暂缺简介...

暂缺简介...

During the years 1903-1914，Ramanujan recorded most of his mathematical dis-coveries without proofs in notebooks.Although many of his results had already becn published by others，most had not.Almost a decade after Ramanujan's death in 1920，G.N.Watson and B.M.Wilson began to edit Ramanujan's notebooks，but，despite devoting over ten years to this project，they never completed their task.An uncdited photostat edition of the notebooks was published by the Tata Institute of Fundamental Research in Bombay in 1957.This book is the fifth and final volume devoted to the editing of Ramanujan's notebooks.PartsⅠ-Ⅲ，published，respectively，in 1985，1989，and 1991，contain accounts of Cbapters 1-21 in the second notebook，a revised enlarged edition of the first.Part IV，published in 1994，contains results from the 100 unorganized pages in the second notebook and the 33 unorganhed pages comprising the third notebook.Also examined in Part Ⅳ are the 16 organized chapters in the first notebook，which contain very little that is not found in the second notebook.In this fifth volume，we examine the remaining contents from the 133 unorganzed pages in the second and third notebooks，and the cIEums in the 198 unorganized pages of the first notebook that cannot be found in the succeeding notebooks.In contrast to the organzed portion of the first notebook，the unorganized material in the first notebook contains several results，particularly about class invariants，singular moduli，and values of theta-functions，which are not recorded in the second and tlurd notebooks.As in the first four volumes，either proofs are provided for claims not previously established in the literature，or citations are given for results already proved in the literature.

Readers will learn in the introduction to this volume that mathematicians owe a huge debt to R.A. Rankin and J.M. Whittaker for their efforts in preserving Ramanujan's "Lost Notebook." If it were not for them， Ramanujan's lost notebook likely would have been permanently lost. Rankin was born in Garlieston， Scotland， in October 1915 and died in Glasgow in January 2001. For several years he was professor of Mathematics at the University of Glasgow. An account of his life and work has been given by B.C. Berndt， W. Kohnen， and K. Ono in [79]. Whittaker was born in March 1905 in Cambridge and died in Sheffield in January 1984. At his retirement， he was vicechancellor of Sheffield University. A description of Whittaker's life and work has been written by W.K， Hayman.

During the years 1903-1914， Ramanujan recorded most of his mathematical discoveries without proofs in notebooks. Although many of his results were already found in the literature， most were not. Almost a decade after Ramanujan's death in 1920， G. N. Watson and B. M. Wilson began to edit Ramanujan's notebooks， but they never completed the task. A photostat edition， with no editing， was published by the Tata Institute of Fundamental Research in Bombay in 1957.This book is the fourth of five volumes devoted to the editing of Ramanujan's notebooks. Part I， published in 1985， contains an account of Chapters 1-9 in the second notebook as well as a description of Ramanujan's quarterly reports. Part II， published in 1989， comprises accounts of Chapters 10-15 in the second notebook. Part III， published in 1991， provides an account of Chapters 16-21 in the second notebook. This is the first of two volumes devoted to proving the results found in the unorganized portions of the second notebook and in the tlurd notebook. We also shall prove those results in the first notebook that are not found in the second or third notebooks. For those results that are known， we provide references in the literature where proofs may be found. Otherwise， we give complete proofs.

暂缺简介...

暂缺简介...

暂缺简介...

本书致力于探讨的问题有：府际合作治理作为区域大气污染防治的全新范式之理论证成、规范分析与实践样本探讨；继而分析宪法、行政法和环境法如何为区域大气污染府际合作治理提供正当性基础，阐释区域大气污染府际合作治理的基本原理，探究如何以既有制度资源为基础构建完备的区域大气污染府际合作治理制度体系；本书的*后两章从程序制度的视角探讨区域大气污染府际合作治理的利益协调机制和区域大气污染府际合作治理的纠纷解决之道。

《有机化学学习指导》是编者结合多年从事理科化学专业有机化学课程的教学实践编写的。全书包括二十四章内容，涵盖了目前国内流行的多种专业的多种有机化学教材所涉及的主要内容。《有机化学学习指导》的每章按照基本要求、内容提要、习题和参考答案四个部分编写。基本要求的提出，旨在帮助学生在学习中了解知识点的重点和难点；内容提要部分则对各章所包含的内容进行了全面系统的概括和总结，从而使学生对有机化学内容的规律性知识和特殊知识有比较系统的了解；习题部分结合内容提要的各个知识点设置了多层次的练习（包括完成反应、写出主要产物，立体化学、分离提纯、化合物鉴别，产物结构分析、反应机制以及有机合成等）。随后给出了详细的参考答案。因此，在使用《有机化学学习指导》的过程中，可以通过内容提要了解习题所涉及的内容，也可以结合国内流行的有机化学教材进行系统练习，从而巩固有机化学知识。