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Diagram Genus, Generators, and Applications (Chapman & Hall/CRC Monographs and Research Notes in Mathematics)
by Alexander StoimenowIn knot theory, diagrams of a given canonical genus can be described by means of a finite number of patterns ("generators"). Diagram Genus, Generators and Applications presents a self-contained account of the canonical genus: the genus of knot diagrams. The author explores recent research on the combinatorial theory of knots and supplies proofs for a number of theorems. The book begins with an introduction to the origin of knot tables and the background details, including diagrams, surfaces, and invariants. It then derives a new description of generators using Hirasawa’s algorithm and extends this description to push the compilation of knot generators one genus further to complete their classification for genus 4. Subsequent chapters cover applications of the genus 4 classification, including the braid index, polynomial invariants, hyperbolic volume, and Vassiliev invariants. The final chapter presents further research related to generators, which helps readers see applications of generators in a broader context.
Diagram Geometry: Related to Classical Groups and Buildings
by Arjeh M. Cohen Francis BuekenhoutThis book provides a self-contained introduction to diagram geometry. Tight connections with group theory are shown. It treats thin geometries (related to Coxeter groups) and thick buildings from a diagrammatic perspective. Projective and affine geometry are main examples. Polar geometry is motivated by polarities on diagram geometries and the complete classification of those polar geometries whose projective planes are Desarguesian is given. It differs from Tits' comprehensive treatment in that it uses Veldkamp's embeddings. The book intends to be a basic reference for those who study diagram geometry. Group theorists will find examples of the use of diagram geometry. Light on matroid theory is shed from the point of view of geometry with linear diagrams. Those interested in Coxeter groups and those interested in buildings will find brief but self-contained introductions into these topics from the diagrammatic perspective. Graph theorists will find many highly regular graphs. The text is written so graduate students will be able to follow the arguments without needing recourse to further literature. A strong point of the book is the density of examples.
Diagrammatic Representation and Inference: 10th International Conference, Diagrams 2018, Edinburgh, UK, June 18-22, 2018, Proceedings (Lecture Notes in Computer Science #10871)
by Peter Chapman Amirouche Moktefi Gem Stapleton Sarah Perez-Kriz Francesco BellucciThis book constitutes the refereed proceedings of the 10th International Conference on the Theory and Application of Diagrams, Diagrams 2018, held in Edinburgh, UK, in June 2018.The 26 revised full papers and 28 short papers presented together with 32 posters were carefully reviewed and selected from 124 submissions. The papers are organized in the following topical sections: generating and drawing Euler diagrams; diagrams in mathematics; diagram design, principles and classification; reasoning with diagrams; Euler and Venn diagrams; empirical studies and cognition; Peirce and existential graphs; and logic and diagrams.
Diagrammatic Representation and Inference: 11th International Conference, Diagrams 2020, Tallinn, Estonia, August 24–28, 2020, Proceedings (Lecture Notes in Computer Science #12169)
by Peter Chapman Ahti-Veikko Pietarinen Leonie Bosveld-de Smet Valeria Giardino James Corter Sven LinkerThis book constitutes the refereed proceedings of the 11th International Conference on the Theory and Application of Diagrams, Diagrams 2020, held in Tallinn, Estonia, in August 2020.*The 20 full papers and 16 short papers presented together with 18 posters were carefully reviewed and selected from 82 submissions. The papers are organized in the following topical sections: diagrams in mathematics; diagram design, principles, and classification; reasoning with diagrams; Euler and Venn diagrams; empirical studies and cognition; logic and diagrams; and posters. *The conference was held virtually due to the COVID-19 pandemic. The chapters ‘Modality and Uncertainty in Data Visualization: A Corpus Approach to the Use of Connecting Lines,’ ‘On Effects of Changing Multi-Attribute Table Design on Decision Making: An Eye Tracking Study,’ ‘Truth Graph: A Novel Method for Minimizing Boolean Algebra Expressions by Using Graphs,’ ‘The DNA Framework of Visualization’ and ‘Visualizing Curricula’ are available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.
Diagrammatic Representation and Inference: 12th International Conference, Diagrams 2021, Virtual, September 28–30, 2021, Proceedings (Lecture Notes in Computer Science #12909)
by Amrita Basu Gem Stapleton Emmanuel Manalo Sven Linker Catherine Legg Petrucio VianaThis book constitutes the refereed proceedings of the 12th International Conference on the Theory and Application of Diagrams, Diagrams 2021, held virtually in September 2021. The 16 full papers and 25 short papers presented together with 16 posters were carefully reviewed and selected from 94 submissions. The papers are organized in the following topical sections: design of concrete diagrams; theory of diagrams; diagrams and mathematics; diagrams and logic; new representation systems; analysis of diagrams; diagrams and computation; cognitive analysis; diagrams as structural tools; formal diagrams; and understanding thought processes. 10 chapters are available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.
Diagrams and Gestures: Mathematics, Philosophy, and Linguistics (Lecture Notes in Morphogenesis)
by Fernando Zalamea Francesco La Mantia Charles AlunniDrawing a line, and then another, and another. Go back from the lines to the movements they capture and see gestures in them: not spatial displacements, but modes of knowledge that pass through the exercise of the body. Discovering something new in a gesture: the line that contracts into a point or the point that expands into a zone, perhaps sinking into a hole. Thus experiencing a diagram: a becoming other inscribed in the novelty of the gesture and in the changes of the forms it shapes. This and much more is discussed in the essays gathered in Diagrams and Gestures. Resulting from trans-disciplinary work between mathematicians, philosophers, linguists and semioticians, the volume delivers an up-to-date account of the most valuable research on the connections between gesture and diagram. As one of the most important themes in contemporary thought, the study of these connections poses a challenge for the future: to elaborate a theory that is equal to new and stimulating research methodologies. We call this theory a philosophy of diagrammatic gestures.
Diagrams, Visual Imagination, and Continuity in Peirce's Philosophy of Mathematics (Mathematics in Mind)
by Vitaly KiryushchenkoThis book is about the relationship between necessary reasoning and visual experience in Charles S. Peirce’s mathematical philosophy. It presents mathematics as a science that presupposes a special imaginative connection between our responsiveness to reasons and our most fundamental perceptual intuitions about space and time. Central to this view on the nature of mathematics is Peirce’s idea of diagrammatic reasoning. In practicing this kind of reasoning, one treats diagrams not simply as external auxiliary tools, but rather as immediate visualizations of the very process of the reasoning itself. Thus conceived, one's capacity to diagram their thought reveals a set of characteristics common to ordinary language, visual perception, and necessary mathematical reasoning. The book offers an original synthetic approach that allows tracing the roots of Peirce’s conception of a diagram in certain patterns of interrelation between his semiotics, his pragmaticist philosophy, his logical and mathematical ideas, bits and pieces of his biography, his personal intellectual predispositions, and his scientific practice as an applied mathematician.
Dial-A-Ride Problems in Transportation Service (Lecture Notes in Economics and Mathematical Systems #694)
by Jonathan GrimmAlthough the dial-a-ride problem currently plays a crucial role in providing transportation services to specific demographics such as the elderly, those with serious illnesses, or individuals with limited mobility due to disabilities, its potential impact on the overall mobility of the population remains underexplored. Surprisingly, the focus is often narrow, leaving potentials untapped and negatively impacting service providers’ profitability. This book proposes several solutions, including strategies for increasing revenue, offering supplementary services, and fostering collaboration. Further, it presents ideas and approaches that address the corresponding problems using operations research methods. The proposals presented here can be used not only to enhance the economic viability of dial-a-ride systems but also boost their impact and visibility. As such, the book shares fundamental insights into solving the dial-a-ride problem and anticipates future trends, leading the way to new frontiers of research. The book offers a valuable resource for academics and professionals engaged in the field of transportation or those interested in the design and development of advanced mathematical programming techniques.
Dialetheism and its Applications (Trends in Logic #52)
by Adam Rieger Gareth YoungThe purpose of this book is to present unpublished papers at the cutting edge of research on dialetheism and to reflect recent work on the applications of the theory. It includes contributions from some of the most respected scholars in the field, as well as from young, up-and-coming philosophers working on dialetheism.Moving from the fringes of philosophy to become a main player in debates concerning truth and the logical paradoxes, dialetheism has thrived since the publication of Graham Priest’s In Contradiction, and several of the papers find their roots in a conference on dialetheism held in Glasgow to mark the 25th anniversary of Priest’s book. The content presented here demonstrates the considerable body of work produced in this field in recent years.With a broad focus, this book also addresses the applications of dialetheism outside the more familiar area of the logical paradoxes, and includes pieces discussing the application of dialetheism in metaphysics, philosophy of language, and philosophy of mind.
Dialogues in Dying
by Connie Wiskin Mageshwaran SivashenmugavelThis is a unique resource to improve this difficult and highly sensitive area of communication, ideal for both individual use and by groups or in teaching. It offers a visual, interactive training experience, linking with supportive care frameworks. It is accompanied bya DVD which contains filmed scenes illustrating a range of challenging dialogues between health workers and a patient and his family through the journey of his terminal illness. Accompanying booklet highlights communication issues with suggested exercises, reflection points and advice. It is available as individual-use-only product for self-reflective learning, or institutional-use product for tutored learning, both priced to give excellent value.
Dichotomies and Stability in Nonautonomous Linear Systems (Stability and Control: Theory, Methods and Applications)
by Yu. A. Mitropolsky A.M. Samoilenko V.L. KulikLinear nonautonomous equations arise as mathematical models in mechanics, chemistry, and biology. The investigation of bounded solutions to systems of differential equations involves some important and challenging problems of perturbation theory for invariant toroidal manifolds. This monograph is a detailed study of the application of Lyapunov func
Dicing with Death: Chance, Risk and Health
by Stephen SennIf you think that statistics has nothing to say about what you do or how you could do it better, then you are either wrong or in need of a more interesting job. Stephen Senn explains here how statistics determines many decisions about medical care, from allocating resources for health, to determining which drugs to license, to cause-and-effect in relation to disease. He tackles big themes: clinical trials and the development of medicines, life tables, vaccines and their risks or lack of them, smoking and lung cancer and even the power of prayer. He entertains with puzzles and paradoxes and covers the lives of famous statistical pioneers. By the end of the book the reader will see how reasoning with probability is essential to making rational decisions in medicine, and how and when it can guide us when faced with choices that impact on our health and even life.
Dicing with Death: Living by Data
by Stephen SennAs a result of the COVID-19 pandemic, medical statistics and public health data have become staples of newsfeeds worldwide, with infection rates, deaths, case fatality and the mysterious R figure featuring regularly. However, we don't all have the statistical background needed to translate this information into knowledge. In this lively account, Stephen Senn explains these statistical phenomena and demonstrates how statistics is essential to making rational decisions about medical care. The second edition has been thoroughly updated to cover developments of the last two decades and includes a new chapter on medical statistical challenges of COVID-19, along with additional material on infectious disease modelling and representation of women in clinical trials. Senn entertains with anecdotes, puzzles and paradoxes, while tackling big themes including: clinical trials and the development of medicines, life tables, vaccines and their risks or lack of them, smoking and lung cancer, and even the power of prayer.
Dick de Jongh on Intuitionistic and Provability Logics (Outstanding Contributions to Logic #28)
by Fan Yang Rosalie Iemhoff Nick BezhanishviliThis book is dedicated to Dick de Jongh’s contributions to the theory of intuitionistic and provability logics. Consisting of 13 chapters, written by leading experts, this book discusses de Jongh’s original contributions and consequent developments that have helped to shape these fields. The book begins with an autobiographic note by Dick de Jongh, which discusses the main themes of his work and places the other contributions in context. The next four chapters explore the De Jongh-Sambin fixed point theorem and other contributions to provability and interpretability logics. The following four chapters focus on modal, intuitionistic and intuitionistic modal logics. They discuss independence of formulas, unification and de Jongh formulas in intuitionistic and modal logics. Then there follow two chapters on the other two areas to which Dick de Jongh made important contributions: the theory of well-partial orders, and formal learning theory. The second to last chapter on Origami Geometry can be seen as representing the Master of Logic program of the Institute for Logic, Language and Computation (ILLC) in which de Jongh invested a lot of energy. The book ends with a complete bibliography of Dick de Jongh in the last chapter. This volume provides a vital overview – and continuation of - de Jongh’s prolfic work in the theory of intuitionistic and provability logics.
Dictators and Democrats: Masses, Elites, and Regime Change
by Stephan Haggard Robert R. KaufmanFrom the 1980s through the first decade of the twenty-first century, the spread of democracy across the developing and post-Communist worlds transformed the global political landscape. What drove these changes and what determined whether the emerging democracies would stabilize or revert to authoritarian rule? Dictators and Democrats takes a comprehensive look at the transitions to and from democracy in recent decades. Deploying both statistical and qualitative analysis, Stephen Haggard and Robert Kaufman engage with theories of democratic change and advocate approaches that emphasize political and institutional factors. While inequality has been a prominent explanation for democratic transitions, the authors argue that its role has been limited, and elites as well as masses can drive regime change. Examining seventy-eight cases of democratic transition and twenty-five reversions since 1980, Haggard and Kaufman show how differences in authoritarian regimes and organizational capabilities shape popular protest and elite initiatives in transitions to democracy, and how institutional weaknesses cause some democracies to fail. The determinants of democracy lie in the strength of existing institutions and the public's capacity to engage in collective action. There are multiple routes to democracy, but those growing out of mass mobilization may provide more checks on incumbents than those emerging from intra-elite bargains.Moving beyond well-known beliefs regarding regime changes, Dictators and Democrats explores the conditions under which transitions to democracy are likely to arise.
Dictionary Learning Algorithms and Applications
by Bogdan Dumitrescu Paul IroftiThis book covers all the relevant dictionary learning algorithms, presenting them in full detail and showing their distinct characteristics while also revealing the similarities. It gives implementation tricks that are often ignored but that are crucial for a successful program. Besides MOD, K-SVD, and other standard algorithms, it provides the significant dictionary learning problem variations, such as regularization, incoherence enforcing, finding an economical size, or learning adapted to specific problems like classification. Several types of dictionary structures are treated, including shift invariant; orthogonal blocks or factored dictionaries; and separable dictionaries for multidimensional signals. Nonlinear extensions such as kernel dictionary learning can also be found in the book. The discussion of all these dictionary types and algorithms is enriched with a thorough numerical comparison on several classic problems, thus showing the strengths and weaknesses of each algorithm. A few selected applications, related to classification, denoising and compression, complete the view on the capabilities of the presented dictionary learning algorithms. The book is accompanied by code for all algorithms and for reproducing most tables and figures.Presents all relevant dictionary learning algorithms - for the standard problem and its main variations - in detail and ready for implementation;Covers all dictionary structures that are meaningful in applications;Examines the numerical properties of the algorithms and shows how to choose the appropriate dictionary learning algorithm.
Dictionary of Algebra, Arithmetic, and Trigonometry
by Steven G. KrantzClear, rigorous definitions of mathematical terms are crucial to good scientific and technical writing-and to understanding the writings of others. Scientists, engineers, mathematicians, economists, technical writers, computer programmers, along with teachers, professors, and students, all have the need for comprehensible, working definitions of ma
Dictionary of Applied Math for Engineers and Scientists
by Emma PreviatoDespite the seemingly close connections between mathematics and other scientific and engineering fields, practical explanations intelligible to those who are not primarily mathematicians are even more difficult to find. The Dictionary of Applied Mathematics for Engineers and Scientists fills that void. It contains authoritative yet accessible defin
Dictionary of Classical and Theoretical Mathematics
by Cahterine Cavagnaro William T. HaightContaining more than 1,000 entries, the Dictionary of Classical and Theoretical Mathematics focuses on mathematical terms and definitions of critical importance to practicing mathematicians and scientists. This single-source reference provides working definitions, meanings of terms, related references, and a list of alternative terms and definition
Dictionary of Contemporary Chinese Economics
by Hong YinxingThis Dictionary provides the theoretical summary and conceptual framework around the milestones obtained through Chinese reform and development and highlights the research achievements of Chinese economics over the past 40 years. It also presents Chinese economics to the world, featuring the Belt and Road Initiative and the Chinese theory and Chinese system to be known and shared internationally with a Chinese intellectual foundation. It sets out to frame the theoretical achievements of extraction and summary of practice experience from Chinese reform and development. The choice of entries in the Dictionary seeks to embody the very Chinese characteristics of economics and the combination of theory and practice is illuminated. Furthermore, the dictionary explores examples of scientific achievements that traditional economics has brought forward and how they fit and unify within both a Chinese, as well as an international context.
Dictionary of Inequalities (Chapman & Hall/CRC Monographs and Research Notes in Mathematics)
by Peter BullenAdding new results that have appeared in the last 15 years, Dictionary of Inequalities, Second Edition provides an easy way for researchers to locate an inequality by name or subject. This edition offers an up-to-date, alphabetical listing of each inequality with a short statement of the result, some comments, references to related inequalities, an
Dictionary of Statistics & Methodology: A Nontechnical Guide for the Social Sciences
by W. Paul VogtThis reference provides definitions of commonly used statistical terms in easily-understood language.
Didaktik der Algebra: nach der Vorlage von Hans-Joachim Vollrath (Mathematik Primarstufe und Sekundarstufe I + II)
by Hans-Georg Weigand Guido Pinkernell Alexander Schüler-Meyer(Autor) Hans J. Vollrath / Hans - Georg Weigand (Titel) Algebra in der Sekundarstufe (HL) Jetzt mit über 120 neuen Aufgaben (copy) Dieses Buch behandelt ausführlich die klassischen Themenstränge, die den Algebraunterricht durchziehen: - Zahlen - Terme - Funktionen - Gleichungen Für diese Themen werden ihre historischen Wurzeln, didaktisch relevante mathematische Grundlagen, Lernmodelle und Unterrichtsvorschläge dargestellt. Dabei wird auch auf typische Lernschwierigkeiten und ihre Überwindung eingegangen. Das Buch liegt nun in der vollständig überarbeiteten dritten Auflage von jetzt zwei Verfassern vor. Mit zahlreichen Hinweisen und Beispielen für den Einsatz des Taschenrechners und des Computers werden Anregungen zu einer Neugestaltung des Algebraunterrichts gegeben. (Biblio)
Didaktik der Geometrie für die Sekundarstufe I (Mathematik Primarstufe und Sekundarstufe I + II)
by Jürgen Roth Barbara Schmidt-Thieme Hans-Georg Weigand Gerald Wittmann Andreas Filler Sebastian Kuntze Reinhard Hölzl Matthias LudwigDieses Buch führt Studierende, Referendare und Lehrkräfte aller Schularten in die didaktischen und methodischen Grundlagen des Geometrieunterrichts der Sekundarstufe I ein und zeigt anhand zahlreicher unterrichtspraktischer Beispiele Möglichkeiten einer problemorientierten Unterrichtsgestaltung auf. Aufbauend auf den Bildungsstandards werden zum einen die wichtigen Aspekte Beweisen und Argumentieren, Konstruieren, Problemlösen sowie Begriffslernen und Begriffslehren behandelt. Zum anderen wird auf die zentralen Themenbereiche des Geometrieunterrichts eingegangen: Figuren und Körper, Flächeninhalt und Volumen, Symmetrie und Kongruenz, Ähnlichkeit und Trigonometrie. Der Einsatz des Computers ist in alle Kapitel integriert, ein Überblick über die Entwicklung zentraler Ideen in der Geometrie und im Geometrieunterricht rundet das Buch ab. In diese Neuauflage sind aktuelle Erweiterungen und Neuansätze integriert, insbesondere auch im Hinblick auf Fortentwicklung digitaler Medien.
Die Arbeit mit dem Radium: Radioaktivitätsforschung 1896 -1914 (Studien zur Geschichte der Naturwissenschaften, Medizin und Technik - Studies on the History of Sciences, Medicine and Technology)
by Beate CeranskiDieses Buch macht die überraschende Vielfalt der Personen und Tätigkeiten in der Radioaktivitätsforschung sichtbar. Dabei wird der Begriff der wissenschaftlichen Arbeit neu konzeptualisiert. Neben die Forschungsarbeit im Labor treten scheinbare Rand-, Neben- und Routinetätigkeiten, die für die Radioaktivitätsforschung als Disziplin von zentraler Bedeutung waren.Badeärzte, Industriechemiker und Bergbaubeamte waren an der Erforschung der neuen Substanzen und Strahlen ebenso beteiligt wie eine vergleichsweise hohe Zahl von Frauen. Die erste umfassende Studie zur deutschsprachigen Radioaktivitätsforschung im vorderen Teil des Buches offenbart die Ausnahmestellung der Hauptstädte Berlin und Wien für die Forschung ebenso wie fruchtbares akademisches Leben in der Provinz; sie zeigt, wie das neue Gebiet an den Hochschulen in die Lehre einzog und welchen Beitrag Professoren, Privatdozenten und Promovierende zur Forschung leisteten. Erstmals wird auch die Bedeutung der Wasseruntersuchungen aufgezeigt, die durch die Hoffnung auf radioaktive Heilquellen angetrieben wurden.Im zweiten Teil werden in internationaler Perspektive unsichtbare und in der Geschichtsschreibung oft wenig beachtete Facetten der „Arbeit mit dem Radium“ untersucht. So mussten Instrumente und radioaktive Präparate überhaupt erst hergestellt und in Umlauf gebracht werden. Auch die Etablierung von Nachweismethoden für Radioaktivität erforderte viel Arbeit, von der niemand sprach. Dienstleistungen wie die Entwicklung therapeutisch nutzbarer Präparate, Gutachtertätigkeiten, die Herausgabe einer Zeitschrift oder die Organisation eines Kongresses werden als integraler Bestandteil der wissenschaftlichen Arbeit in ihrer Bedeutung dargestellt. Eine Reflexion zur Arbeitsorganisation und zum disziplinären Status bündelt die Ergebnisse in einer neuen Gesamtsicht auf die frühe Radioaktivitätsforschung.