Algebraic Structures and Applications

Algebraic Structures and Applications

Algebraic structures and Applications, Springer Proceedings in Mathematics and Statistics, vol. 317. Springer (2020) 4. Muhumuza, A. K., Lundengård, K., Österberg, J., Silvestrov, S., Mango, J. M., Kakuba, G.: Optimization ...

Author: Sergei Silvestrov

Publisher: Springer Nature

ISBN: 9783030418502

Category: Mathematics

Page: 968

View: 576

This book explores the latest advances in algebraic structures and applications, and focuses on mathematical concepts, methods, structures, problems, algorithms and computational methods important in the natural sciences, engineering and modern technologies. In particular, it features mathematical methods and models of non-commutative and non-associative algebras, hom-algebra structures, generalizations of differential calculus, quantum deformations of algebras, Lie algebras and their generalizations, semi-groups and groups, constructive algebra, matrix analysis and its interplay with topology, knot theory, dynamical systems, functional analysis, stochastic processes, perturbation analysis of Markov chains, and applications in network analysis, financial mathematics and engineering mathematics. The book addresses both theory and applications, which are illustrated with a wealth of ideas, proofs and examples to help readers understand the material and develop new mathematical methods and concepts of their own. The high-quality chapters share a wealth of new methods and results, review cutting-edge research and discuss open problems and directions for future research. Taken together, they offer a source of inspiration for a broad range of researchers and research students whose work involves algebraic structures and their applications, probability theory and mathematical statistics, applied mathematics, engineering mathematics and related areas.
Categories: Mathematics

Abstract Algebra

Abstract Algebra

It emphasizes the more general concept of an algebraic structure while simultaneously covering applications. The text can be used in a variety of courses, from a one-semester int

Author: Stephen Lovett

Publisher: CRC Press

ISBN: 9781482248913

Category: Mathematics

Page: 720

View: 722

A Discovery-Based Approach to Learning about Algebraic Structures Abstract Algebra: Structures and Applications helps students understand the abstraction of modern algebra. It emphasizes the more general concept of an algebraic structure while simultaneously covering applications. The text can be used in a variety of courses, from a one-semester introductory course to a full two-semester sequence. The book presents the core topics of structures in a consistent order: Definition of structure Motivation Examples General properties Important objects Description Subobjects Morphisms Subclasses Quotient objects Action structures Applications The text uses the general concept of an algebraic structure as a unifying principle and introduces other algebraic structures besides the three standard ones (groups, rings, and fields). Examples, exercises, investigative projects, and entire sections illustrate how abstract algebra is applied to areas of science and other branches of mathematics. "Lovett (Wheaton College) takes readers through the variegated landscape of algebra, from elementary modular arithmetic through groups, semigroups, and monoids, past rings and fields and group actions, beyond modules and algebras, to Galois theory, multivariable polynomial rings, and Gröbner bases." Choice Reviewed: Recommended
Categories: Mathematics

Handbook of Research on Emerging Applications of Fuzzy Algebraic Structures

Handbook of Research on Emerging Applications of Fuzzy Algebraic Structures

Various algebraic structures like Groups, Rings etc. based on Fuzzy Sets are already being used in many fields such as Computer Science, Chemistry, Physics and other subjects. These structures on Fuzzy Sets have been deliberated on for ...

Author: Jana, Chiranjibe

Publisher: IGI Global

ISBN: 9781799801924

Category: Mathematics

Page: 439

View: 338

In the world of mathematics, the study of fuzzy relations and its theories are well-documented and a staple in the area of calculative methods. What many researchers and scientists overlook is how fuzzy theory can be applied to industries outside of arithmetic. The framework of fuzzy logic is much broader than professionals realize. There is a lack of research on the full potential this theoretical model can reach. The Handbook of Research on Emerging Applications of Fuzzy Algebraic Structures provides emerging research exploring the theoretical and practical aspects of fuzzy set theory and its real-life applications within the fields of engineering and science. Featuring coverage on a broad range of topics such as complex systems, topological spaces, and linear transformations, this book is ideally designed for academicians, professionals, and students seeking current research on innovations in fuzzy logic in algebra and other matrices.
Categories: Mathematics

Algebraic Modeling of Topological and Computational Structures and Applications

Algebraic Modeling of Topological and Computational Structures and Applications

8(2), 201–229, (2013), [24], J. Pure Appl. Algebra 219(4), 839–863, (2015), [25]) and place them in the context of algebraic ... Algebraic Modeling of Topological and Computational Structures and Applications, Springer Proceedings in ...

Author: Sofia Lambropoulou

Publisher: Springer

ISBN: 9783319681030

Category: Mathematics

Page: 482

View: 327

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 workshop in connection with the research project Thales on Algebraic Modeling of Topological and Computational Structures and Applications, held at the National Technical University of Athens, Greece in July 2015. The reader will benefit from the innovative approaches to tackling difficult questions in topology, applications and interrelated research areas, which largely employ algebraic tools.
Categories: Mathematics

Basic Neutrosophic Algebraic Structures and Their Application to Fuzzy and Neutrosophic Models

Basic Neutrosophic Algebraic Structures and Their Application to Fuzzy and Neutrosophic Models

Preface Study of neutrosophic algebraic structures is very recent. The introduction of neutrosophic theory has put forth a significant concept by giving representation to indeterminates. Uncertainty or indeterminacy happen to be one of ...

Author: W. B. Vasantha Kandasamy

Publisher: Infinite Study

ISBN: 9781931233873

Category: Mathematics

Page: 149

View: 147

For the involvement of uncertainty of varying degrees, when the total of the membership degree exceeds one or less than one, then the newer mathematical paradigm shift, Fuzzy Theory proves appropriate.For the past two or three decades, Fuzzy Theory has become the potent tool to study and analyze uncertainty involved in all problems. But, many real world problems also abound with the concept of indeterminacy.In this book, the new, powerful tool of neutrosophy that deals with indeterminacy is utilized. Innovative neutrosophic models are described.The theory of neutrosophic graphs is introduced and applied to fuzzy and neutrosophic models.Neutrosophic Logic and Neutrosophic Set (generalizations of Intuitionistic Fuzzy Logic and Intuitionistic Fuzzy Set respectively) became strong tools for applications.
Categories: Mathematics

Two dimensional event set and its application in algebraic structures

Two dimensional event set and its application in algebraic structures

Two dimensional event set is introduced, and it is applied to algebraic structures. Two dimensional BCK/BCI-eventful algebra, paired B-algebra and paired BCK/BCI-algebra are defined, and several properties are investigated.

Author: Y.B. Jun

Publisher: Infinite Study

ISBN:

Category: Mathematics

Page: 13

View: 227

Two dimensional event set is introduced, and it is applied to algebraic structures. Two dimensional BCK/BCI-eventful algebra, paired B-algebra and paired BCK/BCI-algebra are de ned, and several properties are investigated. Conditions for two dimensional eventful algebra to be a B-algebra and a BCK/BCI-algebra are provided. The process of inducing a paired B-algebra using a group is discussed. Using two dimensional BCI-eventful algebra, a commutative group is established.
Categories: Mathematics

Algebraic Structures of Neutrosophic Triplets Neutrosophic Duplets or Neutrosophic Multisets

Algebraic Structures of Neutrosophic Triplets  Neutrosophic Duplets  or Neutrosophic Multisets

We discuss some basic results and an application of the proposed structure at the end. ... Kandasamy, W.B.V.; Smarandache, F. Basic Neutrosophic Algebraic Structures and Their Applications to Fuzzy and Neutrosophic Models; ...

Author: Florentin Smarandache

Publisher: MDPI

ISBN: 9783038974758

Category: Mathematics

Page: 450

View: 942

Neutrosophy (1995) is a new branch of philosophy that studies triads of the form (, , ), where is an entity {i.e. element, concept, idea, theory, logical proposition, etc.}, is the opposite of , while is the neutral (or indeterminate) between them, i.e., neither nor . Based on neutrosophy, the neutrosophic triplets were founded, which have a similar form (x, neut(x), anti(x)), that satisfy several axioms, for each element x in a given set. This collective book presents original research papers by many neutrosophic researchers from around the world, that report on the state-of-the-art and recent advancements of neutrosophic triplets, neutrosophic duplets, neutrosophic multisets and their algebraic structures – that have been defined recently in 2016 but have gained interest from world researchers. Connections between classical algebraic structures and neutrosophic triplet / duplet / multiset structures are also studied. And numerous neutrosophic applications in various fields, such as: multi-criteria decision making, image segmentation, medical diagnosis, fault diagnosis, clustering data, neutrosophic probability, human resource management, strategic planning, forecasting model, multi-granulation, supplier selection problems, typhoon disaster evaluation, skin lesson detection, mining algorithm for big data analysis, etc.
Categories: Mathematics

Algebraic Structures of Neutrosophic Triplets Neutrosophic Duplets or Neutrosophic Multisets Volume II

Algebraic Structures of Neutrosophic Triplets  Neutrosophic Duplets  or Neutrosophic Multisets  Volume II

We discuss some basic results and an application of the proposed structure at the end. ... Kandasamy, W.B.V.; Smarandache, F. Basic Neutrosophic Algebraic Structures and Their Applications to Fuzzy and Neutrosophic Models; ...

Author: Florentin Smarandache

Publisher: Infinite Study

ISBN: 9783038974765

Category: Mathematics

Page: 450

View: 853

Neutrosophy (1995) is a new branch of philosophy that studies triads of the form (, , ), where is an entity (i.e., element, concept, idea, theory, logical proposition, etc.), is the opposite of , while is the neutral (or indeterminate) between them, i.e., neither nor . Based on neutrosophy, the neutrosophic triplets were founded; they have a similar form: (x, neut(x), anti(x), that satisfy some axioms, for each element x in a given set. This book contains the successful invited submissions to a special issue of Symmetry, reporting on state-of-the-art and recent advancements of neutrosophic triplets, neutrosophic duplets, neutrosophic multisets, and their algebraic structures—that have been defined recently in 2016, but have gained interest from world researchers, and several papers have been published in first rank international journals.
Categories: Mathematics

Ordered Algebraic Structures

Ordered Algebraic Structures

F. Van Oystaeyen and A. Verschoren , Reflectors and Localization : Application to Sheaf Theory 42. ... P. Schultz , C. Praeger , and R. Sullivan , Algebraic Structures and Applications Proceedings of the First Western Australian ...

Author: W. B. Powell

Publisher: CRC Press

ISBN: 082477342X

Category: Mathematics

Page: 216

View: 566

Ordered Algebraic Structures combines the work of 22 research mathematicians to give full details on the diversifying fields of ordered algebraic structures. It covers order relations on groups, semigroups and rings. It investigates completions, embeddings and amalgamations finitely presented and free lattice-ordered groups, varieties of lattice-ordered groups and Mathiak valuation, intrinsic metrics and more
Categories: Mathematics