Exploring Mathematical Analysis Approximation Theory And Optimization
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Exploring Mathematical Analysis Approximation Theory And Optimization
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Author : Nicholas J. Daras
language : en
Publisher: Springer Nature
Release Date : 2024-01-04
Exploring Mathematical Analysis Approximation Theory And Optimization written by Nicholas J. Daras and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-01-04 with Mathematics categories.
This book compiles research and surveys devoted to the areas of mathematical analysis, approximation theory, and optimization. Being dedicated to A.-M. Legendre's work, contributions to this volume are devoted to those branches of mathematics and its applications that have been influenced, directly or indirectly, by the mathematician. Additional contributions provide a historical background as it relates to Legendre's work and its association to the foundation of Greece's higher education. Topics covered in this book include the investigation of the Jensen-Steffensen inequality, Ostrowski and trapezoid type inequalities, a Hilbert-Type Inequality, Hardy’s inequality, dynamic unilateral contact problems, square-free values of a category of integers, a maximum principle for general nonlinear operators, the application of Ergodic Theory to an alternating series expansion for real numbers, bounds for similarity condition numbers of unbounded operators, finite element methods with higher order polynomials, generating functions for the Fubini type polynomials, local asymptotics for orthonormal polynomials, trends in geometric function theory, quasi variational inclusions, Kleene fixed point theorems, ergodic states, spontaneous symmetry breaking and quasi-averages. It is hoped that this book will be of interest to a wide spectrum of readers from several areas of pure and applied sciences, and will be useful to undergraduate students, graduate level students, and researchers who want to be kept up to date on the results and theories in the subjects covered in this volume.
Mathematical Analysis Approximation Theory And Their Applications
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Author : Themistocles M. Rassias
language : en
Publisher: Springer
Release Date : 2016-06-03
Mathematical Analysis Approximation Theory And Their Applications written by Themistocles M. Rassias and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-03 with Mathematics categories.
Designed for graduate students, researchers, and engineers in mathematics, optimization, and economics, this self-contained volume presents theory, methods, and applications in mathematical analysis and approximation theory. Specific topics include: approximation of functions by linear positive operators with applications to computer aided geometric design, numerical analysis, optimization theory, and solutions of differential equations. Recent and significant developments in approximation theory, special functions and q-calculus along with their applications to mathematics, engineering, and social sciences are discussed and analyzed. Each chapter enriches the understanding of current research problems and theories in pure and applied research.
Essential Math For Ai
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Author : Hala Nelson
language : en
Publisher: "O'Reilly Media, Inc."
Release Date : 2023-01-04
Essential Math For Ai written by Hala Nelson and has been published by "O'Reilly Media, Inc." this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-04 with Computers categories.
Many sectors and industries are eager to integrate AI and data-driven technologies into their systems and operations. But to build truly successful AI systems, you need a firm grasp of the underlying mathematics. This comprehensive guide bridges the current gap in presentation between the unlimited potential and applications of AI and its relevant mathematical foundations. Rather than discussing dense academic theory, author Hala Nelson surveys the mathematics necessary to thrive in the AI field, focusing on real-world applications and state-of-the-art models. You'll explore topics such as regression, neural networks, convolution, optimization, probability, Markov processes, differential equations, and more within an exclusive AI context. Engineers, data scientists, mathematicians, and scientists will gain a solid foundation for success in the AI and math fields.
Foundations Of Probability Theory
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Author : Himadri Deshpande
language : en
Publisher: Educohack Press
Release Date : 2025-02-20
Foundations Of Probability Theory written by Himadri Deshpande and has been published by Educohack Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-20 with Science categories.
"Foundations of Probability Theory" offers a thorough exploration of probability theory's principles, methods, and applications. Designed for students, researchers, and practitioners, this comprehensive guide covers both foundational concepts and advanced topics. We begin with basic probability concepts, including sample spaces, events, probability distributions, and random variables, progressing to advanced topics like conditional probability, Bayes' theorem, and stochastic processes. This approach lays a solid foundation for further exploration. Our book balances theory and application, emphasizing practical applications and real-world examples. We cover topics such as statistical inference, estimation, hypothesis testing, Bayesian inference, Markov chains, Monte Carlo methods, and more. Each topic includes clear explanations, illustrative examples, and exercises to reinforce learning. Whether you're a student building a solid understanding of probability theory, a researcher exploring advanced topics, or a practitioner applying probabilistic methods to solve real-world problems, this book is an invaluable resource. We equip readers with the knowledge and tools necessary to tackle complex problems, make informed decisions, and explore probability theory's rich landscape with confidence.
Analysis Geometry Nonlinear Optimization And Applications
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Author : Panos M Pardalos
language : en
Publisher: World Scientific
Release Date : 2023-03-20
Analysis Geometry Nonlinear Optimization And Applications written by Panos M Pardalos and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-20 with Mathematics categories.
This volume features an extensive account of both research and expository papers in a wide area of engineering and mathematics and its various applications.Topics treated within this book include optimization of control points, game theory, equilibrium points, algorithms, Cartan matrices, integral inequalities, Volterra integro-differential equations, Caristi-Kirk theorems, Laplace type integral operators, etc.This useful reference text benefits graduate students, beginning research engineers and mathematicians as well as established researchers in these domains.
Inequalities
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Author : Shigeru Furuichi
language : en
Publisher: MDPI
Release Date : 2020-01-15
Inequalities written by Shigeru Furuichi and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-15 with Mathematics categories.
Inequalities appear in various fields of natural science and engineering. Classical inequalities are still being improved and/or generalized by many researchers. That is, inequalities have been actively studied by mathematicians. In this book, we selected the papers that were published as the Special Issue ‘’Inequalities’’ in the journal Mathematics (MDPI publisher). They were ordered by similar topics for readers’ convenience and to give new and interesting results in mathematical inequalities, such as the improvements in famous inequalities, the results of Frame theory, the coefficient inequalities of functions, and the kind of convex functions used for Hermite–Hadamard inequalities. The editor believes that the contents of this book will be useful to study the latest results for researchers of this field.
Exploring The Advancements And Future Directions Of Digital Twins In Healthcare 6 0
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Author : Dubey, Archi
language : en
Publisher: IGI Global
Release Date : 2024-07-18
Exploring The Advancements And Future Directions Of Digital Twins In Healthcare 6 0 written by Dubey, Archi and has been published by IGI Global this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-18 with Computers categories.
The healthcare industry is increasingly complex, demanding personalized treatments and efficient operational processes. Traditional research methods need help to keep pace with these demands, often leading to inefficiencies and suboptimal outcomes. Integrating digital twin technology presents a promising solution to these challenges, offering a virtual platform for modeling and simulating complex healthcare scenarios. However, the full potential of digital twins still needs to be explored mainly due to a lack of comprehensive guidance and practical insights for researchers and practitioners. Exploring the Advancements and Future Directions of Digital Twins in Healthcare 6.0 is not just a theoretical exploration. It is a practical guide that bridges the gap between theory and practice, offering real-world case studies, best practices, and insights into personalized medicine, real-time patient monitoring, and healthcare process optimization. By equipping you with the knowledge and tools needed to effectively integrate digital twins into your healthcare research and operations, this book is a valuable resource for researchers, academicians, medical practitioners, scientists, and students.
Fixed Point Theory And Graph Theory
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Author : Monther Alfuraidan
language : en
Publisher: Academic Press
Release Date : 2016-06-20
Fixed Point Theory And Graph Theory written by Monther Alfuraidan and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-20 with Mathematics categories.
Fixed Point Theory and Graph Theory provides an intersection between the theories of fixed point theorems that give the conditions under which maps (single or multivalued) have solutions and graph theory which uses mathematical structures to illustrate the relationship between ordered pairs of objects in terms of their vertices and directed edges. This edited reference work is perhaps the first to provide a link between the two theories, describing not only their foundational aspects, but also the most recent advances and the fascinating intersection of the domains. The authors provide solution methods for fixed points in different settings, with two chapters devoted to the solutions method for critically important non-linear problems in engineering, namely, variational inequalities, fixed point, split feasibility, and hierarchical variational inequality problems. The last two chapters are devoted to integrating fixed point theory in spaces with the graph and the use of retractions in the fixed point theory for ordered sets. - Introduces both metric fixed point and graph theory in terms of their disparate foundations and common application environments - Provides a unique integration of otherwise disparate domains that aids both students seeking to understand either area and researchers interested in establishing an integrated research approach - Emphasizes solution methods for fixed points in non-linear problems such as variational inequalities, split feasibility, and hierarchical variational inequality problems that is particularly appropriate for engineering and core science applications
Soft Computing
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Author : Pradip Debnath
language : en
Publisher: CRC Press
Release Date : 2024-09-30
Soft Computing written by Pradip Debnath and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-30 with Computers categories.
This book examines the latest developments in the area of soft computing with engineering applications. It explores topics such as fuzzy sets, intuitionistic fuzzy sets, unmanned aerial vehicles, soft sets, neutrosophic sets, fractional calculus, big data analytics, and the mathematical foundations of convolutional neural network (CNNs). Soft Computing: Engineering Applications offers readers a comprehensive and in-depth understanding of various cutting-edge technologies that are transforming industries worldwide. The book explores soft computing techniques in a very systematic manner. It elucidates the concepts, theories, and applications of fuzzy sets, enabling readers to grasp the fundamentals and explore their applications in various fields. It provides new insight into unmanned aerial vehicle applications to fuzzy soft set based decision making. It then discusses new fixed point results in orthogonal neutrosophic generalized metric spaces and explores statistical convergence of triple sequences in a credibility space. The authors then provide readers with a solid grasp of the mathematical underpinnings of CNNs, enabling them to design, train, and optimize neural networks for image recognition, object detection, and other computer vision tasks. The authors also present new studies in fractional calculus and explores advanced visualization algorithms and techniques for big data analytics. Soft Computing will be useful for beginners and advanced researchers in engineering, applied sciences and healthcare professionals working in soft computing applications.
Operator Inequalities Of Ostrowski And Trapezoidal Type
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Author : Silvestru Sever Dragomir
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-12-08
Operator Inequalities Of Ostrowski And Trapezoidal Type written by Silvestru Sever Dragomir and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-12-08 with Mathematics categories.
Inequalities of Ostrowski and Trapezoidal Type for Functions of Selfadjoint Operators on Hilbert Spaces presents recent results concerning Ostrowski and Trapezoidal type inequalities for continuous functions of bounded Selfadjoint operators on complex Hilbert spaces. The first chapter recalls some fundamental facts concerning bounded Selfadjoint operators on complex Hilbert spaces. The generalized Schwarz’s inequality for positive Selfadjoint operators as well as some results for the spectrum of this class of operators are presented. The author also introduces and explores the fundamental results for polynomials in a linear operator, continuous functions of selfadjoint operators that will play a central role throughout the book. The following chapter is devoted to the Ostrowski’s type inequalities, which provide sharp error estimates in approximating the value of a function by its integral mean and can be used to obtain a priory error bounds for different quadrature rules in approximating the Riemann integral by different Riemann sums. The author also presents recent results extending Ostrowski inequality in various directions for continuous functions of selfadjoint operators in complex Hilbert spaces. The final chapter illustrates recent results obtained in extending trapezoidal type inequality in various directions for continuous functions of selfadjoint operators in complex Hilbert spaces. Applications for mid-point inequalities and some elementary functions of operators as also provided. This book is intended for use by researchers in various fields of Linear Operator Theory and Mathematical Inequalities. As well as postgraduate students and scientists applying inequalities in their specific areas.