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The Calculus of Braids
This introduction to braid groups keeps prerequisites to a minimum, while discussing their rich mathematical properties and applications.
Braids, Conformal Module, Entropy, and Gromov's Oka Principle
This book studies the relation between conformal invariants and dynamical invariants and their applications, taking the reader on an excursion through a wide range of topics. The conformal invariants, called here the conformal modules of conjugacy classes of elements of the fundamental group, were proposed by Gromov in the case of the twice punctured complex plane. They provide obstructions to Gromov's Oka Principle. The invariants of the space of monic polynomials of degree n appeared earlier in relation to Hilbert's 13th Problem, and are called the conformal modules of conjugacy classes of braids. Interestingly, the conformal module of a conjugacy class of braids is inversely proportional ...
Braid Groups
Braids and braid groups, the focus of this text, have been at the heart of important mathematical developments over the last two decades. Their association with permutations has led to their presence in a number of mathematical fields and physics. As central objects in knot theory and 3-dimensional topology, braid groups has led to the creation of a new field called quantum topology. In this well-written presentation, motivated by numerous examples and problems, the authors introduce the basic theory of braid groups, highlighting several definitions that show their equivalence; this is followed by a treatment of the relationship between braids, knots and links. Important results then treat the linearity and orderability of the subject. Relevant additional material is included in five large appendices. Braid Groups will serve graduate students and a number of mathematicians coming from diverse disciplines.
Braid and Knot Theory in Dimension Four
Braid theory and knot theory are related via two famous results due to Alexander and Markov. Alexander's theorem states that any knot or link can be put into braid form. Markov's theorem gives necessary and sufficient conditions to conclude that two braids represent the same knot or link. Thus, one can use braid theory to study knot theory and vice versa. In this book, the author generalizes braid theory to dimension four. He develops the theory of surface braids and applies it tostudy surface links. In particular, the generalized Alexander and Markov theorems in dimension four are given. This book is the first to contain a complete proof of the generalized Markov theorem. Surface links are ...
The Delineator
Issue for Oct. 1894 has features articles on Mount Holyoke College and Millinery as an employment for women.
Stabilization of Hypersonic Boundary-Layer: Acoustic Metasurfaces
This book explores the mechanisms and applications of acoustic metasurfaces in the hypersonic transition control area. It begins with an introduction of the concepts of acoustic metasurface and hypersonic boundary-layer stabilization, which also provides a full scene of the research progress in the past two decades. This book then discusses the modeling methods of various acoustic metasurfaces, including the regular and irregular ones, and describes how the models are to be used in theoretical analysis and numerical calculations. The design strategies and optimization methods are presented to promote the applications in the engineering community. The possible stabilization mechanisms are explored, and the proposed analysis methods are used to clarify other flow instabilities. This book delivers valuable insight for aerospace engineers, postgraduate students, and researchers.
Modern Mechanism
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House documents
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