Part of London Mathematical Society Lecture Note Series
Publication planned for: August 2016
availability: Not yet published - available from August 2016
format: Paperback
isbn: 9781316619582
This study of graded rings includes the first systematic account of the graded Grothendieck group, a powerful and crucial invariant in algebra which has recently been adopted to classify the Leavitt path algebras. The book begins with a concise introduction to the theory of graded rings and then focuses in more detail on Grothendieck groups, Morita theory, Picard groups and K-theory. The author extends known results in the ungraded case to the graded setting and gathers together important results which are currently scattered throughout the literature. The book is suitable for advanced undergraduate and graduate students, as well as researchers in ring theory.
Introduction
1. Graded rings and graded modules
2. Graded Morita theory
3. Graded Grothendieck groups
4. Graded Picard groups
5. Classification of graded ultramatricial algebras
6. Graded versus ungraded K-theory
References
Index.
Part of New Mathematical Monographs
available from August 2016
format: Hardback
isbn: 9781107097612
scriminant equations are an important class of Diophantine equations with close ties to algebraic number theory, Diophantine approximation and Diophantine geometry. This book is the first comprehensive account of discriminant equations and their applications. It brings together many aspects, including effective results over number fields, effective results over finitely generated domains, estimates on the number of solutions, applications to algebraic integers of given discriminant, power integral bases, canonical number systems, root separation of polynomials and reduction of hyperelliptic curves. The authors' previous title, Unit Equations in Diophantine Number Theory, laid the groundwork by presenting important results that are used as tools in the present book. This material is briefly summarized in the introductory chapters along with the necessary basic algebra and algebraic number theory, making the book accessible to experts and young researchers alike.
Gathers important results on discriminant equations and makes them accessible to experts and young researchers alike
Considers many different aspects that may stimulate further research in the area
The authors draw on their 40 years of experience in the field
Part of Cambridge Studies in Advanced Mathematics
Publication planned for: October 2016
availability: Not yet published - available from October 2016
format: Hardback
isbn: 9781107019669
This book provides a rigorous but accessible introduction to the mathematical theory of the three-dimensional Navier?Stokes equations, providing self-contained proofs of some of the most significant results in the area, many of which can only be found in research papers. Highlights include the existence of global-in-time Leray?Hopf weak solutions and the local existence of strong solutions; the conditional local regularity results of Serrin and others; and the partial regularity results of Caffarelli, Kohn and Nirenberg. Appendices provide background material and proofs of some 'standard results' that are hard to find in the literature. A substantial number of exercises are included, with full solutions given at the end of the book. As the only introductory text on the topic to treat all of the mainstream results in detail, this book is an ideal text for a one- or two-semester graduate course. It is also a useful resource for anyone working in mathematical fluid dynamics.
Covers three cornerstone 'classical results' in the theory of the Navier?Stokes equations
Provides a thorough grounding of all the essential results in one convenient location
A self-contained source, accessible to graduates, which can be used for a one- or two-semester course
Series:De Gruyter Textbook
Paperback
Publication Date:
February 2016
ISBN:
978-3-11-037815-3
Covers point set topology and combinatorial topology
Contains abundant examples and exercises to facilitate the study
Entry level textbook, allowing easy access to the topic
The aim of the book is to give a broad introduction of topology to undergraduate students. It covers the most important and useful parts of the point-set as well as the combinatorial topology. The development of the material is from simple to complex, concrete to abstract, and appeals to the intuition of readers. Attention is also paid to how topology is actually used in the other fields of mathematics. Over 150 illustrations, 160 examples and 600 exercises will help readers to practice and fully understand the subject.
ii+155 pages, soft cover, ISBN 978-3-88538-234-8,
Graph theory belongs to the most dynamic disciplines within present mathematics, and due to its beauty and wide applications, also to the most popular areas of mathematics. The area of graph labellings, on whose selected part this monograph is focussing, is very young. Roughly speaking, a graph labelling is an assignment of integers to the vertices or edges, or both, of a graph, subject to certain conditions. The bases of the theory of graph labellings were laid out in the late 1960s, and since then a plethora of graph labellings methods and techniques have been studied in over 1900 research papers, monographs and theses.
One of the most famous open problems in graph theory nowadays is the Graceful Tree Conjecture which says that every tree can be gracefully labelled. A tree with m edges has a graceful labelling if its vertices can be assigned the labels 0,1,...,m such that the absolute values of the differences in vertex labels between adjacent vertices form the set {1,...,m}. The conjecture dates back to the 1960s and it is also known as the Ringel-Kotzig, Rosa or Ringel-Kotzig-Rosa Conjecture. Only limited progress has been made on the conjecture over the last fifty years despite numerous research papers and various theses and surveys.
This monograph adds new results and new approaches to the existing knowledge about vertex labellings of graphs. We believe that it brings advances in the study of vertex labellings of graphs and that it will be of interest to researchers in this area. We hope that the book will initiate further development in the study of the newly introduced concepts of Graph Chessboards and Labelling Relations as useful tools to investigate vertex labellings of graphs and to tackle the Graceful Tree Conjecture. We believe that especially the visualization provided via the graph chessboards, and the Graph Processor, developed and described in this book, could make this topic more accessible to working mathematicians as well as to students starting their research work in this area.
Morningside Lectures in Mathematics, Volume 4
Published: 29 March 2016
Paperback
408 pages
The works presented in this volume originated in lectures on analysis in partial differential equations, given in at the Academy of Mathematics and Systems Science, Chinese Academy of Sciences.
Included are: Jean-Yves Chemin, on profile decomposition and its applications to the Navier?Stokes system; Hongjie Dong, on Lp estimates for parabolic equations; Xiaochun Li, on the Hardy?Littlewood circle method; Fanghua Lin, on elliptic free boundary problems; Alexis Vasseur, on the De Giorgi method for elliptic and parabolic equations; Jiahong Wu, on 2D Boussinesq equations with partial or fractional dissipation; and Xiaoyi Zhang, on analytic tools for critical dispersive PDEs.