around Strichartz's inequalities and its relevance to nonlinear PDE is presented. Several topics in NLS theory on bounded domains are reviewed. Using the NLS as an example， the book offers comprehensive insight on current research related to dispersive equations and Hamiltonian PDEs.

《转移定价模型与方法》以转移定价决策模型与方法为核心主题，以不同产品环境和市场环境为背景展开研究。《转移定价模型与方法》共分为八章，分别研究不同市场竞争环境和不同产品类型下的企业转移定价决策问题，涉及垄断环境下的转移定价、竞争环境下的转移定价、考虑库存的转移定价、多产品转移定价、技术产品转移定价和动态转移定价等研究问题。《转移定价模型与方法》的研究结果发展和完善了转移定价决策理论模型与优化方法，为解决不同环境下的企业转移定价决策实践问题提供了重要的理论依据和实践指导。

本书以通俗易懂的方式系统地介绍和阐述结构方程模型 （SEM） 的基本概念和统计原理，侧重结构方程模型的实际运用，介绍和示范各种常用结构方程模型，以及许多新近发展的模型，包括带分类条目的验证性因子分析 （CFA） 模型、双因子CFA模型、贝叶斯CFA 模型、缺失值多重插补 （MI）、潜变量合理值的估计和应用、调节中介效应模型、贝叶斯路径分析模型、带个体差异观察时间的潜发展模型 （LGM）、检验带分类变量的量表的测量不变性、纵向潜类别分析 （LLCA）、潜转换分析 （LTA）、带协变量和远端结局变量的潜发展混合模型 （GMM）、手动实施 BCH 方法和三步法混合模型建模、各种结构方程模型的蒙特卡罗模拟功效分析以及潜类别分析 （LCA） 模型的样本量估计。本书采用国际著名 SEM 软件Mplus估计所有模型，使用真实数据演示各种模型估计，详细解读程序代码及输出结果。本书提供用于示范模型的数据和相应的Mplus程序，参照本书提供的例题和相应的计算机程序，读者便能自己实践各种结构方程模型。本书可作为大学社会科学及公共卫生学院研究生以及统计和生物统计专业本科生的参考书，也可作为相关学科的研究人员从事统计分析的工具书。