Convergence Problems

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Convergence Problems of Orthogonal Series

Author : G. Alexits
Publisher : Elsevier
ISBN 13 : 1483222772
Total Pages : 362 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Convergence Problems of Orthogonal Series by : G. Alexits

Download or read book Convergence Problems of Orthogonal Series written by G. Alexits and published by Elsevier. This book was released on 2014-07-23 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Convergence Problems of Orthogonal Series deals with the theory of convergence and summation of the general orthogonal series in relation to the general theory and classical expansions. The book reviews orthogonality, orthogonalization, series of orthogonal functions, complete orthogonal systems, and the Riesz-Fisher theorem. The text examines Jacobi polynomials, Haar's orthogonal system, and relations to the theory of probability using Rademacher's and Walsh's orthogonal systems. The book also investigates the convergence behavior of orthogonal series by methods belonging to the general theory of series. The text explains some Tauberian theorems and the classical Abel transform of the partial sums of a series which the investigator can use in the theory of orthogonal series. The book examines the importance of the Lebesgue functions for convergence problems, the generalization of the Walsh series, the order of magnitude of the Lebesgue functions, and the Lebesgue functions of the Cesaro summation. The text also deals with classical convergence problems in which general orthogonal series have limited significance as orthogonal expansions react upon the structural properties of the expanded function. This reaction happens under special assumptions concerning the orthogonal system in whose functions the expansion proceeds. The book can prove beneficial to mathematicians, students, or professor of calculus and advanced mathematics.

Weak Convergence Methods and Singularly Perturbed Stochastic Control and Filtering Problems

Author : Harold Kushner
Publisher : Springer Science & Business Media
ISBN 13 : 146124482X
Total Pages : 245 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Weak Convergence Methods and Singularly Perturbed Stochastic Control and Filtering Problems by : Harold Kushner

Download or read book Weak Convergence Methods and Singularly Perturbed Stochastic Control and Filtering Problems written by Harold Kushner and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book deals with several closely related topics concerning approxima tions and perturbations of random processes and their applications to some important and fascinating classes of problems in the analysis and design of stochastic control systems and nonlinear filters. The basic mathematical methods which are used and developed are those of the theory of weak con vergence. The techniques are quite powerful for getting weak convergence or functional limit theorems for broad classes of problems and many of the techniques are new. The original need for some of the techniques which are developed here arose in connection with our study of the particular applica tions in this book, and related problems of approximation in control theory, but it will be clear that they have numerous applications elsewhere in weak convergence and process approximation theory. The book is a continuation of the author's long term interest in problems of the approximation of stochastic processes and its applications to problems arising in control and communication theory and related areas. In fact, the techniques used here can be fruitfully applied to many other areas. The basic random processes of interest can be described by solutions to either (multiple time scale) Ito differential equations driven by wide band or state dependent wide band noise or which are singularly perturbed. They might be controlled or not, and their state values might be fully observable or not (e. g. , as in the nonlinear filtering problem).

The Master Equation and the Convergence Problem in Mean Field Games

Author : Pierre Cardaliaguet
Publisher : Princeton University Press
ISBN 13 : 0691190712
Total Pages : 224 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis The Master Equation and the Convergence Problem in Mean Field Games by : Pierre Cardaliaguet

Download or read book The Master Equation and the Convergence Problem in Mean Field Games written by Pierre Cardaliaguet and published by Princeton University Press. This book was released on 2019-08-13 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes the latest advances in the theory of mean field games, which are optimal control problems with a continuum of players, each of them interacting with the whole statistical distribution of a population. While it originated in economics, this theory now has applications in areas as diverse as mathematical finance, crowd phenomena, epidemiology, and cybersecurity. Because mean field games concern the interactions of infinitely many players in an optimal control framework, one expects them to appear as the limit for Nash equilibria of differential games with finitely many players as the number of players tends to infinity. This book rigorously establishes this convergence, which has been an open problem until now. The limit of the system associated with differential games with finitely many players is described by the so-called master equation, a nonlocal transport equation in the space of measures. After defining a suitable notion of differentiability in the space of measures, the authors provide a complete self-contained analysis of the master equation. Their analysis includes the case of common noise problems in which all the players are affected by a common Brownian motion. They then go on to explain how to use the master equation to prove the mean field limit. This groundbreaking book presents two important new results in mean field games that contribute to a unified theoretical framework for this exciting and fast-developing area of mathematics.

Brownian Motion

Author : Peter Mörters
Publisher : Cambridge University Press
ISBN 13 : 1139486578
Total Pages : pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Brownian Motion by : Peter Mörters

Download or read book Brownian Motion written by Peter Mörters and published by Cambridge University Press. This book was released on 2010-03-25 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This eagerly awaited textbook covers everything the graduate student in probability wants to know about Brownian motion, as well as the latest research in the area. Starting with the construction of Brownian motion, the book then proceeds to sample path properties like continuity and nowhere differentiability. Notions of fractal dimension are introduced early and are used throughout the book to describe fine properties of Brownian paths. The relation of Brownian motion and random walk is explored from several viewpoints, including a development of the theory of Brownian local times from random walk embeddings. Stochastic integration is introduced as a tool and an accessible treatment of the potential theory of Brownian motion clears the path for an extensive treatment of intersections of Brownian paths. An investigation of exceptional points on the Brownian path and an appendix on SLE processes, by Oded Schramm and Wendelin Werner, lead directly to recent research themes.

Convergence

Author : National Research Council
Publisher : National Academies Press
ISBN 13 : 0309301645
Total Pages : 234 pages
Book Rating : 4.3/5 (93 download)

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Book Synopsis Convergence by : National Research Council

Download or read book Convergence written by National Research Council and published by National Academies Press. This book was released on 2014-06-16 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: Convergence of the life sciences with fields including physical, chemical, mathematical, computational, engineering, and social sciences is a key strategy to tackle complex challenges and achieve new and innovative solutions. However, institutions face a lack of guidance on how to establish effective programs, what challenges they are likely to encounter, and what strategies other organizations have used to address the issues that arise. This advice is needed to harness the excitement generated by the concept of convergence and channel it into the policies, structures, and networks that will enable it to realize its goals. Convergence investigates examples of organizations that have established mechanisms to support convergent research. This report discusses details of current programs, how organizations have chosen to measure success, and what has worked and not worked in varied settings. The report summarizes the lessons learned and provides organizations with strategies to tackle practical needs and implementation challenges in areas such as infrastructure, student education and training, faculty advancement, and inter-institutional partnerships.

The Convergence Problem for Dissipative Autonomous Systems

Author : Alain Haraux
Publisher : Springer
ISBN 13 : 3319234072
Total Pages : 147 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis The Convergence Problem for Dissipative Autonomous Systems by : Alain Haraux

Download or read book The Convergence Problem for Dissipative Autonomous Systems written by Alain Haraux and published by Springer. This book was released on 2015-09-05 with total page 147 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book investigates classical and more recent methods of study for the asymptotic behavior of dissipative continuous dynamical systems with applications to ordinary and partial differential equations, the main question being convergence (or not) of the solutions to an equilibrium. After reviewing the basic concepts of topological dynamics and the definition of gradient-like systems on a metric space, the authors present a comprehensive exposition of stability theory relying on the so-called linearization method. For the convergence problem itself, when the set of equilibria is infinite, the only general results that do not require very special features of the non-linearities are presently consequences of a gradient inequality discovered by S. Lojasiewicz. The application of this inequality jointly with the so-called Liapunov-Schmidt reduction requires a rigorous exposition of Semi-Fredholm operator theory and the theory of real analytic maps on infinite dimensional Banach spaces, which cannot be found anywhere in a readily applicable form. The applications covered in this short text are the simplest, but more complicated cases are mentioned in the final chapter, together with references to the corresponding specialized papers.

Real Infinite Series

Author : Daniel D. Bonar
Publisher : American Mathematical Soc.
ISBN 13 : 1470447827
Total Pages : 278 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Real Infinite Series by : Daniel D. Bonar

Download or read book Real Infinite Series written by Daniel D. Bonar and published by American Mathematical Soc.. This book was released on 2018-12-12 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a widely accessible introductory treatment of infinite series of real numbers, bringing the reader from basic definitions and tests to advanced results. An up-to-date presentation is given, making infinite series accessible, interesting, and useful to a wide audience, including students, teachers, and researchers. Included are elementary and advanced tests for convergence or divergence, the harmonic series, the alternating harmonic series, and closely related results. One chapter offers 107 concise, crisp, surprising results about infinite series. Another gives problems on infinite series, and solutions, which have appeared on the annual William Lowell Putnam Mathematical Competition. The lighter side of infinite series is treated in the concluding chapter where three puzzles, eighteen visuals, and several fallacious proofs are made available. Three appendices provide a listing of true or false statements, answers to why the harmonic series is so named, and an extensive list of published works on infinite series.

Applied Problems of Radon Transform

Author : Semen Grigorʹevich Gindikin
Publisher : American Mathematical Soc.
ISBN 13 : 9780821875087
Total Pages : 276 pages
Book Rating : 4.8/5 (75 download)

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Book Synopsis Applied Problems of Radon Transform by : Semen Grigorʹevich Gindikin

Download or read book Applied Problems of Radon Transform written by Semen Grigorʹevich Gindikin and published by American Mathematical Soc.. This book was released on 1994 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection is designed to acquaint readers with advances in Radon transforms carried out in the former Soviet Union. The papers focus on mathematical problems related to applications of Radon transforms. Some of the problems arose from practical tomography, while others are theoretical problems originating in tomography. The book should be of use to mathematicians working in integral geometry and mathematical problems of tomography, as well as scientists who work on inverse problems and their computer realization.

Unsolved Problems in Mathematical Systems and Control Theory

Author : Vincent D. Blondel
Publisher : Princeton University Press
ISBN 13 : 1400826152
Total Pages : 351 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Unsolved Problems in Mathematical Systems and Control Theory by : Vincent D. Blondel

Download or read book Unsolved Problems in Mathematical Systems and Control Theory written by Vincent D. Blondel and published by Princeton University Press. This book was released on 2009-04-11 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides clear presentations of more than sixty important unsolved problems in mathematical systems and control theory. Each of the problems included here is proposed by a leading expert and set forth in an accessible manner. Covering a wide range of areas, the book will be an ideal reference for anyone interested in the latest developments in the field, including specialists in applied mathematics, engineering, and computer science. The book consists of ten parts representing various problem areas, and each chapter sets forth a different problem presented by a researcher in the particular area and in the same way: description of the problem, motivation and history, available results, and bibliography. It aims not only to encourage work on the included problems but also to suggest new ones and generate fresh research. The reader will be able to submit solutions for possible inclusion on an online version of the book to be updated quarterly on the Princeton University Press website, and thus also be able to access solutions, updated information, and partial solutions as they are developed.

Numerical Issues in Statistical Computing for the Social Scientist

Author : Micah Altman
Publisher : John Wiley & Sons
ISBN 13 : 0471475742
Total Pages : 349 pages
Book Rating : 4.4/5 (714 download)

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Book Synopsis Numerical Issues in Statistical Computing for the Social Scientist by : Micah Altman

Download or read book Numerical Issues in Statistical Computing for the Social Scientist written by Micah Altman and published by John Wiley & Sons. This book was released on 2004-02-15 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: At last—a social scientist's guide through the pitfalls of modern statistical computing Addressing the current deficiency in the literature on statistical methods as they apply to the social and behavioral sciences, Numerical Issues in Statistical Computing for the Social Scientist seeks to provide readers with a unique practical guidebook to the numerical methods underlying computerized statistical calculations specific to these fields. The authors demonstrate that knowledge of these numerical methods and how they are used in statistical packages is essential for making accurate inferences. With the aid of key contributors from both the social and behavioral sciences, the authors have assembled a rich set of interrelated chapters designed to guide empirical social scientists through the potential minefield of modern statistical computing. Uniquely accessible and abounding in modern-day tools, tricks, and advice, the text successfully bridges the gap between the current level of social science methodology and the more sophisticated technical coverage usually associated with the statistical field. Highlights include: A focus on problems occurring in maximum likelihood estimation Integrated examples of statistical computing (using software packages such as the SAS, Gauss, Splus, R, Stata, LIMDEP, SPSS, WinBUGS, and MATLAB®) A guide to choosing accurate statistical packages Discussions of a multitude of computationally intensive statistical approaches such as ecological inference, Markov chain Monte Carlo, and spatial regression analysis Emphasis on specific numerical problems, statistical procedures, and their applications in the field Replications and re-analysis of published social science research, using innovative numerical methods Key numerical estimation issues along with the means of avoiding common pitfalls A related Web site includes test data for use in demonstrating numerical problems, code for applying the original methods described in the book, and an online bibliography of Web resources for the statistical computation Designed as an independent research tool, a professional reference, or a classroom supplement, the book presents a well-thought-out treatment of a complex and multifaceted field.

Problem Solving

Author : S. Ian Robertson
Publisher : Psychology Press
ISBN 13 : 1317496019
Total Pages : 287 pages
Book Rating : 4.3/5 (174 download)

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Book Synopsis Problem Solving by : S. Ian Robertson

Download or read book Problem Solving written by S. Ian Robertson and published by Psychology Press. This book was released on 2016-11-10 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: The way that we assess and overcome problems is an essential part of everyday life. Problem Solving provides a clear introduction to the underlying mental processes involved in solving problems. Drawing on research from cognitive psychology and neuroscience, it examines the methods and techniques used by both novices and experts in familiar and unfamiliar situations. This edition has been comprehensively updated throughout, and now features cutting-edge content on creative problem solving, insight and neuroscience. Each chapter is written in an accessible way, and contains a range of student-friendly features such as activities, chapter summaries and further reading. The book also provides clear examples of studies and approaches that help the reader fully understand important and complex concepts in greater detail. Problem Solving fully engages the reader with the difficulties and methodologies associated with problem solving. This book will be of great use to undergraduate students of cognitive psychology, education and neuroscience, as well as readers and professionals with an interest in problem solving.

A Cp-Theory Problem Book

Author : Vladimir V. Tkachuk
Publisher : Springer Science & Business Media
ISBN 13 : 1441974423
Total Pages : 497 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis A Cp-Theory Problem Book by : Vladimir V. Tkachuk

Download or read book A Cp-Theory Problem Book written by Vladimir V. Tkachuk and published by Springer Science & Business Media. This book was released on 2011-03-23 with total page 497 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of function spaces endowed with the topology of point wise convergence, or Cp-theory, exists at the intersection of three important areas of mathematics: topological algebra, functional analysis, and general topology. Cp-theory has an important role in the classification and unification of heterogeneous results from each of these areas of research. Through over 500 carefully selected problems and exercises, this volume provides a self-contained introduction to Cp-theory and general topology. By systematically introducing each of the major topics in Cp-theory, this volume is designed to bring a dedicated reader from basic topological principles to the frontiers of modern research. Key features include: - A unique problem-based introduction to the theory of function spaces. - Detailed solutions to each of the presented problems and exercises. - A comprehensive bibliography reflecting the state-of-the-art in modern Cp-theory. - Numerous open problems and directions for further research. This volume can be used as a textbook for courses in both Cp-theory and general topology as well as a reference guide for specialists studying Cp-theory and related topics. This book also provides numerous topics for PhD specialization as well as a large variety of material suitable for graduate research.

Slope Stability Analysis and Stabilization

Author : Y. M. Cheng
Publisher : CRC Press
ISBN 13 : 0203927958
Total Pages : 260 pages
Book Rating : 4.2/5 (39 download)

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Book Synopsis Slope Stability Analysis and Stabilization by : Y. M. Cheng

Download or read book Slope Stability Analysis and Stabilization written by Y. M. Cheng and published by CRC Press. This book was released on 2008-06-03 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: A number of methods currently exist for the analysis and design of slopes. This book provides a critical review of these and offers several more appropriate approaches for overcoming numerical convergence and the location of critical failure surfaces in two-dimensional and three-dimensional cases. New concepts in three-dimensional stability analysis, finite element analysis and the extension of slope stability problems to lateral earth pressure problems are also addressed. It gives helpful practical advice and design resources in the form of recommendations for good analysis and design practice, design charts and tables for the engineer. Limitations are detailed of both limit equilibrium and the finite element method in the assessment of the stability of a slope, and guidance is provided for assessing the fundamental assumptions and limitations of stability analysis methods and computer modelling. The book provides ample examples to illustrate how this range of problems should be dealt with. The final chapter touches on design and its implementation on site. The emphasis is on the transfer of the design to its physical implementation on site in a holistic way, taking full account of the latest developments in construction technology. Engineering and construction problems tend to be pigeonholed into different classes of problem such as slope stability, bearing capacity and earth pressure behind retaining structures. This is quite unnecessary. This book offers a unified approach, which is conceptually, practically and philosophically more satisfying.

Knowledge Acquisition from Text and Pictures

Author : H. Mandl
Publisher : Elsevier
ISBN 13 : 008086712X
Total Pages : 347 pages
Book Rating : 4.0/5 (88 download)

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Book Synopsis Knowledge Acquisition from Text and Pictures by : H. Mandl

Download or read book Knowledge Acquisition from Text and Pictures written by H. Mandl and published by Elsevier. This book was released on 1989-04-01 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: Media-didactics have recently become more firmly grounded on cognitive theory, with an increasing concern for the internal processes of knowledge representation and acquisition. With this cognitive aspect in mind, an international group of researchers held a meeting in Tübingen, Federal Republic of Germany, to present and discuss the theoretical approaches to and empirical investigations of knowledge acquisition from text and pictures. This volume contains the revised contributions resulting from that meeting.

50 Years of CFD in Engineering Sciences

Author : Akshai Runchal
Publisher : Springer Nature
ISBN 13 : 9811526702
Total Pages : 950 pages
Book Rating : 4.8/5 (115 download)

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Book Synopsis 50 Years of CFD in Engineering Sciences by : Akshai Runchal

Download or read book 50 Years of CFD in Engineering Sciences written by Akshai Runchal and published by Springer Nature. This book was released on 2020-03-09 with total page 950 pages. Available in PDF, EPUB and Kindle. Book excerpt: Prof. D. Brian Spalding, working with a small group of students and colleagues at Imperial College, London in the mid-to late-1960’s, single-handedly pioneered the use of Computational Fluid Dynamics (CFD) for engineering practice.This book brings together advances in computational fluid dynamics in a collection of chapters authored by leading researchers, many of them students or associates of Prof. Spalding. The book intends to capture the key developments in specific fields of activity that have been transformed by application of CFD in the last 50 years. The focus is on review of the impact of CFD on these selected fields and of the novel applications that CFD has made possible. Some of the chapters trace the history of developments in a specific field and the role played by Spalding and his contributions. The volume also includes a biographical summary of Brian Spalding as a person and as a scientist, as well as tributes to Brian Spalding by those whose life was impacted by his innovations. This volume would be of special interest to researchers, practicing engineers, and graduate students in various fields, including aerospace, energy, power and propulsion, transportation, combustion, management of the environment, health and pharmaceutical sciences.

Curbside Consultation in Pediatric Ophthalmology

Author : Rudolph Wagner
Publisher : CRC Press
ISBN 13 : 1040137075
Total Pages : 320 pages
Book Rating : 4.0/5 (41 download)

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Book Synopsis Curbside Consultation in Pediatric Ophthalmology by : Rudolph Wagner

Download or read book Curbside Consultation in Pediatric Ophthalmology written by Rudolph Wagner and published by CRC Press. This book was released on 2024-06-01 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Are you looking for concise, practical answers to those questions that are often left unanswered by traditional pediatric ophthalmology references? Are you seeking brief, evidence-based advice for complicated cases or controversial decisions? Curbside Consultation in Pediatric Ophthalmology: 49 Clinical Questions provides quick answers to the tricky questions most commonly posed during a “curbside consultation” between pediatricians. Dr. Rudolph Wagner has designed this unique reference which offers expert advice, preferences, and opinions on tough clinical questions commonly associated with pediatric ophthalmology. The unique Q&A format provides quick access to current information related to pediatric ophthalmology with the simplicity of a conversation between two colleagues. Numerous images, diagrams, and references allow readers to browse large amounts of information in an expedited fashion. Some of the questions that are answered: • How do I make the diagnosis of amblyopia? • How can I differentiate a true strabismus from a pseudo-strabismus? • How do I diagnose and treat corneal abrasions? Does patching remain an important component of therapy? • What is naso-lacrimal duct obstruction? How is it managed? When should I refer these children? • How can I determine if a “red eye” is caused by a bacterial infection, viral infection or an allergic reaction? How are they managed? Curbside Consultation in Pediatric Ophthalmology: 49 Clinical Questions provides information basic enough for residents while also incorporating expert advice that even high-volume pediatricians will appreciate. Pediatricians, nurse practitioners, emergency room physicians, physician assistants and family practitioners will benefit from the user-friendly, casual format and the expert advice contained within.

Bayesian Statistics 6

Author : J. M. Bernardo
Publisher : Oxford University Press
ISBN 13 : 9780198504856
Total Pages : 886 pages
Book Rating : 4.5/5 (48 download)

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Book Synopsis Bayesian Statistics 6 by : J. M. Bernardo

Download or read book Bayesian Statistics 6 written by J. M. Bernardo and published by Oxford University Press. This book was released on 1999-08-12 with total page 886 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bayesian statistics is a dynamic and fast-growing area of statistical research and the Valencia International Meetings provide the main forum for discussion. These resulting proceedings form an up-to-date collection of research.