Ordinary And Fractional Approximation By Non Additive Integrals Choquet Shilkret And Sugeno Integral Approximators PDF Download
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| Author | : George A. Anastassiou |
| Publisher | : Springer |
| Total Pages | : 347 |
| Release | : 2018-12-07 |
| Genre | : Technology & Engineering |
| ISBN | : 3030042871 |
Download Ordinary and Fractional Approximation by Non-additive Integrals: Choquet, Shilkret and Sugeno Integral Approximators Book in PDF, ePub and Kindle
Ordinary and fractional approximations by non-additive integrals, especially by integral approximators of Choquet, Silkret and Sugeno types, are a new trend in approximation theory. These integrals are only subadditive and only the first two are positive linear, and they produce very fast and flexible approximations based on limited data. The author presents both the univariate and multivariate cases. The involved set functions are much weaker forms of the Lebesgue measure and they were conceived to fulfill the needs of economic theory and other applied sciences. The approaches presented here are original, and all chapters are self-contained and can be read independently. Moreover, the book’s findings are sure to find application in many areas of pure and applied mathematics, especially in approximation theory, numerical analysis and mathematical economics (both ordinary and fractional). Accordingly, it offers a unique resource for researchers, graduate students, and for coursework in the above-mentioned fields, and belongs in all science and engineering libraries.
| Author | : George A. Anastassiou |
| Publisher | : Springer Nature |
| Total Pages | : 429 |
| Release | : 2022-10-01 |
| Genre | : Technology & Engineering |
| ISBN | : 3031164008 |
Download Banach Space Valued Neural Network Book in PDF, ePub and Kindle
This book is about the generalization and modernization of approximation by neural network operators. Functions under approximation and the neural networks are Banach space valued. These are induced by a great variety of activation functions deriving from the arctangent, algebraic, Gudermannian, and generalized symmetric sigmoid functions. Ordinary, fractional, fuzzy, and stochastic approximations are exhibited at the univariate, fractional, and multivariate levels. Iterated-sequential approximations are also covered. The book’s results are expected to find applications in the many areas of applied mathematics, computer science and engineering, especially in artificial intelligence and machine learning. Other possible applications can be in applied sciences like statistics, economics, etc. Therefore, this book is suitable for researchers, graduate students, practitioners, and seminars of the above disciplines, also to be in all science and engineering libraries.
| Author | : George A. Anastassiou |
| Publisher | : Springer Nature |
| Total Pages | : 155 |
| Release | : 2022-03-11 |
| Genre | : Technology & Engineering |
| ISBN | : 3030959430 |
Download Abstract Fractional Monotone Approximation, Theory and Applications Book in PDF, ePub and Kindle
This book employs an abstract kernel fractional calculus with applications to Prabhakar and non-singular kernel fractional calculi. The results are univariate and bivariate. In the univariate case, abstract fractional monotone approximation by polynomials and splines is presented. In the bivariate case, the abstract fractional monotone constrained approximation by bivariate pseudo-polynomials and polynomials is given. This book’s results are expected to find applications in many areas of pure and applied mathematics, especially in fractional approximation and fractional differential equations. Other interesting applications are applied in sciences like geophysics, physics, chemistry, economics, and engineering. This book is appropriate for researchers, graduate students, practitioners, and seminars of the above disciplines.
| Author | : George A. Anastassiou |
| Publisher | : Springer Nature |
| Total Pages | : 312 |
| Release | : 2022-05-12 |
| Genre | : Technology & Engineering |
| ISBN | : 3031051483 |
Download Fractional Inequalities In Banach Algebras Book in PDF, ePub and Kindle
This book presents generalized Caputo fractional Ostrowski and Grüss-type inequalities involving several Banach algebra valued functions. Furthermore, the author gives generalized Canavati fractional Ostrowski, Opial, Grüss, and Hilbert-Pachpatte-type inequalities for multiple Banach algebra valued functions. By applying the p-Schatten norms over the von Neumann–Schatten classes, the author produces the analogous refined and interesting inequalities. The author provides many applications. This book’s results are expected to find applications in many areas of pure and applied mathematics, especially in fractional inequalities and fractional differential equations. Other interesting applications are in applied sciences like geophysics, physics, chemistry, economics, and engineering. This book is appropriate for researchers, graduate students, practitioners, and seminars of the above disciplines, also to be in all science and engineering libraries.
| Author | : George A. Anastassiou |
| Publisher | : Springer Nature |
| Total Pages | : 854 |
| Release | : 2023-09-29 |
| Genre | : Technology & Engineering |
| ISBN | : 3031430212 |
Download Parametrized, Deformed and General Neural Networks Book in PDF, ePub and Kindle
In this book, we introduce the parametrized, deformed and general activation function of neural networks. The parametrized activation function kills much less neurons than the original one. The asymmetry of the brain is best expressed by deformed activation functions. Along with a great variety of activation functions, general activation functions are also engaged. Thus, in this book, all presented is original work by the author given at a very general level to cover a maximum number of different kinds of neural networks: giving ordinary, fractional, fuzzy and stochastic approximations. It presents here univariate, fractional and multivariate approximations. Iterated sequential multi-layer approximations are also studied. The functions under approximation and neural networks are Banach space valued.
| Author | : Vicenc Torra |
| Publisher | : Springer |
| Total Pages | : 207 |
| Release | : 2013-10-23 |
| Genre | : Technology & Engineering |
| ISBN | : 3319031554 |
Download Non-Additive Measures Book in PDF, ePub and Kindle
This book provides a comprehensive and timely report in the area of non-additive measures and integrals. It is based on a panel session on fuzzy measures, fuzzy integrals and aggregation operators held during the 9th International Conference on Modeling Decisions for Artificial Intelligence (MDAI 2012) in Girona, Spain, November 21-23, 2012. The book complements the MDAI 2012 proceedings book, published in Lecture Notes in Computer Science (LNCS) in 2012. The individual chapters, written by key researchers in the field, cover fundamental concepts and important definitions (e.g. the Sugeno integral, definition of entropy for non-additive measures) as well some important applications (e.g. to economics and game theory) of non-additive measures and integrals. The book addresses students, researchers and practitioners working at the forefront of their field.
| Author | : Ronald A. Devore |
| Publisher | : Academic Press |
| Total Pages | : 337 |
| Release | : 2014-05-10 |
| Genre | : Mathematics |
| ISBN | : 1483265129 |
Download Quantitative Approximation Book in PDF, ePub and Kindle
Quantitative Approximation provides information pertinent to nonlinear approximation, including rational approximation and optimal knot spline approximation. This book discusses spline approximation with the most emphasis on multivariate and knot independent questions. Organized into 26 chapters, this book begins with an overview of the inequality for the sharp function in terms of the maximal rearrangement. This text then examines the best co-approximation in a Hilbert space wherein the existence ad uniqueness sets are the closed flats. Other chapters consider the inverse of the coefficient matrix for the system satisfied by the B-spline coefficients of the cubic spline interpolant at knots. This book discusses as well the relationship between the structural properties of a function and its degree of approximation by rational functions. The final chapter deals with the problem of existence of continuous selections for metric projections and provides a solution for this problem. This book is a valuable resource for mathematicians.
| Author | : Shantanu Das |
| Publisher | : Cambridge Scholars Publishing |
| Total Pages | : 533 |
| Release | : 2020-02-18 |
| Genre | : Mathematics |
| ISBN | : 1527547116 |
Download Kindergarten of Fractional Calculus Book in PDF, ePub and Kindle
This book presents a simplified deliberation of fractional calculus, which will appeal not only to beginners, but also to various applied science mathematicians and engineering researchers. The text develops the ideas behind this new field of mathematics, beginning at the most elementary level, before discussing its actual applications in different areas of science and engineering. This book shows that the simple, classical laws based on Newtonian calculus, which work quite well under limiting and idealized conditions, are not of much use in describing the dynamics of actual systems. As such, the application of non-Newtonian, or generalized, calculus in the governing equations, allows the order of differentiation and integration to take on non-integer values.
| Author | : Hemen Dutta |
| Publisher | : John Wiley & Sons |
| Total Pages | : 336 |
| Release | : 2020-08-06 |
| Genre | : Mathematics |
| ISBN | : 1119654238 |
Download Fractional Order Analysis Book in PDF, ePub and Kindle
A guide to the new research in the field of fractional order analysis Fractional Order Analysis contains the most recent research findings in fractional order analysis and its applications. The authors—noted experts on the topic—offer an examination of the theory, methods, applications, and the modern tools and techniques in the field of fractional order analysis. The information, tools, and applications presented can help develop mathematical methods and models with better accuracy. Comprehensive in scope, the book covers a range of topics including: new fractional operators, fractional derivatives, fractional differential equations, inequalities for different fractional derivatives and fractional integrals, fractional modeling related to transmission of Malaria, and dynamics of Zika virus with various fractional derivatives, and more. Designed to be an accessible text, several useful, relevant and connected topics can be found in one place, which is crucial for an understanding of the research problems of an applied nature. This book: Contains recent development in fractional calculus Offers a balance of theory, methods, and applications Puts the focus on fractional analysis and its interdisciplinary applications, such as fractional models for biological models Helps make research more relevant to real-life applications Written for researchers, professionals and practitioners, Fractional Order Analysis offers a comprehensive resource to fractional analysis and its many applications as well as information on the newest research.
| Author | : Zhenyuan Wang |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 352 |
| Release | : 2013-03-09 |
| Genre | : Mathematics |
| ISBN | : 1475753039 |
Download Fuzzy Measure Theory Book in PDF, ePub and Kindle
Providing the first comprehensive treatment of the subject, this groundbreaking work is solidly founded on a decade of concentrated research, some of which is published here for the first time, as well as practical, ''hands on'' classroom experience. The clarity of presentation and abundance of examples and exercises make it suitable as a graduate level text in mathematics, decision making, artificial intelligence, and engineering courses.
