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Unified Signal Theory
by Gianfranco CariolaroUnified Signal Theory is an indispensible textbook dealing with the theory of deterministic signals; a topic of fundamental interest to graduates and senior undergraduates in the areas of information engineering (telecommunications, control, systems theory and electronics), astronomy, oceanography, earth science, biology and medicine. The unified theory follows an innovative approach - that of combining all signal classes into just one. The fundamental signal operations (convolution, Fourier transform, linear systems, sampling and interpolation) are established simultaneously for all the signal classes. This unified approach avoids the repetition of similar concepts consequent on other approaches' separate treatment of definitions and properties for each signal class. Modern wavelet ideas are developed in harmony with the rest of the text. Unified Signal Theory provides: * exercises and examples, to give the student practice; * solutions which are available for download and save the tutor time; and * a choice of two suggested reading paths depending on the level of the student, for an enhanced learning experience. The advantages of the unified approach are many: it permits a global vision of the topic, it is economical in teaching and learning, and it can be adjusted easily to fit new applications. This textbook presents the theory in five chapters, and goes on to demonstrate specific applications such as fast Fourier transform implementation, sampling and reconstructions of signals, and multicolor modulation systems, in a further six chapters. Mathematical concepts are introduced conceptually within the body of the book with more rigorous treatment being reserved for the appendices.
Unified Theory for Fractional and Entire Differential Operators: An Approach via Differential Quadruplets and Boundary Restriction Operators (Frontiers in Mathematics)
by Arnaud RougirelThis monograph proposes a unified theory of the calculus of fractional and standard derivatives by means of an abstract operator-theoretic approach. By highlighting the axiomatic properties shared by standard derivatives, Riemann-Liouville and Caputo derivatives, the author introduces two new classes of objects. The first class concerns differential triplets and differential quadruplets; the second concerns boundary restriction operators. Instances of boundary restriction operators can be generalized fractional differential operators supplemented with homogeneous boundary conditions. The analysis of these operators comprises: The computation of adjoint operators; The definition of abstract boundary values; The solvability of equations supplemented with inhomogeneous abstract linear boundary conditions; The analysis of fractional inhomogeneous Dirichlet Problems. As a result of this approach, two striking consequences are highlighted: Riemann-Liouville and Caputo operators appear to differ only by their boundary conditions; and the boundary values of functions in the domain of fractional operators are closely related to their kernel. Unified Theory for Fractional and Entire Differential Operators will appeal to researchers in analysis and those who work with fractional derivatives. It is mostly self-contained, covering the necessary background in functional analysis and fractional calculus.
Uniform Distribution of Sequences (Dover Books on Mathematics)
by L. Kuipers H. NiederreiterThe theory of uniform distribution began with Hermann Weyl's celebrated paper of 1916. In later decades, the theory moved beyond its roots in diophantine approximations to provide common ground for topics as diverse as number theory, probability theory, functional analysis, and topological algebra. This book summarizes the theory's development from its beginnings to the mid-1970s, with comprehensive coverage of both methods and their underlying principles.A practical introduction for students of number theory and analysis as well as a reference for researchers in the field, this book covers uniform distribution in compact spaces and in topological groups, in addition to examinations of sequences of integers and polynomials. Notes at the end of each section contain pertinent bibliographical references and a brief survey of additional results. Exercises range from simple applications of theorems to proofs of propositions that expand upon results stated in the text.
Uniform Spaces and Measures
by Jan PachlThis book addresses the need for an accessible comprehensive exposition of the theory of uniform measures; the need that became more critical when recently uniform measures reemerged in new results in abstract harmonic analysis. Until now, results about uniform measures have been scattered through many papers written by a number of authors, some unpublished, written using a variety of definitions and notations. Uniform measures are certain functionals on the space of bounded uniformly continuous functions on a uniform space. They are a common generalization of several classes of measures and measure-like functionals studied in abstract and topological measure theory, probability theory, and abstract harmonic analysis. They offer a natural framework for results about topologies on spaces of measures and about the continuity of convolution of measures on topological groups and semitopological semigroups. The book is a reference for the theory of uniform measures. It includes a self-contained development of the theory with complete proofs, starting with the necessary parts of the theory of uniform spaces. It presents diverse results from many sources organized in a logical whole, and includes several new results. The book is also suitable for graduate or advanced undergraduate courses on selected topics in topology and functional analysis. The text contains a number of exercises with solution hints, and four problems with suggestions for further research.
Unifying Business, Data, and Code
by Ron Itelman Juan Cruz ViottiIn the modern symphony of business, each section-from the technical to the managerial-must play in harmony. Authors Ron Itelman and Juan Cruz Viotti introduce a bold methodology to synchronize your business and technical teams, transforming them into a single, high-performing unit. Misalignment between business and technical teams halts innovation. You'll learn how to transcend the root causes of project failure-the ambiguity, knowledge gaps, and blind spots that lead to wasted efforts. The unifying methodology in this book will teach you these alignment tools and more: The four facets of data products: A simple blueprint that encapsulates data and business logic helps eliminate the most common causes of wasted time and misunderstandingThe concept compass: An easy way to identify the biggest sources of misalignmentSuccess spectrums: Define the required knowledge and road map your team needs to achieve successJSON Schema: Leverage JSON and JSON Schema to technically implement the strategy at scale, including extending JSON Schema with custom keywords, understanding JSON Schema annotations, and hosting your own schema registryData hygiene: Learn how to design high-quality datasets aligned with creating real business value, and protect your organization from the most common sources of pain
Unifying Political Methodology: The Likelihood Theory Of Statistical Inference (Techniques In Political Analysis Series)
by Gary KingThis book is about methodology in political science. Its purpose is to unify existing methods and formulate some new methods, under a general theory of statistical inference. As explained in Section 1.1, it is also intended to stimulate and centralize methodological debate in political science.
Unifying the Universe: The Physics of Heaven and Earth
by Hasan PadamseeUnifying the Universe: The Physics of Heaven and Earth presents a non-technical approach to physics for the lay-science enthusiast. This popular textbook, which evolved from a conceptual course at Cornell University, is intended for non-science undergraduate students taking their first physics module. This second edition maintains its unique approach in crossing boundaries between physics and humanities, with connections to art, poetry, history, and philosophy. It explores how the process of scientific thought is inextricably linked with cultural, creative, and aesthetic aspects of human endeavor, opening the readers up to new ways of looking at the world. The text has been fully updated throughout to address current and exciting new topics in the field, such as exo-planets, the accelerating Universe, dark matter, dark energy, gravitational waves, super-symmetry, string theory, big bang cosmology, and the Higgs boson. There is also an entirely new chapter on the Quantum World, which connects the fascinating topics of quantum entanglement and quantum computing. Key Features: Provides a solid, yet accessible, background to basic physics without complex mathematics Uses a human interest approach to show how science is significant for more than its technological consequences Discusses the arts and philosophies of historical periods that are pertinent to the subject.
Unifying Themes in Complex Systems IX: Proceedings of the Ninth International Conference on Complex Systems (Springer Proceedings in Complexity)
by Alfredo J. Morales Carlos Gershenson Dan Braha Ali A. Minai Yaneer Bar-YamUnifying Themes in Complex Systems is a well-established series of carefully edited conference proceedings that serve to document and archive the progress made regarding cross-fertilization in this field. The International Conference on Complex Systems (ICCS) creates a unique atmosphere for scientists from all fields, engineers, physicians, executives, and a host of other professionals, allowing them to explore common themes and applications of complex systems science. With this new volume, Unifying Themes in Complex Systems continues to establish common ground between the wide-ranging domains of complex systems science.
Unifying Themes In Complex Systems, Volume 2: Proceedings Of The Second International Conference On Complex Systems (New England Complex Systems Inst Ser. #Vol. 4)
by Yaneer Bar-YamThe International Conference on Complex Systems provides a unique opportunity for scientists to rise above the disciplinary boundaries and explore unity in complex systems. This volume contains the proceedings of the Second International Conference on Complex Systems. The sessions ranged from the opening talk by Nobel laureate Philip Anderson on emergence and the relevance of complex systems to physics to the final panel that included many of the great management gurus of this generation. The plenary session topics for the second conference were emergence, description and modeling, self-organization, networks, time series, agents in action, and complexity and management. Talks in these sessions often focused on contributions in specific disciplines, but each session contained a diverse set of disciplines to show the strategies and concepts that can be applied generally to complex systems. Overall, the conference presentations dealt with issues of significant public interest, including individual psychology, dynamics of social and economic change, the human genome, and ecology.The New England Complex Systems Institute is an independent educational and research institution dedicated to advancing the study of complex systems, including new concepts and methodologies that are affecting all fields of science and engineering, and are being applied to technology, business, and even social policy. NECSI organizes conferences, workshops, short courses, and other activities from which books will be produced for the NECSI Series on Complexity. The books will range from conference proceedings and graduate textbooks to general-audience trade books, and will address fundamental concepts, new frontiers, and innovative applications of complex systems.
Unifying Themes in Complex Systems X: Proceedings of the Tenth International Conference on Complex Systems (Springer Proceedings in Complexity)
by Dan Braha Marcus A. M. de Aguiar Carlos Gershenson Alfredo J. Morales Les Kaufman Elena N. Naumova Ali A. Minai Yaneer Bar-YamThe International Conference on Complex Systems (ICCS) offers a unique interdisciplinary venue for researchers from the physical and biological sciences, social sciences, psychology and cognitive science, engineering, medicine, human systems, and global systems. This proceedings volume gathers selected papers from the conference. The New England Complex Systems Institute (NECSI) has been instrumental in the development of complex systems science and its applications. NECSI pursues research, education, knowledge dissemination, and community development efforts around the world to promote the study of complex systems and its application for the benefit of society. NECSI hosts the International Conference on Complex Systems and publishes the NECSI Book.
Unit 1 of Illustrative Mathematics Grade 2
by Illustrative MathematicsLearnZillion Illustrative Mathematics for grades K–5, an IM-certified program, offers the highest quality math curricula powered by a best-in-class integrated learning experience. The comprehensive, flexible solution equips teachers with easy-to-use lesson cards and teaching notes, digital interactives and assessments, and built-in differentiation. The instructional design engages students through collaborative math discourse, inclusive instructional routines, and digital tools that promote thinking and reasoning. LearnZillion IM supports all students on their college and career readiness journey — whether they are learning in a classroom, hybrid, or distance learning model. The LZ IM Print + Digital Bundle 5 years offers consumable print student workbooks (all volumes) and a student digital license for 5 years. The digital student license includes access to student workbook content, interactive lessons, videos, digital interactives, digital assessments, digital practice sets, and more!
Unit Equations in Diophantine Number Theory
by Jan-Hendrik EvertseDiophantine number theory is an active area that has seen tremendous growth over the past century, and in this theory unit equations play a central role. This comprehensive treatment is the first volume devoted to these equations. The authors gather together all the most important results and look at many different aspects, including effective results on unit equations over number fields, estimates on the number of solutions, analogues for function fields and effective results for unit equations over finitely generated domains. They also present a variety of applications. Introductory chapters provide the necessary background in algebraic number theory and function field theory, as well as an account of the required tools from Diophantine approximation and transcendence theory. This makes the book suitable for young researchers as well as experts who are looking for an up-to-date overview of the field.
Unit Root Tests in Time Series Volume 1: Key Concepts and Problems
by Kerry PattersonTesting for a unit root is now an essential part of time series analysis. This volume provides a critical overview and assessment of tests for a unit root in time series, developing the concepts necessary to understand the key theoretical and practical models in unit root testing.
Unit Root Tests in Time Series Volume 2
by Kerry PattersonTesting for a Unit Root is now an essential part of time series analysis but the literature on the topic is so large that knowing where to start is difficult even for the specialist. This book provides a way into the techniques of unit root testing, explaining the pitfalls and nonstandard cases, using practical examples and simulation analysis.
Unity from Diversity: Pluralist Systemic Thinking for Social and Behavioural Research
by Ray W. CookseyThis book is about the choices that researchers can make when building knowledge in social and behavioural spaces. Knowledge is the unity we seek and, given that social and behavioural research is a human endeavour focusing on human lives and experiences, there are diverse and ever-evolving pathways towards achieving that unity. Any one pathway will only ever yield partial glimpses into human life and diversity of potential choices serves to enrich, expand, and enlarge those glimpses in pursuit of more complete understanding. The book shows that researchers and the researched are far more connected than disconnected in this world and those connections are spread out through a network of interlinked complex systems. The book argues that pluralist systemic thinking provides the means by which a researcher’s methodological choices for navigating the ‘Data Triangle’ (comprising data source, data gathering, and data analysis strategies) and the learning they provide can be fully and robustly contextualised with respect to those systems and the expectations and influences that emerge from them. Such contextualisations facilitate the refinement, augmentation, and/or narrowing of those choices during the researcher’s journey. Anticipating choices downstream may have implications for more immediate choices and more immediate choices may create a cascade of necessary downstream choices. An essential part of contextualisation involves making choices about patterns of guiding assumptions, modes of knowledge building, and research frames. Researchers must develop the capacity to be flexible and adapt to unanticipated emergent events, obstacles, and political influences, making trade-offs where necessary throughout their research journey, always with an eye on both feasibility and quality. Importantly, research has no meaning unless the researcher can ensure that it connects with intended audiences via specific research outcomes, especially since the ultimate judgments about the convincingness, meaningfulness, quality, and utility of the research are vested in those audiences. Throughout the book, special attention is devoted to the role(s) that stakeholders and gatekeepers play in shaping the researcher’s journey as well as to what can be learned from Indigenous/First Nations perspectives on social and behavioural research.
Univariate and Multivariate General Linear Models: Theory and Applications with SAS, Second Edition
by Kevin Kim Neil TimmReviewing the theory of the general linear model (GLM) using a general framework, Univariate and Multivariate General Linear Models: Theory and Applications with SAS, Second Edition presents analyses of simple and complex models, both univariate and multivariate, that employ data sets from a variety of disciplines, such as the social and behavioral
Univariate, Bivariate, and Multivariate Statistics Using R: Quantitative Tools for Data Analysis and Data Science
by Daniel J. DenisA practical source for performing essential statistical analyses and data management tasks in R Univariate, Bivariate, and Multivariate Statistics Using R offers a practical and very user-friendly introduction to the use of R software that covers a range of statistical methods featured in data analysis and data science. The author— a noted expert in quantitative teaching —has written a quick go-to reference for performing essential statistical analyses and data management tasks in R. Requiring only minimal prior knowledge, the book introduces concepts needed for an immediate yet clear understanding of statistical concepts essential to interpreting software output. The author explores univariate, bivariate, and multivariate statistical methods, as well as select nonparametric tests. Altogether a hands-on manual on the applied statistics and essential R computing capabilities needed to write theses, dissertations, as well as research publications. The book is comprehensive in its coverage of univariate through to multivariate procedures, while serving as a friendly and gentle introduction to R software for the newcomer. This important resource: Offers an introductory, concise guide to the computational tools that are useful for making sense out of data using R statistical software Provides a resource for students and professionals in the social, behavioral, and natural sciences Puts the emphasis on the computational tools used in the discovery of empirical patterns Features a variety of popular statistical analyses and data management tasks that can be immediately and quickly applied as needed to research projects Shows how to apply statistical analysis using R to data sets in order to get started quickly performing essential tasks in data analysis and data science Written for students, professionals, and researchers primarily in the social, behavioral, and natural sciences, Univariate, Bivariate, and Multivariate Statistics Using R offers an easy-to-use guide for performing data analysis fast, with an emphasis on drawing conclusions from empirical observations. The book can also serve as a primary or secondary textbook for courses in data analysis or data science, or others in which quantitative methods are featured.
Univariate Stable Distributions: Models for Heavy Tailed Data (Springer Series in Operations Research and Financial Engineering)
by John P. NolanThis textbook highlights the many practical uses of stable distributions, exploring the theory, numerical algorithms, and statistical methods used to work with stable laws. Because of the author’s accessible and comprehensive approach, readers will be able to understand and use these methods. Both mathematicians and non-mathematicians will find this a valuable resource for more accurately modelling and predicting large values in a number of real-world scenarios.Beginning with an introductory chapter that explains key ideas about stable laws, readers will be prepared for the more advanced topics that appear later. The following chapters present the theory of stable distributions, a wide range of applications, and statistical methods, with the final chapters focusing on regression, signal processing, and related distributions. Each chapter ends with a number of carefully chosen exercises. Links to free software are included as well, where readers can put these methods into practice.Univariate Stable Distributions is ideal for advanced undergraduate or graduate students in mathematics, as well as many other fields, such as statistics, economics, engineering, physics, and more. It will also appeal to researchers in probability theory who seek an authoritative reference on stable distributions.
Universal Algebra: Fundamentals and Selected Topics
by Clifford BergmanStarting with the most basic notions, Universal Algebra: Fundamentals and Selected Topics introduces all the key elements needed to read and understand current research in this field. Based on the author's two-semester course, the text prepares students for research work by providing a solid grounding in the fundamental constructions and concepts o
Universal Coding and Order Identification by Model Selection Methods (Springer Monographs in Mathematics)
by Élisabeth Gassiat Anna Ben-HamouThe purpose of these notes is to highlight the far-reaching connections between Information Theory and Statistics. Universal coding and adaptive compression are indeed closely related to statistical inference concerning processes and using maximum likelihood or Bayesian methods. The book is divided into four chapters, the first of which introduces readers to lossless coding, provides an intrinsic lower bound on the codeword length in terms of Shannon’s entropy, and presents some coding methods that can achieve this lower bound, provided the source distribution is known. In turn, Chapter 2 addresses universal coding on finite alphabets, and seeks to find coding procedures that can achieve the optimal compression rate, regardless of the source distribution. It also quantifies the speed of convergence of the compression rate to the source entropy rate. These powerful results do not extend to infinite alphabets. In Chapter 3, it is shown that there are no universal codes over the class of stationary ergodic sources over a countable alphabet. This negative result prompts at least two different approaches: the introduction of smaller sub-classes of sources known as envelope classes, over which adaptive coding may be feasible, and the redefinition of the performance criterion by focusing on compressing the message pattern. Finally, Chapter 4 deals with the question of order identification in statistics. This question belongs to the class of model selection problems and arises in various practical situations in which the goal is to identify an integer characterizing the model: the length of dependency for a Markov chain, number of hidden states for a hidden Markov chain, and number of populations for a population mixture. The coding ideas and techniques developed in previous chapters allow us to obtain new results in this area. This book is accessible to anyone with a graduate level in Mathematics, and will appeal to information theoreticians and mathematical statisticians alike. Except for Chapter 4, all proofs are detailed and all tools needed to understand the text are reviewed.
The Universal Computer: The Road from Leibniz to Turing, Third Edition
by Martin DavisThe breathtakingly rapid pace of change in computing makes it easy to overlook the pioneers who began it all. The Universal Computer: The Road from Leibniz to Turing explores the fascinating lives, ideas, and discoveries of seven remarkable mathematicians. It tells the stories of the unsung heroes of the computer age – the logicians.
A Universal Construction for Groups Acting Freely on Real Trees
by Ian Chiswell Thomas MüllerThe theory of R-trees is a well-established and important area of geometric group theory and in this book the authors introduce a construction that provides a new perspective on group actions on R-trees. They construct a group RF(G), equipped with an action on an R-tree, whose elements are certain functions from a compact real interval to the group G. They also study the structure of RF(G), including a detailed description of centralizers of elements and an investigation of its subgroups and quotients. Any group acting freely on an R-tree embeds in RF(G) for some choice of G. Much remains to be done to understand RF(G), and the extensive list of open problems included in an appendix could potentially lead to new methods for investigating group actions on R-trees, particularly free actions. This book will interest all geometric group theorists and model theorists whose research involves R-trees.
Universal Logic, Ethics, and Truth: Essays in Honor of John Corcoran (1937-2021) (Studies in Universal Logic)
by Jean-Yves Béziau Timothy J. MadiganJohn Corcoran was a very well-known logician who worked on several areas of logic. He produced decisive works giving a better understanding of two major figures in the history of logic, Aristotle and Boole. Corcoran had a close association with Alfred Tarski, a prominent 20th-century logician. This collaboration manifested in Corcoran's substantial introduction to Tarski's seminal book, Logic, Semantics, Metamathematics (1956). Additionally, Corcoran's posthumous editorial involvement in 'What are logical notions?' (1986) breathed new life into this seminal paper authored by Tarski. His scholarly pursuits extended to the intricate explication of fundamental concepts in modern logic, including variables, propositions, truth, consequences, and categoricity. Corcoran's academic curiosity extended further to the intersection of ethics and logic, reflecting his contemplation of their interrelation. Beyond these theoretical contributions, Corcoran was deeply engaged in the pedagogical dimensions of logic instruction. This volume serves as a compilation of articles contributed by Corcoran's students, colleagues, and international peers. By encompassing a diverse range of subjects, this collection aptly mirrors Corcoran's wide-ranging interests, offering insights that not only deepen our understanding of his work but also advance the theoretical frameworks he explored.
The Universal Machine
by Ian WatsonThe computer unlike other inventions is universal; you can use a computer for many tasks: writing, composing music, designing buildings, creating movies, inhabiting virtual worlds, communicating... This popular science history isn't just about technology but introduces the pioneers: Babbage, Turing, Apple's Wozniak and Jobs, Bill Gates, Tim Berners-Lee, Mark Zuckerberg. This story is about people and the changes computers have caused. In the future ubiquitous computing, AI, quantum and molecular computing could even make us immortal. The computer has been a radical invention. In less than a single human life computers are transforming economies and societies like no human invention before.
The Universe and the Teacup: The Mathematics of Truth and Beauty
by K. C. ColeFrom the acclaimed Los Angeles Times science writer, a wise, witty, and elegant study of how math provides practical solutions to everyday problems. Are the secrets of the universe written in words—or is it all about the digits? K.C. Cole follows up her paean to the power of physics, Sympathetic Vibrations, with this engaging and accessible guide to the might and majesty of mathematics. The Universe and the Teacup uses relatable examples, humorous prose, and whimsical line drawings to demonstrate math&’s ability to &“translate the complexity of the world into manageable patterns.&” Cole shows how mathematical concepts illuminate everything from human risk-taking behavior to astronomical investigation, game theory to logic problems—not to mention the very structure of the universe itself. Brimming with trivia stressing the importance of math throughout history, this is a book both math nerds and the &“innumerate&” everyday person can enjoy in equal measure. &“Cole writes clearly, simply and vividly,&” noted The New York Times. &“She so obviously likes mathematics, the reader can't help liking it too.&” Filled with &“a thousand fascinating facts and shrewd observations (Martin Gardner, Los Angeles Times), this book demonstrates how the truth and beauty of everything, from relativity to rainbows, is all in the numbers.