1. Homotopía cónica - Díaz, F. J.
Desde los inicios de la Topología Algebraica hasta nuestros días se han ido consiguiendo axiomáticas de las distintas teorías encuadradas dentro de esta denominación. En este sentido, aunque se han dado diversas de la homotopía, ninguna de ellas llega a interpretar plenamente dicho concepto, pues siempre existe alguna teoría que se puede considerar de homotopía no encuadrada en las axiomáticas. El autor, interrelacionando axiomáticas como las construcciones standard de P. J. Huber y las categorías cofibradas de H. J. Baues, logra extraer las condiciones precisas que permiten al cono generar la homotopía clásica de los espacios topológicos. Expresándolas axiomáticamente desde...

2. Homotopía cónica - Díaz, F. J.
Desde los inicios de la Topología Algebraica hasta nuestros días se han ido consiguiendo axiomáticas de las distintas teorías encuadradas dentro de esta denominación. En este sentido, aunque se han dado diversas de la homotopía, ninguna de ellas llega a interpretar plenamente dicho concepto, pues siempre existe alguna teoría que se puede considerar de homotopía no encuadrada en las axiomáticas. El autor, interrelacionando axiomáticas como las construcciones standard de P. J. Huber y las categorías cofibradas de H. J. Baues, logra extraer las condiciones precisas que permiten al cono generar la homotopía clásica de los espacios topológicos. Expresándolas axiomáticamente desde...

3. Homotopía cilíndrica generalizada - Remedios-Gómez, Josué
Desde el punto de vista algebraico, son varios los autores que han estudiado la homotopía a través de un funtor cilindro. Tomando como modelo la axiomática de Baues [H.J. Baues "Algebraic Homotopy", Cambridge University Pressm 1989], el autor presenta en esta tesis unos axiomas para un funtor cilindro, transformaciones naturales y una familia de cofibraciones, que permiten obtener homotopía en categorías más generales (I-categorías generalizadas), sin necesidad de que los objetos sean cofibrantes y sin necesidad de emplear puntos base para obtener los grupos de homotopía. Esta homotopía se define relativa a la familia de cofibraciones de la categoría, y...

4. Homotopía cilíndrica generalizada - Remedios-Gómez, Josué
Desde el punto de vista algebraico, son varios los autores que han estudiado la homotopía a través de un funtor cilindro. Tomando como modelo la axiomática de Baues [H.J. Baues "Algebraic Homotopy", Cambridge University Pressm 1989], el autor presenta en esta tesis unos axiomas para un funtor cilindro, transformaciones naturales y una familia de cofibraciones, que permiten obtener homotopía en categorías más generales (I-categorías generalizadas), sin necesidad de que los objetos sean cofibrantes y sin necesidad de emplear puntos base para obtener los grupos de homotopía. Esta homotopía se define relativa a la familia de cofibraciones de la categoría, y...

5. Homotopía propia simplicial - García Calcines, José Manuel
En esta memoria se desarrollan las técnicas simpliciales para las categorías de homotopía propía, se buscan los modelos axiomáticos adecuados para dichas categorías y se estudian las teorías de homologías derivadas de las construcciones simpliciales correspondientes. El marco de trabajo usado para la categoría propia será la categoría de los espacios exteriores, recientemente introducida por García-Pinillos (véase Tesis (1998) Universidad de La Rioja) y García-Calcines, García-Pinillos, Hernández (véase A closed simplicial model category for proper homotopy and shape theories, Bull. Austr. Math. Soc. 57, 221-242, 1998). Para ello, se investiga más esta categoría obteniendo propiedades básicas, interpretación de la categoría,...

6. Homotopia de trajetorias de sistemas dinamicos - Marcelo Gonçalves Oliveira Vieira
Este trabalho aborda a homotopia monotônica, uma variante apropriada de homotopia, de trajetórias de sistemas de controle. Primeiro é introduzido um conceito de regularidade para funções de controle e depois é considerada a definição de homotopia monotônica de trajetórias regulares de um sistema de controle 'sigma' evoluindo sobre uma variedade M. Em seguida são mostrados que o conjunto 'gama' ('sigma', x) de classes de homotopia monotônica das trajetórias regulares do sistema 'sigma' a partir de um estado fixo tem um estrutura de variedade diferenciável. Outro resultado importante é a caracterização para trajetórias monotonicamente homotópicas (contidas no conjunto dos pontos acessíveis...

7. Smooth And Continuous Homotopies - Andreas Kriegl,Peter W. Michor
Continuous and smooth homotopies agree from smooth nite dimensional manifolds into in nite dimensional ones which are modeled on convenient vector spaces. Since convex charts do not exist we use radial charts.

8. Toric Newton Method for Polynomial Homotopies
This paper defines a generalization of Newton's method to deal with solution paths defined by polynomial homotopies that lead to extremal values. Embedding the solutions in a toric variety leads to explicit scaling relations between coefficients and solutions. Toric Newton is a symbolicnumeric algorithm where the symbolic pre-processing exploits the polyhedral structures. The numerical stage uses the additional variables introduced by the homogenization to scale the components of the solution vectors to the complex unit circle. Toric Newton generates appropriate affine charts and enables to approximate the magnitude of large solutions of polynomial systems. AMS Subject Classification. 14M25, 52B55, 65H10, 68Q40. Keywords. polynomial system, toric varieties, Newton's method,...

9. Toric Newton Method for Polynomial Homotopies
This paper defines a generalization of Newton's method to deal with solution paths defined by polynomial homotopies that lead to extremal values. Embedding the solutions in a toric variety leads to explicit scaling relations between coefficients and solutions. Toric Newton is a symbolicnumeric algorithm where the symbolic pre-processing exploits the polyhedral structures. The numerical stage uses the additional variables introduced by the homogenization to scale the components of the solution vectors to the complex unit circle. Toric Newton generates appropriate affine charts and enables to approximate the magnitude of large solutions of polynomial systems. AMS Subject Classification. 14M25, 52B55, 65H10, 68Q40. Keywords. polynomial system, toric varieties, Newton's method,...

10. Toric Newton Method For Polynomial Homotopies
. This paper defines a generalization of Newton's method to deal with solution paths defined by polynomial homotopies that lead to extremal values. Embedding the solutions in a toric variety leads to explicit scaling relations between coefficients and solutions. Toric Newton is a symbolic-numeric algorithm where the symbolic pre-processing exploits the polyhedral structures. The numerical stage uses the additional variables introduced by the homogenization to scale the components of the solution vectors to the complex unit circle. Toric Newton generates appropriate affine charts and enables to approximate the magnitude of large solutions of polynomial systems. AMS Subject Classification. 14M25, 52B55, 65H10, 68Q40. Keywords. polynomial system, toric varieties, Newton's method,...

11. Toric Newton Method for Polynomial Homotopies
This paper defines a generalization of Newton's method to deal with solution paths defined by polynomial homotopies that lead to extremal values. Embedding the solutions in a toric variety leads to explicit scaling relations between coefficients and solutions. Toric Newton is a symbolic-numeric algorithm where the symbolic pre-processing exploits the polyhedral structures. The numerical stage uses the additional variables introduced by the homogenization to scale the components of the solution vectors to the complex unit circle. Toric Newton generates appropriate affine charts and enables to approximate the magnitude of large solutions of polynomial systems.

12. Piecewise Linear Homotopies And Affine Variational Inequalities - Menglin Cao
PIECEWISE LINEAR HOMOTOPIES AND AFFINE VARIATIONAL INEQUALITIES Menglin Cao Under Supervision of Assistant Professor Michael C. Ferris at the University of Wisconsin--Madison The purpose of this thesis is to apply the theory of piecewise linear homotopies and the notion of a normal map in the construction and analysis of algorithms for affine variational inequalities. An affine variational inequality can be expressed as a piecewise linear equation AC (x) = a, where A is a linear transformation from IR n to IR n , C is a polyhedral convex subset of IR n , and AC is the associated normal map. We introduce a path-following algorithm for solving the equation AC (x) = a. When AC is coherently oriented,...

13. Piecewise Linear Homotopies And Affine Variational Inequalities - Menglin Cao
PIECEWISE LINEAR HOMOTOPIES AND AFFINE VARIATIONAL INEQUALITIES Menglin Cao Under Supervision of Assistant Professor Michael C. Ferris at the University of Wisconsin--Madison The purpose of this thesis is to apply the theory of piecewise linear homotopies and the notion of a normal map in the construction and analysis of algorithms for affine variational inequalities. An affine variational inequality can be expressed as a piecewise linear equation AC (x) = a, where A is a linear transformation from IR n to IR n , C is a polyhedral convex subset of IR n , and AC is the associated normal map. We introduce a path-following algorithm for solving the equation AC (x) = a. When AC is coherently oriented,...

14. Los grupos de homotopía : una invariante topológica / Alberto Rafael Mejías Espinoza - Mejías espinoza, Alberto Rafael; Universidad de Los Andes.. Facultad de Ciencias, Departamento de Matemática, Tesis, 1980
Tesis (Lic. en Matematica)-- Universidad de Los Andes, Facultad de Ciencias, Departamento de Matemática, Mérida, 1980

15. Solution of Bounded Nonlinear Systems of Equations Using Homotopies With Inexact Restoration - E. G. Birgin,J. M. Martnez
Nonlinear systems of equations represent often mathematical models of chemical production processes and other engineering problems. Homotopic techniques (in particular, the bounded homotopies introduced by Paloschi) are used for enhancing convergence to solutions, especially when a good initial estimate is not available. In this paper, the homotopy curve is considered as the feasible set of a mathematical programming problem, where the objective is to nd the optimal value of the homotopic parameter. Inexact restoration techniques can then be used to generate approximations in a neighborhood of the homotopy, the size of which is theoretically justied. Numerical examples are given. Key words: Nonlinear programming, homotopies, bounded homotopies, inexact restoration. 1

16. Noninvertibility And "Semi-" Analogs Of (Super) Manifolds, Fiber Bundles And Homotopies - Steven Duplij
Supersymmetry contains initially noninvertible objects, but it is common to deal with the invertible ones only, factorizing former in some extent. We propose to reconsider this ansatz and try to redefine such fundamental notions as supermanifolds, fiber bundles and homotopies using some weakening invertibility conditions. The prefix semireflects the fact that the underlying morphisms form corresponding semigroups consisting of a known group part and a new ideal noninvertible part. We found that the absence of invertibility gives us the generalization of the cocycle conditions for transition functions of supermanifolds and fiber bundles in a natural way, which can lead to construction of noninvertible analogs of Cech cocycles. We define semi-homotopies, which can...

17. Noninvertibility And "semi-" Analogs Of (super) Manifolds, Fiber Bundles And Homotopies - Steven Duplij
Supersymmetry contains initially noninvertible objects, but it is common to deal with the invertible ones only, factorizing former in some extent. We propose to reconsider this ansatz and try to redefine such fundamental notions as supermanifolds, fiber bundles and homotopies using some weakening invertibility conditions. The prefix semireflects the fact that the underlying morphisms form corresponding semigroups consisting of a known group part and a new ideal noninvertible part. We found that the absence of invertibility gives us the generalization of the cocycle conditions for transition functions of supermanifolds and fiber bundles in a natural way, which can lead to construction of noninvertible analogs of Cech cocycles. We define semi-homotopies, which can...

18. Noninvertibility And "semi-" Analogs Of (super) Manifolds, Fiber Bundles And Homotopies - Steven Duplij
Supersymmetry contains initially noninvertible objects, but it is common to deal with the invertible ones only, factorizing former in some extent. We propose to reconsider this ansatz and try to redefine such fundamental notions as supermanifolds, fiber bundles and homotopies using some weakening invertibility conditions. The prefix semireflects the fact that the underlying morphisms form corresponding semigroups consisting of a known group part and a new ideal noninvertible part. We found that the absence of invertibility gives us the generalization of the cocycle conditions for transition functions of supermanifolds and fiber bundles in a natural way, which can lead to construction of noninvertible analogs of Cech cocycles. We define semi-homotopies, which can...

19. Threading Homotopies and DC Operating Points of Nonlinear Circuits - Ross Geoghegan,Jeffrey C. Lagarias,Robert C. Melville
This paper studies continuation methods for finding isolated zeros of nonlinear functions. Given a nonlinear function F : R n ! R n , a threading homotopy is a function H(x; ) : R n+1 ! R n with H(x; 0) j F (x), such that the zero set of H is a single connected curve containing all zeros of F (x). For a C 1 function F , a necessary condition for the existence of a nondegenerate C 1 threading homotopy is that the topological degree of F (x) be 1, 0 or Gamma1. For C 2 mappings in all dimensions except possibly n = 2 this condition is also a sufficient condition for existence of a C 2 threading homotopy...

20. Numerical Homotopies to compute generic Points on positive dimensional Algebraic Sets - Andrew J. Sommese,Jan Verschelde
Many applications modeled by polynomial systems have positive dimensional solution components (e.g., the path synthesis problems for four-bar mechanisms) that are challenging to compute numerically by homotopy continuation methods. A procedure of A. Sommese and C. Wampler consists in slicing the components with linear subspaces in general position to obtain generic points of the components as the isolated solutions of an auxiliary system. Since this requires the solution of a number of larger overdetermined systems, the procedure is computationally expensive and also wasteful because many solution paths diverge. In this article an embedding of the original polynomial system is presented, which leads to a sequence of homotopies, with...

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