Affine Arithmetic Based Solution Of Uncertain Static And Dynamic Problems

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Affine Arithmetic Based Solution of Uncertain Static and Dynamic Problems

Author : Snehashish Chakraverty
Publisher : Morgan & Claypool Publishers
ISBN 13 : 1681737728
Total Pages : 172 pages
Book Rating : 4.6/5 (817 download)

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Book Synopsis Affine Arithmetic Based Solution of Uncertain Static and Dynamic Problems by : Snehashish Chakraverty

Download or read book Affine Arithmetic Based Solution of Uncertain Static and Dynamic Problems written by Snehashish Chakraverty and published by Morgan & Claypool Publishers. This book was released on 2020-04-01 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: Uncertainty is an inseparable component of almost every measurement and occurrence when dealing with real-world problems. Finding solutions to real-life problems in an uncertain environment is a difficult and challenging task. As such, this book addresses the solution of uncertain static and dynamic problems based on affine arithmetic approaches. Affine arithmetic is one of the recent developments designed to handle such uncertainties in a different manner which may be useful for overcoming the dependency problem and may compute better enclosures of the solutions. Further, uncertain static and dynamic problems turn into interval and/or fuzzy linear/nonlinear systems of equations and eigenvalue problems, respectively. Accordingly, this book includes newly developed efficient methods to handle the said problems based on the affine and interval/fuzzy approach. Various illustrative examples concerning static and dynamic problems of structures have been investigated in order to show the reliability and efficacy of the developed approaches.

Affine Arithmetic Based Solution of Uncertain Static and Dynamic Problems

Author : Snehashish Chakraverty
Publisher :
ISBN 13 : 9787576707311
Total Pages : 0 pages
Book Rating : 4.7/5 (73 download)

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Book Synopsis Affine Arithmetic Based Solution of Uncertain Static and Dynamic Problems by : Snehashish Chakraverty

Download or read book Affine Arithmetic Based Solution of Uncertain Static and Dynamic Problems written by Snehashish Chakraverty and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Affine Arithmetic Based Solution of Uncertain Static and Dynamic Problems

Author : Snehashish Chakraverty
Publisher : Springer Nature
ISBN 13 : 3031024249
Total Pages : 152 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Affine Arithmetic Based Solution of Uncertain Static and Dynamic Problems by : Snehashish Chakraverty

Download or read book Affine Arithmetic Based Solution of Uncertain Static and Dynamic Problems written by Snehashish Chakraverty and published by Springer Nature. This book was released on 2022-05-31 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: Uncertainty is an inseparable component of almost every measurement and occurrence when dealing with real-world problems. Finding solutions to real-life problems in an uncertain environment is a difficult and challenging task. As such, this book addresses the solution of uncertain static and dynamic problems based on affine arithmetic approaches. Affine arithmetic is one of the recent developments designed to handle such uncertainties in a different manner which may be useful for overcoming the dependency problem and may compute better enclosures of the solutions. Further, uncertain static and dynamic problems turn into interval and/or fuzzy linear/nonlinear systems of equations and eigenvalue problems, respectively. Accordingly, this book includes newly developed efficient methods to handle the said problems based on the affine and interval/fuzzy approach. Various illustrative examples concerning static and dynamic problems of structures have been investigated in order to show the reliability and efficacy of the developed approaches.

Soft Computing in Interdisciplinary Sciences

Author : S. Chakraverty
Publisher : Springer Nature
ISBN 13 : 9811647135
Total Pages : 264 pages
Book Rating : 4.8/5 (116 download)

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Book Synopsis Soft Computing in Interdisciplinary Sciences by : S. Chakraverty

Download or read book Soft Computing in Interdisciplinary Sciences written by S. Chakraverty and published by Springer Nature. This book was released on 2021-11-01 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book meets the present and future needs for the interaction between various science and technology/engineering areas on the one hand and different branches of soft computing on the other. Soft computing is the recent development about the computing methods which include fuzzy set theory/logic, evolutionary computation (EC), probabilistic reasoning, artificial neural networks, machine learning, expert systems, etc. Soft computing refers to a partnership of computational techniques in computer science, artificial intelligence, machine learning, and some other engineering disciplines, which attempt to study, model, and analyze complex problems from different interdisciplinary problems. This, as opposed to traditional computing, deals with approximate models and gives solutions to complex real-life problems. Unlike hard computing, soft computing is tolerant of imprecision, uncertainty, partial truth, and approximations. Interdisciplinary sciences include various challenging problems of science and engineering. Recent developments in soft computing are the bridge to handle different interdisciplinary science and engineering problems. In recent years, the correspondingly increased dialog between these disciplines has led to this new book. This is done, firstly, by encouraging the ways that soft computing may be applied in traditional areas, as well as point towards new and innovative areas of applications and secondly, by encouraging other scientific disciplines to engage in a dialog with the above computation algorithms outlining their problems to both access new methods as well as to suggest innovative developments within itself.

Interval Methods for Uncertain Power System Analysis

Author : Alfredo Vaccaro
Publisher : John Wiley & Sons
ISBN 13 : 1119855047
Total Pages : 148 pages
Book Rating : 4.1/5 (198 download)

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Book Synopsis Interval Methods for Uncertain Power System Analysis by : Alfredo Vaccaro

Download or read book Interval Methods for Uncertain Power System Analysis written by Alfredo Vaccaro and published by John Wiley & Sons. This book was released on 2023-10-31 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explore the applications of range analysis to power systems under conditions of uncertainty In Interval Methods for Uncertain Power System Analysis, accomplished engineer Dr. Alfredo Vaccaro delivers a comprehensive discussion of the mathematical foundations of range analysis and its application to solving traditional power system operation problems in the presence of strong and correlated uncertainties. The book explores highly relevant topics in the area, from interval methods for uncertainty representation and management to a variety of application examples. The author offers readers the latest methodological breakthroughs and roadmaps to implementing the mathematics discussed within, as well as best practices commonly employed across the industry. Interval Methods for Uncertain Power System Analysis includes examinations of linear and non-linear equations, as well as: A thorough introduction to reliable computing, including discussions of interval arithmetic and interval-based operators Comprehensive explorations of uncertain power flow analysis, including discussions of problem formulation and sources of uncertainty in power flow analysis In-depth examinations of uncertain optimal power flow analysis Fulsome discussions of uncertain small signal stability analysis, including treatments of how to compute eigenvalues of uncertain matrices Perfect for engineers working in power flow and optimal power flow analyses, optimization theory, and computer aided simulation, Interval Methods for Uncertain Power System Analysis will also earn a place in the libraries of researchers and graduate students studying decision making under uncertainty in power systems operation.

Affine Arithmetic-Based Methods for Uncertain Power System Analysis

Author : Alfredo Vaccaro
Publisher : Elsevier
ISBN 13 : 032390503X
Total Pages : 166 pages
Book Rating : 4.3/5 (239 download)

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Book Synopsis Affine Arithmetic-Based Methods for Uncertain Power System Analysis by : Alfredo Vaccaro

Download or read book Affine Arithmetic-Based Methods for Uncertain Power System Analysis written by Alfredo Vaccaro and published by Elsevier. This book was released on 2022-04-07 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: Affine Arithmetic-Based Methods for Uncertain Power System Analysis presents the unique properties and representative applications of Affine Arithmetic in power systems analysis, particularly as they are deployed for reliability optimization. The work provides a comprehensive foundation in Affine Arithmetic necessary to understand the central computing paradigms that can be adopted for uncertain power flow and optimal power flow analyses. These paradigms are adapted and applied to case studies, which integrate benchmark test systems and full step-by-step procedure for implementation so that readers are able to replicate and modify. The work is presented with illustrative numerical examples and MATLAB computations. Provides a uniquely comprehensive review of affine arithmetic in both its core theoretical underpinnings and their developed applications to power system analysis Details the exemplary benefits derived by the deployment of affine arithmetic methods for uncertainty handling in decision-making processes Clarifies arithmetical complexity and eases the understanding of illustrative methodologies for researchers in both power system and decision-making fields

Mathematical Problem Factories

Author : Andrew McEachern
Publisher : Springer Nature
ISBN 13 : 3031024362
Total Pages : 147 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Mathematical Problem Factories by : Andrew McEachern

Download or read book Mathematical Problem Factories written by Andrew McEachern and published by Springer Nature. This book was released on 2022-05-31 with total page 147 pages. Available in PDF, EPUB and Kindle. Book excerpt: A problem factory consists of a traditional mathematical analysis of a type of problem that describes many, ideally all, ways that the problems of that type can be cast in a fashion that allows teachers or parents to generate problems for enrichment exercises, tests, and classwork. Some problem factories are easier than others for a teacher or parent to apply, so we also include banks of example problems for users. This text goes through the definition of a problem factory in detail and works through many examples of problem factories. It gives banks of questions generated using each of the examples of problem factories, both the easy ones and the hard ones. This text looks at sequence extension problems (what number comes next?), basic analytic geometry, problems on whole numbers, diagrammatic representations of systems of equations, domino tiling puzzles, and puzzles based on combinatorial graphs. The final chapter previews other possible problem factories.

Crowd Dynamics by Kinetic Theory Modeling

Author : Bouchra Aylaj
Publisher : Springer Nature
ISBN 13 : 3031024281
Total Pages : 86 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Crowd Dynamics by Kinetic Theory Modeling by : Bouchra Aylaj

Download or read book Crowd Dynamics by Kinetic Theory Modeling written by Bouchra Aylaj and published by Springer Nature. This book was released on 2022-06-01 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt: The contents of this brief Lecture Note are devoted to modeling, simulations, and applications with the aim of proposing a unified multiscale approach accounting for the physics and the psychology of people in crowds. The modeling approach is based on the mathematical theory of active particles, with the goal of contributing to safety problems of interest for the well-being of our society, for instance, by supporting crisis management in critical situations such as sudden evacuation dynamics induced through complex venues by incidents.

The Navier–Stokes Problem

Author : Alexander G. Ramm
Publisher : Springer Nature
ISBN 13 : 3031024311
Total Pages : 61 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis The Navier–Stokes Problem by : Alexander G. Ramm

Download or read book The Navier–Stokes Problem written by Alexander G. Ramm and published by Springer Nature. This book was released on 2022-06-01 with total page 61 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main result of this book is a proof of the contradictory nature of the Navier‒Stokes problem (NSP). It is proved that the NSP is physically wrong, and the solution to the NSP does not exist on R+ (except for the case when the initial velocity and the exterior force are both equal to zero; in this case, the solution (, ) to the NSP exists for all ≥ 0 and (, ) = 0). It is shown that if the initial data 0() ≢ 0, (,) = 0 and the solution to the NSP exists for all ε R+, then 0() := (, 0) = 0. This Paradox proves that the NSP is physically incorrect and mathematically unsolvable, in general. Uniqueness of the solution to the NSP in the space 21(R3) × C(R+) is proved, 21(R3) is the Sobolev space, R+ = [0, ∞). Theory of integral equations and inequalities with hyper-singular kernels is developed. The NSP is reduced to an integral inequality with a hyper-singular kernel.

Continuous Distributions in Engineering and the Applied Sciences -- Part II

Author : Rajan Chattamvelli
Publisher : Springer Nature
ISBN 13 : 3031024354
Total Pages : 145 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Continuous Distributions in Engineering and the Applied Sciences -- Part II by : Rajan Chattamvelli

Download or read book Continuous Distributions in Engineering and the Applied Sciences -- Part II written by Rajan Chattamvelli and published by Springer Nature. This book was released on 2022-06-01 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second part of our book on continuous statistical distributions. It covers inverse-Gaussian, Birnbaum-Saunders, Pareto, Laplace, central 2, , , Weibull, Rayleigh, Maxwell, and extreme value distributions. Important properties of these distribution are documented, and most common practical applications are discussed. This book can be used as a reference material for graduate courses in engineering statistics, mathematical statistics, and econometrics. Professionals and practitioners working in various fields will also find some of the chapters to be useful. Although an extensive literature exists on each of these distributions, we were forced to limit the size of each chapter and the number of references given at the end due to the publishing plan of this book that limits its size. Nevertheless, we gratefully acknowledge the contribution of all those authors whose names have been left out. Some knowledge in introductory algebra and college calculus is assumed throughout the book. Integration is extensively used in several chapters, and many results discussed in Part I (Chapters 1 to 9) of our book are used in this volume. Chapter 10 is on Inverse Gaussian distribution and its extensions. The Birnbaum-Saunders distribution and its extensions along with applications in actuarial sciences is discussed in Chapter 11. Chapter 12 discusses Pareto distribution and its extensions. The Laplace distribution and its applications in navigational errors is discussed in the next chapter. This is followed by central chi-squared distribution and its applications in statistical inference, bioinformatics and genomics. Chapter 15 discusses Student's distribution, its extensions and applications in statistical inference. The distribution and its applications in statistical inference appears next. Chapter 17 is on Weibull distribution and its applications in geology and reliability engineering. Next two chapters are on Rayleigh and Maxwell distributions and its applications in communications, wind energy modeling, kinetic gas theory, nuclear and thermal engineering, and physical chemistry. The last chapter is on Gumbel distribution, its applications in the law of rare exceedances. Suggestions for improvement are welcome. Please send them to [email protected].

Select Ideas in Partial Differential Equations

Author : Peter J Costa
Publisher : Springer Nature
ISBN 13 : 3031024346
Total Pages : 228 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Select Ideas in Partial Differential Equations by : Peter J Costa

Download or read book Select Ideas in Partial Differential Equations written by Peter J Costa and published by Springer Nature. This book was released on 2022-06-01 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text provides an introduction to the applications and implementations of partial differential equations. The content is structured in three progressive levels which are suited for upper–level undergraduates with background in multivariable calculus and elementary linear algebra (chapters 1–5), first– and second–year graduate students who have taken advanced calculus and real analysis (chapters 6-7), as well as doctoral-level students with an understanding of linear and nonlinear functional analysis (chapters 7-8) respectively. Level one gives readers a full exposure to the fundamental linear partial differential equations of physics. It details methods to understand and solve these equations leading ultimately to solutions of Maxwell’s equations. Level two addresses nonlinearity and provides examples of separation of variables, linearizing change of variables, and the inverse scattering transform for select nonlinear partial differential equations. Level three presents rich sources of advanced techniques and strategies for the study of nonlinear partial differential equations, including unique and previously unpublished results. Ultimately the text aims to familiarize readers in applied mathematics, physics, and engineering with some of the myriad techniques that have been developed to model and solve linear and nonlinear partial differential equations.

Aspects of Differential Geometry V

Author : Esteban Calviño-Louzao
Publisher : Springer Nature
ISBN 13 : 303102432X
Total Pages : 140 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Aspects of Differential Geometry V by : Esteban Calviño-Louzao

Download or read book Aspects of Differential Geometry V written by Esteban Calviño-Louzao and published by Springer Nature. This book was released on 2022-05-31 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: Book V completes the discussion of the first four books by treating in some detail the analytic results in elliptic operator theory used previously. Chapters 16 and 17 provide a treatment of the techniques in Hilbert space, the Fourier transform, and elliptic operator theory necessary to establish the spectral decomposition theorem of a self-adjoint operator of Laplace type and to prove the Hodge Decomposition Theorem that was stated without proof in Book II. In Chapter 18, we treat the de Rham complex and the Dolbeault complex, and discuss spinors. In Chapter 19, we discuss complex geometry and establish the Kodaira Embedding Theorem.

Statistics is Easy

Author : Manpreet Singh Katari
Publisher : Springer Nature
ISBN 13 : 3031024338
Total Pages : 62 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Statistics is Easy by : Manpreet Singh Katari

Download or read book Statistics is Easy written by Manpreet Singh Katari and published by Springer Nature. This book was released on 2022-05-31 with total page 62 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational analysis of natural science experiments often confronts noisy data due to natural variability in environment or measurement. Drawing conclusions in the face of such noise entails a statistical analysis. Parametric statistical methods assume that the data is a sample from a population that can be characterized by a specific distribution (e.g., a normal distribution). When the assumption is true, parametric approaches can lead to high confidence predictions. However, in many cases particular distribution assumptions do not hold. In that case, assuming a distribution may yield false conclusions. The companion book Statistics is Easy, gave a (nearly) equation-free introduction to nonparametric (i.e., no distribution assumption) statistical methods. The present book applies data preparation, machine learning, and nonparametric statistics to three quite different life science datasets. We provide the code as applied to each dataset in both R and Python 3. We also include exercises for self-study or classroom use.

Continuous Distributions in Engineering and the Applied Sciences -- Part I

Author : Rajan Chattamvelli
Publisher : Springer Nature
ISBN 13 : 3031024303
Total Pages : 151 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Continuous Distributions in Engineering and the Applied Sciences -- Part I by : Rajan Chattamvelli

Download or read book Continuous Distributions in Engineering and the Applied Sciences -- Part I written by Rajan Chattamvelli and published by Springer Nature. This book was released on 2022-06-01 with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an introductory book on continuous statistical distributions and its applications. It is primarily written for graduate students in engineering, undergraduate students in statistics, econometrics, and researchers in various fields. The purpose is to give a self-contained introduction to most commonly used classical continuous distributions in two parts. Important applications of each distribution in various applied fields are explored at the end of each chapter. A brief overview of the chapters is as follows. Chapter 1 discusses important concepts on continuous distributions like location-and-scale distributions, truncated, size-biased, and transmuted distributions. A theorem on finding the mean deviation of continuous distributions, and its applications are also discussed. Chapter 2 is on continuous uniform distribution, which is used in generating random numbers from other distributions. Exponential distribution is discussed in Chapter 3, and its applications briefly mentioned. Chapter 4 discusses both Beta-I and Beta-II distributions and their generalizations, as well as applications in geotechnical engineering, PERT, control charts, etc. The arcsine distribution and its variants are discussed in Chapter 5, along with arcsine transforms and Brownian motion. This is followed by gamma distribution and its applications in civil engineering, metallurgy, and reliability. Chapter 7 is on cosine distribution and its applications in signal processing, antenna design, and robotics path planning. Chapter 8 discusses the normal distribution and its variants like lognormal, and skew-normal distributions. The last chapter of Part I is on Cauchy distribution, its variants and applications in thermodynamics, interferometer design, and carbon-nanotube strain sensing. A new volume (Part II) covers inverse Gaussian, Laplace, Pareto, 2, T, F, Weibull, Rayleigh, Maxwell, and Gumbel distributions.

Monte Carlo Methods

Author : Sujaul Chowdhury
Publisher : Springer Nature
ISBN 13 : 303102429X
Total Pages : 123 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Monte Carlo Methods by : Sujaul Chowdhury

Download or read book Monte Carlo Methods written by Sujaul Chowdhury and published by Springer Nature. This book was released on 2022-06-01 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended for undergraduate students of Mathematics, Statistics, and Physics who know nothing about Monte Carlo Methods but wish to know how they work. All treatments have been done as much manually as is practicable. The treatments are deliberately manual to let the readers get the real feel of how Monte Carlo Methods work. Definite integrals of a total of five functions (), namely Sin(), Cos(), e, loge(), and 1/(1+2), have been evaluated using constant, linear, Gaussian, and exponential probability density functions (). It is shown that results agree with known exact values better if () is proportional to (). Deviation from the proportionality results in worse agreement. This book is on Monte Carlo Methods which are numerical methods for Computational Physics. These are parts of a syllabus for undergraduate students of Mathematics and Physics for the course titled "Computational Physics." Need for the book: Besides the three referenced books, this is the only book that teaches how basic Monte Carlo methods work. This book is much more explicit and easier to follow than the three referenced books. The two chapters on the Variational Quantum Monte Carlo method are additional contributions of the book. Pedagogical features: After a thorough acquaintance with background knowledge in Chapter 1, five thoroughly worked out examples on how to carry out Monte Carlo integration is included in Chapter 2. Moreover, the book contains two chapters on the Variational Quantum Monte Carlo method applied to a simple harmonic oscillator and a hydrogen atom. The book is a good read; it is intended to make readers adept at using the method. The book is intended to aid in hands-on learning of the Monte Carlo methods.

A First Course in Complex Analysis

Author : Allan R. Willms
Publisher : Morgan & Claypool Publishers
ISBN 13 : 1636393152
Total Pages : 237 pages
Book Rating : 4.6/5 (363 download)

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Book Synopsis A First Course in Complex Analysis by : Allan R. Willms

Download or read book A First Course in Complex Analysis written by Allan R. Willms and published by Morgan & Claypool Publishers. This book was released on 2022-04-20 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces complex analysis and is appropriate for a first course in the subject at typically the third-year University level. It introduces the exponential function very early but does so rigorously. It covers the usual topics of functions, differentiation, analyticity, contour integration, the theorems of Cauchy and their many consequences, Taylor and Laurent series, residue theory, the computation of certain improper real integrals, and a brief introduction to conformal mapping. Throughout the text an emphasis is placed on geometric properties of complex numbers and visualization of complex mappings.

Mathematical Methods in Dynamical Systems

Author : S. Chakraverty
Publisher : CRC Press
ISBN 13 : 1000833771
Total Pages : 393 pages
Book Rating : 4.0/5 (8 download)

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Book Synopsis Mathematical Methods in Dynamical Systems by : S. Chakraverty

Download or read book Mathematical Methods in Dynamical Systems written by S. Chakraverty and published by CRC Press. This book was released on 2023-05-19 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: The art of applying mathematics to real-world dynamical problems such as structural dynamics, fluid dynamics, wave dynamics, robot dynamics, etc. can be extremely challenging. Various aspects of mathematical modelling that may include deterministic or uncertain (fuzzy, interval, or stochastic) scenarios, along with integer or fractional order, are vital to understanding these dynamical systems. Mathematical Methods in Dynamical Systems offers problem-solving techniques and includes different analytical, semi-analytical, numerical, and machine intelligence methods for finding exact and/or approximate solutions of governing equations arising in dynamical systems. It provides a singular source of computationally efficient methods to investigate these systems and includes coverage of various industrial applications in a simple yet comprehensive way.