Triangular Products of Group Representations and Their Applications

Triangular Products of Group Representations and Their Applications
Author: S.M. Vovsi
Publisher: Springer Science & Business Media
Total Pages: 140
Release: 2012-12-06
Genre: Mathematics
ISBN: 1468467212

The construction considered in these notes is based on a very simple idea. Let (A, G ) and (B, G ) be two group representations, for definiteness faithful and finite 1 2 dimensional, over an arbitrary field. We shall say that a faithful representation (V, G) is an extension of (A, G ) by (B, G ) if there is a G-submodule W of V such that 1 2 the naturally arising representations (W, G) and (V/W, G) are isomorphic, modulo their kernels, to (A, G ) and (B, G ) respectively. 1 2 Question. Among all the extensions of (A, G ) by (B, G ), does there exist 1 2 such a "universal" extension which contains an isomorphic copy of any other one? The answer is in the affirmative. Really, let dim A = m and dim B = n, then the groups G and G may be considered as matrix groups of degrees m and n 1 2 respectively. If (V, G) is an extension of (A, G ) by (B, G ) then, under certain 1 2 choice of a basis in V, all elements of G are represented by (m + n) x (m + n) mat rices of the form (*) ~1-~ ~-J lh I g2 I .

Sparse and Redundant Representations

Sparse and Redundant Representations
Author: Michael Elad
Publisher: Springer Science & Business Media
Total Pages: 376
Release: 2010-08-12
Genre: Mathematics
ISBN: 1441970118

A long long time ago, echoing philosophical and aesthetic principles that existed since antiquity, William of Ockham enounced the principle of parsimony, better known today as Ockham’s razor: “Entities should not be multiplied without neces sity. ” This principle enabled scientists to select the ”best” physical laws and theories to explain the workings of the Universe and continued to guide scienti?c research, leadingtobeautifulresultsliketheminimaldescriptionlength approachtostatistical inference and the related Kolmogorov complexity approach to pattern recognition. However, notions of complexity and description length are subjective concepts anddependonthelanguage“spoken”whenpresentingideasandresults. The?eldof sparse representations, that recently underwent a Big Bang like expansion, explic itly deals with the Yin Yang interplay between the parsimony of descriptions and the “language” or “dictionary” used in them, and it became an extremely exciting area of investigation. It already yielded a rich crop of mathematically pleasing, deep and beautiful results that quickly translated into a wealth of practical engineering applications. You are holding in your hands the ?rst guide book to Sparseland, and I am sure you’ll ?nd in it both familiar and new landscapes to see and admire, as well as ex cellent pointers that will help you ?nd further valuable treasures. Enjoy the journey to Sparseland! Haifa, Israel, December 2009 Alfred M. Bruckstein vii Preface This book was originally written to serve as the material for an advanced one semester (fourteen 2 hour lectures) graduate course for engineering students at the Technion, Israel.

Representations of Finite and Compact Groups

Representations of Finite and Compact Groups
Author: Barry Simon
Publisher: American Mathematical Soc.
Total Pages: 280
Release: 1996
Genre: Mathematics
ISBN: 0821804537

This text is a comprehensive pedagogical presentation of the theory of representation of finite and compact Lie groups. It considers both the general theory and representation of specific groups. Representation theory is discussed on the following types of groups: finite groups of rotations, permutation groups, and classical compact semisimple Lie groups. Along the way, the structure theory of the compact semisimple Lie groups is exposed. This is aimed at research mathematicians and graduate students studying group theory.

Product Design and the Role of Representation

Product Design and the Role of Representation
Author: EUJIN. SELF PEI (JAMES ANDREW.)
Publisher: CRC Press
Total Pages: 232
Release: 2021-11-19
Genre:
ISBN: 9780367630010

This book extends understanding of the design process by exploring design representation types and examining them as theoretical constructs. It shows how fidelity and ambiguity inform the creative act of design, and considers design thinking through the lens of design representation. Design thinking is a method that has the potential to stimulate and enhance creativity. This book enhances understanding of what constitutes design thinking, why it is used and how it can be applied in practice to explore and develop ideas. The book positions a particular type of thinking through design representations, exploring this from its roots in design history, to the types of thinking in action associated with contemporary design practice. A taxonomy of design representations as a scaffold to express design intent, is applied to real world case studies. Product Design and the Role of Representation will be of interest to those working in or studying product development, engineering design and additive manufacturing. "This book responds to the expression 'all you always wanted to know about design representation but didn't know where to ask'. Indeed, the book is a thematic guide to design representation, and the amount of information about design representations it holds is phenomenal." Professor Gabriela Goldschmidt Technion - Israel Institute of Technology

Reduction of the Direct Product of Representations of the Poincareʹ Group

Reduction of the Direct Product of Representations of the Poincareʹ Group
Author: H. E. Moses
Publisher:
Total Pages: 52
Release: 1969
Genre: Conformal mapping
ISBN:

The factors of the direct product and the representations which appear in the expansion are expressed in terms of a particular momentum representation called 'the standard helicity representation' which enables one to use a uniform notation for all masses, whether real, zero, or imaginary. The earlier portions of the present paper summarizes the properties of these representations.

Tau-Rings and Wreath Product Representations

Tau-Rings and Wreath Product Representations
Author: Peter Hoffman
Publisher: Springer
Total Pages: 154
Release: 2006-11-15
Genre: Mathematics
ISBN: 3540348603

Signal Transduction in Cardiovascular System in Health and Disease Madhu B. Anand- Srivastava and Ashok K. Srivastava This book has addressed the contributions of several key signal transduction pathways which are central to our understanding of cardiovascular physiology and pathophysiology. Aberrations in these signaling events have been suggested to be involved in a host of cardiovascular pathologies, such as cardiac arrhythmias, congenital heart failure and hypertension. All the chapters have been written by well known leaders in the fields, which cover a wide range of intracellular events that regulate various aspects of cardiovascular functions. This book will be of interest to both basic as well as clinical scientists seeking to understand the molecular basis of cardiovascular diseases, and also to those interested in defining targets for cardiovascular pharmacotherapy. About the Authors Dr. Madhu B. Anand-Srivastava is a Professor, Department of Physiology, and a member of the Group de recherche sur le système nerveux autonome, University of Montréal. In 1990, she received a prestigious Scientist Award from Medical Research Council of Canada and in 2004, she was bestowed with the Vincenzo Panagia Distinguished Lecturer award from the Institute of Cardiovascular Sciences of the University of Manitoba, Winnipeg. She is an internationally recognized expert in the area of G-protein and natriuretic peptide receptor-C signaling, and has made significant contributions in defining the role of Gia proteins in the pathogenesis of hypertension. She has published more than 125 papers in refereed journals and edited 3 books in the area of G-proteins, hypertension and NPR-C receptor and cell signaling, and has been invited to several National and International conferences and academic institutions to present her work. Dr. Anand-Srivastava has served or is currently on different committees of the Canadian Institutes of Health Research and Heart and Stroke Foundation of Canada, and is also on the editorial boards of several scientific publications, including the Journal of Molecular and Cellular Cardiology and Molecular and Cellular Biochemistry. She has also organized several National and International conferences on cell signaling in cardiovascular system. Dr. Ashok K. Srivastava is a Professor at the Department of Medicine, Université de Montréal, and Head of the Laboratory of Cell Signaling at the Research Center of the Centre hospitalier de l'Université de Montréal (CHUM). He has over 100 publications in fields of insulin, vasoactive peptide and redox signaling, and cardiovascular complications. He has served or is serving as a guest editor of many journals such as Antioxidant and Redox Signaling, Canadian Journal of Physiology and Pharmacology, Cell Biochemistry and Biophysics and Molecular and Cellular Biochemistry, and is currently a member of the editorial boards of Advances in Biochemistry in Health and Disease and Recent Patents on Endocrine, Metabolic and Immune Drug Discovery. Dr. Srivastava is also on the grant review panels of the Canadian Institutes of Health Research, the Heart and Stroke Foundation of Canada and the National Institutes of Health. He has also organized several International symposia and workshops on Second Messengers and cell signaling.

Groups, Representations and Physics

Groups, Representations and Physics
Author: H.F Jones
Publisher: CRC Press
Total Pages: 348
Release: 2020-07-14
Genre: Mathematics
ISBN: 9781420050295

Illustrating the fascinating interplay between physics and mathematics, Groups, Representations and Physics, Second Edition provides a solid foundation in the theory of groups, particularly group representations. For this new, fully revised edition, the author has enhanced the book's usefulness and widened its appeal by adding a chapter on the Cartan-Dynkin treatment of Lie algebras. This treatment, a generalization of the method of raising and lowering operators used for the rotation group, leads to a systematic classification of Lie algebras and enables one to enumerate and construct their irreducible representations. Taking an approach that allows physics students to recognize the power and elegance of the abstract, axiomatic method, the book focuses on chapters that develop the formalism, followed by chapters that deal with the physical applications. It also illustrates formal mathematical definitions and proofs with numerous concrete examples.

Symmetries, Lie Algebras and Representations

Symmetries, Lie Algebras and Representations
Author: Jürgen Fuchs
Publisher: Cambridge University Press
Total Pages: 464
Release: 2003-10-07
Genre: Mathematics
ISBN: 9780521541190

This book gives an introduction to Lie algebras and their representations. Lie algebras have many applications in mathematics and physics, and any physicist or applied mathematician must nowadays be well acquainted with them.

Women and the Machine

Women and the Machine
Author: Julie Wosk
Publisher: JHU Press
Total Pages: 360
Release: 2001
Genre: Art
ISBN: 9780801873133

Julie Wosk examines the role of machines in helping women reconfigure and transform their lives. She takes her readers through a gallery of fiction and high and low art which depicts women in their association with machines.