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Many-Body Schrödinger Dynamics of Bose-Einstein Condensates
by Kaspar SakmannAt extremely low temperatures, clouds of bosonic atoms form what is known as a Bose-Einstein condensate. Recently, it has become clear that many different types of condensates -- so called fragmented condensates -- exist. In order to tell whether fragmentation occurs or not, it is necessary to solve the full many-body Schrödinger equation, a task that remained elusive for experimentally relevant conditions for many years. In this thesis the first numerically exact solutions of the time-dependent many-body Schrödinger equation for a bosonic Josephson junction are provided and compared to the approximate Gross-Pitaevskii and Bose-Hubbard theories. It is thereby shown that the dynamics of Bose-Einstein condensates is far more intricate than one would anticipate based on these approximations. A special conceptual innovation in this thesis are optimal lattice models. It is shown how all quantum lattice models of condensed matter physics that are based on Wannier functions, e.g. the Bose/Fermi Hubbard model, can be optimized variationally. This leads to exciting new physics.
Many-Electron Approaches in Physics, Chemistry and Mathematics
by Volker Bach Luigi Delle SiteThis book provides a broad description of the development and (computational) application of many-electron approaches from a multidisciplinary perspective. In the context of studying many-electron systems Computer Science, Chemistry, Mathematics and Physics are all intimately interconnected. However, beyond a handful of communities working at the interface between these disciplines, there is still a marked separation of subjects. This book seeks to offer a common platform for possible exchanges between the various fields and to introduce the reader to perspectives for potential further developments across the disciplines. The rapid advances of modern technology will inevitably require substantial improvements in the approaches currently used, which will in turn make exchanges between disciplines indispensable. In essence this book is one of the very first attempts at an interdisciplinary approach to the many-electron problem.
Many-body Approaches at Different Scales: A Tribute To N. H. March On The Occasion Of His 90th Birthday
by G.G.N Angilella C. AmovilliThis book presents a collection of invited research and review contributions on recent advances in (mainly) theoretical condensed matter physics, theoretical chemistry, and theoretical physics. The volume celebrates the 90th birthday of N.H. March (Emeritus Professor, Oxford University, UK), a prominent figure in all of these fields. Given the broad range of interests in the research activity of Professor March, who collaborated with a number of eminent scientists in physics and chemistry, the volume embraces quite diverse topics in physics and chemistry, at various dimensions and energy scales. One thread connecting all these topics is correlation in aggregated states of matter, ranging from nuclear physics to molecules, clusters, disordered condensed phases such as the liquid state, and solid state physics, and the various phase transitions, both structural and electronic, occurring therein. A final chapter leaps to an even larger scale of matter aggregation, namely the universe and gravitation. A further no less important common thread is methodological, with the application of theoretical physics and chemistry, particularly density functional theory and statistical field theory, to both nuclear and condensed matter.
Many-valued Semantics and Modal Logics: Essays in Honour of Yuriy Vasilievich Ivlev (Synthese Library #485)
by Marcelo Esteban Coniglio Dmitry Zaitsev Ekaterina KubyshkinaThis volume is a collection of essays related to the work of Professor Yuriy Vasilievich Ivlev, a distinguished Russian logician and philosopher renowned for his expertise in many-valued and modal logics. Notably, his groundbreaking work on quasi-matrices for logics, now recognized as non-deterministic matrices and non-deterministic semantics, emerged in the 1970s. From a philosophical standpoint, Ivlev’s research delves into the formal analysis of indeterminacy, offering a logical framework to understand how sequences of indeterminate events can yield determinate outcomes. The volume follows two complementary lines of research. Firstly, it serves as a platform for the exploration and discussion of Ivlev’s seminal contributions to the algebraic characterization of both normal and non-normal modal logics, aimed at making these insights accessible to an international audience. Secondly, it features contributions from esteemed logicians and philosophers worldwide, offering diverseperspectives on the logical analysis of indeterminacy. This comprehensive volume will appeal to scholars and researchers in logic, philosophy, and mathematics who are engaged in the study of many-valued and modal methodologies for modeling situations of indeterminacy.
Map ProjectionsTheory and Applications
by II PearsonAbout the Author: Frederick Pearson has extensive experience in teaching map projection at the Air Force Cartography School and Virginia Polytechnic Institute. He developed star charts, satellite trajectory programs, and a celestial navigation device for the Aeronautical Chart and Information Center. He is an expert in orbital analysis of satellites, and control and guidance systems. At McDonnell-Douglas, he worked on the guidance system for the space shuttle.This text develops the plotting equations for the major map projections. The emphasis is on obtaining usable algorithms for computed aided plotting and CRT display. The problem of map projection is stated, and the basic terminology is introduced. The required fundamental mathematics is reviewed, and transformation theory is developed. Theories from differential geometry are particularized for the transformation from a sphere or spheroid as the model of the earth onto a selected plotting surface. The most current parameters to describe the figure of the earth are given. Formulas are included to calculate meridian length, parallel length, geodetic and geocentric latitude, azimuth, and distances on the sphere or spheroid. Equal area, conformal, and conventional projection transformations are derived. All result in direct transformation from geographic to cartesian coordinates. For selected projections, inverse transformations from cartesian to geographic coordinates are given. Since the avoidance of distortion is important, the theory of distortion is explored. Formulas are developed to give a quantitative estimate of linear, area, and angular distortions. Extended examples are given for several mapping problems of interest. Computer applications, and efficient algorithms are presented. This book is an appropriate text for a course in the mathematical aspects of mapping and cartography. Map projections are of interest to workers in many fields. Some of these are mathematicians, engineers, surveyors, geodi
Map of the World: An Introduction to Mathematical Geodesy
by Martin Vermeer Antti RasilaCarl Friedrich Gauss, the "foremost of mathematicians," was a land surveyor. Measuring and calculating geodetic networks on the curved Earth was the inspiration for some of his greatest mathematical discoveries. This is just one example of how mathematics and geodesy, the science and art of measuring and mapping our world, have evolved together throughout history. This text is for students and professionals in geodesy, land surveying, and geospatial science who need to understand the mathematics of describing the Earth and capturing her in maps and geospatial data: the discipline known as mathematical geodesy. Map of the World: An Introduction to Mathematical Geodesy aims to provide an accessible introduction to this area, presenting and developing the mathematics relating to maps, mapping, and the production of geospatial data. Described are the theory and its fundamental concepts, its application for processing, analyzing, transforming, and projecting geospatial data, and how these are used in producing charts and atlases. Also touched upon are the multitude of cross-overs into other sciences sharing in the adventure of discovering what our world really looks like. FEATURES • Written in a fluid and accessible style, replete with exercises; adaptable for courses on different levels. • Suitable for students and professionals in the mapping sciences, but also for lovers of maps and map making.
Maple Animation
by John F. PutzThere is nothing quite like that feeling you get when you see that look of recognition and enjoyment on your students' faces. Not just the strong ones, but everyone is nodding in agreement during your first explanation of the geometry of directional derivatives. If you have incorporated animated demonstrations into your teaching, you know how effective they can be in eliciting this kind of response. You know the value of giving students vivid moving images to tie to concepts. But learning to make animations generally requires extensive searching through a vast computer algebra system for the pertinent functions. Maple Animation brings together virtually all of the functions and procedures useful in creating sophisticated animations using Maple 7, 8, or 9 and it presents them in a logical, accessible way. The accompanying downloadable resources provide all of the Maple code used in the book, including the code for more than 30 ready-to-use demonstrations. From Newton's method to linear transformations, the complete animations included in this book allow you to use them straight out of the box. Careful explanations of the methods teach you how to implement your own creative ideas. Whether you are a novice or an experienced Maple user, Maple Animation provides the tools and skills to enhance your teaching and your students' enjoyment of the subject through animation.
Maple in Mathematics Education and Research: 4th Maple Conference, MC 2020, Waterloo, Ontario, Canada, November 2–6, 2020, Revised Selected Papers (Communications in Computer and Information Science #1414)
by Ilias S. Kotsireas Jürgen Gerhard Robert M. CorlessThis book constitutes refereed proceedings of the 4th Maple Conference, MC 2020, held in Waterloo, Ontario, Canada, in November 2020. The 25 revised full papers and 3 short papers were carefully reviewed and selected out of 75 submissions, one invited paper is also presented in the volume. The papers included in this book cover topics in education, algorithms, and applciations of the mathematical software Maple.
Mapmatics: A Mathematician's Guide to Navigating the World
by Paulina Rowińska“I love maps. I love math. And gosh, do I love this book, which so beautifully and clearly sounds the depths of both.” —Ben Orlin, author of Math with Bad DrawingsExplore the surprising connections between math and maps—and the myriad ways they’ve shaped our world and us.Why are coastlines and borders so difficult to measure? How does a UPS driver deliver hundreds of packages in a single day? And where do elusive serial killers hide? The answers lie in the crucial connection between maps and math.In Mapmatics, mathematician Paulina Rowińska leads us on a riveting journey around the globe to discover how maps and math are deeply entwined, and always have been. From a sixteenth-century map, an indispensable navigation tool that exaggerates the size of northern countries, to public transport maps that both guide and confound passengers, to congressional maps that can empower or silence whole communities, she reveals how maps and math have shaped not only our sense of space but our worldview. In her hands, we learn how to read maps like a mathematician—to extract richer information and, just as importantly, to question our conclusions by asking what we don’t see.Written with authority and compassion, wit and unforgettable storytelling, this is math exposition at its best. By unpacking the math behind the maps we depend on, Mapmatics illuminates how our world works and, ultimately, how we can better look after it.
Mapping Across Academia
by Stanley D. Brunn Martin DodgeThis book addresses the role and importance of space in the respective fields of the social sciences and the humanities. It discusses how map representations and mapping processes can inform ongoing intellectual debates or open new avenues for scholarly inquiry within and across disciplines, including a wide array of significant developments in spatial processes, including the Internet, global positioning system (GPS), affordable digital photography and mobile technologies. Last but not least it reviews and assesses recent research challenges across disciplines that enhance our understanding of spatial processes and mapping at scales ranging from the molecular to the galactic.
Mapping Equity and Quality in Mathematics Education
by Paola Valero Mellony Graven Bill Atweh Walter SecadaConcerns about quality mathematics education are often posed in terms of the types of mathematics that are worthwhile and valuable for both the student and society in general, and about how to best support students so that they can develop this mathematics. Concerns about equity are about who is excluded from the opportunity to develop quality mathematics within our current practices and systems, and about how to remove social barriers that systematically disadvantage those students. This collection of chapters summarises our learning about the achievement of both equity and quality agendas in mathematics education and to move forward the debate on their importance for the field.
Mapping Identity-Induced Marginalisation in India: Inclusion and Access in the Land of Unequal Opportunities
by Raosaheb K Kale Sanghmitra S AcharyaThis book discusses the issues of inequality and marginalization in India. The first section of the book contextualizes sociological traditions for the scrutiny of subaltern discourse on discrimination. The chapters in the section explore self-identity, ‘margins’ in sociological traditions, subalternity and exclusion, citizenship issues of de-notified tribes, the role of religion for scheduled tribe Dalits and Ambedkar’s ideas on tribes. The second section deals with the political economy of higher education, health and employment. The efforts of BR Ambedkar and the consequences of those efforts, his critique of education policies during British time and its alteration for independent India have been meticulously dealt with. The third section illustrates an application of theoretical understanding through narratives of labour bondage in Varanasi, sanitation workers in Mumbai and rickshaw pullers in Delhi. The last section establishes that unequal access to resources is a consequence of discrimination and marginalization induced by social identities. The book argues for equitable access to resources and opportunities to ensure health equity. The audience for this publication includes academics, researchers, health professionals, policymakers engaged with discrimination, exclusion, marginalization and inequity in health.
Mapping Transnational Habitus: Epistemology, Theory and Boundaries (Migration, Diasporas and Citizenship)
by Guanglun Michael Mu Garth Stahl Hannah Soong Kun DaiThis book surveys and critiques existing empirical and theoretical literature on the Bourdieu-informed concept of transnational habitus. The term "transnational” has been used widely in studies of migration research where it has allowed scholars to have a deeper understanding of the practices not only of migrants moving across national borders but also of agents taking positions in transnational spaces without necessarily criss-crossing different nation states. Focusing on the potential of transnational habitus as an analytical tool, the authors propose a model of transnational habitus to identify integral key factors for the operationalisation in research. Drawing on reflexivity, the authors analyse transnational selves and map transnational spaces of classification. Identifying strengths, inconsistencies and key problems in this rapidly developing body of literature, this interdisciplinary and international book will be of interest to students and scholars in sociology, anthropology, migration studies, cultural studies, human geography, as well as diaspora studies.
Mapping of Parent Hamiltonians
by Martin GreiterThis monograph introduces an exact model for a critical spin chain with arbitrary spin S, which includes the Haldane--Shastry model as the special case S=1/2. While spinons in the Haldane-Shastry model obey abelian half-fermi statistics, the spinons in the general model introduced here obey non-abelian statistics. This manifests itself through topological choices for the fractional momentum spacings. The general model is derived by mapping exact models of quantized Hall states onto spin chains. The book begins with pedagogical review of all the relevant models including the non-abelian statistics in the Pfaffian Hall state, and is understandable to every student with a graduate course in quantum mechanics.
Mapping of Parent Hamiltonians: From Abelian and non-Abelian Quantum Hall States to Exact Models of Critical Spin Chains (Springer Tracts in Modern Physics #244)
by Martin GreiterThis monograph introduces an exact model for a critical spin chain with arbitrary spin S, which includes the Haldane--Shastry model as the special case S=1/2. While spinons in the Haldane-Shastry model obey abelian half-fermi statistics, the spinons in the general model introduced here obey non-abelian statistics. This manifests itself through topological choices for the fractional momentum spacings. The general model is derived by mapping exact models of quantized Hall states onto spin chains. The book begins with pedagogical review of all the relevant models including the non-abelian statistics in the Pfaffian Hall state, and is understandable to every student with a graduate course in quantum mechanics.
Mapping the Spatial Divisions of Europe (ISTE Invoiced)
by Guy Baudelle Emmanuelle BoulineauThe European continent has given rise to the greatest number of spatial divisions. Its limits have provoked numerous debates, both within and outside of the continent. The European Union, for its part, has become a laboratory for the production of divisions. Each of these divisions, a vector of identity and territoriality, reflects an intentionality, as revealed in Mapping the Spatial Divisions of Europe. The book shows the multiplicity of forms and modalities of these divisions and the actors who produce, use and question them in a globalized, and reticular world. From the continent as a whole to the individual regions via metropolitan areas and their networks, from meshing to zoning, from regionalization to representations, this book explores how these divisions are used to govern, plan, imagine and build European territories beyond the heritage of states and their borders. The chapters shed new light on the theoretical and practical issues involved in carving Europe on different time and space scales.
Mappings with Direct and Inverse Poletsky Inequalities (Developments in Mathematics #78)
by Evgeny Sevost'yanovThe monograph is devoted to the use of the moduli method in mapping theory, in particular, the meaning of direct and inverse modulus inequalities and their possible applications. The main goal is the development of a modulus technique in the Euclidean space and some metric spaces (manifolds, surfaces, quotient spaces, etc.). Particular attention is paid to the local and boundary behavior of mappings, as well as to obtaining modulus inequalities for some classes. The reader is invited to familiarize himself with all the main achievements of the author, synthesized in this book. The results presented here are of a high scientific level, are new and have no analogues in the world with such a degree of generality.
Marcel Grossmann: For the Love of Mathematics (Springer Biographies)
by William D. Brewer Claudia Graf-GrossmannZurich, summer 1912. Albert Einstein has just returned from Prague to the city on the Limmat. He sends a plea for help to his former fellow student, the mathematician Marcel Grossmann (1878-1936), for he is in need of assistance with the mathematical calculations of his general theory of relativity. What then follows is one of the most fascinating chapters of science history, with far-reaching consequences for the lives of the two friends. Marcel Grossmann’s granddaughter paints here a picture of a fiery and many-talented scientist and patriot. She traces the influence of an entrepreneurial family during Germany’s rapid industrial expansion in the late 19th century. The family’s fluctuating fortunes take the story to the vibrant city of Budapest on the Danube; they enable readers to sense the pioneering spirit at Zurich’s young Polytechnic Institute (now ETH Zurich) – but also reflect the worries and hardships of the First World War and interwar years. The Foreword is written by Prof. Remo Ruffini, founder and president of the International Center for Relativistic Astrophysics and the Marcel Grossmann Meetings. Last but not least, an extensive contribution by Dr. Tilman Sauer offers a scientific-historical appreciation of Marcel Grossmann’s enduring contributions.
Margaret and the Moon
by Dean RobbinsA true story from one of the Women of NASA!Margaret Hamilton loved numbers as a young girl. She knew how many miles it was to the moon (and how many back). She loved studying algebra and geometry and calculus and using math to solve problems in the outside world. Soon math led her to MIT and then to helping NASA put a man on the moon! She handwrote code that would allow the spacecraft&’s computer to solve any problems it might encounter. Apollo 8. Apollo 9. Apollo 10. Apollo 11. Without her code, none of those missions could have been completed. Dean Robbins and Lucy Knisley deliver a lovely portrayal of a pioneer in her field who never stopped reaching for the stars.
Marginal Models in Analysis of Correlated Binary Data with Time Dependent Covariates (Emerging Topics in Statistics and Biostatistics)
by Jeffrey R. Wilson (Din) Ding-Geng Chen Elsa Vazquez-ArreolaThis monograph provides a concise point of research topics and reference for modeling correlated response data with time-dependent covariates, and longitudinal data for the analysis of population-averaged models, highlighting methods by a variety of pioneering scholars. While the models presented in the volume are applied to health and health-related data, they can be used to analyze any kind of data that contain covariates that change over time. The included data are analyzed with the use of both R and SAS, and the data and computing programs are provided to readers so that they can replicate and implement covered methods. It is an excellent resource for scholars of both computational and methodological statistics and biostatistics, particularly in the applied areas of health.
Marginal Revolution in Economics: A Reappraisal (Monographs in Mathematical Economics #6)
by Toru MaruyamaThis volume is devoted to a reappraisal of the Marginal Revolution on the occasion of its 150th anniversary. The year 1871 should be remembered as one of the most important turning points in the history of economics. W. S. Jevons, C. Menger, and L. Walras published epochal works at the very beginning of the 1870s. Although these works were written independently, they shared a common mathematical structure based on classical analysis. For this reason, the emergence of the trio is called the Marginal Revolution. Indeed, 1871 is the starting point of modern economics in the proper sense. In 1971, several academic conferences were held on the occasion of the 100th anniversary of the Revolution, which exerted the stimulating influence upon the historical researches into the Revolution. Now more than fifty years have passed since then. Economic theory has experienced further substantial changes in researchers’ central interest, the way of reasonings and the styles of description during this period. In view of the new achievements acquired in recent fifty years, it seems an indispensable task for us to review and reevaluate the Marginal Revolution based upon the present status of economics.We also keep in mind that some concepts and doctrines once discarded could reappear in a later stage of history in a more or less transfigured form. The introductory chapter will be a guide for readers not only from the economics community but also from the mathematics community.
Marine Biochemistry: Applications
by Se-Kwon KimThis book provides the latest comprehensive methods for isolation and other novel techniques for marine product development. Furthermore, this book offers knowledge on the biological, medical, and industrial applications of marine-derived medicinal food substances. There has been a tremendous increase in the products derived from marine organisms for commercial application in industries every year. Functional foods of medicinal value are particularly in demand as new technology allows the stabilization of natural ingredients and their availability in pure forms to solve various human diseases. Marine flora and fauna have essential elements and trace minerals that nurture various hormones produced in the endocrine system to regulate the respective metabolisms, thereby providing a safe and healthy life to humans. The overall presentation and clear demarcation of the contents by worldwide contributions is a novel entry point into the market of medicinal foods from the sea. The exploration of marine habitats for novel materials are discussed throughout the book. The exploration and exploitation of the biochemistry of sea flora and fauna are limited, and this book extends the research possibilities into numerous marine habitats. Various approaches for extracting and applying the flora and fauna are discussed. This book will be of value to researchers, marine biotechnologists, and medical practitioners, due to the vast information, as well as industrial and medical applications of marine substances all in one place.
Marine Biochemistry: Isolations and Techniques
by Se-Kwon KimThis book provides the latest comprehensive methods for isolation and other novel techniques for marine product development. Furthermore, this book offers knowledge on the biological, medical, and industrial applications of marine-derived medicinal food substances. There has been a tremendous increase in the products derived from marine organisms for commercial application in industries every year. Functional foods of medicinal value are particularly in demand as new technology allows the stabilization of natural ingredients and their availability in pure forms to solve various human diseases. Marine flora and fauna have essential elements and trace minerals that nurture various hormones produced in the endocrine system to regulate the respective metabolisms, thereby providing a safe and healthy life to humans. The overall presentation and clear demarcation of the contents by worldwide contributions is a novel entry point into the market of medicinal foods from the sea. The exploration of marine habitats for novel materials are discussed throughout the book. The exploration and exploitation of the biochemistry of sea flora and fauna are limited, and this book extends the research possibilities into numerous marine habitats. Various approaches for extracting and applying the flora and fauna are discussed. This book will be of value to researchers, marine biotechnologists, and medical practitioners, due to the vast information, as well as industrial and medical applications of marine substances all in one place.
Marine Navigation and Safety of Sea Transportation: Navigational Problems
by Adam WeintritThe TransNav 2013 Symposium held at the Gdynia Maritime University, Poland in June 2013 has brought together a wide range of participants from all over the world. The program has offered a variety of contributions, allowing to look at many aspects of the navigational safety from various different points of view. Topics presented and discussed at th
Market Assessment with OR Applications (Mathematical Engineering, Manufacturing, and Management Sciences)
by Adarsh Anand Deepti Aggrawal Mohini AgarwalThis book provides an understanding of the concept of marketing and its role in business and public organization including the need for scientific marketing analysis. It includes a variety of mathematical models applied for better decision making, promotional decisions in the presence of competition, and sales forecasting using an Operational Research (OR) approach. The book also provides a platform to academicians, practitioners, and researchers to gain understanding of marketing management concepts from an OR perspective. This book offers relevant, international perspectives on techniques for market assessment under one canopy. It will be helpful for those who want to gain insight into understanding the managerial aspects from an OR analyst point of view and is a collaboration that contains plenty of related and valuable techniques used in real-life problems faced by industries.