Benjamín A. Itzá-Ortiz

Autonomous University of Hidalgo | UAEH · Centro de Investigación en Matemáticas

In this paper we give conditions on a matrix which guarantee that it is similar to a centrosymmetric matrix. We use this conditions to show that some $4 \times 4$ and $6 \times 6$ Toeplitz matrices are similar to centrosymmetric matrices. Furthermore, we give conditions for a matrix to be similar to a matrix which has a centrosymmetric principal su...

In this paper, a fractional Lotka-Volterra mathematical model for a bioreactor is proposed and used to fit the data provided by a bioprocess known as continuous fermentation of Zymomonas mobilis. The model contemplates a time-delay due to the dead-time (non-trivial) that the microbe needed to metabolize the substrate. A Hopf bifurcation analysis is...

Cell structures were introduced by W. Debski and E. Tymchatyn as a way to study some classes of topological spaces and their continuous functions through discrete approximations. In this work we weaken the notion of cell structure and prove that, the resulting class of topological space admitting such a generalized cell structure includes non-regul...

En este artículo damos una prueba alternativa y elemental a un resultado propuesto por los primeros dos autores sobre la expresión de la envolvente convexa de dos círculos como la unión de una familia no-numerable de elipses. Las herramientas empleadas incluyen cálculo elemental y geometría analítica. Es de hacer notar que el empleo de estas herram...

Based on the well-known Detrended Fluctuation Analysis (DFA) for time series, in this work we describe a DFA for continuous real variable functions. Under certain conditions, DFA accurately predicts the long-term auto-correlation of the time series, depending on the value of certain scaling parameter. We show that for continuous functions, the prop...

In this paper, we prove a conjecture stated by the first two authors establishing the closure of the numerical range of a certain class of n + 1-periodic tridiagonal operators as the convex hull of the numerical ranges of two tridiagonal (n+1)×(n+1) matrices. Furthermore, when n + 1 is odd, we show that the size of such matrices simplifies to n2+1.

In this paper we show that the closure of the numerical range of an n+1-periodic tridiagonal operator is equal to the numerical range of a 2(n+1)×2(n+1) complex matrix.

En este art´ıculo se propone un m´etodo basado en topolog´ıa algebraica para el an´alisis de colecciones de series de tiempo simult´aneas. Cada serie de tiempo corresponde a una variable. Se construye la matriz de correlaci´on de las variables y la red con pesos en las aristas asociada a dicha matriz. A trav´es de variar un par´ametro p entre 0 y 1...

The pandemic caused by the SARS-CoV-2 virus spreads more rapidly in densely populated areas. The number of confirmed cases is counted by the millions in some countries, such as USA, Brazil, and Mexico. These three countries also report the world’s highest cumulative death tolls caused by the disease as of February 2021. In this study, a comparative...

A fault-tolerant control algorithm based on sliding modes is proposed to ensure the tracking of the desired trajectory for time-varying systems even in the presence of actuator faults. The proposed algorithm uses a continuous integral sliding mode and a linear quadratic regulator, together with control allocation and system inversion techniques, re...

In this paper a stability analysis for a Cournot duopoly model with tax evasion and time-delay in a continuous-time framework is presented. The mathematical model under consideration follows a gradient dynamics approach, is nonlinear and four-dimensional with state variables given by the production and declared revenue of each competitor. We prove...

In this paper we prove a conjecture stated by the first two authors in \cite{IM} establishing the closure of the numerical range of a certain class of $n+1$-periodic tridiagonal operators as the convex hull of the numerical ranges of two tridiagonal $(n+1) \times (n+1)$ matrices. Furthermore, when $n+1$ is odd, we show that the size of such matrice...

In this paper we show that the closure of the numerical range of a $n+1$-periodic tridiagonal operator is equal to the numerical range of a $2(n+1)\times 2(n+1)$ complex matrix.

Cell structures were introduced by W. Debski and E. Tymchatyn as a way to study some classes of topological spaces and their continuous functions by means of discrete approximations. In this work we weaken the notion of cell structure and prove that the resulting class of topological space admitting such a generalized cell structure includes non-re...

Given a point $(p,q)$ with nonnegative integer coordinates and $p\not=q$, we prove that the quadratic B\'ezier curve relative to the points $(p,q)$, $(0,0)$ and $(q,p)$ is approximately the envelope of a family of segments whose endpoints are the B\'ezout coefficients of coprime numbers belonging to neighborhoods of $(p,q)$ and $(q,p)$, respectivel...

In this paper, a fractional Lotka-Volterra mathematical model for a bioreactor is proposed and used to fit the data provided by a bioprocess known as continuous fermentation of Zymomonas mobilis. The model contemplates a time-delay $\tau$ due to the dead-time in obtaining the measurement of biomass $x(t)$. A Hopf bifurcation analysis is performed t...

Despu´es de una breve rese˜na sobre la divisibilidad de n´umeros enteros, en este trabajo presentaremos el siguiente criterio sencillo de divisibilidad entre 11, el cual es in´edito en lo que a los autores respecta: un n´umero entero es divisible entre 11 si y solo si la suma del n´umero formado por sus dos ´ultimos d´ıgitos m´as el n´umero resulta...

In this paper a stability analysis for a Cournot duopoly model with tax evasion and time-delay in a continuous-time framework is presented. The mathematical model under consideration follows a gradient dynamics approach, is nonlinear and four-dimensional with state variables given by the production and declared revenue of each competitor. We prove...

We provide conditions for stable equilibrium in Cournot duopoly models with tax evasion and time delay. We prove that our conditions actually imply asymptotically stable equilibrium and delay independence. Conditions include the same marginal cost and equal probability for evading taxes. We give examples of cost and inverse demand functions satisfy...

In this paper, we compute the closure of the numerical range of certain periodic tridiagonal operators. This is achieved by showing that the closure of the numerical range of such operators can be expressed as the closure of the convex hull of the uncountable union of numerical ranges of certain symbol matrices. For a special case, this result can...

In this paper we compute the closure of the numerical range of certain periodic tridiagonal operators. This is achieved by showing that the closure of the numerical range of such operators can be expressed as the closure of the convex hull of the uncountable union of numerical ranges of certain symbol matrices. For a special case, this result can b...

We study a Cournot duopoly model with tax evasion and time delay. We prove that if the marginal production costs of both competing firms are equal then the equilibrium point is asymptotically stable and independent of time delay. As consequence, our model can not have bifurcations if the delay, as a parameter, is varied. It further imply that less...

Introduction In time series, brown noise by means of the Detrended Fluctuation Analysis in Mild Cognitive Impaired (MCI) subjects during the NREM to REM sleep transition has been reported, so an application that may show different colors of noise of MCI, demented or normal Older Adults (OAs) was tested during REM sleep and wakefulness. To achieve t...

Introduction In sleep recordings, Arousals and Leg Movements (LMs) in Older Adults (OAs) represent non-stationarities that are often avoided and are rejected when linear quantitative analyses are performed. Nevertheless, their frequency is fundamental to evaluate the health status of OAs, but there is little work on the influence of these events on...

We present a transformation, based on the B\'ezout's identity, which maps the set of pairs of relatively prime numbers $(p,q)$ with fixed $p$ and $0<q<p$, to pairs of relatively prime numbers in the $p\times p$ square in $\mathbb R^2$, in such a way that intriguing quadratic arcs show up. We exhibit parametrizations of quadratic curves which fit su...

In Older Adults (OAs), Electroencephalogram (EEG) slowing in frontal lobes and a diminished muscle atonia during Rapid Eye Movement sleep (REM) have each been effective tracers of Mild Cognitive Impairment (MCI), but this relationship remains to be explored by non-linear analysis. Likewise, data provided by EEG, EMG (Electromyogram) and EOG (Electr...

We provide a classification of eventually periodic subshifts up to conjugacy and flow equivalence. We use our results to prove that each skew Sturmian subshift is conjugate to exactly one other skew Sturmian subshift and that all skew Sturmian subshifts are flow equivalent to one another.

We give a topological classification of the minimal proper subspaces of aperiodic flows on the torus in terms of the conjugacy invariants of their corresponding Denjoy homeomorphisms. Several examples and some connections to operator algebras are discussed.

We consider a class of tridiagonal operators induced by not necessary pseudoergodic biinfinite sequences. Using only elementary techniques we prove that the numerical range of such operators is contained in the convex hull of the union of the numerical ranges of the operators corresponding to the constant biinfinite sequences; whilst the other incl...

En el presente artículo analizamos modelos estático y dinámico del duopolio de Cournot con evasión de impuestos y se discuten las interpretaciones económicas de los resultados. En el caso del modelo dinámico, se introduce un tiempo de retardo y se presentan fórmulas para calcular el polinomio característico de su linealización.

In this work we analyze the stability of a PID multiresolution controller, which uses wavelet theory for the decomposition of the tracking error signal. We present a general error function in terms of partial errors which gives us the various frequencies appearing in the general errors. Once we obtain the spectrum of the error signal, we divide t...

The analysis of the interaction and synchronization of relatively large ensembles of neurons is fundamental for the understanding of complex functions of the nervous system. It is known that the temporal synchronization of neural ensembles is involved in the generation of specific motor, sensory or cognitive processes. Also, the intersegmental cohe...

A classification of D-branes in Type IIB Op− orientifolds and orbifolds in terms of Real and equivariant KK-groups is given. We classify D-branes intersecting orientifold planes from which are recovered some special limits such as the spectrum for D-branes on top of Type I Op− orientifold and the bivariant classification of Type I D-branes. The gau...

The crossed product construction provides a bridge between operator algebras and dynamical systems. For instance, it is known that two ergodic non singular dynamical systems are orbit equivalent if and only if their associated von Neumann crossed products are isomorphic. In the topological setting, it is known that two minimal dynamical systems on...

Let θ be a nondegenerate skew symmetric real d×d matrix, and let Aθ be the corresponding simple higher-dimensional noncommutative torus. Suppose that d is odd, or that d≥4 and the entries of θ are not contained in a quadratic extension of ℚ. Then Aθ is isomorphic to the transformation group C*-algebra obtained from a minimal homeomorphism of a comp...

Let $(N,\R,\theta)$ be a centrally ergodic W* dynamical system. When $N$ is not a factor, we show that, for each $t\not=0$, the crossed product induced by the time $t$ automorphism $\theta_t$ is not a factor if and only if there exist a rational number $r$ and an eigenvalue $s$ of the restriction of $\theta$ to the center of $N$, such that $rst=2\p...

We find the range of a trace on the $K_0$ group of a crossed product by a time-$t$ automorphism of a mapping torus. We also find a formula to compute the Voiculescu-Brown entropy for such an automorphism. By specializing to the commutative setting, we prove that the crossed products by minimal time-t homeomorphisms of suspensions built over strongl...

Let $(Y,T)$ be a minimal suspension flow built over a dynamical system $(X,S)$ and with (strictly positive, continuous) ceiling function $f\colon X\to\R$. We show that the eigenvalues of $(Y,T)$ are contained in the range of a trace on the $K_0$-group of $(X,S)$. Moreover, a trace gives an order isomorphism of a subgroup of $K_0(C(X)\rtimes_S\mathb...

Typescript. Thesis (Ph. D.)--University of Oregon, 2003. Includes vita and abstract. Includes bibliographical references (leaves 68-69).