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The Geographies of COVID-19: Geospatial Stories of a Global Pandemic (Global Perspectives on Health Geography)
by Melinda Laituri Robert B. Richardson Junghwan KimThis volume of case studies focuses on the geographies of COVID-19 around the world. These geographies are located in both time and space concentrating on both first- and second-order impacts of the COVID-19 pandemic. First-order impacts are those associated with the immediate response to the pandemic that include tracking number of deaths and cases, testing, access to hospitals, impacts on essential workers, searching for the origins of the virus and preventive treatments such as vaccines and contact tracing. Second-order impacts are the result of actions, practices, and policies in response to the spread of the virus, with longer-term effects on food security, access to health services, loss of livelihoods, evictions, and migration. Further, the COVID-19 pandemic will be prolonged due to the onset of variants as well as setting the stage for similar future events. This volume provides a synopsis of how geography and geospatial approaches are used to understand this event and the emerging “new normal.” The volume's approach is necessarily selective due to the global reach of the pandemic and the broad sweep of second-order impacts where important issues may be left out. However, the book is envisioned as the prelude to an extended conversation about adaptation to complex circumstances using geospatial tools.Using case studies and examples of geospatial analyses, this volume adopts a geographic lens to highlight the differences and commonalities across space and time where fundamental inequities are exposed, the governmental response is varied, and outcomes remain uncertain. This moment of global collective experience starkly reveals how inequality is ubiquitous and vulnerable populations – those unable to access basic needs – are increasing. This place-based approach identifies how geospatial analyses and resulting maps depict the pandemic as it ebbs and flows across the globe. Data-driven decision making is needed as we navigate the pandemic and determine ways to address future such events to enable local and regional governments in prioritizing limited resources to mitigate the long-term consequences of COVID-19.
The Geography of Bosnia and Herzegovina: Between East and West (World Regional Geography Book Series)
by Haris Gekić Aida Bidžan-Gekić Nusret Drešković Ranko Mirić Péter ReményiThis monograph provides a comprehensive overview of fundamental scientific insights into the geographical features of a country which was and still is in the centre of the geopolitical battle of the large world powers and especially neighboring countries. The book presents the scientifically proven reserves of individual resources such as: mineral riches, land, forests, flora and fauna, water and climate features, to the extent needed, through statistical indicators and geographic maps. The authors point to features and specifics of the existing interdependence of economic and political development and impact of natural resources on spatial development which can be useful for potential investors, spatial planers, decision makers, politicians, geographers, students, large Bosnian diaspora and anyone interested in area of Bosnia and Herzegovina. This book fills the gap in geographical literature on Bosnia and Herzegovina in the English language. The monograph appeals to researchers and scholars of all levels in the fields of geography, geopolitics, history and related fields and everyone interested in this country between East and West.
The Geography of the Third World: Progress and Prospect (Routledge Library Editions: Development)
by Michael PacioneFirst published in 1988, this reissue presents a comprehensive overview of contemporary developments and research into the geography of the Third World, at a time when economies and societies there were changing at a much more rapid rate than their counterparts in the developing world. It covers the topic both systematically and by region, showing how the unique background of each region affects developments there.
The Geometric Theory of Complex Variables
by Steven G. Krantz Peter V. DovbushThis book provides the reader with a broad introduction to the geometric methodology in complex analysis. It covers both single and several complex variables, creating a dialogue between the two viewpoints. Regarded as one of the 'grand old ladies' of modern mathematics, complex analysis traces its roots back 500 years. The subject began to flourish with Carl Friedrich Gauss's thesis around 1800. The geometric aspects of the theory can be traced back to the Riemann mapping theorem around 1850, with a significant milestone achieved in 1938 with Lars Ahlfors's geometrization of complex analysis. These ideas inspired many other mathematicians to adopt this perspective, leading to the proliferation of geometric theory of complex variables in various directions, including Riemann surfaces, Teichmüller theory, complex manifolds, extremal problems, and many others. This book explores all these areas, with classical geometric function theory as its main focus. Its accessible and gentle approach makes it suitable for advanced undergraduate and graduate students seeking to understand the connections among topics usually scattered across numerous textbooks, as well as experienced mathematicians with an interest in this rich field.
The Geometrical Beauty of Plants
by Johan GielisThis book focuses on the origin of the Gielis curves, surfaces and transformations in the plant sciences. It is shown how these transformations, as a generalization of the Pythagorean Theorem, play an essential role in plant morphology and development. New insights show how plants can be understood as developing mathematical equations, which opens the possibility of directly solving analytically any boundary value problems (stress, diffusion, vibration. . . ) . The book illustrates how form, development and evolution of plants unveil as a musical symphony. The reader will gain insight in how the methods are applicable in many divers scientific and technological fields.
The Geometry Toolbox for Graphics and Modeling
by Gerald Farin Dianne HansfordThe Geometry Toolbox takes a novel and particularly visual approach to teaching the basic concepts of two- and three-dimensional geometry. It explains the geometry essential for today's computer modeling, computer graphics, and animation systems. While the basic theory is completely covered, the emphasis of the book is not on abstract proofs but rather on examples and algorithms. The Geometry Toolbox is the ideal text for professionals who want to get acquainted with the latest geometric tools. The chapters on basic curves and surfaces form an ideal stepping stone into the world of graphics and modeling. It is also a unique textbook for a modern introduction to linear algebra and matrix theory.
The Geometry of Accounting: From Debits and Credits to Cartesian Coordinates (Springer Texts in Business and Economics)
by Byung T. RoThis book demonstrates how geometry along with linear algebra can be used to learn and study accounting. It explains how to present (record) economic transactions (accounting transactions or events) and explores the features and principles of double entry accounting based on geometric concepts and theories in multidimensional Cartesian geometric and vector spaces. The geometric approach in this book is concerned with the production of accounting numbers and the entry rather than exit side of accounting. It is markedly different from the traditional approach to learning, studying, and teaching accounting. This book is intended for graduate accounting students, accounting educators, and accounting scholars alike, who are interested in accounting beyond the basics and have some knowledge of geometry and linear algebra.
The Geometry of Geodesics
by Herbert BusemannA comprehensive approach to qualitative problems in intrinsic differential geometry, this text for upper-level undergraduates and graduate students emphasizes cases in which geodesics possess only local uniqueness properties--and consequently, the relations to the foundations of geometry are decidedly less relevant, and Finsler spaces become the principal subject.This direct approach has produced many new results and has materially generalized many known phenomena. Author Herbert Busemann begins with an explanation of the basic concepts, including compact metric spaces, convergence of point sets, motion and isometry, segments, and geodesics. Subsequent topics include Desarguesian spaces, with discussions of Riemann and Finsler spaces and Beltrami's theorem; perpendiculars and parallels, with examinations of higher-dimensional Minkowskian geometry and the Minkowski plane; and covering spaces, including locally isometric space, the universal covering space, fundamental sets, free homotopy and closed geodesics, and transitive geodesics on surfaces of higher genus. Concluding chapters explore the influence of the sign of the curvature on the geodesics, and homogenous spaces, including those with flat bisectors.
The Geometry of Intelligence: Foundations of Transformer Networks in Deep Learning (Studies in Big Data #175)
by Balasubramanian Raman Pradeep SinghThis book offers an in-depth exploration of the mathematical foundations underlying transformer networks, the cornerstone of modern AI across various domains. Unlike existing literature that focuses primarily on implementation, this work delves into the elegant geometry, symmetry, and mathematical structures that drive the success of transformers. Through rigorous analysis and theoretical insights, the book unravels the complex relationships and dependencies that these models capture, providing a comprehensive understanding of their capabilities. Designed for researchers, academics, and advanced practitioners, this text bridges the gap between practical application and theoretical exploration. Readers will gain a profound understanding of how transformers operate in abstract spaces, equipping them with the knowledge to innovate, optimize, and push the boundaries of AI. Whether you seek to deepen your expertise or pioneer the next generation of AI models, this book is an essential resource on the mathematical principles of transformers.
The Geometry of Musical Rhythm: What Makes a "Good" Rhythm Good?, Second Edition
by Godfried T. ToussaintThe original edition of The Geometry of Musical Rhythm was the first book to provide a systematic and accessible computational geometric analysis of the musical rhythms of the world. It explained how the study of the mathematical properties of musical rhythm generates common mathematical problems that arise in a variety of seemingly disparate fields. The book also introduced the distance approach to phylogenetic analysis and illustrated its application to the study of musical rhythm. The new edition retains all of this, while also adding 100 pages, 93 figures, 225 new references, and six new chapters covering topics such as meter and metric complexity, rhythmic grouping, expressive timbre and timing in rhythmic performance, and evolution phylogenetic analysis of ancient Greek paeonic rhythms. In addition, further context is provided to give the reader a fuller and richer insight into the historical connections between music and mathematics.
The Geometry of Physics
by Theodore FrankelThis book provides a working knowledge of those parts of exterior differential forms, differential geometry, algebraic and differential topology, Lie groups, vector bundles and Chern forms that are essential for a deeper understanding of both classical and modern physics and engineering. Included are discussions of analytical and fluid dynamics, electromagnetism (in flat and curved space), thermodynamics, the Dirac operator and spinors, and gauge fields, including Yang–Mills, the Aharonov–Bohm effect, Berry phase and instanton winding numbers, quarks and quark model for mesons. Before discussing abstract notions of differential geometry, geometric intuition is developed through a rather extensive introduction to the study of surfaces in ordinary space. The book is ideal for graduate and advanced undergraduate students of physics, engineering or mathematics as a course text or for self study. This third edition includes an overview of Cartan's exterior differential forms, which previews many of the geometric concepts developed in the text.
The Geometry of René Descartes: with a Facsimile of the First Edition
by René DescartesThis is an unabridged republication of the definitive English translation of one of the very greatest classics of science. Originally published in 1637, it has been characterized as "the greatest single step ever made in the progress of the exact sciences" (John Stuart Mill); as a book which "remade geometry and made modern geometry possible" (Eric Temple Bell). It "revolutionized the entire conception of the object of mathematical science" (J. Hadamard).With this volume Descartes founded modern analytical geometry. Reducing geometry to algebra and analysis and, conversely, showing that analysis may be translated into geometry, it opened the way for modern mathematics. Descartes was the first to classify curves systematically and to demonstrate algebraic solution of geometric curves. His geometric interpretation of negative quantities led to later concepts of continuity and the theory of function. The third book contains important contributions to the theory of equations.This edition contains the entire definitive Smith-Latham translation of Descartes' three books: Problems the Construction of which Requires Only Straight Lines and Circles; On the Nature of Curved Lines; and On the Construction of Solid and Supersolid Problems. Interleaved page by page with the translation is a complete facsimile of the 1637 French text, together with all Descartes' original illustrations; 248 footnotes explain the text and add further bibliography.
The Geometry of Spacetime: A Mathematical Introduction to Relativity Theory (Graduate Texts in Physics)
by Rainer OloffThis book systematically develops the mathematical foundations of the theory of relativity and links them to physical relations. For this purpose, differential geometry on manifolds is introduced first, including differentiation and integration, and special relativity is presented as tensor calculus on tangential spaces. Using Einstein's field equations relating curvature to matter, the relativistic effects in the solar system including black holes are discussed in detail. The text is aimed at students of physics and mathematics and assumes only basic knowledge of classical differential and integral calculus and linear algebra.
The Geometry of Special Relativity (Textbooks in Mathematics)
by Tevian DrayThis unique book presents a particularly beautiful way of looking at special relativity. The author encourages students to see beyond the formulas to the deeper structure.The unification of space and time introduced by Einstein’s special theory of relativity is one of the cornerstones of the modern scientific description of the universe. Yet the unification is counterintuitive because we perceive time very differently from space. Even in relativity, time is not just another dimension, it is one with different propertiesThe book treats the geometry of hyperbolas as the key to understanding special relativity. The author simplifies the formulas and emphasizes their geometric content. Many important relations, including the famous relativistic addition formula for velocities, then follow directly from the appropriate (hyperbolic) trigonometric addition formulas.Prior mastery of (ordinary) trigonometry is sufficient for most of the material presented, although occasional use is made of elementary differential calculus, and the chapter on electromagnetism assumes some more advanced knowledge.Changes to the Second Edition The treatment of Minkowski space and spacetime diagrams has been expanded. Several new topics have been added, including a geometric derivation of Lorentz transformations, a discussion of three-dimensional spacetime diagrams, and a brief geometric description of "area" and how it can be used to measure time and distance. Minor notational changes were made to avoid conflict with existing usagein the literature. Table of Contents Preface1. Introduction.2. The Physics of Special Relativity.3. Circle Geometry.4. Hyperbola Geometry. 5. The Geometry of Special Relativity. 6. Applications.7. Problems III.8. Paradoxes.9. Relativistic Mechanics.10. Problems II.11. Relativistic Electromagnetism. 12. Problems III.13. Beyond Special Relativity. 14. Three-Dimensional Spacetime Diagrams.15. Minkowski Area via Light Boxes.16. Hyperbolic Geometry.17. Calculus.Bibliography. Author Biography Tevian Dray is a Professor of Mathematics at Oregon State University. His research lies at the interface between mathematics and physics, involving differential geometry and general relativity, as well as nonassociative algebra and particle physics; he also studies student understanding of "middle-division" mathematics and physics content. Educated at MIT and Berkeley, he held postdoctoral positions in both mathematics and physics in several countries prior to coming to OSU in 1988. Professor Dray is a Fellow of the American Physical Society for his work in relativity, and an award-winning teacher.
The Geometry of Special Relativity - a Concise Course
by Norbert DragonIn this concise primer it is shown that, with simple diagrams, the phenomena of time dilatation, length contraction and Lorentz transformations can be deduced from the fact that in a vacuum one cannot distinguish physically straight and uniform motion from rest, and that the speed of light does not depend on the speed of either the source or the observer. The text proceeds to derive the important results of relativistic physics and to resolve its apparent paradoxes. A short introduction into the covariant formulation of electrodynamics is also given. This publication addresses, in particular, students of physics and mathematics in their final undergraduate year.
The Geroch-Held-Penrose Calculus: Fundamentals and Applications (SpringerBriefs in Physics)
by Pedro Bargueño Ernesto ContrerasThis book offers a primer on the fundamentals and applications of the Geroch-Held-Penrose (GHP) calculus, a powerful formalism designed for spacetimes that occur frequently in the teaching of General Relativity. Specifically, the book shows in detail the power of the calculus when dealing with spherically symmetric spacetimes. After introducing the basics, a new look at all the classical spherically symmetric black hole solutions is given within the GHP formalism. This is then employed to give new insights into the Tolman-Oppenheimer-Volkoff equations for stellar structure, including a derivation of new exact anisotropic fluid solutions. Finally, a re-writing of some essential features of black hole thermodynamics within the GHP formalism is performed. The book is based on the authors' lecture notes, used in their undergraduate and graduate lectures and while supervising their upper undergraduate and graduate students. To fully benefit from this concise primer, readers only need an undergraduate background in general relativity.
The Gini Methodology
by Shlomo Yitzhaki Edna SchechtmanGini's mean difference (GMD) was first introduced by Corrado Gini in 1912 as an alternative measure of variability. GMD and the parameters which are derived from it (such as the Gini coefficient or the concentration ratio) have been in use in the area of income distribution for almost a century. In practice, the use of GMD as a measure of variability is justified whenever the investigator is not ready to impose, without questioning, the convenient world of normality. This makes the GMD of critical importance in the complex research of statisticians, economists, econometricians, and policy makers. This book focuses on imitating analyses that are based on variance by replacing variance with the GMD and its variants. In this way, the text showcases how almost everything that can be done with the variance as a measure of variability, can be replicated by using Gini. Beyond this, there are marked benefits to utilizing Gini as opposed to other methods. One of the advantages of using Gini methodology is that it provides a unified system that enables the user to learn about various aspects of the underlying distribution. It also provides a systematic method and a unified terminology. Using Gini methodology can reduce the risk of imposing assumptions that are not supported by the data on the model. With these benefits in mind the text uses the covariance-based approach, though applications to other approaches are mentioned as well.
The Global Politics of Census Taking: Quantifying Populations, Institutional Autonomy, Innovation (Routledge Studies in Governance and Public Policy)
by Christian Suter Walter Bartl Alberto Veira-RamosThis book examines in detail the state of the art on census taking to spark a more vivid debate on what some may see as a rather technical – and hence uncontroversial – field of inquiry.Against the backdrop of controversy between instrumental and performative theoretical stances towards census taking, it analyses the historical trajectories and political implications of seemingly technical decisions made during the quantification process by focusing on the 2020 round of censuses, which have been particularly revealing as activities have been affected by the ongoing COVID-19 pandemic and the ensuing containment policies. Through case studies of countries from the Global North and the Global South, the book highlights the consequences of, and innovations and challenges in census taking focusing on three particular areas of concern – the politics of the census in terms of identity politics; the institutional autonomy of the census; and significant and transformative methodological innovations.This book will be of key interest to scholars, students and practitioners of quantification studies, and social demography and more broadly to public policy, governance, comparative politics and the broader social sciences.
The Global Prehistory of Human Migration
by Immanuel NessPreviously published as the first volume of The Encyclopedia of Global Human Migration, this work is devoted exclusively to prehistoric migration, covering all periods and places from the first hominin migrations out of Africa through the end of prehistory. Presents interdisciplinary coverage of this topic, including scholarship from the fields of archaeology, anthropology, genetics, biology, linguistics, and more Includes contributions from a diverse international team of authors, representing 17 countries and a variety of disciplines Divided into two sections, covering the Pleistocene and Holocene; each section examines human migration through chapters that focus on different regional and disciplinary lenses
The Glorious Golden Ratio
by Alfred S. PosamentierWhat exactly is the Golden Ratio? How was it discovered? Where is it found? These questions and more are thoroughly explained in this engaging tour of one of mathematics' most interesting phenomena. Veteran educators and prolific mathematics writers trace the appearance of the Golden Ratio throughout history and demonstrate a variety of ingenious techniques used to construct it and illustrate the many surprising geometric figures in which the Golden Ratio is embedded. Requiring no more than an elementary knowledge of geometry and algebra, the authors give readers a new appreciation of the indispensable qualities and inherent beauty of mathematics.
The Golden Ratio: Geometric and Number Theoretical Considerations
by Hans WalserThis book illustrates key mathematical aspects of the Golden Ratio: It particularly delves into geometric and number theoretical connections and examples, and makes further considerations and generalizations accessible. The book is primarily aimed at students, pupils, mathematics teachers, and interested laypeople. It is modular in structure, so the individual chapters can be read independently of one another. The reading is intended to encourage one's own geometric activities. Tips and procedural hints from the craft-creative realm are also provided. Supplementary animations can be accessed with the SN More Media App: simply download the SN More Media App for free, scan a picture or link with the play button, and immediately play the animation on your smartphone or tablet. The translation was done with the help of artificial intelligence. A subsequent human revision was done primarily in terms of content.
The Golden Ratio: The Divine Beauty of Mathematics
by Gary B. MeisnerThis enlightening and gorgeously illustrated book explores the beauty and mystery of the divine proportion in art, architecture, nature, and beyond.From the pyramids of Giza, to quasicrystals, to the proportions of the human face, the golden ratio has an infinite capacity to generate shapes with exquisite properties. Author Gary Meisner has spent decades researching the subject, investigating and collaborating with people across the globe in dozens of professions and walks of life. In The Golden Ratio, he shares his enlightening journey. Exploring the long history of this fascinating number, as well as new insights into its power and potential applications, The Golden Ratio invites you to take a new look at this timeless topic.
The Golden Ratio: The Story of PHI, the World's Most Astonishing Number
by Mario LivioThroughout history, thinkers from mathematicians to theologians have pondered the mysterious relationship between numbers and the nature of reality. In this fascinating book, Mario Livio tells the tale of a number at the heart of that mystery: phi, or 1.6180339887...This curious mathematical relationship, widely known as "The Golden Ratio," was discovered by Euclid more than two thousand years ago because of its crucial role in the construction of the pentagram, to which magical properties had been attributed. Since then it has shown a propensity to appear in the most astonishing variety of places, from mollusk shells, sunflower florets, and rose petals to the shape of the galaxy. Psychological studies have investigated whether the Golden Ratio is the most aesthetically pleasing proportion extant, and it has been asserted that the creators of the Pyramids and the Parthenon employed it. It is believed to feature in works of art from Leonardo da Vinci's Mona Lisa to Salvador Dali's The Sacrament of the Last Supper, and poets and composers have used it in their works. It has even been found to be connected to the behavior of the stock market!The Golden Ratio is a captivating journey through art and architecture, botany and biology, physics and mathematics. It tells the human story of numerous phi-fixated individuals, including the followers of Pythagoras who believed that this proportion revealed the hand of God; astronomer Johannes Kepler, who saw phi as the greatest treasure of geometry; such Renaissance thinkers as mathematician Leonardo Fibonacci of Pisa; and such masters of the modern world as Goethe, Cezanne, Bartok, and physicist Roger Penrose. Wherever his quest for the meaning of phi takes him, Mario Livio reveals the world as a place where order, beauty, and eternal mystery will always coexist.From the Hardcover edition.
The Golden Rule of Ethics: A Dynamic Game-Theoretic Framework Based on Berge Equilibrium (Communications in Cybernetics, Systems Science and Engineering #9)
by Mindia E. Salukvadze Vladislav I. ZhukovskiyThis book synthesizes the game-theoretic modeling of decision-making processes and an ancient moral requirement called the Golden Rule of ethics (GR). This rule states "Behave to others as you would like them to behave to you." The GR is one of the oldest, most widespread, and specific moral requirements that appear in Christianity, Islam, Judaism, Buddhism, and Confucianism. This book constructs and justifies mathematical models of dynamic socio-economic processes and phenomena that reveal the mechanism of the GR and are based on the concept of Berge equilibrium. The GR can be naturally used for resolving or balancing conflicts, and its "altruistic character" obviously excludes wars, blood-letting, and armed clashes. The previous book by the authors, The Berge Equilibrium: A Game-Theoretic Framework for the Golden Rule of Ethics, covers the static case of the GR. In this book, the dynamic case of the GR is investigated using the altruistic concept of Berge equilibrium and three factors as follows: 1) a modification of N.N. Krasovskii’s mathematical formalization of differential positional games (DPGs), in view of the counterexamples given by A.I. Subbotin and A.F. Kononenko; 2) the method of guiding control, proposed by N.N. Krasovskii; and 3) the Germier convolution of the payoff functions of different players. Additionally, this book features exercises, problems, and solution tips collected together in Appendix 1, as well as new approaches to conflict resolution as presented in Appendices 2 to 4. This book will be of use to undergraduate and graduate students and experts in the field of decision-making in complex control and management systems, as well as anyone interested in game theory and applications.
The Golden Ticket: P, NP, and the Search for the Impossible
by Lance FortnowThe computer science problem whose solution could transform life as we know itThe P-NP problem is the most important open problem in computer science, if not all of mathematics. Simply stated, it asks whether every problem whose solution can be quickly checked by computer can also be quickly solved by computer. The Golden Ticket provides a nontechnical introduction to P-NP, its rich history, and its algorithmic implications for everything we do with computers and beyond. Lance Fortnow traces the history and development of P-NP, giving examples from a variety of disciplines, including economics, physics, and biology. He explores problems that capture the full difficulty of the P-NP dilemma, from discovering the shortest route through all the rides at Disney World to finding large groups of friends on Facebook. The Golden Ticket explores what we truly can and cannot achieve computationally, describing the benefits and unexpected challenges of this compelling problem.