Singularities and Computer Algebra


Author: Christoph Lossen,Gerhard Pfister
Publisher: Cambridge University Press
ISBN: 9780521683098
Category: Computers
Page: 371
View: 3095
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A collection of articles giving overviews and open questions in singularities and their computational aspects.

Singularities of Smooth Functions and Maps


Author: J. Martinet
Publisher: CUP Archive
ISBN: 9780521233989
Category: Mathematics
Page: 256
View: 4628
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Complex Algebraic Curves


Author: Frances Clare Kirwan
Publisher: Cambridge University Press
ISBN: 9780521423533
Category: Mathematics
Page: 264
View: 1075
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This development of the theory of complex algebraic curves was one of the peaks of nineteenth century mathematics. They have many fascinating properties and arise in various areas of mathematics, from number theory to theoretical physics, and are the subject of much research. By using only the basic techniques acquired in most undergraduate courses in mathematics, Dr. Kirwan introduces the theory, observes the algebraic and topological properties of complex algebraic curves, and shows how they are related to complex analysis.

Singularities in Geometry, Topology, Foliations and Dynamics

A Celebration of the 60th Birthday of José Seade, Merida, Mexico, December 2014
Author: José Luis Cisneros-Molina,Dũng Tráng Lê,Mutsuo Oka,Jawad Snoussi
Publisher: Birkhäuser
ISBN: 3319393391
Category: Mathematics
Page: 231
View: 5982
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This book features state-of-the-art research on singularities in geometry, topology, foliations and dynamics and provides an overview of the current state of singularity theory in these settings. Singularity theory is at the crossroad of various branches of mathematics and science in general. In recent years there have been remarkable developments, both in the theory itself and in its relations with other areas. The contributions in this volume originate from the “Workshop on Singularities in Geometry, Topology, Foliations and Dynamics”, held in Merida, Mexico, in December 2014, in celebration of José Seade’s 60th Birthday. It is intended for researchers and graduate students interested in singularity theory and its impact on other fields.

Singularities of Plane Curves


Author: Eduardo Casas-Alvero
Publisher: Cambridge University Press
ISBN: 9780521789592
Category: Mathematics
Page: 345
View: 6049
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Comprehensive and self-contained exposition of singularities of plane curves, including new, previously unpublished results.

Isolated Singular Points on Complete Intersections


Author: Eduard Looijenga
Publisher: Cambridge University Press
ISBN: 0521286743
Category: Mathematics
Page: 200
View: 1466
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This book will be of use to professional mathematicians working in algebraic geometry, complex-analytical geometry and, to some extent, differential analysis.

Zeta Functions in Algebra and Geometry

Second International Workshop, May 3-7, 2010, Universitat de Les Illes Balears, Palma de Mallorca, Spain
Author: Antonio Campillo
Publisher: American Mathematical Soc.
ISBN: 0821869000
Category: Algebraic varieties
Page: 344
View: 4178
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The volume contains the proceedings of the ``Second International Workshop on Zeta Functions in Algebra and Geometry'' held May 3-7, 2010 at the Universitat de les Illes Balears, Palma de Mallorca, Spain. Zeta functions can be naturally attached to several mathematical objects, including fields, groups, and algebras. The conference focused on the following topics: arithmetic and geometric aspects of local, topological, and motivic zeta functions, Poincare series of valuations, zeta functions of groups, rings, and representations, prehomogeneous vector spaces and their zeta functions, and height zeta functions. This book is published in cooperation with Real Sociedad Matematica Espanola (RSME).

Real and Complex Singularities


Author: M. Manoel,M. C. Romero Fuster,C. T. C. Wall
Publisher: Cambridge University Press
ISBN: 1139489917
Category: Mathematics
Page: N.A
View: 7402
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The biennial meetings at São Carlos have helped create a worldwide community of experts and young researchers working on singularity theory, with a special focus on applications to a wide variety of topics in both pure and applied mathematics. The tenth meeting, celebrating the 60th birthdays of Terence Gaffney and Maria Aparecida Soares Ruas, was a special occasion attracting the best known names in the area. This volume contains contributions by the attendees, including three articles written or co-authored by Gaffney himself, and survey articles on the existence of Milnor fibrations, global classifications and graphs, pairs of foliations on surfaces, and Gaffney's work on equisingularity.

The British National Bibliography


Author: Arthur James Wells
Publisher: N.A
ISBN: N.A
Category: English literature
Page: N.A
View: 2048
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Foundations of Computational Mathematics


Author: Ronald Devore,Arieh Iserles,Endre Süli
Publisher: Cambridge University Press
ISBN: 9780521003490
Category: Mathematics
Page: 400
View: 6674
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Collection of papers by leading researchers in computational mathematics, suitable for graduate students and researchers.

A Study of Singularities on Rational Curves Via Syzygies


Author: David A. Cox,Andrew R. Kustin,Claudia Polini,Bernd Ulrich
Publisher: American Mathematical Soc.
ISBN: 0821887432
Category: Mathematics
Page: 116
View: 9618
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Consider a rational projective curve $\mathcal{C}$ of degree $d$ over an algebraically closed field $\pmb k$. There are $n$ homogeneous forms $g_{1},\dots, g_{n}$ of degree $d$ in $B=\pmb k[x, y]$ which parameterize $\mathcal{C}$ in a birational, base point free, manner. The authors study the singularities of $\mathcal{C}$ by studying a Hilbert-Burch matrix $\varphi$ for the row vector $[g_{1},\dots, g_{n}]$. In the ``General Lemma'' the authors use the generalized row ideals of $\varphi$ to identify the singular points on $\mathcal{C}$, their multiplicities, the number of branches at each singular point, and the multiplicity of each branch. Let $p$ be a singular point on the parameterized planar curve $\mathcal{C}$ which corresponds to a generalized zero of $\varphi$. In the `'triple Lemma'' the authors give a matrix $\varphi'$ whose maximal minors parameterize the closure, in $\mathbb{P}^{2}$, of the blow-up at $p$ of $\mathcal{C}$ in a neighborhood of $p$. The authors apply the General Lemma to $\varphi'$ in order to learn about the singularities of $\mathcal{C}$ in the first neighborhood of $p$. If $\mathcal{C}$ has even degree $d=2c$ and the multiplicity of $\mathcal{C}$ at $p$ is equal to $c$, then he applies the Triple Lemma again to learn about the singularities of $\mathcal{C}$ in the second neighborhood of $p$. Consider rational plane curves $\mathcal{C}$ of even degree $d=2c$. The authors classify curves according to the configuration of multiplicity $c$ singularities on or infinitely near $\mathcal{C}$. There are $7$ possible configurations of such singularities. They classify the Hilbert-Burch matrix which corresponds to each configuration. The study of multiplicity $c$ singularities on, or infinitely near, a fixed rational plane curve $\mathcal{C}$ of degree $2c$ is equivalent to the study of the scheme of generalized zeros of the fixed balanced Hilbert-Burch matrix $\varphi$ for a parameterization of $\mathcal{C}$.

Complexity Science

The Warwick Master's Course
Author: Robin Ball,Vassili Kolokoltsov,Robert S. MacKay
Publisher: Cambridge University Press
ISBN: 1107513553
Category: Mathematics
Page: N.A
View: 6711
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Complexity science is the study of systems with many interdependent components. Such systems - and the self-organization and emergent phenomena they manifest - lie at the heart of many challenges of global importance. This book is a coherent introduction to the mathematical methods used to understand complexity, with plenty of examples and real-world applications. It starts with the crucial concepts of self-organization and emergence, then tackles complexity in dynamical systems using differential equations and chaos theory. Several classes of models of interacting particle systems are studied with techniques from stochastic analysis, followed by a treatment of the statistical mechanics of complex systems. Further topics include numerical analysis of PDEs, and applications of stochastic methods in economics and finance. The book concludes with introductions to space-time phases and selfish routing. The exposition is suitable for researchers, practitioners and students in complexity science and related fields at advanced undergraduate level and above.

Reversibility in Dynamics and Group Theory


Author: Anthony G. O'Farrell,Ian Short
Publisher: Cambridge University Press
ISBN: 1107442885
Category: Mathematics
Page: 292
View: 6684
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An accessible yet systematic account of reversibility that demonstrates its impact throughout many diverse areas of mathematics.

London Mathematical Society lecture note series


Author: Michael Sh Braverman
Publisher: N.A
ISBN: N.A
Category:
Page: N.A
View: 386
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Computer Algebra and Differential Equations


Author: E. Tournier
Publisher: Cambridge University Press
ISBN: 9780521447577
Category: Mathematics
Page: 259
View: 9756
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Selected papers from the Computer Algebra and Differential Equations meeting held in France in June 1992.

Synthetic Differential Topology


Author: Marta Bunge,Felipe Gago,Ana María San Luis
Publisher: Cambridge University Press
ISBN: 110856335X
Category: Mathematics
Page: 223
View: 7024
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This book formally introduces synthetic differential topology, a natural extension of the theory of synthetic differential geometry which captures classical concepts of differential geometry and topology by means of the rich categorical structure of a necessarily non-Boolean topos and of the systematic use of logical infinitesimal objects in it. Beginning with an introduction to those parts of topos theory and synthetic differential geometry necessary for the remainder, this clear and comprehensive text covers the general theory of synthetic differential topology and several applications of it to classical mathematics, including the calculus of variations, Mather's theorem, and Morse theory on the classification of singularities. The book represents the state of the art in synthetic differential topology and will be of interest to researchers in topos theory and to mathematicians interested in the categorical foundations of differential geometry and topology.

Asymptotic Analysis in General Relativity


Author: Thierry Daudé,Dietrich Häfner,Jean-Philippe Nicolas
Publisher: Cambridge University Press
ISBN: 1316649407
Category: Mathematics
Page: N.A
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Introduction to modern methods for classical and quantum fields in general relativity / Thierry Daudé, Dietrich Häfner, and Jean-Philippe Nicolas -- Geometry of black hole spacetimes / Lars Andersson, Thomas B. Ackdahl, and Pieter Blue -- An introduction to Quantum Field Theory on curved space-times / Christian Gerard -- A minicourse on microlocal analysis for wave propagation / Andras Vasy -- An introduction to conformal geometry and tractor calculus, with a view to applications in general relativity / Sean N. Curry and A. Rod Gover

Undergraduate Algebraic Geometry


Author: Miles Reid
Publisher: Cambridge University Press
ISBN: 9780521356626
Category: Mathematics
Page: 129
View: 3773
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This short and readable introduction to algebraic geometry will be ideal for all undergraduate mathematicians coming to the subject for the first time.

London Mathematical Society lecture note series


Author: Boris I. Botvinnik
Publisher: N.A
ISBN: N.A
Category:
Page: N.A
View: 2243
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New Trends in Algebraic Geometry


Author: K. Hulek
Publisher: Cambridge University Press
ISBN: 9780521646598
Category: Mathematics
Page: 484
View: 6292
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Seventeen articles from the most outstanding contemporary topics in algebraic geometry.