Wagner’s Theory of Generalised Heaps
Wagner’s Theory of Generalised Heaps

Author: Christopher D. Hollings

Publisher: Springer

Published: 2017-09-09

Total Pages: 195

ISBN-13: 3319636219

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The theories of V. V. Wagner (1908-1981) on abstractions of systems of binary relations are presented here within their historical and mathematical contexts. This book contains the first translation from Russian into English of a selection of Wagner’s papers, the ideas of which are connected to present-day mathematical research. Along with a translation of Wagner’s main work in this area, his 1953 paper ‘Theory of generalised heaps and generalised groups,’ the book also includes translations of three short precursor articles that provide additional context for his major work. Researchers and students interested in both algebra (in particular, heaps, semiheaps, generalised heaps, semigroups, and groups) and differential geometry will benefit from the techniques offered by these translations, owing to the natural connections between generalised heaps and generalised groups, and the role played by these concepts in differential geometry. This book gives examples from present-day mathematics where ideas related to Wagner’s have found fruitful applications.

Mathematics across the Iron Curtain
Mathematics across the Iron Curtain

Author: Christopher Hollings

Publisher: American Mathematical Society

Published: 2014-07-16

Total Pages: 457

ISBN-13: 1470414937

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The theory of semigroups is a relatively young branch of mathematics, with most of the major results having appeared after the Second World War. This book describes the evolution of (algebraic) semigroup theory from its earliest origins to the establishment of a full-fledged theory. Semigroup theory might be termed `Cold War mathematics' because of the time during which it developed. There were thriving schools on both sides of the Iron Curtain, although the two sides were not always able to communicate with each other, or even gain access to the other's publications. A major theme of this book is the comparison of the approaches to the subject of mathematicians in East and West, and the study of the extent to which contact between the two sides was possible.

Inverse Semigroups, The Theory Of Partial Symmetries
Inverse Semigroups, The Theory Of Partial Symmetries

Author: Mark V Lawson

Publisher: World Scientific

Published: 1998-11-06

Total Pages: 426

ISBN-13: 9814496715

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Symmetry is one of the most important organising principles in the natural sciences. The mathematical theory of symmetry has long been associated with group theory, but it is a basic premise of this book that there are aspects of symmetry which are more faithfully represented by a generalization of groups called inverse semigroups. The theory of inverse semigroups is described from its origins in the foundations of differential geometry through to its most recent applications in combinatorial group theory, and the theory tilings.

Polyadic Groups
Polyadic Groups

Author: Wieslaw A. Dudek

Publisher: CRC Press

Published: 2024-03-22

Total Pages: 1736

ISBN-13: 1040001106

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This book provides a general, unified approach to the theory of polyadic groups, their normal subgroups and matrix representations. The author focuses on those properties of polyadic groups which are not present in the binary case. These properties indicate a strong relationship between polyadic groups and various group-like algebras, as well as ternary Hopf algebras and n-Lie algebras that are widely used in theoretical physics. The relationships of polyadic groups with special types of binary groups, called covering groups and binary retracts, are described. These relationships allow the study of polyadic groups using these binary groups and their automorphisms. The book also describes the affine geometry induced by polyadic groups and fuzzy subsets defined on polyadic groups. Finally, we discuss the categories of polyadic groups and the relationships between the different varieties of polyadic groups. In many cases, we give elegant new proofs of known theorems. We also give many interesting examples and applications. The book contains many little-known results from articles previously published in hard-to-reach Russian, Ukrainian and Macedonian journals. These articles are not in English.

Monoids, Acts, and Categories
Monoids, Acts, and Categories

Author: M. Kilʹp

Publisher: Walter de Gruyter

Published: 2000

Total Pages: 556

ISBN-13: 9783110152487

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The aim of the Expositions is to present new and important developments in pure and applied mathematics. Well established in the community over more than two decades, the series offers a large library of mathematical works, including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers interested in a thorough study of the subject. Editorial Board Lev Birbrair, Universidade Federal do Cear , Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany Katrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbański, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Bostjan Gabrovsek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)

Two-dimensional Flow on General Surfaces of Revolution in Turbomachines
Two-dimensional Flow on General Surfaces of Revolution in Turbomachines

Author: John D. Stanitz

Publisher:

Published: 1952

Total Pages: 734

ISBN-13:

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A method of analysis is developed for two dimensional flow on general surfaces of revolution in turbomachines with arbitrary blade shapes. The method of analysis is developed for steady, compressible, nonviscous, irrotational flow that is assumed uniform normal to the surfaces of revolution. Incompressible solutions on a mean surface of revolution between the hub and shroud are presented for four rates through each of two centrifugal impellers with the same hub-shroud contours but with different blade spacings. In addition, correlation equations are developed whereby the velocity components and the stream function distribution can be predicted for compressible or incompressible flow in straight-blade impellers only, with any tip speed, flow rate, area variation, blade spacing, and for any flow surface of revolution.

Delphi Masterworks of Richard Wagner (Illustrated)
Delphi Masterworks of Richard Wagner (Illustrated)

Author: Peter Russell

Publisher: Delphi Classics

Published: 2018-08-15

Total Pages: 3683

ISBN-13: 1786564025

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The operas of the German composer Richard Wagner had a revolutionary influence on the course of Western music. Unlike most opera composers, Wagner wrote both the libretto and the music for each of his works. He went on to revolutionise the music form through his concept of the Gesamtkunstwerk (total work of art), by which he sought to synthesise the poetic, visual, musical and dramatic arts, with music subsidiary to drama. He achieved these ideas most fully in his epic cycle of operas 'Der Ring des Nibelungen', notable for complex textures, rich harmonies and the elaborate use of leitmotifs. Delphi’s Great Composers Series offers concise illustrated guides to the life and works of our greatest composers. Analysing the masterworks of each composer, these interactive eBooks include links to popular streaming services, allowing you to listen to the pieces of music you are reading about. Evaluating the masterworks of each composer, you will explore the development of their works, tracing how they changed the course of music history. Whether a classical novice or a cultivated connoisseur, this series offers an intriguing overview of the world’s most famous and iconic compositions. This volume presents Wagner’s masterworks in succinct detail, with informative introductions, accompanying illustrations and the usual Delphi bonus features. (Version 1) * Concise and informative overview of Wagner’s masterworks* Learn about the operas that made Wagner a celebrated composer* Links to popular streaming services (free and paid), allowing you to listen to the masterpieces you’re reading about* Features a special ‘Complete Compositions’ section, with an index of Wagner’s complete works and links to streaming services* English translations of the librettos for the major operas, including works appearing for the first time in digital print* A wide selection of the composer’s prose works, including fiction, pioneering essays and Wagner’s celebrated autobiography* Includes Wagner’s letters to Franz Liszt — explore the composer’s personal correspondence* Features six biographies on the great composer — explore Wagner's intriguing musical and personal life Please visit www.delphiclassics.com to browse through our range of exciting eBooks CONTENTS: The MasterworksSymphony in C MajorDas LiebesverbotFaust OvertureRienziDer fliegende HolländerTannhäuserLohengrinDas RhinegoldDie WalküreTristan und IsoldeWesendonck LiederDie Meistersinger von NürnbergSiegfriedSiegfried IdyllGötterdämmerungParsifal Complete CompositionsIndex of Wagner’s Compositions Selected LibrettosDer fliegende HolländerLohengrinDas RhinegoldDie WalküreTristan und IsoldeSiegfriedGötterdämmerungParsifal Selected ProseAutobiographic SketchOn German OperaArt and RevolutionThe Art-Work of the FutureJudaism in MusicA Communication to My FriendsOpera and DramaBeethovenWhat is German?An End in ParisOn ConductingReligion and Art The LettersCorrespondence of Wagner and Liszt The AutobiographyMy Life The BiographiesRichard Wagner: His Life and His Dramas by W. J. HendersonLife of Wagner by Ludwig NohlRichard Wagner, Composer of Operas by John F. RuncimanWagner by Paul RosenfeldWagner as I Knew Him by Ferdinand PraegerRichard Wagner by Rupert Hughes Please visit www.delphiclassics.com to learn more about our wide range of exciting titles

Many-Sorted Algebras for Deep Learning and Quantum Technology
Many-Sorted Algebras for Deep Learning and Quantum Technology

Author: Charles R. Giardina

Publisher: Elsevier

Published: 2024-02-03

Total Pages: 423

ISBN-13: 044313698X

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Many-Sorted Algebras for Deep Learning and Quantum Technology presents a precise and rigorous description of basic concepts in Quantum technologies and how they relate to Deep Learning and Quantum Theory. Current merging of Quantum Theory and Deep Learning techniques provides a need for a text that can give readers insight into the algebraic underpinnings of these disciplines. Although analytical, topological, probabilistic, as well as geometrical concepts are employed in many of these areas, algebra exhibits the principal thread. This thread is exposed using Many-Sorted Algebras (MSA). In almost every aspect of Quantum Theory as well as Deep Learning more than one sort or type of object is involved. For instance, in Quantum areas Hilbert spaces require two sorts, while in affine spaces, three sorts are needed. Both a global level and a local level of precise specification is described using MSA. At a local level operation involving neural nets may appear to be very algebraically different than those used in Quantum systems, but at a global level they may be identical. Again, MSA is well equipped to easily detail their equivalence through text as well as visual diagrams. Among the reasons for using MSA is in illustrating this sameness. Author Charles R. Giardina includes hundreds of well-designed examples in the text to illustrate the intriguing concepts in Quantum systems. Along with these examples are numerous visual displays. In particular, the Polyadic Graph shows the types or sorts of objects used in Quantum or Deep Learning. It also illustrates all the inter and intra sort operations needed in describing algebras. In brief, it provides the closure conditions. Throughout the text, all laws or equational identities needed in specifying an algebraic structure are precisely described. - Includes hundreds of well-designed examples to illustrate the intriguing concepts in quantum systems - Provides precise description of all laws or equational identities that are needed in specifying an algebraic structure - Illustrates all the inter and intra sort operations needed in describing algebras

Lattices, Semigroups, and Universal Algebra
Lattices, Semigroups, and Universal Algebra

Author: Jorge Almeida

Publisher: Springer Science & Business Media

Published: 2013-11-11

Total Pages: 325

ISBN-13: 1489926089

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This volume contains papers which, for the most part, are based on talks given at an international conference on Lattices, Semigroups, and Universal Algebra that was held in Lisbon, Portugal during the week of June 20-24, 1988. The conference was dedicated to the memory of Professor Antonio Almeida Costa, a Portuguese mathematician who greatly contributed to the development of th algebra in Portugal, on the 10 anniversary of his death. The themes of the conference reflect some of his research interests and those of his students. The purpose of the conference was to gather leading experts in Lattices, Semigroups, and Universal Algebra and to promote a discussion of recent developments and trends in these areas. All three fields have grown rapidly during the last few decades with varying degrees of interaction. Lattice theory and Universal Algebra have historically evolved alongside with a large overlap between the groups of researchers in the two fields. More recently, techniques and ideas of these theories have been used extensively in the theory of semigroups. Conversely, some developments in that area may inspire further developments in Universal Algebra. On the other hand, techniques of semi group theory have naturally been employed in the study of semilattices. Several papers in this volume elaborate on these interactions.