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Author: Gunther Schmidt
Publisher: Springer
ISBN: 3319744518
Category : Mathematics
Languages : en
Pages : 200
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Book Description
This book introduces and develops new algebraic methods to work with relations, often conceived as Boolean matrices, and applies them to topology. Although these objects mirror the matrices that appear throughout mathematics, numerics, statistics, engineering, and elsewhere, the methods used to work with them are much less well known. In addition to their purely topological applications, the volume also details how the techniques may be successfully applied to spatial reasoning and to logics of computer science. Topologists will find several familiar concepts presented in a concise and algebraically manipulable form which is far more condensed than usual, but visualized via represented relations and thus readily graspable. This approach also offers the possibility of handling topological problems using proof assistants.
Author: Gunther Schmidt
Publisher: Springer
ISBN: 3319744518
Category : Mathematics
Languages : en
Pages : 200
Get Book Here
Book Description
This book introduces and develops new algebraic methods to work with relations, often conceived as Boolean matrices, and applies them to topology. Although these objects mirror the matrices that appear throughout mathematics, numerics, statistics, engineering, and elsewhere, the methods used to work with them are much less well known. In addition to their purely topological applications, the volume also details how the techniques may be successfully applied to spatial reasoning and to logics of computer science. Topologists will find several familiar concepts presented in a concise and algebraically manipulable form which is far more condensed than usual, but visualized via represented relations and thus readily graspable. This approach also offers the possibility of handling topological problems using proof assistants.
Author: Michael Epperson
Publisher: Lexington Books
ISBN: 0739180339
Category : Philosophy
Languages : en
Pages : 441
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Book Description
If there is a central conceptual framework that has reliably borne the weight of modern physics as it ascends into the twenty-first century, it is the framework of quantum mechanics. Because of its enduring stability in experimental application, physics has today reached heights that not only inspire wonder, but arguably exceed the limits of intuitive vision, if not intuitive comprehension. For many physicists and philosophers, however, the currently fashionable tendency toward exotic interpretation of the theoretical formalism is recognized not as a mark of ascent for the tower of physics, but rather an indicator of sway—one that must be dampened rather than encouraged if practical progress is to continue. In this unique two-part volume, designed to be comprehensible to both specialists and non-specialists, the authors chart out a pathway forward by identifying the central deficiency in most interpretations of quantum mechanics: That in its conventional, metrical depiction of extension, inherited from the Enlightenment, objects are characterized as fundamental to relations—i.e., such that relations presuppose objects but objects do not presuppose relations. The authors, by contrast, argue that quantum mechanics exemplifies the fact that physical extensiveness is fundamentally topological rather than metrical, with its proper logico-mathematical framework being category theoretic rather than set theoretic. By this thesis, extensiveness fundamentally entails not only relations of objects, but also relations of relations. Thus, the fundamental quanta of quantum physics are properly defined as units of logico-physical relation rather than merely units of physical relata as is the current convention. Objects are always understood as relata, and likewise relations are always understood objectively. In this way, objects and relations are coherently defined as mutually implicative. The conventional notion of a history as “a story about fundamental objects” is thereby reversed, such that the classical “objects” become the story by which we understand physical systems that are fundamentally histories of quantum events. These are just a few of the novel critical claims explored in this volume—claims whose exemplification in quantum mechanics will, the authors argue, serve more broadly as foundational principles for the philosophy of nature as it evolves through the twenty-first century and beyond.
Author: Stanisław Gniłka
Publisher:
ISBN:
Category : Closure operators
Languages : en
Pages : 110
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Book Description
Author: Z. Frolík
Publisher: Academic Press
ISBN: 1483223531
Category : Mathematics
Languages : en
Pages : 366
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Book Description
General Topology and Its Relations to Modern Analysis and Algebra II is comprised of papers presented at the Second Symposium on General Topology and its Relations to Modern Analysis and Algebra, held in Prague in September 1966. The book contains expositions and lectures that discuss various subject matters in the field of General Topology. The topics considered include the algebraic structure for a topology; the projection spectrum and its limit space; some special methods of homeomorphism theory in infinite-dimensional topology; types of ultrafilters on countable sets; the compactness operator in general topology; and the algebraic generalization of the topological theorems of Bolzano and Weierstrass. This publication will be found useful by all specialists in the field of Topology and mathematicians interested in General Topology.
Author: Andrew Witt
Publisher: MIT Press
ISBN: 0262366851
Category : Architecture
Languages : en
Pages : 433
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Book Description
An investigation of mathematics as it was drawn, encoded, imagined, and interpreted by architects on the eve of digitization in the mid-twentieth century. In Formulations, Andrew Witt examines the visual, methodological, and cultural intersections between architecture and mathematics. The linkages Witt explores involve not the mystic transcendence of numbers invoked throughout architectural history, but rather architecture’s encounters with a range of calculational systems—techniques that architects inventively retooled for design. Witt offers a catalog of mid-twentieth-century practices of mathematical drawing and calculation in design that preceded and anticipated digitization as well as an account of the formal compendia that became a cultural currency shared between modern mathematicians and modern architects. Witt presents a series of extensively illustrated “biographies of method”—episodes that chart the myriad ways in which mathematics, particularly the mathematical notion of modeling and drawing, was spliced into the creative practice of design. These include early drawing machines that mechanized curvature; the incorporation of geometric maquettes—“theorems made flesh”—into the toolbox of design; the virtualization of buildings and landscapes through surveyed triangulation and photogrammetry; formal and functional topology; stereoscopic drawing; the economic implications of cubic matrices; and a strange synthesis of the technological, mineral, and biological: crystallographic design. Trained in both architecture and mathematics, Witt uses mathematics as a lens through which to understand the relationship between architecture and a much broader set of sciences and visual techniques. Through an intercultural exchange with other disciplines, he argues, architecture adapted not only the shapes and surfaces of mathematics but also its values and epistemic ideals.
Author: Fiorenza Belussi
Publisher: Routledge
ISBN: 1134048548
Category : Business & Economics
Languages : en
Pages : 512
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Book Description
During the 1980s the Marshallian concept of industrial district (ID) became widely popular due to the resurgence of interest in the reasons that make the agglomeration of specialised industries a territorial phenomenon worth being analysed. The analysis of clusters and IDs has often been limited, considering only the local dimension of the created business networks. The external links of these systems have been systematically under-evaluated. This book offers a deep insight into the evolution of these systems and the internal-external mechanism of knowledge circulation and learning. This means that the access to external knowledge (information or R&D cooperative research) or to productive networks (global supply chains) is studied in order to describe how external knowledge is absorbed and how local clusters or districts become global systems. It provides a unified approach; showing that existing capabilities expand when locally embedded knowledge is combined with accessible external knowledge. In this view, external knowledge linkages reduce the danger of cognitive ‘lock-in’ and ‘over-embeddedness’, which may become important obstacles to local learning and innovation when technological trajectories and global economic conditions change. A selection of international experts
Author: Matthias Middell
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110643006
Category : History
Languages : en
Pages : 400
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Book Description
Contributions to this volume summarize and discuss the theoretical foundations of the Collaborative Research Centre at Leipzig University which address the relationship between processes of (re-)spatialization on the one hand and the establishment and characteristics of spatial formats on the other hand. Under the global condition spatial formats are products of collective negotiations on the most effective and widely acceptable balance between the claim for sovereignty and the need for interconnectedness.
Author: Peter Höfner
Publisher: Springer
ISBN: 3319574183
Category : Mathematics
Languages : en
Pages : 335
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Book Description
This book constitutes the proceedings of the 16th International Conference on Relational and Algebraic Methods in Computer Science, RAMiCS 2017, held in Lyon, France, in May 2017. The 17 revised full papers and 2 invited papers presented together with 1 invited abstract were carefully selected from 28 submissions. Topics covered range from mathematical foundations to applications as conceptual and methodological tools in computer science and beyond.
Author: Thanasis Hadzilacos
Publisher: Springer Science & Business Media
ISBN: 3540405356
Category : Business & Economics
Languages : en
Pages : 541
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Book Description
This book constitutes the refereed proceedings of the 8th International Symposium on Spatial and Temporal Databases, SSTD 2003, held at Santorini Island, Greece in July 2003. The 28 revised full papers presented together with a keynote paper were carefully reviewed and selected from 105 submissions. the papers are organized in topical sections on access methods, advanced query processing, data mining and data warehousing, distance-based queries, mobility and moving points management, modeling and languages, similarity processing, systems and implementation issues.
Author: R. Jeffrey Ringer
Publisher: NYU Press
ISBN: 0814774407
Category : Social Science
Languages : en
Pages : 361
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Book Description
In many arenas the debate is raging over the nature of sexual orientation. Queer Words, Queer Images addresses this debate, but with a difference, arguing that homosexuality has become an issue precisely because of the way in which we discuss, debate, and communicate about the concept and experience of homosexuality. The debate over homosexuality is fundamentally an issue of communication—as we can see by the recent controversy over gays in the military. This controversy, termed by one gay man as the annoying habit of heterosexual men to overestimate their own attractiveness, has been debated in communication-sensitive terms, such as morale and discipline. The twenty chapters address such subjects as gay political language, homosexuality and AIDS on prime-time television, the politics of male homosexuality in young adult fiction, the identification of female athleticism with lesbianism, the politics of identity in the works of Edmund White, and coming out strategies. This is must reading for students of communication practices and theory, and for everyone interested in human sexuality. Contributing to the book are: James Chesebro (Indiana State), James Darsey (Ohio State), Joseph A. Devito (Hunter College, CUNY), Timothy Edgar (Purdue), Mary Anne Fitzpatrick (Wisconsin, Madison), Karen A. Foss (Humboldt State), Kirk Fuoss (St. Lawrence), Larry Gross (Pennsylvania), Darlene Hantzis (Indiana State), Fred E. Jandt (California State, San Bernardino), Mercilee Jenkins (San Francisco State), Valerie Lehr (St. Lawrence), Lynn C. Miller (Texas, Austin), Marguerite Moritz (Colorado, Boulder), Fred L. Myrick (Spring Hill), Emile Netzhammer (Buffalo State), Elenie Opffer, Dorothy S. Painter (Ohio State), Karen Peper (Michigan), Nicholas F. Radel (Furman), R. Jeffrey Ringer (St. Cloud State), Scott Shamp (Georgia), Paul Siegel (Gallaudet), Jacqueline Taylor (Depaul), Julia T. Wood (North Carolina, Chapel Hill).
