Algebraic Modeling of Topological and Computational Structures and Applications : THALES, Athens, Greece, July 1-3, 2015. 1st ed. 2017

種類:

電子ブック

責任表示:

edited by Sofia Lambropoulou, Doros Theodorou, Petros Stefaneas, Louis H. Kauffman

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2017

著者名:

• Lambropoulou, Sofia.
• Theodorou, Doros.
• Stefaneas, Petros.
• Kauffman, Louis H.
• SpringerLink (Online service)

シリーズ名:

Springer Proceedings in Mathematics & Statistics ; 219

ISBN:

9783319681030 [3319681036]    

注記:

PART ONE: Konstantinos Karvounis and Sofia Lambropoulou, Link invariants from the Yokonuma Hecke algebras -- Dimos  Goundaroulis, A survey on Temperley-Lieb-type quotients from the Yokonuma-Hecke algebras -- Maria Chlouveraki, Representation theory of framisations of knot algebras -- Loic Poulain d'Andecy, Invariants for links from classical and affine Yokonuma- Hecke algebras -- Marcelo Flores, On the framization of the Hecke algebra of type B -- Bostjan Gabrovsek and Maciej Mroczkowski, Link diagrams in Seifert manifolds and applications to skein modules -- Ioannis Diamantis and Sofia Lambropoulou, “On the HOMFLYPT skein module of the lens spaces $L(p,1)$ via braids -- Dimitrios Kodokostas and Sofia Lambropoulou, Some Hecke-type algebras derived from the braid group with two fixed strands -- Valerij G. Bardakov, Braid groups in handlebodies and corresponding Hecke algebras -- Nondas E. Kechagias, Infinite loop spaces, Dyer-Lashof algebra, cohomology of the infinite symmetric group and modular invariants.- P
This interdisciplinary book covers a wide range of subjects, from pure mathematics (knots, braids, homotopy theory, number theory) to more applied mathematics (cryptography, algebraic specification of algorithms, dynamical systems) and concrete applications (modeling of polymers and ionic liquids, video, music and medical imaging). The main mathematical focus throughout the book is on algebraic modeling with particular emphasis on braid groups. The research methods include algebraic modeling using topological structures, such as knots, 3-manifolds, classical homotopy groups, and braid groups. The applications address the simulation of polymer chains and ionic liquids, as well as the modeling of natural phenomena via topological surgery. The treatment of computational structures, including finite fields and cryptography, focuses on the development of novel techniques. These techniques can be applied to the design of algebraic specifications for systems modeling and verification. This book is the outcome of a w

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