An Introduction To Frames
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| Author | : Ole Christensen |
| Publisher | : Birkhäuser |
| Total Pages | : 719 |
| Release | : 2016-05-24 |
| Genre | : Mathematics |
| ISBN | : 3319256130 |
This revised and expanded monograph presents the general theory for frames and Riesz bases in Hilbert spaces as well as its concrete realizations within Gabor analysis, wavelet analysis, and generalized shift-invariant systems. Compared with the first edition, more emphasis is put on explicit constructions with attractive properties. Based on the exiting development of frame theory over the last decade, this second edition now includes new sections on the rapidly growing fields of LCA groups, generalized shift-invariant systems, duality theory for as well Gabor frames as wavelet frames, and open problems in the field. Key features include: *Elementary introduction to frame theory in finite-dimensional spaces * Basic results presented in an accessible way for both pure and applied mathematicians * Extensive exercises make the work suitable as a textbook for use in graduate courses * Full proofs includ ed in introductory chapters; only basic knowledge of functional analysis required * Explicit constructions of frames and dual pairs of frames, with applications and connections to time-frequency analysis, wavelets, and generalized shift-invariant systems * Discussion of frames on LCA groups and the concrete realizations in terms of Gabor systems on the elementary groups; connections to sampling theory * Selected research topics presented with recommendations for more advanced topics and further readin g * Open problems to stimulate further research An Introduction to Frames and Riesz Bases will be of interest to graduate students and researchers working in pure and applied mathematics, mathematical physics, and engineering. Professionals working in digital signal processing who wish to understand the theory behind many modern signal processing tools may also find this book a useful self-study reference. Review of the first edition: "Ole Christensen’s An Introduction to Frames and Riesz Bases is a first-rate introduction to the field ... . The book provides an excellent exposition of these topics. The material is broad enough to pique the interest of many readers, the included exercises supply some interesting challenges, and the coverage provides enough background for those new to the subject to begin conducting original research." — Eric S. Weber, American Mathematical Monthly, Vol. 112, February, 2005
| Author | : Jelena Kovacevic |
| Publisher | : Now Publishers Inc |
| Total Pages | : 110 |
| Release | : 2008 |
| Genre | : Computers |
| ISBN | : 160198068X |
An Introduction to Frames is an introduction to redundant signal representations called frames. These representations have recently emerged as yet another powerful tool in the signal processing toolbox, spurred by a host of recent applications requiring some level of redundancy. It asks the question: Why and where should one use frames? And answers emphatically: Anywhere where redundancy is a must. It then goes on to discuss a host of applications that richly illustrate that answer. An Introduction to Frames is geared primarily toward engineering students and those without extensive mathematical training. It is also intended to help researchers and practitioners decide whether frames are the right tool for their application.
| Author | : Giandomenico Toniolo |
| Publisher | : Springer |
| Total Pages | : 386 |
| Release | : 2019-05-27 |
| Genre | : Technology & Engineering |
| ISBN | : 3030146642 |
This textbook presents the principal methods of stress analysis for the design of frame structures, beginning with a description of the basic criteria for probabilistic safety verification used in modern codes. The Force Method and the Displacement Method are dealt with, together with their applications to more common structural situations. A special chapter is dedicated to the second order analysis required for slender structures and for the elaboration of instability problems. In turn, a thorough set of numerical examples rounds out the text. Given its scope, the book offers an ideal learning resource for students of Civil and Building Engineering and Architecture, and a valuable reference guide for practicing structural design professionals.
| Author | : Deguang Han |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 314 |
| Release | : 2007 |
| Genre | : Mathematics |
| ISBN | : 0821842129 |
"The early chapters contain the topics from linear algebra that students need to know in order to read the rest of the book. The later chapters are devoted to advanced topics, which allow students with more experience to study more intricate types of frames. Toward that end, a Student Presentation section gives detailed proofs of fairly technical results with the intention that a student could work out these proofs independently and prepare a presentation to a class or research group. The authors have also presented some stories in the Anecdotes section about how this material has motivated and influenced their students."--BOOK JACKET.
| Author | : Peter G. Casazza |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 492 |
| Release | : 2012-09-14 |
| Genre | : Mathematics |
| ISBN | : 0817683739 |
Hilbert space frames have long served as a valuable tool for signal and image processing due to their resilience to additive noise, quantization, and erasures, as well as their ability to capture valuable signal characteristics. More recently, finite frame theory has grown into an important research topic in its own right, with a myriad of applications to pure and applied mathematics, engineering, computer science, and other areas. The number of research publications, conferences, and workshops on this topic has increased dramatically over the past few years, but no survey paper or monograph has yet appeared on the subject. Edited by two of the leading experts in the field, Finite Frames aims to fill this void in the literature by providing a comprehensive, systematic study of finite frame theory and applications. With carefully selected contributions written by highly experienced researchers, it covers topics including: * Finite Frame Constructions; * Optimal Erasure Resilient Frames; * Quantization of Finite Frames; * Finite Frames and Compressed Sensing; * Group and Gabor Frames; * Fusion Frames. Despite the variety of its chapters' source and content, the book's notation and terminology are unified throughout and provide a definitive picture of the current state of frame theory. With a broad range of applications and a clear, full presentation, this book is a highly valuable resource for graduate students and researchers across disciplines such as applied harmonic analysis, electrical engineering, quantum computing, medicine, and more. It is designed to be used as a supplemental textbook, self-study guide, or reference book.
| Author | : Thomas Gamerschlag |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 360 |
| Release | : 2013-11-26 |
| Genre | : Language Arts & Disciplines |
| ISBN | : 3319015419 |
This volume showcases the potential richness of frame representations. The presentation includes introductory articles on the application of frames to linguistics and philosophy of science, offering readers the tools to conduct the interdisciplinary investigation of concepts that frames allow. * Introductory articles on the application of frames to linguistics and philosophy of science * Frame analysis of changes in scientific concepts * Event frames and lexical decomposition * Properties, frame attributes and adjectives * Frames in concept composition * Nominal concept types and determination "This volume deals with frame representations and their relations to concept types in linguistics and philosophy of science. It aims at reviving concepts and frames as a common model across disciplines for representing semantic and conceptual knowledge. Departing from the general assumption that frames are not just an arbitrary format of representation but essential to human cognition, a number of case studies apply frames as an analytical tool to a wide range of phenomena, from changes in scientific concepts to particular linguistic phenomena. This provides new insights into long-standing semantic issues, such as the lexical representation of verbs (as predicative frames specifying particular event descriptions or situation types and their participants), adjectives and nominals (as concept frames, which provide attributes and properties of an entity), as well as modification, complementation, possessive constructions, compounding, nominal concept types, determination, or definiteness marking." Bert Gehrke, Pompeu, Fabra University, Barcelona, Spain
| Author | : Jeanne N. Clelland |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 433 |
| Release | : 2017-03-29 |
| Genre | : Mathematics |
| ISBN | : 1470429527 |
The method of moving frames originated in the early nineteenth century with the notion of the Frenet frame along a curve in Euclidean space. Later, Darboux expanded this idea to the study of surfaces. The method was brought to its full power in the early twentieth century by Elie Cartan, and its development continues today with the work of Fels, Olver, and others. This book is an introduction to the method of moving frames as developed by Cartan, at a level suitable for beginning graduate students familiar with the geometry of curves and surfaces in Euclidean space. The main focus is on the use of this method to compute local geometric invariants for curves and surfaces in various 3-dimensional homogeneous spaces, including Euclidean, Minkowski, equi-affine, and projective spaces. Later chapters include applications to several classical problems in differential geometry, as well as an introduction to the nonhomogeneous case via moving frames on Riemannian manifolds. The book is written in a reader-friendly style, building on already familiar concepts from curves and surfaces in Euclidean space. A special feature of this book is the inclusion of detailed guidance regarding the use of the computer algebra system Maple™ to perform many of the computations involved in the exercises.
| Author | : Niklas Torneke |
| Publisher | : New Harbinger Publications |
| Total Pages | : 290 |
| Release | : 2010-11-01 |
| Genre | : Psychology |
| ISBN | : 1572249080 |
Relational frame theory, or RFT, is the little-understood behavioral theory behind a recent development in modern psychology: the shift from the cognitive paradigm underpinning cognitive behavioral therapy to a new understanding of language and cognition. Learning RFT presents a basic yet comprehensive introduction to this fascinating theory, which forms the basis of acceptance and commitment therapy. The book also offers practical guidance for directly applying it in clinical work. In the book, author Niklas Törneke presents the building blocks of RFT: language as a particular kind of relating, derived stimulus relations, and transformation of stimulus functions. He then shows how these concepts are essential to understanding acceptance and commitment therapy and other therapeutic models. Learning RFT shows how to use experiential exercises and metaphors in psychological treatment and explains how they can help your clients. This book belongs on the bookshelves of psychologists, psychotherapists, students, and others seeking to deepen their understanding of psychological treatment from a behavioral perspective.
| Author | : John Pollock |
| Publisher | : McGraw-Hill/Osborne Media |
| Total Pages | : 580 |
| Release | : 2004 |
| Genre | : Computers |
| ISBN | : 9780072227901 |
A hands-on, step-by-step tutorial, this comprehensive resource teaches new programmers and those new to JavaScript.
| Author | : Johannes C.P. Schmid |
| Publisher | : Springer Nature |
| Total Pages | : 292 |
| Release | : 2021-05-12 |
| Genre | : Comics & Graphic Novels |
| ISBN | : 3030633039 |
Frames and Framing in Documentary Comics explores how graphic narratives reframe global crises while also interrogating practices of fact-finding. An analog print phenomenon in an era shaped by digitalization, documentary comics formulates a distinct counterapproach to conventional journalism. In what ways are ‘facts’ being presented and framed? What is documentary honesty in a world of fake news and post-truth politics? How can the stories of marginalized peoples and neglected crises be told? The author investigates documentary comics in its unique relationship to framing: graphic narratives are essentially shaped by a reciprocal relationship between the manifest frames on the page and the attention to the cognitive frames that they generate. To account for both the textuality of comics and its strategic use as rhetoric, the author combines theories of framing analysis and cognitive narratology with comics studies and its attention toward the medium’s visual frames.
