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Books in Algebraic geometry

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Computational Morphology

  • 1st Edition
  • Volume 6
  • June 28, 2014
  • G.T. Toussaint
  • English
  • eBook
    9 7 8 - 1 - 4 8 3 2 - 9 6 7 2 - 2
Computational Geometry is a new discipline of computer science that deals with the design and analysis of algorithms for solving geometric problems. There are many areas of study in different disciplines which, while being of a geometric nature, have as their main component the extraction of a description of the shape or form of the input data. This notion is more imprecise and subjective than pure geometry. Such fields include cluster analysis in statistics, computer vision and pattern recognition, and the measurement of form and form-change in such areas as stereology and developmental biology.This volume is concerned with a new approach to the study of shape and form in these areas. Computational morphology is thus concerned with the treatment of morphology from the computational geometry point of view. This point of view is more formal, elegant, procedure-oriented, and clear than many previous approaches to the problem and often yields algorithms that are easier to program and have lower complexity.

Algebraic Geometry and Commutative Algebra

  • 1st Edition
  • May 10, 2014
  • Hiroaki Hijikata + 2 more
  • English
  • eBook
    9 7 8 - 1 - 4 8 3 2 - 6 5 0 5 - 6
Algebraic Geometry and Commutative Algebra in Honor of Masayoshi Nagata presents a collection of papers on algebraic geometry and commutative algebra in honor of Masayoshi Nagata for his significant contributions to commutative algebra. Topics covered range from Weierstrass models and endomorphism algebras of abelian varieties to the generic Torelli theorem for hypersurfaces in compact irreducible hermitian symmetric spaces. Coarse moduli spaces for curves are also discussed, along with discriminants of curves of genus 2 and arithmetic surfaces. Comprised of 14 chapters, this volume begins by describing a basic fibration as a Weierstrass model, with emphasis on elliptic threefolds with a section. The reader is then introduced to canonical bundles of analytic surfaces of class VII0 with curves; Lifting Problem on ideal-adically complete noetherian rings; and the canonical ring of a curve. Subsequent chapters deal with algebraic surfaces for regular systems of weights; elementary transformations of algebraic vector bundles; the irreducibility of the first differential equation of Painlevé; and F-pure normal rings of dimension two. The book concludes with an assessment of the existence of some curves. This monograph will be a useful resource for practitioners and researchers in algebra and geometry.

Boundary Value Problems For Second Order Elliptic Equations

  • 1st Edition
  • November 12, 2012
  • A.V. Bitsadze
  • English
  • eBook
    9 7 8 - 0 - 3 2 3 - 1 6 2 2 6 - 5
Applied Mathematics and Mechanics, Volume 5: Boundary Value Problems: For Second Order Elliptic Equations is a revised and augmented version of a lecture course on non-Fredholm elliptic boundary value problems, delivered at the Novosibirsk State University in the academic year 1964-1965. This seven-chapter text is devoted to a study of the basic linear boundary value problems for linear second order partial differential equations, which satisfy the condition of uniform ellipticity. The opening chapter deals with the fundamental aspects of the linear equations theory in normed linear spaces. This topic is followed by discussions on solutions of elliptic equations and the formulation of Dirichlet problem for a second order elliptic equation. A chapter focuses on the solution equation for the directional derivative problem. Another chapter surveys the formulation of the Poincaré problem for second order elliptic systems in two independent variables. This chapter also examines the theory of one-dimensional singular integral equations that allow the investigation of highly important classes of boundary value problems. The final chapter looks into other classes of multidimensional singular integral equations and related boundary value problems.

Real Elliptic Curves

  • 1st Edition
  • Volume 54
  • August 18, 2011
  • N.L. Alling
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 8 7 1 6 5 - 3

Geometric Computations with Interval and New Robust Methods

  • 1st Edition
  • December 1, 2003
  • H Ratschek + 1 more
  • English
  • eBook
    9 7 8 - 0 - 8 5 7 0 9 - 9 5 1 - 8
This undergraduate and postgraduate text will familiarise readers with interval arithmetic and related tools to gain reliable and validated results and logically correct decisions for a variety of geometric computations plus the means for alleviating the effects of the errors. It also considers computations on geometric point-sets, which are neither robust nor reliable in processing with standard methods. The authors provide two effective tools for obtaining correct results: (a) interval arithmetic, and (b) ESSA the new powerful algorithm which improves many geometric computations and makes them rounding error free.

Power Geometry in Algebraic and Differential Equations

  • 1st Edition
  • Volume 57
  • August 3, 2000
  • A.D. Bruno
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 5 3 9 3 3 - 1
The geometry of power exponents includes the Newton polyhedron, normal cones of its faces, power and logarithmic transformations. On the basis of the geometry universal algorithms for simplifications of systems of nonlinear equations (algebraic, ordinary differential and partial differential) were developed.The algorithms form a new calculus which allows to make local and asymptotical analysis of solutions to those systems.The efficiency of the calculus is demonstrated with regard to several complicated problems from Robotics, Celestial Mechanics, Hydrodynamics and Thermodynamics. The calculus also gives classical results obtained earlier intuitively and is an alternative to Algebraic Geometry, Differential Algebra, Lie group Analysis and Nonstandard Analysis.

Groups - Modular Mathematics Series

  • 1st Edition
  • July 1, 1994
  • Camilla Jordan + 1 more
  • English
  • Paperback
    9 7 8 - 0 - 3 4 0 - 6 1 0 4 5 - 9
  • eBook
    9 7 8 - 0 - 0 8 - 0 5 7 1 6 5 - 2
This text provides an introduction to group theory with an emphasis on clear examples. The authors present groups as naturally occurring structures arising from symmetry in geometrical figures and other mathematical objects. Written in a 'user-friendly' style, where new ideas are always motivated before being fully introduced, the text will help readers to gain confidence and skill in handling group theory notation before progressing on to applying it in complex situations. An ideal companion to any first or second year course on the topic.

Cubic Forms

  • 2nd Edition
  • Volume 4
  • February 1, 1986
  • Yu.I. Manin
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 9 6 3 1 6 - 7
Since this book was first published in English, there has been important progress in a number of related topics. The class of algebraic varieties close to the rational ones has crystallized as a natural domain for the methods developed and expounded in this volume. For this revised edition, the original text has been left intact (except for a few corrections) and has been brought up to date by the addition of an Appendix and recent references.The Appendix sketches some of the most essential new results, constructions and ideas, including the solutions of the Luroth and Zariski problems, the theory of the descent and obstructions to the Hasse principle on rational varieties, and recent applications of K-theory to arithmetic.