Download or read book The History of Continua written by Stewart Shapiro and published by Oxford University Press, USA. This book was released on 2021 with total page 593 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical and philosophical thought about continuity has changed considerably over the ages, from Aristotle's insistence that a continuum is a unified whole, to the dominant account today, that a continuum is composed of infinitely many points. This book explores the key ideas and debates concerning continuity over more than 2500 years.

Download or read book The History of Continua written by Stewart Shapiro and published by Oxford University Press. This book was released on 2020-12-01 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical and philosophical thought about continuity has changed considerably over the ages. Aristotle insisted that continuous substances are not composed of points, and that they can only be divided into parts potentially. There is something viscous about the continuous. It is a unified whole. This is in stark contrast with the prevailing contemporary account, which takes a continuum to be composed of an uncountably infinite set of points. This vlume presents a collective study of key ideas and debates within this history. The opening chapters focus on the ancient world, covering the pre-Socratics, Plato, Aristotle, and Alexander. The treatment of the medieval period focuses on a (relatively) recently discovered manuscript, by Bradwardine, and its relation to medieval views before, during, and after Bradwardine's time. In the so-called early modern period, mathematicians developed the calculus and, with that, the rise of infinitesimal techniques, thus transforming the notion of continuity. The main figures treated here include Galileo, Cavalieri, Leibniz, and Kant. In the early party of the nineteenth century, Bolzano was one of the first important mathematicians and philosophers to insist that continua are composed of points, and he made a heroic attempt to come to grips with the underlying issues concerning the infinite. The two figures most responsible for the contemporary orthodoxy regarding continuity are Cantor and Dedekind. Each is treated in an article, investigating their precursors and influences in both mathematics and philosophy. A new chapter then provides a lucid analysis of the work of the mathematician Paul Du Bois-Reymond, to argue for a constructive account of continuity, in opposition to the dominant Dedekind-Cantor account. This leads to consideration of the contributions of Weyl, Brouwer, and Peirce, who once dubbed the notion of continuity "the master-key which . . . unlocks the arcana of philosophy". And we see that later in the twentieth century Whitehead presented a point-free, or gunky, account of continuity, showing how to recover points as a kind of "extensive abstraction". The final four chapters each focus on a more or less contemporary take on continuity that is outside the Dedekind-Cantor hegemony: a predicative approach, accounts that do not take continua to be composed of points, constructive approaches, and non-Archimedean accounts that make essential use of infinitesimals.

Download or read book A Luta Continua written by Lizette Rabe and published by African Sun Media. This book was released on 2020-10-16 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: What has media freedom entailed over the couple of centuries and successive governments of the geopolitical region that became South Africa since it was colonised by Westerners? And why can media freedom be described as both pillar and cornerstone of a democracy? It’s simple, as in the words of Nelson Mandela, first state president of a democratic South Africa: Press freedom is the “lifeblood of democracy”. This book tells the tale of the various states of press freedom, or unfreedom, from colonial times to today – from a British governor called a dictator and a despot, through apartheid’s “pigmentocracy”, or “sjambokracy”, where the rule of law “has been replaced by the rule of the whip”, up to the dawn of liberation, with media freedom entrenched in Article 16 of South Africa’s Bill of Rights. And why should all of this concern you? Because media freedom is not about the freedom of the media. It is about your freedom. As was formulated by an editor under apartheid: “If we don’t have a public sympathetic to a free press, not only will we not have a free press, we won’t have a democracy either.” Or, in the words of former Sowetan editor and SANEF chair, Mpumelelo Mhkabela: “Media freedom has nothing to do with the media, but with the freedom of citizens.” And that is why you should know that a free media is the only guarantee for your freedom. As we have seen, both under apartheid and also under a democratic dispensation, it is a matter of a luta continua. The struggle continues. But you, the public, are the guardian of those that guard democracy. Help ensure the rights of a free media, and thereby your democratic rights and a democratic South Africa.

Download or read book Handbook of the History of General Topology written by C.E. Aull and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first one of a work in several volumes, treating the history of the development of topology. The work contains papers which can be classified into 4 main areas. Thus there are contributions dealing with the life and work of individual topologists, with specific schools of topology, with research in topology in various countries, and with the development of topology in different periods. The work is not restricted to topology in the strictest sense but also deals with applications and generalisations in a broad sense. Thus it also treats, e.g., categorical topology, interactions with functional analysis, convergence spaces, and uniform spaces. Written by specialists in the field, it contains a wealth of information which is not available anywhere else.

Download or read book The Mechanics and Thermodynamics of Continua written by Morton E. Gurtin and published by Cambridge University Press. This book was released on 2010-04-19 with total page 721 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Mechanics and Thermodynamics of Continua presents a unified treatment of continuum mechanics and thermodynamics that emphasises the universal status of the basic balances and the entropy imbalance. These laws are viewed as fundamental building blocks on which to frame theories of material behaviour. As a valuable reference source, this book presents a detailed and complete treatment of continuum mechanics and thermodynamics for graduates and advanced undergraduates in engineering, physics and mathematics. The chapters on plasticity discuss the standard isotropic theories and, in addition, crystal plasticity and gradient plasticity.

Download or read book Mechanics of Generalized Continua written by Gérard A. Maugin and published by Springer Science & Business Media. This book was released on 2010-03-24 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: In their 1909 publication Théorie des corps déformables, Eugène and François Cosserat made a historic contribution to materials science by establishing the fundamental principles of the mechanics of generalized continua. The chapters collected in this volume showcase the many areas of continuum mechanics that grew out of the foundational work of the Cosserat brothers. The included contributions provide a detailed survey of the most recent theoretical developments in the field of generalized continuum mechanics and can serve as a useful reference for graduate students and researchers in mechanical engineering, materials science, applied physics and applied mathematics.

Download or read book Continua written by Howard Cook and published by CRC Press. This book was released on 2020-12-17 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the special session on Modern Methods in Continuum Theory presented at the 100th Annual Joint Mathematics Meetings held in Cincinnati, Ohio. It also features the Houston Problem Book which includes a recently updated set of 200 problems accumulated over several years at the University of Houston.;These proceedings and problems are aimed at pure and applied mathematicians, topologists, geometers, physicists and graduate-level students in these disciplines.

Download or read book The History of the Theory of Structures written by Karl-Eugen Kurrer and published by John Wiley & Sons. This book was released on 2018-06-19 with total page 1248 pages. Available in PDF, EPUB and Kindle. Book excerpt: Zehn Jahre nach der 1. Auflage in englischer Sprache legt der Autor sein Buch The History of the Theory of Structures in wesentlich erweiterter Form vor, nunmehr mit dem Untertitel Searching for Equilibrium. Mit dem vorliegenden Buch lädt der Verfasser seine Leser zur Suche nach dem Gleichgewicht von Tragwerken auf Zeitreisen ein. Die Zeitreisen setzen mit der Entstehung der Statik und Festigkeitslehre eines Leonardo und Galilei ein und erreichen ihren ersten Höhepunkt mit den baustatischen Theorien über den Balken, Erddruck und das Gewölbe von Coulomb am Ende des 18. Jahrhunderts. Im folgenden Jahrhundert formiert sich die Baustatik mit Navier, Culmann, Maxwell, Rankine, Mohr, Castigliano und Müller-Breslau zu einer technikwissenschaftlichen Grundlagendisziplin, die im 20. Jahrhundert in Gestalt der modernen Strukturmechanik bei der Herausbildung der konstruktiven Sprache des Stahl-, Stahlbeton-, Flugzeug-, Automobil- und des Schiffbaus eine tragende Rolle spielt. Dabei setzt der Autor den inhaltlichen Schwerpunkt auf die Formierung und Entwicklung moderner numerischer Ingenieurmethoden wie der Finite-Elemente-Methode und beschreibt ihre disziplinäre Integration in der Computational Mechanics. Kurze, durch historische Skizzen unterstützte Einblicke in gängige Berechnungsverfahren erleichtern den Zugang zur Geschichte der Strukturmechanik und Erddrucktheorie vom heutigen Stand der Ingenieurpraxis und stellen einen auch einen wichtigen Beitrag zur Ingenieurpädagogik dar. Dem Autor gelingt es, die Unterschiedlichkeit der Akteure hinsichtlich ihres technisch-wissenschaftlichen Profils und ihrer Persönlichkeit plastisch zu schildern und das Verständnis für den gesellschaftlichen Kontext zu erzeugen. So werden in 260 Kurzbiografien die subjektive Dimension der Baustatik und der Strukturmechanik von der frühen Neuzeit bis heute entfaltet. Dabei werden die wesentlichen Beiträge der Protagonisten der Baustatik besprochen und in die nachfolgende Bibliografie integriert. Berücksichtigt wurden nicht nur Bauingenieure und Architekten, sondern auch Mathematiker, Physiker, Maschinenbauer sowie Flugzeug- und Schiffbauer. Neben den bekannten Persönlichkeiten der Baustatik, wie Coulomb, Culmann, Maxwell, Mohr, Müller-Breslau, Navier, Rankine, Saint-Venant, Timoshenko und Westergaard, wurden u. a. auch G. Green, A. N. Krylov, G. Li, A. J. S. Pippard, W. Prager, H. A. Schade, A. W. Skempton, C. A. Truesdell, J. A. L. Waddell und H. Wagner berücksichtigt. Den Wegbereitern der Moderne in der Baustatik J. H. Argyris, R. W. Clough, Th. v. Kármán, M. J. Turner und O. C. Zienkiewicz wurden umfangreiche Biografien gewidmet. Eine ca. 4500 Titel umfassende Bibliografie rundet das Werk ab. Neue Inhalte der 2. Auflage sind: Erddrucktheorie, Traglastverfahren, historische Lehrbuchanalyse, Stahlbrückenbau, Leichtbau, Platten- und Schalentheorie, Greensche Funktion, Computerstatik, FEM, Computergestützte Graphostatik und Historische Technikwissenschaft. Gegenüber der 1., englischen Ausgabe wurde der Seitenumfang um 50 % auf nunmehr etwas über 1200 Druckseiten gesteigert. Das vorliegende Buch ist die erste zusammenfassende historische Gesamtdarstellung der Baustatik vom 16. Jahrhundert bis heute. Über die Reihe edition Bautechnikgeschichte: Mit erstaunlicher Dynamik hat sich die Bautechnikgeschichte in den vergangenen Jahrzehnten zu einer höchst lebendigen, international vernetzten und viel beachteten eigenständigen Disziplin entwickelt. Auch wenn die nationalen Forschungszugänge unterschiedliche Akzente setzen, eint sie doch das Bewusstsein, dass gerade die inhaltliche und methodische Vielfalt und das damit verbundene synthetische Potenzial die Stärke des neuen Forschungsfeldes ausmachen. Bautechnikgeschichte erschließt neue Formen des Verstehens von Bauen zwischen Ingenieurwesen und Architektur, zwischen Bau- und Kunst-, Technik- und Wissenschaftsgeschichte. Mit der edition Bautechnikgeschichte erhält die neue Disziplin erstmals einen Ort für die Publikation wichtiger Arbeiten auf angemessenem Niveau in hochwertiger Gestaltung. Die Bücher erscheinen in deutscher oder englischer Sprache. Beide Hauptrichtungen der Bautechnikgeschichte, der eher konstruktionsgeschichtlich und der eher theoriegeschichtlich geleitete Zugang, finden Berücksichtigung; das Spektrum der Bände reicht von Überblickswerken über Monographien zu Einzelaspekten oder -bauten bis hin zu Biographien bedeutender Ingenieurpersönlichkeiten. Ein international besetzter Wissenschaftlicher Beirat unterstützt die Herausgeber in der Umsetzung des Konzepts.

Download or read book Theoretical Mechanics of Particles and Continua written by Alexander L. Fetter and published by Courier Corporation. This book was released on 2003-12-16 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-part text fills what has often been a void in the first-year graduate physics curriculum. Through its examination of particles and continua, it supplies a lucid and self-contained account of classical mechanics — which in turn provides a natural framework for introducing many of the advanced mathematical concepts in physics. The text opens with Newton's laws of motion and systematically develops the dynamics of classical particles, with chapters on basic principles, rotating coordinate systems, lagrangian formalism, small oscillations, dynamics of rigid bodies, and hamiltonian formalism, including a brief discussion of the transition to quantum mechanics. This part of the book also considers examples of the limiting behavior of many particles, facilitating the eventual transition to a continuous medium. The second part deals with classical continua, including chapters on string membranes, sound waves, surface waves on nonviscous fluids, heat conduction, viscous fluids, and elastic media. Each of these self-contained chapters provides the relevant physical background and develops the appropriate mathematical techniques, and problems of varying difficulty appear throughout the text.

Download or read book The Continuous the Discrete and the Infinitesimal in Philosophy and Mathematics written by John L. Bell and published by Springer Nature. This book was released on 2019-09-09 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores and articulates the concepts of the continuous and the infinitesimal from two points of view: the philosophical and the mathematical. The first section covers the history of these ideas in philosophy. Chapter one, entitled ‘The continuous and the discrete in Ancient Greece, the Orient and the European Middle Ages,’ reviews the work of Plato, Aristotle, Epicurus, and other Ancient Greeks; the elements of early Chinese, Indian and Islamic thought; and early Europeans including Henry of Harclay, Nicholas of Autrecourt, Duns Scotus, William of Ockham, Thomas Bradwardine and Nicolas Oreme. The second chapter of the book covers European thinkers of the sixteenth and seventeenth centuries: Galileo, Newton, Leibniz, Descartes, Arnauld, Fermat, and more. Chapter three, 'The age of continuity,’ discusses eighteenth century mathematicians including Euler and Carnot, and philosophers, among them Hume, Kant and Hegel. Examining the nineteenth and early twentieth centuries, the fourth chapter describes the reduction of the continuous to the discrete, citing the contributions of Bolzano, Cauchy and Reimann. Part one of the book concludes with a chapter on divergent conceptions of the continuum, with the work of nineteenth and early twentieth century philosophers and mathematicians, including Veronese, Poincaré, Brouwer, and Weyl. Part two of this book covers contemporary mathematics, discussing topology and manifolds, categories, and functors, Grothendieck topologies, sheaves, and elementary topoi. Among the theories presented in detail are non-standard analysis, constructive and intuitionist analysis, and smooth infinitesimal analysis/synthetic differential geometry. No other book so thoroughly covers the history and development of the concepts of the continuous and the infinitesimal.

Download or read book Nonlinear Finite Elements for Continua and Structures written by Ted Belytschko and published by John Wiley & Sons. This book was released on 2014-01-07 with total page 834 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear Finite Elements for Continua and Structures p>Nonlinear Finite Elements for Continua and Structures This updated and expanded edition of the bestselling textbook provides a comprehensive introduction to the methods and theory of nonlinear finite element analysis. New material provides a concise introduction to some of the cutting-edge methods that have evolved in recent years in the field of nonlinear finite element modeling, and includes the eXtended Finite Element Method (XFEM), multiresolution continuum theory for multiscale microstructures, and dislocation- density-based crystalline plasticity. Nonlinear Finite Elements for Continua and Structures, Second Edition focuses on the formulation and solution of discrete equations for various classes of problems that are of principal interest in applications to solid and structural mechanics. Topics covered include the discretization by finite elements of continua in one dimension and in multi-dimensions; the formulation of constitutive equations for nonlinear materials and large deformations; procedures for the solution of the discrete equations, including considerations of both numerical and multiscale physical instabilities; and the treatment of structural and contact-impact problems. Key features: Presents a detailed and rigorous treatment of nonlinear solid mechanics and how it can be implemented in finite element analysis Covers many of the material laws used in today’s software and research Introduces advanced topics in nonlinear finite element modelling of continua Introduction of multiresolution continuum theory and XFEM Accompanied by a website hosting a solution manual and MATLAB® and FORTRAN code Nonlinear Finite Elements for Continua and Structures, Second Edition is a must-have textbook for graduate students in mechanical engineering, civil engineering, applied mathematics, engineering mechanics, and materials science, and is also an excellent source of information for researchers and practitioners.

Download or read book The Oxford Handbook of the History of English written by Terttu Nevalainen and published by Oxford University Press. This book was released on 2012-10-10 with total page 983 pages. Available in PDF, EPUB and Kindle. Book excerpt: The availability of large electronic corpora has caused major shifts in linguistic research, including the ability to analyze much more data than ever before, and to perform micro-analyses of linguistic structures across languages. This has historical linguists to rethink many standard assumptions about language history, and methods and approaches that are relevant to the study of it. The field is now interested in, and attracts, specialists whose fields range from statistical modeling to acoustic phonetics. These changes have even transformed linguists' perceptions of the very processes of language change, particularly in English, the most studied language in historical linguistics due to the size of available data and its status as a global language. The Oxford Handbook of the History of English takes stock of recent advances in the study of the history of English, broadening and deepening the understanding of the field. It seeks to suggest ways to rethink the relationship of English's past with its present, and make transparent the variety of conditions and processes that have been instrumental in shaping that history. Setting a new standard of cross-theoretical collaboration, it covers the field in an innovative way, providing diachronic accounts of major influences such as language contact, and typological processes that have shaped English and its varieties, as well as highlighting recent and ongoing developments of Englishes--celebrating the vitality of language change over the centuries and the many contexts and processes through which language change occurs.

Download or read book A History and Development of Indecomposable Continua Theory written by Francis Leon Jones and published by . This book was released on 1971 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Oxford Handbook of the History of English written by Terttu Nevalainen (linguiste) and published by Oxford University Press. This book was released on 2016 with total page 983 pages. Available in PDF, EPUB and Kindle. Book excerpt: This ambitious handbook takes advantage of recent advances in the study of the history of English to rethink the understanding of the field.

Download or read book Continua of Biliteracy written by Nancy H. Hornberger and published by Multilingual Matters. This book was released on 2003-05-23 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: Biliteracy - the use of two or more languages in and around writing- is an inescapable feature of lives and schools worldwide, yet one which most educational policy and practice continue blithely to ignore. The continua of biliteracy featured in the present volume offers a comprehensive yet flexible model to guide educators, researchers, and policy-makers in designing, carrying out, and evaluating educational programs for the development of bilingual and multilingual learners, each program adapted to its own specific context, media, and contents.

Download or read book Mathematical Structuralism written by Geoffrey Hellman and published by Cambridge University Press. This book was released on 2018-11-29 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present work is a systematic study of five frameworks or perspectives articulating mathematical structuralism, whose core idea is that mathematics is concerned primarily with interrelations in abstraction from the nature of objects. The first two, set-theoretic and category-theoretic, arose within mathematics itself. After exposing a number of problems, the Element considers three further perspectives formulated by logicians and philosophers of mathematics: sui generis, treating structures as abstract universals, modal, eliminating structures as objects in favor of freely entertained logical possibilities, and finally, modal-set-theoretic, a sort of synthesis of the set-theoretic and modal perspectives.

Download or read book The Historical Roots of Political Violence written by Ignacio Sánchez-Cuenca and published by Cambridge University Press. This book was released on 2019-06-06 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offers the first comprehensive analysis of the wave of revolutionary terrorism in affluent countries.