Spelling suggestions: "subject:"ofminimal"" "subject:"orminimal""
1 |
Cohomologia de feixes em estruturas O-minimais / Sheaf cohomology in O-minimal structuresJonas Renan Moreira Gomes 15 June 2018 (has links)
Este trabalho estuda a demonstração de existência de uma teoria de cohomologia em estruturas o-minimais arbitrárias, conforme o trabalho de Edmundo, Jones e Peatfield. / This work studies the proof of the existence of sheaf cohomology theory in arbitrary o-minimal structures, following the work of Edmundo, Jones and Peatfield.
|
2 |
Cohomologia de feixes em estruturas O-minimais / Sheaf cohomology in O-minimal structuresGomes, Jonas Renan Moreira 15 June 2018 (has links)
Este trabalho estuda a demonstração de existência de uma teoria de cohomologia em estruturas o-minimais arbitrárias, conforme o trabalho de Edmundo, Jones e Peatfield. / This work studies the proof of the existence of sheaf cohomology theory in arbitrary o-minimal structures, following the work of Edmundo, Jones and Peatfield.
|
3 |
Geometría de sistemas de descenso: estudio asintótico mediante desingularizaciónBobadilla Solari, Roberto Javier January 2016 (has links)
Magíster en Ciencias de la Ingeniería, Mención Matemáticas Aplicadas. Ingeniero Civil Matemático / Los sistemas de tipo gradiente son relevantes como sistemas dinámicos en sí y además sirven como marco teórico para estudiar algoritmos de optimización, en particular algoritmos de descenso. Relacionado con este último aspecto, es natural preguntarse si las órbitas tienen longitud finita y convergen, cuando están en un conjunto acotado.
El presente trabajo presenta respuestas a tales preguntas, bajo suposiciones especiales pero no restringidas en la práctica: se adoptará el marco de la geometría o-minimal que permite establecer resultados pertinentes sobre el comportamiento de las órbitas en torno a los puntos críticos. Como se verá a coninuación, una función suave f definible en una estructura o-minimal satisface la llamada desigualdad de Kurdyka-Lojasiewicz: en torno a cualquier valor crítico se acotan los gradientes de f inferiormente por una constante. Dicho resultado se adapta en el caso no suave (siempre gracias a las herramientas de la geometría o~-minimal) y se obtiene una cota análoga válida uniformemente para la norma de los subgradientes de f.
A grandes rasgos el resultado de Kurdyka-Lojasiewicz consiste en encontrar una función auxiliar (la función desingularizante) estrictamente monótona y suave, de forma que por una parte el sistema gradiente (o bien subgradiente) inducido por la composición de dicha función con f tiene las mismas órbitas, y por otra parte los gradientes (o subgradientes) de dicha composición están acotados inferiormente por una constante. Este proceso es llamado desingularización de la función f, cuya potencia se aprecia explícitamente mediante la parametrización de las trayectorias a través de los niveles de la función f.
Por último existe un resultado similar para multiaplicaciones definibles, donde se desingulariza la coderivada, en un sentido que se determinará más adelante. En este caso el sistema dinámico de estudio ya no es un sistema de tipo gradiente o subgradiente, sino que es un sweeping process. Se muestra que si dicho \textit{sweeping process} proviene de una función definible y continua, entonces mediante la desingularización de su coderivada se recuperan los resultados anteriores. En particular se pondrá en evidencia la relación entre la desingularización del sweeping process y la desingularización de la función f que lo define. / Este trabajo ha sido parcialmente financiado por FONDECYT 1130176
|
4 |
The first order theory of a dense pair and a discrete groupKhani, Mohsen January 2013 (has links)
In this thesis we have shown that a seemingly complicated mathematical structure can exhibit 'tame behaviour'. The structure we have dealt with is a field (a space in which there are addition and multiplication which satisfy natural properties) together with a dense subset (a subset which has spread in all parts of the this set, as Q does in R) and a discrete subset (a subset comprised of single points which keep certain distances from one another). This tameness is essentially with regards to not being trapped with the 'Godel phenomeonon' as the Peano arithmetic does.
|
5 |
Tameness Results for Expansions of the Real Field by GroupsTychonievich, Michael Andrew 27 August 2013 (has links)
No description available.
|
6 |
O-minimal De Rham cohomology / Cohomologia de De Rham o-minimalFigueiredo, Rodrigo 15 December 2017 (has links)
The aim of this dissertation lies in establishing an o-minimal de Rham cohomology theory for smooth abstract-definable manifolds in an o-minimal expansion of the real field which admits smooth cell decomposition and defines the exponential function, by following the classical de Rham cohomology. We can specify the o-minimal cohomology groups and attain some properties as the existence of Mayer-Vietoris sequence and the invariance under smooth abstract-definable diffeomorphisms. However, in order to obtain the invariance of our o-minimal cohomology under abstract-definable homotopy we must, working in a tame context that defines sufficiently many primitives, assume the validity of a statement related to Bröcker\'s problem. / O objetivo desta tese reside em estabelecer uma cohomologia de De Rham o-minimal para variedades definíveis abstratas lisas em uma expansão o-minimal do corpo ordenado dos reais, a qual admite decomposição celular lisa e define a função exponencial, seguindo a cohomologia de De Rham clássica. Além de especificarmos os grupos da cohomologia de Rham o-minimal, obtemos algumas propriedades, como a existência da sequência de Mayer-Vietoris e a invariância sob difeomorfismos definíveis abstratos lisos. Todavia, a fim de lograrmos a invariância de nossa cohomologia o-minimal sob homotopia definível abstrata devemos, além de trabalhar num contexto moderado no qual muitas primitivas são definidas, assumir a validade de uma asserção relacionada ao problema de Bröcker.
|
7 |
Um resultado geral de modelo completude de expansões do corpo ordenado dos reais / A general model completeness result for expansions of the real ordered fieldFigueiredo, Rodrigo 17 October 2012 (has links)
Este trabalho tem como foco principal estabelecer condições gerais suficientes para que uma expansão do corpo ordenado dos reais por funções com domínio em Rn seja modelo completa e o-minimal. Para tanto, faremos uma abordagem sob o ponto de vista de estruturas fracas o-minimais, conforme o trabalho de Charbonnel e Wilkie. Além disso, ao analisar condições adicionais, podemos obter a seguinte generalização de um trabalho de Gabrielov: uma expansão o-minimal do corpo ordenado dos reais por funções C infinito restritas, que é polinomialmente limitada e fechada sob diferenciação parcial, é modelo completa. / The main focus of this dissertation lies in establishing some general sufficient conditions for an expansion of the real ordered field by functions with domains Rn to be model complete and o-minimal. We approach this subject from the point of view of the o-minimal weak structures, by following the work of Charbonnel and Wilkie. Furthermore, when considering additional conditions, we are able to obtain the following generalization of a Gabrielovs result: an expansion of the real ordered field by restricted smooth functions, which is polynomially bounded and closed under partial differentiation, is model complete.
|
8 |
Um resultado geral de modelo completude de expansões do corpo ordenado dos reais / A general model completeness result for expansions of the real ordered fieldRodrigo Figueiredo 17 October 2012 (has links)
Este trabalho tem como foco principal estabelecer condições gerais suficientes para que uma expansão do corpo ordenado dos reais por funções com domínio em Rn seja modelo completa e o-minimal. Para tanto, faremos uma abordagem sob o ponto de vista de estruturas fracas o-minimais, conforme o trabalho de Charbonnel e Wilkie. Além disso, ao analisar condições adicionais, podemos obter a seguinte generalização de um trabalho de Gabrielov: uma expansão o-minimal do corpo ordenado dos reais por funções C infinito restritas, que é polinomialmente limitada e fechada sob diferenciação parcial, é modelo completa. / The main focus of this dissertation lies in establishing some general sufficient conditions for an expansion of the real ordered field by functions with domains Rn to be model complete and o-minimal. We approach this subject from the point of view of the o-minimal weak structures, by following the work of Charbonnel and Wilkie. Furthermore, when considering additional conditions, we are able to obtain the following generalization of a Gabrielovs result: an expansion of the real ordered field by restricted smooth functions, which is polynomially bounded and closed under partial differentiation, is model complete.
|
9 |
Power functions and exponentials in o-minimal expansions of fieldsFoster, T. D. January 2010 (has links)
The principal focus of this thesis is the study of the real numbers regarded as a structure endowed with its usual addition and multiplication and the operations of raising to real powers. For our first main result we prove that any statement in the language of this structure is equivalent to an existential statement, and furthermore that this existential statement can be chosen independently of the concrete interpretations of the real power functions in the statement; i.e. one existential statement will work for any choice of real power functions. This result we call uniform model completeness. For the second main result we introduce the first order theory of raising to an infinite power, which can be seen as the theory of a class of real closed fields, each expanded by a power function with infinite exponent. We note that it follows from the first main theorem that this theory is model-complete, furthermore we prove that it is decidable if and only if the theory of the real field with the exponential function is decidable. For the final main theorem we consider the problem of expanding an arbitrary o-minimal expansion of a field by a non-trivial exponential function whilst preserving o-minimality. We show that this can be done under the assumption that the structure already defines exponentiation on a bounded interval, and a further assumption about the prime model of the structure.
|
10 |
Bounding Betti numbers of sets definable in o-minimal structures over the realsClutha, Mahana January 2011 (has links)
A bound for Betti numbers of sets definable in o-minimal structures is presented. An axiomatic complexity measure is defined, allowing various concrete complexity measures for definable functions to be covered. This includes common concrete measures such as the degree of polynomials, and complexity of Pfaffian functions. A generalisation of the Thom-Milnor Bound [17, 19] for sets defined by the conjunction of equations and non-strict inequalities is presented, in the new context of sets definable in o-minimal structures using the axiomatic complexity measure. Next bounds are produced for sets defined by Boolean combinations of equations and inequalities, through firstly considering sets defined by sign conditions, then using this to produce results for closed sets, and then making use of a construction to approximate any set defined by a Boolean combination of equations and inequalities by a closed set. Lastly, existing results [12] for sets defined using quantifiers on an open or closed set are generalised, using a construction from Gabrielov and Vorobjov [11] to approximate any set by a compact set. This results in a method to find a general bound for any set definable in an o-minimal structure in terms of the axiomatic complexity measure. As a consequence for the first time an upper bound for sub-Pfaffian sets defined by arbitrary formulae with quantifiers is given. This bound is singly exponential if the number of quantifier alternations is fixed.
|
Page generated in 0.0345 seconds