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.


Elements of Quasigroup Theory and Applications

Elements of Quasigroup Theory and Applications

Author: Victor Shcherbacov

Publisher: CRC Press

Published: 2017-05-12

Total Pages: 423

ISBN-13: 1351646362

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This book provides an introduction to quasigroup theory along with new structural results on some of the quasigroup classes. Many results are presented with some of them from mathematicians of the former USSR. These included results have not been published before in the western mathematical literature. In addition, many of the achievements obtained with regard to applications of quasigroups in coding theory and cryptology are described.


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.


The Origins of Evolutionary Innovations

The Origins of Evolutionary Innovations

Author: Andreas Wagner

Publisher: OUP Oxford

Published: 2011-07-14

Total Pages: 264

ISBN-13: 0191621285

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The history of life is a nearly four billion year old story of transformative change. This change ranges from dramatic macroscopic innovations such as the evolution of wings or eyes, to a myriad of molecular changes that form the basis of macroscopic innovations. We are familiar with many examples of innovations (qualitatively new phenotypes that provide a critical benefit) but have no systematic understanding of the principles that allow organisms to innovate. This book proposes several such principles as the basis of a theory of innovation, integrating recent knowledge about complex molecular phenotypes with more traditional Darwinian thinking. Central to the book are genotype networks: vast sets of connected genotypes that exist in metabolism and regulatory circuitry, as well as in protein and RNA molecules. The theory can successfully unify innovations that occur at different levels of organization. It captures known features of biological innovation, including the fact that many innovations occur multiple times independently, and that they combine existing parts of a system to new purposes. It also argues that environmental change is important to create biological systems that are both complex and robust, and shows how such robustness can facilitate innovation. Beyond that, the theory can reconcile neutralism and selectionism, as well as explain the role of phenotypic plasticity, gene duplication, recombination, and cryptic variation in innovation. Finally, its principles can be applied to technological innovation, and thus open to human engineering endeavours the powerful principles that have allowed life's spectacular success.