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Pluripotential Theory: Filippo Bracci, John Erik Fornæss
by Francois Berteloot Jean Pierre Demailly Filippo Bracci Giorgio Patrizio John Erik Fornæss Zbigniew BłockiPluripotential theory is a very powerful tool in geometry, complex analysis and dynamics. This volume brings together the lectures held at the 2011 CIME session on "pluripotential theory" in Cetraro, Italy. This CIME course focused on complex Monge-Ampére equations, applications of pluripotential theory to Kahler geometry and algebraic geometry and to holomorphic dynamics. The contributions provide an extensive description of the theory and its very recent developments, starting from basic introductory materials and concluding with open questions in current research.
Pluses and Minuses: How Math Solves Our Problems
by Stefan BuijsmanA guide to changing how you think about numbers and mathematics, from the prodigy changing the way the world thinks about math.We all know math is important: we live in the age of big data, our lives are increasingly governed by algorithms, and we're constantly faced with a barrage of statistics about everything from politics to our health. But what might be less obvious is how math factors into your daily life, and what memorizing all of those formulae in school had to do with it. Math prodigy Stefan Buijsman is beginning to change that through his pioneering research into the way we learn math. Plusses and Minuses is based in the countless ways that math is engrained in our daily lives, and shows readers how math can actually be used to make problems easier to solve. Taking readers on a journey around the world to visit societies that have developed without the use of math, and back into history to learn how and why various disciples of mathematics were invented, Buijsman shows the vital importance of math, and how a better understanding of mathematics will give us a better understanding of the world as a whole. Stefan Buijsman has become one of the most sought-after experts in math education after he completed his PhD at age 20. In Plusses and Minuses, he puts his research into practice to help anyone gain a better grasp of mathematics than they have ever had.
Pluses and Minuses: How Maths Makes the World More Manageable
by Stefan BuijsmanWhat is the relationship between the number of films Nicolas Cage appears in and the number of deaths by drowning in swimming pools?How in 1850s London did John Snow calculate the relationship between the city's water suppliers and the number of deaths from cholera?Thousands of years ago the inhabitants of Mesopotamia became the first to use numbers. Since then, mathematics has been unstoppable. It's behind almost everything, from search-engines to cruise-control, from coffee-makers to timetables. But now that we hardly ever need to do arithmetic any longer, how relevant is mathematics to everyday life? Plusses and Minuses demonstrates which role mathematics play in human endeavour. It begins with the mathematical skills we all possess from birth, to arrive at the many applications of mathematics today. It turns out that without knowledge of the ideas behind mathematical calculations we find ourselves sidelined. Stefan Buijsman answers questions such as: What is life without numbers? Does mathematics add anything? What are mistakes in mathematics? Is it all mere chance? How can we get a grip on uncertainty? Can mathematics help us to treat cancer more effectively? Buijsman makes connections between philosophy, psychology and history, while explaining the wonderful world of mathematics for absolutely everyone.
Pocket Book of Integrals and Mathematical Formulas
by Ronald J. TallaridaPocket Book of Integrals and Mathematical Formulas, 5th Edition covers topics ranging from precalculus to vector analysis and from Fourier series to statistics, presenting numerous worked examples to demonstrate the application of the formulas and methods. This popular pocket book is an essential source for students of calculus and higher mathemati
Pocket Evidence Based Medicine: A Survival Guide for Clinicians and Students
by Walter R. PalmasThis concise, easy-to-read pocket guide offers medical trainees, researchers, and clinicians at every level the perfect resource on Evidence Based Medicine (EBM). Based on the author’s many years of experience teaching EBM to medical students and medical residents at Columbia University, this handy title addresses not only all the basic concepts and issues in EBM, but also takes an example-based approach and is replete with numerous illustrations. This brief book provides readers with all the tools needed to tell the good from the bad in healthcare research. It discusses every type of study design, from the assessment of diagnostic tests to clinical trials and meta-analysis. The work also introduces readers to novel methods, such as the Bayesian analysis of clinical trials. In addition, to help readers better retain the information, the guide includes thought-provoking review questions and answers in an appendix. In all, Pocket Evidence-Based Medicine: A Survival Guide for Clinicians and Students is an ideal resource for anyone who encounters statistics in their studies or career, including clinicians, researchers, trainees in medicine and graduate students in a wide range of other disciplines
Pocket Piggies Numbers!: Featuring the Teacup Pigs of Pennywell Farm
by Richard AustinCould there be a cuter way to learn colors and numbers? Announcing a new line of board books featuring the irresistible Teacup Pigs of Pennywell Farm. Small enough to hold in the palm of your hand, the Pennywell pigs are an adorable lot. They’re also naturals in front of the camera—especially the camera belonging to Richard Austin who, as their exclusive photographer, knows just how to capture their big personalities. The Pocket Piggies board books marry the inherent appeal of Teacup Pigs to the sweetness of the board book format. The photographs are full-color, full-page, and up-close. The subjects are classics: Pocket Piggies Numbers! celebrates an ever-growing crowd of piggies, from one to ten, through a rhyming text that’s sweet and charming, to read again and again: <p>1 Pocket Piggy in a boat,<p> <p>2 Pocket Piggies in a cup,<p> <p>3 Pocket Piggies in a basket,<p> <p>4 Pocket Piggies with a pup!<p>
Poems and Paradoxes
by Hana Ayoob Kyle D. Evans17 Chapters of Paradoxes and Fascinating Ideas...a poems and pictures to help you remember them! How big is a billion? How much would you pay for a one coin? Why are no numbers boring? This collection answers these questions and many more, setting fun poetry and illustrations against fascinating mathematical ideas in a unique and amusing way. This book will appeal to math-hungry teens and young adults, but also to anyone who enjoys wordplay and mind-bending concepts. Teachers of students at various levels will find content that can be applied to lessons.
Poetic Logic and the Origins of the Mathematical Imagination (Mathematics in Mind)
by Marcel DanesiThis book treats eighteenth-century Italian philosopher Giambattista Vico’s theory of poetic logic for the first time as the originating force in mathematics, transforming instinctive counting and spatial perception into poetic (metaphorical) symbolism that dovetails with the origin of language. It looks at current work on mathematical cognition (from Lakoff and Núñez to Butterworth, Dehaene, and beyond), matching it against the poetic logic paradigm. In a sense, it continues from where Kasner and Newman left off, connecting contemporary research on the mathematical mind to the idea that the products of early mathematics were virtually identical to the first forms of poetic language. As such, this book informs the current research on mathematical cognition from a different angle, by looking back at a still relatively unknown philosopher within mathematics.The aim of this volume is to look broadly at what constitutes the mathematical mind through the Vichian lens of poetic logic. Vico was among the first to suggest that the essential nature of mind could be unraveled indirectly by reconstructing the sources of its “modifications” (his term for “creations”); that is, by examining the creation and function of symbols, words, and all the other uniquely human artifacts—including mathematics—the mind has allowed humans to establish “the world of civil society,” Vico’s term for culture and civilization.The book is of interest to cognitive scientists working on math cognition. It presents the theory of poetic logic as Vico articulated it in his book The New Science, examining its main premises and then applying it to an interpretation of the ongoing work in math cognition. It will also be of interest to the general public, since it presents a history of early mathematics through the lens of an idea that has borne fruit in understanding the origin of language and symbols more broadly.
Poetry of the Universe
by Robert OssermanAn exciting intellectual tour through the ages showing how mathematical concepts and imagination have helped to illuminate the nature of the observable universe, this book is a delightful narrative "math for poets."
Poincare's Prize: The Hundred-Year Quest to Solve One of Math's Greatest Puzzles
by George G. SzpiroThe amazing story of one of the greatest math problems of all time and the reclusive genius who solved itIn the tradition of Fermat's Enigma and Prime Obsession, George Szpiro brings to life the giants of mathematics who struggled to prove a theorem for a century and the mysterious man from St. Petersburg, Grigory Perelman, who fi nally accomplished the impossible.<P><P> In 1904 Henri Poincaré developed the Poincaré Conjecture, an attempt to understand higher-dimensional space and possibly the shape of the universe. The problem was he couldn't prove it. A century later it was named a Millennium Prize problem, one of the seven hardest problems we can imagine. Now this holy grail of mathematics has been found.Accessibly interweaving history and math, Szpiro captures the passion, frustration, and excitement of the hunt, and provides a fascinating portrait of a contemporary noble-genius.
Point Processes (Chapman And Hall/crc Monographs On Statistics And Applied Probability Ser. #12)
by D.R. Cox Valerie IshamThere has been much recent research on the theory of point processes, i.e., on random systems consisting of point events occurring in space or time. Applications range from emissions from a radioactive source, occurrences of accidents or machine breakdowns, or of electrical impluses along nerve fibres, to repetitive point events in an individual's medical or social history. Sometimes the point events occur in space rather than time and the application here raneg from statistical physics to geography. The object of this book is to develop the applied mathemathics of point processes at a level which will make the ideas accessible both to the research worker and the postgraduate student in probability and statistics and also to the mathemathically inclined individual in another field interested in using ideas and results. A thorough knowledge of the key notions of elementary probability theory is required to understand the book, but specialised "pure mathematical" coniderations have been avoided.
Point Processes and Their Statistical Inference (Probability: Pure And Applied Ser. #7)
by Alan KarrFirst Published in 2017. Routledge is an imprint of Taylor & Francis, an Informa company.
Point Set Theory (Chapman And Hall/crc Pure And Applied Mathematics Ser. #131)
by MorganInvestigations by Baire, Lebesgue, Hausdorff, Marczewski, and othes have culminated invarious schemes for classifying point sets. This important reference/text bringstogether in a single theoretical framework the properties common to these classifications.Providing a clear, thorough overview and analysis of the field, Point Set Theoryutilizes the axiomatically determined notion of a category base for extending generaltopological theorems to a higher level of abstraction ... axiomatically unifies analogiesbetween Baire category and Lebesgue measure . .. enhances understanding of thematerial with numerous examples and discussions of abstract concepts ... and more.Imparting a solid foundation for the modem theory of real functions and associated areas,this authoritative resource is a vital reference for set theorists, logicians, analysts, andresearch mathematicians involved in topology, measure theory, or real analysis. It is anideal text for graduate mathematics students in the above disciplines who havecompleted undergraduate courses in set theory and real analysis.
Point-Set Topology: A Working Textbook (Springer Undergraduate Mathematics Series)
by Rafael LópezThis textbook offers a hands-on introduction to general topology, a fundamental tool in mathematics and its applications. It provides solid foundations for further study in mathematics in general, and topology in particular. Aimed at undergraduate students in mathematics with no previous exposure to topology, the book presents key concepts in a mathematically rigorous yet accessible manner, illustrated by numerous examples. The essential feature of the book is the large sets of worked exercises at the end of each chapter. All of the basic topics are covered, namely, metric spaces, continuous maps, homeomorphisms, connectedness, and compactness. The book also explains the main constructions of new topological spaces such as product spaces and quotient spaces. The final chapter makes a foray into algebraic topology with the introduction of the fundamental group. Thanks to nearly 300 solved exercises and abundant examples, Point-Set Topology is especially suitable for supplementing a first lecture course on topology for undergraduates, and it can also be utilized for independent study. The only prerequisites for reading the book are familiarity with mathematical proofs, some elements of set theory, and a good grasp of calculus.
Point Sources and Multipoles in Inverse Scattering Theory (Chapman & Hall/CRC Research Notes in Mathematics Series)
by Roland PotthastOver the last twenty years, the growing availability of computing power has had an enormous impact on the classical fields of direct and inverse scattering. The study of inverse scattering, in particular, has developed rapidly with the ability to perform computational simulations of scattering processes and led to remarkable advances in a range of
Points, Lines, and Surfaces at Criticality (Springer Theses)
by Edoardo LauriaThis thesis offers a fascinating journey through various non-perturbative aspects of Conformal Theories, in particular focusing on the Conformal Bootstrap Programme and its extensions to theories with various degrees of symmetry. Because of the preeminent role of Conformal Theories in Nature, as well as the great generality of the results here obtained, this analysis directly applies to many different areas of research. The content of this thesis is certainly relevant for the physics community as a whole and this relevance is well motivated and discussed along the various chapters of this work.The work is self-contained and starts with an original introduction to conformal theories, defects in such theories and how they lead to constraints on data and an extension of the bootstrap programme. This situation is often realized by critical systems with impurities, topological insulators, or – in the high-energy context – by Wilson and 't Hooft operators. The thesis continues with original research results of the author, including supersymmetric extensions. These results may be relevant non only in the high energy physics context - where supersymmetry is required for the theory to be consistent - but also for condensed matter systems that enjoy supersymmetry emergence at long distances.
The Poisson-Boltzmann Equation: An Introduction (SpringerBriefs in Physics)
by Ralf BlosseyThis brief book introduces the Poisson-Boltzmann equation in three chapters that build upon one another, offering a systematic entry to advanced students and researchers. Chapter one formulates the equation and develops the linearized version of Debye-Hückel theory as well as exact solutions to the nonlinear equation in simple geometries and generalizations to higher-order equations. Chapter two introduces the statistical physics approach to the Poisson-Boltzmann equation. It allows the treatment of fluctuation effects, treated in the loop expansion, and in a variational approach. First applications are treated in detail: the problem of the surface tension under the addition of salt, a classic problem discussed by Onsager and Samaras in the 1930s, which is developed in modern terms within the loop expansion, and the adsorption of a charged polymer on a like-charged surface within the variational approach. Chapter three finally discusses the extension of Poisson-Boltzmann theory to explicit solvent. This is done in two ways: on the phenomenological level of nonlocal electrostatics and with a statistical physics model that treats the solvent molecules as molecular dipoles. This model is then treated in the mean-field approximation and with the variational method introduced in Chapter two, rounding up the development of the mathematical approaches of Poisson-Boltzmann theory. After studying this book, a graduate student will be able to access the research literature on the Poisson-Boltzmann equation with a solid background.
Poisson Hyperplane Tessellations (Springer Monographs in Mathematics)
by Rolf Schneider Daniel HugThis book is the first comprehensive presentation of a central topic of stochastic geometry: random mosaics that are generated by Poisson processes of hyperplanes. It thus connects a basic notion from probability theory, Poisson processes, with a fundamental object of geometry. The independence properties of Poisson processes and the long-range influence of hyperplanes lead to a wide range of phenomena which are of interest from both a geometric and a probabilistic point of view. A Poisson hyperplane tessellation generates many random polytopes, also a much-studied object of stochastic geometry. The book offers a variety of different perspectives and covers in detail all aspects studied in the original literature. The work will be useful to graduate students (advanced students in a Master program, PhD students), and professional mathematicians. The book can also serve as a reference for researchers in fields of physics, computer science, economics or engineering.
Poisson Point Processes
by Roy L. Streit"Poisson Point Processes provides an overview of non-homogeneous and multidimensional Poisson point processes and their numerous applications. Readers will find constructive mathematical tools and applications ranging from emission and transmission computed tomography to multiple target tracking and distributed sensor detection, written from an engineering perspective. A valuable discussion of the basic properties of finite random sets is included. Maximum likelihood estimation techniques are discussed for several parametric forms of the intensity function, including Gaussian sums, together with their Cramer-Rao bounds. These methods are then used to investigate: -Several medical imaging techniques, including positron emission tomography (PET), single photon emission computed tomography (SPECT), and transmission tomography (CT scans) -Various multi-target and multi-sensor tracking applications, -Practical applications in areas like distributed sensing and detection, -Related finite point processes such as marked processes, hard core processes, cluster processes, and doubly stochastic processes, Perfect for researchers, engineers and graduate students working in electrical engineering and computer science, Poisson Point Processes will prove to be an extremely valuable volume for those seeking insight into the nature of these processes and their diverse applications.
Poisson Point Processes and Their Application to Markov Processes
by Kiyosi ItôAn extension problem (often called a boundary problem) of Markov processes has been studied, particularly in the case of one-dimensional diffusion processes, by W. Feller, K. Itô, and H. P. McKean, among others. In this book, Itô discussed a case of a general Markov process with state space S and a specified point a ∈ S called a boundary. The problem is to obtain all possible recurrent extensions of a given minimal process (i. e. , the process on S \ {{a}} which is absorbed on reaching the boundary a). The study in this lecture is restricted to a simpler case of the boundary a being a discontinuous entrance point, leaving a more general case of a continuous entrance point to future works. He established a one-to-one correspondence between a recurrent extension and a pair of a positive measure k(db) on S \ {{a}} (called the jumping-in measure and a non-negative number m< (called the stagnancy rate). The necessary and sufficient conditions for a pair k, m was obtained so that the correspondence is precisely described. For this, Itô used, as a fundamental tool, the notion of Poisson point processes formed of all excursions of the process on S \ {{a}}. This theory of Itô's of Poisson point processes of excursions is indeed a breakthrough. It has been expanded and applied to more general extension problems by many succeeding researchers. Thus we may say that this lecture note by Itô is really a memorial work in the extension problems of Markov processes. Especially in Chapter 1 of this note, a general theory of Poisson point processes is given that reminds us of Itô's beautiful and impressive lectures in his day.
Polar Bear Math: Learning About Fractions from Klondike and Snow
by Ann Whitehead Nagda Cindy Bickel<p><i>That night Cindy took the tiny cubs home with her. She didn't sleep at all-she was too busy feeding milk to the twins, cleaning them, and checking on every little cry. When dawn came, the small bears were still clinging to life.</i> <p>Children learn about fractions while following the Denver Zoo's baby polar bears, Klondike and Snow <p>Early one morning at the Denver Zoo, a polar bear gives birth to two tiny babies, then abandons them. <p>The zoo staff must raise the babies, but there are many things they don't know. What foods are best? How much should the cubs eat? Once they figure out the answers, the cubs quickly become healthy, happy young bears. <p>Young readers follow Klondike and Snow as they grow from fragile newborns to large, lively bears, and along the way they'll learn about fractions.</p>
Polarization and CP Violation Measurements
by Michael PrimThis thesis describes the thorough analysis of the rare B meson decay into ϕ K* on data taken by the Belle Collaboration at the B-meson-factory KEKB over 10 years. This reaction is very interesting, because it in principle allows the observation of CP-violation effects. In the Standard Model however, no CP violation in this reaction is expected. An observation of CP asymmetries thus immediately implies new physics. This thesis presents an amplitude analysis of this decay and the search for CP violation in detail and discusses methods to solve related problems: The quantification of multivariate dependence and the improvement of numeric evaluation speed of normalization integrals in amplitude analysis. In addition it provides an overview of the theory, experimental setup, (blind) statistical data analysis and estimation of systematic uncertainties.
Polarization Theory of Nuclear Reactions
by Qing-Biao ShenThis book provides the reader with a modern and comprehensive overview of nuclear polarization theory. The understanding of polarization phenomena greatly enriches data obtained from scattering and nuclear reactions by providing information on the interaction that can change spin orientation as well as important verification data for the study of nuclear structures and reaction mechanisms. The author methodically derives the polarization theory of nuclear reactions for various types of elastic scattering and two-body direct reactions between particles of different spin and unpolarized target nuclei with arbitrary spin, as well as the reactions between two polarized light particles and the polarization theory for photon beams. In addition, the polarization theories of relativistic nuclear reactions are rigorously covered in great scope and detail. A chapter on polarized particle transport theory presents the Monte-Carlo method for describing the transport of polarized particles and formalizes the polarized particle transport equation. Here, the author also illustrates a novel and concrete scheme for establishing a polarization nuclear database. Nuclear polarization is important not only for microscopic nuclear structure and reaction studies but also for nuclear engineering, applied nuclear physics, and medical physics. With the development of radioactive beam facilities and, on the theoretical side, the development of consistent microscopic nuclear reaction and structure theories, this book on the polarization theory of nuclear reactions serves as a timely source of reference for students and researchers alike.
Polarized Light and the Mueller Matrix Approach (Series in Optics and Optoelectronics)
by José J. Gil Razvigor OssikovskiAn Up-to-Date Compendium on the Physics and Mathematics of Polarization Phenomena Now thoroughly revised, Polarized Light and the Mueller Matrix Approach cohesively integrates basic concepts of polarization phenomena from the dual viewpoints of the states of polarization of electromagnetic waves and the transformations of these states by the action of material media. Through selected examples, it also illustrates actual and potential applications in materials science, biology, and optics technology. The book begins with the basic concepts related to two- and three-dimensional polarization states. It next describes the nondepolarizing linear transformations of the states of polarization through the Jones and Mueller-Jones approaches. The authors then discuss the forms and properties of the Jones and Mueller matrices associated with different types of nondepolarizing media, address the foundations of the Mueller matrix, and delve more deeply into the analysis of the physical parameters associated with Mueller matrices. The authors proceed with introducing the arbitrary decomposition and other useful parallel decompositions, and compare the powerful serial decompositions of depolarizing Mueller matrices. They also analyze the general formalism and specific algebraic quantities and notions related to the concept of differential Mueller matrix. Useful approaches that provide a geometric point of view on the polarization effects exhibited by different types of media are also comprehensively described. The book concludes with a new chapter devoted to the main procedures for filtering measured Mueller matrices. Suitable for advanced graduates and more seasoned professionals, this book covers the main aspects of polarized radiation and polarization effects of material media. It expertly combines physical and mathematical concepts with important approaches for representing media through equivalent systems composed of simple components.
Polarized Light and the Mueller Matrix Approach (Series in Optics and Optoelectronics)
by Jose Jorge Perez Razvigor OssikovskiAn Up-to-Date Compendium on the Physics and Mathematics of Polarization Phenomena Polarized Light and the Mueller Matrix Approach thoroughly and cohesively integrates basic concepts of polarization phenomena from the dual viewpoints of the states of polarization of electromagnetic waves and the transformations of these states by the action of material media. Through selected examples, it also illustrates actual and potential applications in materials science, biology, and optics technology. The book begins with the basic concepts related to two- and three-dimensional polarization states. It next describes the nondepolarizing linear transformations of the states of polarization through the Jones and Mueller–Jones approaches. The authors then discuss the forms and properties of the Jones and Mueller matrices associated with different types of nondepolarizing media, address the foundations of the Mueller matrix, and delve more deeply into the analysis of the physical parameters associated with Mueller matrices. The authors proceed to interpret arbitrary decomposition and other interesting parallel decompositions as well as compare the powerful serial decompositions of depolarizing Mueller matrix M. They also analyze the general formalism and specific algebraic quantities and notions related to the concept of differential Mueller matrix. The book concludes with useful approaches that provide a geometric point of view on the polarization effects exhibited by different types of media. Suitable for novices and more seasoned professionals, this book covers the main aspects of polarized radiation and polarization effects of material media. It expertly combines physical and mathematical concepts with important approaches for representing media through equivalent systems composed of simple components.