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Ulam’s Conjecture on Invariance of Measure in the Hilbert Cube (Frontiers in Mathematics)
by Soon-Mo JungThis book discusses the process by which Ulam's conjecture is proved, aptly detailing how mathematical problems may be solved by systematically combining interdisciplinary theories. It presents the state-of-the-art of various research topics and methodologies in mathematics, and mathematical analysis by presenting the latest research in emerging research areas, providing motivation for further studies. The book also explores the theory of extending the domain of local isometries by introducing a generalized span.For the reader, working knowledge of topology, linear algebra, and Hilbert space theory, is essential. The basic theories of these fields are gently and logically introduced. The content of each chapter provides the necessary building blocks to understanding the proof of Ulam’s conjecture and are summarized as follows: Chapter 1 presents the basic concepts and theorems of general topology. In Chapter 2, essential concepts and theorems in vector space, normed space, Banach space, inner product space, and Hilbert space, are introduced. Chapter 3 gives a presentation on the basics of measure theory. In Chapter 4, the properties of first- and second-order generalized spans are defined, examined, and applied to the study of the extension of isometries. Chapter 5 includes a summary of published literature on Ulam’s conjecture; the conjecture is fully proved in Chapter 6.
Ultimate Explanations of the Universe
by Michael HellerWe humans are collectively driven by a powerful - yet not fully explained - instinct to understand. We would like to see everything established, proven, laid bare. The more important an issue, the more we desire to see it clarified, stripped of all secrets, all shades of gray. What could be more important than to understand the Universe and ourselves as a part of it? To find a window onto our origin and our destiny? This book examines how far our modern cosmological theories - with their sometimes audacious models, such as inflation, cyclic histories, quantum creation, parallel universes - can take us towards answering these questions. Can such theories lead us to ultimate truths, leaving nothing unexplained? Last, but not least, Heller addresses the thorny problem of why and whether we should expect to find theories with all-encompassing explicative power.
Ultrametric Pseudodifferential Equations and Applications (Encyclopedia of Mathematics and Its Applications #168)
by W. A. Zúñiga-Galindo Andrei Yu. Khrennikov Sergei V. KozyrevStarting from physical motivations and leading to practical applications, this book provides an interdisciplinary perspective on the cutting edge of ultrametric pseudodifferential equations. It shows the ways in which these equations link different fields including mathematics, engineering, and geophysics. <P><P>In particular, the authors provide a detailed explanation of the geophysical applications of p-adic diffusion equations, useful when modeling the flows of liquids through porous rock. p-adic wavelets theory and p-adic pseudodifferential equations are also presented, along with their connections to mathematical physics, representation theory, the physics of disordered systems, probability, number theory, and p-adic dynamical systems. Material that was previously spread across many articles in journals of many different fields is brought together here, including recent work on the van der Put series technique. <P>This book provides an excellent snapshot of the fascinating field of ultrametric pseudodifferential equations, including their emerging applications and currently unsolved problems.<P> Covers not only the mathematical underpinnings, but also the practical applications of ultrametric pseudodifferential equations.<P> Discusses many fascinating interdisciplinary connections.<P> Contains a chapter devoted to the application of p-adic diffusion equations to model flows of fluids (e.g. oil and water) in capillary networks in porous disordered media, particularly useful for geophysicists.<P>
Ultrasonics: Fundamentals, Technologies, and Applications, Third Edition
by Dale Ensminger Leonard J. BondThe book provides a unique and comprehensive treatment of the science, technology, and applications for industrial and medical ultrasonics, including low- and high-power implementations. The discussion of applications is combined with the fundamental physics, the reporting of the sensors/transducers, and systems for the full spectrum of industrial, nondestructive testing, and medical/bio-medical uses. It includes citations of numerous references and covers both mainstream and the more unusual and obscure applications of ultrasound.
Um dia de diversão para o pequeno Tomás
by Linda HendersonUm dia de diversão para o pequeno Tomás por Linda Henderson Além de treinar matemática, Tomás aprende como tratar as pessoas de maneira igual no parque de exposições. Um parque de exposições pode trazer experiências muito interessantes aos jovens assim como aos jovens de coração. Tomás adorou tudo, especialmente os brinquedos e os animais, além disso, gostou muito de fazer contas de cabeça. Isso tudo o fez descobrir que havia muitas coisas a aprender na exposição. Enquanto ouvia seu tio Aldo somava o preço dos ingressos, compartilhou uma lição de vida na qual Tomás aprendeu como é importante tratar as pessoas de maneira justa e igual. Nós todos também podemos aprender com o que o tio Aldo disse ao Tomás. Neste livro de leitura fácil para idades de 6 a 8 anos, as crianças podem se divertir com Tomás e sua família enquanto caminham pelos jardins do parque de exposições, podem fazer contas de cabeça e praticar matemática. E no final do livro, as crianças são apresentadas ao mais justo de todos os tempos! Gênero: JUVENIL / Matemática / Geral Gênero Secundário: JUVENIL NÃO FICÇÃO / Religioso / Cristão / Família e Relacionamentos Língua: Português BR Palavras-chave: Parque de Exposições, diversão, matemática, igualdade, soma, adição, família Contagem de palavra: 1115 Links para livros: Amazon
The Umbral Calculus
by Steven RomanGeared toward upper-level undergraduates and graduate students, this elementary introduction to classical umbral calculus requires only an acquaintance with the basic notions of algebra and a bit of applied mathematics (such as differential equations) to help put the theory in mathematical perspective. Subjects include Sheffer sequences and operators and their adjoints, with numerous examples of associated and other sequences. Related topics encompass the connection constants problem and duplication formulas, the Lagrange inversion formula, operational formulas, inverse relations, and binomial convolution. The final chapter offers a glimpse of the newer and less well-established forms of umbral calculus. 1984 edition.
The Umbral Calculus (Dover Books on Mathematics #Volume 111)
by Steven RomanGeared toward upper-level undergraduates and graduate students, this elementary introduction to classical umbral calculus requires only an acquaintance with the basic notions of algebra and a bit of applied mathematics (such as differential equations) to help put the theory in mathematical perspective.The text focuses on classical umbral calculus, which dates back to the 1850s and continues to receive the attention of modern mathematicians. Subjects include Sheffer sequences and operators and their adjoints, with numerous examples of associated and other sequences. Related topics encompass the connection constants problem and duplication formulas, the Lagrange inversion formula, operational formulas, inverse relations, and binomial convolution. The final chapter offers a glimpse of the newer and less well-established forms of umbral calculus.
Umphred's Neurological Rehabilitation
by Rolando T. LazaroDevelop problem-solving strategies for individualized, effective neurologic care! Under the new leadership of Rolando Lazaro, Umphred’s Neurological Rehabilitation, 7th Edition, covers the therapeutic management of people with activity limitations, participation restrictions, and quality of life issues following a neurological event. This comprehensive reference reviews basic theory and addresses the best evidence for evaluation tools and interventions commonly used in today's clinical practice. It applies a time-tested, evidence-based approach to neurological rehabilitation that is perfect for both the classroom and the clinic. Now fully searchable with additional case studies through Student Consult, this edition includes updated chapters and the latest advances in neuroscience.
Unbestimmt und relativ?: Das Weltbild der modernen Physik
by Helmut Fink Meinard KuhlmannQuantentheorie und Relativitätstheorie haben das Weltbild der Physik revolutioniert. Beide Theorien gelten jedoch als unanschaulich und schwer verständlich. Dieses Sachbuch schafft neue Zugänge und lädt zum Mitdenken ein. Renommierte Experten aus Physik und Philosophie erläutern Grundbegriffe, Erkenntnisfortschritte und Deutungsfragen zu Raum, Zeit und Materie.Dabei kommen typische Themen aus der Philosophie der Physik zur Sprache, wie etwa die Interpretationsdebatte der Quantentheorie oder Modellbildungen in der Kosmologie. Weltbildrelevante Fragen nach dem Verhältnis von Mathematik, Empirie und Anschauung oder nach der Verlässlichkeit physikalischer Erkenntnis erfordern die Verbindung von Physik und Philosophie, von fachwissenschaftlicher Grundlagenforschung und methodenkritischer Reflexion. Der thematische Bogen geht zurück auf ein hochkarätig besetztes Symposium mit populärwissenschaftlicher Ausrichtung. Das Buch enthält Beiträge von Andreas Bartels, Robert Harlander, Paul Hoyningen-Huene, Gert-Ludwig Ingold, Claus Kiefer, Meinard Kuhlmann, Klaus Mainzer, Oliver Passon, Manfred Stöckler, Rüdiger Vaas und Reinhard Werner.
Unbiased Stereology: A Concise Guide
by Peter R. MoutonThis update to Peter R. Mouton’s pioneering work provides bioscientists with the concepts needed in order to apply the principles and practices of unbiased stereology to research involving biological tissues.Mouton starts with a brief explanation of the history and theory of the process before defining the terms, concepts, and tools of unbiased stereological procedures. He compares and contrasts the procedures with less-exacting approaches to quantitative analysis of biological structure using specific examples from biomedical literature. The book incorporates existing best practices with new methodologies, such as the Rare Event Protocol, while simplifying the dense, often difficult literature on the subject to show the utility and importance of unbiased stereology. This clear, insightful guide goes a step further than other books on this subject by demonstrating not only how to use unbiased stereology but also how to interpret and present the results.Written by the official U.S. representative to the International Society for Stereology, this is the most complete, up-to-date resource on the science of unbiased stereology. Those new to bioscience research as well as experienced practitioners will find that Mouton’s explanations are the perfect companion for stereology courses and workshops.
Unbound: How Eight Technologies Made Us Human and Brought Our World to the Brink
by Richard L. CurrierAlthough we usually think of technology as something unique to modern times, our ancestors began to create the first technologies millions of years ago in the form of prehistoric tools and weapons. Over time, eight key technologies gradually freed us from the limitations of our animal origins. The fabrication of weapons, the mastery of fire, and the technologies of clothing and shelter radically restructured the human body, enabling us to walk upright, shed our body hair, and migrate out of tropical Africa. Symbolic communication transformed human evolution from a slow biological process into a fast cultural process. The invention of agriculture revolutionized the relationship between humanity and the environment, and the technologies of interaction led to the birth of civilization. Precision machinery spawned the industrial revolution and the rise of nation-states; and in the next metamorphosis, digital technologies may well unite all of humanity for the benefit of future generations. Synthesizing the findings of primatology, paleontology, archeology, history, and anthropology, Richard Currier reinterprets and retells the modern narrative of human evolution that began with the discovery of Lucy and other Australopithecus fossils. But the same forces that allowed us to integrate technology into every aspect of our daily lives have also brought us to the brink of planetary catastrophe. Unbound explains both how we got here and how human society must be transformed again to achieve a sustainable future. Technology: "The deliberate modification of any natural object or substance with forethought to achieve a specific end or to serve a specific purpose. ”
Unbounded Functionals in the Calculus of Variations: Representation, Relaxation, and Homogenization (Monographs and Surveys in Pure and Applied Mathematics)
by Luciano CarboneOver the last few decades, research in elastic-plastic torsion theory, electrostatic screening, and rubber-like nonlinear elastomers has pointed the way to some interesting new classes of minimum problems for energy functionals of the calculus of variations. This advanced-level monograph addresses these issues by developing the framework of a gener
Unbounded Self-adjoint Operators on Hilbert Space
by Konrad SchmüdgenThe book is a graduate text on unbounded self-adjoint operators on Hilbert space and their spectral theory with the emphasis on applications in mathematical physics (especially, Schrödinger operators) and analysis (Dirichlet and Neumann Laplacians, Sturm-Liouville operators, Hamburger moment problem) . Among others, a number of advanced special topics are treated on a text book level accompanied by numerous illustrating examples and exercises. The main themes of the book are the following: - Spectral integrals and spectral decompositions of self-adjoint and normal operators - Perturbations of self-adjointness and of spectra of self-adjoint operators - Forms and operators - Self-adjoint extension theory :boundary triplets, Krein-Birman-Vishik theory of positive self-adjoint extension
Unbounded Weighted Composition Operators in L²-Spaces (Lecture Notes in Mathematics #2209)
by Piotr Budzyński Zenon Jabłoński Il Bong Jung Jan StochelThis book establishes the foundations of the theory of bounded and unbounded weighted composition operators in L²-spaces. It develops the theory in full generality, meaning that the corresponding composition operators are not assumed to be well defined. A variety of seminormality properties of unbounded weighted composition operators are characterized.The first-ever criteria for subnormality of unbounded weighted composition operators are provided and the subtle interplay between the classical moment problem, graph theory and the injectivity problem for weighted composition operators is revealed. The relationships between weighted composition operators and the corresponding multiplication and composition operators are investigated. The optimality of the obtained results is illustrated by a variety of examples, including those of discrete and continuous types.The book is primarily aimed at researchers in single or multivariable operator theory.
Uncertain Data Envelopment Analysis
by Meilin WenThis book is intended to present the milestones in the progression of uncertain Data envelopment analysis (DEA). Chapter 1 gives some basic introduction to uncertain theories, including probability theory, credibility theory, uncertainty theory and chance theory. Chapter 2 presents a comprehensive review and discussion of basic DEA models. The stochastic DEA is introduced in Chapter 3, in which the inputs and outputs are assumed to be random variables. To obtain the probability distribution of a random variable, a lot of samples are needed to apply the statistics inference approach. Chapter 4 and 5 provide two uncertain DEA methods to evaluate the DMUs with limited or insufficient statistical data, named fuzzy DEA and uncertain DEA. In order to evaluate the DMUs in which uncertainty and randomness appear simultaneously, the hybrid DEA based on chance theory is presented in Chapter 6.
Uncertain Differential Equations
by Kai YaoThis book introduces readers to the basic concepts of and latest findings in the area of differential equations with uncertain factors. It covers the analytic method and numerical method for solving uncertain differential equations, as well as their applications in the field of finance. Furthermore, the book provides a number of new potential research directions for uncertain differential equation. It will be of interest to researchers, engineers and students in the fields of mathematics, information science, operations research, industrial engineering, computer science, artificial intelligence, automation, economics, and management science.
Uncertain Optimal Control (Springer Uncertainty Research Ser.)
by Yuanguo ZhuThis book introduces the theory and applications of uncertain optimal control, and establishes two types of models including expected value uncertain optimal control and optimistic value uncertain optimal control. These models, which have continuous-time forms and discrete-time forms, make use of dynamic programming. The uncertain optimal control theory relates to equations of optimality, uncertain bang-bang optimal control, optimal control with switched uncertain system, and optimal control for uncertain system with time-delay. Uncertain optimal control has applications in portfolio selection, engineering, and games. The book is a useful resource for researchers, engineers, and students in the fields of mathematics, cybernetics, operations research, industrial engineering, artificial intelligence, economics, and management science.
Uncertain Renewal Processes (Springer Uncertainty Research)
by Kai YaoThis book explores various renewal processes in the context of probability theory, uncertainty theory and chance theory. It also covers the applications of these renewal processes in maintenance models and insurance risk models. The methods used to derive the limit of the renewal rate, the reward rate, and the availability rate are of particular interest, as they can easily be extended to the derivation of other models. Its comprehensive and systematic treatment of renewal processes, renewal reward processes and the alternating renewal process is one of the book’s major features, making it particularly valuable for readers who are interested in learning about renewal theory. Given its scope, the book will benefit researchers, engineers, and graduate students in the fields of mathematics, information science, operations research, industrial engineering, etc.
Uncertain Rule-Based Fuzzy Systems: Introduction And New Directions
by Jerry M. Mendel*Type-2 fuzzy logic: Breakthrough techniques for modeling uncertainty *Key applications: digital mobile communications, computer networking, and video traffic classification *Detailed case studies: Forecasting time series and knowledge mining *Contains 90+ worked examples, 110+ figures, and brief introductory primers on fuzzy logic and fuzzy sets Breakthrough fuzzy logic techniques for handling real-world uncertainty. The world is full of uncertainty that classical fuzzy logic cant model. Now, however, theres an approach to fuzzy logic that can model uncertainty: type-2 fuzzy logic. In this book, the developer of type-2 fuzzy logic demonstrates how it overcomes the limitations of classical fuzzy logic, enabling a wide range of applications from digital mobile communications to knowledge mining. Dr. Jerry Mendel presents a bottom-up approach that begins by introducing traditional type-1 fuzzy logic, explains how it can be modified to handle uncertainty, and, finally, adds layers of complexity to handle increasingly sophisticated applications. Coverage includes: *The sources of uncertainty and the role of membership functions *Type-2 fuzzy sets: operations, properties, and centro
Uncertainty Analyses in Environmental Sciences and Hydrogeology: Methods and Applications to Subsurface Contamination (SpringerBriefs in Applied Sciences and Technology)
by Rachid Ababou Juliette Chastanet Jean-Marie Côme Manuel Marcoux Michel QuintardThis book highlights several methods and quantitative implementations of both probabilistic and fuzzy-based approaches to uncertainty quantification and uncertainty propagation through environmental subsurface pollution models with uncertain input parameters. The book focuses on methods as well as applications in hydrogeology, soil hydrology, groundwater contamination, and related areas (e.g., corrosion of nuclear waste canisters). The methods are illustrated for a broad spectrum of models, from non-differential I/O models to complex PDE solvers, including a novel 3D quasi-analytical model of contaminant transport, and a site-specific computer model of dissolved contaminant migration from a DNAPL (Dense Non Aqueous Phase Liquid) pollution source.
Uncertainty Analysis for Engineers and Scientists: A Practical Guide
by Faith A. MorrisonBuild the skills for determining appropriate error limits for quantities that matter with this essential toolkit. Understand how to handle a complete project and how uncertainty enters into various steps. Provides a systematic, worksheet-based process to determine error limits on measured quantities, and all likely sources of uncertainty are explored, measured or estimated. Features instructions on how to carry out error analysis using Excel and MATLAB®, making previously tedious calculations easy. Whether you are new to the sciences or an experienced engineer, this useful resource provides a practical approach to performing error analysis. Suitable as a text for a junior or senior level laboratory course in aerospace, chemical and mechanical engineering, and for professionals.
Uncertainty Analysis of Experimental Data with R
by Benjamin Shaw"This would be an excellent book for undergraduate, graduate and beyond….The style of writing is easy to read and the author does a good job of adding humor in places. The integration of basic programming in R with the data that is collected for any experiment provides a powerful platform for analysis of data…. having the understanding of data analysis that this book offers will really help researchers examine their data and consider its value from multiple perspectives – and this applies to people who have small AND large data sets alike! This book also helps people use a free and basic software system for processing and plotting simple to complex functions." Michelle Pantoya, Texas Tech University Measurements of quantities that vary in a continuous fashion, e.g., the pressure of a gas, cannot be measured exactly and there will always be some uncertainty with these measured values, so it is vital for researchers to be able to quantify this data. Uncertainty Analysis of Experimental Data with R covers methods for evaluation of uncertainties in experimental data, as well as predictions made using these data, with implementation in R. The books discusses both basic and more complex methods including linear regression, nonlinear regression, and kernel smoothing curve fits, as well as Taylor Series, Monte Carlo and Bayesian approaches. Features: 1. Extensive use of modern open source software (R). 2. Many code examples are provided. 3. The uncertainty analyses conform to accepted professional standards (ASME). 4. The book is self-contained and includes all necessary material including chapters on statistics and programming in R. Benjamin D. Shaw is a professor in the Mechanical and Aerospace Engineering Department at the University of California, Davis. His research interests are primarily in experimental and theoretical aspects of combustion. Along with other courses, he has taught undergraduate and graduate courses on engineering experimentation and uncertainty analysis. He has published widely in archival journals and became an ASME Fellow in 2003.
The Uncertainty Analysis of Model Results: A Practical Guide
by Eduard HoferThis book is a practical guide to the uncertainty analysis of computer model applications. Used in many areas, such as engineering, ecology and economics, computer models are subject to various uncertainties at the level of model formulations, parameter values and input data. Naturally, it would be advantageous to know the combined effect of these uncertainties on the model results as well as whether the state of knowledge should be improved in order to reduce the uncertainty of the results most effectively. The book supports decision-makers, model developers and users in their argumentation for an uncertainty analysis and assists them in the interpretation of the analysis results.
Uncertainty-aware Integration of Control with Process Operations and Multi-parametric Programming Under Global Uncertainty (Springer Theses)
by Vassilis M. CharitopoulosThis book introduces models and methodologies that can be employed towards making the Industry 4.0 vision a reality within the process industries, and at the same time investigates the impact of uncertainties in such highly integrated settings. Advances in computing power along with the widespread availability of data have led process industries to consider a new paradigm for automated and more efficient operations. The book presents a theoretically proven optimal solution to multi-parametric linear and mixed-integer linear programs and efficient solutions to problems such as process scheduling and design under global uncertainty. It also proposes a systematic framework for the uncertainty-aware integration of planning, scheduling and control, based on the judicious coupling of reactive and proactive methods. Using these developments, the book demonstrates how the integration of different decision-making layers and their simultaneous optimisation can enhance industrial process operations and their economic resilience in the face of uncertainty.
Uncertainty, Expectations and Asset Price Dynamics: Essays in Honor of Georges Prat (Dynamic Modeling and Econometrics in Economics and Finance #24)
by Fredj JawadiWritten in honor of Emeritus Professor Georges Prat (University of Paris Nanterre, France), this book includes contributions from eminent authors on a range of topics that are of interest to researchers and graduates, as well as investors and portfolio managers. The topics discussed include the effects of information and transaction costs on informational and allocative market efficiency, bubbles and stock price dynamics, paradox of rational expectations and the principle of limited information, uncertainty and expectation hypotheses, oil price dynamics, and nonlinearity in asset price dynamics.