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Approximation Methods in Science and Engineering
by Reza N. JazarApproximation Methods in Engineering and Science covers fundamental and advanced topics in three areas: Dimensional Analysis, Continued Fractions, and Stability Analysis of the Mathieu Differential Equation. Throughout the book, a strong emphasis is given to concepts and methods used in everyday calculations. Dimensional analysis is a crucial need for every engineer and scientist to be able to do experiments on scaled models and use the results in real world applications. Knowing that most nonlinear equations have no analytic solution, the power series solution is assumed to be the first approach to derive an approximate solution. However, this book will show the advantages of continued fractions and provides a systematic method to develop better approximate solutions in continued fractions. It also shows the importance of determining stability chart of the Mathieu equation and reviews and compares several approximate methods for that. The book provides the energy-rate method to study the stability of parametric differential equations that generates much better approximate solutions.
Approximation of Euclidean Metric by Digital Distances
by Jayanta MukhopadhyayThis book discusses different types of distance functions defined in an n-D integral space for their usefulness in approximating the Euclidean metric. It discusses the properties of these distance functions and presents various kinds of error analysis in approximating Euclidean metrics. It also presents a historical perspective on efforts and motivation for approximating Euclidean metrics by digital distances from the mid-sixties of the previous century. The book also contains an in-depth presentation of recent progress, and new research problems in this area.
Approximation of Stochastic Invariant Manifolds: Stochastic Manifolds for Nonlinear SPDEs I (SpringerBriefs in Mathematics)
by Mickaël D. Chekroun Honghu Liu Shouhong WangThis first volume is concerned with the analytic derivation of explicit formulas for the leading-order Taylor approximations of (local) stochastic invariant manifolds associated with a broad class of nonlinear stochastic partial differential equations. These approximations take the form of Lyapunov-Perron integrals, which are further characterized in Volume II as pullback limits associated with some partially coupled backward-forward systems. This pullback characterization provides a useful interpretation of the corresponding approximating manifolds and leads to a simple framework that unifies some other approximation approaches in the literature. A self-contained survey is also included on the existence and attraction of one-parameter families of stochastic invariant manifolds, from the point of view of the theory of random dynamical systems.
Approximation-solvability of Nonlinear Functional and Differential Equations (Chapman And Hall/crc Pure And Applied Mathematics Ser. #171)
by Wolodymyr V. PetryshynThis reference/text develops a constructive theory of solvability on linear and nonlinear abstract and differential equations - involving A-proper operator equations in separable Banach spaces, and treats the problem of existence of a solution for equations involving pseudo-A-proper and weakly-A-proper mappings, and illustrates their applications.;Facilitating the understanding of the solvability of equations in infinite dimensional Banach space through finite dimensional appoximations, this book: offers an elementary introductions to the general theory of A-proper and pseudo-A-proper maps; develops the linear theory of A-proper maps; furnishes the best possible results for linear equations; establishes the existence of fixed points and eigenvalues for P-gamma-compact maps, including classical results; provides surjectivity theorems for pseudo-A-proper and weakly-A-proper mappings that unify and extend earlier results on monotone and accretive mappings; shows how Friedrichs' linear extension theory can be generalized to the extensions of densely defined nonlinear operators in a Hilbert space; presents the generalized topological degree theory for A-proper mappings; and applies abstract results to boundary value problems and to bifurcation and asymptotic bifurcation problems.;There are also over 900 display equations, and an appendix that contains basic theorems from real function theory and measure/integration theory.
Approximation Techniques for Engineers: Second Edition
by Louis KomzsikThis second edition includes eleven new sections based on the approximation of matrix functions, deflating the solution space and improving the accuracy of approximate solutions, iterative solution of initial value problems of systems of ordinary differential equations, and the method of trial functions for boundary value problems. The topics of th
Approximation Theory: In Memory of A.K. Varma (Chapman And Hall/crc Pure And Applied Mathematics Ser. #212)
by N. K. Govil R. N. Mahapatra Z. Nashed A. Sharma J. Szabados"Contains the contributions of 45 internationally distinguished mathematicians covering all areas of approximation theory-written in honor of the pioneering work of Arun K. Varma to the fields of interpolation and approximation of functions, including Birhoff interpolation and approximation by spline functions."
Approximation Theory and Analytic Inequalities
by Themistocles M. RassiasThis contributed volume focuses on various important areas of mathematics in which approximation methods play an essential role. It features cutting-edge research on a wide spectrum of analytic inequalities with emphasis on differential and integral inequalities in the spirit of functional analysis, operator theory, nonlinear analysis, variational calculus, featuring a plethora of applications, making this work a valuable resource. The reader will be exposed to convexity theory, polynomial inequalities, extremal problems, prediction theory, fixed point theory for operators, PDEs, fractional integral inequalities, multidimensional numerical integration, Gauss–Jacobi and Hermite–Hadamard type inequalities, Hilbert-type inequalities, and Ulam’s stability of functional equations. Contributions have been written by eminent researchers, providing up-to-date information and several results which may be useful to a wide readership including graduate students and researchers working in mathematics, physics, economics, operational research, and their interconnections.
Approximation Theory and Harmonic Analysis on Spheres and Balls (Springer Monographs in Mathematics)
by Feng Dai Yuan XuThis monograph records progress in approximation theory and harmonic analysis on balls and spheres, and presents contemporary material that will be useful to analysts in this area. While the first part of the book contains mainstream material on the subject, the second and the third parts deal with more specialized topics, such as analysis in weight spaces with reflection invariant weight functions, and analysis on balls and simplexes. The last part of the book features several applications, including cubature formulas, distribution of points on the sphere, and the reconstruction algorithm in computerized tomography. This book is directed at researchers and advanced graduate students in analysis. Mathematicians who are familiar with Fourier analysis and harmonic analysis will understand many of the concepts that appear in this manuscript: spherical harmonics, the Hardy-Littlewood maximal function, the Marcinkiewicz multiplier theorem, the Riesz transform, and doubling weights are all familiar tools to researchers in this area.
Approximation Theory and Numerical Analysis Meet Algebra, Geometry, Topology (Springer INdAM Series #60)
by Martina Lanini Carla Manni Henry SchenckThe book, based on the INdAM Workshop "Approximation Theory and Numerical Analysis Meet Algebra, Geometry, Topology" provides a bridge between different communities of mathematicians who utilize splines in their work. Splines are mathematical objects which allow researchers in geometric modeling and approximation theory to tackle a wide variety of questions. Splines are interesting for both applied mathematicians, and also for those working in purely theoretical mathematical settings. This book contains contributions by researchers from different mathematical communities: on the applied side, those working in numerical analysis and approximation theory, and on the theoretical side, those working in GKM theory, equivariant cohomology and homological algebra.
Approximation Theory XIV: San Antonio 2013 (Springer Proceedings in Mathematics & Statistics #83)
by Gregory E. Fasshauer Larry L. SchumakerThese proceedings were prepared in connection with the 14th International Conference on Approximation Theory, which was held April 7-10, 2013 in San Antonio, Texas. The conference was the fourteenth in a series of meetings in Approximation Theory held at various locations in the United States. The included invited and contributed papers cover diverse areas of approximation theory with a special emphasis on the most current and active areas such as compressed sensing, isogeometric analysis, anisotropic spaces, radial basis functions and splines. Classical and abstract approximation is also included The book will be of interest to mathematicians, engineers\ and computer scientists working in approximation theory, computer-aided geometric design, numerical analysis and related application areas.
Approximation Theory XV: San Antonio 2016 (Springer Proceedings in Mathematics & Statistics #201)
by Gregory E. Fasshauer Larry L. SchumakerThese proceedings are based on papers presented at the international conference Approximation Theory XV, which was held May 22-25, 2016 in San Antonio, Texas. The conference was the fifteenth in a series of meetings in Approximation Theory held at various locations in the United States, and was attended by 146 participants. The book contains longer survey papers by some of the invited speakers covering topics such as compressive sensing, isogeometric analysis, and scaling limits of polynomials and entire functions of exponential type. The book also includes papers on a variety of current topics in Approximation Theory drawn from areas such as advances in kernel approximation with applications, approximation theory and algebraic geometry, multivariate splines for applications, practical function approximation, approximation of PDEs, wavelets and framelets with applications, approximation theory in signal processing, compressive sensing, rational interpolation, spline approximation in isogeometric analysis, approximation of fractional differential equations, numerical integration formulas, and trigonometric polynomial approximation.
Approximation Theory XVI: Nashville, TN, USA, May 19-22, 2019 (Springer Proceedings in Mathematics & Statistics #336)
by Gregory E. Fasshauer Marian Neamtu Larry L. SchumakerThese proceedings are based on the international conference Approximation Theory XVI held on May 19–22, 2019 in Nashville, Tennessee. The conference was the sixteenth in a series of meetings in Approximation Theory held at various locations in the United States. Over 130 mathematicians from 20 countries attended. The book contains two longer survey papers on nonstationary subdivision and Prony’s method, along with 11 research papers on a variety of topics in approximation theory, including Balian-Low theorems, butterfly spline interpolation, cubature rules, Hankel and Toeplitz matrices, phase retrieval, positive definite kernels, quasi-interpolation operators, stochastic collocation, the gradient conjecture, time-variant systems, and trivariate finite elements. The book should be of interest to mathematicians, engineers, and computer scientists working in approximation theory, computer-aided geometric design, numerical analysis, and related approximation areas.
Approximation with Positive Linear Operators and Linear Combinations (Developments in Mathematics #50)
by Vijay Gupta Gancho TachevThis book presents a systematic overview of approximation by linear combinations of positive linear operators, a useful tool used to increase the order of approximation. Fundamental and recent results from the past decade are described with their corresponding proofs. The volume consists of eight chapters that provide detailed insight into the representation of monomials of the operators Ln , direct and inverse estimates for a broad class of positive linear operators, and case studies involving finite and unbounded intervals of real and complex functions. Strong converse inequalities of Type A in terminology of Ditzian-Ivanov for linear combinations of Bernstein and Bernstein-Kantorovich operators and various Voronovskaja-type estimates for some linear combinations are analyzed and explained. Graduate students and researchers in approximation theory will find the list of open problems in approximation of linear combinations useful. The book serves as a reference for graduate and postgraduate courses as well as a basis for future study and development.
Approximation with Quasi-Splines
by G.H KirovIn the theory of splines, a function is approximated piece-wise by (usually cubic) polynomials. Quasi-splines is the natural extension of this, allowing us to use any useful class of functions adapted to the problem.Approximation with Quasi-Splines is a detailed account of this highly useful technique in numerical analysis.The book presents the requisite approximation theorems and optimization methods, developing a unified theory of one and several variables. The author applies his techniques to the evaluation of definite integrals (quadrature) and its many-variables generalization, which he calls "cubature."This book should be required reading for all practitioners of the methods of approximation, including researchers, teachers, and students in applied, numerical and computational mathematics.
Approximative Justice and Cross-Border Evidence in the EU
by Anna G. WaldenströmThis book confronts the difficulties raised by cross-border evidence in order to propose a new understanding of justice as approximative.Can there be any common sense of justice across the European Union (EU)? This book takes up this question which is raised directly in cases where the understanding of cross-border evidence encounters national and linguistic differences. The interpretive challenges this introduces impact the possibility of justice in a way that, the book argues, cannot be resolved with recourse to some ideal of harmonization that would simply flatten these differences. Rather, these cases – taken here from Sweden and France – raise a practical, but also a theoretical, question about how justice can be done. In response, the book draws on contemporary theorizations of justice to argue against a common sense of justice in the sense of what would be a correct legal judgment. In its place, the book elaborates an idea of justice that maintains, rather than collapsing, the differences presented in cases of cross-border evidence; and which therefore aims to be ‘approximative,’ or ‘good enough,’ rather than simply correct.This book will be of interest to readers in legal theory, socio-legal studies, comparative law and European Union law.
Apps: From Mobile Phones to Digital Lives (Digital Media and Society)
by Gerard GogginSince the rise of the smartphone, apps have become entrenched in billions of users' daily lives. Accessible across phones and tablets, watches and wearables, connected cars, sensors, and cities, they are an inescapable feature of our current culture. In this book, Gerard Goggin provides a comprehensive and authoritative guide to the development of apps as a digital media technology. Covering the technological, social, cultural, and policy dynamics of apps, Goggin ultimately considers what a post-app world might look like. He argues that apps represent a pivowtal moment in the development of digital media, acting as a hinge between the visions and realities of the “mobile,” “cyber,” and “online” societies envisaged since the late 1980s and the imaginaries and materialities of the digital societies that emerged from 2010. Apps offer frames, construct tools, and constitute “small worlds” for users to reorient themselves in digital media settings. This fascinating book will reframe the conversation about the software that underwrites our digital worlds. It is essential reading for students and scholars of media and communication, as well as for anyone interested in this ubiquitous technology.
Apps and Services with .NET 7: Build practical projects with Blazor, .NET MAUI, gRPC, GraphQL, and other enterprise technologies
by Mark J. PriceBestselling author Mark Price is back to guide you through the coolest and most common technologies a .NET developer should know: Blazor, .NET MAUI, gRPC, GraphQL, SQL Server, Cosmos DB, OData, SignalR, Azure Functions, and more!Purchase of the print or Kindle book includes a free eBook in PDF format.Key FeaturesBuild services using a variety of technologies including Web API, OData, gRPC, GraphQL, SignalR, and Azure FunctionsLearn how to use specialized libraries to improve all aspects of your applications, including performance and localizationLeverage .NET MAUI to develop cross-platform desktop and mobile apps with easeBook DescriptionApps and Services with .NET 7 is for .NET 6 and .NET 7 developers who want to kick their C# and .NET understanding up a gear by learning the practical skills and knowledge they need to build real-world applications and services. It covers specialized libraries that will help you monitor and improve performance, secure your data and applications, and internationalize your code and apps.With chapters that put a variety of technologies into practice, including Web API, OData, gRPC, GraphQL, SignalR, and Azure Functions, this book will give you a broader scope of knowledge than other books that often focus on only a handful of .NET technologies. It covers the latest developments, libraries, and technologies that will help keep you up to date.You'll also leverage .NET MAUI to develop mobile apps for iOS and Android as well as desktop apps for Windows and macOS.What you will learnLearn how to build more efficient, secure, and scalable apps and servicesLeverage specialized .NET libraries to improve your applicationsImplement popular third-party libraries like Serilog and FluentValidationBuild cross-platform apps with .NET MAUI and integrate with native mobile featuresGet familiar with a variety of technologies for implementing services like gRPC and GraphQLExplore Blazor WebAssembly and use open-source Blazor component librariesStore and manage data locally and in the cloud with SQL Server and Cosmos DBWho this book is forThis book is for .NET developers interested in exploring more specialized libraries and implementation fundamentals behind building services and apps.You'll need to know your way around .NET and C# quite well before you can dive in, so if you want to work your way up to this book, pick up Mark's other .NET book, C# 11 and .NET 7 – Modern Cross-Platform Development Fundamentals, first.
Apps and Services with .NET 8: Build practical projects with Blazor, .NET MAUI, gRPC, GraphQL, and other enterprise technologies
by Mark J. PriceBestselling author Mark Price is back to guide you through the latest and most common technologies a .NET developer should know: Blazor Full Stack, ASP.NET Core MVC, ASP.NET Core Minimal APIs, .NET MAUI, gRPC, GraphQL, SQL Server, Cosmos DB, SignalR, Azure Functions, and more! Purchase of the print or Kindle book includes a free eBook in PDF format.Key FeaturesUse specialized libraries to improve all aspects of your apps, including performance, security, and localizationHarness the full potential of .NET using cloud-native data stores like Cosmos DB, and unlock scalability, performance, and resilience in your service implementationsUnleash the capabilities of Blazor Full Stack and.NET MAUI to develop stunning, truly cross-platform apps for web and mobileBook DescriptionElevate your practical C# and .NET skills to the next level with this new edition of Apps and Services with .NET 8. With chapters that put a variety of technologies into practice, including Web API, gRPC, GraphQL, and SignalR, this book will give you a broader scope of knowledge than other books that often focus on only a handful of .NET technologies. You’ll dive into the new unified model for Blazor Full Stack and leverage .NET MAUI to develop mobile and desktop apps. This new edition introduces the latest enhancements, including the seamless implementation of web services with ADO.NET SqlClient's native Ahead-of-Time (AOT) support. Popular library coverage now includes Humanizer and Noda Time. There’s also a brand-new chapter that delves into service architecture, caching, queuing, and robust background services. By the end of this book, you’ll have a wide range of best practices and deep insights under your belt to help you build rich apps and efficient services.What you will learnFamiliarize yourself with a variety of technologies to implement services, such as gRPC and GraphQLStore and manage data locally and cloud-natively with SQL Server and Cosmos DBUse ADO.NET SqlClient to implement web services with native AOT publish supportLeverage Dapper for improved performance over EF CoreImplement popular third-party libraries such as Serilog, FluentValidation, Humanizer, and Noda TimeExplore the new unified hosting model of Blazor Full StackWho this book is forThis book is for .NET developers interested in exploring more specialized libraries and implementation fundamentals behind building services and apps. You’ll need to know your way around .NET and C# quite well before you can dive in, so if you want to work your way up to this book, you can pick up Mark’s other .NET book, C# 12 and .NET 8 – Modern Cross-Platform Development Fundamentals, first.
Apps, Technology and Younger Learners: International evidence for teaching
by Natalia Kucirkova Garry FalloonThis book provides an in-depth analysis of the challenges, potential and theoretical possibilities of apps and considers the processes of change for education and home learning environments. Drawing together a diverse team of international contributors, it addresses the specific features, context of use and content of apps to uncover the importance of these tools for young children’s learning. Apps, Technology and Younger Learners focuses on ways that apps support early years and primary school learning, connect various learning spaces and engage children in a range of edutainment and knowledge-building activities. In each chapter, the current state of knowledge and key research questions in the field for future study are identified, with clear messages provided at the end of each chapter. Focusing on empirical studies and strong theoretical frameworks, this book covers four key parts: Understanding the learning potential of children’s apps; Key app challenges; Empirical evidence; Future avenues. This book is an essential guide for educators, post-graduate students, researchers and all those interested in the advantages or challenges that may result from integrating apps into early education.
Apraxia: The Neuropsychology of Action (Brain, Behaviour and Cognition)
by Leslie J. Gonzalez Rothi Kenneth M. HeilmanThe purpose of this book is to provide the reader with a perspective on apraxia that considers a link between the pathology of apraxia and normal motor skill. In addition, it is the intention of the authors to provide information that is theoretically interesting as well as clinically applicable. The book is a collection of papers by various authors working in the area of apraxia, almost exclusively with limb aparaxia specifically. Beginning with Hugo Liepman's work of the late 19th century, a cognitive neuropsychological model of limb apraxia is reviewed, the use of new technologies that are informative about the mechanisms of limb praxis are discussed, and issues related to research as well as clinical assessment/management of the disorder are provided. While acquired limb apraxia is the focus of the book, there are also chapters on handedness, developmental apraxia of speech, and disorders of handwriting.
Apraxia: The Neural Network Model (Neural Network Model: Applications and Implications)
by Theodore Wasserman Lori Drucker WassermanThe work will be a reanalysis and reconceptualization of the concept of apraxia. Apraxia is currently understood as a motor speech disorder but an analysis of the neural network properties of apraxia indicate a more complex and far reaching disorder with implications for intentionality, motor coordination and motor control of response inhibition in a variety of human behavioral and emotional reactions. A thorough redefinition of apraxia will be provided along with suggestions for diagnoses and treatment. The primary audience will be diagnostic and treating professionals in a variety of disciplines (outlined above). Secondarily, the book will provide an argument and justification for considering developmental apraxia pf speech to be a separate and discrete white matter based disorder. Finally, this work will serve as a driver of future research in the area.
Aprendamos de los Gigantes: Lecciones Tomadas de la Biblia Acerca de la Vida y el Liderazgo (Giants of the Bible)
by John C. MaxwellSi pudieras pasar tiempo en persona con los gigantes de la fe del Antiguo Testamento, ¿cómo sus percepciones afectarían tu vida? En este libro, John Maxwell se basa en más de cincuenta años estudiando la Biblia para transmitir la valiosa sabiduría de Elías, Eliseo, Job, Jacob, Débora, Isaías, Jonás, Josué y Daniel: Job forjó su fortaleza de carácter y se mostró optimista mientras se enfrentaba a una gran pérdida. Su reto para ti es: "¿Puedes mantenerte siendo positivo y fiel cuando las circunstancias son abrumadoras?"Débora fue escogida por Dios para ser una líder en un momento difícil. Ella te invita a que vuelvas a imaginar la envergadura de tu potencial: "Dios quiere sorprender al mundo a través de ti".Maxwell explora las historias notables de estos nueve héroes de la fe para compartir las lecciones eternas que puedes descubrir en cada una de ellas. Asimila sus experiencias y utiliza las preguntas de discusión para aprender sobre el liderazgo, sobre ti mismo y tu relación con Dios. La sabiduría que estos héroes comparten te ayudará a superar los retos de hoy.
The Aprentice of the past: The experience that changed a life
by Danilo H. GomesOne single experience rich in meaning was enough for Douglas to have his life transformed forever. So much is said about time travel and fixing past mistakes, but what if we could just interact with other lives instead of our own? Douglas won this strange opportunity and became involved in conversations that he never imagined having. Get to know the experience that this young man had and, who knows, have his life transformed too.
Apres All Day: 65+ Cozy Recipes to Share with Family and Friends
by Kelley EpsteinFor ski bums and non-skiers who enjoy the snow, here is a cozy winter cookbook of 65+ hearty recipes, plus beautiful photography that captures the après-ski culture and mountain town life.Après-ski is more than just an afternoon beer in the lodge. It's an opportunity to gather with friends and family over delicious food and drinks during the cold winter months. This cozy cookbook invites home cooks of all levels to embrace the après culture all season long, whether they're the first skier on the slopes in the morning or a nonskier who prefers to snuggle up by the fireplace. There are recipes for every meal—because yes, you really can "après all day"—including Apple Pie Oatmeal as pre-ski fuel, Tater Tot Nachos, a.k.a. "Tatchos" for an indulgent snack on the couch, Classic Beef Stew with Cheesy Garlic Bread for a family potluck, and a well-deserved Kitchen Sink Skillet Cookie to end the day. There is a section with helpful tips on cooking at altitude, plus fun sidebars featuring must-know ski lingo, ideas for game night, and more. Ski bums, outdoor enthusiasts, and anyone who lives in cold climates will appreciate the hearty recipes and beautiful photography of mountain scenery.FOR ANYONE IN COLD CLIMES: Après-ski isn't just for skiers, and neither is this cookbook—anyone can après, at any time of day! The recipes in this book are perfect for anyone who lives somewhere with cold winters or loves the mountains or the idea of mountain living.GOOD GIFT FOR A RANGE OF FOLKS: With beautiful mountain scenery and photos of charming ski towns, Après All Day encapsulates a way of life. This is a lovely gift for anyone who likes to cook, as well as those who enjoy or aspire to an outdoorsy life in the mountains.COMPELLING PACKAGE: Après All Day is full of evocative photography: a stack of blankets, signage on the slopes, chairlifts in the fog, snow-dusted pine trees, and more. The approachable recipes, informal tone, and aspirational photography will make you feel as if you are enjoying a ski weekend in the mountains with your best friend.Perfect for:• Home cooks who love the mountains and mountain dwellers who like to cook• Skiers and snowboarders of all levels• Anyone who enjoys snow activities and the après-ski culture• Those who live in places with cold winters• Armchair travelers
Après-coup in Psychoanalysis: The Fulfilment of Desire and Thought
by Bernard ChervetThis important book argues that après-coup, a concept that has blossomed in French psychoanalytic discourse, not only allows an understanding of how repressed early memories determine adult life, and how human sexuality develops, but also allows for a richer and wider explanation of our mental structures and thinking. The book outlines how après-coup has been understood and defined by Freud, Lacan and other authors, considers it in diverse psychoanalytic cultures and explores its resonance in dream-work, sexual drives, thought, and the experience of trauma. Bernard Chervet considers that the totality of human thought can be approached according to the theory of après-coup. It offers a metapsychological approach to the operation of après-coup, bodily erogeneity and the regeneration of libido. Chervet’s compelling work argues that the phenomenon of après-coup allowed for the development of the psychoanalytic theories of causality, sexuality, temporality, memory and trauma. Illustrated by clinical vignettes and written by one of the leading theorists on the topic, Après-coup in Psychoanalysis will be an invaluable resource for psychoanalysts in training and in practice.