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Author :
Publisher :
ISBN 13 :
Total Pages : 238 pages
Book Rating : 4.3/5 (91 download)
Download or read book Geometry and Topology of Caustics -- Caustics ... written by and published by . This book was released on 2006 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Stanisław Janeczko
Publisher :
ISBN 13 :
Total Pages : 225 pages
Book Rating : 4.:/5 (17 download)
Download or read book Geometry and Topology of Caustics written by Stanisław Janeczko and published by . This book was released on 2008 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Stanisław Janeczko
Publisher :
ISBN 13 :
Total Pages : 324 pages
Book Rating : 4.5/5 (566 download)
Download or read book Geometry and Topology of Caustics written by Stanisław Janeczko and published by . This book was released on 1999 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Stanisław Janeczko
Publisher :
ISBN 13 :
Total Pages : 270 pages
Book Rating : 4.E/5 ( download)
Download or read book Geometry and Topology of Caustics - Caustics '02 written by Stanisław Janeczko and published by . This book was released on 2004 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :
Publisher :
ISBN 13 :
Total Pages : 268 pages
Book Rating : 4.3/5 (91 download)
Download or read book Geometry and Topology of Caustics -- Caustics ... written by and published by . This book was released on 2002 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :
Publisher :
ISBN 13 :
Total Pages : 225 pages
Book Rating : 4.:/5 (288 download)
Download or read book Geometry and Topology of Caustics - Caustics '06 written by and published by . This book was released on 2008 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Stanisław Janeczko
Publisher :
ISBN 13 :
Total Pages : 326 pages
Book Rating : 4.E/5 ( download)
Download or read book Geometry and Topology of Caustics written by Stanisław Janeczko and published by . This book was released on 1999 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Vladimir Arnold
Publisher : Springer Science & Business Media
ISBN 13 : 9401133301
Total Pages : 271 pages
Book Rating : 4.4/5 (11 download)
Download or read book Singularities of Caustics and Wave Fronts written by Vladimir Arnold and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: One service mathematics has rendered the 'Et moi ...) si j'avait su comment en revenir, human race. It has put common sense back je n'y serais point aile.' Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non The series is divergent; therefore we may be sense'. ErieT. Bell able to do something with it. O. Heaviside 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.
Author : Vladimir M.. Zakalyukin
Publisher :
ISBN 13 :
Total Pages : 320 pages
Book Rating : 4.:/5 (313 download)
Download or read book Geometry and Topology of Caustics written by Vladimir M.. Zakalyukin and published by . This book was released on 2000 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Vladimir Igorevich Arnolʹd
Publisher : American Mathematical Soc.
ISBN 13 : 0821803085
Total Pages : 70 pages
Book Rating : 4.8/5 (218 download)
Download or read book Topological Invariants of Plane Curves and Caustics written by Vladimir Igorevich Arnolʹd and published by American Mathematical Soc.. This book was released on 1994 with total page 70 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes recent progress in the topological study of plane curves. The theory of plane curves is much richer than knot theory, which may be considered the commutative version of the theory of plane curves. This study is based on singularity theory: the infinite-dimensional space of curves is subdivided by the discriminant hypersurfaces into parts consisting of generic curves of the same type. The invariants distinguishing the types are defined by their jumps at the crossings of these hypersurfaces. Arnold describes applications to the geometry of caustics and of wavefronts in symplectic and contact geometry. These applications extend the classical four-vertex theorem of elementary plane geometry to estimates on the minimal number of cusps necessary for the reversion of a wavefront and to generalizations of the last geometrical theorem of Jacobi on conjugated points on convex surfaces. These estimates open a new chapter in symplectic and contact topology: the theory of Lagrangian and Legendrian collapses, providing an unusual and far-reaching higher-dimensional extension of Sturm theory of the oscillations of linear combinations of eigenfunctions.
Author : V.I. Arnold
Publisher : Springer Science & Business Media
ISBN 13 : 1461251540
Total Pages : 390 pages
Book Rating : 4.4/5 (612 download)
Download or read book Singularities of Differentiable Maps written by V.I. Arnold and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: ... there is nothing so enthralling, so grandiose, nothing that stuns or captivates the human soul quite so much as a first course in a science. After the first five or six lectures one already holds the brightest hopes, already sees oneself as a seeker after truth. I too have wholeheartedly pursued science passionately, as one would a beloved woman. I was a slave, and sought no other sun in my life. Day and night I crammed myself, bending my back, ruining myself over my books; I wept when I beheld others exploiting science fot personal gain. But I was not long enthralled. The truth is every science has a beginning, but never an end - they go on for ever like periodic fractions. Zoology, for example, has discovered thirty-five thousand forms of life ... A. P. Chekhov. "On the road" In this book a start is made to the "zoology" of the singularities of differentiable maps. This theory is a young branch of analysis which currently occupies a central place in mathematics; it is the crossroads of paths leading from very abstract corners of mathematics (such as algebraic and differential geometry and topology, Lie groups and algebras, complex manifolds, commutative algebra and the like) to the most applied areas (such as differential equations and dynamical systems, optimal control, the theory of bifurcations and catastrophes, short-wave and saddle-point asymptotics and geometrical and wave optics).
Author : Arkady Leonidovich Kholodenko
Publisher : World Scientific
ISBN 13 : 9814412090
Total Pages : 492 pages
Book Rating : 4.8/5 (144 download)
Download or read book Applications of Contact Geometry and Topology in Physics written by Arkady Leonidovich Kholodenko and published by World Scientific. This book was released on 2013 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although contact geometry and topology is briefly discussed in V I Arnol''d''s book Mathematical Methods of Classical Mechanics (Springer-Verlag, 1989, 2nd edition), it still remains a domain of research in pure mathematics, e.g. see the recent monograph by H Geiges An Introduction to Contact Topology (Cambridge U Press, 2008). Some attempts to use contact geometry in physics were made in the monograph Contact Geometry and Nonlinear Differential Equations (Cambridge U Press, 2007). Unfortunately, even the excellent style of this monograph is not sufficient to attract the attention of the physics community to this type of problems. This book is the first serious attempt to change the existing status quo. In it we demonstrate that, in fact, all branches of theoretical physics can be rewritten in the language of contact geometry and topology: from mechanics, thermodynamics and electrodynamics to optics, gauge fields and gravity; from physics of liquid crystals to quantum mechanics and quantum computers, etc. The book is written in the style of famous Landau-Lifshitz (L-L) multivolume course in theoretical physics. This means that its readers are expected to have solid background in theoretical physics (at least at the level of the L-L course). No prior knowledge of specialized mathematics is required. All needed new mathematics is given in the context of discussed physical problems. As in the L-L course some problems/exercises are formulated along the way and, again as in the L-L course, these are always supplemented by either solutions or by hints (with exact references). Unlike the L-L course, though, some definitions, theorems, and remarks are also presented. This is done with the purpose of stimulating the interest of our readers in deeper study of subject matters discussed in the text.
Author : V.I. Arnold
Publisher : Birkhäuser
ISBN 13 : 9781461251552
Total Pages : 396 pages
Book Rating : 4.2/5 (515 download)
Download or read book Singularities of Differentiable Maps written by V.I. Arnold and published by Birkhäuser. This book was released on 2011-12-06 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: ... there is nothing so enthralling, so grandiose, nothing that stuns or captivates the human soul quite so much as a first course in a science. After the first five or six lectures one already holds the brightest hopes, already sees oneself as a seeker after truth. I too have wholeheartedly pursued science passionately, as one would a beloved woman. I was a slave, and sought no other sun in my life. Day and night I crammed myself, bending my back, ruining myself over my books; I wept when I beheld others exploiting science fot personal gain. But I was not long enthralled. The truth is every science has a beginning, but never an end - they go on for ever like periodic fractions. Zoology, for example, has discovered thirty-five thousand forms of life ... A. P. Chekhov. "On the road" In this book a start is made to the "zoology" of the singularities of differentiable maps. This theory is a young branch of analysis which currently occupies a central place in mathematics; it is the crossroads of paths leading from very abstract corners of mathematics (such as algebraic and differential geometry and topology, Lie groups and algebras, complex manifolds, commutative algebra and the like) to the most applied areas (such as differential equations and dynamical systems, optimal control, the theory of bifurcations and catastrophes, short-wave and saddle-point asymptotics and geometrical and wave optics).
Author : Jean-paul Brasselet
Publisher : World Scientific
ISBN 13 : 9814477044
Total Pages : 917 pages
Book Rating : 4.8/5 (144 download)
Download or read book Singularities In Geometry And Topology - Proceedings Of The Trieste Singularity Summer School And Workshop written by Jean-paul Brasselet and published by World Scientific. This book was released on 2007-01-16 with total page 917 pages. Available in PDF, EPUB and Kindle. Book excerpt: Singularity theory appears in numerous branches of mathematics, as well as in many emerging areas such as robotics, control theory, imaging, and various evolving areas in physics. The purpose of this proceedings volume is to cover recent developments in singularity theory and to introduce young researchers from developing countries to singularities in geometry and topology.The contributions discuss singularities in both complex and real geometry. As such, they provide a natural continuation of the previous school on singularities held at ICTP (1991), which is recognized as having had a major influence in the field.
Author : Jean-Paul Brasselet
Publisher : World Scientific
ISBN 13 : 981270681X
Total Pages : 918 pages
Book Rating : 4.8/5 (127 download)
Download or read book Singularities in Geometry and Topology written by Jean-Paul Brasselet and published by World Scientific. This book was released on 2007 with total page 918 pages. Available in PDF, EPUB and Kindle. Book excerpt: Singularity theory appears in numerous branches of mathematics, as well as in many emerging areas such as robotics, control theory, imaging, and various evolving areas in physics. The purpose of this proceedings volume is to cover recent developments in singularity theory and to introduce young researchers from developing countries to singularities in geometry and topology. The contributions discuss singularities in both complex and real geometry. As such, they provide a natural continuation of the previous school on singularities held at ICTP (1991), which is recognized as having had a major influence in the field.
Author : James F. Peters
Publisher : Springer Nature
ISBN 13 : 303022192X
Total Pages : 440 pages
Book Rating : 4.0/5 (32 download)
Download or read book Computational Geometry, Topology and Physics of Digital Images with Applications written by James F. Peters and published by Springer Nature. This book was released on 2019-10-03 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses the computational geometry, topology and physics of digital images and video frame sequences. This trio of computational approaches encompasses the study of shape complexes, optical vortex nerves and proximities embedded in triangulated video frames and single images, while computational geometry focuses on the geometric structures that infuse triangulated visual scenes. The book first addresses the topology of cellular complexes to provide a basis for an introductory study of the computational topology of visual scenes, exploring the fabric, shapes and structures typically found in visual scenes. The book then examines the inherent geometry and topology of visual scenes, and the fine structure of light and light caustics of visual scenes, which bring into play catastrophe theory and the appearance of light caustic folds and cusps. Following on from this, the book introduces optical vortex nerves in triangulated digital images. In this context, computational physics is synonymous with the study of the fine structure of light choreographed in video frames. This choreography appears as a sequence of snapshots of light reflected and refracted from surface shapes, providing a solid foundation for detecting, analyzing and classifying visual scene shapes.
Author : Vladimir Igorevič Arnolʹd
Publisher :
ISBN 13 : 9789075351019
Total Pages : 259 pages
Book Rating : 4.3/5 (51 download)
Download or read book Singularities of Caustics and Wave Fronts written by Vladimir Igorevič Arnolʹd and published by . This book was released on 1990 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt:
