Gaussian Quantum Markov Semigroups on a One-Mode Fock Space: Irreducibility and Normal Invariant States

Agredo Echeverry, Julián Andrés | 2021

We consider the most general Gaussian quantum Markov semigroup on a one-mode Fock space, discuss its construction from the generalized GKSL representation of the generator. We prove the known explicit formula on Weyl operators, characterize irreducibility and its equivalence to a H¨ormander type condition on commutators and establish necessary and sufficient conditions for existence and uniqueness of normal invariant states. We illustrate these results by applications to the open quantum oscillator and the quantum Fokker-Planck model.

A generalization of connectedness via ideals

Pachón Rubiano, Néstor Raúl | 2022

Connected spaces as a generalization of the connectedness, and thus of the Ekici-Noiri and Modak-Noiri notions, through ideals.

The 𝒫�-Hausdorff, 𝒫�-regular and 𝒫�-normal ideal spaces

Pachón R., Néstor Raúl | 2020

We introduce and study new extensions of some separation axioms to ideal topological spaces, which we have called 𝒫����-Hausdorff, 𝒫����-regular and 𝒫����-normal. These extensions are quite natural and represent a good improvement with respect to other extensions that have recently occurred, in which a level of separation that can be considered acceptable is not perceived.

Matemáticas con LaTeX. Elaboración de gráficos y textos

Alvarez Perez, Carlos Abel | 2020

Modeling the effects of light wavelength on the growth of Nostoc ellipsosporum

Ortiz Moreno, Martha Lucia | 2020

Mathematical models provide information about population dynamics under different conditions. In the study, four models were evaluated and employed to describe the growth kinetics of Nostoc ellipsosporum with different light wavelengths: Baranyi-Roberts, Modified Gompertz, Modified Logistic, and Richards. N. ellipsosporum was grown in BG-11 liquid medium for 9 days, using 12 hours of photoperiod and the following treatments: white light (400-800 nm), red light (650-800 nm), yellow light (550-580 nm) and blue light (460-480 nm). Each experiment was performed in triplicate. The optical density (OD) was measured on days 1, 3, 5, 7 and 9, using a spectrophotometer at 650 nm. The maximum cell growth was obtained under white light (OD650 : 0.090 ± 0.008), followed by the yellow light (OD650 : 0.057 ± 0.004). Conversely, blue light showed a marked inhibitory effect on the growth of N. ellipsosporum (OD650 : 0.009 ± 0.001). The results revealed that the Baranyi-Roberts model had a better fit with the experimental data from N. ellipsosporum growth in all four treatments. The findings from this modeling study could be used in several biotechnological applications that require the production of N. ellipsosporum and its bioproducts.

Negafibonacci Numbers via Matrices

Triana Laverde, Juan Gabriel | 2019

In this paper, negafibonacci numbers are generated by means of matrix methods. A 2×2 matrix is used to obtain some properties of negafibonacci numbers; on the other hand, families of tridiagonal matrices are introduced to generate negafibonacci numbers through determinants.

New forms of strong compactness in terms of ideals

Pachon Rubiano, Néstor Raúl | 2016

The aim of this paper is to introduce and study new types of strong compactness, modulo an ideal, called ρI-compactness and σI-compactness. Several of their properties are presented and some effects of various kinds of functions on them are studied. We compare this new spaces with other known types of strong compactness modulo an ideal.

On exponential convergence of generic quantum Markov semigroups in a Wasserstein-type distance

Agredo Echeverry, Julian Andres | 2016

We investigate about exponential convergence for generic quantum Markov semigroups using an generalization of the Lipschitz seminorm and a noncommutative analogue of Wasserstein distance. We show turns out to be closely related with classical convergence rate of reductions to diagonal subalgebras of the given generic quantum Markov semigroups.In particular we compute the convergence rates of generic quantum Markov semigroups.

On quantum versions of the classical Wasserstein distance

Agredo Echeverry, Julian Andrès | 2017

Investigamos una definición de la distancia cuántica de Wasserstein de dos estados basada en sus acoplamientos en el álgebra de productos como en el caso clásico. Un análisis detallado del modelo de dos qubits conduce a una definición formal que cumple algunos requisitos mínimos. También muestra que no se puede lograr una definición clara, mediante la generalización directa de la clásica.

Other forms of continuity modulo an ideal

Pachón Rubiano, Néstor Raúl | 2020

El tema analizado en este artículo es la continuidad módulo un ideal. Usamos los conjuntos de I abierto para introducir nuevas formas de continuidad débil. Se investigarán algunas propiedades básicas de las funciones C-continuas y D-continuas, así como algunas aplicaciones relacionadas con la compacidad y la separabilidad. Todos los resultados obtenidos en este trabajo constituyen generalizaciones de resultados conocidos de la topología general. Demostramos que estos nuevos conceptos son independientes de otras formas de continuidad débil, módulo un ideal, introducidas por Abd El-Monsef, Özkurt, Çobankaya y Kaniewski.

A possible predictive mathematical model for the growth of a periphytic alga

Agredo, Julián | 2022

Algae are photosynthetic organisms and have qualities that are very attractive for cultivation and industrial development for commercial purposes. When algal growth is analyzed for the production of biomass usually only the exponential phase of the growth curve is considered and the other phases are ignored. The objective of the work is to present a possible predictive mathematical model that allows a better understanding of the kinetic behavior of a periphytic microalgae by means of the use of the Smoluchowski discrete equation, with special emphasis on the lag phase. More specifically, unknown connection between the discrete Smoluchowski equation and the deterministic Baranyi model is shown in the present study. Analysis of this connection leads to a possible predictive mathematical model about of the kinetic behavior of a periphytic microalgae.

Problemas de valoración en proyectos de explotación de minas bajo incertidumbre

Clavijo Penagos, Yesid Esteban | 2016

Las compañías del sector minero se enfrentan con el problema de la planificación del proyecto de extracción de mineral y la valoración de dicho proyecto. El problema conlleva la existencia de diversas fuentes de incertidumbre como, por ejemplo, la incertidumbre en el precio del mineral, la proporción del mineral en el material extraído (Ore-Grade) y la cantidad de roca que se podrá extraer. Una metodologíıa para abordar el problema se basa en su formulación en términos de problema de opciones reales, lo que tiene su paralelismo en la valoración de derivados financieros. El presente trabajo se enmarca en esta metodología.

Regularity and normality in ideal bitopological spaces

Pachon Rubiano, Néstor Raúl | 2021

We introduce, and study, the regularity and normality in ideal bitopological spaces, absent subject in literature. Our definitions have the advantage of using only the open sets of the two underlying topologies. These new concepts represent generalizations of Kelly's concepts of pairwise regularity and pairwise normality. The extension of the T 0 , T 1 and T 2 axioms to these spaces is due to Caldas et al.

Semigrupos cuánticos de Markov: Pasado, presente y futuro

Agredo Echeverry, Julián Andrés | 2017

Los semigrupos cuánticos de Markov (SCM) son una extensión no conmutativa de los semigrupos de Markov definidos en probabilidad clásica. Ellos representan una evolución sin memoria de un sistema microscopico acorde a las leyes de la física cuántica y a la estructura de los sistemas cuánticos abiertos. Esto significa que la dinámica reducida del sistema principal es descrita por un espacio de Hilbert separable complejo h por medio de un semigrupo T=(Tt)t≥0, el cual actúa sobre una subálgebra de von Neumann M del álgebra P(h) de todos los operadores lineales acotados definidos en h. Por simplicidad, algunas veces asumiremos que M=P(h). El semigrupo T corresponde al cuadro de Heisenberg en el sentido que dado cualquier observable x, Tt(x) describe su evolución en el tiempo t. De esta forma, dada una matriz de densidad p, su dinámica (cuadro de Schrödinger) es dada por el semigrupo predual T*t(ρ) , donde tr(ρTt(x))=tr(T*t(ρ)x), tr(⋅) denota p, su dinámica (cuadro de Schrödinger) es dada por el semigrupo predual T*t(ρ) , donde tr(ρTt(x))=tr(T*t(ρ)x), tr(⋅) denota la operación traza. En este trabajo ofrecemos una exposición de varios resultados básicos sobre SCM. Además, discutimos aplicaciones de SCM en teoría de la información cuántica y computación cuántica.

Semigrupos cuánticos de Markov: Pasado, presente y futuro

Agregado Echeverry, Julián Andrés | 2017-04-24

Los semigrupos cuánticos de Markov (SCM) son una extensión no conmutativa de los semigrupos de Markov definidos en probabilidad clásica. Ellos representan una evolución sin memoria de un sistema microscopico acorde a las leyes de la física cuántica y a la estructura de los sistemas cuánticos abiertos. Esto significa que la dinámica reducida del sistema principal es descrita por un espacio de Hilbert separable complejo 𝔥 por medio de un semigrupo 𝒯=(𝒯t)t≥0, el cual actúa sobre una subálgebra de von Neumann 𝔐 del álgebra 𝔓(𝔥) de todos los operadores lineales acotados definidos en 𝔥. Por simplicidad, algunas veces asumiremos que 𝔐=𝔓(𝔥). El semigrupo 𝓣 corresponde al cuadro de Heisenberg en el sentido que dado cualquier observable x, 𝓣t(x) describe su evolución en el tiempo t. De esta forma, dada una matriz de densidad p, su dinámica (cuadro de Schrödinger) es dada por el semigrupo predual 𝓣*t(ρ) , donde tr(ρ𝓣t(x))=tr(𝓣*t(ρ)x), tr(⋅) denota la operación traza. En este trabajo ofrecemos una exposición de varios resultados básicos sobre SCM. Además discutimos aplicaciones de SCM en teoría de la información cuántica y computación cuántica.

Soluciones de la Ecuación de Smoluchowski caso discreto y caso continuo

Gacharná González, Juan Manuel | 2020

In this work solutions of the discrete version Smoluchowski equation are presented using some probability concepts and methods to solve partial differential equations. The procedure to arrive at the solution of the Smoluchowski Equation continuous case is also shown, making use of some concepts of measurement theory when this equation has a constant nucleus. In addition, some results of great importance are presented in which the relationship between the equation with multiplicative nucleus and additive nucleus in the continuous version is highlighted. This equation is of great importance since it models the rate of change of the average number of polymers of mass k with respect to time t and also does not have to be solved using traditional methods due to its difficulty, which is why it is of great importance for mathematicians as it opens new paths for the solution of different types of equations.

SOME PROPERTIES OF J -HAUSDORFF, J -REGULAR AND J -NORMAL SPACES

Pachon Rubiano, Néstor Raúl | 2018

In this paper we present new properties about the J - Hausdorff, J -regular and J -normal spaces, introduced recently by Suriyakala-Vembu. Additionally we introduce the J -Urysohn spaces, an intermediate concept between the Urysohn spaces and the J - Hausdorff spaces. We present some of its properties.

TWO NEW FORMS OF QUASI-H-CLOSEDNESS VIA IDEALS

Pachon Rubiano, Néstor Raúl | 2017

In this paper we introduce two new ideal topological spaces, which are strong forms of the QHC spaces and the I -QHC spaces. We present several properties and characterizatios of these new spaces.

ρC(I)-COMPACT AND ρI-QHC SPACES

Pachón Rubiano, Néstor Raúl | 2016

In this paper we introduce and investigate two new ideal topological spaces, which are strong forms of Gupta-Noiri concepts. Interesting characterizations of this spaces are presented, as well as several useful properties of these. We compare this new spaces with C-compact and quasi-H-closed spaces

ρC(I)-COMPACT AND ρI-QHC SPACES

Pachon Rubiano, Néstor Raúl | 2016

In this paper we introduce and investigate two new ideal topological spaces, which are strong forms of Gupta-Noiri concepts. Interesting characterizations of this spaces are presented, as well as several useful properties of these. We compare this new spaces with C-compact and quasi-H-closed spaces.