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Polyadic Groups
by Wieslaw A. DudekThis book provides a general, unified approach to the theory of polyadic groups, their normal subgroups and matrix representations.The author focuses on those properties of polyadic groups which are not present in the binary case. These properties indicate a strong relationship between polyadic groups and various group-like algebras, as well as ternary Hopf algebras and n-Lie algebras that are widely used in theoretical physics.The relationships of polyadic groups with special types of binary groups, called covering groups and binary retracts, are described. These relationships allow the study of polyadic groups using these binary groups and their automorphisms.The book also describes the affine geometry induced by polyadic groups and fuzzy subsets defined on polyadic groups. Finally, we discuss the categories of polyadic groups and the relationships between the different varieties of polyadic groups. In many cases, we give elegant new proofs of known theorems. We also give many interesting examples and applications.The book contains many little-known results from articles previously published in hard-to-reach Russian, Ukrainian and Macedonian journals. These articles are not in English.
Polygons Galore: A Mathematics Unit for High-Ability Learners in Grades 3-5
by Clg Of William And Mary/Ctr Gift Ed Marguerite M. Mason Jill AdelsonPolygons Galore! is a mathematics unit for high-ability learners in grades 3-5 focusing on 2-D and 3-D components of geometry by exploring polygons and polyhedra and their properties. The van Hiele levels of geometric understanding provide conceptual underpinnings for unit activities. The unit consists of nine lessons that include student discovery of properties of polygons and polyhedra, investigations for finding areas of triangles and quadrilaterals, study of the Platonic solids, and real-world applications of polygons and polyhedra. It also includes activities related to identifying, comparing, and analyzing polygons by using properties of the polygons; constructing meanings for geometric terms; developing strategies to find areas of specific polygons; identifying and building regular and nonregular polyhedra; and recognizing geometric ideas and relationships as applied in daily life and in other disciplines, such as art.Grades 3-5
Polyhedra and Beyond: Contributions from Geometrias’19, Porto, Portugal, September 05-07 (Trends in Mathematics)
by Vera Viana Helena Mena Matos João Pedro XavierThis volume collects papers based on talks given at the conference “Geometrias'19: Polyhedra and Beyond”, held in the Faculty of Sciences of the University of Porto between September 5-7, 2019 in Portugal. These papers explore the conference’s theme from an interdisciplinary standpoint, all the while emphasizing the relevance of polyhedral geometry in contemporary academic research and professional practice. They also investigate how this topic connects to mathematics, art, architecture, computer science, and the science of representation. Polyhedra and Beyond will help inspire scholars, researchers, professionals, and students of any of these disciplines to develop a more thorough understanding of polyhedra.
Polyhedral and Algebraic Methods in Computational Geometry
by Michael Joswig Thorsten TheobaldPolyhedral and Algebraic Methods in Computational Geometry provides a thorough introduction into algorithmic geometry and its applications. It presents its primary topics from the viewpoints of discrete, convex and elementary algebraic geometry. The first part of the book studies classical problems and techniques that refer to polyhedral structures. The authors include a study on algorithms for computing convex hulls as well as the construction of Voronoi diagrams and Delone triangulations. The second part of the book develops the primary concepts of (non-linear) computational algebraic geometry. Here, the book looks at Gröbner bases and solving systems of polynomial equations. The theory is illustrated by applications in computer graphics, curve reconstruction and robotics. Throughout the book, interconnections between computational geometry and other disciplines (such as algebraic geometry, optimization and numerical mathematics) are established. Polyhedral and Algebraic Methods in Computational Geometry is directed towards advanced undergraduates in mathematics and computer science, as well as towards engineering students who are interested in the applications of computational geometry.
Polyhedral Methods in Geosciences (SEMA SIMAI Springer Series #27)
by Daniele Antonio Di Pietro Luca Formaggia Roland MassonThe last few years have witnessed a surge in the development and usage of discretization methods supporting general meshes in geoscience applications. The need for general polyhedral meshes in this context can arise in several situations, including the modelling of petroleum reservoirs and basins, CO2 and nuclear storage sites, etc. In the above and other situations, classical discretization methods are either not viable or require ad hoc modifications that add to the implementation complexity. Discretization methods able to operate on polyhedral meshes and possibly delivering arbitrary-order approximations constitute in this context a veritable technological jump. The goal of this monograph is to establish a state-of-the-art reference on polyhedral methods for geoscience applications by gathering contributions from top-level research groups working on this topic. This book is addressed to graduate students and researchers wishing to deepen their knowledge of advanced numerical methods with a focus on geoscience applications, as well as practitioners of the field.
Polymers for Electronic Applications
by J.H. LaiThe object of this book is to review and to discuss some important applications of polymers in electronics. The first three chapters discuss the current primary applications of polymers in semiconductor device manufacturing: polymers as resist materials for integrated circuit fabrication, polyimides as electronics packaging materials, and polymers as integrated circuits encapsulates.
A Polynomial Approach to Linear Algebra (Universitext)
by Paul A. FuhrmannA Polynomial Approach to Linear Algebra is a text which is heavily biased towards functional methods. In using the shift operator as a central object, it makes linear algebra a perfect introduction to other areas of mathematics, operator theory in particular. This technique is very powerful as becomes clear from the analysis of canonical forms (Frobenius, Jordan). It should be emphasized that these functional methods are not only of great theoretical interest, but lead to computational algorithms. Quadratic forms are treated from the same perspective, with emphasis on the important examples of Bezoutian and Hankel forms. These topics are of great importance in applied areas such as signal processing, numerical linear algebra, and control theory. Stability theory and system theoretic concepts, up to realization theory, are treated as an integral part of linear algebra. This new edition has been updated throughout, in particular new sections have been added on rational interpolation, interpolation using H^{\nfty} functions, and tensor products of models. Review from first edition: "...the approach pursed by the author is of unconventional beauty and the material covered by the book is unique." (Mathematical Reviews)
Polynomial Automorphisms and the Jacobian Conjecture: New Results from the Beginning of the 21st Century (Frontiers in Mathematics #190)
by Arno van den Essen Shigeru Kuroda Anthony J. CrachiolaThis book is an extension to Arno van den Essen's Polynomial Automorphisms and the Jacobian Conjecture published in 2000. Many new exciting results have been obtained in the past two decades, including the solution of Nagata's Conjecture, the complete solution of Hilbert's fourteenth problem, the equivalence of the Jacobian Conjecture and the Dixmier Conjecture, the symmetric reduction of the Jacobian Conjecture, the theory of Mathieu-Zhao spaces and counterexamples to the Cancellation problem in positive characteristic. These and many more results are discussed in detail in this work.The book is aimed at graduate students and researchers in the field of Affine Algebraic Geometry. Exercises are included at the end of each section.
Polynomial Formal Verification of Approximate Functions (BestMasters)
by Martha SchnieberDuring the development of digital circuits, their functional correctness has to be ensured, for which formal verification methods have been established. However, the verification process using formal methods can have an exponential time or space complexity, causing the verification to fail. While exponential in general, recently it has been proven that the verification complexity of several circuits is polynomially bounded. Martha Schnieber proves the polynomial verifiability of several approximate circuits, which are beneficial in error-tolerant applications, where the circuit approximates the exact function in some cases, while having a lower delay or being more area-efficient. Here, upper bounds for the BDD size and the time and space complexity are provided for the verification of general approximate functions and several state-of-the-art approximate adders.
Polynomial Fuzzy Model-Based Control Systems
by Hak-Keung LamThis book presents recent research on the stability analysis of polynomial-fuzzy-model-based control systems where the concept of partially/imperfectly matched premises and membership-function dependent analysis are considered. The membership-function-dependent analysis offers a new research direction for fuzzy-model-based control systems by taking into account the characteristic and information of the membership functions in the stability analysis. The book presents on a research level the most recent and advanced research results, promotes the research of polynomial-fuzzy-model-based control systems, and provides theoretical support and point a research direction to postgraduate students and fellow researchers. Each chapter provides numerical examples to verify the analysis results, demonstrate the effectiveness of the proposed polynomial fuzzy control schemes, and explain the design procedure. The book is comprehensively written enclosing detailed derivation steps and mathematical derivations also for readers without extensive knowledge on the topics including students with control background who are interested in polynomial fuzzy model-based control systems.
Polynomial Identities in Algebras (Springer INdAM Series #44)
by Onofrio Mario Di Vincenzo Antonio GiambrunoThis volume contains the talks given at the INDAM workshop entitled "Polynomial identites in algebras", held in Rome in September 2019. The purpose of the book is to present the current state of the art in the theory of PI-algebras. The review of the classical results in the last few years has pointed out new perspectives for the development of the theory. In particular, the contributions emphasize on the computational and combinatorial aspects of the theory, its connection with invariant theory, representation theory, growth problems. It is addressed to researchers in the field.
Polynomial Operator Equations in Abstract Spaces and Applications
by Ioannis K. ArgyrosPolynomial operators are a natural generalization of linear operators. Equations in such operators are the linear space analog of ordinary polynomials in one or several variables over the fields of real or complex numbers. Such equations encompass a broad spectrum of applied problems including all linear equations. Often the polynomial nature of many nonlinear problems goes unrecognized by researchers. This is more likely due to the fact that polynomial operators - unlike polynomials in a single variable - have received little attention. Consequently, this comprehensive presentation is needed, benefiting those working in the field as well as those seeking information about specific results or techniques. Polynomial Operator Equations in Abstract Spaces and Applications - an outgrowth of fifteen years of the author's research work - presents new and traditional results about polynomial equations as well as analyzes current iterative methods for their numerical solution in various general space settings.Topics include:Special cases of nonlinear operator equationsSolution of polynomial operator equations of positive integer degree nResults on global existence theorems not related with contractionsGalois theoryPolynomial integral and polynomial differential equations appearing in radiative transfer, heat transfer, neutron transport, electromechanical networks, elasticity, and other areasResults on the various Chandrasekhar equationsWeierstrass theoremMatrix representationsLagrange and Hermite interpolationBounds of polynomial equations in Banach space, Banach algebra, and Hilbert spaceThe materials discussed can be used for the following studiesAdvanced numerical analysisNumerical functional analysisFunctional analysisApproximation theoryIntegral and differential equation
Polynomial Optimization, Moments, and Applications (Springer Optimization and Its Applications #206)
by Michal Kočvara Bernard Mourrain Cordian RienerPolynomial optimization is a fascinating field of study that has revolutionized the way we approach nonlinear problems described by polynomial constraints. The applications of this field range from production planning processes to transportation, energy consumption, and resource control.This introductory book explores the latest research developments in polynomial optimization, presenting the results of cutting-edge interdisciplinary work conducted by the European network POEMA. For the past four years, experts from various fields, including algebraists, geometers, computer scientists, and industrial actors, have collaborated in this network to create new methods that go beyond traditional paradigms of mathematical optimization. By exploiting new advances in algebra and convex geometry, these innovative approaches have resulted in significant scientific and technological advancements. This book aims to make these exciting developments accessible to a wider audience by gathering high-quality chapters on these hot topics.Aimed at both aspiring and established researchers, as well as industry professionals, this book will be an invaluable resource for anyone interested in polynomial optimization and its potential for real-world applications.
Polynomial Rings and Affine Algebraic Geometry: PRAAG 2018, Tokyo, Japan, February 12−16 (Springer Proceedings in Mathematics & Statistics #319)
by Gene Freudenburg Shigeru Kuroda Nobuharu OnodaThis proceedings volume gathers selected, peer-reviewed works presented at the Polynomial Rings and Affine Algebraic Geometry Conference, which was held at Tokyo Metropolitan University on February 12-16, 2018. Readers will find some of the latest research conducted by an international group of experts on affine and projective algebraic geometry. The topics covered include group actions and linearization, automorphism groups and their structure as infinite-dimensional varieties, invariant theory, the Cancellation Problem, the Embedding Problem, Mathieu spaces and the Jacobian Conjecture, the Dolgachev-Weisfeiler Conjecture, classification of curves and surfaces, real forms of complex varieties, and questions of rationality, unirationality, and birationality. These papers will be of interest to all researchers and graduate students working in the fields of affine and projective algebraic geometry, as well as on certain aspects of commutative algebra, Lie theory, symplectic geometry and Stein manifolds.
Polynomials and the mod 2 Steenrod Algebra: Representations of GL (London Mathematical Society Lecture Note Series #442)
by Grant Walker Reginald M. W. WoodThis is the first book to link the mod 2 Steenrod algebra, a classical object of study in algebraic topology, with modular representations of matrix groups over the field F of two elements. The link is provided through a detailed study of Peterson's `hit problem' concerning the action of the Steenrod algebra on polynomials, which remains unsolved except in special cases. The topics range from decompositions of integers as sums of 'powers of 2 minus 1', to Hopf algebras and the Steinberg representation of GL(n, F). Volume 1 develops the structure of the Steenrod algebra from an algebraic viewpoint and can be used as a graduate-level textbook. Volume 2 broadens the discussion to include modular representations of matrix groups. Algebraic and combinatorial treatment of Steenrod algebra. Accessible to those without a background in topology. Largely self-contained with detailed proofs.
Polynomials and the mod 2 Steenrod Algebra: The Peterson Hit Problem (London Mathematical Society Lecture Note Series #441)
by Grant Walker Reginald M. W. WoodThis is the first book to link the mod 2 Steenrod algebra, a classical object of study in algebraic topology, with modular representations of matrix groups over the field F of two elements. The link is provided through a detailed study of Peterson's 'hit problem' concerning the action of the Steenrod algebra on polynomials, which remains unsolved except in special cases. The topics range from decompositions of integers as sums of 'powers of 2 minus 1', to Hopf algebras and the Steinberg representation of GL(n,F). Volume 1 develops the structure of the Steenrod algebra from an algebraic viewpoint and can be used as a graduate-level textbook. Volume 2 broadens the discussion to include modular representations of matrix groups.
Polynomials, Dynamics, and Choice: The Price We Pay for Symmetry
by Scott CrassWorking out solutions to polynomial equations is a mathematical problem that dates from antiquity. Galois developed a theory in which the obstacle to solving a polynomial equation is an associated collection of symmetries. Obtaining a root requires "breaking" that symmetry. When the degree of an equation is at least five, Galois Theory established that there is no formula for the solutions like those found in lower degree cases. However, this negative result doesn't mean that the practice of equation-solving ends. In a recent breakthrough, Doyle and McMullen devised a solution to the fifth-degree equation that uses geometry, algebra, and dynamics to exploit icosahedral symmetry.Polynomials, Dynamics, and Choice: The Price We Pay for Symmetry is organized in two parts, the first of which develops an account of polynomial symmetry that relies on considerations of algebra and geometry. The second explores beyond polynomials to spaces consisting of choices ranging from mundane decisions to evolutionary algorithms that search for optimal outcomes. The two algorithms in Part I provide frameworks that capture structural issues that can arise in deliberative settings. While decision-making has been approached in mathematical terms, the novelty here is in the use of equation-solving algorithms to illuminate such problems.Features Treats the topic—familiar to many—of solving polynomial equations in a way that’s dramatically different from what they saw in school Accessible to a general audience with limited mathematical background Abundant diagrams and graphics.
Popular Lectures on Mathematical Logic
by Hao WangA noted logician and philosopher addresses various forms of mathematical logic, discussing both theoretical underpinnings and practical applications. Author Hao Wang surveys the central concepts and theories of the discipline in a historical and developmental context, and then focuses on the four principal domains of contemporary mathematical logic: set theory, model theory, recursion theory and constructivism, and proof theory.Topics include the place of problems in the development of theories of logic and logic's relation to computer science. Specific attention is given to Gödel's incompleteness theorems, predicate logic and its decision and reduction problems, constructibility and Cantor's continuum hypothesis, proof theory and Hilbert's program, hierarchies and unification, proof of the four-color problem, the Diophantine problem, the tautology problem, and many other subjects. Three helpful Appendixes conclude the text.
Population 10 Billion
by Danny DorlingBefore May 2011 the top demographics experts of the United Nations had suggested that world population would peak at 9.1 billion in 2100, and then fall to 8.5 billion people by 2150. In contrast, the 2011 revision suggested that 9.1 billion would be achieved much earlier, maybe by 2050 or before, and by 2100 there would be 10.1 billion of us. What's more, they implied that global human population might still be slightly rising in our total numbers a century from now. So what shall we do? Are there too many people on the planet? Is this the end of life as we know it?Distinguished geographer Professor Danny Dorling thinks we should not worry so much and that, whatever impending doom may be around the corner, we will deal with it when it comes. In a series of fascinating chapters he charts the rise of the human race from its origins to its end-point of population 10 billion. Thus he shows that while it took until about 1988 to reach 5 billion we reached 6 billion by 2000, 7 billion eleven years later and will reach 8 billion by 2025. By recording how we got here, Dorling is able to show us the key issues that we face in the coming decades: how we will deal with scarcity of resources; how our cities will grow and become more female; why the change that we should really prepare for is the population decline that will occur after 10 billion.Population 10 Billion is a major work by one of the world's leading geographers and will change the way you think about the future. Packed full of counter-intuitive ideas and observations, this book is a tool kit to prepare for the future and to help us ask the right questions
Population 10 Billion
by Professor Danny DorlingBefore May 2011 the top demographics experts of the United Nations had suggested that world population would peak at 9.1 billion in 2100, and then fall to 8.5 billion people by 2150. In contrast, the 2011 revision suggested that 9.1 billion would be achieved much earlier, maybe by 2050 or before, and by 2100 there would be 10.1 billion of us. What's more, they implied that global human population might still be slightly rising in our total numbers a century from now. So what shall we do? Are there too many people on the planet? Is this the end of life as we know it?Distinguished geographer Professor Danny Dorling thinks we should not worry so much and that, whatever impending doom may be around the corner, we will deal with it when it comes. In a series of fascinating chapters he charts the rise of the human race from its origins to its end-point of population 10 billion. Thus he shows that while it took until about 1988 to reach 5 billion we reached 6 billion by 2000, 7 billion eleven years later and will reach 8 billion by 2025. By recording how we got here, Dorling is able to show us the key issues that we face in the coming decades: how we will deal with scarcity of resources; how our cities will grow and become more female; why the change that we should really prepare for is the population decline that will occur after 10 billion.Population 10 Billion is a major work by one of the world's leading geographers and will change the way you think about the future. Packed full of counter-intuitive ideas and observations, this book is a tool kit to prepare for the future and to help us ask the right questions
Population Ageing - A Threat to the Welfare State?: The Case of Sweden
by Tommy BengtssonThis book is the first to take a comprehensive view of the challenges that population ageing present in the near future taking Sweden as the case. Can the increasing number of retirees per worker be stopped by immigration or increasing fertility or will we need to increase pension age instead? Cost for the social-care system is readily increasing; even more is the costs for health care. Can the galloping costs be funded by an increase in taxes or do we need to make reforms, similar to the ones already made in the pension system, which has been used as a model for many other countries. The fact that it is difficult to make health care dependent on personal contributions, as is the case of the pension system, funding of health care is a true test of solidarity across generations. The book ends with a discussion on whether the demographic challenge to the welfare system is also a threat to the welfare state as such.
Population Aging and Age-Friendly Transport in China (Population, Regional Development and Transport)
by Pengjun Zhao Jinxin XieThis book is the first book that investigates aging and its impacts on transport system in China. Using various data, this book covers, but is not limited to, the development of population aging, the changes of travel demand, the features of travel behavior of China’s elderly, progress and prospect of age-friendly transport in China. The book has international academic novelty in three points. Firstly, it discovers the long-term supply-demand relationship between population aging and transport infrastructure development. Secondly, it finds the changes and factors in travel behavior of the elderly people. Thirdly, it discusses the advantages or disadvantages of age-friendly transport policy. The findings in the book provide fresh evidences for the challenges posed by aging to transport and enhance readers’ existing knowledge of the elderly people’s travel behavior and the related determinants. These findings are helpful for planners and politicians to make age-friendly transport policies and useful for investors and enterprises to supply proper transport services to the elderly people. This book is of great interest to scholars and practitioners interested in transport development, transport policy, social transition, sustainable mobility, urban planning, urban governance and is relevant to China and other developing countries.
Population Aging, Fertility and Social Security
by Akira YakitaThis book provides a comprehensive, theory-based analysis of current issues in population economics. It addresses the most important problems caused by demographic changes using the popular overlapping generations growth model by Samuelson and Diamond. Taking into account families' fertility decisions, it examines not only the demographic changes due to longer life expectancy but also the effects of social security policy on demography and labor supply/individual retirement behaviors. Conducting all analyses in a dynamic general equilibrium setting, the book offers a valuable theoretical reference guide in the field of population economics.
Population and Development Issues
by Yves CharbitOne of the major challenges facing the world today is the interaction between demographic changes and development. Rather than the usual view that the population itself is the main problem, Population and Development Issues argues that it is just one factor among many others, such as poverty, illiteracy, poor health, unemployment, the condition of women and climate change.This book analyzes the relationships between the key demographic variables (fertility, morbidity and mortality, migration, etc.) and major development issues, notably education, employment, health, gender, social and geographical inequalities and climate concerns. Bringing together contributions from specialists across every field, it presents empirical data simply and clearly alongside theoretical reflections.
Population and Health in Developing Countries
by Maryse GaimardThis book provides an overview of the health of developing nations in the early twenty-first century. The basic assumption is that the health of a population is not independent of broader demographic trends, and does follow the health transition model. The coverage is broad, ranging from health transition in developing countries, to the health of women, to an analysis of morbidity. Population health is an essential component of human and social development. As both a means and an end of development, health lies at the heart of underdevelopment, and ranks first on the list of international priorities. The WHO slogan 'Health for all in 2000' reflects the spirit of a more general movement in favor of health promotion throughout the world. But the developing world is far from reaching this aim. The health of populations has improved in developing regions but there are still deep inequalities, and serious problems remain, especially in Sub-Saharan Africa. After reviewing the core concepts of population health, the book examines health transition in developing countries, a process that has resulted in a double burden of diseases. A discussion of mortality in developing countries serves to highlight the high rates of child mortality in these regions. The book devotes a full chapter to women's health, and its chapter-length analysis of morbidity highlights the double burden weighing down developing populations and concludes with an analysis of health systems in developing countries.