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Symmetry through the Eyes of a Chemist, 3rd Edition Magdolna Hargittai and István Hargittai are PhD's (Eötvös University), DSc's (Hungarian Academy of Sciences), and Dr.h.c.'s (University of North Carolina). They are currently affiliated with the Department of Inorganic and Analytical Chemistry and Materials Structure and Modeling Research Group of the Hungarian Academy of Sciences at the Budapest University of Technology and Economics. They are also members of the Hungarian Academy of Sciences and the Academia Europaea (London). Reviews of previous editions This has to be the most delightful book on symmetry ever written! F.L. Pilar, Elementary Quantum Chemistry The book gives a fascinating overview of the rich variety of applications of symmetry, showing both its power and its aesthetic appeal. Science Education by aesthetic appeal. Nature The cosmopolitan eye ¦ good-humored and clearly delighted by diversity, informs this entire book. The work offers a broad new perspective. Scientific American In the refreshing style of scientists with an almost renaissance versatility. New Scientist This beautiful book ¦ looks at symmetry as a unifying theme in the nature of things. Mathematical Reviews ¦gives the reader a broad perspective ¦ The Mathematical Intelligencer An outstanding book that succeeds admirably on a number of levels ¦ Bowker's Good Reading I warmly recommend it to all chemists. Journal of Chemical Education Succeeds not only in demonstrating how central [in] the study of all fields of chemistry symmetry consideration [is] but how these same concepts of symmetry can be traced through all our cultural traditions unifying and contrasting diverse endeavors in literature, music, and art. Journal of the American Chemical Society The book ¦to which I shall return frequently and with considerable pleasure. Chemistry and Industry
Molecular theory --- Symmetry (Physics) --- Fysische chemie --- Symmetrie ; natuurwetenschappen --- Invariance principles (Physics) --- Symmetry (Chemistry) --- Conservation laws (Physics) --- Physics --- Chemistry, Physical and theoretical --- Matter --- Constitution
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The essays in this book explore the ancient affinity between the mathematical and the aesthetic, focusing on the fundamental connections between these two modes of reasoning and communicating. From historical, philosophical and psychological perspectives, with particular attention to certain mathematical areas such as geometry and analysis, the authors examine the ways in which the aesthetic is ever present in mathematical thinking and contributes to the growth and value of mathematical knowledge. This book includes the following essays: • A Historical Gaze at the Mathematical Aesthetic, by Nathalie Sinclair and David Pimm • Aesthetics for the Working Mathematician, by Jonathan M. Borwein • Beauty and Truth in Mathematics, by Doris Schattschneider • Experiencing Meanings in Geometry, by David W. Henderson and Daina Taimina • The Aesthetic Sensibilities of Mathematicians, by Nathalie Sinclair • The Meaning of Pattern, by Martin Schiralli • Mathematics, Aesthetics and Being Human, by William Higginson • Mechanism and Magic in the Psychology of Dynamic Geometry, by R. Nicholas Jackiw • Drawing on the Image in Mathematics and Art, by David Pimm • Sensible Objects, by Dick Tahta • Aesthetics and the ‘Mathematical Mind’, by David Pimm and Nathalie Sinclair.
7.01 --- 72.01 --- Mathematics. --- Aesthetics. --- 51 --- Beautiful, The --- Beauty --- Esthetics --- Taste (Aesthetics) --- Philosophy --- Art --- Criticism --- Literature --- Proportion --- Symmetry --- Math --- Science --- Kunst (esthetica) --- Kunstesthetica --- Architectuur (esthetica) --- Architectuuresthetica --- Mathematica --- Wiskunde --- Psychology --- Aesthetics --- Mathematics --- Radio broadcasting Aesthetics
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In 1915 Emmy Noether was invited by Klein and Hilbert to Göttingen to assist them in understanding the law of conservation of energy in Einstein’s new general theory of relativity. She succeeded brilliantly. In the Invariante Variationsprobleme, published in 1918, she proved a fundamental theorem linking invariance properties and conservation laws in any theory formulated in terms of a variational principle, and she stated a second theorem which put a conjecture of Hilbert in perspective and furnished a proof of a much more general result. This book makes the Invariante Variationsprobleme accessible in an English translation. It presents an analysis of the work of Noether’s precursors, reformulates her argument in a more modern mathematical language, and recounts the strange history of the article’s reception in the mathematics and physics communities. This study shows how her two theorems ultimately became the basis for any deep understanding of the role of symmetries in both classical and quantum physics. The Noether Theorems, a translation of Les Théorèmes de Noether whose French text has been revised and expanded, provides rich documentation drawn from both primary and secondary sources. This book will be of interest to historians of science, to teachers of mathematics, mechanics and physics, and to mathematicians and mathematical physicists. Also by Yvette Kosmann-Schwarzbach: Groups and Symmetries: From Finite Groups to Lie Groups, © 2010 Springer, ISBN: 978-0-387-78865-4.
Mathematics --- geschiedenis --- wiskunde --- Calculus of variations. --- Noether's theorem. --- Symmetry (Physics). --- Mathematics. --- History. --- History of Mathematical Sciences. --- Annals --- Auxiliary sciences of history --- Math --- Science --- Noether, Emmy, --- Influence. --- Noether, Amalie Emmy, --- Noether, E. --- Noether's theorems.
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This book aims to coherently present applications of group analysis to integro-differential equations in an accessible way. The book will be useful to both physicists and mathematicians interested in general methods to investigate nonlinear problems using symmetries. Differential and integro-differential equations, especially nonlinear, present the most effective way for describing complex processes. Therefore, methods to obtain exact solutions of differential equations play an important role in physics, applied mathematics and mechanics. This book provides an easy to follow, but comprehensive, description of the application of group analysis to integro-differential equations. The book is primarily designed to present both fundamental theoretical and algorithmic aspects of these methods. It introduces new applications and extensions of the group analysis method. The authors have designed a flexible text for postgraduate courses spanning a variety of topics.
Physics. --- Mathematical Methods in Physics. --- Atoms and Molecules in Strong Fields, Laser Matter Interaction. --- Plasma Physics. --- Classical Continuum Physics. --- Mathematical physics. --- Physique --- Physique mathématique --- Integro-differential equations --- Symmetry (Physics) --- Invariance principles (Physics) --- Symmetry (Chemistry) --- Integrodifferential equations --- Differential equations --- Integral equations --- Conservation laws (Physics) --- Physics --- Integro-differential equations. --- Mechanics. --- Theoretical, Mathematical and Computational Physics. --- Classical Mechanics. --- Classical and Continuum Physics. --- Physical mathematics --- Classical mechanics --- Newtonian mechanics --- Dynamics --- Quantum theory --- Mathematics --- Atoms. --- Plasma (Ionized gases). --- Continuum physics. --- Classical field theory --- Continuum physics --- Continuum mechanics --- Gaseous discharge --- Gaseous plasma --- Magnetoplasma --- Ionized gases --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Chemistry, Physical and theoretical --- Matter --- Stereochemistry --- Constitution
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Symmetry is a key ingredient in many mathematical, physical, and biological theories. Using representation theory and invariant theory to analyze the symmetries that arise from group actions, and with strong emphasis on the geometry and basic theory of Lie groups and Lie algebras, Symmetry, Representations, and Invariants is a significant reworking of an earlier highly-acclaimed work by the authors. The result is a comprehensive introduction to Lie theory, representation theory, invariant theory, and algebraic groups, in a new presentation that is more accessible to students and includes a broader range of applications. The philosophy of the earlier book is retained, i.e., presenting the principal theorems of representation theory for the classical matrix groups as motivation for the general theory of reductive groups. The wealth of examples and discussion prepares the reader for the complete arguments now given in the general case. Key Features of Symmetry, Representations, and Invariants: • Early chapters suitable for honors undergraduate or beginning graduate courses, requiring only linear algebra, basic abstract algebra, and advanced calculus • Applications to geometry (curvature tensors), topology (Jones polynomial via symmetry), and combinatorics (symmetric group and Young tableaux) • Self-contained chapters, appendices, comprehensive bibliography • More than 350 exercises (most with detailed hints for solutions) further explore main concepts • Serves as an excellent main text for a one-year course in Lie group theory • Benefits physicists as well as mathematicians as a reference work.
algebra --- topologie (wiskunde) --- Mathematical physics --- Topological groups. Lie groups --- Algebra --- wiskunde --- Group theory --- fysica --- Representations of groups --- Invariants --- Symmetry (Mathematics) --- Lie groups --- Représentations de groupes --- Analyse multidimensionnelle --- Symétrie (Mathématiques) --- Groupes de Lie --- Algèbre --- EPUB-LIV-FT LIVMATHE LIVSTATI SPRINGER-B --- Representations of groups. --- Invariants. --- Symmetry (Mathematics). --- Algebra. --- Lie groups. --- Group theory. --- Geometry. --- Mathematical physics. --- Topological Groups. --- Group Theory and Generalizations. --- Mathematical Methods in Physics. --- Topological Groups, Lie Groups. --- General Algebraic Systems. --- Groups, Topological --- Continuous groups --- Physical mathematics --- Physics --- Mathematics --- Euclid's Elements --- Mathematical analysis --- Groups, Theory of --- Substitutions (Mathematics) --- Physics. --- Topological groups. --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics
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Symmetries in various forms pervade mathematics and physics. Globally, there are the symmetries of a homogenous space induced by the action of a Lie group. Locally, there are the infinitesimal symmetries induced by differential operators, including not only those of first order but of higher order too. This three-week summer program considered the symmetries preserving various natural geometric structures. Often these structures are themselves derived from partial differential equations whilst their symmetries turn out to be contrained by overdetermined systems. This leads to further topics including separation of variables, conserved quantities, superintegrability, parabolic geometry, represantation theory, the Bernstein-Gelfand-Gelfand complex, finite element schemes, exterior differential systems and moving frames. There are two parts to the Proceedings. The articles in the first part are expository but all contain significant new material. The articles in the second part are concerned with original research. All articles were thoroughly refereed and the range of interrelated work ensures that this will be an extremely useful collection. These Proceedings are dedicated to the memory of Thomas P. Branson who played a leading role in the conception and organization of this Summer Program but did not live to see its realization. .
Mathematics. --- Partial Differential Equations. --- Applications of Mathematics. --- Differential equations, partial. --- Mathématiques --- Differential equations, Partial. --- Differential equations, Partial --- Symmetry (Mathematics) --- Global analysis (Mathematics) --- Geometry, Differential --- Calculus --- Geometry --- Mathematics --- Physical Sciences & Mathematics --- Invariance (Mathematics) --- Partial differential equations. --- Applied mathematics. --- Engineering mathematics. --- Group theory --- Automorphisms --- Math --- Science --- Partial differential equations --- Engineering --- Engineering analysis --- Mathematical analysis
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The potentiality of phenomenological aesthetics is enormous, many figures have contributed to it during a time span of over a century, but this is the first work thoroughly to show its breadth, depth, and continuing fecundity. Moritz Geiger, Roman Ingarden, Fritz Kaufmann, Jean-Paul Sartre, Maurice Merleau-Ponty, and Mikel Dufrenne are the central figures and receive substantial treatment. A score of other influential individuals, including Antonio Banfi, Simone de Beauvoir, Oskar Becker, Jacques Derrida, Hans-Georg Gadamer, Martin Heidegger, Michel Henry, Dietrich von Hildebrand, Maurice Natanson, Nishida Kitaro, Jose Ortega y Gasset, Jan Patocka, Paul Ricoeur, Heinrich Rombach, Max Scheler, Alfred Schutz, Gustav Spet, and France Veber also have entries devoted to them. In addition, there are over two dozen entries on such topics such as dream, empathy, enjoyment, imagination, sensation, on style, ecology, gender, and interculturality, and then on areas including architecture, film, and theater. The introduction includes an extensive sketch of the history of phenomenological investigation in this sub-discipline of philosophy. All entries are written by the best relevant specialists, all the entries have bibliographies, and a selected bibliography for the whole is appended. This handbook will be the foundation for many more decades of investigation.
Theory of knowledge --- Aesthetics --- Phenomenology --- Phénoménologie --- Esthétique --- EPUB-LIV-FT LIVHUMAI SPRINGER-B --- Philosophy, Modern --- Beautiful, The --- Beauty --- Esthetics --- Taste (Aesthetics) --- Philosophy --- Art --- Criticism --- Literature --- Proportion --- Symmetry --- Psychology --- Aesthetics. --- Phenomenology. --- Phenomenology . --- Philosophy. --- Modern philosophy. --- Philosophy, general. --- Modern Philosophy. --- History of Philosophy. --- Modern philosophy --- Mental philosophy --- Humanities --- Radio broadcasting Aesthetics --- Phénoménologie --- Esthétique --- Philosophy, Modern. --- Early Modern Philosophy. --- History.
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Symmetries, coupled with the mathematical concept of group theory, are an essential conceptual backbone in the formulation of quantum field theories capable of describing the world of elementary particles. This primer is an introduction to and survey of the underlying concepts and structures needed in order to understand and handle these powerful tools. Specifically, in Part I of the book the symmetries and related group theoretical structures of the Minkowskian space-time manifold are analyzed, while Part II examines the internal symmetries and their related unitary groups, where the interactions between fundamental particles are encoded as we know them from the present standard model of particle physics. This book, based on several courses given by the authors, addresses advanced graduate students and non-specialist researchers wishing to enter active research in the field, and having a working knowledge of classical field theory and relativistic quantum mechanics. Numerous end-of-chapter problems and their solutions will facilitate the use of this book as self-study guide or as course book for topical lectures.
geofysica --- Geophysics --- Theory of relativity. Unified field theory --- Mathematical physics --- elementaire deeltjes --- Elementary particles --- relativiteitstheorie --- geophysics --- wiskunde --- zwaartekracht --- kwantumleer --- Symmetry (Physics) --- Group theory --- Symétrie (Physique) --- Théorie des groupes --- Problems, exercises, etc. --- Problems, exercices, etc --- Problèmes et exercices --- EPUB-LIV-FT LIVPHYSI SPRINGER-B --- Problems, exercices, etc.
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Artworks potentially convey two kinds of knowledge. They obviously afford knowledge of art itself, and they also afford general empirical knowledge, especially knowledge of human psychology and value. Knowing Art collects ten original essays written by leading philosophers who distill and build upon recent work at the intersection of aesthetics and epistemology. Specific topics addressed include the objectivity of critical knowledge, the quality of critical testimony, the roles of principles and perception in critical reasoning, phenomenal knowledge of what a work of art is like, the acquisition of factual information and psychological understanding from fictions, and the limits of images as sources of historical evidence. In addressing these topics, the volume also explores the challenges that art poses for theories of knowledge as well as the challenges that artistic knowledge poses to traditional views about art.
ethiek --- Theory of knowledge --- kennisleer --- kunst --- epistomologie --- General ethics --- Aesthetics --- esthetica --- epistemologists --- Art --- aesthetics --- Aesthetics. --- Knowledge, Theory of. --- Beautiful, The --- Beauty --- Esthetics --- Taste (Aesthetics) --- Philosophy --- Criticism --- Literature --- Proportion --- Symmetry --- Psychology --- Knowledge, Theory of --- Epistemology --- Genetic epistemology. --- Ethics. --- Arts. --- Epistemology. --- Arts, Fine --- Arts, Occidental --- Arts, Western --- Fine arts --- Humanities --- Deontology --- Ethics, Primitive --- Ethology --- Moral philosophy --- Morality --- Morals --- Philosophy, Moral --- Science, Moral --- Values --- Developmental psychology --- Arts, Primitive --- Radio broadcasting Aesthetics
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Cell biologists have recently become aware that the asymmetry of cell division is an important regulatory phenomenon in the fate of a cell. During development, cell diversity originates through asymmetry; in the adult organism asymmetric divisions regulate the stem cell reservoir and are a source of the drift that contributes to the aging of organisms with renewable cell compartments. Because of the concept of semi-conservative DNA synthesis, it was thought that the distribution of DNA between daughter cells was symmetric. The analysis of the phenomenon in cells during mitosis, however, revealed the asymmetry in the distribution of the genetic material that creates the drift contributing to aging of mammals. On the other hand, cancer cells can originate from a deregulation of asymmetry during mitosis in particular during stem cell expansion. The book describes the phenomenon in different organisms from plants to animals and addresses its implications for the development of the organism, cell differentiation, human aging and the biology of cancers.
embryologie (geneeskunde) --- histologie --- Histology. Cytology --- Oncology. Neoplasms --- General embryology. Developmental biology --- oncologie --- cytologie --- Cell division --- Cell differentiation --- Genetic recombination --- Symmetry (Biology) --- Biodiversity --- Cellules --- Recombinaison génétique --- Molecular aspects --- Genetic aspects --- Division --- Life Sciences --- Biology --- Molecular biology --- Biologie moléculaire --- Biologie moléculaire --- MDBIOCHE --- Cell differentiation. --- Cell division. --- Developmental biology. --- Cytology. --- Oncology. --- Developmental Biology. --- Cell Biology. --- Cancer Research. --- Tumors --- Cell biology --- Cellular biology --- Cells --- Cytologists --- Development (Biology) --- Growth --- Ontogeny --- Cell biology. --- Cancer research. --- Cancer research
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