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Normal Forms and Stability of Hamiltonian Systems (Applied Mathematical Sciences #218)
by Hildeberto E. Cabral Lúcia Brandão DiasThis book introduces the reader to the study of Hamiltonian systems, focusing on the stability of autonomous and periodic systems and expanding to topics that are usually not covered by the canonical literature in the field. It emerged from lectures and seminars given at the Federal University of Pernambuco, Brazil, known as one of the leading research centers in the theory of Hamiltonian dynamics. This book starts with a brief review of some results of linear algebra and advanced calculus, followed by the basic theory of Hamiltonian systems. The study of normal forms of Hamiltonian systems is covered by Ch.3, while Chapters 4 and 5 treat the normalization of Hamiltonian matrices. Stability in non-linear and linear systems are topics in Chapters 6 and 7. This work finishes with a study of parametric resonance in Ch. 8. All the background needed is presented, from the Hamiltonian formulation of the laws of motion to the application of the Krein-Gelfand-Lidskii theory of strongly stable systems. With a clear, self-contained exposition, this work is a valuable help to advanced undergraduate and graduate students, and to mathematicians and physicists doing research on this topic.
Normal Forms, Melnikov Functions and Bifurcations of Limit Cycles
by Maoan Han Pei YuDynamical system theory has developed rapidly over the past fifty years. It is a subject upon which the theory of limit cycles has a significant impact for both theoretical advances and practical solutions to problems. Hopf bifurcation from a center or a focus is integral to the theory of bifurcation of limit cycles, for which normal form theory is a central tool. Although Hopf bifurcation has been studied for more than half a century, and normal form theory for over 100 years, efficient computation in this area is still a challenge with implications for Hilbert's 16th problem. This book introduces the most recent developments in this field and provides major advances in fundamental theory of limit cycles. Split into two parts, the first focuses on the study of limit cycles bifurcating from Hopf singularity using normal form theory with later application to Hilbert's 16th problem, while the second considers near Hamiltonian systems using Melnikov function as the main mathematical tool. Classic topics with new results are presented in a clear and concise manner and are accompanied by the liberal use of illustrations throughout. Containing a wealth of examples and structured algorithms that are treated in detail, a good balance between theoretical and applied topics is demonstrated. By including complete Maple programs within the text, this book also enables the reader to reconstruct the majority of formulas provided, facilitating the use of concrete models for study. Through the adoption of an elementary and practical approach, this book will be of use to graduate mathematics students wishing to study the theory of limit cycles as well as scientists, across a number of disciplines, with an interest in the applications of periodic behavior.
Normalization of Multidimensional Data for Multi-Criteria Decision Making Problems: Inversion, Displacement, Asymmetry (International Series in Operations Research & Management Science #348)
by Irik Z. MukhametzyanovThis book presents a systematic review of multidimensional normalization methods and addresses problems frequently encountered when using various methods and ways to eliminate them. The invariant properties of the linear normalization methods presented here can be used to eliminate simple problems and avoid obvious errors when choosing a normalization method. The book introduces valuable, novel techniques for the multistep normalization of multidimensional data. One of these methods involves inverting the normalized values of cost attributes into profit attributes based on the reverse sorting algorithm (ReS algorithm). Another approach presented is the IZ method, which addresses the issue of shift in normalized attribute values. Additionally, a new method for normalizing the decision matrix is proposed, called the MS method, which ensures the equalization of average values and variances of attributes. Featuring numerous illustrative examples throughout, the book helps readers to understand what difficulties can arise in multidimensional normalization, what to expect from such problems, and how to solve them. It is intended for academics and professionals in various areas of data science, computing in mathematics, and statistics, as well as decision-making and operations.
Normalization Techniques in Deep Learning (Synthesis Lectures on Computer Vision)
by Lei HuangThis book presents and surveys normalization techniques with a deep analysis in training deep neural networks. In addition, the author provides technical details in designing new normalization methods and network architectures tailored to specific tasks. Normalization methods can improve the training stability, optimization efficiency, and generalization ability of deep neural networks (DNNs) and have become basic components in most state-of-the-art DNN architectures. The author provides guidelines for elaborating, understanding, and applying normalization methods. This book is ideal for readers working on the development of novel deep learning algorithms and/or their applications to solve practical problems in computer vision and machine learning tasks. The book also serves as a resource researchers, engineers, and students who are new to the field and need to understand and train DNNs.
Normally Hyperbolic Invariant Manifolds: The Noncompact Case
by Jaap ElderingThis monograph treats normally hyperbolic invariant manifolds, with a focus on noncompactness. These objects generalize hyperbolic fixed points and are ubiquitous in dynamical systems. First, normally hyperbolic invariant manifolds and their relation to hyperbolic fixed points and center manifolds, as well as, overviews of history and methods of proofs are presented. Furthermore, issues (such as uniformity and bounded geometry) arising due to noncompactness are discussed in great detail with examples. The main new result shown is a proof of persistence for noncompact normally hyperbolic invariant manifolds in Riemannian manifolds of bounded geometry. This extends well-known results by Fenichel and Hirsch, Pugh and Shub, and is complementary to noncompactness results in Banach spaces by Bates, Lu and Zeng. Along the way, some new results in bounded geometry are obtained and a framework is developed to analyze ODEs in a differential geometric context. Finally, the main result is extended to time and parameter dependent systems and overflowing invariant manifolds.
North Carolina Coach End-of-Grade Practice Tests, Mathematics, Grade 6
by School Specialty Inc.North Carolina Coach End-of-Grade Practice Tests, Mathematics, Grade 6
North Carolina Practice Coach Plus Grade 7 Practice Tests
by School Specialty IncNORTH CAROLINA PRACTICE COACH PLUS MATH GRADE 7 PRACTICE TESTS with Practice Check-Ins
North Carolina Practice Coach Plus Math Grade 6
by Triumph Learning LlcNORTH CAROLINA PRACTICE COACH PLUS, MATHEMATICS, GRADE 6
North Carolina Practice Coach Plus Math Grade 8 Practice Tests
by School Specialty Inc.NORTH CAROLINA PRACTICE COACH PLUS MATH GRADE 8 PRACTICE TESTS with Practice Check-Ins
North Carolina Practice Coach PLUS, Mathematics, Grade 7
by North Carolina Practice CoachNorth Carolina Practice Coach PLUS, Mathematics, Grade 7 content includes: Domain 1 The Number System, North Carolina Standard Course of Study, Domain 2 Ratios and Proportional Relationships, Domain 3 Expressions and Equations, Domain 4 Geometry, Domain 5 Statistics and Probability, Glossary.
North Carolina Practice Coach PLUS, Mathematics, Grade 8
by North Carolina Practice CoachNorth Carolina Practice Coach PLUS, Mathematics, Grade 8 content includes: Domain 1 The Number System, North Carolina Standard Course of Study, Domain 2 Expressions and Equations, Domain 3 Functions, Domain 4 Geometry, Domain 5 Statistics and Probability, Glossary
NoSQL: Database for Storage and Retrieval of Data in Cloud (Advances In Computers Ser. #Volume 109)
by Ganesh Chandra DekaThis book discusses the advanced databases for the cloud-based application known as NoSQL. It will explore the recent advancements in NoSQL database technology. Chapters on structured, unstructured and hybrid databases will be included to explore bigdata analytics, bigdata storage and processing. The book is likely to cover a wide range of topics such as cloud computing, social computing, bigdata and advanced databases processing techniques.
Not So Weird After All: The Changing Relationship Between Status and Fertility (Evolutionary Analysis in the Social Sciences)
by Rosemary L. Hopcroft Martin Fieder Susanne HuberThis is the first book to fully examine, from an evolutionary point of view, the association of social status and fertility in human societies before, during, and after the demographic transition. In most nonhuman social species, social status or relative rank in a social group is positively associated with the number of offspring, with high-status individuals typically having more offspring than low-status individuals. However, humans appear to be different. As societies have gotten richer, fertility has dipped to unprecedented lows, with some developed societies now at or below replacement fertility. Within rich societies, women in higher-income families often have fewer children than women in lower-income families. Evolutionary theory suggests that the relationship between social status and fertility is likely to be somewhat different for men and women, so it is important to examine this relationship for men and women separately. When this is done, the positive association between individual social status and fertility is often clear in less-developed, pre-transitional societies, particularly for men. Once the demographic transition begins, it is elite families, particularly the women of elite families, who lead the way in fertility decline. Post-transition, the evidence from a variety of developed societies in Europe, North America and East Asia is that high-status men (particularly men with high personal income) do have more children on average than lower-status men. The reverse is often true of women, although there is evidence that this is changing in Nordic countries. The implications of these observations for evolutionary theory are also discussed. This book will be of interest to students and researchers in the social sciences with an interest in evolutionary sociology, evolutionary anthropology, evolutionary psychology, demography, and fertility.
Notable Modern Indian Mathematicians and Statisticians: During the 19th and 20th Centuries of Bengal
by Purabi MukherjiThis book provides a comprehensive portrayal of the history of Indian mathematicians and statisticians and uncovers many missing parts of the scientific representation of mathematical and statistical research during the 19th and 20th centuries of Bengal (now West Bengal), India. This book gives a brief historical account about the establishment of the first-two departments in an Indian university, where graduate teaching and research were initiated. This was a unique distinction for the University of Calcutta which was established in 1857. The creation of the world famous Indian Statistical Institute (ISI) in Calcutta (now Kolkata) is also briefly described. The lives and works of the 16 pioneer mathematical scientists who adorned the above mentioned institutions and the first Indian Institute Technology (IIT) of India have been elaborated in lucid language. Some outstanding scholars who were trained at the ISI but left India permanently have also been discussed briefly in a separate chapter. This book fulfils a long-standing gap in the history of modern Indian mathematics, which will make the book very useful to researchers in the history of science and mathematics. Written in very lucid English with little mathematical or statistical jargon makes the book immensely readable even to general readers with interest in scientific history even from non-mathematical, non-statistical background. This book is a clear portrayal of the struggle and success of researchers in mathematical sciences in Bengal (an important part of the colonial India), unveils before the international community of mathematical scientists. The real connoisseurs will appreciate the value of the book, as it will clear up many prevailing misconceptions.
Note Taking Activities in E-Learning Environments (Behaviormetrics: Quantitative Approaches to Human Behavior #11)
by Minoru NakayamaThe main focus of this book is presenting practical procedures for improving learning effectiveness using note taking activities during e-learning courses. Although presentation of e-learning activities recently has been spreading to various education sectors, some practical problems have been discussed such as evaluation of learning performance and encouragement of students. The authors introduce note taking activity as a conventional learning tool in order to promote individual learning activity and learning efficacy. The effectiveness of note taking has been measured in practical teaching in a Japanese university using techniques of learning analytics, and the results are shown here. The relationships between note taking activity and students’ characteristics, the possibility of predicting the final learning performance using metrics of students’ note taking, and the effectiveness for individual emotional learning factors are evaluated. Some differences between blended learning and fully online learning courses are also discussed. The authors provide novel analytical procedures and ideas to manage e-learning courses. In particular, the assessment of note taking activity may help to track individual learning progress and to encourage learning motivation.
Notes on Consumption Theory: Deterministic and Stochastic Dynamic Models (Classroom Companion: Economics)
by Giuseppe Travaglini Giorgio Calcagnini Alessandro BellocchiThis textbook offers a compact, yet formal, synthesis of the broad field of consumption theory. Written in a coherent and accessible way, this book introduces graduate and postgraduate students to dynamic optimization applied to consumption under certainty and uncertainty, in discrete and continuous time. Delving into deterministic and stochastic models, including the use of Brownian motions, the book offers a deeper understanding of consumption decisions and their impact on asset pricing and investment in partial and general equilibrium. This book compiles lecture notes from advanced courses in micro- and macroeconomics, ensuring a self-contained introduction to the subject. Balancing simplicity with analytical rigor, the book equips readers with essential methodological tools for advanced research in economics. With empirical evidence and exercises integrated throughout, this textbook stands as the go-to resource for scholars and students alike, fostering further theoretical explorations in the field. Basic knowledge of economics, mathematics, and econometrics is recommended for a comprehensive understanding.
Notes on Counting: An Introduction to Enumerative Combinatorics (Australian Mathematical Society Lecture Series #26)
by Peter J. CameronEnumerative combinatorics, in its algebraic and analytic forms, is vital to many areas of mathematics, from model theory to statistical mechanics. This book, which stems from many years' experience of teaching, invites students into the subject and prepares them for more advanced texts. It is suitable as a class text or for individual study. The author provides proofs for many of the theorems to show the range of techniques available, and uses examples to link enumerative combinatorics to other areas of study. The main section of the book introduces the key tools of the subject (generating functions and recurrence relations), which are then used to study the most important combinatorial objects, namely subsets, partitions, and permutations of a set. Later chapters deal with more specialised topics, including permanents, SDRs, group actions and the Redfield-P#65533;lya theory of cycle indices, M#65533;bius inversion, the Tutte polynomial, and species.
Notes on Geometry and Arithmetic (Universitext)
by Daniel CorayThis English translation of Daniel Coray’s original French textbook Notes de géométrie et d’arithmétique introduces students to Diophantine geometry. It engages the reader with concrete and interesting problems using the language of classical geometry, setting aside all but the most essential ideas from algebraic geometry and commutative algebra. Readers are invited to discover rational points on varieties through an appealing ‘hands on’ approach that offers a pathway toward active research in arithmetic geometry. Along the way, the reader encounters the state of the art on solving certain classes of polynomial equations with beautiful geometric realizations, and travels a unique ascent towards variations on the Hasse Principle. Highlighting the importance of Diophantus of Alexandria as a precursor to the study of arithmetic over the rational numbers, this textbook introduces basic notions with an emphasis on Hilbert’s Nullstellensatz over an arbitrary field. A digression on Euclidian rings is followed by a thorough study of the arithmetic theory of cubic surfaces. Subsequent chapters are devoted to p-adic fields, the Hasse principle, and the subtle notion of Diophantine dimension of fields. All chapters contain exercises, with hints or complete solutions. Notes on Geometry and Arithmetic will appeal to a wide readership, ranging from graduate students through to researchers. Assuming only a basic background in abstract algebra and number theory, the text uses Diophantine questions to motivate readers seeking an accessible pathway into arithmetic geometry.
Notes on Numerical Modeling in Geomechanics
by William G. PariseauThis book is an introduction to numerical analysis in geomechanics and is intended for advanced undergraduate and beginning graduate study of the mechanics of porous, jointed rocks and soils. Although familiarity with the concepts of stress, strain and so on is assumed, a review of the fundamentals of solid mechanics including concepts of physical laws, kinematics and material laws is presented in an appendix. Emphasis is on the popular finite element method but brief explanations of the boundary element method, the distinct element method (also known as the discrete element method) and discontinuous deformation analysis are included. Familiarity with a computer programming language such as Fortran, C++ or Python is not required, although programming excerpts in Fortran are presented at the end of some chapters. This work begins with an intuitive approach to interpolation over a triangular element and thus avoids making the simple complex by not doing energy minimization via a calculus of variations approach so often found in reference books on the finite element method. The presentation then proceeds to a principal of virtual work via the well-known divergence theorem to obtain element equilibrium and then global equilibrium, both expressed as stiffness equations relating force to displacement. Solution methods for the finite element approach including elimination and iteration methods are discussed. Hydro-mechanical coupling is described and extension of the finite element method to accommodate fluid flow in porous geological media is made. Example problems illustrate important concepts throughout the text. Additional problems for a 15-week course of study are presented in an appendix; solutions are given in another appendix.
Notes on the Ellipsoidal Function
by Chang-Hong LiangThis book focuses on the ellipsoidal function, which serves as an evolution and extension of the circular function (trigonometric function) and elliptic function. It presents an in-depth discussion of the ellipsoidal function (algebra) theory and the conformal mapping (geometry) theory of the ellipsoid function, demonstrating the outstanding performance of the ellipsoid function response filter. Applications of the ellipsoidal function include the capacitance of ellipsoidal conductors and the surface area of ellipsoids, which in turn correspond to ellipsoidal integrals of the first kind and the second kind, respectively. The book offers a valuable reference guide for undergraduates, graduate students and researchers in the related fields.
Notes on the Stationary p-Laplace Equation (SpringerBriefs in Mathematics)
by Peter LindqvistThis book in the BCAM SpringerBriefs series is a treatise on the p-Laplace equation. It is based on lectures by the author that were originally delivered at the Summer School in Jyväskylä, Finland, in August 2005 and have since been updated and extended to cover various new topics, including viscosity solutions and asymptotic mean values. The p-Laplace equation is a far-reaching generalization of the ordinary Laplace equation, but it is non-linear and degenerate (p>2) or singular (p
Notes on Tug-of-War Games and the p-Laplace Equation (SpringerBriefs on PDEs and Data Science)
by Mikko ParviainenThis book addresses the interplay between stochastic processes and partial differential equations. More specifically, it focuses on the connection between the nonlinear p-Laplace equation and the stochastic game called tug-of-war with noise. The connection in this context was discovered approximately 15 years ago and has since provided new insights and approaches. These lecture notes provide a brief but detailed and accessible introduction to the subject and to the more research-oriented literature. The book also presents the parabolic case side by side with the elliptic case, highlighting the fact that elliptic and parabolic equations are close in spirit in certain aspects. Moreover, it covers some parts of the regularity theory for these problems. Graduate students and advanced undergraduate students with a basic understanding of probability and partial differential equations will find this book useful.
Nothing: Surprising Insights Everywhere from Zero to Oblivion
by New Scientist Jeremy WebbIncredible discoveries from the fringes of the universe to the inner workings of our minds—all from nothing! It turns out that almost nothing is as curious—or as enlightening—as, well, nothing. What is nothingness? Where can it be found? The writers of the world's top-selling science magazine investigate—from the big bang, dark energy, and the void to superconductors, vestigial organs, hypnosis, and the placebo effect—and discover that understanding nothing may be the key to understanding everything: What came before the big bang, and will our universe end? How might cooling matter down almost to absolute zero help solve our energy crisis? How can someone suffer from a false diagnosis as though it were true? Does nothingness even exist? Recent experiments suggest that squeezing a perfect vacuum somehow creates light. Why is it unfair to accuse sloths—animals who do nothing—of being lazy? And more! Contributors Paul Davies, Jo Marchant, and Ian Stewart, along with two former editors of Nature and 16 other leading writers and scientists, marshal up-to-the-minute research to make one of the most perplexing realms in science dazzlingly clear. Prepare to be amazed at how much more there is to nothing than you ever realized.
Nothing Stopped Sophie: The Story of Unshakable Mathematician Sophie Germain
by Cheryl Bardoe Barbara McClintockThe true story of eighteenth-century mathematician Sophie Germain, who solved the unsolvable to achieve her dream.When her parents took away her candles to keep their young daughter from studying math...nothing stopped Sophie. When a professor discovered that the homework sent to him under a male pen name came from a woman...nothing stopped Sophie. And when she tackled a math problem that male scholars said would be impossible to solve...still, nothing stopped Sophie.For six years Sophie Germain used her love of math and her undeniable determination to test equations that would predict patterns of vibrations. She eventually became the first woman to win a grand prize from France's prestigious Academy of Sciences for her formula, which laid the groundwork for much of modern architecture (and can be seen in the book's illustrations).Award-winning author Cheryl Bardoe's inspiring and poetic text is brought to life by acclaimed artist Barbara McClintock's intricate pen-and-ink, watercolor, and collage illustrations in this true story about a woman who let nothing stop her.
Nothing To Come: A Defense Of The Growing Block Theory Of Time (Synthese Library #395)
by Fabrice Correia Sven RosenkranzThis monograph is a detailed study, and systematic defence, of the Growing Block Theory of time (GBT), first conceived by C.D. Broad. The book offers a coherent, logically perspicuous and ideologically lean formulation of GBT, defends it against the most notorious objections to be found in the extant philosophical literature, and shows how it can be derived from a more general theory, consistent with relativistic spacetime, on the pre-relativistic assumption of an absolute and total temporal order.The authors devise axiomatizations of GBT and its competitors which, against the backdrop of a shared quantified tense logic, significantly improves the prospects of their comparative assessment. Importantly, neither of these axiomatizations involves commitment to properties of presentness, pastness or futurity. The authors proceed to address, and defuse, a number of objections that have been marshaled against GBT, including the so-called epistemic objection according to which the theory invites skepticism about our temporal location. The challenge posed by relativistic physics is met head-on, by replacing claims about temporal variation by claims about variation across spacetime.The book aims to achieve the greatest possible rigor. The background logic is set out in detail, as are the principles governing the notions of precedence and temporal location. The authors likewise devise a novel spacetime logic suited for the articulation, and comparative assessment, of relativistic theories of time. The book comes with three technical appendices which include soundness and completeness proofs for the systems corresponding to GBT and its competitors, in both their pre-relativistic and relativistic forms. The book is primarily directed at researchers and graduate students working on the philosophy of time or temporal logic, but is of interest to metaphysicians and philosophical logicians more generally.