Hardcover ISBN
978-3-031-31815-3
Published: 28 May 2023
This textbook provides a straightforward, clear explanation of probability and random variables for communications engineering students. The author focuses on the most essential subjects of probability and random variables, eliminating unnecessary details of this difficult subject. After an introduction to the topic, the author covers the essentials of experiments, sample spaces, events, and probability laws, while investigating how they relate to communications engineering work. He goes on to discuss total probability theorems, after which he covers discrete random variables and continuous random variables. The author uses his years of teaching probability and random variable concepts to engineering students to form the text in a very understandable manner. The book features exercises, examples, case studies, and other key classroom materials
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Front Matter
Pages i-ix
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Experiments, Sample Spaces, Events, and Probability Laws
Orhan Gazi
Pages 1-27
Total Probability Theorem, Independence, Combinatorial
Orhan Gazi
Pages 29-66
Discrete Random Variables
Orhan Gazi
Pages 67-109
Functions of Random Variables
Orhan Gazi
Pages 111-139
Continuous Random Variables
Orhan Gazi
Pages 141-181
More Than One Random Variables
Orhan Gazi
Pages 183-231
Back Matter
Pages 233-236
ISBN: 978-981-99-0596-6
Subject: Mathematics and Statistics
Published At: 2023年6月11日
Series Title: Springer Proceedings in Mathematics & Statistics
This book contains select contributions presented at the International Conference on Nonlinear Applied Analysis and Optimization (ICNAAO-2021), held at the Department of Mathematics Sciences, Indian Institute of Technology (BHU) Varanasi, India, from 21?23 December 2021. The book discusses topics in the areas of nonlinear analysis, fixed point theory, dynamical systems, optimization, fractals, applications to differential/integral equations, signal and image processing, and soft computing, and exposes the young talents with the newer dimensions in these areas with their practical approaches and to tackle the real-life problems in engineering, medical and social sciences. Scientists from the U.S.A., Austria, France, Mexico, Romania, and India have contributed their research. All the submissions are peer reviewed by experts in their fields.
Front Matter
Pages i-xii
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Fixed Point Theory
Front Matter
Pages 1-1
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Large Contractions and Surjectivity in Banach Spaces
M?d?lina Moga, Adrian Petru?el
Pages 3-12
On Hick’s Contraction Using a Control Function
Vandana Tiwari, Binayak S. Choudhury, Tanmoy Som
Pages 13-19
Coupled Fixed Points for Multivalued Feng?Liu-Type Contractions with Application to Nonlinear Integral Equation
Binayak S. Choudhury, N. Metiya, S. Kundu, P. Maity
Pages 21-30
Fractals
Front Matter
Pages 31-31
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Clifford-Valued Fractal Interpolation
Peter R. Massopust
Pages 33-42
Optimal Quantizers for a Nonuniform Distribution on a Sierpi?ski Carpet
Mrinal Kanti Roychowdhury
Pages 43-62
Fractal Dimension for a Class of Complex-Valued Fractal Interpolation Functions
Manuj Verma, Amit Priyadarshi, Saurabh Verma
Pages 63-77
A Note on Complex-Valued Fractal Functions on the Sierpi?ski Gasket
V. Agrawal, T. Som
Pages 79-92
Dimensional Analysis of Mixed Riemann?Liouville Fractional Integral of Vector-Valued Functions
Megha Pandey, Tanmoy Som, Saurabh Verma
Pages 93-109
Fractional Operator Associated with the Fractal Integral of A-Fractal Function
T. M. C. Priyanka, A. Gowrisankar
Pages 111-121
Mathematical Modeling
Front Matter
Pages 123-123
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A Multi-strain Model for COVID-19
Samiran Ghosh, Malay Banerjee
Pages 125-141
Effect of Nonlinear Prey Refuge on Predator?Prey Dynamics
Shilpa Samaddar, Mausumi Dhar, Paritosh Bhattacharya
Pages 143-152
Effects of Magnetic Field and Thermal Conductivity Variance on Thermal Excitation Developed by Laser Pulses and Thermal Shock
Rakhi Tiwari
Pages 153-167
Differential and Integral Equations
Front Matter
Pages 169-169
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On Unique Positive Solution of Hadamard Fractional Differential Equation Involving p-Laplacian
Ramesh Kumar Vats, Ankit Kumar Nain, Manoj Kumar
Pages 171-181
Eigenvalue Criteria for Existence and Nonexistence of Positive Solutions for α
-Order Fractional Differential Equations on the Half-Line ( 2<α?3
) with Integral Condition
Abdelhamid Benmezai, Souad Chentout, Wassila Esserhan
Pages 183-202
A Collocation Method for Solving Proportional Delay Riccati Differential Equations of Fractional Order
Basharat Hussain, Afroz Afroz
Pages 203-217
ISBN: 978-3-031-28427-4
Subject: Mathematics and Statistics
Planned Publication Date: 2023年7月24日
This book provides an elementary introduction, complete with detailed proofs, to the celebrated tilings of the plane discovered by Sir Roger Penrose in the '70s. Quasi-periodic tilings of the plane, of which Penrose tilings are the most famous example, started as recreational mathematics and soon attracted the interest of scientists for their possible application in the description of quasi-crystals. The purpose of this survey, illustrated with more than 200 figures, is to introduce the curious reader to this beautiful topic and be a reference for some proofs that are not easy to find in the literature. The volume covers many aspects of Penrose tilings, including the study, from the point of view of Connes' Noncommutative Geometry, of the space parameterizing these tilings.
Francesco D'Andrea has a master in Theoretical Physics (Univ. Sapienza of Rome) and a Ph.D. in Mathematics (SISSA, Trieste). He is currently an associate professor in Geometry at the University of Naples Federico II. In the past, he has been a junior research fellow at the Erwin Schroedinger Institute of Vienna, a postdoctoral researcher at the Catholic University of Louvain-La-Neuve, Belgium, a visiting professor at IMPAN, Warsaw (Simons Professorship), and at Penn State University, USA (Shapiro Visitor Program).
His main interests are in Connes' noncommutative geometry, C*-algebras, and differential geometry.
ISBN: 978-3-031-33439-9
Subject: Mathematics and Statistics
Planned Publication Date: 2023年7月15日
Series Title: Mathematics of Data
This book explores and demonstrates how geometric tools can be used in data analysis. Beginning with a systematic exposition of the mathematical prerequisites, covering topics ranging from category theory to algebraic topology, Riemannian geometry, operator theory and network analysis, it goes on to describe and analyze some of the most important machine learning techniques for dimension reduction, including the different types of manifold learning and kernel methods. It also develops a new notion of curvature of generalized metric spaces, based on the notion of hyperconvexity, which can be used for the topological representation of geometric information.
In recent years there has been a fascinating development: concepts and methods originally created in the context of research in pure mathematics, and in particular in geometry, have become powerful tools in machine learning for the analysis of data. The underlying reason for this is that data are typically equipped with some kind of notion of distance, quantifying the differences between data points. Of course, to be successfully applied, the geometric tools usually need to be redefined, generalized, or extended appropriately.
Primarily aimed at mathematicians seeking an overview of the geometric concepts and methods that are useful for data analysis, the book will also be of interest to researchers in machine learning and data analysis who want to see a systematic mathematical foundation of the methods that they use.
Parvaneh Joharinad received her PhD in mathematics from Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran in March 2013. She worked as an assistant professor in the geometry group at the Institute for Advanced Studies in Basic Sciences (IASBS) in Zanjan, Iran, for seven years. She is interested in the use of geometry in data science and machine learning, and in particular in dimensionality reduction, a fundamental problem in topological and geometric data analysis.
Her collaboration with Jurgen Jost began in 2017, via a project on a generalization of the concept of sectional curvature to datasets. In 2020, she received a grant from the Max-Planck society to continue her collaboration at the Max-Planck Institute for Mathematics in the Sciences, Leipzig, Germany. As of August 2022, she started a new position at the Center for Scalable Data Analytics and Artificial Intelligence, as a senior postdoc.
Jurgen Jost worked as a Professor of Mathematics at Ruhr University Bochum from 1984 to 1996 and since 1996 has been director and a permanent member of the Max Planck Institute for Mathematics in the Sciences, Leipzig. In 1998 he became an Honorary Professor at the University of Leipzig. He is also an external member of the Santa Fe Institute for the Sciences of Complexity, New Mexico.
He pursues both topical research in different fields of pure mathematics and theoretical physics (Riemannian and algebraic geometry, geometric analysis, calculus of variations, partial differential equations, dynamical systems, graph and hypergraph theory) and interdisciplinary research in complex systems, including evolutionary and theoretical molecular biology, mathematical and theoretical neuroscience, nonlinear dynamics and statistical physics, economics and social sciences, strategy science, history and philosophy of science. He directs a group of about 40 scientists, postdocs and PhD students, and has many international cooperation partners.
ISBN: 978-981-99-3028-9
Subject: Mathematics and Statistics
Planned Publication Date: 2023年7月28日
This textbook offers a comprehensive exploration of functional analysis, covering a wide range of topics. With over 150 solved examples and more than 320 problems, the book is designed to be both motivational and user-friendly for students for senior undergraduate and graduate courses in mathematics, providing clear and thorough explanations of all concepts. The second volume in a three-part series, this book delves into normed spaces, linear functionals, locally convex spaces, Banach spaces, Hilbert spaces, topology of Banach spaces, operators on Banach spaces and geometry of Banach spaces. The text is written in a clear and engaging style, making it ideal for independent study. It offers a valuable source for students seeking a deeper understanding of functional analysis, and provides a solid understanding of the topic.
Ammar Khanfer earned his Ph.D. from Wichita State University, USA. He taught mathematics courses at several universities in the USA: Western Michigan University, Wichita State University and Southwestern College in Winfield. He then moved to Saudi Arabia, where he taught and supervised undergraduate and graduate students of mathematics at IMSIU in Riyadh. He is currently teaching at Prince Sultan University, Riyadh. His area of interest is analysis and partial differential equations (PDEs), and focusing on elliptic theory, where he notably contributed to the field by providing prototypes studying the behaviour of generalized solutions of elliptic PDEs in higher dimensions in connection to the behaviour of hypersurfaces near nonsmooth boundaries. He also works in the area of inverse problems of mathematical physics and the qualitative theory of differential equations. He published articles of high quality in reputable journals.
ISBN: 978-3-031-33428-3
Subject: Mathematics and Statistics
Planned Publication Date: 2023年7月7日
Series Title: Probability and Its Applications
This book extends the theory and applications of random evolutions to semi-Markov random media in discrete time, essentially focusing on semi-Markov chains as switching or driving processes. After giving the definitions of discrete-time semi-Markov chains and random evolutions, it presents the asymptotic theory in a functional setting, including weak convergence results in the series scheme, and their extensions in some additional directions, including reduced random media, controlled processes, and optimal stopping. Finally, applications of discrete-time semi-Markov random evolutions in epidemiology and financial mathematics are discussed. This book will be of interest to researchers and graduate students in applied mathematics and statistics, and other disciplines, including engineering, epidemiology, finance and economics, who are concerned with stochastic models of systems.
Nikolaos Limnios is a Professor at the Applied Mathematics Laboratory at the Universite de Technologie de Compiegne, France. His research interests include stochastic processes, random evolutions, with a focus on semi-Markov processes, and statistics, and applications in reliability, biology, seismology, insurance, and finance. He has published more than 150 journal articles and 10 books on the theory and applications of stochastic processes and statistics. He serves on editorial boards for several research journals.
Anatoliy Swishchuk is a Professor in Mathematical Finance at the Department of Mathematics and Statistics, University of Calgary, Canada. His research areas include financial mathematics, random evolutions and their applications, biomathematics, and stochastic calculus. He serves on editorial boards for several research journals and is the author of more than 180 publications, including 15 books and more than 120 articles in peer-reviewed journals. In 2018 he received a Peak Scholar award.