GIAA

Skew PBW Extensions

This monograph is devoted to a new class of non-commutative rings, skew Poincaré–Birkhoff–Witt (PBW) extensions. Beginning with the basic definitions and ring-module theoretic/homological properties, it goes on to investigate finitely generated …

A geometric realization of socle-projective categories for posets of type A

This paper establishes a link between the theory of cluster algebras and the theory of representations of partially ordered sets. We introduce a class of posets by requiring avoidance of certain types of peak-subposets and show that these posets can …

CMV block matrices for symmetric matrix measures on the unit circle

In this contribution, we study the relationship between the CMV block matrices associated with two symmetric positive definite matrix measures supported on the unit circle. We also consider certain transformations of an orthogonality matrix measure …

Modelo matemático para estimar curvas de intensidad, duración y frecuencia de lluvias extremas en Tunja, Colombia

Este articulo propone y resuelve un modelo matemático para predecir el comportamiento de la precipitación en la ciudad de Tunja. Para esto, la información pluviométrica se sometió a pruebas de ajuste a funciones de distribución de probabilidad, …

On a Christoffel Transformation for Matrix Measures Supported on the Unit Circle

Let 𝜎 be a Hermitian matrix measure supported on the unit circle. In this contribution, we study some algebraic and analytic properties of the orthogonal matrix polynomials associated with the Christoffel matrix transformation of 𝜎 defined by …

Skew Poincaré-Birkhoff-Witt extensions over weak compatible rings

In this paper, we introduce weak (Σ,Δ)-compatible rings and study skew Poincaré–Birkhoff–Witt extensions over these rings. We characterize the weak notion of compatibility for several noncommutative rings appearing in noncommutative algebraic …

Matrix moment perturbations and the inverse Szegő matrix transformation

Given a perturbation of a matrix measure supported on the unit circle, we analyze the perturbation obtained on the corresponding matrix measure on the real line, when both measures are related through the Szegő matrix transformation. Moreover, using …

La cognición y la enseñanza del concepto de diferencial, desde la teoría APO

El propósito de la investigación denominada “La cognición y la enseñanza del concepto de diferencial, desde la teoría APOE. Un aporte a la formación de profesores en matemáticas”, es describir y explicar la forma en que los estudiantes de pregrado comprenden la diferencial de una función en varias variables, que es una propiedad de algunas aplicaciones matemáticas con dominio en un subconjunto abierto del de poder ser aproximadas por una transformación lineal en un punto de su dominio.

Double Ore extensions versus graded skew PBW extensions

In this article, we present necessary and sufficient conditions for a graded (trimmed) double Ore extension to be a graded (quasi-commutative) skew PBW extension. Using this fact, we prove that a graded skew PBW extension A=σ(R)⟨x1,x2⟩ of an …

A Computational Maple Library for Skew PBW Extensions

In this paper we present a computational package developed for making computations involved in many homological applications of the Gr"obner theory of skew PBW extensions.