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DNINFOA - SIA
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Doctorado en Ciencias - Matemáticas
Recent Submissions
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Morphisms between semi-graded rings and polynomial applications
In this thesis, we study several kinds of morphisms between families of semi-graded rings with their corresponding polynomial applications. First, we present some ring-theoretical notions of these objects that are necessary ... -
On the cluster complex and theta functions for cluster Poisson varieties
In this thesis, we establish an explicit description of the cluster complex, denoted as ∆^+_s(X), associated to a skew-symmetrizable cluster Poisson variety X and a seed s. Our approach involves a detailed description of ... -
Algebro-geometric characterizations of commuting differential operators in semi-graded rings
In this thesis, we study algebro-geometric characterizations of commuting differential operators in families of semi-graded rings. First, we present some ring-theoretical notions of semi-graded rings that are necessary ... -
Involutive and SAGBI bases for skew PBW extensions
In this thesis, we study homological properties and SAGBI and Involutive bases of the noncommutative rings known as skew PBW extensions. First, we present some ring- theoretical notions of these extensions that are necessary ... -
On the noncommutative geometry of semi-graded rings
En esta tesis, establecemos diversas caracterizaciones topológicas del espectro no conmutativo de anillos semi-graduados al considerar la noción de topología débil de Zariski. Con este propósito, formulamos condiciones ... -
On generalized multiscale methods for flow in complex porous media and their applications
In this document, the Generalized Multiscale Finite Element Method (GMsFEM) is studied, which deals with constructing multiscale spectral basis functions designed for high-contrast multiscale problems. The multiscale basis ... -
Conte de simetrías en objetos discretos
En este trabajo se estudia la ocurrencia en palabras, particiones de conjuntos y composiciones de enteros de las estadísticas pico simétrico, asociada a la ocurrencia del patrón 121, y pico asimétrico, asociada a la ... -
Algebraic properties of weak quantum symmetries
This thesis investigates the properties of weak bialgebras and weak Hopf algebras, their (co)representations, and applications in groupoids, path algebras, and Lie algebroids. The research employs algebraic and categorical ... -
Algorithms of differentiation for posets with an involution
En las últimas décadas, el estudio y clasificación de álgebras de dimensión finita con respecto a su tipo de representación ha sido uno de los principales objetivos en la teoría de representaciones de álgebras. Nazarova, ... -
Propiedades de algunos sistemas de polinomios ortogonales Sobolev en varias variables
En este trabajo estudiamos algunas propiedades algebraicas y analíticas de los polinomios ortogonales en varias variables reales con respecto a un producto interno Sobolev continuo-discreto. Consideramos los polinomios ... -
Effective computation of invariants of finite topological spaces
Hasta el momento, los métodos conocidos para el cálculo de invariantes de espacios topológicos finitos eran aplicables solamente a los posets de caras de complejos simpliciales o de CW-complejos regulares. En este trabajo ... -
Procesos de conteo, sobredispersión y extensiones
Se presenta una revisión detallada de modelos sobredispersos de regresión lineal y no lineal para datos de conteo, desde un enfoque Bayesiano. Se propone la función de distribución beta inclinada binomial, se estudian ... -
El problema de Cauchy asociado a una generalización de la ecuación Zakharov-Kuznetsov
En el presente trabajo, se tratan cuestiones tales como el buen planteamiento local en los espacios de Sobolev, espacios anisotrópicos con pesos y la existencia de ondas solitarias para el problema de valor inicial asociado ... -
El problema de Cauchy asociado a una generalización de la ecuación Zakharov-Kuznetsov sobre el cilindro
In this work, we study questions related to the local well-posedness for the initial value problem associated to the partial differential equation, u_{t} − ∂_{x}(D_{x}^{α+1}u ± D_{y}^{β+1}u) + u^{p}u_{x} = 0, where 0 ≤ ... -
Categorification of Some Integer Sequences and Its Applications
Categorification of real valued sequences, and in particular of integer sequences is a novel line of investigation in the theory of representation of algebras. In this theory introduced by Ringel and Fahr, numbers of a ... -
Dynkin Functions and Its Applications
Dynkin functions were introduced by Ringel as a tool to investigate combinatorial properties of hereditary artin algebras. According to Ringel, a Dynkin function consists of four sequences associated to An, Bn, Cn, Dn and ... -
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 ... -
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 ... -
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 ...
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