64 research outputs found
Mathematical Fuzzy Logic in the Emerging Fields of Engineering, Finance, and Computer Sciences
Mathematical fuzzy logic (MFL) specifically targets many-valued logic and has significantly contributed to the logical foundations of fuzzy set theory (FST). It explores the computational and philosophical rationale behind the uncertainty due to imprecision in the backdrop of traditional mathematical logic. Since uncertainty is present in almost every real-world application, it is essential to develop novel approaches and tools for efficient processing. This book is the collection of the publications in the Special Issue âMathematical Fuzzy Logic in the Emerging Fields of Engineering, Finance, and Computer Sciencesâ, which aims to cover theoretical and practical aspects of MFL and FST. Specifically, this book addresses several problems, such as:- Industrial optimization problems- Multi-criteria decision-making- Financial forecasting problems- Image processing- Educational data mining- Explainable artificial intelligence, etc
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Taking topological field theory at phase value
In this thesis, we use methods of topological field theory to model and study topological phases of matter. This includes computing TFTs that capture low-energy information for the GDS model and for the Majorana chain with time-reversal symmetry. We then investigate phases of matter with spatial symmetries that mix with the internal symmetry type; we provide a mathematical model for these phases and prove a âfermionic crystalline equivalence principleâ theorem as predicted in the physics literature. Some of our computations lead to a bonus theorem on the classification of some unorientable 4-manifolds up to stable diffeomorphism.Mathematic
Topics in Topology and Homotopy Theory
This book is an account of certain topics in general and algebraic topology
Foundations of Software Science and Computation Structures
This open access book constitutes the proceedings of the 23rd International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2020, which took place in Dublin, Ireland, in April 2020, and was held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2020. The 31 regular papers presented in this volume were carefully reviewed and selected from 98 submissions. The papers cover topics such as categorical models and logics; language theory, automata, and games; modal, spatial, and temporal logics; type theory and proof theory; concurrency theory and process calculi; rewriting theory; semantics of programming languages; program analysis, correctness, transformation, and verification; logics of programming; software specification and refinement; models of concurrent, reactive, stochastic, distributed, hybrid, and mobile systems; emerging models of computation; logical aspects of computational complexity; models of software security; and logical foundations of data bases.
2018 Touro College & University System Faculty Publications
This is the 2018 edition of the Faculty Publications Book of the Touro College & University System. It includes all eligible 2018 publication citations of faculty within the Touro College & University System, including New York Medical College (NYMC). It was produced as a joint effort of the Touro College Libraries and the Health Sciences Library at NYMC.https://touroscholar.touro.edu/facpubs/1008/thumbnail.jp
Equivariant instanton homology
We define four versions of equivariant instanton Floer homology ( and ) for a class of 3-manifolds and -bundles
over them including all rational homology spheres. These versions are analogous
to the four flavors of monopole and Heegaard Floer homology theories. This
construction is functorial for a large class of 4-manifold cobordisms, and
agrees with Donaldson's definition of equivariant instanton homology for
integer homology spheres. Furthermore, one of our invariants is isomorphic to
Floer's instanton homology for admissible bundles, and we calculate
in all cases it is defined, away from characteristic 2.
The appendix, possibly of independent interest, defines an algebraic
construction of three equivariant homology theories for dg-modules over a
dg-algebra, the equivariant homology , the coBorel homology
, and the Tate homology . The constructions of the
appendix are used to define our invariants.Comment: 221 page
A historical perspective of the theory of isotopisms
In the middle of the twentieth century, Albert and Bruck introduced the theory of isotopisms of non-associative algebras and quasigroups as a generalization of the classical theory of isomorphisms in order to study and classify such structures according to more general symmetries. Since then, a wide range of applications have arisen in the literature concerning the classification and enumeration of different algebraic and combinatorial structures according to their isotopism classes. In spite of that, there does not exist any contribution dealing with the origin and development of such a theory. This paper is a first approach in this regard.Junta de AndalucĂ
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