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A ground-breaking and practical treatment of probability and stochastic processes A Modern Theory of Random Variation is a new and radical re-formulation of the mathematical underpinnings of subjects as diverse as investment, communication engineering, and quantum mechanics. Setting aside the classical theory of probability measure spaces, the book utilizes a mathematically rigorous version of the theory of random variation that bases itself exclusively on finitely additive probability distribution functions. In place of twentieth century Lebesgue integration and measure theory, the author uses the simpler concept of Riemann sums, and the non-absolute Riemann-type integration of Henstock. Readers are supplied with an accessible approach to standard elements of probability theory such as the central limmit theorem and Brownian motion as well as remarkable, new results on Feynman diagrams and stochastic integrals. Throughout the book, detailed numerical demonstrations accompany the discussions of abstract mathematical theory, from the simplest elements of the subject to the most complex. In addition, an array of numerical examples and vivid illustrations showcase how the presented methods and applications can be undertaken at various levels of complexity. A Modern Theory of Random Variation is a suitable book for courses on mathematical analysis, probability theory, and mathematical finance at the upper-undergraduate and graduate levels. The book is also an indispensible resource for researchers and practitioners who are seeking new concepts, techniques and methodologies in data analysis, numerical calculation, and financial asset valuation. Patrick Muldowney, PhD, served as lecturer at the Magee Business School of the UNiversity of Ulster for over twenty years. Dr. Muldowney has published extensively in his areas of research, including integration theory, financial mathematics, and random variation.
This book presents a unified course in BE-algebras with a comprehensive introduction, general theoretical basis and several examples. It introduces the general theoretical basis of BE-algebras, adopting a credible style to offer students a conceptual understanding of the subject. BE-algebras are important tools for certain investigations in algebraic logic, because they can be considered as fragments of any propositional logic containing a logical connective implication and the constant "1", which is considered as the logical value “true”. Primarily aimed at graduate and postgraduate students of mathematics, it also helps researchers and mathematicians to build a strong foundation in applied abstract algebra. Presenting insights into some of the abstract thinking that constitutes modern abstract algebra, it provides a transition from elementary topics to advanced topics in BE-algebras. With abundant examples and exercises arranged after each section, it offers readers a comprehensive, easy-to-follow introduction to this field.
The book discusses important results in modern mathematical models and high performance computing, such as applied operations research, simulation of operations, statistical modeling and applications, invisibility regions and regular meta-materials, unmanned vehicles, modern radar techniques/SAR imaging, satellite remote sensing, coding, and robotic systems. Furthermore, it is valuable as a reference work and as a basis for further study and research. All contributing authors are respected academicians, scientists and researchers from around the globe. All the papers were presented at the international conference on Modern Mathematical Methods and High Performance Computing in Science & Technology (M3HPCST 2015), held at Raj Kumar Goel Institute of Technology, Ghaziabad, India, from 27–29 December 2015, and peer-reviewed by international experts. The conference provided an exceptional platform for leading researchers, academicians, developers, engineers and technocrats from a broad range of disciplines to meet and discuss state-of-the-art mathematical methods and high performance computing in science & technology solutions. This has brought new prospects for collaboration across disciplines and ideas that facilitate novel breakthroughs.
In this paper we introduced the notions of neutrosophic (strong, weak, s-weak) hyper BCK-ideal and reflexive neutrosophic hyper BCK-ideal. Some relevant properties and their relations are indicated. Characterization of neutrosophic (weak) hyper BCK-ideal is considered.
This book constitutes the thoroughly refereed post-proceedings of the International Workshop of the TYPES Working Group, TYPES 2000, held in Durham, UK in December 2000. The 15 revised full papers presented were carefully reviewed and selected during two rounds of refereeing and revision. All current issues on type theory and type systems and their applications to programming, systems design, and proof theory are addressed.
“Neutrosophic Sets and Systems” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc. Some articles from this issue: BMBJ-neutrosophic ideals in BCK/BCI-algebras, Neutrosophic General Finite Automata, Generalized Neutrosophic Exponential map, Implementation of Neutrosophic Function Memberships Using MATLAB Program.
This volume contains the papers presented at the 13th Annual Conference on Algorithmic Learning Theory (ALT 2002), which was held in Lub ̈ eck (Germany) during November 24–26, 2002. The main objective of the conference was to p- vide an interdisciplinary forum discussing the theoretical foundations of machine learning as well as their relevance to practical applications. The conference was colocated with the Fifth International Conference on Discovery Science (DS 2002). The volume includes 26 technical contributions which were selected by the program committee from 49 submissions. It also contains the ALT 2002 invited talks presented by Susumu Hayashi (Kobe University, Japan) on “Mathematics Based on Learning”, by John Shawe-Taylor (Royal Holloway University of L- don, UK) on “On the Eigenspectrum of the Gram Matrix and Its Relationship to the Operator Eigenspectrum”, and by Ian H. Witten (University of Waikato, New Zealand) on “Learning Structure from Sequences, with Applications in a Digital Library” (joint invited talk with DS 2002). Furthermore, this volume - cludes abstracts of the invited talks for DS 2002 presented by Gerhard Widmer (Austrian Research Institute for Arti?cial Intelligence, Vienna) on “In Search of the Horowitz Factor: Interim Report on a Musical Discovery Project” and by Rudolf Kruse (University of Magdeburg, Germany) on “Data Mining with Graphical Models”. The complete versions of these papers are published in the DS 2002 proceedings (Lecture Notes in Arti?cial Intelligence, Vol. 2534). ALT has been awarding the E.
Integral equations are functional equations in which an unknown function appears under an integral sign. This can involve aspects of function theory and their integral transforms when the unknown function appears with a functional non-degenerated kernel under the integral sign. The close relation between differential and integral equations does that in some functional analysis, and function theory problems may be formulated either way. This book establishes the fundamentals of integral equations and considers some deep research aspects on integral equations of first and second kind, operator theory applied to integral equations, methods to solve some nonlinear integral equations, and singular integral equations, among other things. This is the first volume on this theme, hoping that other volumes of this important functional analysis theme and operator theory to formal functional equations will be realized in the future.