Topology Of Singular Fibers Of Differentiable Maps

Author : Osamu Saeki
Publisher : Springer
Page : 154 pages
File Size : 40,5 Mb
Release : 2004-08-30
Category : Mathematics
ISBN : 9783540446484

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Topology of Singular Fibers of Differentiable Maps by Osamu Saeki Pdf

The volume develops a thorough theory of singular fibers of generic differentiable maps. This is the first work that establishes the foundational framework of the global study of singular differentiable maps of negative codimension from the viewpoint of differential topology. The book contains not only a general theory, but also some explicit examples together with a number of very concrete applications. This is a very interesting subject in differential topology, since it shows a beautiful interplay between the usual theory of singularities of differentiable maps and the geometric topology of manifolds.

Author : Osamu Saeki
Publisher : Springer Science & Business Media
Page : 164 pages
File Size : 42,7 Mb
Release : 2004
Category : Differentiable mappings
ISBN : 3540230211

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Topology of Singular Fibers of Differentiable Maps by Osamu Saeki Pdf

Author : Ingrid Hotz,Talha Bin Masood,Filip Sadlo,Julien Tierny
Publisher : Springer Nature
Page : 372 pages
File Size : 53,7 Mb
Release : 2021-09-28
Category : Mathematics
ISBN : 9783030835002

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Topological Methods in Data Analysis and Visualization VI by Ingrid Hotz,Talha Bin Masood,Filip Sadlo,Julien Tierny Pdf

This book is a result of a workshop, the 8th of the successful TopoInVis workshop series, held in 2019 in Nyköping, Sweden. The workshop regularly gathers some of the world’s leading experts in this field. Thereby, it provides a forum for discussions on the latest advances in the field with a focus on finding practical solutions to open problems in topological data analysis for visualization. The contributions provide introductory and novel research articles including new concepts for the analysis of multivariate and time-dependent data, robust computational approaches for the extraction and approximations of topological structures with theoretical guarantees, and applications of topological scalar and vector field analysis for visualization. The applications span a wide range of scientific areas comprising climate science, material sciences, fluid dynamics, and astronomy. In addition, community efforts with respect to joint software development are reported and discussed.

Author : Raimundo Nonato Araújo dos Santos,Aurélio Menegon Neto,David Mond,Marcelo J. Saia,Jawad Snoussi
Publisher : Springer
Page : 553 pages
File Size : 43,5 Mb
Release : 2018-03-21
Category : Mathematics
ISBN : 9783319736396

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Singularities and Foliations. Geometry, Topology and Applications by Raimundo Nonato Araújo dos Santos,Aurélio Menegon Neto,David Mond,Marcelo J. Saia,Jawad Snoussi Pdf

This proceedings book brings selected works from two conferences, the 2nd Brazil-Mexico Meeting on Singularity and the 3rd Northeastern Brazilian Meeting on Singularities, that were hold in Salvador, in July 2015. All contributions were carefully peer-reviewed and revised, and cover topics like Equisingularity, Topology and Geometry of Singularities, Topological Classification of Singularities of Mappings, and more. They were written by mathematicians from several countries, including Brazil, Spain, Mexico, Japan and the USA, on relevant topics on Theory of Singularity, such as studies on deformations, Milnor fibration, foliations, Catastrophe theory, and myriad applications. Open problems are also introduced, making this volume a must-read both for graduate students and active researchers in this field.

Author : Marcelo José Saia,José Seade
Publisher : American Mathematical Soc.
Page : 274 pages
File Size : 53,7 Mb
Release : 2008
Category : Singularities (Mathematics)
ISBN : 9780821844977

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Real and Complex Singularities by Marcelo José Saia,José Seade Pdf

This book offers a selection of papers based on talks at the Ninth International Workshop on Real and Complex Singularities, a series of biennial workshops organized by the Singularity Theory group at Sao Carlos, S.P., Brazil. The papers deal with all the different topics in singularity theory and its applications, from pure singularity theory related to commutative algebra and algebraic geometry to those topics associated with various aspects of geometry to homotopytheory.

Author : Hamish Carr,Christoph Garth,Tino Weinkauf
Publisher : Springer
Page : 363 pages
File Size : 46,6 Mb
Release : 2017-06-01
Category : Mathematics
ISBN : 9783319446844

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Topological Methods in Data Analysis and Visualization IV by Hamish Carr,Christoph Garth,Tino Weinkauf Pdf

This book presents contributions on topics ranging from novel applications of topological analysis for particular problems, through studies of the effectiveness of modern topological methods, algorithmic improvements on existing methods, and parallel computation of topological structures, all the way to mathematical topologies not previously applied to data analysis. Topological methods are broadly recognized as valuable tools for analyzing the ever-increasing flood of data generated by simulation or acquisition. This is particularly the case in scientific visualization, where the data sets have long since surpassed the ability of the human mind to absorb every single byte of data. The biannual TopoInVis workshop has supported researchers in this area for a decade, and continues to serve as a vital forum for the presentation and discussion of novel results in applications in the area, creating a platform to disseminate knowledge about such implementations throughout and beyond the community. The present volume, resulting from the 2015 TopoInVis workshop held in Annweiler, Germany, will appeal to researchers in the fields of scientific visualization and mathematics, domain scientists with an interest in advanced visualization methods, and developers of visualization software systems.

Author : Osamu Saeki
Publisher : Springer
Page : 154 pages
File Size : 45,9 Mb
Release : 2004-09-22
Category : Mathematics
ISBN : 3540230211

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Topology of Singular Fibers of Differentiable Maps by Osamu Saeki Pdf

The volume develops a thorough theory of singular fibers of generic differentiable maps. This is the first work that establishes the foundational framework of the global study of singular differentiable maps of negative codimension from the viewpoint of differential topology. The book contains not only a general theory, but also some explicit examples together with a number of very concrete applications. This is a very interesting subject in differential topology, since it shows a beautiful interplay between the usual theory of singularities of differentiable maps and the geometric topology of manifolds.

Author : V.I. Arnold,A.N. Varchenko,S.M. Gusein-Zade
Publisher : Springer Science & Business Media
Page : 390 pages
File Size : 45,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461251545

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Singularities of Differentiable Maps by V.I. Arnold,A.N. Varchenko,S.M. Gusein-Zade Pdf

... 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 : Masato Wakayama,Robert S. Anderssen,Jin Cheng,Yasuhide Fukumoto,Robert McKibbin,Konrad Polthier,Tsuyoshi Takagi,Kim-Chuan Toh
Publisher : Springer
Page : 367 pages
File Size : 44,9 Mb
Release : 2014-07-18
Category : Mathematics
ISBN : 9784431549079

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The Impact of Applications on Mathematics by Masato Wakayama,Robert S. Anderssen,Jin Cheng,Yasuhide Fukumoto,Robert McKibbin,Konrad Polthier,Tsuyoshi Takagi,Kim-Chuan Toh Pdf

This book is a collection of papers presented at the Forum “The Impact of Applications on Mathematics” in October 2013. It describes an appropriate framework in which to highlight how real-world problems, over the centuries and today, have influenced and are influencing the development of mathematics and thereby, how mathematics is reshaped, in order to advance mathematics and its application. The contents of this book address productive and successful interaction between industry and mathematicians, as well as the cross-fertilization and collaboration that result when mathematics is involved with the advancement of science and technology.

Author : Laurentiu Paunescu
Publisher : World Scientific
Page : 475 pages
File Size : 43,7 Mb
Release : 2007
Category : Science
ISBN : 9789812705518

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Real and Complex Singularities by Laurentiu Paunescu Pdf

The modern theory of singularities provides a unifying theme that runs through fields of mathematics as diverse as homological algebra and Hamiltonian systems. It is also an important point of reference in the development of a large part of contemporary algebra, geometry and analysis. Presented by internationally recognized experts, the collection of articles in this volume yields a significant cross-section of these developments. The wide range of surveys includes an authoritative treatment of the deformation theory of isolated complex singularities by prize-winning researcher K Miyajima. Graduate students and even ambitious undergraduates in mathematics will find many research ideas in this volume and non-experts in mathematics can have an overview of some classic and fundamental results in singularity theory. The explanations are detailed enough to capture the interest of the curious reader, and complete enough to provide the necessary background material needed to go further into the subject and explore the research literature.

Author : Victor Goryunov,Kevin Houston,Roberta Wik-Atique
Publisher : American Mathematical Soc.
Page : 218 pages
File Size : 55,7 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821853597

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Real and Complex Singularities by Victor Goryunov,Kevin Houston,Roberta Wik-Atique Pdf

"This volume is a collection of papers presented at the 11th International Workshop on Real and Complex Singularities, held July 26-30, 2010, in Sao Carlos, Brazil, in honor of David Mond's 60th birthday. This volume reflects the high level of the conference discussing the most recent results and applications of singularity theory. Articles in the first part cover pure singularity theory: invariants, classification theory, and Milnor fibres. Articles in the second part cover singularities in topology and differential geometry, as well as algebraic geometry and bifurcation theory: Artin-Greenberg function of a plane curve singularity, metric theory of singularities, symplectic singularities, cobordisms of fold maps, Goursat distributions, sections of analytic varieties, Vassiliev invariants, projections of hypersurfaces, and linearity of the Jacobian ideal."--P. [4] of cover.

Author : V.I. Arnold,S.M. Gusein-Zade,Alexander N. Varchenko
Publisher : Springer Science & Business Media
Page : 282 pages
File Size : 49,7 Mb
Release : 2012-05-24
Category : Mathematics
ISBN : 9780817683405

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Singularities of Differentiable Maps, Volume 1 by V.I. Arnold,S.M. Gusein-Zade,Alexander N. Varchenko Pdf

​Singularity theory is a far-reaching extension of maxima and minima investigations of differentiable functions, with implications for many different areas of mathematics, engineering (catastrophe theory and the theory of bifurcations), and science. The three parts of this first volume of a two-volume set deal with the stability problem for smooth mappings, critical points of smooth functions, and caustics and wave front singularities. The second volume describes the topological and algebro-geometrical aspects of the theory: monodromy, intersection forms, oscillatory integrals, asymptotics, and mixed Hodge structures of singularities. The first volume has been adapted for the needs of non-mathematicians, presupposing a limited mathematical background and beginning at an elementary level. With this foundation, the book's sophisticated development permits readers to explore more applications than previous books on singularities.

Author : Shyuichi Izumiya,Maria del Carmen Romero Fuster,Maria Aparecida Soares Ruas,Farid Tari
Publisher : World Scientific
Page : 400 pages
File Size : 54,6 Mb
Release : 2015-10-29
Category : Mathematics
ISBN : 9789814590464

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Differential Geometry from a Singularity Theory Viewpoint by Shyuichi Izumiya,Maria del Carmen Romero Fuster,Maria Aparecida Soares Ruas,Farid Tari Pdf

Differential Geometry from a Singularity Theory Viewpoint provides a new look at the fascinating and classical subject of the differential geometry of surfaces in Euclidean spaces. The book uses singularity theory to capture some key geometric features of surfaces. It describes the theory of contact and its link with the theory of caustics and wavefronts. It then uses the powerful techniques of these theories to deduce geometric information about surfaces embedded in 3, 4 and 5-dimensional Euclidean spaces. The book also includes recent work of the authors and their collaborators on the geometry of sub-manifolds in Minkowski spaces. Contents:The Case for the Singularity Theory ApproachSubmanifolds of the Euclidean SpaceSingularities of Germs of Smooth MappingsContact Between Submanifolds of ℝnLagrangian and Legendrian SingularitiesSurfaces in the Euclidean 3-SpaceSurfaces in the Euclidean 4-SpaceSurfaces in the Euclidean 5-SpaceSpacelike Surfaces in the Minkowski Space-TimeGlobal Viewpoint Readership: Advanced undergraduates and post-graduate students, and researchers in the fields of differential geometry and singularity theory. Key Features:The book is unique in its nature. It provides a coherent approach for studying the geometry of sub-manifolds of various ambient spaces from the singularity theory point of viewThe book informs the reader about the progress in the field of extrinsic differential geometry and singularity theory. The information is new and has not been treated in previous textbooksThe book gathers scattered work from various research articles, most of which are recent, and describes techniques that could be used to tackle problems in other areas of mathematicsKeywords:Contact;Extrinsic Geometry;Genericity;Caustics;Singularities;Surfaces;Transversality;Wave Fronts

Author : Ana Claudia Nabarro,Juan J. Nuño-Ballesteros,Raúl Oset Sinha,Maria Aparecida Soares Ruas
Publisher : American Mathematical Soc.
Page : 355 pages
File Size : 46,8 Mb
Release : 2016-10-25
Category : Differential geometry -- Classical differential geometry -- Classical differential geometry
ISBN : 9781470422059

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Real and Complex Singularities by Ana Claudia Nabarro,Juan J. Nuño-Ballesteros,Raúl Oset Sinha,Maria Aparecida Soares Ruas Pdf

This volume is a collection of papers presented at the XIII International Workshop on Real and Complex Singularities, held from July 27–August 8, 2014, in São Carlos, Brazil, in honor of María del Carmen Romero Fuster's 60th birthday. The volume contains the notes from two mini-courses taught during the workshop: on intersection homology by J.-P. Brasselet, and on non-isolated hypersurface singularities and Lê cycles by D. Massey. The remaining contributions are research articles which cover topics from the foundations of singularity theory (including classification theory and invariants) to topology of singular spaces (links of singularities and semi-algebraic sets), as well as applications to topology (cobordism and Lefschetz fibrations), dynamical systems (Morse-Bott functions) and differential geometry (affine geometry, Gauss-maps, caustics, frontals and non-Euclidean geometries). This book is published in cooperation with Real Sociedad Matemática Española (RSME)

Author : Ryuei Nishii,Shin-ichiro Ei,Miyuki Koiso,Hiroyuki Ochiai,Kanzo Okada,Shingo Saito,Tomoyuki Shirai
Publisher : Springer
Page : 507 pages
File Size : 47,7 Mb
Release : 2014-07-14
Category : Technology & Engineering
ISBN : 9784431550600

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A Mathematical Approach to Research Problems of Science and Technology by Ryuei Nishii,Shin-ichiro Ei,Miyuki Koiso,Hiroyuki Ochiai,Kanzo Okada,Shingo Saito,Tomoyuki Shirai Pdf

This book deals with one of the most novel advances in mathematical modeling for applied scientific technology, including computer graphics, public-key encryption, data visualization, statistical data analysis, symbolic calculation, encryption, error correcting codes, and risk management. It also shows that mathematics can be used to solve problems from nature, e.g., slime mold algorithms. One of the unique features of this book is that it shows readers how to use pure and applied mathematics, especially those mathematical theory/techniques developed in the twentieth century, and developing now, to solve applied problems in several fields of industry. Each chapter includes clues on how to use "mathematics" to solve concrete problems faced in industry as well as practical applications. The target audience is not limited to researchers working in applied mathematics and includes those in engineering, material sciences, economics, and life sciences.