“…This book explores recent developments in the theoretical foundations and novel applications of general and interval type-2 fuzzy sets and systems, including: algebraic properties of type-2 fuzzy sets, geometric-based definition of type-2 fuzzy set operators, generalizations of the continuous KM algorithm, adaptiveness and novelty of interval type-2 fuzzy logic controllers, relations between conceptual spaces and type-2 fuzzy sets, type-2 fuzzy logic systems versus perceptual computers; modeling human perception of real world concepts with type-2 fuzzy sets, different methods for generating membership functions of interval and general type-2 fuzzy sets, and applications of interval type-2 fuzzy sets to control, machine tooling, image processing and diet.  …”
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“…This book includes integral, differential and algebraic models that are used to describe scalar and vector hysteretic nonlinearities originating from various areas of science and engineering. …”
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“…This book aims to present an information-theoretical approach to thermodynamics and its generalisations On the one hand, it generalises the concept of `information thermodynamics' to that of `information dynamics' in order to stress applications outside thermal phenomena On the other hand, it is a synthesis of the dynamics of state change and the theory of complexity, which provide a common framework to treat both physical and nonphysical systems together Both classical and quantum systems are discussed, and two appendices are included to explain principal definitions and some important aspects of the theory of Hilbert spaces and operator algebras The concept of higher-order temperatures is explained and applied to biological and linguistic systems The theory of open systems is presented in a new, much more general form Audience This volume is intended mainly for theoretical and mathematical physicists, but also for mathematicians, experimental physicists, physical chemists, theoretical biologists, communication engineers, and all those interested in entropy and open systems It can also be recommended as a supplementary text…”
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“…Recently ideas based on Feynman path integrals have also played an important role in areas of mathematics like low-dimensional topology and differential geometry, algebraic geometry, infinite-dimensional analysis and geometry, and number theory. …”
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“…The relationship between structures in supergravity and periodic maps of algebraic manifolds, Kodaira-Spencer theory, modularity, and the arithmetic properties of supergravity are also addressed. …”
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“…This edited volume includes both foundational material and a logic perspective. Algebraic logic, model theory, type theory, completeness theorems, philosophical and foundational studies are among the topics covered, as well as mathematical education. …”
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“…This is a book of "impressions" of a journey through the theory of com­ plex algebraic curves. It is neither self-contained, balanced, nor particularly tightly organized. …”
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“…This book begins with exposition on the combinatorial and algebraic techniques that Professor Gould uses for proving binomial identities. …”
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“…In the second edition of this classic monograph, complete with four new chapters and updated references, readers will now have access to content describing and analysing classical and modern methods with emphasis on the algebraic structure of linear iteration, which is usually ignored in other literature. …”
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“…This work presents applications of numerical semigroups in Algebraic Geometry, Number Theory, and Coding Theory. …”
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“…Moreover, it is extremely important in symplectic geometry and Hamiltonian dynamics, and has strong correlations with mathematical physics, Lie theory and algebraic geometry (including mirror symmetry). As such, the book will appeal to experts with a wide range of backgrounds.…”
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“…The book aims to strengthen relations between industry research laboratories and universities in fields such as quantitative logic and soft computing worldwide as follows: (1) Quantitative Logic and Uncertainty Logic; (2) Automata and Quantification of Software; (3) Fuzzy Connectives and Fuzzy Reasoning; (4) Fuzzy Logical Algebras; (5) Artificial Intelligence and Soft Computing; (6) Fuzzy Sets Theory and Applications.…”
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“…The classical relation to both the primal and dual Brunn-Minkowski theories is also well represented, and related algebraic structures pertaining to valuations and valent functions are discussed. …”
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“…He begins with a treatment of the ordinary one-dimensional quantum harmonic oscillator, progresses through the construction of quantum field theory in flat spacetime to possible constructions of quantum field theory in curved spacetime, and, ultimately, to an algebraic formulation of the theory. In his presentation, Wald disentangles essential features of the theory from inessential ones (such as a particle interpretation) and clarifies relationships between various approaches to the formulation of the theory. …”
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“…The book also includes papers on a variety of current topics in Approximation Theory drawn from areas such as advances in kernel approximation with applications, approximation theory and algebraic geometry, multivariate splines for applications, practical function approximation, approximation of PDEs, wavelets and framelets with applications, approximation theory in signal processing, compressive sensing, rational interpolation, spline approximation in isogeometric analysis, approximation of fractional differential equations, numerical integration formulas, and trigonometric polynomial approximation.…”
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“…Beginning with the physical character of the solutions, these are identified and ordered on the basis of their geometrical invariant properties, symmetries, and algebraic classifications, or from the standpoint of their physical nature, for example electrodynamic fields, fluid, scalar field, or dilaton. …”
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“…For its sophisticated account of ancient to modern geometries, this text assumes only a year of college mathematics as it builds towards its conclusion with algebraic curves and quaternions. Euclid’s work has affected geometry for thousands of years, so this text has something to offer to anyone who wants to broaden their appreciation for the field.…”
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“…The focus lies on the combinatorics of the partition into cells for general Coxeter groups, with special attention given to induction methods, cellular maps and the role of Lusztig's conjectures. Using only algebraic and combinatorial methods, the author carefully develops proofs, discusses open conjectures, and presents recent research, including a chapter on the action of the cactus group. …”
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“…The theory of motives was created by Grothendieck in the 1960s as he searched for a universal cohomology theory for algebraic varieties. The theory of pure motives is well established as far as the construction is concerned. …”
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“…Moduli problems in algebraic geometry date back to Riemann's famous count of the 3g-3 parameters needed to determine a curve of genus g. …”
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