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The Problem Of Moments
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Book Synopsis The Moment Problem by : Konrad Schmüdgen
Download or read book The Moment Problem written by Konrad Schmüdgen and published by Springer. This book was released on 2017-11-09 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: This advanced textbook provides a comprehensive and unified account of the moment problem. It covers the classical one-dimensional theory and its multidimensional generalization, including modern methods and recent developments. In both the one-dimensional and multidimensional cases, the full and truncated moment problems are carefully treated separately. Fundamental concepts, results and methods are developed in detail and accompanied by numerous examples and exercises. Particular attention is given to powerful modern techniques such as real algebraic geometry and Hilbert space operators. A wide range of important aspects are covered, including the Nevanlinna parametrization for indeterminate moment problems, canonical and principal measures for truncated moment problems, the interplay between Positivstellensätze and moment problems on semi-algebraic sets, the fibre theorem, multidimensional determinacy theory, operator-theoretic approaches, and the existence theory and important special topics of multidimensional truncated moment problems. The Moment Problem will be particularly useful to graduate students and researchers working on moment problems, functional analysis, complex analysis, harmonic analysis, real algebraic geometry, polynomial optimization, or systems theory. With notes providing useful background information and exercises of varying difficulty illustrating the theory, this book will also serve as a reference on the subject and can be used for self-study.
Book Synopsis The Problem of Moments by : James Alexander Shohat
Download or read book The Problem of Moments written by James Alexander Shohat and published by American Mathematical Soc.. This book was released on 1943-12-31 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book was first published in 1943 and then was reprinted several times with corrections. It presents the development of the classical problem of moments for the first 50 years, after its introduction by Stieltjes in the 1890s. In addition to initial developments by Stieltjes, Markov, and Chebyshev, later contributions by Hamburger, Nevanlinna, Hausdorff, Stone, and others are discussed. The book also contains some results on the trigonometric moment problem and a chapter devoted to approximate quadrature formulas.
Book Synopsis Moments, Positive Polynomials and Their Applications by : Jean-Bernard Lasserre
Download or read book Moments, Positive Polynomials and Their Applications written by Jean-Bernard Lasserre and published by World Scientific. This book was released on 2010 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. The generalized moment problem. 1.1. Formulations. 1.2. Duality theory. 1.3. Computational complexity. 1.4. Summary. 1.5. Exercises. 1.6. Notes and sources -- 2. Positive polynomials. 2.1. Sum of squares representations and semi-definite optimization. 2.2. Nonnegative versus s.o.s. polynomials. 2.3. Representation theorems : univariate case. 2.4. Representation theorems : mutivariate case. 2.5. Polynomials positive on a compact basic semi-algebraic set. 2.6. Polynomials nonnegative on real varieties. 2.7. Representations with sparsity properties. 2.8. Representation of convex polynomials. 2.9. Summary. 2.10. Exercises. 2.11. Notes and sources -- 3. Moments. 3.1. The one-dimensional moment problem. 3.2. The multi-dimensional moment problem. 3.3. The K-moment problem. 3.4. Moment conditions for bounded density. 3.5. Summary. 3.6. Exercises. 3.7. Notes and sources -- 4. Algorithms for moment problems. 4.1. The overall approach. 4.2. Semidefinite relaxations. 4.3. Extraction of solutions. 4.4. Linear relaxations. 4.5. Extensions. 4.6. Exploiting sparsity. 4.7. Summary. 4.8. Exercises. 4.9. Notes and sources. 4.10. Proofs -- 5. Global optimization over polynomials. 5.1. The primal and dual perspectives. 5.2. Unconstrained polynomial optimization. 5.3. Constrained polynomial optimization : semidefinite relaxations. 5.4. Linear programming relaxations. 5.5. Global optimality conditions. 5.6. Convex polynomial programs. 5.7. Discrete optimization. 5.8. Global minimization of a rational function. 5.9. Exploiting symmetry. 5.10. Summary. 5.11. Exercises. 5.12. Notes and sources -- 6. Systems of polynomial equations. 6.1. Introduction. 6.2. Finding a real solution to systems of polynomial equations. 6.3. Finding all complex and/or all real solutions : a unified treatment. 6.4. Summary. 6.5. Exercises. 6.6. Notes and sources -- 7. Applications in probability. 7.1. Upper bounds on measures with moment conditions. 7.2. Measuring basic semi-algebraic sets. 7.3. Measures with given marginals. 7.4. Summary. 7.5. Exercises. 7.6. Notes and sources -- 8. Markov chains applications. 8.1. Bounds on invariant measures. 8.2. Evaluation of ergodic criteria. 8.3. Summary. 8.4. Exercises. 8.5. Notes and sources -- 9. Application in mathematical finance. 9.1. Option pricing with moment information. 9.2. Option pricing with a dynamic model. 9.3. Summary. 9.4. Notes and sources -- 10. Application in control. 10.1. Introduction. 10.2. Weak formulation of optimal control problems. 10.3. Semidefinite relaxations for the OCP. 10.4. Summary. 10.5. Notes and sources -- 11. Convex envelope and representation of convex sets. 11.1. The convex envelope of a rational function. 11.2. Semidefinite representation of convex sets. 11.3. Algebraic certificates of convexity. 11.4. Summary. 11.5. Exercises. 11.6. Notes and sources -- 12. Multivariate integration 12.1. Integration of a rational function. 12.2. Integration of exponentials of polynomials. 12.3. Maximum entropy estimation. 12.4. Summary. 12.5. Exercises. 12.6. Notes and sources -- 13. Min-max problems and Nash equilibria. 13.1. Robust polynomial optimization. 13.2. Minimizing the sup of finitely many rational cunctions. 13.3. Application to Nash equilibria. 13.4. Exercises. 13.5. Notes and sources -- 14. Bounds on linear PDE. 14.1. Linear partial differential equations. 14.2. Notes and sources
Book Synopsis Analytic Theory of Continued Fractions by : Hubert Stanley Wall
Download or read book Analytic Theory of Continued Fractions written by Hubert Stanley Wall and published by Courier Dover Publications. This book was released on 2018-05-16 with total page 449 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the most authoritative and comprehensive books on the subject of continued fractions, this monograph has been widely used by generations of mathematicians and their students. Dr. Hubert Stanley Wall presents a unified theory correlating certain parts and applications of the subject within a larger analytic structure. Prerequisites include a first course in function theory and knowledge of the elementary properties of linear transformations in the complex plane. Some background in number theory, real analysis, and complex analysis may also prove helpful. The two-part treatment begins with an exploration of convergence theory, addressing continued fractions as products of linear fractional transformations, convergence theorems, and the theory of positive definite continued fractions, as well as other topics. The second part, focusing on function theory, covers the theory of equations, matrix theory of continued fractions, bounded analytic functions, and many additional subjects.
Download or read book Moments of Impact written by Chris Ertel and published by Simon and Schuster. This book was released on 2014-02-11 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Two leading experts on designing strategic conversations unveil a simple, creative process that allows teams to tackle their most challenging issues. In our fast-changing world, leaders are increasingly confronted by messy, multifaceted challenges that require collaboration to resolve. But the standard methods for tackling these challenges—meetings packed with data-drenched presentations or brainstorming sessions that circle back to nowhere—just don’t deliver. Great strategic conversations generate breakthrough insights by combining the best ideas of people with different backgrounds and perspectives. In this book, two experts “crack the code” on what it takes to design creative, collaborative problem-solving sessions that soar rather than sink. Drawing on decades of experience as innovation strategists—and supported by cutting-edge social science research, dozens of real-life examples, and interviews with well over 100 thought leaders, executives, and fellow practitioners— they unveil a simple, creative process that leaders and their teams can use to unlock solutions to their most vexing issues. The book also includes a “Starter Kit” full of tools and tips for putting the book’s core principles into practice.
Book Synopsis Great Moments in Mathematics Before 1650 by : Howard Eves
Download or read book Great Moments in Mathematics Before 1650 written by Howard Eves and published by American Mathematical Soc.. This book was released on 1983-12-31 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: Great Moments in Mathematics: Before 1650 is the product of a series of lectures on the history of mathematics given by Howard Eves. He presents here, in chronological order, 20 ``great moments in mathematics before 1650'', which can be appreciated by anyone who enjoys mathematics. These wonderful lectures could be used as the basis of a course on the history of mathematics but can also serve as enrichment to any mathematics course. Included are lectures on the Pythagorean Theorem, Euclid's Elements, Archimedes (on the sphere), Diophantus, Omar Khayyam, and Fibonacci.
Book Synopsis Matrices, Moments and Quadrature with Applications by : Gene H. Golub
Download or read book Matrices, Moments and Quadrature with Applications written by Gene H. Golub and published by Princeton University Press. This book was released on 2009-12-07 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This computationally oriented book describes and explains the mathematical relationships among matrices, moments, orthogonal polynomials, quadrature rules, and the Lanczos and conjugate gradient algorithms. The book bridges different mathematical areas to obtain algorithms to estimate bilinear forms involving two vectors and a function of the matrix. The first part of the book provides the necessary mathematical background and explains the theory. The second part describes the applications and gives numerical examples of the algorithms and techniques developed in the first part. Applications addressed in the book include computing elements of functions of matrices; obtaining estimates of the error norm in iterative methods for solving linear systems and computing parameters in least squares and total least squares; and solving ill-posed problems using Tikhonov regularization. This book will interest researchers in numerical linear algebra and matrix computations, as well as scientists and engineers working on problems involving computation of bilinear forms.
Book Synopsis The Power of Moments by : Chip Heath
Download or read book The Power of Moments written by Chip Heath and published by Simon and Schuster. This book was released on 2017-10-03 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: The New York Times bestselling authors of Switch and Made to Stick explore why certain brief experiences can jolt us and elevate us and change us—and how we can learn to create such extraordinary moments in our life and work. While human lives are endlessly variable, our most memorable positive moments are dominated by four elements: elevation, insight, pride, and connection. If we embrace these elements, we can conjure more moments that matter. What if a teacher could design a lesson that he knew his students would remember twenty years later? What if a manager knew how to create an experience that would delight customers? What if you had a better sense of how to create memories that matter for your children? This book delves into some fascinating mysteries of experience: Why we tend to remember the best or worst moment of an experience, as well as the last moment, and forget the rest. Why “we feel most comfortable when things are certain, but we feel most alive when they’re not.” And why our most cherished memories are clustered into a brief period during our youth. Readers discover how brief experiences can change lives, such as the experiment in which two strangers meet in a room, and forty-five minutes later, they leave as best friends. (What happens in that time?) Or the tale of the world’s youngest female billionaire, who credits her resilience to something her father asked the family at the dinner table. (What was that simple question?) Many of the defining moments in our lives are the result of accident or luck—but why would we leave our most meaningful, memorable moments to chance when we can create them? The Power of Moments shows us how to be the author of richer experiences.
Download or read book Moments of Magic written by Shep Hyken and published by Shepard Presentations, LLC. This book was released on 1993 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Method of Moments for 2D Scattering Problems by : Christophe Bourlier
Download or read book Method of Moments for 2D Scattering Problems written by Christophe Bourlier and published by John Wiley & Sons. This book was released on 2013-08-05 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: Electromagnetic wave scattering from randomly rough surfaces in the presence of scatterers is an active, interdisciplinary area of research with myriad practical applications in fields such as optics, acoustics, geoscience and remote sensing. In this book, the Method of Moments (MoM) is applied to compute the field scattered by scatterers such as canonical objects (cylinder or plate) or a randomly rough surface, and also by an object above or below a random rough surface. Since the problem is considered to be 2D, the integral equations (IEs) are scalar and only the TE (transverse electric) and TM (transverse magnetic) polarizations are addressed (no cross-polarizations occur). In Chapter 1, the MoM is applied to convert the IEs into a linear system, while Chapter 2 compares the MoM with the exact solution of the field scattered by a cylinder in free space, and with the Physical Optics (PO) approximation for the scattering from a plate in free space. Chapter 3 presents numerical results, obtained from the MoM, of the coherent and incoherent intensities scattered by a random rough surface and an object below a random rough surface. The final chapter presents the same results as in Chapter 3, but for an object above a random rough surface. In these last two chapters, the coupling between the two scatterers is also studied in detail by inverting the impedance matrix by blocks. Contents 1. Integral Equations for a Single Scatterer: Method of Moments and Rough Surfaces. 2. Validation of the Method of Moments for a Single Scatterer. 3. Scattering from Two Illuminated Scatterers. 4. Scattering from Two Scatterers Where Only One is Illuminated. Appendix. Matlab Codes. About the Authors Christophe Bourlier works at the IETR (Institut d’Electronique et de Télécommunications de Rennes) laboratory at Polytech Nantes (University of Nantes, France) as well as being a Researcher at the French National Center for Scientific Research (CNRS) on electromagnetic wave scattering from rough surfaces and objects for remote sensing applications and radar signatures. He is the author of more than 160 journal articles and conference papers. Nicolas Pinel is currently working as a Research Engineer at the IETR laboratory at Polytech Nantes and is about to join Alyotech Technologies in Rennes, France. His research interests are in the areas of radar and optical remote sensing, scattering and propagation. In particular, he works on asymptotic methods of electromagnetic wave scattering from random rough surfaces and layers. Gildas Kubické is in charge of the “Expertise in electroMagnetism and Computation” (EMC) laboratory at the DGA (Direction Générale de l’Armement), French Ministry of Defense, where he works in the field of radar signatures and electromagnetic stealth. His research interests include electromagnetic scattering and radar cross-section modeling.
Book Synopsis Moments and Moment Invariants in Pattern Recognition by : Jan Flusser
Download or read book Moments and Moment Invariants in Pattern Recognition written by Jan Flusser and published by John Wiley & Sons. This book was released on 2009-11-04 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: Moments as projections of an image’s intensity onto a proper polynomial basis can be applied to many different aspects of image processing. These include invariant pattern recognition, image normalization, image registration, focus/ defocus measurement, and watermarking. This book presents a survey of both recent and traditional image analysis and pattern recognition methods, based on image moments, and offers new concepts of invariants to linear filtering and implicit invariants. In addition to the theory, attention is paid to efficient algorithms for moment computation in a discrete domain, and to computational aspects of orthogonal moments. The authors also illustrate the theory through practical examples, demonstrating moment invariants in real applications across computer vision, remote sensing and medical imaging. Key features: Presents a systematic review of the basic definitions and properties of moments covering geometric moments and complex moments. Considers invariants to traditional transforms – translation, rotation, scaling, and affine transform - from a new point of view, which offers new possibilities of designing optimal sets of invariants. Reviews and extends a recent field of invariants with respect to convolution/blurring. Introduces implicit moment invariants as a tool for recognizing elastically deformed objects. Compares various classes of orthogonal moments (Legendre, Zernike, Fourier-Mellin, Chebyshev, among others) and demonstrates their application to image reconstruction from moments. Offers comprehensive advice on the construction of various invariants illustrated with practical examples. Includes an accompanying website providing efficient numerical algorithms for moment computation and for constructing invariants of various kinds, with about 250 slides suitable for a graduate university course. Moments and Moment Invariants in Pattern Recognition is ideal for researchers and engineers involved in pattern recognition in medical imaging, remote sensing, robotics and computer vision. Post graduate students in image processing and pattern recognition will also find the book of interest.
Book Synopsis The Problem of Moments by : James Alexander Shohat
Download or read book The Problem of Moments written by James Alexander Shohat and published by American Mathematical Society(RI). This book was released on 1950 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents the development of the classical problem of moments for the first 50 years, after its introduction by Stieltjes in the 1890s. This book discusses the initial developments by Stieltjes, Markov, and Chebyshev, and later contributions by Hamburger, Nevanlinna, Hausdorff, and Stone.
Book Synopsis Moments of Being by : Virginia Woolf
Download or read book Moments of Being written by Virginia Woolf and published by Houghton Mifflin Harcourt. This book was released on 1985 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: Published years after her death, Moments of Being is Virginia Woolf's only autobiographical writing, considered by many to be her most important book. A collection of five memoir pieces written for different audiences spanning almost four decades, Moments of Being reveals the remarkable unity of Virginia Woolf's art, thought, and sensibility. "Reminiscences," written during her apprenticeship period, exposes the childhood shared by Woolf and her sister, Vanessa, while "A sketch of the Past" illuminates the relationship with her father, Leslie Stephens, who played a crucial role in her development as an individual a writer. Of the final three pieces, composed for the Memoir Club, which required absolute candor of its members, two show Woolf at the threshold of artistic maturity and one shows a confident writer poking fun at her own foibles.
Book Synopsis The Moment of Clarity by : Christian Madsbjerg
Download or read book The Moment of Clarity written by Christian Madsbjerg and published by Harvard Business Review Press. This book was released on 2014-02-11 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: Businesses need a new type of problem solving. Why? Because they are getting people wrong. Traditional problem-solving methods taught in business schools serve us well for some of the everyday challenges of business, but they tend to be ineffective with problems involving a high degree of uncertainty. Why? Because, more often than not, these tools are based on a flawed model of human behavior. And that flawed model is the invisible scaffolding that supports our surveys, our focus groups, our R&D, and much of our long-term strategic planning. In The Moment of Clarity, Christian Madsbjerg and Mikkel Rasmussen examine the business world’s assumptions about human behavior and show how these assumptions can lead businesses off track. But the authors chart a way forward. Using theories and tools from the human sciences—anthropology, sociology, philosophy, and psychology—The Moment of Clarity introduces a practical framework called sensemaking. Sensemaking’s nonlinear problem-solving approach gives executives a better way to understand business challenges involving shifts in human behavior. This new methodology, a fundamentally different way to think about strategy, is already taking off in Fortune 100 companies around the world. Through compelling case studies and their direct experience with LEGO, Samsung, Adidas, Coloplast, and Intel, Madsbjerg and Rasmussen will show you how to solve problems as diverse as setting company direction, driving growth, improving sales models, understanding the real culture of your organization, and finding your way in new markets. Over and over again, executives say the same thing after engaging in a process of sensemaking: “Now I see it . . .” This experience—the moment of clarity—has the potential to drive the entire strategic future of your company. Isn’t it time you and your firm started getting people right? Learn more about the innovation and strategy work of ReD Associates at: redassociates.com
Download or read book A Moment written by Marie Hall and published by CreateSpace. This book was released on 2013-10-05 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ryan Cosgrove and Liliana Delgado are on a collision course with destiny. They don't know it yet, but before the night is over their lives will be forever changed.
Download or read book The Eureka Factor written by John Kounios and published by Random House. This book was released on 2015-04-14 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: In a book perfect for readers of Charles Duhigg’s The Power of Habit, David Eagleman’s Incognito, and Leonard Mlodinow’s Subliminal, the cognitive neuroscientists who discovered how the brain has aha moments—sudden creative insights—explain how they happen, when we need them, and how we can have more of them to enrich our lives and empower personal and professional success. Eureka or aha moments are sudden realizations that expand our understanding of the world and ourselves, conferring both personal growth and practical advantage. Such creative insights, as psychological scientists call them, were what conveyed an important discovery in the science of genetics to Nobel laureate Barbara McClintock, the melody of a Beatles ballad to Paul McCartney, and an understanding of the cause of human suffering to the Buddha. But these moments of clarity are not given only to the famous. Anyone can have them. In The Eureka Factor, John Kounios and Mark Beeman explain how insights arise and what the scientific research says about stimulating more of them. They discuss how various conditions affect the likelihood of your having an insight, when insight is helpful and when deliberate methodical thought is better suited to a task, what the relationship is between insight and intuition, and how the brain’s right hemisphere contributes to creative thought. Written in a lively, engaging style, this book goes beyond scientific principles to offer productive techniques for realizing your creative potential—at home and at work. The authors provide compelling anecdotes to illustrate how eureka experiences can be a key factor in your life. Attend a dinner party with Christopher Columbus to learn why we need insights. Go to a baseball game with the director of a classic Disney Pixar movie to learn about one important type of aha moment. Observe the behind-the-scenes arrangements for an Elvis Presley concert to learn why the timing of insights is crucial. Accessible and compelling, The Eureka Factor is a fascinating look at the human brain and its seemingly infinite capacity to surprise us. Praise for The Eureka Factor “Delicious . . . In The Eureka Factor, neuroscientists John Kounios and Mark Beeman give many other examples of [a] kind of lightning bolt of insight, but back this up with the latest brain-imaging research.”—Newsweek “An incredible accomplishment . . . [The Eureka Factor] is not just a chronicle of the journey that numerous scientists (including the authors) have taken to examine insight but is also a fascinating guide to how advances in science are made in general. Messrs. Kounios and Beeman examine how a parade of clever experiments can be designed to answer specific questions and rule out alternative possibilities. . . . Wonderful ideas appear as if out of nowhere—and we are delighted.”—The Wall Street Journal “An excellent title for those interested in neuroscience or creativity . . . The writing is engaging and readable, mixing stories of famous perceptions with explanations of how such revelations happen.”—Library Journal (starred review) “A lively and accessible ‘brain’ book with wide appeal.”—Booklist “[An] ingenious, thoughtful update on how the mind works.”—Kirkus Reviews “The Eureka Factor presents a fascinating and illuminating account of the creative process and how to foster it.”—James J. Heckman, Nobel laureate in economics
Book Synopsis Moments of Disruption by : Kris Sealey
Download or read book Moments of Disruption written by Kris Sealey and published by SUNY Press. This book was released on 2013-12-01 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explores the ethical and political implications of Levinass and Sartres accounts of human existence. In Moments of Disruption, Kris Sealey considers Emmanuel Levinas and Jean-Paul Sartre together to fully realize the ethical and political implications of their similar descriptions of human existence. Focusing on points of contact and difference between their writings on transcendence, identity, existence, and alterity, Sealey presents not only an understanding of Sartrean politics in which Levinass somewhat apolitical program might be taken into the political, but also an explicitly political reading of Levinas that resonates well with Sartres work. In bringing together both thinkers accounts of disrupted existence in this way, a theoretical place is found from which to question the claim that politics and ethics are mutually exclusive.
