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The Reasoning of Quantum Mechanics: Operator Theory and the Harmonic Oscillator (Synthesis Lectures on Engineering, Science, and Technology)
by Horst R. BeyerThis Second Edition presents and details the process of quantization of a classical mechanical system in a relevant physical system, the harmonic oscillator. As mathematics and physics are inextricably interwoven in quantum theories, the author takes a mathematically rigorous approach. The book focuses on properties of the quantum system that can be observed and measured, and the author then interprets the resulting theory. The book covers methods of operator theory in the formulation of the theory as well as in the calculation of the consequences of the theory. The author addresses the mathematical foundation of the probabilistic interpretation of quantum mechanics through the spectral theorems for (densely-defined and linear) self-adjoint operators in complex Hilbert spaces. The book also explains the measurement process and questions the challenges of the wave function, the EPR paradox, and Bell’s inequality.
The Red Book of Mathematical Problems (Dover Books on Mathematics)
by Kenneth Hardy Kenneth S. WilliamsIn North America, the most prestigious competition in mathematics at the undergraduate level is the William Lowell Putnam Mathematical Competition. This volume is a handy compilation of 100 practice problems, hints, and solutions indispensable for students preparing for the Putnam and other undergraduate mathematical competitions. Indeed, it will be of use to anyone engaged in the posing and solving of mathematical problems.Many of the problems in this book were suggested by ideas originating in a variety of sources, including Crux Mathematicorum, Mathematics Magazine, and the American Mathematical Monthly, as well as various mathematical competitions. This result is a rich selection of carefully chosen problems that will challenge and stimulate mathematical problem-solvers at varying degrees of proficiency.
The Red Record: Large Print
by Ida B. WellsA shocking and powerful account of lynching written by activist, journalist, and former slave Ida B. Wells In the postbellum American South, lynching was a frightfully common occurrence, perpetrated so frequently that most Southern politicians and leaders turned a blind eye to the practice. This vicious form of vigilante "justice" was in truth a thinly veiled racist justification for murderous violence. In 1892 alone, more than two hundred African Americans were lynched, with alleged offenses ranging from "attempted stock poisoning" to "insulting whites." The Red Record tabulates these scenes of brutality in clear, objective statistics, allowing the horrifying facts to speak for themselves. Alongside the tally, author Ida B. Wells describes actual occurrences of lynching, and enumerates the standard rationalizations for these extrajudicial killings, her original intent for the pamphlet to shame and shock the apathetic public--and spark change. This ebook has been professionally proofread to ensure accuracy and readability on all devices.
The Reduction of Physical Theories: A Contribution to the Unity of Physics Part 1: Foundations and Elementary Theory (Fundamental Theories of Physics #207)
by Erhard ScheibeUsing simple physical examples, this work by Erhard Scheibe presents an important and powerful approach to the reduction of physical theories. Novel to the approach is that it is not based, as usual, on a single reduction concept that is fixed once and for all, but on a series of recursively constructed reductions, with which all reductions appear as combinations of very specific elementary reductions. This leaves the general notion of theory reduction initially open and is beneficial for the treatment of the difficult cases of reduction from the fields of special and general relativity, thermodynamics, statistical mechanics,and quantum mechanics, which are treated in the second volume. The book is systematically organized and intended for readers interested in philosophy of science as well as physicists without deep philosophical knowledge.
The Reflection of Life
by A. H. LouieA. H. Louie's The Reflection of Life: Functional Entailment and Imminence in Relational Biology is a continuation of the exploratory journey in relational biology which began with his 2009 monograph More Than Life Itself: A Synthetic Continuation in Relational Biology. The theme of his first book was 'What is life?'; the theme of this sequel is "How do two life forms interact?" Biology is a subject concerned with organization of relations. Relational biology is the approach that advocates 'function dictates structure", rather than 'structure implies function'. It is mathematics decoded into biological realizations. The book demonstrates some of the powers of the approach of relational biology, and illustrates how pertinent problems in biology can be better addressed this way. In the first volume the theory was developed by using partially ordered sets, lattices, simulations, models, Aristotle's four causes, graphs, categories, simple and complex systems, anticipatory systems, and metabolism-repair [(M,R)-] systems. Here in the second volume, these tools are expanded to employ set-valued mappings, adjacency matrices, random graphs, and interacting entailment networks. The theory of set-valued mappings culminates in the imminence mapping, which equips the further investigation of functional entailment in complex relational networks. Imminence in (M,R)-networks that model living systems addresses the topics of biogenesis and natural selection. Interacting (M,R)-networks with mutually entailing processes serve as models in the study of symbiosis and pathophysiology. The formalism also provides a natural framework for a relational theory of virology and oncology. This book will serve researchers and graduate students in mathematics and biology.
The Refugee System: A Sociological Approach
by David Scott FitzGerald Rawan ArarSome people facing violence and persecution flee. Others stay. How do households in danger decide who should go, where to relocate, and whether to keep moving? What are the conditions in countries of origin, transit, and reception that shape people's options? This incisive book tells the story of how one Syrian family, spread across several countries, tried to survive the civil war and live in dignity. This story forms a backdrop to explore and explain the refugee system. Departing from studies that create siloes of knowledge about just one setting or ""solution"" to displacement, the book's sociological approach describes a global system that shapes refugee movements. Changes in one part of the system reverberate elsewhere. Feedback mechanisms change processes across time and place. Earlier migrations shape later movements. Immobility on one path redirects migration along others. Past policies, laws, population movements, and regional responses all contribute to shape states&’ responses in the present. As Arar and FitzGerald illustrate, all these processes are forged by deep inequalities of economic, political, military, and ideological power. Presenting a sharp analysis of refugee structures worldwide, this book offers invaluable insights for students and scholars of international migration and refugee studies across the social sciences, as well as policy makers and those involved in refugee and asylum work.
The Regularization Cookbook: Explore practical recipes to improve the functionality of your ML models
by Vincent VandenbusscheMethodologies and recipes to regularize any machine learning and deep learning model using cutting-edge technologies such as stable diffusion, Dall-E and GPT-3 Purchase of the print or Kindle book includes a free PDF eBookKey FeaturesLearn to diagnose the need for regularization in any machine learning modelRegularize different ML models using a variety of techniques and methodsEnhance the functionality of your models using state of the art computer vision and NLP techniquesBook DescriptionRegularization is an infallible way to produce accurate results with unseen data, however, applying regularization is challenging as it is available in multiple forms and applying the appropriate technique to every model is a must. The Regularization Cookbook provides you with the appropriate tools and methods to handle any case, with ready-to-use working codes as well as theoretical explanations. After an introduction to regularization and methods to diagnose when to use it, you’ll start implementing regularization techniques on linear models, such as linear and logistic regression, and tree-based models, such as random forest and gradient boosting. You’ll then be introduced to specific regularization methods based on data, high cardinality features, and imbalanced datasets. In the last five chapters, you’ll discover regularization for deep learning models. After reviewing general methods that apply to any type of neural network, you’ll dive into more NLP-specific methods for RNNs and transformers, as well as using BERT or GPT-3. By the end, you’ll explore regularization for computer vision, covering CNN specifics, along with the use of generative models such as stable diffusion and Dall-E. By the end of this book, you’ll be armed with different regularization techniques to apply to your ML and DL models.What you will learnDiagnose overfitting and the need for regularizationRegularize common linear models such as logistic regression Understand regularizing tree-based models such as XGBoosUncover the secrets of structured data to regularize ML modelsExplore general techniques to regularize deep learning modelsDiscover specific regularization techniques for NLP problems using transformers Understand the regularization in computer vision models and CNN architecturesApply cutting-edge computer vision regularization with generative modelsWho this book is forThis book is for data scientists, machine learning engineers, and machine learning enthusiasts, looking to get hands-on knowledge to improve the performances of their models. Basic knowledge of Python is a prerequisite.
The Regularized Fast Hartley Transform
by Keith JonesThe Regularized Fast Hartley Transform provides the reader with the tools necessary to both understand the proposed new formulation and to implement simple design variations that offer clear implementational advantages, both practical and theoretical, over more conventional complex-data solutions to the problem. The highly-parallel formulation described is shown to lead to scalable and device-independent solutions to the latency-constrained version of the problem which are able to optimize the use of the available silicon resources, and thus to maximize the achievable computational density, thereby making the solution a genuine advance in the design and implementation of high-performance parallel FFT algorithms.
The Relationship of Affect and Creativity in Mathematics: How the Five Legs of Creativity Influence Math Talent
by Eric Mann Scott ChamberlinThe Relationship of Affect and Creativity in Mathematics explores the five legs of creativity—Iconoclasm, Impartiality, Investment, Intuition, and Inquisitiveness—as they relate to mathematical giftedness. This book:Discusses these affective components relevant to mathematical learning experiences.Shares how affective components impact students' creative processes and products.Shows the influence of learning facilitators, including teachers, afterschool mentors, and parents.Describes facilitating environments that may enhance the likelihood that creative process and ultimately product emerge.Utilizes the expertise of two young scholars to discuss the practical effects of affect and creativity in learning experiences.This practical, research-based book is a must-read for stakeholders in gifted education, as many advanced students are underidentified in the area of creativity in mathematics.
The Relevance of René Thom: The Morphological Dimension in Today’s Sciences (Lecture Notes in Morphogenesis)
by Isabel Marcos Clément MorierThe body of work presented in this book comes from research carried out since 2017 as part of the international "Actualité de René Thom" project. This project was initially entitled "Morphology and qualitative dynamics: Knowledge of forms / Forms of knowledge". Subsequently, the name "Relevance of René Thom" was chosen for its clarity and evocative power.The aim of this research project is to promote the scientific relevance of René Thom's thinking on forms, and to demonstrate the importance of his method and discoveries. It is based on discussions of Thom's thinking and the method he proposes - i.e., to seek out dynamic structures in order to understand changes of form in nature and at the human-social level, to explain the transformation of these dynamic forms, to study the morphologies of process in various fields in order to advance scientific knowledge...The relevance of this thinker has manifested itself in the form of monthly sessions of a research seminar, held from 2017 to 2022, as well as in the form of international congresses (2018, 2019), bringing together the greatest friends and continuators, both of the work of René Thom himself, and of reflection on morphogenetic dynamics in the most diverse disciplines. This created a space for dialogue and listening between the exact sciences and the social and human sciences. Indeed, the fields of study are necessarily interdisciplinary, since, as René Thom teaches us, morphological organization, or form, in its exchanges with matter, must be considered as "independent" of its substrate, i.e. the environment in which this morphogenesis unfolds. Finally, this book marks a symbolic moment: it takes shape in the year that marks the centenary of the birth of René Thom, who was born in the French town of Montbéliard in 1923. To mark this centenary (1923-2023), a number of initiatives have been launched to celebrate the discoveries and advances of this mathematician-philosopher, ashe liked to call himself… The publication of the present book is one more, which we hope will shed light that will stimulate the morphological gaze Thom so urged us to adopt.
The Religious Roots of Longevity Risk Sharing: The Genesis of Annuity Funds in the Scottish Enlightenment and the Path to Modern Pension Management
by Moshe A. MilevskyThis book presents a unique historical study on the origins of longevity risk management and its links to religious institutions in the eighteenth century. Throughout history, monarchs, affluent patrons, and wealthy benefactors routinely pledged to provide their devotees with pensions or life annuities, mirroring the biblical concept of ‘daily bread for life’. Until the eighteenth century, however, the uncertainty around the longevity of beneficiaries’ lives and the difficulty of budgeting for random financial obligations had posed economic challenges that often led to insufficient funding and high default rates. This book narrates the genesis of longevity risk pooling and the first successfully funded annuity scheme in history, an eventual prototype for national pension plans around the world. It examines how a group of Protestant clergymen, scientists, and intellectuals associated with the Presbyterian Church of Scotland pioneered innovative methods for setting up a reversionary annuity and widow’s pension plan, guided by actuarial principles. Unknown to many, the economist Adam Smith, and other literati of the Scottish Enlightenment, invested in this novel annuity. Illuminating the social and theological contexts of this scheme, the book argues that religious belief played a critical role in the development of best practices around the prudent management of longevity risk. The practices, values and beliefs in divine probabilities were at the heart of these thought leaders’ confidence in long-term financial projections. Shedding light on this fascinating aspect of actuarial history by an examination of the archival records, while also linking to contextual discussions of modern pension challenges, this book will be of interest to scholars and readers interested in finance, insurance, pensions, and religion.
The Renaissance of General Relativity in Context (Einstein Studies #16)
by Jürgen Renn Roberto Lalli Alexander S. BlumThis contributed volume explores the renaissance of general relativity after World War II, when it transformed from a marginal theory into a cornerstone of modern physics. Chapters explore key historical processes related to the theory of general relativity, in addition to presenting a thorough treatment of the relevant science behind these episodes. A broad historiographical framework is introduced first, thus providing the broad context in which the given computational approaches and case studies occurred. Written by an international and interdisciplinary group of expert authors, these chapters will bring readers to a more complete understanding of Einstein’s theory. Specific topics include:Social and citation networksThe Fock-Infeld disputeWheeler’s turn to gravitation theoryThe position of general relativity in theories of fundamental interactionsThe pursuit of a quantum theory of gravityThe emergence of dark matter in relation to cosmological modelsInstitutional frameworks for gravitational wave search in EuropeThe Renaissance of General Relativity in Context is ideal for historians, philosophers, and sociologists of science. Students and researchers in physics will also be interested in the topics explored.
The Renormalization Group and Condensed Matter Physics
by David R. Nelson Grace H. ZhangA graduate-level entrée to the application of renormalization group theory to condensed matter physicsRenormalization group ideas have had a major impact on condensed matter physics for more than a half century. This book develops the theory and illustrates the broad applicability of the renormalization group to major problems in condensed matter physics. Based on course materials developed and class-tested by the authors at Harvard University, the book will be especially useful for students, as well as researchers in condensed matter physics, soft matter physics, biophysics, and statistical physics. After reviewing Ising models, lattice gases, and critical point phenomena, the book covers quantum critical phenomena; the statistical mechanics of linear polymer chains; fluctuating sheet polymers; the dynamics associated with the Navier-Stokes equations and simplified models of randomly stirred fluids; the properties of &“active matter&”; and more.Explores the broad applicability of renormalization groups to condensed matterCovers critical phenomena in different dimensions, quantum critical points, polymer physics and flexural phonons in free-standing graphene, nonequilibrium fluid dynamics, and moreProvides a modern, physics-centered entrée, suitable for both course use and self-studyFeatures material ideal for graduate-level students as well as researchersIncludes exercises throughoutOffers a solutions manual for exercises (available only to instructors)
The Repopulation of New Orleans After Hurricane Katrina
by Kevin F. Mccarthy Michael Pollard D. J. Peterson Narayan SastryIn November 2005, New Orleans city leaders asked RAND to estimate the repopulation of the city in the aftermath of Hurricane Katrina. The Bring New Orleans Back Commission needed estimates of the city's population in the immediate and near-term future to guide the redevelopment planning process. An assessment of flood damage to housing based on the depth of floodwater and the likely pace of reconstruction of damaged housing guided the estimates.
The Reputation Risk Handbook: Surviving and Thriving in the Age of Hyper-Transparency
by Andrea Bonime-BlancThis book will show you how to build a sustainable reputation risk management framework and how to handle your next reputation risk crisis. It will help you identify ways in which reputation risk can impact bottom line, and then show you how to set up a framework for turning that risk into an opportunity for good, sustainable business. Reputation risk is a strategic risk and a potentially material risk, all the more so in the "age of hyper-transparency". This needs to be clearly understood by both management and boards of directors so that the people tasked with reputation risk have the support they need to align their reputation risk management with business strategy and planning. The Reputation Risk Handbook provides a clear framework to identify, manage and resolve reputation risk, including: a clear description of what reputation risk is and how it fits within the pantheon of corporate and institutional risk and strategic management; a practical process for creating early warning systems and on-going management and monitoring of reputation risks; techniques for aligning reputation risk management with business strategy and business planning; several case studies, including examples of when reputation risk management has gone wrong; examples of how to manage specific reputation risks successfully or deal with a reputation risk crisis. The Reputation Risk Handbook is not just for practitioners – those who manage risk and reputation directly – but for those who have oversight of risk management – namely boards, their committees and the c-suite. In addition to a framework for practitioners, the book provides specific suggestions for boards, including questions to ask management and what to look for within their organizations.
The Resource Transfer Problem: A Framework For Integrated Scheduling And Routing Problems (Contributions to Management Science)
by Illa WeissThe resource transfer problem (RTP) is a modeling and solution framework for integrated complex scheduling and rich vehicle routing problems. It allows the modeling of a wide variety of scheduling problems, vehicle routing problems, their combination with integrated problems, as well as various specific requirements and restrictions arising in practical scheduling and vehicle routing. Based on the unifying resource transfer problem framework, this book proposes a generic constraint propagation approach that exploits the specific structure of scheduling and routing problems.
The Respiratory System in Equations
by Bertrand MauryThis book proposes an introduction to the mathematical modeling of the respiratory system. A detailed introduction on the physiological aspects makes it accessible to a large audience without any prior knowledge on the lung. Different levels of description are proposed, from the lumped models with a small number of parameters (Ordinary Differential Equations), up to infinite dimensional models based on Partial Differential Equations. Besides these two types of differential equations, two chapters are dedicated to resistive networks, and to the way they can be used to investigate the dependence of the resistance of the lung upon geometrical characteristics. The theoretical analysis of the various models is provided, together with state-of-the-art techniques to compute approximate solutions, allowing comparisons with experimental measurements. The book contains several exercises, most of which are accessible to advanced undergraduate students.
The Revolution Generation: How Millennials Can Save America and the World (Before It's Too Late)
by Josh TickellFrom the activist and Sundance Award-winning filmmaker of Fuel and Kiss the Ground comes an ambitious book showcasing the captivating stories of Millennial change-makers in order to empower and motivate today’s young adults to rise up to their potential for greatness.With eye-opening research and inspiring interviews, The Revolution Generation is the first in-depth exploration of the world-changing activism and potential of people born between 1980 and 2000. Labeled Generation Y or Millennials, theirs is the first digitally fluent generation. From sex and dating, to parental relationships, to jobs and the economy, Millennials live within a dynamic interplay of technological advances and real world setbacks. Their connectivity and global awareness have created astonishing new opportunities, but have also come at a time of peril. According to the United Nations, today’s youth face the ten largest global crises in human history (including the sixth major species extinction, a rapidly changing climate, and a worldwide refugee crisis). In no uncertain terms, the future of humanity rests on their shoulders. While these challenges may be daunting, Millennials are part of the largest, most educated, most digitally plugged-in generation to date and The Revolution Generation elucidates their often-overlooked strengths and shows how they can build a brighter, more sustainable and democratic future for themselves—and all of humanity. The Revolution Generation is also soon to be a full-length documentary featuring Bernie Sanders, Shailene Woodley, Rosario Dawson, and more.
The Richness of the History of Mathematics: A Tribute to Jeremy Gray (Archimedes #66)
by Karine Chemla José Ferreirós Erhard Scholz Lizhen Ji Chang WangThis book, a tribute to historian of mathematics Jeremy Gray, offers an overview of the history of mathematics and its inseparable connection to philosophy and other disciplines. Many different approaches to the study of the history of mathematics have been developed. Understanding this diversity is central to learning about these fields, but very few books deal with their richness and concrete suggestions for the “what, why and how” of these domains of inquiry. The editors and authors approach the basic question of what the history of mathematics is by means of concrete examples. For the “how” question, basic methodological issues are addressed, from the different perspectives of mathematicians and historians. Containing essays by leading scholars, this book provides a multitude of perspectives on mathematics, its role in culture and development, and connections with other sciences, making it an important resource for students and academics in the history and philosophy of mathematics.
The Riemann Hypothesis for Function Fields
by Machiel Van FrankenhuijsenThis book provides a lucid exposition of the connections between non-commutative geometry and the famous Riemann Hypothesis, focusing on the theory of one-dimensional varieties over a finite field. The reader will encounter many important aspects of the theory, such as Bombieri's proof of the Riemann Hypothesis for function fields, along with an explanation of the connections with Nevanlinna theory and non-commutative geometry. The connection with non-commutative geometry is given special attention, with a complete determination of the Weil terms in the explicit formula for the point counting function as a trace of a shift operator on the additive space, and a discussion of how to obtain the explicit formula from the action of the idele class group on the space of adele classes. The exposition is accessible at the graduate level and above, and provides a wealth of motivation for further research in this area.
The Riemann Hypothesis in Characteristic p in Historical Perspective (Lecture Notes in Mathematics #2222)
by Peter RoquetteThis book tells the story of the Riemann hypothesis for function fields (or curves) starting with Artin's 1921 thesis, covering Hasse's work in the 1930s on elliptic fields and more, and concluding with Weil's final proof in 1948. The main sources are letters which were exchanged among the protagonists during that time, found in various archives, mostly the University Library in Göttingen. The aim is to show how the ideas formed, and how the proper notions and proofs were found, providing a particularly well-documented illustration of how mathematics develops in general. The book is written for mathematicians, but it does not require any special knowledge of particular mathematical fields.
The Riemann Hypothesis: The Greatest Unsolved Problem in Mathematics
by Karl SabbaghHistorical discussion of the still unsolved problem of the Riemann Hypothesis.
The Riemann Problem in Continuum Physics (Applied Mathematical Sciences #219)
by Philippe G. LeFloch Mai Duc ThanhThis monograph provides a comprehensive study of the Riemann problem for systems of conservation laws arising in continuum physics. It presents the state-of-the-art on the dynamics of compressible fluids and mixtures that undergo phase changes, while remaining accessible to applied mathematicians and engineers interested in shock waves, phase boundary propagation, and nozzle flows. A large selection of nonlinear hyperbolic systems is treated here, including the Saint-Venant, van der Waals, and Baer-Nunziato models. A central theme is the role of the kinetic relation for the selection of under-compressible interfaces in complex fluid flows. This book is recommended to graduate students and researchers who seek new mathematical perspectives on shock waves and phase dynamics.
The Riemann Zeta-Function: Theory and Applications (Dover Books on Mathematics)
by Aleksandar IvicThis extensive survey presents a comprehensive and coherent account of Riemann zeta-function theory and applications. Starting with elementary theory, it examines exponential integrals and exponential sums, the Voronoi summation formula, the approximate functional equation, the fourth power moment, the zero-free region, mean value estimates over short intervals, higher power moments, and omega results. Additional topics include zeros on the critical line, zero-density estimates, the distribution of primes, the Dirichlet divisor problem and various other divisor problems, and Atkinson's formula for the mean square. End-of-chapter notes supply the history of each chapter's topic and allude to related results not covered by the book. 1985 edition.
The Rise and Fall of Business Firms: A Stochastic Framework on Innovation, Creative Destruction and Growth
by S. V. Buldyrev F. Pammolli M. Riccaboni H. E. StanleyAt the intersection between statistical physics and rigorous econometric analysis, this powerful new framework sheds light on how innovation and competition shape the growth and decline of companies and industries. Analyzing various sources of data including a unique micro level database which collects historic data on the sales of more than 3,000 firms and 50,000 products in 20 countries, the authors introduce and test a model of innovation and proportional growth, which relies on minimal assumptions and accounts for the empirically observed regularities. Through a combination of extensive stochastic simulations and statistical tests, the authors investigate to what extent their simple assumptions are falsified by empirically observable facts. Physicists looking for application of their mathematical and modelling skills to relevant economic problems as well as economists interested in the explorative analysis of extensive data sets and in a physics-orientated way of thinking will find this book a key reference.