Departamento de Matemáticas
Recent Submissions
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A distributional approach to asymptotics of the Spectral Action
La acción espectral es el concepto natural y apropiado para hablar de una acción en el espacio de triplas espectrales, y fue introducido por primera vez por Chamseddine y Connes en 1997. Después de incluir definiciones y ... -
Valoración de opciones europeas en el modelo telegráfico con saltos doble exponenciales vía transformada de Laplace
This thesis studies the application of the Laplace transform for the valuation of European call and put options in the telegraphic model with constant and random jumps, where the jumps in the price of the underlying asset ... -
Fórmulas explícitas y cuerpos p-ádicos
Explicit formulae has been extensively studied through the years, producing deep conections between number theory, harmonic analysis and commutative algebra, among other branches of mathematics. In this work we will be ... -
Mayorización, politopos y clases de matrices combinatorias
En este trabajo, investigamos el retículo de caras, la propiedad de aditividad, el f-vector y algunas conexiones con clases de matrices combinatorias de unos politopos asociados con tres conceptos de mayorización. El ... -
Global lipschitz continuous solutions for a linear damped p-system
In this proposal we present an alternative point of view for the mathematical treatment of a linearly damped p-system through a variant of the vanishing viscosity method and the use of the theory of compensated compactness. ... -
Restauración de imágenes borrosas usando programación lineal
In the process of capturing images, it is common to deal with deteriorated images. These appear in various fields such as: astronomy, medicine, among others. In this work, a method is developed for the restoration of blurred ... -
Problema de Cauchy asociado a un ecuación del tipo KZKP con dispersión transversal fraccionaria
In this work it shall be studied the Cauchy problem for the following ZK-KP type equation u_{t}=u_{xxx}+HD_x^{\alpha}u_{yy}+uu_{x}, u(0)=\psi where 1\leq \alpha\leq 1, H denotes the Hilbert transform in the x variable ... -
Some remarks about the fusible property of noncommutative polynomial extensions
In this work, we focus on three objectives: first, we investigate fusible property on skew PBW extensions, recognizing conditions that guarantee the property for this family of algebras. Later, we turn our attention to the ... -
Non-commutative differential calculus of some algebras of polynomial type having PBW bases
In this work, we study the notion of differential calculus associated to an associative algebra, from its origin in manifolds geometry, to some generalizations in non commutative differential geometry. In particular, we ... -
A view toward the geometry of normalizing sequences in finitely semi-graded algebras
En este trabajo vemos el comportamiento de la sucesión normalizadora en álgebras semi-graduadas. Primero, definimos la sucesión regular y el complejo de Koszul en el caso conmutativo. Usando la variedad de ideales máximos, ... -
Existencia y unicidad de soluciones para un problema de difusión no local reescalado
We study a nonlocal difusion problem with the aim to decide on existence and uniqueness of solutions, and if that solutions satisfy some comparison principle. -
Portafolios cointegrados en el mercado Colombiano
Markowitz explains in his article (Markowitz 1999) that portfolio analysis dates back to before the 19th century in countries like England. This was long before he published one of the most important papers on modern ... -
La importancia de la estructura de comunicación de una comunidad para la reducción del miedo al crimen
The fear of crime is a determining factor in the security of a population, usually, through surveys, the relationships of this phenomenon with some social variables have been established and strategies to mitigate its ... -
The Auslander-Reiten Quiver of Equipped Posets of Finite Growth Representation Type, some Functorial Descriptions and Its Applications
The theory of representation of partially ordered sets or posets was introduced in the early 1970's as an effort to give an answer to the second Brauer-Thrall conjecture. Recall that one of the main goals of this theory ... -
Elección racional del consumidor en economías de Riesz: una comparación con la modelación tradicional y comentarios desde la economía comportamental
This paper develops the structure of consumer's rational choice problem inside the decision theory framework taking the consumption set as a Riesz space under different information conditions. It shows traditional concepts ... -
Sobre la superestabilidad en Q-Clases elementales abstractas
In the present work we study the concept of Q-abstract elementary class and we do an approximation to superestability in this context, adapting Shelah-Villaveces theorem. With the help of this theorem and based on chapter ... -
Zariski cancellation problem for skew PBW extensions
A special question for noncommutative algebras is Zariski cancellation problem. In this thesis we establish cancellation for some special classes of algebras such as skew PBW extensions, some Artin--Schelter regular algebras ... -
New characteristic dependent linear rank inequalities
En este trabajo estudiamos como construir desigualdades rango lineales dependientes de la característica y sus aplicaciones a la Teoría de Codificación de Redes y a la Teoría de Repartición de Secretos en protocolos ... -
On Sectional-Hyperbolic Sets
Sea M una variedad compacta Rimeniana de dimensión mayor o igual que tres. Dado X un campo vectorial C1 , transversal hacia el interior en la frontera (si no es vacı́a), llamamos Xt el flujo inducido sobre M . Un ... -
Optimización de un Modelo de Rentas Pensionales de Uso Comercial
Universidad Nacional de Colombia Sede Bogotá Facultad de Ciencias Departamento de Matemáticas.