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Period Mappings with Applications to Symplectic Complex Spaces
by Tim KirschnerExtending Griffiths' classical theory of period mappings for compact Kähler manifolds, this book develops and applies a theory of period mappings of "Hodge-de Rham type" for families of open complex manifolds. The text consists of three parts. The first part develops the theory. The second part investigates the degeneration behavior of the relative Frölicher spectral sequence associated to a submersive morphism of complex manifolds. The third part applies the preceding material to the study of irreducible symplectic complex spaces. The latter notion generalizes the idea of an irreducible symplectic manifold, dubbed an irreducible hyperkähler manifold in differential geometry, to possibly singular spaces. The three parts of the work are of independent interest, but intertwine nicely.
Periodic Character and Patterns of Recursive Sequences
by Michael A. RadinThis textbook on periodic character and patterns of recursive sequences focuses on discrete periodic patterns of first order, second order and higher order difference equations. Aimed toward advanced undergraduate students and graduate students who have taken a basic course in Calculus I and Discrete Mathematics, this book serves as a core text for a course in Difference Equations and Discrete Dynamical Systems. The text contains over 200 exercises to provide readers with a hands-on experience working with the material; the exercises include computations of specific examples and proofs of general results. Readers will receive a first-hand introduction to patterns of periodic cycles and patterns of transient terms with exercises for most sections of the text, preparing them for significant research work in the area.
Periodic Feedback Stabilization for Linear Periodic Evolution Equations
by Gengsheng Wang Yashan XuThis book introduces a number of recent advances regarding periodic feedback stabilization for linear and time periodic evolution equations. First, it presents selected connections between linear quadratic optimal control theory and feedback stabilization theory for linear periodic evolution equations. Secondly, it identifies several criteria for the periodic feedback stabilization from the perspective of geometry, algebra and analyses respectively. Next, it describes several ways to design periodic feedback laws. Lastly, the book introduces readers to key methods for designing the control machines. Given its coverage and scope, it offers a helpful guide for graduate students and researchers in the areas of control theory and applied mathematics.
Periodic Monopoles and Difference Modules (Lecture Notes in Mathematics #2300)
by Takuro MochizukiThis book studies a class of monopoles defined by certain mild conditions, called periodic monopoles of generalized Cherkis–Kapustin (GCK) type. It presents a classification of the latter in terms of difference modules with parabolic structure, revealing a kind of Kobayashi–Hitchin correspondence between differential geometric objects and algebraic objects. It also clarifies the asymptotic behaviour of these monopoles around infinity.The theory of periodic monopoles of GCK type has applications to Yang–Mills theory in differential geometry and to the study of difference modules in dynamical algebraic geometry. A complete account of the theory is given, including major generalizations of results due to Charbonneau, Cherkis, Hurtubise, Kapustin, and others, and a new and original generalization of the nonabelian Hodge correspondence first studied by Corlette, Donaldson, Hitchin and Simpson.This work will be of interest to graduate students and researchers in differential and algebraic geometry, as well as in mathematical physics.
Periodic Review Inventory Systems
by Thomas WensingThe focus of the work is twofold. First, it provides an introduction into fundamental structural and behavioral aspects of periodic review inventory systems. Second, it includes a comprehensive study on analytical and optimization aspects of a specific class of those systems. For the latter purpose, general solution methods for problems of inventory management in discrete time are described and developed along with highly specialized methods to solve very specific problems related to the model variants examined. The work is thus addressed to students and practitioners who seek a deeper understanding of managing inventories in discrete time as well as to software developers who require implementation aids on specific problems of inventory management.
Periodic Solutions of First-Order Functional Differential Equations in Population Dynamics
by Seshadev Padhi John R. Graef P D N SrinivasuThis book provides cutting-edge results on the existence of multiple positive periodic solutions of first-order functional differential equations. It demonstrates how the Leggett-Williams fixed-point theorem can be applied to study the existence of two or three positive periodic solutions of functional differential equations with real-world applications, particularly with regard to the Lasota-Wazewska model, the Hematopoiesis model, the Nicholsons Blowflies model, and some models with Allee effects. Many interesting sufficient conditions are given for the dynamics that include nonlinear characteristics exhibited by population models. The last chapter provides results related to the global appeal of solutions to the models considered in the earlier chapters. The techniques used in this book can be easily understood by anyone with a basic knowledge of analysis. This book offers a valuable reference guide for students and researchers in the field of differential equations with applications to biology, ecology, and the environment.
Periodicities in Nonlinear Difference Equations
by E.A. Grove G. LadasSharkovsky's Theorem, Li and Yorke's "period three implies chaos" result, and the (3x+1) conjecture are beautiful and deep results that demonstrate the rich periodic character of first-order, nonlinear difference equations. To date, however, we still know surprisingly little about higher-order nonlinear difference equations. During the last
Periods and Nori Motives
by Annette Huber Stefan Müller-StachThis book casts the theory of periods of algebraic varieties in the natural setting of Madhav Nori's abelian category of mixed motives. It develops Nori's approach to mixed motives from scratch, thereby filling an important gap in the literature, and then explains the connection of mixed motives to periods, including a detailed account of the theory of period numbers in the sense of Kontsevich-Zagier and their structural properties. Period numbers are central to number theory and algebraic geometry, and also play an important role in other fields such as mathematical physics. There are long-standing conjectures about their transcendence properties, best understood in the language of cohomology of algebraic varieties or, more generally, motives. Readers of this book will discover that Nori's unconditional construction of an abelian category of motives (over fields embeddable into the complex numbers) is particularly well suited for this purpose. Notably, Kontsevich's formal period algebra represents a torsor under the motivic Galois group in Nori's sense, and the period conjecture of Kontsevich and Zagier can be recast in this setting. Periods and Nori Motives is highly informative and will appeal to graduate students interested in algebraic geometry and number theory as well as researchers working in related fields. Containing relevant background material on topics such as singular cohomology, algebraic de Rham cohomology, diagram categories and rigid tensor categories, as well as many interesting examples, the overall presentation of this book is self-contained.
Periods in Quantum Field Theory and Arithmetic: ICMAT, Madrid, Spain, September 15 – December 19, 2014 (Springer Proceedings in Mathematics & Statistics #314)
by Kurusch Ebrahimi-Fard José Ignacio Burgos Gil Herbert GanglThis book is the outcome of research initiatives formed during the special ``Research Trimester on Multiple Zeta Values, Multiple Polylogarithms, and Quantum Field Theory'' at the ICMAT (Instituto de Ciencias Matemáticas, Madrid) in 2014. The activity was aimed at understanding and deepening recent developments where Feynman and string amplitudes on the one hand, and periods and multiple zeta values on the other, have been at the heart of lively and fruitful interactions between theoretical physics and number theory over the past few decades. In this book, the reader will find research papers as well as survey articles, including open problems, on the interface between number theory, quantum field theory and string theory, written by leading experts in the respective fields. Topics include, among others, elliptic periods viewed from both a mathematical and a physical standpoint; further relations between periods and high energy physics, including cluster algebras and renormalisation theory; multiple Eisenstein series and q-analogues of multiple zeta values (also in connection with renormalisation); double shuffle and duality relations; alternative presentations of multiple zeta values using Ecalle's theory of moulds and arborification; a distribution formula for generalised complex and l-adic polylogarithms; Galois action on knots. Given its scope, the book offers a valuable resource for researchers and graduate students interested in topics related to both quantum field theory, in particular, scattering amplitudes, and number theory.
Perl Testing: A Developer's Notebook
by Ian LangworthIs there any sexier topic in software development than software testing? That is, besides game programming, 3D graphics, audio, high-performance clustering, cool websites, et cetera? Okay, so software testing is low on the list. And that's unfortunate, because good software testing can increase your productivity, improve your designs, raise your quality, ease your maintenance burdens, and help to satisfy your customers, coworkers, and managers. Perl has a strong history of automated tests. A very early release of Perl 1.0 included a comprehensive test suite, and it's only improved from there. Learning how Perl's test tools work and how to put them together to solve all sorts of previously intractable problems can make you a better programmer in general. Besides, it's easy to use the Perl tools described to handle all sorts of testing problems that you may encounter, even in other languages. Like all titles in O'Reilly's Developer's Notebook series, this "all lab, no lecture" book skips the boring prose and focuses instead on a series of exercises that speak to you instead of at you. Perl Testing: A Developer's Notebook will help you dive right in and: Write basic Perl tests with ease and interpret the results Apply special techniques and modules to improve your tests Bundle test suites along with projects Test databases and their data Test websites and web projects Use the "Test Anything Protocol" which tests projects written in languages other than Perl With today's increased workloads and short development cycles, unit tests are more vital to building robust, high-quality software than ever before. Once mastered, these lessons will help you ensure low-level code correctness, reduce software development cycle time, and ease maintenance burdens. You don't have to be a die-hard free and open source software developer who lives, breathes, and dreams Perl to use this book. You just have to want to do your job a little bit better.
Perl Testing: A Developer's Notebook
by Ian Langworth ChromaticIs there any sexier topic in software development than software testing? That is, besides game programming, 3D graphics, audio, high-performance clustering, cool websites, et cetera? Okay, so software testing is low on the list. And that's unfortunate, because good software testing can increase your productivity, improve your designs, raise your quality, ease your maintenance burdens, and help to satisfy your customers, coworkers, and managers.Perl has a strong history of automated tests. A very early release of Perl 1.0 included a comprehensive test suite, and it's only improved from there. Learning how Perl's test tools work and how to put them together to solve all sorts of previously intractable problems can make you a better programmer in general. Besides, it's easy to use the Perl tools described to handle all sorts of testing problems that you may encounter, even in other languages.Like all titles in O'Reilly's Developer's Notebook series, this "all lab, no lecture" book skips the boring prose and focuses instead on a series of exercises that speak to you instead of at you. Perl Testing: A Developer's Notebook will help you dive right in and:Write basic Perl tests with ease and interpret the resultsApply special techniques and modules to improve your testsBundle test suites along with projectsTest databases and their dataTest websites and web projectsUse the "Test Anything Protocol" which tests projects written in languages other than PerlWith today's increased workloads and short development cycles, unit tests are more vital to building robust, high-quality software than ever before. Once mastered, these lessons will help you ensure low-level code correctness, reduce software development cycle time, and ease maintenance burdens. You don't have to be a die-hard free and open source software developer who lives, breathes, and dreams Perl to use this book. You just have to want to do your job a little bit better.
Perlen der Mathematik: 20 geometrische Figuren als Ausgangspunkte für mathematische Erkundungsreisen
by Claudi Alsina Roger B. NelsenDieses Buch handelt von 20 geometrischen Figuren (Icons), die eine wichtige Rolle bei der Veranschaulichung mathematischer Beweise spielen. Alsina und Nelsen untersuchen die Mathematik, die hinter diesen Figuren steckt und die sich aus ihnen ableiten lässt.Jedem in diesem Buch behandelten Icons ist ein eigenes Kapitel gewidmet, in dem sein Alltagsbezug, seine wesentlichen mathematischen Eigenschaften sowie seine Bedeutung für visuelle Beweise vieler mathematischer Sätze betont werden. Diese Sätze umfassen unter anderem auch klassische Ergebnisse aus der ebenen Geometrie, Eigenschaften der natürlichen Zahlen, Mittelwerte und Ungleichungen, Beziehungen zwischen Winkelfunktionen, Sätze aus der Differenzial- und Integralrechnung sowie Rätsel aus dem Bereich der Unterhaltungsmathematik. Darüber hinaus enthält jedes Kapitel eine Auswahl an Aufgaben, anhand derer die Leser weitere Eigenschaften und Anwendungen der Diagramme erkunden können.Das Buch ist für alle geschrieben, die Freude an der Mathematik haben; Lehrkräfte und Dozenten der Mathematik werden in diesem Buch sehr nützliche Beispiele für Problemlösungen sowie umfangreiches Unterrichts- und Seminarmaterial zu Beweisen und mathematischer Argumentation finden.
Permittivity and Permeability Tensors for Cloaking Applications
by Balamati Choudhury Pavani Vijay Reddy Rakesh Mohan JhaThis book is focused on derivations of analytical expressions for stealth and cloaking applications. An optimal version of electromagnetic (EM) stealth is the design of invisibility cloak of arbitrary shapes in which the EM waves can be controlled within the cloaking shell by introducing a prescribed spatial variation in the constitutive parameters. The promising challenge in design of invisibility cloaks lies in the determination of permittivity and permeability tensors for all the layers. This book provides the detailed derivation of analytical expressions of the permittivity and permeability tensors for various quadric surfaces within the eleven Eisenhart co-ordinate systems. These include the cylinders and the surfaces of revolutions. The analytical modeling and spatial metric for each of these surfaces are provided along with their tensors. This mathematical formulation will help the EM designers to analyze and design of various quadratics and their hybrids, which can eventually lead to design of cloaking shells of arbitrary shapes.
Permutation Groups (Dover Books on Mathematics)
by Donald S. PassmanThis volume by a prominent authority on permutation groups consists of lecture notes that provide a self-contained account of distinct classification theorems. A ready source of frequently quoted but usually inaccessible theorems, it is ideally suited for professional group theorists as well as students with a solid background in modern algebra.The three-part treatment begins with an introductory chapter and advances to an economical development of the tools of basic group theory, including group extensions, transfer theorems, and group representations and characters. The final chapter features thorough discussions of the work of Zassenhaus on Frobenius elements and sharply transitive groups in addition to an exploration of Huppert's findings on solvable doubly transitive groups.
Permutation Groups and Cartesian Decompositions (London Mathematical Society Lecture Note Ser. #449)
by Cheryl E. Praeger Csaba SchneiderPermutation groups, their fundamental theory and applications are discussed in this introductory book. It focuses on those groups that are most useful for studying symmetric structures such as graphs, codes and designs. Modern treatments of the O'Nan–Scott theory are presented not only for primitive permutation groups but also for the larger families of quasiprimitive and innately transitive groups, including several classes of infinite permutation groups. Their precision is sharpened by the introduction of a cartesian decomposition concept. This facilitates reduction arguments for primitive groups analogous to those, using orbits and partitions, that reduce problems about general permutation groups to primitive groups. The results are particularly powerful for finite groups, where the finite simple group classification is invoked. Applications are given in algebra and combinatorics to group actions that preserve cartesian product structures. Students and researchers with an interest in mathematical symmetry will find the book enjoyable and useful.
Permutation Statistical Methods
by Kenneth J. Berry Paul W. Mielke Janis E. JohnstonThis researchmonograph provides a synthesis of a number of statistical tests and measures,which, at first consideration, appear disjoint and unrelated. Numerouscomparisons of permutation and classical statistical methods are presented, andthe two methods are compared via probability values and, where appropriate,measures of effect size. Permutationstatistical methods, compared to classical statistical methods, do not rely ontheoretical distributions, avoid the usual assumptions of normality andhomogeneity of variance, and depend only on the data at hand. This text takes aunique approach to explaining statistics by integrating a large variety ofstatistical methods, and establishing the rigor of a topic that to many mayseem to be a nascent field in statistics. This topic is new in that it tookmodern computing power to make permutation methods available to people working inthe mainstream of research.
Permutation Testing for Isotonic Inference on Association Studies in Genetics
by Rosa Arboretti Livio Corain Luigi Salmaso Dario MazzaroThe purpose of this book is to illustrate a new statistical approach to test allelic association and genotype-specific effects in the genetic study of diseases. There are some parametric and non-parametric methods available for this purpose. We deal with population-based association studies, but comparisons with other methods will also be drawn, analysing the advantages and disadvantages of each one, particularly with regard to power properties with small sample sizes. In this framework we will work out some nonparametric statistical permutation tests and likelihood-based tests to perform case-control analyses to study allelic association between marker, disease-gene and environmental factors. Permutation tests, in particular, will be extended to multivariate and more complex studies, where we deal with several genes and several alleles together. Furthermore, we show simulations under different assumptions on the genetic model and analyse real data sets by simply studying one locus with the permutation test.
Permutation Tests in Shape Analysis
by Chiara Brombin Luigi SalmasoStatistical shape analysis is a geometrical analysis from a set of shapes in which statistics are measured to describe geometrical properties from similar shapes or different groups, for instance, the difference between male and female Gorilla skull shapes, normal and pathological bone shapes, etc. Some of the important aspects of shape analysis are to obtain a measure of distance between shapes, to estimate average shapes from a (possibly random) sample and to estimate shape variability in a sample[1]. One of the main methods used is principal component analysis. Specific applications of shape analysis may be found in archaeology, architecture, biology, geography, geology, agriculture, genetics, medical imaging, security applications such as face recognition, entertainment industry (movies, games), computer-aided design and manufacturing. This is a proposal for a new Brief on statistical shape analysis and the various new parametric and non-parametric methods utilized to facilitate shape analysis.
¿Pero esto también es matemática?
by Adrián Paenza¡Todo es matemática! Máquinas tragaperras, claves secretas, laberintos, puentes flexibles y moscas que vuelan rápido como trenes. ¡Estamos rodeados de números! Fechas de nacimiento, números de documentos, id del ordenador, teléfonos... Números que repetimos automáticamente y comienzan a tener sentido cuando los asociamos y logramos pensar de forma distinta. En ese momento aprendemos a educar la intuición y encontramos soluciones inesperadas. Desde cómo mejorar el tráfico en una gran ciudad hasta cómo realizar menos pasos para montar un rompecabezas. Desde cómo elegir una clave bancaria segura hasta cómo encontrar la estrategia adecuada para no perder nunca a las damas o adivinar un número o una carta. La lógica matemática envuelve todos nuestros actos cotidianos y es mucho más divertida de lo que imaginábamos. Adrián Paenza nos invita a sumergirnos en el mundo de las matemáticas recreativas, de la matemagia. Un universo donde se aprende jugando.
Perplexing Paradoxes: Unraveling Enigmas in the World Around Us
by George G. SzpiroWhy does it always seem like the elevator is going down when you need to go up? Is it really true that 0.99999 . . . with an infinite number of 9s after the decimal point, is equal to 1? What do tea leaves and river erosion have in common, per Albert Einstein? Does seeing a bed of red flowers help prove that all ravens are black? Can we make sense of a phrase like “this statement is unprovable”?Exploring these questions and many more, George G. Szpiro guides readers through the puzzling world of paradoxes, from Socratic dialogues to the Monty Hall problem. Perplexing Paradoxes presents sixty counterintuitive conundrums drawn from diverse areas of thought—not only mathematics, statistics, logic, and philosophy but also social science, physics, politics, and religion. Szpiro offers a brisk history of each paradox, unpacks its inner workings, and considers where one might encounter it in daily life. Ultimately, he argues, paradoxes are not simple brain teasers or abstruse word games—they challenge us to hone our reasoning and become more alert to the flaws in received wisdom and common habits of thought.Lighthearted, witty, and conversational, Perplexing Paradoxes presents sophisticated material in an accessible way for all readers interested in the world’s boundless possibilities—and impossibilities.
Person-Centered Methods
by Mark StemmlerThis book takes an easy-to-understand look at the statistical approach called the person-centered method. Instead of analyzing means, variances and covariances of scale scores as in the common variable-centered approach, the person-centered approach analyzes persons or objects grouped according to their characteristic patterns or configurations in contingency tables. The main focus of the book will be on Configural Frequency Analysis (CFA; Lienert and Krauth, 1975) which is a statistical method that looks for over and under-frequented cells or patterns. Over frequented means that the observations in this cell or configuration are observed more often than expected, under-frequented means that this cell or configuration is observed less often than expected. In CFA a pattern or configuration that contains more observed cases than expected is called a type; similarly, a pattern or configuration that is less observed than expected are called an antitype. CFA is similar to log-linear modeling. In log-linear modeling the goal is to come up with a fitting model including all important variables. Instead of fitting a model, CFA looks at the significant residuals of a log-linear model. The book describes the use of an R-package called confreq (derived from Configural Frequency Analysis). The use of the software package is described and demonstrated with data examples.
Person-Centered Methods: Configural Frequency Analysis (CFA) and Other Methods for the Analysis of Contingency Tables (SpringerBriefs in Statistics)
by Mark StemmlerThis book offers a comprehensible overview of the statistical approach called the person-centered method. Instead of analyzing means, variances and covariances of scale scores as in the common variable-centered approach, the person-centered approach analyzes persons or objects grouped according to their characteristic patterns or configurations in contingency tables. This second edition explores the relationship between two statistical methods: log-linear modeling (LLM) and configural frequency analysis (CFA). Both methods compare expected frequencies with observed frequencies. However, while LLM searches for the underlying dependencies of the involved variables in the data (model-fitting), CFA examines significant residuals in non-fitting models. New developments in the second edition include: Configural Mediation Models, CFA with covariates, moderator CFA, and CFA modeling branches in tree-based methods. The new developments enable the use of categorical together with continuous variables, which makes CFA a very powerful statistical tool. This new edition continues to utilize R-package confreq (derived from Configural Frequency Analysis), much updated since the first edition and newly adjusted to the new R base program 4.0. An electronic supplement is now available with 18 R-scripts and many datasets.
Persona – über die Funktion der Maske in den Künsten: Ein Vergleich zwischen Theater, Computerspiel und sozialem Rollenspiel (Simulatio. Theatertechniken in Literatur, Medien und Wissenschaft)
by Kirsten Dickhaut Daniel Martin Feige Sven Thorsten KilianDer Sammelband thematisiert Masken und Maskierungen. Im Vergleich der Künste untersucht er die funktionale Verwendung dieses Theaterrequisits, das eine Technik impliziert, und die Ausgestaltungen von Persona in den Künsten, Maskenverwendungen, -gestaltungen und -problematisierungen, die stets die Produktion von Fiktion und/oder Simulation reflektieren. Zehn Beiträge analysieren Beispiele seit dem 18. Jahrhundert der bildenden Kunst, des Digitalen, des Computerspiels, des Theaters, der erzählenden Literatur und der sozialen Rolle, die jeweils die Maske als Fiktions- oder Simulationsgenerator verstehen, thematisieren und kulturell vergleichend beschreiben. Pirandello stellt dabei grundsätzlich einen wichtigen, aber nicht den einzigen Referenzpunkt dar.
Personal Financial Literacy
by Joan S. RyanLearn how to plan and manage your personal finances, achieve a financially successful life, and take responsibility as a citizen. PERSONAL FINANCIAL LITERACY is aligned with the Jump$tart Coalition's National Standards for Personal Financial Literacy. The personal focus of this course makes it relevant and meaningful to all; in particular, to those just starting down the path to personal financial independence.