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Ab Initio Studies on Superconductivity in Alkali-Doped Fullerides (Springer Theses)
by Yusuke NomuraThis book covers high-transition temperature (Tc) s-wave superconductivity and the neighboring Mott insulating phase in alkali-doped fullerides. The author presents (1) a unified theoretical description of the phase diagram and (2) a nonempirical calculation of Tc. For these purposes, the author employs an extension of the DFT+DMFT (density-functional theory + dynamical mean-field theory). He constructs a realistic electron-phonon-coupled Hamiltonian with a newly formulated downfolding method. The Hamiltonian is analyzed by means of the extended DMFT. A notable aspect of the approach is that it requires only the crystal structure as a priori knowledge. Remarkably, the nonempirical calculation achieves for the first time a quantitative reproduction of the experimental phase diagram including the superconductivity and the Mott phase. The calculated Tc agrees well with the experimental data, with the difference within 10 K. The book provides details of the computational scheme, which can also be applied to other superconductors and other phonon-related topics. The author clearly describes a superconducting mechanism where the Coulomb and electron-phonon interactions show an unusual cooperation in the superconductivity thanks to the Jahn-Teller nature of the phonons.
Ab initio Theory of Magnetic Ordering: Electronic Origin of Pair- and Multi-Spin Interactions (Springer Theses)
by Eduardo Mendive TapiaMany technological applications exploit a variety of magnetic structures, or magnetic phases, to produce and optimise solid-state functionality. However, most research advances are restricted to a reduced number of phases owing to computational and resource constraints. This thesis presents an ab-initio theory to efficiently describe complex magnetic phases and their temperature-dependent properties. The central assumption is that magnetic phases evolve slowly compared with the underlying electronic structure from which they emerge. By describing how the electronic structure adapts to the type and extent of magnetic order, a theory able to describe multi-spin correlations and their effect on the magnetism at finite temperature is obtained. It is shown that multi-spin correlations are behind the temperature and magnetic field dependence of the diverse magnetism in the heavy rare earth elements. Magnetically frustrated Mn-based materials and the effect of strain are also investigated. These studies demonstrate that the performance of solid-state refrigeration can be enhanced by multi-spin effects.
Abacus Basic Competency: A Counting Method
by Susan M. MillawayLearn the parts of an abacus, how to "set" numbers and how to do calculations! There are competency tests with answers in the back of the book.
Abelian Groups
by Laszlo Fuchs Rüdiger GöbelThis volume contains information offered at the international conference held in Curacao, Netherlands Antilles. It presents the latest developments in the most active areas of abelian groups, particularly in torsion-free abelian groups.;For both researchers and graduate students, it reflects the current status of abelian group theory.;Abelian Groups discusses: finite rank Butler groups; almost completely decomposable groups; Butler groups of infinite rank; equivalence theorems for torsion-free groups; cotorsion groups; endomorphism algebras; and interactions of set theory and abelian groups.;This volume contains contributions from international experts. It is aimed at algebraists and logicians, research mathematicians, and advanced graduate students in these disciplines.
Abelian Groups (Springer Monographs in Mathematics)
by László FuchsWritten by one of the subject's foremost experts, this book focuses on the central developments and modern methods of the advanced theory of abelian groups, while remaining accessible, as an introduction and reference, to the non-specialist. It provides a coherent source for results scattered throughout the research literature with lots of new proofs. The presentation highlights major trends that have radically changed the modern character of the subject, in particular, the use of homological methods in the structure theory of various classes of abelian groups, and the use of advanced set-theoretical methods in the study of un decidability problems. The treatment of the latter trend includes Shelah's seminal work on the un decidability in ZFC of Whitehead's Problem; while the treatment of the former trend includes an extensive (but non-exhaustive) study of p-groups, torsion-free groups, mixed groups and important classes of groups arising from ring theory. To prepare the reader to tackle these topics, the book reviews the fundamentals of abelian group theory and provides some background material from category theory, set theory, topology and homological algebra. An abundance of exercises are included to test the reader's comprehension, and to explore noteworthy extensions and related sidelines of the main topics. A list of open problems and questions, in each chapter, invite the reader to take an active part in the subject's further development.
Abelian Groups, Module Theory, and Topology: Proceedings In Honor Of Adalberto Orsatti's 60th Birthday (Lecture Notes in Pure and Applied Mathematics #Vol. 201)
by Dikran Dikranjan Luigi SalceFeatures a stimulating selection of papers on abelian groups, commutative and noncommutative rings and their modules, and topological groups. Investigates currently popular topics such as Butler groups and almost completely decomposable groups.
Abelian Groups, Rings, Modules, and Homological Algebra (Lecture Notes in Pure and Applied Mathematics)
by Pat Goeters Overtoun M. G. JendaAbout the bookIn honor of Edgar Enochs and his venerable contributions to a broad range of topics in Algebra, top researchers from around the world gathered at Auburn University to report on their latest work and exchange ideas on some of today's foremost research topics. This carefully edited volume presents the refereed papers of the par
Abelian Varieties (Dover Books on Mathematics)
by Serge LangBased on the work in algebraic geometry by Norwegian mathematician Niels Henrik Abel (1802–29), this monograph was originally published in 1959 and reprinted later in author Serge Lang's career without revision. The treatment remains a basic advanced text in its field, suitable for advanced undergraduates and graduate students in mathematics. Prerequisites include some background in elementary qualitative algebraic geometry and the elementary theory of algebraic groups.The book focuses exclusively on Abelian varieties rather than the broader field of algebraic groups; therefore, the first chapter presents all the general results on algebraic groups relevant to this treatment. Each chapter begins with a brief introduction and concludes with a historical and bibliographical note. Topics include general theorems on Abelian varieties, the theorem of the square, divisor classes on an Abelian variety, functorial formulas, the Picard variety of an arbitrary variety, the I-adic representations, and algebraic systems of Abelian varieties. The text concludes with a helpful Appendix covering the composition of correspondences.
Abelian l-Adic Representations and Elliptic Curves (Research Notes in Mathematics)
by Jean-Pierre SerreThis classic book contains an introduction to systems of l-adic representations, a topic of great importance in number theory and algebraic geometry, as reflected by the spectacular recent developments on the Taniyama-Weil conjecture and Fermat's Last Theorem. The initial chapters are devoted to the Abelian case (complex multiplication), where one
Abenteuer Mathematik: Brücken zwischen Wirklichkeit und Fiktion
by Pierre BasieuxNicht Mathematik zu betreiben, sondern zu erfahren ist das Abenteuer, das dieses Buch bietet - Denkexpeditionen, deren Ausgangspunkt Fragen sind: Was steckt hinter mathematischen Fiktionen wie den unendlich vielen Stufen des Unendlichen oder dem Letzten Fermatschen Satz? Worin liegt ihre Schönheit, worin ihr Bezug zur Realität? Welchen Köpfen sind solche Ideen entsprungen, welche Schicksale mit ihnen verbunden? Das Buch wurde für die vorliegende 5. Auflage vollständig durchgesehen und aktualisiert.
Abgründe der Informatik: Geheimnisse und Gemeinheiten
by Alois PottonWas Sie schon immer über die Informatik und "die Informatiker" wissen wollten, aber nie zu fragen wagten, Alois Potton hat es notiert: Über mehr als zwei Jahrzehnte hat er hinter die Kulissen geblickt und Anekdoten in 80 Glossen gegossen. Schonungslos, bösartig und zum Teil politisch nicht ganz korrekt analysiert er den alltäglichen Wahnsinn und die Absurditäten der IT-Szene. Allgemein verständlich geschrieben, werden sich auch Nichtinformatiker angesichts analoger Vorgänge in ihrem Arbeitsbereich amüsieren - oder aber beleidigt fühlen.
Abiogenesis: The Physical Basis for Living Systems
by Laurel O. SillerudThis textbook serves to teach readers about the origins of life, the probabilistic process of self-assembly underpinning all living systems, from a biophysics perspective. The author cohesively summarizes the various organizing principles that led to the development of an ordered physical basis on which the evolution of life operates. This book answers critical questions, such as why life depends on the properties of inanimate objects and how the laws of physics, chemistry, and biology convolved to spontaneously produce the periodic table and, of course, life itself. Readers are provided with an introduction to probability distributions as well as detailed descriptions of important concepts in thermodynamics, statistical mechanics, and quantum mechanics. As the book progresses, an understanding for the inevitability of life is developed through topics such as stellar nucleosynthesis and prebiotic evolution. Each chapter also includes problems for readers to gain a better understanding of the material. This textbook is accessible to students and researchers of all levels and serves as a comprehensive guide on the physics behind abiogenesis.
Abiotic Selection in Earth Surface Systems (Geophysics and Environmental Physics)
by Jonathan D. PhillipsThis book is about abiotic selection in Earth surface systems. It demonstrates that seemingly purposeful or goal-oriented phenomena in Earth's processes actually emerge from selection dynamics. While many think of selection in the context of biological evolution, it extends to abiotic processes crucial in understanding Earth's function and evolution. The author delineates four forms of geophysical selection: gradient, resistance, network, and thermodynamic. These selections manifest in various natural systems, from fluid flows shaping landscapes to the efficient transport of mass and energy. The book acknowledges the interplay of geophysical and ecological processes, employing them as pedagogical tools. Structured with an introduction to abiotic selection and its context, the book delves into the application of key principles—such as thermodynamics and flow dynamics—to Earth surface systems. Each subsequent chapter examines one of the four types of selection, featuring diverse real-world examples from climate dynamics to oceanography. Geared toward researchers, graduate students, and practitioners in fields such as geophysics, geology, geography, hydrology, and ecosystem sciences, it also appeals to those interested in evolutionary thinking beyond traditional life sciences.
Abitur Mathematik für Dummies (Für Dummies)
by André FischerSo klappt es mit dem Mathe-Abi Nutzen Sie die Zeit bis zu Ihrer Abiturprüfung im Fach Mathematik und bereiten Sie sich mit diesem Buch vor, um die Prüfung so gut wie möglich zu bestehen. Egal, wie gut der geforderte Lernstoff fürs Abi bereits sitzt: André Fischer erklärt Ihnen in einfachen und verständlichen Worten, was Sie über Analysis, Vektorgeometrie, lineare Algebra und Stochastik wissen müssen. Grundlegender Schulstoff wird dabei so wiederholt, dass Sie einfach folgen können. Beispielrechnungen veranschaulichen die Erklärungen und mit den enthaltenen Übungsaufgaben können Sie Ihr Wissen festigen. Sie erfahren Welche mathematischen Grundlagen unerlässlich sind Was es mit Kurven-diskussionen, linearen Gleichungssystemen und Zufallsvariablen auf sich hat Was Sie bei der Prüfungs-vorbereitung beachten sollten
Abortion and Contraception in Modern Greece, 1830-1967: Medicine, Sexuality and Popular Culture (Medicine and Biomedical Sciences in Modern History)
by Violetta HionidouThe book examines the history of abortion and contraception in Modern Greece from the time of its creation in the 1830s to 1967, soon after the Pill became available. It situates the history of abortion and contraception within the historiography of the fertility decline and the question of whether the decline was due to adjustment to changing social conditions or innovation of contraceptive methods. The study reveals that all methods had been in use for other purposes before they were employed as contraceptives. For example, Greek women were employing emmenagogues well before fertility was controlled; they did so in order to ‘put themselves right’ and to enhance their fertility. When they needed to control their fertility, they employed abortifacients, some of which were also emmenagogues, while others had been used as expellants in earlier times. Curettage was also employed since the late nineteenth century as a cure for sterility; once couples desired to control their fertility curettage was employed to procure abortion. Thus couples did not need to innovate but rather had to repurpose old methods and materials to new birth control methods. Furthermore, the role of physicians was found to have been central in advising and encouraging the use of birth control for ‘health’ reasons, thus facilitating and speeding fertility decline in Greece. All this occurred against the backdrop of a state and a church that were at times neutral and at other times disapproving of fertility control.
About Teaching Mathematics: A K-8 Resource
by Marilyn BurnsIn this fourth edition of her signature resource, Marilyn presents her current thinking and insights and includes ideas from her most recent teaching experiences. <P><P> Part 1, “Starting Points,” reflects the major overhaul of this book and addresses twenty-three issues important to thinking about teaching mathematics today. Part 2, “Problem-Solving Investigations,” opens with how to plan problem-solving lessons; followed by whole-class, small-group, and individual investigations organized into five areas of the curriculum: Measurement, Data, Geometry, Patterns and Algebraic Thinking, and Number and Operations. Part 3, “Teaching Arithmetic,” focuses on the cornerstone of elementary mathematics curriculum, offering ideas and assessments that build students’ understanding, confidence, and competence in arithmetic. In Part 4, “Questions Teachers Ask,” features Marilyn’s responses to pedagogical questions she’s received from teachers over the years. <P><P> More than forty reproducibles for About Teaching Mathematics are available to download in a printable format.
About Vectors (Dover Books on Mathematics)
by Banesh HoffmannFrom his unusual beginning in "Defining a vector" to his final comments on "What then is a vector?" author Banesh Hoffmann has written a book that is provocative and unconventional. In his emphasis on the unresolved issue of defining a vector, Hoffmann mixes pure and applied mathematics without using calculus. The result is a treatment that can serve as a supplement and corrective to textbooks, as well as collateral reading in all courses that deal with vectors. Major topics include vectors and the parallelogram law; algebraic notation and basic ideas; vector algebra; scalars and scalar products; vector products and quotients of vectors; and tensors. The author writes with a fresh, challenging style, making all complex concepts readily understandable. Nearly 400 exercises appear throughout the text. Professor of Mathematics at Queens College at the City University of New York, Banesh Hoffmann is also the author of The Strange Story of the Quantum and other important books. This volume provides much that is new for both students and their instructors, and it will certainly generate debate and discussion in the classroom.
About the Hearth
by David G. Anderson Virginie Vate Robert P. WishartDue to changing climates and demographics, questions of policy in the circumpolar north have focused attention on the very structures that people call home. Dwellings lie at the heart of many forms of negotiation. Based on years of in-depth research, this book presents and analyzes how the people of the circumpolar regions conceive, build, memorialize, and live in their dwellings. This book seeks to set a new standard for interdisciplinary work within the humanities and social sciences and includes anthropological work on vernacular architecture, environmental anthropology, household archaeology and demographics.
Abraham Lincoln’s Cyphering Book and Ten other Extraordinary Cyphering Books
by M. A. Ken Clements Nerida F. EllertonThis well-illustrated book provides strong qualitative and comparative support for the main arguments developed by Nerida Ellerton and Ken Clements in their groundbreaking Rewriting this History of School Mathematics in North America 1607-1861: The Central Role of Cyphering Books. Eleven extraordinary handwritten school mathematics manuscripts are carefully analyzed--six were prepared entirely in Great Britain, four entirely in North America, and 1 partly in Great Britain and partly in North America. The earliest of the 11 cyphering books was prepared around 1630, and the latest in 1835. Seven of the manuscripts were arithmetic cyphering books; three were navigation cyphering books, and one was a mensuration/surveying manuscript. One of the cyphering books examined in this book was prepared, over the period 1819-1826, by a young Abraham Lincoln, when he was attending small one-teacher schools in remote Spencer County, Indiana. Chapter 6 in this book provides the first detailed analysis of young Abraham's cyphering book--which is easily the oldest surviving Lincoln manuscript. Another cyphering book, this one prepared by William Beattie in 1835, could have been prepared as a special gift for the King of England. The analyses make clear the extent of the control which the cyphering tradition had over school mathematics in North America and Great Britain between 1630 and 1840. In their final chapter Ellerton and Clements identify six lessons from their research into the cyphering tradition which relate to present-day circumstances surrounding school mathematics. These lessons are concerned with sharp differences between intended, implemented and attained curricula, the remarkable value that many students placed upon their cyphering books, the ethnomathematical circumstances which surrounded the preparations of the extraordinary cyphering books, and qualitative differences between British and North American school mathematics.
Absolute Risk: Methods and Applications in Clinical Management and Public Health (Chapman & Hall/CRC Monographs on Statistics and Applied Probability)
by Ruth M. Pfeiffer Mitchell H. GailAbsolute Risk: Methods and Applications in Clinical Management and Public Health provides theory and examples to demonstrate the importance of absolute risk in counseling patients, devising public health strategies, and clinical management. The book provides sufficient technical detail to allow statisticians, epidemiologists, and clinicians to build, test, and apply models of absolute risk. Features: Provides theoretical basis for modeling absolute risk, including competing risks and cause-specific and cumulative incidence regression Discusses various sampling designs for estimating absolute risk and criteria to evaluate models Provides details on statistical inference for the various sampling designs Discusses criteria for evaluating risk models and comparing risk models, including both general criteria and problem-specific expected losses in well-defined clinical and public health applications Describes many applications encompassing both disease prevention and prognosis, and ranging from counseling individual patients, to clinical decision making, to assessing the impact of risk-based public health strategies Discusses model updating, family-based designs, dynamic projections, and other topics Ruth M. Pfeiffer is a mathematical statistician and Fellow of the American Statistical Association, with interests in risk modeling, dimension reduction, and applications in epidemiology. She developed absolute risk models for breast cancer, colon cancer, melanoma, and second primary thyroid cancer following a childhood cancer diagnosis. Mitchell H. Gail developed the widely used "Gail model" for projecting the absolute risk of invasive breast cancer. He is a medical statistician with interests in statistical methods and applications in epidemiology and molecular medicine. He is a member of the National Academy of Medicine and former President of the American Statistical Association. Both are Senior Investigators in the Division of Cancer Epidemiology and Genetics, National Cancer Institute, National Institutes of Health.
Abstract Algebra
by David S. Dummit Richard M. FooteThis revision of Dummit and Foote's widely acclaimed introduction to abstract algebra helps students experience the power and beauty that develops from the rich interplay between different areas of mathematics. The book carefully develops the theory of different algebraic structures, beginning from basic definitions to some in-depth results, using numerous examples and exercises to aid the student's understanding. With this approach, students gain an appreciation for how mathematical structures and their interplay lead to powerful results and insights in a number of different settings. <P><P> The text is designed for a full-year introduction to abstract algebra at the advanced undergraduate or graduate level, but contains substantially more material than would normally be covered in one year. Portions of the book may also be used for various one-semester topics courses in advanced algebra, each of which would provide a solid background for a follow-up course delving more deeply into one of many possible areas: algebraic number theory, algebraic topology, algebraic geometry, representation theory, Lie groups, etc.
Abstract Algebra
by Paul B. GarrettDesigned for an advanced undergraduate- or graduate-level course, Abstract Algebra provides an example-oriented, less heavily symbolic approach to abstract algebra. The text emphasizes specifics such as basic number theory, polynomials, finite fields, as well as linear and multilinear algebra. This classroom-tested, how-to manual takes a more narra
Abstract Algebra (Dover Books on Mathematics)
by W. E. DeskinsThis excellent textbook provides undergraduates with an accessible introduction to the basic concepts of abstract algebra and to the analysis of abstract algebraic systems. These systems, which consist of sets of elements, operations, and relations among the elements, and prescriptive axioms, are abstractions and generalizations of various models which evolved from efforts to explain or discuss physical phenomena.In Chapter 1, the author discusses the essential ingredients of a mathematical system, and in the next four chapters covers the basic number systems, decompositions of integers, diophantine problems, and congruences. Chapters 6 through 9 examine groups, rings, domains, fields, polynomial rings, and quadratic domains.Chapters 10 through 13 cover modular systems, modules and vector spaces, linear transformations and matrices, and the elementary theory of matrices. The author, Professor of Mathematics at the University of Pittsburgh, includes many examples and, at the end of each chapter, a large number of problems of varying levels of difficulty.
Abstract Algebra (Third Edition)
by John A. Beachy William D. BlairBeachy and Blair’s clear narrative presentation responds to the needs of inexperienced students who stumble over proof writing, who understand definitions and theorems but cannot do the problems, and who want more examples that tie into their previous experience. The authors introduce chapters by indicating why the material is important and, at the same time, relating the new material to things from the student’s background and linking the subject matter of the chapter to the broader picture.
Abstract Algebra via Numbers
by Lars TusetThis book is a concise, self-contained treatise on abstract algebra with an introduction to number theory, where students normally encounter rigorous mathematics for the first time. The authors build up things slowly, by explaining the importance of proofs. Number theory with its focus on prime numbers is then bridged via complex numbers and linear algebra, to the standard concepts of a course in abstract algebra, namely groups, representations, rings, and modules. The interplay between these notions becomes evident in the various topics studied. Galois theory connects field extensions with automorphism groups. The group algebra ties group representations with modules over rings, also at the level of induced representations. Quadratic reciprocity occurs in the study of Fourier analysis over finite fields. Jordan decomposition of matrices is obtained by decomposition of modules over PID’s of complex polynomials. This latter example is just one of many stunning generalizations of the fundamental theorem of arithmetic, which in its various guises penetrates abstract algebra and figures multiple times in the extensive final chapter on modules.