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General Theory Of Irregular Curves
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Book Synopsis General Theory of Irregular Curves by : V.V. Alexandrov
Download or read book General Theory of Irregular Curves written by V.V. Alexandrov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: One service mathematics has rendered the "Et moi ... si j'a\'ait su comment en revenir, human race. It has put common sense back je n'y scrais point alit: Jules Verne where it belongs, on the topmost shelf next to the dusty canister labc\led 'discarded non The series is divergent; therefore we may be sense'. Eric T. 8c\l able to do something with it. O. Hcaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.
Book Synopsis General theory of irregular curves by : Alexander Danilovič Alexandrov
Download or read book General theory of irregular curves written by Alexander Danilovič Alexandrov and published by . This book was released on 1989 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis General Theory of Irregular Curves by : V. V. Alexandrov
Download or read book General Theory of Irregular Curves written by V. V. Alexandrov and published by . This book was released on 1989-10-31 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Reshetnyak's Theory of Subharmonic Metrics by : François Fillastre
Download or read book Reshetnyak's Theory of Subharmonic Metrics written by François Fillastre and published by Springer Nature. This book was released on 2023-10-20 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: Despite the fundamental role played by Reshetnyak's work in the theory of surfaces of bounded integral curvature, the proofs of his results were only available in his original articles, written in Russian and often hard to find. This situation used to be a serious problem for experts in the field. This book provides English translations of the full set of Reshetnyak's articles on the subject. Together with the companion articles, this book provides an accessible and comprehensive reference for the subject. In turn, this book should concern any researcher (confirmed or not) interested in, or active in, the field of bounded integral curvature surfaces, or more generally interested in surface geometry and geometric analysis. Due to the analytic nature of Reshetnyak's approach, it appears that his articles are very accessible for a modern audience, comparing to the works using a more synthetic approach. These articles of Reshetnyak concern more precisely the work carried by the author following the completion of his PhD thesis, under the supervision of A.D. Alexandrov. Over the period from the 1940’s to the 1960’s, the Leningrad School of Geometry, developed a theory of the metric geometry of surfaces, similar to the classical theory of Riemannian surfaces, but with lower regularity, allowing greater flexibility. Let us mention A.D. Alexandrov, Y.D. Burago and V.A. Zalgaller. The types of surfaces studied by this school are now known as surfaces of bounded curvature. Particular cases are that of surfaces with curvature bounded from above or below, the study of which gained special attention after the works of M. Gromov and G. Perelman. Nowadays, these concepts have been generalized to higher dimensions, to graphs, and so on, and the study of metrics of weak regularity remains an active and challenging field. Reshetnyak developed an alternative and analytic approach to surfaces of bounded integral curvature. The underlying idea is based on the theorem of Gauss which states that every Riemannian surface is locally conformal to Euclidean space. Reshetnyak thus studied generalized metrics which are locally conformal to the Euclidean metric with conformal factor given by the logarithm of the difference between two subharmonic functions on the plane. Reshetnyak's condition appears to provide the correct regularity required to generalize classical concepts such as measure of curvature, integral geodesic curvature for curves, and so on, and in turn, to recover surfaces of bounded curvature. Chapter-No.7, Chapter-No.8, Chapter-No.12 and Chapter-No.13 are available open access under Creative Commons Attribution-NonCommercial 4.0 International License via link.springer.com.
Book Synopsis The General Theory of Eco-Social Science by : Jianfang Jin
Download or read book The General Theory of Eco-Social Science written by Jianfang Jin and published by Author House. This book was released on 2014 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: The General Theory of Eco-Social Science has made fundamental changes to Social Science; it introduces five new theories to the field of humanities and social science. ECO-ENTITY--An Entirely New Sociology It lays out an all new system of ecological theory integrating the social and natural sciences. At its core is the new concept of the "eco-entity," its roles and inner systems, its rules, operation laws and operating mechanism. ECO-RESOURCES--New Philosophy and Management It advances the concept of "eco-resources", expanding to the social relations of human beings, and puts forth the new theories of the monist world outlook of eco-resources, the dichotomy between positive and negative eco-resources, and the strategic management of eco-resources, through which it reveals a new dimension to humanities and social sciences. ECOLOGICAL SOCIETY--A Brand New Political Science It introduces the doctrine of an "ecological society" where the rule of law is replaced by the "rule of organicism," and explains the operating principles and governance of the future ecological society. ECO-ECONOMICS--A New Economics It demonstrates with flow charts the economic growth cycle. It depicts the laws of commodity value and "eco-value." It stresses the organic inter-relations between the government and the market. The author systematically expounded the economic growth cycle, the starting point, the methods, the principles, the mechanisms and the formulas, in his eco-economy growth theory. ECO -CURRENCY--A Complete New Theory of Currency It creates the new theory of Eco-currency, three basic attributes of currency and three major functions of currency. The author proposes a new eco-monetary policy: management of role currencies, or a "visible hand" in adjusting the economy. In addition, he also illustrates the elements of eco-currency, a new currency, in detail.
Book Synopsis General Theory of Curves by : Thomas Gilmer Proctor
Download or read book General Theory of Curves written by Thomas Gilmer Proctor and published by . This book was released on 1962 with total page 78 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Bulletin of the American Mathematical Society by : American Mathematical Society
Download or read book Bulletin of the American Mathematical Society written by American Mathematical Society and published by . This book was released on 1927 with total page 912 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Nonlinear Universe by : Alwyn C. Scott
Download or read book The Nonlinear Universe written by Alwyn C. Scott and published by Springer Science & Business Media. This book was released on 2007-10-02 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written in Alwyn Scott’s inimitable style, one that readers will find both lucid and accessible, this masterwork elucidates the explosion of activity in nonlinear science in recent decades. The book explains the wide-ranging implications of nonlinear phenomena for future developments in many areas of modern science, including mathematics, physics, engineering, chemistry, biology, and neuroscience. Arguably as important as quantum theory, modern nonlinear science is essential for understanding the scientific developments of the twenty-first century.
Book Synopsis From Catastrophe to Chaos: A General Theory of Economic Discontinuities by : J. Barkley Rosser
Download or read book From Catastrophe to Chaos: A General Theory of Economic Discontinuities written by J. Barkley Rosser and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Now, however, weface an Age of Discontinuity in world economy and tech nology. We might succeed in making it an age of great economic growth as weil. But the one thing that is certain so far is that it will be a period of change-in technology and in economic policy, in industry structures and in economic theo ry, in the knowledge needed to govern and manage, and in economic issues. While we have been busy finishing the great nineteenth-century economic ed ijice, the foundations have shifted beneath our feet." Peter F. Drucker, 1968 The A~e Qf DiscQntinuity, p. 10 This project has had a lQng gestatiQn period, probably ultimately dating to a YQuthful QbsessiQn with watershed divides and bQundaries. My awareness Qf the problem Qf discQntinuity in eCQnQmics dates tQ my first enCQunter with the capi tal theQry paradQxes in the late 1960s, the fruits Qf which can be seen in Chapter 8 Qf this book. This awareness led tQ a frostratiQn Qver the apparent lack Qf a mathematics Qf discQntinuity, a lack that was in the process of rapidly being QverCQme at that time.
Book Synopsis Geometry of Lie Groups by : B. Rosenfeld
Download or read book Geometry of Lie Groups written by B. Rosenfeld and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the result of many years of research in Non-Euclidean Geometries and Geometry of Lie groups, as well as teaching at Moscow State University (1947- 1949), Azerbaijan State University (Baku) (1950-1955), Kolomna Pedagogical Col lege (1955-1970), Moscow Pedagogical University (1971-1990), and Pennsylvania State University (1990-1995). My first books on Non-Euclidean Geometries and Geometry of Lie groups were written in Russian and published in Moscow: Non-Euclidean Geometries (1955) [Ro1] , Multidimensional Spaces (1966) [Ro2] , and Non-Euclidean Spaces (1969) [Ro3]. In [Ro1] I considered non-Euclidean geometries in the broad sense, as geometry of simple Lie groups, since classical non-Euclidean geometries, hyperbolic and elliptic, are geometries of simple Lie groups of classes Bn and D , and geometries of complex n and quaternionic Hermitian elliptic and hyperbolic spaces are geometries of simple Lie groups of classes An and en. [Ro1] contains an exposition of the geometry of classical real non-Euclidean spaces and their interpretations as hyperspheres with identified antipodal points in Euclidean or pseudo-Euclidean spaces, and in projective and conformal spaces. Numerous interpretations of various spaces different from our usual space allow us, like stereoscopic vision, to see many traits of these spaces absent in the usual space.
Book Synopsis Lectures on Spaces of Nonpositive Curvature by : Werner Ballmann
Download or read book Lectures on Spaces of Nonpositive Curvature written by Werner Ballmann and published by Birkhäuser. This book was released on 2012-12-06 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: Singular spaces with upper curvature bounds and, in particular, spaces of nonpositive curvature, have been of interest in many fields, including geometric (and combinatorial) group theory, topology, dynamical systems and probability theory. In the first two chapters of the book, a concise introduction into these spaces is given, culminating in the Hadamard-Cartan theorem and the discussion of the ideal boundary at infinity for simply connected complete spaces of nonpositive curvature. In the third chapter, qualitative properties of the geodesic flow on geodesically complete spaces of nonpositive curvature are discussed, as are random walks on groups of isometries of nonpositively curved spaces. The main class of spaces considered should be precisely complementary to symmetric spaces of higher rank and Euclidean buildings of dimension at least two (Rank Rigidity conjecture). In the smooth case, this is known and is the content of the Rank Rigidity theorem. An updated version of the proof of the latter theorem (in the smooth case) is presented in Chapter IV of the book. This chapter contains also a short introduction into the geometry of the unit tangent bundle of a Riemannian manifold and the basic facts about the geodesic flow. In an appendix by Misha Brin, a self-contained and short proof of the ergodicity of the geodesic flow of a compact Riemannian manifold of negative curvature is given. The proof is elementary and should be accessible to the non-specialist. Some of the essential features and problems of the ergodic theory of smooth dynamical systems are discussed, and the appendix can serve as an introduction into this theory.
Download or read book Catalogue written by Yale University and published by . This book was released on 1897 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Catalogue of the Officers and Graduates of Yale University by : Yale University
Download or read book Catalogue of the Officers and Graduates of Yale University written by Yale University and published by . This book was released on 1897 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Catalogue of the Officers and Students in Yale College by : Yale University
Download or read book Catalogue of the Officers and Students in Yale College written by Yale University and published by . This book was released on 1897 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Catalogue ... by : Yale University. Graduate School
Download or read book Catalogue ... written by Yale University. Graduate School and published by . This book was released on 1897 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Lectures on the Calculus of Variations by : Harris Hancock
Download or read book Lectures on the Calculus of Variations written by Harris Hancock and published by . This book was released on 1904 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Engineering written by and published by . This book was released on 1881 with total page 768 pages. Available in PDF, EPUB and Kindle. Book excerpt:
