Related papers: An Algebraic Structure for the Central Mexican Rit…
We study the homogeneous coordinate rings of real multiplication noncommutative tori as defined by A. Polishchuk. Our aim is to understand how these rings give rise to an arithmetic structure on the noncommutative torus. We start by giving…
As shown in the previous publications, the shape of the histograms constructed by measurements of alpha-activity of samples of Pu-239, changes with periods equal approximately 24 hours, 27 days, and a year. At a higher resolution each of…
In this document the author proves that several problems in data-driven numerical approximation of dynamical systems in $\mathbb{C}^n$, can be reduced to the computation of a family of constrained matrix representations of elements of the…
Circulant matrices are an important tool widely used in coding theory and cryptography. A circulant matrix is a square matrix whose rows are the cyclic shifts of the first row. Such a matrix can be efficiently stored in memory because it is…
For a sequence of tasks, each with a positive integer period, the pinwheel scheduling problem involves finding a valid schedule in the sense that the schedule performs one task per day and each task is performed at least once every…
We present a method for solving the lightcurve of an eclipsing binary system which contains a Cepheid variable as one of its components as well as the solutions for three eclipsing Cepheids in the Large Magellanic Cloud (LMC). A geometric…
We define in an axiomatic fashion a \emph{Coxeter datum} for an arbitrary Coxeter group $W$. This Coxeter datum will specify a pair of reflection representations of $W$ in two vector spaces linked only by a bilinear paring without any…
Algebraic representations of time series are symbolic representations whose symbols belong to a finite group. Precisely, the framework of the present paper is the analysis of coupled time series in algebraic representations and, more…
The aim of this project is to review and expand upon the model proposed by Father Jose Domingo Duquesne de la Madrid (1745-1821) regarding the calendar of the ancient Muisca culture of the central Colombia. This model was dismissed by…
We construct an explicit canonical cycle in the top-dimensional homology of the Voronoi complex associated with an arithmetic group. This cycle relates to the cohomology of SL$_n(\mathbb{Z})$ with rational coefficients at the virtual…
We study the perturbations of a relatively close third star on a tidally distorted eccentric eclipsing binary. We consider both the observational consequences of the variations of the orbital elements and the interactions of the stellar…
This paper introduces the notion of locally algebraic representations and corresponding sheaves in the context of the cohomology of arithmetic groups. These representations are of relevance for the study of integral structures and special…
An algorithm that uses the cycle structure of the rows, or the columns, of a Latin square to compute its autotopy group is introduced. As a result, a bound for the size of the autotopy group is obtained. This bound is used to show that the…
The lunar periods of our moon -- the companion of the Earth -- which date back to the Babylonians until around 600 BCE, are 29.53 days for the synodic, 27.55 days for the anomalistic and 27.21 days for the draconitic month. In this paper we…
We consider separately radial (with corresponding group $\mathbb{T}^n$) and radial (with corresponding group $\mathrm{U}(n))$ symbols on the projective space $\mathbb{P}^n(\mathbb{C})$, as well as the associated Toeplitz operators on the…
To every irreducible finite crystallographic reflection group (i.e., an irreducible finite reflection group G acting faithfully on an abelian variety X), we attach a family of classical and quantum integrable systems on X (with meromorphic…
The horologia are ancient ephemerides, tables of durations of the days and nights during all months of the year. The algorithms used to compute the horologia are here presented and the results are compared with the tables computed by…
We introduce a family of domino tilings that includes tilings of the Aztec diamond and pyramid partitions as special cases. These tilings live in a strip of $\mathbb{Z}^2$ of the form $1 \leq x-y \leq 2\ell$ for some integer $\ell \geq 1$,…
We explore the special structure of the top-dimensional homology of any compact triangulable space $X$ of dimension $d$. Since there are no $(d+1)$-dimensional cells, the top homology equals the top cycles and is thus a free abelian group.…
This manuscript represents the author's PhD dissertation thesis.The first part studies decision problems in Thompson's groups F,T,V and some generalizations. The simultaneous conjugacy problem is determined to be solvable for Thompson's…